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diff --git a/Master/texmf-dist/doc/support/ketcindy/LICENSE b/Master/texmf-dist/doc/support/ketcindy/LICENSE index 6bdf89623f8..4cf87165de3 100644 --- a/Master/texmf-dist/doc/support/ketcindy/LICENSE +++ b/Master/texmf-dist/doc/support/ketcindy/LICENSE @@ -1,6 +1,6 @@ -// Copyright (C) 2014 Setsuo Takato, KETCindy Japan project team +// Copyright (C) 2014-2018 Setsuo Takato, KETCindy Japan project team // -//This program is free software: you can redistribute it and/or modify +// This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation; either version 3 of the License, or // (at your option) any later version. diff --git a/Master/texmf-dist/doc/support/ketcindy/README b/Master/texmf-dist/doc/support/ketcindy/README index b9f34571bc0..6f1287e29b6 100644 --- a/Master/texmf-dist/doc/support/ketcindy/README +++ b/Master/texmf-dist/doc/support/ketcindy/README @@ -1,6 +1,8 @@ KeTCindy ======== +Version: $Version$ + KeTCindy combines a plugin to Cinderella with free mathematical software (R, Maxima, ...) to produce high-quality LaTeX graphics. Using Cinderella to generate graphics in an interactive environment, the diff --git a/Master/texmf-dist/doc/support/ketcindy/README.TeXLive b/Master/texmf-dist/doc/support/ketcindy/README.TeXLive index 4c9b3009b6a..6c9a74140e4 100644 --- a/Master/texmf-dist/doc/support/ketcindy/README.TeXLive +++ b/Master/texmf-dist/doc/support/ketcindy/README.TeXLive @@ -1,8 +1,10 @@ KETCindy for TeX Live ===================== -The files originally distributed by Prof. Takato have been adapted -by Norbert Preining to work within the framework of TeX Live. -At the moment only dirhead.txt was added to the main script location, -and a wrapper script ketcindy(.sh). +Layout of the distribution of KETCindy in TeX Live has been adjusted +to follow TDS standards. In addition, a starter script is provided that +checks for correct and up2date installation of the Cinderella plugin +and the necessary ketcindy.ini file installation. -2018-04-09 Norbert Preining +No further changes to the original sources have been done. + +2018-06-18 Norbert Preining diff --git a/Master/texmf-dist/doc/support/ketcindy/ScriptKeytyped.txt b/Master/texmf-dist/doc/support/ketcindy/ScriptKeytyped.txt deleted file mode 100644 index b06655d548e..00000000000 --- a/Master/texmf-dist/doc/support/ketcindy/ScriptKeytyped.txt +++ /dev/null @@ -1,134 +0,0 @@ -if(key()=="?" % keydownlist()==[32], - if(!isreal(NumTyped),NumTyped=0); - if(NumTyped==0, - DispStr= - "Figure(1) Parent(2) Parapara(3) Movie(4) Surf(5)"; - ); - if(NumTyped==1, - DispStr= - "Shift+ Title(T) Para(P) AniF(A) Slide(S) Digest(D)"; - ); - if(NumTyped==2, - DispStr="Shift+ Meshlab(M) KeTCindyJS(J)"; - ); - if(NumTyped==3, - DispStr= - "Ch : disp(0) chg(9) N(+,-) add(<) rmv(>)"; - ); - drawtext(mouse().xy,DispStr,size->24); - NumTyped=mod(NumTyped+1,4); -, - NumTyped=0; -); -if(key()=="1",//Mkfigure - Viewtex(); - kc(); -); -if(key()=="2",//Mkparent - Viewparent(); -); -if(key()=="3",//Flipbook(Parapara) - Flipbook(); -); -if(key()=="4",//Texmovie - Texmovie(); - kc(); -); -if(key()=="5",//Surface - Cheader(); - Cmain(); - kcC(); - if(ChNum>0, - Ch=[ChNum]; - , - Ch=[1]; - ); - ChNum=0; -); -if(key()=="T",//Title - Maketitle(); -); -if(key()=="P",//ParaF - Parafolder(); -); -if(key()=="A",//Animatefile - Animatefile(); -); -if(key()=="S",//Slide - Mkslides(); -); -if(key()=="D",//Digest(Summary) - Mkslidesummary(); -); -if(key()=="M",//Meshlab - Mkviewobj(OCNAME,OBJCMD,OCOPTION); -); -if(key()=="J",//KeTCindyJS - Mkketcindyjs(); -); - -if(key()=="0", - Dispchoice(); -); -if(key()=="9", - if(length(Ch)==0, - Ch=[ChNum]; - , - if(!contains(Ch,ChNum), - Ch=append(Ch,ChNum); - ChNum=Ch_(length(Ch)-1); - Ch=remove(Ch,[ChNum]); - Ch=sort(Ch); - ); - ); - Dispchoice(); -); -if(key()=="+", - ChNum=ChNum+1; - Dispchoice(); -); -if(key()=="-", - ChNum=ChNum-1; - Dispchoice(); -); -if(key()=="<", - if(length(select(Ch,#==ChNum))==0, - Ch=append(Ch,ChNum); - Ch=sort(Ch); - ChNum=ChNum+1; - ); - Dispchoice(); -); -if(key()=="^", - if(length(Ch)==0, - Ch=[ChNum]; - , - if(!contains(Ch,ChNum), - Ch=Ch_(1..(length(Ch)-1)); - Ch=append(Ch,ChNum); - Ch=sort(Ch); - ); - ); - ChNum=ChNum+1; - Dispchoice(); -); -if(key()=="~", - if(length(Ch)==0, - Ch=[ChNum]; - , - if(!contains(Ch,ChNum), - Ch=Ch_(1..(length(Ch)-1)); - Ch=append(Ch,ChNum); - Ch=sort(Ch); - ); - ); - ChNum=max(ChNum-1,1); - Dispchoice(); -); -if(key()==">", - if(length(Ch)>0, - ChNum=Ch_(length(Ch)); - Ch=Remove(Ch,[ChNum]); - ); - Dispchoice(); -); diff --git a/Master/texmf-dist/doc/support/ketcindy/Scriptfigure.txt b/Master/texmf-dist/doc/support/ketcindy/Scriptfigure.txt deleted file mode 100644 index 8026df529f4..00000000000 --- a/Master/texmf-dist/doc/support/ketcindy/Scriptfigure.txt +++ /dev/null @@ -1,16 +0,0 @@ -Ketinit(); -Texparent=""; - -Putpoint("A",[-4,0],A.xy); -Putpoint("B",[4,0],B.xy); -Putpoint("C",[1,4],C.xy); - // points can be put with Cindy button. - -Listplot([A,B,C,A]); -Plotdata("1","sin(x)","x",["da"]); -Paramplot("1","3*[cos(3*t),sin(2*t)]","t=[0,4*pi]",["Num=200","do"]); - -Windispg(); - -//Help("Plotdata"); -//Help("Option"); diff --git a/Master/texmf-dist/doc/support/ketcindy/Scriptketlibsci.txt b/Master/texmf-dist/doc/support/ketcindy/Scriptketlibsci.txt deleted file mode 100644 index 287b1bcadd5..00000000000 --- a/Master/texmf-dist/doc/support/ketcindy/Scriptketlibsci.txt +++ /dev/null @@ -1,8 +0,0 @@ -use("KetCindyPlugin"); -Dircdy=loaddirectory; -setdirectory(plugindirectory); -import("dirheadsci.txt"); -//PathS=replace(PathS,"6.0.0","5.5.2"); - -//Ketinit(); -//Ketinit3d(); diff --git a/Master/texmf-dist/doc/support/ketcindy/ketmanual/KeTCindyReferenceE.pdf b/Master/texmf-dist/doc/support/ketcindy/ketmanual/KeTCindyReferenceE.pdf Binary 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a/Master/texmf-dist/doc/support/ketcindy/samples/s07slides/howtouseslideJ.txt b/Master/texmf-dist/doc/support/ketcindy/samples/s07slides/howtouseslideJ.txt index db262b1b9ac..69ce201a905 100644 --- a/Master/texmf-dist/doc/support/ketcindy/samples/s07slides/howtouseslideJ.txt +++ b/Master/texmf-dist/doc/support/ketcindy/samples/s07slides/howtouseslideJ.txt @@ -1,4 +1,4 @@ -ketslideによるプレゼンテーション 2018.05.31 +ketslideによるプレゼンテーション 2018.07.29 ０．作成の流れ @@ -21,20 +21,17 @@ ketslideによるプレゼンテーション 2018.05.31 注）urlの指定で//を用いるとき，||||とすると//に変換される． ２）各ブロックの引数の区切りは :: ３）コマンド - ・タイトル::読込ファイル名(::壁紙ファイル)// + ・タイトル(またはtitle)::読込ファイル名(::壁紙ファイル)// タイトルページを作成（１行目におく） 注）壁紙(例えばwallpaperとする）を背景に入れるとき ・例えばwallpaper.texを作成してfigフォルダに入れる． （figにあるサンプルwallpaper.texを参照） - ・sample.txtでの指定は - タイトル::slide0::wallpaper// - ・壁紙を一時的に外すときは - タイトル::slide0::%wallpaper// + ・タイトル(title)::slide0::wallpaper// 注）preambleに追加するとき １行目の//を外す． 次の行から，::区切りで書き加え，最後に//をおく． 注）タイトル画面が不要の場合は， - タイトル(またはtitle)::notitle// + タイトル(またはtitle)::// 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2c4a4398813..00000000000 --- a/Master/texmf-dist/doc/support/ketcindy/samples/s15surfaceR/s1510conecut.cdy +++ /dev/null diff --git a/Master/texmf-dist/doc/support/ketcindy/samples/s15surfaceR/s1510conecutR.cdy b/Master/texmf-dist/doc/support/ketcindy/samples/s15surfaceR/s1510conecutR.cdy Binary files differnew file mode 100644 index 00000000000..56613fb35df --- /dev/null +++ b/Master/texmf-dist/doc/support/ketcindy/samples/s15surfaceR/s1510conecutR.cdy diff --git a/Master/texmf-dist/doc/support/ketcindy/source/KetCindyPlugin/src/KetCindyPlugin.java b/Master/texmf-dist/doc/support/ketcindy/source/KetCindyPlugin/src/KetCindyPlugin.java index 16fe6ae454a..ce158837837 100644 --- a/Master/texmf-dist/doc/support/ketcindy/source/KetCindyPlugin/src/KetCindyPlugin.java +++ b/Master/texmf-dist/doc/support/ketcindy/source/KetCindyPlugin/src/KetCindyPlugin.java @@ -13,7 +13,7 @@ public class KetCindyPlugin extends CindyScriptPlugin { @CindyScript("ketjavaversion") public String ketjavaversion() { 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868 -1087}\special{pa 861 -1076}% +\special{pa 854 -1066}\special{pa 848 -1055}\special{pa 841 -1045}\special{pa 834 -1034}% +\special{pa 828 -1024}\special{pa 822 -1013}\special{pa 815 -1002}\special{pa 809 -991}% +\special{pa 803 -981}\special{pa 797 -970}\special{pa 791 -959}\special{pa 785 -948}% +\special{pa 779 -937}\special{pa 773 -926}\special{pa 767 -915}\special{pa 761 -904}% +\special{pa 756 -892}\special{pa 750 -881}\special{pa 745 -870}% +\special{fp}% +\special{pa 642 -614}\special{pa 639 -603}\special{pa 635 -591}\special{pa 631 -579}% +\special{pa 628 -567}\special{pa 624 -555}\special{pa 621 -543}\special{pa 618 -531}% +\special{pa 615 -519}\special{pa 611 -507}\special{pa 608 -494}\special{pa 605 -482}% +\special{pa 602 -470}\special{pa 600 -458}\special{pa 597 -446}\special{pa 594 -434}% +\special{pa 592 -421}\special{pa 589 -409}\special{pa 587 -397}\special{pa 584 -385}% +\special{pa 582 -372}\special{pa 580 -360}\special{pa 578 -348}\special{pa 576 -336}% +\special{pa 574 -323}\special{pa 572 -311}\special{pa 570 -299}\special{pa 568 -286}% +\special{pa 567 -274}\special{pa 565 -261}\special{pa 564 -249}\special{pa 562 -237}% +\special{pa 561 -224}\special{pa 560 -212}\special{pa 559 -199}\special{pa 558 -187}% +\special{pa 557 -175}\special{pa 556 -162}\special{pa 555 -150}\special{pa 554 -137}% +\special{pa 553 -125}\special{pa 553 -112}\special{pa 552 -100}\special{pa 552 -87}% +\special{pa 552 -75}\special{pa 551 -62}\special{pa 551 -50}\special{pa 551 -37}% +\special{pa 551 -25}\special{pa 551 -12}\special{pa 551 -0}% +\special{fp}% +\settowidth{\Width}{\rotatebox[units=-360,origin=c]{112}{$a$}}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{\rotatebox[units=-360,origin=c]{112}{$a$}}\settodepth{\Depth}{\rotatebox[units=-360,origin=c]{112}{$a$}}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(4.5000000,2.7000000){\hspace*{\Width}\raisebox{\Height}{\rotatebox[units=-360,origin=c]{112}{$a$}}}% +% +\special{pa 1654 -1378}\special{pa 1645 -1369}\special{pa 1636 -1360}\special{pa 1628 -1351}% +\special{pa 1619 -1342}\special{pa 1611 -1333}\special{pa 1602 -1323}\special{pa 1594 -1314}% +\special{pa 1586 -1305}\special{pa 1577 -1296}\special{pa 1569 -1286}\special{pa 1561 -1277}% +\special{pa 1553 -1267}\special{pa 1545 -1257}\special{pa 1537 -1248}\special{pa 1529 -1238}% +\special{pa 1521 -1228}\special{pa 1514 -1219}\special{pa 1506 -1209}\special{pa 1498 -1199}% +\special{pa 1491 -1189}\special{pa 1483 -1179}\special{pa 1476 -1169}\special{pa 1469 -1159}% +\special{pa 1461 -1149}\special{pa 1454 -1139}\special{pa 1447 -1128}\special{pa 1440 -1118}% +\special{pa 1433 -1108}\special{pa 1426 -1097}\special{pa 1419 -1087}\special{pa 1412 -1076}% +\special{pa 1405 -1066}\special{pa 1399 -1055}\special{pa 1392 -1045}\special{pa 1386 -1034}% +\special{pa 1379 -1024}\special{pa 1373 -1013}\special{pa 1366 -1002}\special{pa 1360 -991}% +\special{pa 1354 -981}\special{pa 1348 -970}\special{pa 1342 -959}\special{pa 1336 -948}% +\special{pa 1330 -937}\special{pa 1324 -926}\special{pa 1318 -915}\special{pa 1313 -904}% +\special{pa 1307 -892}\special{pa 1301 -881}\special{pa 1296 -870}% +\special{fp}% +\special{pa 1194 -614}\special{pa 1190 -603}\special{pa 1186 -591}\special{pa 1183 -579}% +\special{pa 1179 -567}\special{pa 1176 -555}\special{pa 1172 -543}\special{pa 1169 -531}% +\special{pa 1166 -519}\special{pa 1163 -507}\special{pa 1160 -494}\special{pa 1157 -482}% +\special{pa 1154 -470}\special{pa 1151 -458}\special{pa 1148 -446}\special{pa 1145 -434}% +\special{pa 1143 -421}\special{pa 1140 -409}\special{pa 1138 -397}\special{pa 1136 -385}% +\special{pa 1133 -372}\special{pa 1131 -360}\special{pa 1129 -348}\special{pa 1127 -336}% +\special{pa 1125 -323}\special{pa 1123 -311}\special{pa 1121 -299}\special{pa 1120 -286}% +\special{pa 1118 -274}\special{pa 1116 -261}\special{pa 1115 -249}\special{pa 1114 -237}% +\special{pa 1112 -224}\special{pa 1111 -212}\special{pa 1110 -199}\special{pa 1109 -187}% +\special{pa 1108 -175}\special{pa 1107 -162}\special{pa 1106 -150}\special{pa 1105 -137}% +\special{pa 1105 -125}\special{pa 1104 -112}\special{pa 1104 -100}\special{pa 1103 -87}% +\special{pa 1103 -75}\special{pa 1102 -62}\special{pa 1102 -50}\special{pa 1102 -37}% +\special{pa 1102 -25}\special{pa 1102 -12}\special{pa 1102 0}% +\special{fp}% +\settowidth{\Width}{\rotatebox[units=-360,origin=c]{112}{$a$}}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{\rotatebox[units=-360,origin=c]{112}{$a$}}\settodepth{\Depth}{\rotatebox[units=-360,origin=c]{112}{$a$}}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(6.5800000,2.9000000){\hspace*{\Width}\raisebox{\Height}{\rotatebox[units=-360,origin=c]{112}{$a$}}}% +% +\special{pa 2205 -1378}\special{pa 2196 -1369}\special{pa 2187 -1360}\special{pa 2179 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-162}\special{pa 1657 -150}\special{pa 1656 -137}% +\special{pa 1656 -125}\special{pa 1655 -112}\special{pa 1655 -100}\special{pa 1654 -87}% +\special{pa 1654 -75}\special{pa 1654 -62}\special{pa 1653 -50}\special{pa 1653 -37}% +\special{pa 1653 -25}\special{pa 1653 -12}\special{pa 1654 0}% +\special{fp}% +\settowidth{\Width}{no}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{no}\settodepth{\Depth}{no}\setlength{\Height}{-\Height}% +\put(-4.0000000,-0.0714286){\hspace*{\Width}\raisebox{\Height}{no}}% +% +\settowidth{\Width}{option}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{option}\settodepth{\Depth}{option}\setlength{\Height}{-\Height}% +\put(-4.0000000,-0.3571429){\hspace*{\Width}\raisebox{\Height}{option}}% +% +\settowidth{\Width}{t3n0}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{t3n0}\settodepth{\Depth}{t3n0}\setlength{\Height}{-\Height}% +\put(-2.0000000,-0.0714286){\hspace*{\Width}\raisebox{\Height}{t3n0}}% +% 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-\settoheight{\Height}{\rotatebox[origin=c]{59}{$a$}}\settodepth{\Depth}{\rotatebox[origin=c]{59}{$a$}}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(2.0772,2.9286){\hspace*{\Width}\raisebox{\Height}{\rotatebox[origin=c]{59}{$a$}}}% -% -% -\settowidth{\Width}{\rotatebox[origin=c]{59}{$a$}}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{\rotatebox[origin=c]{59}{$a$}}\settodepth{\Depth}{\rotatebox[origin=c]{59}{$a$}}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(4.9228,2.6714){\hspace*{\Width}\raisebox{\Height}{\rotatebox[origin=c]{59}{$a$}}}% -% -% -\settowidth{\Width}{\rotatebox[origin=c]{59}{$a$}}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{\rotatebox[origin=c]{59}{$a$}}\settodepth{\Depth}{\rotatebox[origin=c]{59}{$a$}}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(7.8714,2.8772){\hspace*{\Width}\raisebox{\Height}{\rotatebox[origin=c]{59}{$a$}}}% -% -% -\settowidth{\Width}{\rotatebox[units=-360,origin=c]{121}{$a$}}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{\rotatebox[units=-360,origin=c]{121}{$a$}}\settodepth{\Depth}{\rotatebox[units=-360,origin=c]{121}{$a$}}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(11.0000,2.8000){\hspace*{\Width}\raisebox{\Height}{\rotatebox[units=-360,origin=c]{121}{$a$}}}% -% -% -\settowidth{\Width}{\rotatebox[units=-360,origin=c]{121}{$a$}}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{\rotatebox[units=-360,origin=c]{121}{$a$}}\settodepth{\Depth}{\rotatebox[units=-360,origin=c]{121}{$a$}}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(13.9228,2.6714){\hspace*{\Width}\raisebox{\Height}{\rotatebox[units=-360,origin=c]{121}{$a$}}}% -% -% -\settowidth{\Width}{rot}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{rot}\settodepth{\Depth}{rot}\setlength{\Height}{-\Height}% -\put(-2.0000,-0.1500){\hspace*{\Width}\raisebox{\Height}{rot}}% -% -% -\settowidth{\Width}{t3}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{t3}\settodepth{\Depth}{t3}\setlength{\Height}{-\Height}% -\put(1.0000,-0.1500){\hspace*{\Width}\raisebox{\Height}{t3}}% -% -% -\settowidth{\Width}{t-3}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{t-3}\settodepth{\Depth}{t-3}\setlength{\Height}{-\Height}% -\put(4.0000,-0.1500){\hspace*{\Width}\raisebox{\Height}{t-3}}% -% -% -\settowidth{\Width}{n3}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{n3}\settodepth{\Depth}{n3}\setlength{\Height}{-\Height}% -\put(7.0000,-0.1500){\hspace*{\Width}\raisebox{\Height}{n3}}% -% -% -\settowidth{\Width}{u}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{u}\settodepth{\Depth}{u}\setlength{\Height}{-\Height}% -\put(10.0000,-0.1500){\hspace*{\Width}\raisebox{\Height}{u}}% -% -% 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3047 -5409}\special{pa 2386 -5409}% +\special{pa 2386 -5220}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0.96,0,0,0}% +\special{pa 5457 -5220}\special{pa 6118 -5220}\special{pa 6118 -5409}\special{pa 5457 -5409}% +\special{pa 5457 -5220}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0,0.85,0.87,0.35}% +\special{pa 2386 -4984}\special{pa 3047 -4984}\special{pa 3047 -5173}\special{pa 2386 -5173}% +\special{pa 2386 -4984}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0.62,0,0.12,0}% +\special{pa 5457 -4984}\special{pa 6118 -4984}\special{pa 6118 -5173}\special{pa 5457 -5173}% +\special{pa 5457 -4984}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0,0.87,0.68,0.32}% +\special{pa 2386 -4748}\special{pa 3047 -4748}\special{pa 3047 -4937}\special{pa 2386 -4937}% +\special{pa 2386 -4748}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0.85,0,0.2,0}% +\special{pa 5457 -4748}\special{pa 6118 -4748}\special{pa 6118 -4937}\special{pa 5457 -4937}% +\special{pa 5457 -4748}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0,0.89,0.94,0.28}% +\special{pa 2386 -4512}\special{pa 3047 -4512}\special{pa 3047 -4701}\special{pa 2386 -4701}% +\special{pa 2386 -4512}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0.86,0,0.34,0.02}% +\special{pa 5457 -4512}\special{pa 6118 -4512}\special{pa 6118 -4701}\special{pa 5457 -4701}% +\special{pa 5457 -4512}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0,1,1,0}% +\special{pa 2386 -4276}\special{pa 3047 -4276}\special{pa 3047 -4465}\special{pa 2386 -4465}% +\special{pa 2386 -4276}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0.82,0,0.3,0}% +\special{pa 5457 -4276}\special{pa 6118 -4276}\special{pa 6118 -4465}\special{pa 5457 -4465}% +\special{pa 5457 -4276}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0,1,0.5,0}% +\special{pa 2386 -4039}\special{pa 3047 -4039}\special{pa 3047 -4228}\special{pa 2386 -4228}% +\special{pa 2386 -4039}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0.85,0,0.33,0}% +\special{pa 5457 -4039}\special{pa 6118 -4039}\special{pa 6118 -4228}\special{pa 5457 -4228}% +\special{pa 5457 -4039}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0,1,0.13,0}% +\special{pa 2386 -3803}\special{pa 3047 -3803}\special{pa 3047 -3992}\special{pa 2386 -3992}% +\special{pa 2386 -3803}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{1,0,0.5,0}% +\special{pa 5457 -3803}\special{pa 6118 -3803}\special{pa 6118 -3992}\special{pa 5457 -3992}% +\special{pa 5457 -3803}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0,0.96,0.39,0}% +\special{pa 2386 -3567}\special{pa 3047 -3567}\special{pa 3047 -3756}\special{pa 2386 -3756}% +\special{pa 2386 -3567}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0.99,0,0.52,0}% +\special{pa 5457 -3567}\special{pa 6118 -3567}\special{pa 6118 -3756}\special{pa 5457 -3756}% +\special{pa 5457 -3567}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0,0.53,0.38,0}% +\special{pa 2386 -3331}\special{pa 3047 -3331}\special{pa 3047 -3520}\special{pa 2386 -3520}% +\special{pa 2386 -3331}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0.69,0,0.5,0}% +\special{pa 5457 -3331}\special{pa 6118 -3331}\special{pa 6118 -3520}\special{pa 5457 -3520}% +\special{pa 5457 -3331}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0,0.63,0,0}% +\special{pa 2386 -3094}\special{pa 3047 -3094}\special{pa 3047 -3283}\special{pa 2386 -3283}% +\special{pa 2386 -3094}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{1,0,1,0}% +\special{pa 5457 -3094}\special{pa 6118 -3094}\special{pa 6118 -3283}\special{pa 5457 -3283}% +\special{pa 5457 -3094}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0,1,0,0}% +\special{pa 2386 -2858}\special{pa 3047 -2858}\special{pa 3047 -3047}\special{pa 2386 -3047}% +\special{pa 2386 -2858}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0.91,0,0.88,0.12}% +\special{pa 5457 -2858}\special{pa 6118 -2858}\special{pa 6118 -3047}\special{pa 5457 -3047}% +\special{pa 5457 -2858}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0,0.81,0,0}% +\special{pa 2386 -2622}\special{pa 3047 -2622}\special{pa 3047 -2811}\special{pa 2386 -2811}% +\special{pa 2386 -2622}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0.92,0,0.59,0.25}% +\special{pa 5457 -2622}\special{pa 6118 -2622}\special{pa 6118 -2811}\special{pa 5457 -2811}% +\special{pa 5457 -2622}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0,0.82,0,0}% +\special{pa 2386 -2386}\special{pa 3047 -2386}\special{pa 3047 -2575}\special{pa 2386 -2575}% +\special{pa 2386 -2386}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0.5,0,1,0}% +\special{pa 5457 -2386}\special{pa 6118 -2386}\special{pa 6118 -2575}\special{pa 5457 -2575}% +\special{pa 5457 -2386}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0.34,0.9,0,0.02}% +\special{pa 2386 -2150}\special{pa 3047 -2150}\special{pa 3047 -2339}\special{pa 2386 -2339}% +\special{pa 2386 -2150}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0.44,0,0.74,0}% +\special{pa 5457 -2150}\special{pa 6118 -2150}\special{pa 6118 -2339}\special{pa 5457 -2339}% +\special{pa 5457 -2150}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0.07,0.9,0,0.34}% +\special{pa 2386 -1913}\special{pa 3047 -1913}\special{pa 3047 -2102}\special{pa 2386 -2102}% +\special{pa 2386 -1913}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0.26,0,0.76,0}% +\special{pa 5457 -1913}\special{pa 6118 -1913}\special{pa 6118 -2102}\special{pa 5457 -2102}% +\special{pa 5457 -1913}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0.47,0.91,0,0.08}% +\special{pa 2386 -1677}\special{pa 3047 -1677}\special{pa 3047 -1866}\special{pa 2386 -1866}% +\special{pa 2386 -1677}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0.64,0,0.95,0.4}% +\special{pa 5457 -1677}\special{pa 6118 -1677}\special{pa 6118 -1866}\special{pa 5457 -1866}% +\special{pa 5457 -1677}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0,0.48,0,0}% +\special{pa 2386 -1441}\special{pa 3047 -1441}\special{pa 3047 -1630}\special{pa 2386 -1630}% +\special{pa 2386 -1441}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0,0.72,1,0.45}% +\special{pa 5457 -1441}\special{pa 6118 -1441}\special{pa 6118 -1630}\special{pa 5457 -1630}% +\special{pa 5457 -1441}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0.12,0.59,0,0}% +\special{pa 2386 -1205}\special{pa 3047 -1205}\special{pa 3047 -1394}\special{pa 2386 -1394}% +\special{pa 2386 -1205}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0,0.83,1,0.7}% +\special{pa 5457 -1205}\special{pa 6118 -1205}\special{pa 6118 -1394}\special{pa 5457 -1394}% +\special{pa 5457 -1205}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0.32,0.64,0,0}% +\special{pa 2386 -969}\special{pa 3047 -969}\special{pa 3047 -1157}\special{pa 2386 -1157}% +\special{pa 2386 -969}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0,0.81,1,0.6}% +\special{pa 5457 -969}\special{pa 6118 -969}\special{pa 6118 -1157}\special{pa 5457 -1157}% +\special{pa 5457 -969}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0.4,0.8,0.2,0}% +\special{pa 2386 -732}\special{pa 3047 -732}\special{pa 3047 -921}\special{pa 2386 -921}% +\special{pa 2386 -732}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0.14,0.42,0.56,0}% +\special{pa 5457 -732}\special{pa 6118 -732}\special{pa 6118 -921}\special{pa 5457 -921}% +\special{pa 5457 -732}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0.45,0.86,0,0}% +\special{pa 2386 -496}\special{pa 3047 -496}\special{pa 3047 -685}\special{pa 2386 -685}% +\special{pa 2386 -496}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0,0,0,0.5}% +\special{pa 5457 -496}\special{pa 6118 -496}\special{pa 6118 -685}\special{pa 5457 -685}% +\special{pa 5457 -496}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0.5,1,0,0}% +\special{pa 2386 -260}\special{pa 3047 -260}\special{pa 3047 -449}\special{pa 2386 -449}% +\special{pa 2386 -260}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0,0,0,1}% +\special{pa 5457 -260}\special{pa 6118 -260}\special{pa 6118 -449}\special{pa 5457 -449}% +\special{pa 5457 -260}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0.79,0.88,0,0}% +\special{pa 2386 -24}\special{pa 3047 -24}\special{pa 3047 -213}\special{pa 2386 -213}% +\special{pa 2386 -24}\special{sh 1}\special{ip}% +}% +{% +\color[cmyk]{0,0,0,0}% +\special{pa 5457 -24}\special{pa 6118 -24}\special{pa 6118 -213}\special{pa 5457 -213}% +\special{pa 5457 -24}\special{sh 1}\special{ip}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -8268}\special{pa 0 -0}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 1181 -8268}\special{pa 1181 -0}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 2362 -8268}\special{pa 2362 -0}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 3071 -8268}\special{pa 3071 -0}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -8268}\special{pa 3071 -8268}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -8031}\special{pa 3071 -8031}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -7795}\special{pa 3071 -7795}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -7559}\special{pa 3071 -7559}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -7323}\special{pa 3071 -7323}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -7087}\special{pa 3071 -7087}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -6850}\special{pa 3071 -6850}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -6614}\special{pa 3071 -6614}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -6378}\special{pa 3071 -6378}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -6142}\special{pa 3071 -6142}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -5906}\special{pa 3071 -5906}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -5669}\special{pa 3071 -5669}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -5433}\special{pa 3071 -5433}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -5197}\special{pa 3071 -5197}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -4961}\special{pa 3071 -4961}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -4724}\special{pa 3071 -4724}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -4488}\special{pa 3071 -4488}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -4252}\special{pa 3071 -4252}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -4016}\special{pa 3071 -4016}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -3780}\special{pa 3071 -3780}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -3543}\special{pa 3071 -3543}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -3307}\special{pa 3071 -3307}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -3071}\special{pa 3071 -3071}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -2835}\special{pa 3071 -2835}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -2598}\special{pa 3071 -2598}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -2362}\special{pa 3071 -2362}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -2126}\special{pa 3071 -2126}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -1890}\special{pa 3071 -1890}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -1654}\special{pa 3071 -1654}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -1417}\special{pa 3071 -1417}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -1181}\special{pa 3071 -1181}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -945}\special{pa 3071 -945}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -709}\special{pa 3071 -709}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -472}\special{pa 3071 -472}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -236}\special{pa 3071 -236}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -0}\special{pa 3071 -0}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -8268}\special{pa 0 -0}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 1181 -8268}\special{pa 1181 -0}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 2362 -8268}\special{pa 2362 -0}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 3071 -8268}\special{pa 3071 -0}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 4252 -8268}\special{pa 4252 -0}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 5433 -8268}\special{pa 5433 -0}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 6142 -8268}\special{pa 6142 -0}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -8268}\special{pa 6142 -8268}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -8031}\special{pa 6142 -8031}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -7795}\special{pa 6142 -7795}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -7559}\special{pa 6142 -7559}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -7323}\special{pa 6142 -7323}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -7087}\special{pa 6142 -7087}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -6850}\special{pa 6142 -6850}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -6614}\special{pa 6142 -6614}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -6378}\special{pa 6142 -6378}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -6142}\special{pa 6142 -6142}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -5906}\special{pa 6142 -5906}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -5669}\special{pa 6142 -5669}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -5433}\special{pa 6142 -5433}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -5197}\special{pa 6142 -5197}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -4961}\special{pa 6142 -4961}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -4724}\special{pa 6142 -4724}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -4488}\special{pa 6142 -4488}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -4252}\special{pa 6142 -4252}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -4016}\special{pa 6142 -4016}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -3780}\special{pa 6142 -3780}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -3543}\special{pa 6142 -3543}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -3307}\special{pa 6142 -3307}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -3071}\special{pa 6142 -3071}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -2835}\special{pa 6142 -2835}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -2598}\special{pa 6142 -2598}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -2362}\special{pa 6142 -2362}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -2126}\special{pa 6142 -2126}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -1890}\special{pa 6142 -1890}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -1654}\special{pa 6142 -1654}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -1417}\special{pa 6142 -1417}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -1181}\special{pa 6142 -1181}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -945}\special{pa 6142 -945}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -709}\special{pa 6142 -709}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -472}\special{pa 6142 -472}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -236}\special{pa 6142 -236}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -0}\special{pa 6142 -0}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 3083 -8268}\special{pa 3083 -0}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\special{pa 0 -8043}\special{pa 6142 -8043}% +\special{fp}% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{name}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{name}\settodepth{\Depth}{name}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(2.5000000,34.5000000){\hspace*{\Width}\raisebox{\Height}{name}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{CMYK}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{CMYK}\settodepth{\Depth}{CMYK}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(7.5000000,34.5000000){\hspace*{\Width}\raisebox{\Height}{CMYK}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{Color}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{Color}\settodepth{\Depth}{Color}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(11.5000000,34.5000000){\hspace*{\Width}\raisebox{\Height}{Color}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{name}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{name}\settodepth{\Depth}{name}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(15.5000000,34.5000000){\hspace*{\Width}\raisebox{\Height}{name}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{CMYK}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{CMYK}\settodepth{\Depth}{CMYK}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(20.5000000,34.5000000){\hspace*{\Width}\raisebox{\Height}{CMYK}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{Color}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{Color}\settodepth{\Depth}{Color}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(24.5000000,34.5000000){\hspace*{\Width}\raisebox{\Height}{Color}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{greenyellow}\setlength{\Width}{-0.5\Width}% 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+\put(20.5000000,31.5000000){\hspace*{\Width}\raisebox{\Height}{[0.57,0.55,0,0]}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{dandelion}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{dandelion}\settodepth{\Depth}{dandelion}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(2.5000000,30.5000000){\hspace*{\Width}\raisebox{\Height}{dandelion}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{[0,0.29,0.84,0]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0,0.29,0.84,0]}\settodepth{\Depth}{[0,0.29,0.84,0]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(7.5000000,30.5000000){\hspace*{\Width}\raisebox{\Height}{[0,0.29,0.84,0]}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{cadetblue}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{cadetblue}\settodepth{\Depth}{cadetblue}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(15.5000000,30.5000000){\hspace*{\Width}\raisebox{\Height}{cadetblue}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{[0.62,0.57,0.23,0]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0.62,0.57,0.23,0]}\settodepth{\Depth}{[0.62,0.57,0.23,0]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(20.5000000,30.5000000){\hspace*{\Width}\raisebox{\Height}{[0.62,0.57,0.23,0]}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{apricot}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{apricot}\settodepth{\Depth}{apricot}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(2.5000000,29.5000000){\hspace*{\Width}\raisebox{\Height}{apricot}}% +% +}% +{% +\color[rgb]{0,0,0}% 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+\put(20.5000000,29.5000000){\hspace*{\Width}\raisebox{\Height}{[0.65,0.13,0,0]}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{peach}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{peach}\settodepth{\Depth}{peach}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(2.5000000,28.5000000){\hspace*{\Width}\raisebox{\Height}{peach}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{[0,0.5,0.7,0]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0,0.5,0.7,0]}\settodepth{\Depth}{[0,0.5,0.7,0]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(7.5000000,28.5000000){\hspace*{\Width}\raisebox{\Height}{[0,0.5,0.7,0]}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{midnightblue}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{midnightblue}\settodepth{\Depth}{midnightblue}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(15.5000000,28.5000000){\hspace*{\Width}\raisebox{\Height}{midnightblue}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{[0.98,0.13,0,0.43]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0.98,0.13,0,0.43]}\settodepth{\Depth}{[0.98,0.13,0,0.43]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(20.5000000,28.5000000){\hspace*{\Width}\raisebox{\Height}{[0.98,0.13,0,0.43]}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{melon}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{melon}\settodepth{\Depth}{melon}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(2.5000000,27.5000000){\hspace*{\Width}\raisebox{\Height}{melon}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{[0,0.46,0.5,0]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0,0.46,0.5,0]}\settodepth{\Depth}{[0,0.46,0.5,0]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(7.5000000,27.5000000){\hspace*{\Width}\raisebox{\Height}{[0,0.46,0.5,0]}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{navyblue}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{navyblue}\settodepth{\Depth}{navyblue}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(15.5000000,27.5000000){\hspace*{\Width}\raisebox{\Height}{navyblue}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{[0.94,0.54,0,0]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0.94,0.54,0,0]}\settodepth{\Depth}{[0.94,0.54,0,0]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(20.5000000,27.5000000){\hspace*{\Width}\raisebox{\Height}{[0.94,0.54,0,0]}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{yelloworange}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{yelloworange}\settodepth{\Depth}{yelloworange}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(2.5000000,26.5000000){\hspace*{\Width}\raisebox{\Height}{yelloworange}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{[0,0.42,1,0]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0,0.42,1,0]}\settodepth{\Depth}{[0,0.42,1,0]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(7.5000000,26.5000000){\hspace*{\Width}\raisebox{\Height}{[0,0.42,1,0]}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{royalblue}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{royalblue}\settodepth{\Depth}{royalblue}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(15.5000000,26.5000000){\hspace*{\Width}\raisebox{\Height}{royalblue}}% +% +}% +{% 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+\settowidth{\Width}{[0.47,0.91,0,0.08]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0.47,0.91,0,0.08]}\settodepth{\Depth}{[0.47,0.91,0,0.08]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(7.5000000,7.5000000){\hspace*{\Width}\raisebox{\Height}{[0.47,0.91,0,0.08]}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{olivegreen}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{olivegreen}\settodepth{\Depth}{olivegreen}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(15.5000000,7.5000000){\hspace*{\Width}\raisebox{\Height}{olivegreen}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{[0.64,0,0.95,0.4]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0.64,0,0.95,0.4]}\settodepth{\Depth}{[0.64,0,0.95,0.4]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(20.5000000,7.5000000){\hspace*{\Width}\raisebox{\Height}{[0.64,0,0.95,0.4]}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{lavender}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{lavender}\settodepth{\Depth}{lavender}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(2.5000000,6.5000000){\hspace*{\Width}\raisebox{\Height}{lavender}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{[0,0.48,0,0]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0,0.48,0,0]}\settodepth{\Depth}{[0,0.48,0,0]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(7.5000000,6.5000000){\hspace*{\Width}\raisebox{\Height}{[0,0.48,0,0]}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{rawsienna}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{rawsienna}\settodepth{\Depth}{rawsienna}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(15.5000000,6.5000000){\hspace*{\Width}\raisebox{\Height}{rawsienna}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{[0,0.72,1,0.45]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0,0.72,1,0.45]}\settodepth{\Depth}{[0,0.72,1,0.45]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(20.5000000,6.5000000){\hspace*{\Width}\raisebox{\Height}{[0,0.72,1,0.45]}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{thistle}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{thistle}\settodepth{\Depth}{thistle}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(2.5000000,5.5000000){\hspace*{\Width}\raisebox{\Height}{thistle}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{[0.12,0.59,0,0]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0.12,0.59,0,0]}\settodepth{\Depth}{[0.12,0.59,0,0]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(7.5000000,5.5000000){\hspace*{\Width}\raisebox{\Height}{[0.12,0.59,0,0]}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{sepia}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{sepia}\settodepth{\Depth}{sepia}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(15.5000000,5.5000000){\hspace*{\Width}\raisebox{\Height}{sepia}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{[0,0.83,1,0.7]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0,0.83,1,0.7]}\settodepth{\Depth}{[0,0.83,1,0.7]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(20.5000000,5.5000000){\hspace*{\Width}\raisebox{\Height}{[0,0.83,1,0.7]}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{orchid}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{orchid}\settodepth{\Depth}{orchid}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(2.5000000,4.5000000){\hspace*{\Width}\raisebox{\Height}{orchid}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{[0.32,0.64,0,0]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0.32,0.64,0,0]}\settodepth{\Depth}{[0.32,0.64,0,0]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(7.5000000,4.5000000){\hspace*{\Width}\raisebox{\Height}{[0.32,0.64,0,0]}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{brown}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{brown}\settodepth{\Depth}{brown}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(15.5000000,4.5000000){\hspace*{\Width}\raisebox{\Height}{brown}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{[0,0.81,1,0.6]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0,0.81,1,0.6]}\settodepth{\Depth}{[0,0.81,1,0.6]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(20.5000000,4.5000000){\hspace*{\Width}\raisebox{\Height}{[0,0.81,1,0.6]}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{darkorchid}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{darkorchid}\settodepth{\Depth}{darkorchid}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(2.5000000,3.5000000){\hspace*{\Width}\raisebox{\Height}{darkorchid}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{[0.4,0.8,0.2,0]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0.4,0.8,0.2,0]}\settodepth{\Depth}{[0.4,0.8,0.2,0]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(7.5000000,3.5000000){\hspace*{\Width}\raisebox{\Height}{[0.4,0.8,0.2,0]}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{tan}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{tan}\settodepth{\Depth}{tan}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(15.5000000,3.5000000){\hspace*{\Width}\raisebox{\Height}{tan}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{[0.14,0.42,0.56,0]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0.14,0.42,0.56,0]}\settodepth{\Depth}{[0.14,0.42,0.56,0]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(20.5000000,3.5000000){\hspace*{\Width}\raisebox{\Height}{[0.14,0.42,0.56,0]}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{purple}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{purple}\settodepth{\Depth}{purple}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(2.5000000,2.5000000){\hspace*{\Width}\raisebox{\Height}{purple}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{[0.45,0.86,0,0]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0.45,0.86,0,0]}\settodepth{\Depth}{[0.45,0.86,0,0]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(7.5000000,2.5000000){\hspace*{\Width}\raisebox{\Height}{[0.45,0.86,0,0]}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{gray}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{gray}\settodepth{\Depth}{gray}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(15.5000000,2.5000000){\hspace*{\Width}\raisebox{\Height}{gray}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{[0,0,0,0.5]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0,0,0,0.5]}\settodepth{\Depth}{[0,0,0,0.5]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(20.5000000,2.5000000){\hspace*{\Width}\raisebox{\Height}{[0,0,0,0.5]}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{plum}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{plum}\settodepth{\Depth}{plum}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(2.5000000,1.5000000){\hspace*{\Width}\raisebox{\Height}{plum}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{[0.5,1,0,0]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0.5,1,0,0]}\settodepth{\Depth}{[0.5,1,0,0]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(7.5000000,1.5000000){\hspace*{\Width}\raisebox{\Height}{[0.5,1,0,0]}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{black}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{black}\settodepth{\Depth}{black}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(15.5000000,1.5000000){\hspace*{\Width}\raisebox{\Height}{black}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{[0,0,0,1]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0,0,0,1]}\settodepth{\Depth}{[0,0,0,1]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(20.5000000,1.5000000){\hspace*{\Width}\raisebox{\Height}{[0,0,0,1]}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{violet}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{violet}\settodepth{\Depth}{violet}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(2.5000000,0.5000000){\hspace*{\Width}\raisebox{\Height}{violet}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{[0.79,0.88,0,0]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0.79,0.88,0,0]}\settodepth{\Depth}{[0.79,0.88,0,0]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(7.5000000,0.5000000){\hspace*{\Width}\raisebox{\Height}{[0.79,0.88,0,0]}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{white}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{white}\settodepth{\Depth}{white}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(15.5000000,0.5000000){\hspace*{\Width}\raisebox{\Height}{white}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{[0,0,0,0]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0,0,0,0]}\settodepth{\Depth}{[0,0,0,0]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(20.5000000,0.5000000){\hspace*{\Width}\raisebox{\Height}{[0,0,0,0]}}% +% +}% +\end{picture}}%
\ No newline at end of file diff --git a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/colortable1-34.tex b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/colortable1-34.tex deleted file mode 100644 index 0138da07bd0..00000000000 --- a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/colortable1-34.tex +++ /dev/null @@ -1,1936 +0,0 @@ -%%% colortable1-34.tex 2015-2-8 17:25 -%%% colortable1-34.sce 2015-2-8 17:25 -{\unitlength=1cm% -\begin{picture}% -( 15.00000, 17.50000)( -0.00000, -0.00000)% -\special{pn 8}% -% -\color[cmyk]{0.15,0,0.69,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,16.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -6693}\special{pa 4626 -6496}\special{pa 5906 -6496}\special{pa 5906 -6693}% -\special{pa 4626 -6693}\special{sh 1}\special{ip}% -\color[cmyk]{0,0,1,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,16.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -6496}\special{pa 4626 -6299}\special{pa 5906 -6299}\special{pa 5906 -6496}% -\special{pa 4626 -6496}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.1,0.84,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,15.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -6299}\special{pa 4626 -6102}\special{pa 5906 -6102}\special{pa 5906 -6299}% -\special{pa 4626 -6299}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.29,0.84,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,15.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -6102}\special{pa 4626 -5906}\special{pa 5906 -5906}\special{pa 5906 -6102}% -\special{pa 4626 -6102}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.32,0.52,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,14.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -5906}\special{pa 4626 -5709}\special{pa 5906 -5709}\special{pa 5906 -5906}% -\special{pa 4626 -5906}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.5,0.7,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,14.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -5709}\special{pa 4626 -5512}\special{pa 5906 -5512}\special{pa 5906 -5709}% -\special{pa 4626 -5709}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.46,0.5,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,13.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -5512}\special{pa 4626 -5315}\special{pa 5906 -5315}\special{pa 5906 -5512}% -\special{pa 4626 -5512}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.42,1,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,13.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -5315}\special{pa 4626 -5118}\special{pa 5906 -5118}\special{pa 5906 -5315}% -\special{pa 4626 -5315}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.61,0.87,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,12.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -5118}\special{pa 4626 -4921}\special{pa 5906 -4921}\special{pa 5906 -5118}% -\special{pa 4626 -5118}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.51,1,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,12.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -4921}\special{pa 4626 -4724}\special{pa 5906 -4724}\special{pa 5906 -4921}% -\special{pa 4626 -4921}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.75,1,0.24}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,11.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -4724}\special{pa 4626 -4528}\special{pa 5906 -4528}\special{pa 5906 -4724}% -\special{pa 4626 -4724}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.77,0.87,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,11.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -4528}\special{pa 4626 -4331}\special{pa 5906 -4331}\special{pa 5906 -4528}% -\special{pa 4626 -4528}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.85,0.87,0.35}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,10.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -4331}\special{pa 4626 -4134}\special{pa 5906 -4134}\special{pa 5906 -4331}% -\special{pa 4626 -4331}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.87,0.68,0.32}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,10.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -4134}\special{pa 4626 -3937}\special{pa 5906 -3937}\special{pa 5906 -4134}% -\special{pa 4626 -4134}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.89,0.94,0.28}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,9.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -3937}\special{pa 4626 -3740}\special{pa 5906 -3740}\special{pa 5906 -3937}% -\special{pa 4626 -3937}\special{sh 1}\special{ip}% -\color[cmyk]{0,1,1,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,9.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -3740}\special{pa 4626 -3543}\special{pa 5906 -3543}\special{pa 5906 -3740}% -\special{pa 4626 -3740}\special{sh 1}\special{ip}% -\color[cmyk]{0,1,0.5,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,8.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -3543}\special{pa 4626 -3346}\special{pa 5906 -3346}\special{pa 5906 -3543}% -\special{pa 4626 -3543}\special{sh 1}\special{ip}% -\color[cmyk]{0,1,0.13,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,8.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -3346}\special{pa 4626 -3150}\special{pa 5906 -3150}\special{pa 5906 -3346}% -\special{pa 4626 -3346}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.96,0.39,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,7.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -3150}\special{pa 4626 -2953}\special{pa 5906 -2953}\special{pa 5906 -3150}% -\special{pa 4626 -3150}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.53,0.38,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,7.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -2953}\special{pa 4626 -2756}\special{pa 5906 -2756}\special{pa 5906 -2953}% -\special{pa 4626 -2953}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.63,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,6.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -2756}\special{pa 4626 -2559}\special{pa 5906 -2559}\special{pa 5906 -2756}% -\special{pa 4626 -2756}\special{sh 1}\special{ip}% -\color[cmyk]{0,1,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,6.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -2559}\special{pa 4626 -2362}\special{pa 5906 -2362}\special{pa 5906 -2559}% -\special{pa 4626 -2559}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.81,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,5.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -2362}\special{pa 4626 -2165}\special{pa 5906 -2165}\special{pa 5906 -2362}% -\special{pa 4626 -2362}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.82,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,5.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -2165}\special{pa 4626 -1969}\special{pa 5906 -1969}\special{pa 5906 -2165}% -\special{pa 4626 -2165}\special{sh 1}\special{ip}% -\color[cmyk]{0.34,0.9,0,0.02}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,4.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -1969}\special{pa 4626 -1772}\special{pa 5906 -1772}\special{pa 5906 -1969}% -\special{pa 4626 -1969}\special{sh 1}\special{ip}% -\color[cmyk]{0.07,0.9,0,0.34}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,4.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -1772}\special{pa 4626 -1575}\special{pa 5906 -1575}\special{pa 5906 -1772}% -\special{pa 4626 -1772}\special{sh 1}\special{ip}% -\color[cmyk]{0.47,0.91,0,0.08}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,3.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -1575}\special{pa 4626 -1378}\special{pa 5906 -1378}\special{pa 5906 -1575}% -\special{pa 4626 -1575}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.48,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,3.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -1378}\special{pa 4626 -1181}\special{pa 5906 -1181}\special{pa 5906 -1378}% -\special{pa 4626 -1378}\special{sh 1}\special{ip}% -\color[cmyk]{0.12,0.59,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,2.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -1181}\special{pa 4626 -984}\special{pa 5906 -984}\special{pa 5906 -1181}% -\special{pa 4626 -1181}\special{sh 1}\special{ip}% -\color[cmyk]{0.32,0.64,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,2.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -984}\special{pa 4626 -787}\special{pa 5906 -787}\special{pa 5906 -984}% -\special{pa 4626 -984}\special{sh 1}\special{ip}% -\color[cmyk]{0.4,0.8,0.2,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,1.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -787}\special{pa 4626 -591}\special{pa 5906 -591}\special{pa 5906 -787}% -\special{pa 4626 -787}\special{sh 1}\special{ip}% -\color[cmyk]{0.45,0.86,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,1.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -591}\special{pa 4626 -394}\special{pa 5906 -394}\special{pa 5906 -591}% -\special{pa 4626 -591}\special{sh 1}\special{ip}% -\color[cmyk]{0.5,1,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,0.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -394}\special{pa 4626 -197}\special{pa 5906 -197}\special{pa 5906 -394}% -\special{pa 4626 -394}\special{sh 1}\special{ip}% -\color[cmyk]{0.79,0.88,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,0.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -197}\special{pa 4626 0}\special{pa 5906 0}\special{pa 5906 -197}% -\special{pa 4626 -197}\special{sh 1}\special{ip}% -\color[cmyk]{0,0,0,1}% -\special{pa 0 -6890}\special{pa 1083 -6890}% -\special{fp}% -\special{pa 1083 -6890}\special{pa 2461 -6890}% -\special{fp}% -\special{pa 2461 -6890}\special{pa 3839 -6890}% -\special{fp}% -\special{pa 3839 -6890}\special{pa 4626 -6890}% -\special{fp}% -\special{pa 4626 -6890}\special{pa 5906 -6890}% -\special{fp}% -\special{pa 0 -6693}\special{pa 1083 -6693}% -\special{fp}% -\special{pa 1083 -6693}\special{pa 2461 -6693}% -\special{fp}% -\special{pa 2461 -6693}\special{pa 3839 -6693}% -\special{fp}% -\special{pa 3839 -6693}\special{pa 4626 -6693}% -\special{fp}% -\special{pa 4626 -6693}\special{pa 5906 -6693}% -\special{fp}% -\special{pa 0 -6496}\special{pa 1083 -6496}% -\special{fp}% -\special{pa 1083 -6496}\special{pa 2461 -6496}% -\special{fp}% -\special{pa 2461 -6496}\special{pa 3839 -6496}% -\special{fp}% -\special{pa 3839 -6496}\special{pa 4626 -6496}% -\special{fp}% -\special{pa 4626 -6496}\special{pa 5906 -6496}% -\special{fp}% -\special{pa 0 -6299}\special{pa 1083 -6299}% -\special{fp}% -\special{pa 1083 -6299}\special{pa 2461 -6299}% -\special{fp}% -\special{pa 2461 -6299}\special{pa 3839 -6299}% -\special{fp}% -\special{pa 3839 -6299}\special{pa 4626 -6299}% -\special{fp}% -\special{pa 4626 -6299}\special{pa 5906 -6299}% -\special{fp}% -\special{pa 0 -6102}\special{pa 1083 -6102}% -\special{fp}% -\special{pa 1083 -6102}\special{pa 2461 -6102}% -\special{fp}% -\special{pa 2461 -6102}\special{pa 3839 -6102}% -\special{fp}% -\special{pa 3839 -6102}\special{pa 4626 -6102}% -\special{fp}% -\special{pa 4626 -6102}\special{pa 5906 -6102}% -\special{fp}% -\special{pa 0 -5906}\special{pa 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-\settoheight{\Height}{plum}\settodepth{\Depth}{plum}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(4.5000,0.7500){\hspace*{\Width}\raisebox{\Height}{plum}}% -% -% -\settowidth{\Width}{[0.5,1,0,0]}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{[0.5,1,0,0]}\settodepth{\Depth}{[0.5,1,0,0]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(8.0000,0.7500){\hspace*{\Width}\raisebox{\Height}{[0.5,1,0,0]}}% -% -% -\settowidth{\Width}{}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{}\settodepth{\Depth}{}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,0.7500){\hspace*{\Width}\raisebox{\Height}{}}% -% -% -\settowidth{\Width}{}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{}\settodepth{\Depth}{}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(13.3800,0.7500){\hspace*{\Width}\raisebox{\Height}{}}% -% -% -\settowidth{\Width}{}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{}\settodepth{\Depth}{}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(1.3800,0.2500){\hspace*{\Width}\raisebox{\Height}{}}% -% -% -\settowidth{\Width}{violet}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{violet}\settodepth{\Depth}{violet}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(4.5000,0.2500){\hspace*{\Width}\raisebox{\Height}{violet}}% -% -% -\settowidth{\Width}{[0.79,0.88,0,0]}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{[0.79,0.88,0,0]}\settodepth{\Depth}{[0.79,0.88,0,0]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(8.0000,0.2500){\hspace*{\Width}\raisebox{\Height}{[0.79,0.88,0,0]}}% -% -% -\settowidth{\Width}{}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{}\settodepth{\Depth}{}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,0.2500){\hspace*{\Width}\raisebox{\Height}{}}% -% -% -\settowidth{\Width}{}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{}\settodepth{\Depth}{}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(13.3800,0.2500){\hspace*{\Width}\raisebox{\Height}{}}% -% -% -\end{picture}}%
\ No newline at end of file diff --git a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/colortable35-68.tex b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/colortable35-68.tex deleted file mode 100644 index c89b555d804..00000000000 --- a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/colortable35-68.tex +++ /dev/null @@ -1,1934 +0,0 @@ -%%% colortable35-68.tex 2015-2-6 18:34 -%%% colortable35-68.sce 2015-2-6 18:29 -{\unitlength=1cm% -\begin{picture}% -( 15.00000, 17.50000)( -0.00000, -0.00000)% -\special{pn 8}% -% -\color[cmyk]{0.75,0.9,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,16.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -6693}\special{pa 4626 -6496}\special{pa 5906 -6496}\special{pa 5906 -6693}% -\special{pa 4626 -6693}\special{sh 1}\special{ip}% -\color[cmyk]{0.86,0.91,0,0.04}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,16.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -6496}\special{pa 4626 -6299}\special{pa 5906 -6299}\special{pa 5906 -6496}% -\special{pa 4626 -6496}\special{sh 1}\special{ip}% -\color[cmyk]{0.57,0.55,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,15.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -6299}\special{pa 4626 -6102}\special{pa 5906 -6102}\special{pa 5906 -6299}% -\special{pa 4626 -6299}\special{sh 1}\special{ip}% -\color[cmyk]{0.62,0.57,0.23,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,15.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -6102}\special{pa 4626 -5906}\special{pa 5906 -5906}\special{pa 5906 -6102}% -\special{pa 4626 -6102}\special{sh 1}\special{ip}% -\color[cmyk]{0.65,0.13,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,14.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -5906}\special{pa 4626 -5709}\special{pa 5906 -5709}\special{pa 5906 -5906}% -\special{pa 4626 -5906}\special{sh 1}\special{ip}% -\color[cmyk]{0.98,0.13,0,0.43}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,14.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -5709}\special{pa 4626 -5512}\special{pa 5906 -5512}\special{pa 5906 -5709}% -\special{pa 4626 -5709}\special{sh 1}\special{ip}% -\color[cmyk]{0.94,0.54,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,13.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -5512}\special{pa 4626 -5315}\special{pa 5906 -5315}\special{pa 5906 -5512}% -\special{pa 4626 -5512}\special{sh 1}\special{ip}% -\color[cmyk]{1,0.5,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,13.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -5315}\special{pa 4626 -5118}\special{pa 5906 -5118}\special{pa 5906 -5315}% -\special{pa 4626 -5315}\special{sh 1}\special{ip}% -\color[cmyk]{1,1,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,12.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -5118}\special{pa 4626 -4921}\special{pa 5906 -4921}\special{pa 5906 -5118}% -\special{pa 4626 -5118}\special{sh 1}\special{ip}% -\color[cmyk]{0.94,0.11,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,12.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -4921}\special{pa 4626 -4724}\special{pa 5906 -4724}\special{pa 5906 -4921}% -\special{pa 4626 -4921}\special{sh 1}\special{ip}% -\color[cmyk]{1,0,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,11.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -4724}\special{pa 4626 -4528}\special{pa 5906 -4528}\special{pa 5906 -4724}% -\special{pa 4626 -4724}\special{sh 1}\special{ip}% -\color[cmyk]{0.96,0,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,11.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -4528}\special{pa 4626 -4331}\special{pa 5906 -4331}\special{pa 5906 -4528}% -\special{pa 4626 -4528}\special{sh 1}\special{ip}% -\color[cmyk]{0.62,0,0.12,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,10.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -4331}\special{pa 4626 -4134}\special{pa 5906 -4134}\special{pa 5906 -4331}% -\special{pa 4626 -4331}\special{sh 1}\special{ip}% -\color[cmyk]{0.85,0,0.2,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,10.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -4134}\special{pa 4626 -3937}\special{pa 5906 -3937}\special{pa 5906 -4134}% -\special{pa 4626 -4134}\special{sh 1}\special{ip}% -\color[cmyk]{0.86,0,0.34,0.02}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,9.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -3937}\special{pa 4626 -3740}\special{pa 5906 -3740}\special{pa 5906 -3937}% -\special{pa 4626 -3937}\special{sh 1}\special{ip}% -\color[cmyk]{0.82,0,0.3,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,9.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -3740}\special{pa 4626 -3543}\special{pa 5906 -3543}\special{pa 5906 -3740}% -\special{pa 4626 -3740}\special{sh 1}\special{ip}% -\color[cmyk]{0.85,0,0.33,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,8.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -3543}\special{pa 4626 -3346}\special{pa 5906 -3346}\special{pa 5906 -3543}% -\special{pa 4626 -3543}\special{sh 1}\special{ip}% -\color[cmyk]{1,0,0.5,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,8.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -3346}\special{pa 4626 -3150}\special{pa 5906 -3150}\special{pa 5906 -3346}% -\special{pa 4626 -3346}\special{sh 1}\special{ip}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,7.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -3150}\special{pa 4626 -2953}\special{pa 5906 -2953}\special{pa 5906 -3150}% -\special{pa 4626 -3150}\special{sh 1}\special{ip}% -\color[cmyk]{0.69,0,0.5,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,7.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -2953}\special{pa 4626 -2756}\special{pa 5906 -2756}\special{pa 5906 -2953}% -\special{pa 4626 -2953}\special{sh 1}\special{ip}% -\color[cmyk]{1,0,1,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,6.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -2756}\special{pa 4626 -2559}\special{pa 5906 -2559}\special{pa 5906 -2756}% -\special{pa 4626 -2756}\special{sh 1}\special{ip}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,6.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -2559}\special{pa 4626 -2362}\special{pa 5906 -2362}\special{pa 5906 -2559}% -\special{pa 4626 -2559}\special{sh 1}\special{ip}% -\color[cmyk]{0.92,0,0.59,0.25}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,5.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -2362}\special{pa 4626 -2165}\special{pa 5906 -2165}\special{pa 5906 -2362}% -\special{pa 4626 -2362}\special{sh 1}\special{ip}% -\color[cmyk]{0.5,0,1,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,5.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -2165}\special{pa 4626 -1969}\special{pa 5906 -1969}\special{pa 5906 -2165}% -\special{pa 4626 -2165}\special{sh 1}\special{ip}% -\color[cmyk]{0.44,0,0.74,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,4.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -1969}\special{pa 4626 -1772}\special{pa 5906 -1772}\special{pa 5906 -1969}% -\special{pa 4626 -1969}\special{sh 1}\special{ip}% -\color[cmyk]{0.26,0,0.76,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,4.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -1772}\special{pa 4626 -1575}\special{pa 5906 -1575}\special{pa 5906 -1772}% -\special{pa 4626 -1772}\special{sh 1}\special{ip}% -\color[cmyk]{0.64,0,0.95,0.4}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,3.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -1575}\special{pa 4626 -1378}\special{pa 5906 -1378}\special{pa 5906 -1575}% -\special{pa 4626 -1575}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.72,1,0.45}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,3.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -1378}\special{pa 4626 -1181}\special{pa 5906 -1181}\special{pa 5906 -1378}% -\special{pa 4626 -1378}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.83,1,0.7}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,2.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -1181}\special{pa 4626 -984}\special{pa 5906 -984}\special{pa 5906 -1181}% -\special{pa 4626 -1181}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.81,1,0.6}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% 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-\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,15.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -6102}\special{pa 4626 -5906}\special{pa 5906 -5906}\special{pa 5906 -6102}% -\special{pa 4626 -6102}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.32,0.52,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,14.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -5906}\special{pa 4626 -5709}\special{pa 5906 -5709}\special{pa 5906 -5906}% -\special{pa 4626 -5906}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.5,0.7,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,14.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -5709}\special{pa 4626 -5512}\special{pa 5906 -5512}\special{pa 5906 -5709}% -\special{pa 4626 -5709}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.46,0.5,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,13.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -5512}\special{pa 4626 -5315}\special{pa 5906 -5315}\special{pa 5906 -5512}% -\special{pa 4626 -5512}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.42,1,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,13.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -5315}\special{pa 4626 -5118}\special{pa 5906 -5118}\special{pa 5906 -5315}% -\special{pa 4626 -5315}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.61,0.87,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,12.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -5118}\special{pa 4626 -4921}\special{pa 5906 -4921}\special{pa 5906 -5118}% -\special{pa 4626 -5118}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.51,1,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,12.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -4921}\special{pa 4626 -4724}\special{pa 5906 -4724}\special{pa 5906 -4921}% -\special{pa 4626 -4921}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.75,1,0.24}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,11.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -4724}\special{pa 4626 -4528}\special{pa 5906 -4528}\special{pa 5906 -4724}% -\special{pa 4626 -4724}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.77,0.87,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,11.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -4528}\special{pa 4626 -4331}\special{pa 5906 -4331}\special{pa 5906 -4528}% -\special{pa 4626 -4528}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.85,0.87,0.35}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,10.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -4331}\special{pa 4626 -4134}\special{pa 5906 -4134}\special{pa 5906 -4331}% -\special{pa 4626 -4331}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.87,0.68,0.32}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,10.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -4134}\special{pa 4626 -3937}\special{pa 5906 -3937}\special{pa 5906 -4134}% -\special{pa 4626 -4134}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.89,0.94,0.28}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,9.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -3937}\special{pa 4626 -3740}\special{pa 5906 -3740}\special{pa 5906 -3937}% -\special{pa 4626 -3937}\special{sh 1}\special{ip}% -\color[cmyk]{0,1,1,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,9.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -3740}\special{pa 4626 -3543}\special{pa 5906 -3543}\special{pa 5906 -3740}% -\special{pa 4626 -3740}\special{sh 1}\special{ip}% -\color[cmyk]{0,1,0.5,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,8.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -3543}\special{pa 4626 -3346}\special{pa 5906 -3346}\special{pa 5906 -3543}% -\special{pa 4626 -3543}\special{sh 1}\special{ip}% -\color[cmyk]{0,1,0.13,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,8.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -3346}\special{pa 4626 -3150}\special{pa 5906 -3150}\special{pa 5906 -3346}% -\special{pa 4626 -3346}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.96,0.39,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,7.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -3150}\special{pa 4626 -2953}\special{pa 5906 -2953}\special{pa 5906 -3150}% -\special{pa 4626 -3150}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.53,0.38,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,7.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -2953}\special{pa 4626 -2756}\special{pa 5906 -2756}\special{pa 5906 -2953}% -\special{pa 4626 -2953}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.63,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,6.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -2756}\special{pa 4626 -2559}\special{pa 5906 -2559}\special{pa 5906 -2756}% -\special{pa 4626 -2756}\special{sh 1}\special{ip}% -\color[cmyk]{0,1,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,6.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -2559}\special{pa 4626 -2362}\special{pa 5906 -2362}\special{pa 5906 -2559}% -\special{pa 4626 -2559}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.81,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,5.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -2362}\special{pa 4626 -2165}\special{pa 5906 -2165}\special{pa 5906 -2362}% -\special{pa 4626 -2362}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.82,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,5.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -2165}\special{pa 4626 -1969}\special{pa 5906 -1969}\special{pa 5906 -2165}% -\special{pa 4626 -2165}\special{sh 1}\special{ip}% -\color[cmyk]{0.34,0.9,0,0.02}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,4.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -1969}\special{pa 4626 -1772}\special{pa 5906 -1772}\special{pa 5906 -1969}% -\special{pa 4626 -1969}\special{sh 1}\special{ip}% -\color[cmyk]{0.07,0.9,0,0.34}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,4.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -1772}\special{pa 4626 -1575}\special{pa 5906 -1575}\special{pa 5906 -1772}% -\special{pa 4626 -1772}\special{sh 1}\special{ip}% -\color[cmyk]{0.47,0.91,0,0.08}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,3.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -1575}\special{pa 4626 -1378}\special{pa 5906 -1378}\special{pa 5906 -1575}% -\special{pa 4626 -1575}\special{sh 1}\special{ip}% -\color[cmyk]{0,0.48,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,3.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -1378}\special{pa 4626 -1181}\special{pa 5906 -1181}\special{pa 5906 -1378}% -\special{pa 4626 -1378}\special{sh 1}\special{ip}% -\color[cmyk]{0.12,0.59,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,2.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -1181}\special{pa 4626 -984}\special{pa 5906 -984}\special{pa 5906 -1181}% -\special{pa 4626 -1181}\special{sh 1}\special{ip}% -\color[cmyk]{0.32,0.64,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,2.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -984}\special{pa 4626 -787}\special{pa 5906 -787}\special{pa 5906 -984}% -\special{pa 4626 -984}\special{sh 1}\special{ip}% -\color[cmyk]{0.4,0.8,0.2,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,1.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -787}\special{pa 4626 -591}\special{pa 5906 -591}\special{pa 5906 -787}% -\special{pa 4626 -787}\special{sh 1}\special{ip}% -\color[cmyk]{0.45,0.86,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,1.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -591}\special{pa 4626 -394}\special{pa 5906 -394}\special{pa 5906 -591}% -\special{pa 4626 -591}\special{sh 1}\special{ip}% -\color[cmyk]{0.5,1,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,0.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -394}\special{pa 4626 -197}\special{pa 5906 -197}\special{pa 5906 -394}% -\special{pa 4626 -394}\special{sh 1}\special{ip}% -\color[cmyk]{0.79,0.88,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,0.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -197}\special{pa 4626 0}\special{pa 5906 0}\special{pa 5906 -197}% -\special{pa 4626 -197}\special{sh 1}\special{ip}% -\color[cmyk]{0,0,0,1}% -\special{pa 0 -6890}\special{pa 1083 -6890}% -\special{fp}% -\special{pa 1083 -6890}\special{pa 2461 -6890}% -\special{fp}% -\special{pa 2461 -6890}\special{pa 3839 -6890}% -\special{fp}% -\special{pa 3839 -6890}\special{pa 4626 -6890}% -\special{fp}% -\special{pa 4626 -6890}\special{pa 5906 -6890}% -\special{fp}% -\special{pa 0 -6693}\special{pa 1083 -6693}% -\special{fp}% -\special{pa 1083 -6693}\special{pa 2461 -6693}% -\special{fp}% -\special{pa 2461 -6693}\special{pa 3839 -6693}% -\special{fp}% -\special{pa 3839 -6693}\special{pa 4626 -6693}% -\special{fp}% -\special{pa 4626 -6693}\special{pa 5906 -6693}% -\special{fp}% -\special{pa 0 -6496}\special{pa 1083 -6496}% -\special{fp}% -\special{pa 1083 -6496}\special{pa 2461 -6496}% -\special{fp}% -\special{pa 2461 -6496}\special{pa 3839 -6496}% -\special{fp}% -\special{pa 3839 -6496}\special{pa 4626 -6496}% -\special{fp}% -\special{pa 4626 -6496}\special{pa 5906 -6496}% -\special{fp}% -\special{pa 0 -6299}\special{pa 1083 -6299}% -\special{fp}% -\special{pa 1083 -6299}\special{pa 2461 -6299}% -\special{fp}% -\special{pa 2461 -6299}\special{pa 3839 -6299}% -\special{fp}% -\special{pa 3839 -6299}\special{pa 4626 -6299}% -\special{fp}% -\special{pa 4626 -6299}\special{pa 5906 -6299}% -\special{fp}% -\special{pa 0 -6102}\special{pa 1083 -6102}% -\special{fp}% -\special{pa 1083 -6102}\special{pa 2461 -6102}% -\special{fp}% -\special{pa 2461 -6102}\special{pa 3839 -6102}% -\special{fp}% -\special{pa 3839 -6102}\special{pa 4626 -6102}% -\special{fp}% -\special{pa 4626 -6102}\special{pa 5906 -6102}% -\special{fp}% -\special{pa 0 -5906}\special{pa 1083 -5906}% -\special{fp}% -\special{pa 1083 -5906}\special{pa 2461 -5906}% -\special{fp}% -\special{pa 2461 -5906}\special{pa 3839 -5906}% -\special{fp}% -\special{pa 3839 -5906}\special{pa 4626 -5906}% -\special{fp}% -\special{pa 4626 -5906}\special{pa 5906 -5906}% -\special{fp}% -\special{pa 0 -5709}\special{pa 1083 -5709}% -\special{fp}% -\special{pa 1083 -5709}\special{pa 2461 -5709}% -\special{fp}% -\special{pa 2461 -5709}\special{pa 3839 -5709}% -\special{fp}% -\special{pa 3839 -5709}\special{pa 4626 -5709}% -\special{fp}% -\special{pa 4626 -5709}\special{pa 5906 -5709}% -\special{fp}% -\special{pa 0 -5512}\special{pa 1083 -5512}% -\special{fp}% -\special{pa 1083 -5512}\special{pa 2461 -5512}% -\special{fp}% -\special{pa 2461 -5512}\special{pa 3839 -5512}% -\special{fp}% -\special{pa 3839 -5512}\special{pa 4626 -5512}% -\special{fp}% -\special{pa 4626 -5512}\special{pa 5906 -5512}% -\special{fp}% -\special{pa 0 -5315}\special{pa 1083 -5315}% -\special{fp}% -\special{pa 1083 -5315}\special{pa 2461 -5315}% -\special{fp}% -\special{pa 2461 -5315}\special{pa 3839 -5315}% -\special{fp}% -\special{pa 3839 -5315}\special{pa 4626 -5315}% -\special{fp}% -\special{pa 4626 -5315}\special{pa 5906 -5315}% -\special{fp}% -\special{pa 0 -5118}\special{pa 1083 -5118}% -\special{fp}% -\special{pa 1083 -5118}\special{pa 2461 -5118}% -\special{fp}% -\special{pa 2461 -5118}\special{pa 3839 -5118}% -\special{fp}% -\special{pa 3839 -5118}\special{pa 4626 -5118}% -\special{fp}% -\special{pa 4626 -5118}\special{pa 5906 -5118}% -\special{fp}% -\special{pa 0 -4921}\special{pa 1083 -4921}% -\special{fp}% -\special{pa 1083 -4921}\special{pa 2461 -4921}% -\special{fp}% -\special{pa 2461 -4921}\special{pa 3839 -4921}% -\special{fp}% -\special{pa 3839 -4921}\special{pa 4626 -4921}% -\special{fp}% -\special{pa 4626 -4921}\special{pa 5906 -4921}% -\special{fp}% -\special{pa 0 -4724}\special{pa 1083 -4724}% -\special{fp}% -\special{pa 1083 -4724}\special{pa 2461 -4724}% -\special{fp}% -\special{pa 2461 -4724}\special{pa 3839 -4724}% -\special{fp}% -\special{pa 3839 -4724}\special{pa 4626 -4724}% -\special{fp}% -\special{pa 4626 -4724}\special{pa 5906 -4724}% -\special{fp}% -\special{pa 0 -4528}\special{pa 1083 -4528}% -\special{fp}% -\special{pa 1083 -4528}\special{pa 2461 -4528}% -\special{fp}% -\special{pa 2461 -4528}\special{pa 3839 -4528}% -\special{fp}% -\special{pa 3839 -4528}\special{pa 4626 -4528}% -\special{fp}% -\special{pa 4626 -4528}\special{pa 5906 -4528}% -\special{fp}% -\special{pa 0 -4331}\special{pa 1083 -4331}% -\special{fp}% -\special{pa 1083 -4331}\special{pa 2461 -4331}% -\special{fp}% -\special{pa 2461 -4331}\special{pa 3839 -4331}% -\special{fp}% -\special{pa 3839 -4331}\special{pa 4626 -4331}% -\special{fp}% -\special{pa 4626 -4331}\special{pa 5906 -4331}% -\special{fp}% -\special{pa 0 -4134}\special{pa 1083 -4134}% -\special{fp}% -\special{pa 1083 -4134}\special{pa 2461 -4134}% -\special{fp}% -\special{pa 2461 -4134}\special{pa 3839 -4134}% -\special{fp}% -\special{pa 3839 -4134}\special{pa 4626 -4134}% -\special{fp}% -\special{pa 4626 -4134}\special{pa 5906 -4134}% -\special{fp}% -\special{pa 0 -3937}\special{pa 1083 -3937}% -\special{fp}% -\special{pa 1083 -3937}\special{pa 2461 -3937}% -\special{fp}% -\special{pa 2461 -3937}\special{pa 3839 -3937}% -\special{fp}% -\special{pa 3839 -3937}\special{pa 4626 -3937}% -\special{fp}% -\special{pa 4626 -3937}\special{pa 5906 -3937}% -\special{fp}% -\special{pa 0 -3740}\special{pa 1083 -3740}% -\special{fp}% -\special{pa 1083 -3740}\special{pa 2461 -3740}% -\special{fp}% -\special{pa 2461 -3740}\special{pa 3839 -3740}% -\special{fp}% -\special{pa 3839 -3740}\special{pa 4626 -3740}% -\special{fp}% -\special{pa 4626 -3740}\special{pa 5906 -3740}% -\special{fp}% -\special{pa 0 -3543}\special{pa 1083 -3543}% -\special{fp}% -\special{pa 1083 -3543}\special{pa 2461 -3543}% -\special{fp}% -\special{pa 2461 -3543}\special{pa 3839 -3543}% -\special{fp}% -\special{pa 3839 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-\settoheight{\Height}{}\settodepth{\Depth}{}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,2.7500){\hspace*{\Width}\raisebox{\Height}{}}% -% -% -\settowidth{\Width}{}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{}\settodepth{\Depth}{}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(13.3800,2.7500){\hspace*{\Width}\raisebox{\Height}{}}% -% -% -\settowidth{\Width}{}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{}\settodepth{\Depth}{}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(1.3800,2.2500){\hspace*{\Width}\raisebox{\Height}{}}% -% -% -\settowidth{\Width}{orchid}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{orchid}\settodepth{\Depth}{orchid}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(4.5000,2.2500){\hspace*{\Width}\raisebox{\Height}{orchid}}% -% -% -\settowidth{\Width}{[0.32,0.64,0,0]}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{[0.32,0.64,0,0]}\settodepth{\Depth}{[0.32,0.64,0,0]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(8.0000,2.2500){\hspace*{\Width}\raisebox{\Height}{[0.32,0.64,0,0]}}% -% -% -\settowidth{\Width}{}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{}\settodepth{\Depth}{}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,2.2500){\hspace*{\Width}\raisebox{\Height}{}}% -% -% -\settowidth{\Width}{}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{}\settodepth{\Depth}{}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(13.3800,2.2500){\hspace*{\Width}\raisebox{\Height}{}}% -% -% -\settowidth{\Width}{}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{}\settodepth{\Depth}{}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(1.3800,1.7500){\hspace*{\Width}\raisebox{\Height}{}}% -% -% -\settowidth{\Width}{darkorchid}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{darkorchid}\settodepth{\Depth}{darkorchid}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(4.5000,1.7500){\hspace*{\Width}\raisebox{\Height}{darkorchid}}% -% -% -\settowidth{\Width}{[0.4,0.8,0.2,0]}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{[0.4,0.8,0.2,0]}\settodepth{\Depth}{[0.4,0.8,0.2,0]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(8.0000,1.7500){\hspace*{\Width}\raisebox{\Height}{[0.4,0.8,0.2,0]}}% -% -% -\settowidth{\Width}{}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{}\settodepth{\Depth}{}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,1.7500){\hspace*{\Width}\raisebox{\Height}{}}% -% -% -\settowidth{\Width}{}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{}\settodepth{\Depth}{}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(13.3800,1.7500){\hspace*{\Width}\raisebox{\Height}{}}% -% -% -\settowidth{\Width}{紫}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{紫}\settodepth{\Depth}{紫}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(1.3800,1.2500){\hspace*{\Width}\raisebox{\Height}{紫}}% -% -% -\settowidth{\Width}{purple}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{purple}\settodepth{\Depth}{purple}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(4.5000,1.2500){\hspace*{\Width}\raisebox{\Height}{purple}}% -% -% -\settowidth{\Width}{[0.45,0.86,0,0]}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{[0.45,0.86,0,0]}\settodepth{\Depth}{[0.45,0.86,0,0]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(8.0000,1.2500){\hspace*{\Width}\raisebox{\Height}{[0.45,0.86,0,0]}}% -% -% -\settowidth{\Width}{}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{}\settodepth{\Depth}{}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,1.2500){\hspace*{\Width}\raisebox{\Height}{}}% -% -% -\settowidth{\Width}{}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{}\settodepth{\Depth}{}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(13.3800,1.2500){\hspace*{\Width}\raisebox{\Height}{}}% -% -% -\settowidth{\Width}{}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{}\settodepth{\Depth}{}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(1.3800,0.7500){\hspace*{\Width}\raisebox{\Height}{}}% -% -% -\settowidth{\Width}{plum}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{plum}\settodepth{\Depth}{plum}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(4.5000,0.7500){\hspace*{\Width}\raisebox{\Height}{plum}}% -% -% -\settowidth{\Width}{[0.5,1,0,0]}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{[0.5,1,0,0]}\settodepth{\Depth}{[0.5,1,0,0]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(8.0000,0.7500){\hspace*{\Width}\raisebox{\Height}{[0.5,1,0,0]}}% -% -% -\settowidth{\Width}{}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{}\settodepth{\Depth}{}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,0.7500){\hspace*{\Width}\raisebox{\Height}{}}% -% -% -\settowidth{\Width}{}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{}\settodepth{\Depth}{}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(13.3800,0.7500){\hspace*{\Width}\raisebox{\Height}{}}% -% -% -\settowidth{\Width}{}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{}\settodepth{\Depth}{}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(1.3800,0.2500){\hspace*{\Width}\raisebox{\Height}{}}% -% -% -\settowidth{\Width}{violet}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{violet}\settodepth{\Depth}{violet}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(4.5000,0.2500){\hspace*{\Width}\raisebox{\Height}{violet}}% -% -% -\settowidth{\Width}{[0.79,0.88,0,0]}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{[0.79,0.88,0,0]}\settodepth{\Depth}{[0.79,0.88,0,0]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(8.0000,0.2500){\hspace*{\Width}\raisebox{\Height}{[0.79,0.88,0,0]}}% -% -% -\settowidth{\Width}{}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{}\settodepth{\Depth}{}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,0.2500){\hspace*{\Width}\raisebox{\Height}{}}% -% -% -\settowidth{\Width}{}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{}\settodepth{\Depth}{}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(13.3800,0.2500){\hspace*{\Width}\raisebox{\Height}{}}% -% -% -\end{picture}}%
\ No newline at end of file diff --git a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/colortablee35-68.tex b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/colortablee35-68.tex deleted file mode 100644 index 017807da8fd..00000000000 --- a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/colortablee35-68.tex +++ /dev/null @@ -1,1934 +0,0 @@ -%%% colortable35-68.tex 2015-2-6 18:34 -%%% colortable35-68.sce 2015-2-6 18:29 -{\unitlength=1cm% -\begin{picture}% -( 15.00000, 17.50000)( -0.00000, -0.00000)% -\special{pn 8}% -% -\color[cmyk]{0.75,0.9,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,16.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -6693}\special{pa 4626 -6496}\special{pa 5906 -6496}\special{pa 5906 -6693}% -\special{pa 4626 -6693}\special{sh 1}\special{ip}% -\color[cmyk]{0.86,0.91,0,0.04}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,16.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -6496}\special{pa 4626 -6299}\special{pa 5906 -6299}\special{pa 5906 -6496}% -\special{pa 4626 -6496}\special{sh 1}\special{ip}% -\color[cmyk]{0.57,0.55,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,15.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -6299}\special{pa 4626 -6102}\special{pa 5906 -6102}\special{pa 5906 -6299}% -\special{pa 4626 -6299}\special{sh 1}\special{ip}% -\color[cmyk]{0.62,0.57,0.23,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,15.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -6102}\special{pa 4626 -5906}\special{pa 5906 -5906}\special{pa 5906 -6102}% -\special{pa 4626 -6102}\special{sh 1}\special{ip}% -\color[cmyk]{0.65,0.13,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,14.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -5906}\special{pa 4626 -5709}\special{pa 5906 -5709}\special{pa 5906 -5906}% -\special{pa 4626 -5906}\special{sh 1}\special{ip}% -\color[cmyk]{0.98,0.13,0,0.43}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,14.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -5709}\special{pa 4626 -5512}\special{pa 5906 -5512}\special{pa 5906 -5709}% -\special{pa 4626 -5709}\special{sh 1}\special{ip}% -\color[cmyk]{0.94,0.54,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,13.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -5512}\special{pa 4626 -5315}\special{pa 5906 -5315}\special{pa 5906 -5512}% -\special{pa 4626 -5512}\special{sh 1}\special{ip}% -\color[cmyk]{1,0.5,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,13.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -5315}\special{pa 4626 -5118}\special{pa 5906 -5118}\special{pa 5906 -5315}% -\special{pa 4626 -5315}\special{sh 1}\special{ip}% -\color[cmyk]{1,1,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,12.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -5118}\special{pa 4626 -4921}\special{pa 5906 -4921}\special{pa 5906 -5118}% -\special{pa 4626 -5118}\special{sh 1}\special{ip}% -\color[cmyk]{0.94,0.11,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,12.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -4921}\special{pa 4626 -4724}\special{pa 5906 -4724}\special{pa 5906 -4921}% -\special{pa 4626 -4921}\special{sh 1}\special{ip}% -\color[cmyk]{1,0,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,11.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -4724}\special{pa 4626 -4528}\special{pa 5906 -4528}\special{pa 5906 -4724}% -\special{pa 4626 -4724}\special{sh 1}\special{ip}% -\color[cmyk]{0.96,0,0,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,11.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -4528}\special{pa 4626 -4331}\special{pa 5906 -4331}\special{pa 5906 -4528}% -\special{pa 4626 -4528}\special{sh 1}\special{ip}% -\color[cmyk]{0.62,0,0.12,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,10.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -4331}\special{pa 4626 -4134}\special{pa 5906 -4134}\special{pa 5906 -4331}% -\special{pa 4626 -4331}\special{sh 1}\special{ip}% -\color[cmyk]{0.85,0,0.2,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,10.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -4134}\special{pa 4626 -3937}\special{pa 5906 -3937}\special{pa 5906 -4134}% -\special{pa 4626 -4134}\special{sh 1}\special{ip}% -\color[cmyk]{0.86,0,0.34,0.02}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,9.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -3937}\special{pa 4626 -3740}\special{pa 5906 -3740}\special{pa 5906 -3937}% -\special{pa 4626 -3937}\special{sh 1}\special{ip}% -\color[cmyk]{0.82,0,0.3,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,9.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -3740}\special{pa 4626 -3543}\special{pa 5906 -3543}\special{pa 5906 -3740}% -\special{pa 4626 -3740}\special{sh 1}\special{ip}% -\color[cmyk]{0.85,0,0.33,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,8.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -3543}\special{pa 4626 -3346}\special{pa 5906 -3346}\special{pa 5906 -3543}% -\special{pa 4626 -3543}\special{sh 1}\special{ip}% -\color[cmyk]{1,0,0.5,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,8.2500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -3346}\special{pa 4626 -3150}\special{pa 5906 -3150}\special{pa 5906 -3346}% -\special{pa 4626 -3346}\special{sh 1}\special{ip}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{あいうえお}\settodepth{\Depth}{あいうえお}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.7500,7.7500){\hspace*{\Width}\raisebox{\Height}{あいうえお}}% -% -% -\special{pa 4626 -3150}\special{pa 4626 -2953}\special{pa 5906 -2953}\special{pa 5906 -3150}% -\special{pa 4626 -3150}\special{sh 1}\special{ip}% -\color[cmyk]{0.69,0,0.5,0}% -\settowidth{\Width}{あいうえお}\setlength{\Width}{-0.5\Width}% 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+\settoheight{\Height}{c3}\settodepth{\Depth}{c3}\setlength{\Height}{\Depth}% +\put(6.0714286,4.2142857){\hspace*{\Width}\raisebox{\Height}{c3}}% % +\settowidth{\Width}{c4}\setlength{\Width}{0\Width}% +\settoheight{\Height}{c4}\settodepth{\Depth}{c4}\setlength{\Height}{\Depth}% +\put(8.0714286,4.2142857){\hspace*{\Width}\raisebox{\Height}{c4}}% % -\settowidth{\Width}{C4}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{C4}\settodepth{\Depth}{C4}\setlength{\Height}{-\Height}% -\put(8.0000,-0.1500){\hspace*{\Width}\raisebox{\Height}{C4}}% +\settowidth{\Width}{c5}\setlength{\Width}{0\Width}% +\settoheight{\Height}{c5}\settodepth{\Depth}{c5}\setlength{\Height}{\Depth}% +\put(10.0714286,4.2142857){\hspace*{\Width}\raisebox{\Height}{c5}}% % +\settowidth{\Width}{r2}\setlength{\Width}{-1\Width}% +\settoheight{\Height}{r2}\settodepth{\Depth}{r2}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(-0.0714286,0.0000000){\hspace*{\Width}\raisebox{\Height}{r2}}% % -\settowidth{\Width}{C5}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{C5}\settodepth{\Depth}{C5}\setlength{\Height}{-\Height}% -\put(10.0000,-0.1500){\hspace*{\Width}\raisebox{\Height}{C5}}% +\settowidth{\Width}{r1}\setlength{\Width}{-1\Width}% +\settoheight{\Height}{r1}\settodepth{\Depth}{r1}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(-0.0714286,2.0000000){\hspace*{\Width}\raisebox{\Height}{r1}}% % +\settowidth{\Width}{r0}\setlength{\Width}{-1\Width}% +\settoheight{\Height}{r0}\settodepth{\Depth}{r0}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(-0.0714286,4.0000000){\hspace*{\Width}\raisebox{\Height}{r0}}% % -\special{pa 0 -945}\special{pa 472 -945}% -\special{fp}% -\special{pa 472 -945}\special{pa 945 -945}% -\special{fp}% -\special{pa 945 -945}\special{pa 1417 -945}% -\special{fp}% -\special{pa 1417 -945}\special{pa 1890 -945}% -\special{fp}% -\special{pa 1890 -945}\special{pa 2362 -945}% -\special{fp}% -\special{pa 0 -472}\special{pa 472 -472}% -\special{fp}% -\special{pa 472 -472}\special{pa 945 -472}% -\special{fp}% -\special{pa 945 -472}\special{pa 1417 -472}% -\special{fp}% -\special{pa 1417 -472}\special{pa 1890 -472}% -\special{fp}% -\special{pa 1890 -472}\special{pa 2362 -472}% -\special{fp}% -\special{pa 0 0}\special{pa 472 0}% -\special{fp}% -\special{pa 472 0}\special{pa 945 0}% -\special{fp}% -\special{pa 945 0}\special{pa 1417 0}% -\special{fp}% -\special{pa 1417 0}\special{pa 1890 0}% -\special{fp}% -\special{pa 1890 0}\special{pa 2362 0}% -\special{fp}% -\special{pa 0 -945}\special{pa 0 -472}% -\special{fp}% -\special{pa 0 -472}\special{pa 0 0}% -\special{fp}% -\special{pa 472 -945}\special{pa 472 -472}% -\special{fp}% -\special{pa 945 -945}\special{pa 945 -472}% -\special{fp}% -\special{pa 945 -472}\special{pa 945 0}% -\special{fp}% -\special{pa 1417 -945}\special{pa 1417 -472}% -\special{fp}% -\special{pa 1417 -472}\special{pa 1417 0}% -\special{fp}% -\special{pa 1890 -945}\special{pa 1890 -472}% -\special{fp}% -\special{pa 2362 -945}\special{pa 2362 -472}% -\special{fp}% -\special{pa 2362 -472}\special{pa 2362 0}% -\special{fp}% \end{picture}}%
\ No newline at end of file diff --git a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/putcol.tex b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/putcol.tex index 380edea4167..fa7e744df13 100644 --- a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/putcol.tex +++ b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/putcol.tex @@ -1,188 +1,122 @@ -%%% test.tex 2014-11-26 11:26 -%%% test.sce 2014-11-26 11:26 -{\unitlength=6mm% +%%% /Users/Hannya/Desktop/KeTCindy/fig/putcol.tex +%%% Generator=template1basic.cdy +{\unitlength=7mm% \begin{picture}% -( 10.00000, 4.50000)( 0.00000, 0.00000)% +(10,4.5)(0,0)% \special{pn 8}% % +\special{pa 0 -1240}\special{pa 0 -0}% +\special{fp}% +\special{pa 1102 -1240}\special{pa 1102 -0}% +\special{fp}% +\special{pa 1654 -1240}\special{pa 1654 -0}% +\special{fp}% +\special{pa 2205 -1240}\special{pa 2205 -0}% +\special{fp}% +\special{pa 2756 -1240}\special{pa 2756 -0}% +\special{fp}% +\special{pa 0 -1240}\special{pa 2756 -1240}% +\special{fp}% +\special{pa 0 -0}\special{pa 2756 -0}% +\special{fp}% +\special{pa 551 -1240}\special{pa 551 -827}% +\special{fp}% +\special{pa 551 -413}\special{pa 551 -0}% +\special{fp}% +\special{pa 0 -827}\special{pa 1102 -827}% +\special{fp}% +\special{pa 1654 -827}\special{pa 2756 -827}% +\special{fp}% +\special{pa 0 -413}\special{pa 1102 -413}% +\special{fp}% +\special{pa 1654 -413}\special{pa 2756 -413}% +\special{fp}% \settowidth{\Width}{A}\setlength{\Width}{-0.5\Width}% \settoheight{\Height}{A}\settodepth{\Depth}{A}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(5.0000,3.7500){\hspace*{\Width}\raisebox{\Height}{A}}% -% +\put(5.0000000,3.7500000){\hspace*{\Width}\raisebox{\Height}{A}}% % \settowidth{\Width}{B}\setlength{\Width}{-0.5\Width}% \settoheight{\Height}{B}\settodepth{\Depth}{B}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(5.0000,2.2500){\hspace*{\Width}\raisebox{\Height}{B}}% -% +\put(5.0000000,2.2500000){\hspace*{\Width}\raisebox{\Height}{B}}% % \settowidth{\Width}{C}\setlength{\Width}{-0.5\Width}% \settoheight{\Height}{C}\settodepth{\Depth}{C}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(5.0000,0.7500){\hspace*{\Width}\raisebox{\Height}{C}}% -% +\put(5.0000000,0.7500000){\hspace*{\Width}\raisebox{\Height}{C}}% % \settowidth{\Width}{$x^2$}\setlength{\Width}{0\Width}% \settoheight{\Height}{$x^2$}\settodepth{\Depth}{$x^2$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(6.0500,3.7500){\hspace*{\Width}\raisebox{\Height}{$x^2$}}% -% +\put(6.0714286,3.7500000){\hspace*{\Width}\raisebox{\Height}{$x^2$}}% % \settowidth{\Width}{$y=\sqrt{x^3}$}\setlength{\Width}{0\Width}% \settoheight{\Height}{$y=\sqrt{x^3}$}\settodepth{\Depth}{$y=\sqrt{x^3}$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(6.0500,2.2500){\hspace*{\Width}\raisebox{\Height}{$y=\sqrt{x^3}$}}% -% +\put(6.0714286,2.2500000){\hspace*{\Width}\raisebox{\Height}{$y=\sqrt{x^3}$}}% % \settowidth{\Width}{1}\setlength{\Width}{-0.5\Width}% \settoheight{\Height}{1}\settodepth{\Depth}{1}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(1.0000,3.7500){\hspace*{\Width}\raisebox{\Height}{1}}% -% +\put(1.0000000,3.7500000){\hspace*{\Width}\raisebox{\Height}{1}}% % \settowidth{\Width}{二}\setlength{\Width}{-0.5\Width}% \settoheight{\Height}{二}\settodepth{\Depth}{二}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(3.0000,3.7500){\hspace*{\Width}\raisebox{\Height}{二}}% -% +\put(3.0000000,3.7500000){\hspace*{\Width}\raisebox{\Height}{二}}% % \settowidth{\Width}{$$}\setlength{\Width}{-0.5\Width}% \settoheight{\Height}{$$}\settodepth{\Depth}{$$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(1.0000,0.7500){\hspace*{\Width}\raisebox{\Height}{$$}}% -% +\put(1.0000000,0.7500000){\hspace*{\Width}\raisebox{\Height}{$$}}% % \settowidth{\Width}{$\frac{\pi}{2}$}\setlength{\Width}{-0.5\Width}% \settoheight{\Height}{$\frac{\pi}{2}$}\settodepth{\Depth}{$\frac{\pi}{2}$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(3.0000,0.7500){\hspace*{\Width}\raisebox{\Height}{$\frac{\pi}{2}$}}% -% +\put(3.0000000,0.7500000){\hspace*{\Width}\raisebox{\Height}{$\frac{\pi}{2}$}}% % \settowidth{\Width}{$$}\setlength{\Width}{-0.5\Width}% \settoheight{\Height}{$$}\settodepth{\Depth}{$$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(5.0000,0.7500){\hspace*{\Width}\raisebox{\Height}{$$}}% -% +\put(5.0000000,0.7500000){\hspace*{\Width}\raisebox{\Height}{$$}}% % \settowidth{\Width}{$$}\setlength{\Width}{-0.5\Width}% \settoheight{\Height}{$$}\settodepth{\Depth}{$$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(7.2000,0.7500){\hspace*{\Width}\raisebox{\Height}{$$}}% -% +\put(7.0000000,0.7500000){\hspace*{\Width}\raisebox{\Height}{$$}}% % \settowidth{\Width}{$\sum{x^2}$}\setlength{\Width}{-0.5\Width}% \settoheight{\Height}{$\sum{x^2}$}\settodepth{\Depth}{$\sum{x^2}$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(9.2000,0.7500){\hspace*{\Width}\raisebox{\Height}{$\sum{x^2}$}}% -% -% -\settowidth{\Width}{R0}\setlength{\Width}{-1\Width}% -\settoheight{\Height}{R0}\settodepth{\Depth}{R0}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(-0.1500,4.5000){\hspace*{\Width}\raisebox{\Height}{R0}}% -% -% -\settowidth{\Width}{R1}\setlength{\Width}{-1\Width}% -\settoheight{\Height}{R1}\settodepth{\Depth}{R1}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(-0.1500,3.0000){\hspace*{\Width}\raisebox{\Height}{R1}}% -% -% -\settowidth{\Width}{R2}\setlength{\Width}{-1\Width}% -\settoheight{\Height}{R2}\settodepth{\Depth}{R2}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(-0.1500,1.5000){\hspace*{\Width}\raisebox{\Height}{R2}}% -% -% -\settowidth{\Width}{R3}\setlength{\Width}{-1\Width}% -\settoheight{\Height}{R3}\settodepth{\Depth}{R3}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(-0.1500,0.0000){\hspace*{\Width}\raisebox{\Height}{R3}}% -% -% -\settowidth{\Width}{C0}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{C0}\settodepth{\Depth}{C0}\setlength{\Height}{-\Height}% -\put(0.0000,-0.1500){\hspace*{\Width}\raisebox{\Height}{C0}}% -% +\put(9.0000000,0.7500000){\hspace*{\Width}\raisebox{\Height}{$\sum{x^2}$}}% % -\settowidth{\Width}{C1}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{C1}\settodepth{\Depth}{C1}\setlength{\Height}{-\Height}% -\put(2.0000,-0.1500){\hspace*{\Width}\raisebox{\Height}{C1}}% +\settowidth{\Width}{c0}\setlength{\Width}{0\Width}% +\settoheight{\Height}{c0}\settodepth{\Depth}{c0}\setlength{\Height}{\Depth}% +\put(0.0714286,4.7142857){\hspace*{\Width}\raisebox{\Height}{c0}}% % +\settowidth{\Width}{c1}\setlength{\Width}{0\Width}% +\settoheight{\Height}{c1}\settodepth{\Depth}{c1}\setlength{\Height}{\Depth}% +\put(2.0714286,4.7142857){\hspace*{\Width}\raisebox{\Height}{c1}}% % -\settowidth{\Width}{C2}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{C2}\settodepth{\Depth}{C2}\setlength{\Height}{-\Height}% -\put(4.0000,-0.1500){\hspace*{\Width}\raisebox{\Height}{C2}}% +\settowidth{\Width}{c2}\setlength{\Width}{0\Width}% +\settoheight{\Height}{c2}\settodepth{\Depth}{c2}\setlength{\Height}{\Depth}% +\put(4.0714286,4.7142857){\hspace*{\Width}\raisebox{\Height}{c2}}% % +\settowidth{\Width}{c3}\setlength{\Width}{0\Width}% +\settoheight{\Height}{c3}\settodepth{\Depth}{c3}\setlength{\Height}{\Depth}% +\put(6.0714286,4.7142857){\hspace*{\Width}\raisebox{\Height}{c3}}% % -\settowidth{\Width}{C3}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{C3}\settodepth{\Depth}{C3}\setlength{\Height}{-\Height}% -\put(6.0000,-0.1500){\hspace*{\Width}\raisebox{\Height}{C3}}% +\settowidth{\Width}{c4}\setlength{\Width}{0\Width}% +\settoheight{\Height}{c4}\settodepth{\Depth}{c4}\setlength{\Height}{\Depth}% +\put(8.0714286,4.7142857){\hspace*{\Width}\raisebox{\Height}{c4}}% % +\settowidth{\Width}{c5}\setlength{\Width}{0\Width}% +\settoheight{\Height}{c5}\settodepth{\Depth}{c5}\setlength{\Height}{\Depth}% +\put(10.0714286,4.7142857){\hspace*{\Width}\raisebox{\Height}{c5}}% % -\settowidth{\Width}{C4}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{C4}\settodepth{\Depth}{C4}\setlength{\Height}{-\Height}% -\put(8.4000,-0.1500){\hspace*{\Width}\raisebox{\Height}{C4}}% +\settowidth{\Width}{r3}\setlength{\Width}{-1\Width}% +\settoheight{\Height}{r3}\settodepth{\Depth}{r3}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(-0.0714286,0.0000000){\hspace*{\Width}\raisebox{\Height}{r3}}% % +\settowidth{\Width}{r2}\setlength{\Width}{-1\Width}% +\settoheight{\Height}{r2}\settodepth{\Depth}{r2}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(-0.0714286,1.5000000){\hspace*{\Width}\raisebox{\Height}{r2}}% % -\settowidth{\Width}{C5}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{C5}\settodepth{\Depth}{C5}\setlength{\Height}{-\Height}% -\put(10.0000,-0.1500){\hspace*{\Width}\raisebox{\Height}{C5}}% +\settowidth{\Width}{r1}\setlength{\Width}{-1\Width}% +\settoheight{\Height}{r1}\settodepth{\Depth}{r1}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(-0.0714286,3.0000000){\hspace*{\Width}\raisebox{\Height}{r1}}% % +\settowidth{\Width}{r0}\setlength{\Width}{-1\Width}% +\settoheight{\Height}{r0}\settodepth{\Depth}{r0}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(-0.0714286,4.5000000){\hspace*{\Width}\raisebox{\Height}{r0}}% % -\special{pa 0 -1063}\special{pa 472 -1063}% -\special{fp}% -\special{pa 472 -1063}\special{pa 945 -1063}% -\special{fp}% -\special{pa 945 -1063}\special{pa 1417 -1063}% -\special{fp}% -\special{pa 1417 -1063}\special{pa 1984 -1063}% -\special{fp}% -\special{pa 1984 -1063}\special{pa 2362 -1063}% -\special{fp}% -\special{pa 0 -709}\special{pa 472 -709}% -\special{fp}% -\special{pa 472 -709}\special{pa 945 -709}% -\special{fp}% -\special{pa 1417 -709}\special{pa 1984 -709}% -\special{fp}% -\special{pa 1984 -709}\special{pa 2362 -709}% -\special{fp}% -\special{pa 0 -354}\special{pa 472 -354}% -\special{fp}% -\special{pa 472 -354}\special{pa 945 -354}% -\special{fp}% -\special{pa 1417 -354}\special{pa 1984 -354}% -\special{fp}% -\special{pa 1984 -354}\special{pa 2362 -354}% -\special{fp}% -\special{pa 0 0}\special{pa 472 0}% -\special{fp}% -\special{pa 472 0}\special{pa 945 0}% -\special{fp}% -\special{pa 945 0}\special{pa 1417 0}% -\special{fp}% -\special{pa 1417 0}\special{pa 1984 0}% -\special{fp}% -\special{pa 1984 0}\special{pa 2362 0}% -\special{fp}% -\special{pa 0 -1063}\special{pa 0 -709}% -\special{fp}% -\special{pa 0 -709}\special{pa 0 -354}% -\special{fp}% -\special{pa 0 -354}\special{pa 0 0}% -\special{fp}% -\special{pa 472 -1063}\special{pa 472 -709}% -\special{fp}% -\special{pa 472 -354}\special{pa 472 0}% -\special{fp}% -\special{pa 945 -1063}\special{pa 945 -709}% -\special{fp}% -\special{pa 945 -709}\special{pa 945 -354}% -\special{fp}% -\special{pa 945 -354}\special{pa 945 0}% -\special{fp}% -\special{pa 1417 -1063}\special{pa 1417 -709}% -\special{fp}% -\special{pa 1417 -709}\special{pa 1417 -354}% -\special{fp}% -\special{pa 1417 -354}\special{pa 1417 0}% -\special{fp}% -\special{pa 1984 -1063}\special{pa 1984 -709}% -\special{fp}% -\special{pa 1984 -709}\special{pa 1984 -354}% -\special{fp}% -\special{pa 1984 -354}\special{pa 1984 0}% -\special{fp}% -\special{pa 2362 -1063}\special{pa 2362 -709}% -\special{fp}% -\special{pa 2362 -709}\special{pa 2362 -354}% -\special{fp}% -\special{pa 2362 -354}\special{pa 2362 0}% -\special{fp}% \end{picture}}%
\ No newline at end of file diff --git a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/putcolE.tex b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/putcolE.tex new file mode 100644 index 00000000000..07a1de3fe3d --- /dev/null +++ b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/putcolE.tex @@ -0,0 +1,122 @@ +%%% /Users/Hannya/Desktop/KeTCindy/fig/putcol.tex +%%% Generator=template1basic.cdy +{\unitlength=7mm% +\begin{picture}% +(10,4.5)(0,0)% +\special{pn 8}% +% +\special{pa 0 -1240}\special{pa 0 -0}% +\special{fp}% +\special{pa 1102 -1240}\special{pa 1102 -0}% +\special{fp}% +\special{pa 1654 -1240}\special{pa 1654 -0}% +\special{fp}% +\special{pa 2205 -1240}\special{pa 2205 -0}% +\special{fp}% +\special{pa 2756 -1240}\special{pa 2756 -0}% +\special{fp}% +\special{pa 0 -1240}\special{pa 2756 -1240}% +\special{fp}% +\special{pa 0 -0}\special{pa 2756 -0}% +\special{fp}% +\special{pa 551 -1240}\special{pa 551 -827}% +\special{fp}% +\special{pa 551 -413}\special{pa 551 -0}% +\special{fp}% +\special{pa 0 -827}\special{pa 1102 -827}% +\special{fp}% +\special{pa 1654 -827}\special{pa 2756 -827}% +\special{fp}% +\special{pa 0 -413}\special{pa 1102 -413}% +\special{fp}% +\special{pa 1654 -413}\special{pa 2756 -413}% +\special{fp}% +\settowidth{\Width}{A}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{A}\settodepth{\Depth}{A}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(5.0000000,3.7500000){\hspace*{\Width}\raisebox{\Height}{A}}% +% +\settowidth{\Width}{B}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{B}\settodepth{\Depth}{B}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(5.0000000,2.2500000){\hspace*{\Width}\raisebox{\Height}{B}}% +% +\settowidth{\Width}{C}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{C}\settodepth{\Depth}{C}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(5.0000000,0.7500000){\hspace*{\Width}\raisebox{\Height}{C}}% +% +\settowidth{\Width}{{\footnotesize $x^2$}}\setlength{\Width}{0\Width}% +\settoheight{\Height}{{\footnotesize $x^2$}}\settodepth{\Depth}{{\footnotesize $x^2$}}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(6.0714286,3.7500000){\hspace*{\Width}\raisebox{\Height}{{\footnotesize $x^2$}}}% +% +\settowidth{\Width}{{\footnotesize $y=\sqrt{x^3}$}}\setlength{\Width}{0\Width}% +\settoheight{\Height}{{\footnotesize $y=\sqrt{x^3}$}}\settodepth{\Depth}{{\footnotesize $y=\sqrt{x^3}$}}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(6.0714286,2.2500000){\hspace*{\Width}\raisebox{\Height}{{\footnotesize $y=\sqrt{x^3}$}}}% +% +\settowidth{\Width}{1}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{1}\settodepth{\Depth}{1}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(1.0000000,3.7500000){\hspace*{\Width}\raisebox{\Height}{1}}% +% +\settowidth{\Width}{two}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{two}\settodepth{\Depth}{two}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(3.0000000,3.7500000){\hspace*{\Width}\raisebox{\Height}{two}}% +% +\settowidth{\Width}{$$}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{$$}\settodepth{\Depth}{$$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(1.0000000,0.7500000){\hspace*{\Width}\raisebox{\Height}{$$}}% +% +\settowidth{\Width}{$\frac{\pi}{2}$}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{$\frac{\pi}{2}$}\settodepth{\Depth}{$\frac{\pi}{2}$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(3.0000000,0.7500000){\hspace*{\Width}\raisebox{\Height}{$\frac{\pi}{2}$}}% +% +\settowidth{\Width}{$$}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{$$}\settodepth{\Depth}{$$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(5.0000000,0.7500000){\hspace*{\Width}\raisebox{\Height}{$$}}% +% +\settowidth{\Width}{$$}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{$$}\settodepth{\Depth}{$$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(7.0000000,0.7500000){\hspace*{\Width}\raisebox{\Height}{$$}}% +% +\settowidth{\Width}{{\footnotesize $\sum{x^2}$}}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{{\footnotesize $\sum{x^2}$}}\settodepth{\Depth}{{\footnotesize $\sum{x^2}$}}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(9.0000000,0.7500000){\hspace*{\Width}\raisebox{\Height}{{\footnotesize $\sum{x^2}$}}}% +% +\settowidth{\Width}{c0}\setlength{\Width}{0\Width}% +\settoheight{\Height}{c0}\settodepth{\Depth}{c0}\setlength{\Height}{\Depth}% +\put(0.0714286,4.7142857){\hspace*{\Width}\raisebox{\Height}{c0}}% +% +\settowidth{\Width}{c1}\setlength{\Width}{0\Width}% +\settoheight{\Height}{c1}\settodepth{\Depth}{c1}\setlength{\Height}{\Depth}% +\put(2.0714286,4.7142857){\hspace*{\Width}\raisebox{\Height}{c1}}% +% +\settowidth{\Width}{c2}\setlength{\Width}{0\Width}% +\settoheight{\Height}{c2}\settodepth{\Depth}{c2}\setlength{\Height}{\Depth}% +\put(4.0714286,4.7142857){\hspace*{\Width}\raisebox{\Height}{c2}}% +% +\settowidth{\Width}{c3}\setlength{\Width}{0\Width}% +\settoheight{\Height}{c3}\settodepth{\Depth}{c3}\setlength{\Height}{\Depth}% +\put(6.0714286,4.7142857){\hspace*{\Width}\raisebox{\Height}{c3}}% +% +\settowidth{\Width}{c4}\setlength{\Width}{0\Width}% +\settoheight{\Height}{c4}\settodepth{\Depth}{c4}\setlength{\Height}{\Depth}% 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-1232}\special{pa 1152 -1248}\special{pa 1144 -1262}\special{sh 1}\special{fp}% +}% \special{pn 8}% -\special{pa 0 -53}\special{pa 1299 -1286}\special{pa 2434 -2362}% +{% +\color[rgb]{0,1,0}% +\special{pa -18 232}\special{pa 2756 -2567}% \special{fp}% -\special{pa 0 0}\special{pa 2598 0}\special{pa 2598 -2362}\special{pa 0 -2362}\special{pa 0 0}% -\special{fp}% -\settowidth{\Width}{$r=0.968,\ y=0.948x+0.226$}\setlength{\Width}{0\Width}% -\settoheight{\Height}{$r=0.968,\ y=0.948x+0.226$}\settodepth{\Depth}{$r=0.968,\ y=0.948x+0.226$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(0.5990,9.5583){\hspace*{\Width}\raisebox{\Height}{$r=0.968,\ y=0.948x+0.226$}}% -% +}% +\settowidth{\Width}{$r=0.535,\ y=1.009x-0.545$}\setlength{\Width}{0\Width}% +\settoheight{\Height}{$r=0.535,\ y=1.009x-0.545$}\settodepth{\Depth}{$r=0.535,\ y=1.009x-0.545$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(0.9500000,6.4300000){\hspace*{\Width}\raisebox{\Height}{$r=0.535,\ y=1.009x-0.545$}}% % +\special{pa 0 -2756}\special{pa 0 -0}\special{pa 2756 -0}% +\special{fp}% \settowidth{\Width}{$0$}\setlength{\Width}{-0.5\Width}% \settoheight{\Height}{$0$}\settodepth{\Depth}{$0$}\setlength{\Height}{-\Height}% -\put(0.0000,-0.1500){\hspace*{\Width}\raisebox{\Height}{$0$}}% -% +\put(0.0000000,-0.1500000){\hspace*{\Width}\raisebox{\Height}{$0$}}% % +\special{pa 0 -0}\special{pa 0 39}% +\special{fp}% \settowidth{\Width}{$1$}\setlength{\Width}{-0.5\Width}% \settoheight{\Height}{$1$}\settodepth{\Depth}{$1$}\setlength{\Height}{-\Height}% -\put(1.0000,-0.1500){\hspace*{\Width}\raisebox{\Height}{$1$}}% -% +\put(1.0000000,-0.1500000){\hspace*{\Width}\raisebox{\Height}{$1$}}% % +\special{pa 394 -0}\special{pa 394 39}% +\special{fp}% \settowidth{\Width}{$2$}\setlength{\Width}{-0.5\Width}% \settoheight{\Height}{$2$}\settodepth{\Depth}{$2$}\setlength{\Height}{-\Height}% -\put(2.0000,-0.1500){\hspace*{\Width}\raisebox{\Height}{$2$}}% -% +\put(2.0000000,-0.1500000){\hspace*{\Width}\raisebox{\Height}{$2$}}% % +\special{pa 787 -0}\special{pa 787 39}% +\special{fp}% \settowidth{\Width}{$3$}\setlength{\Width}{-0.5\Width}% \settoheight{\Height}{$3$}\settodepth{\Depth}{$3$}\setlength{\Height}{-\Height}% -\put(3.0000,-0.1500){\hspace*{\Width}\raisebox{\Height}{$3$}}% -% +\put(3.0000000,-0.1500000){\hspace*{\Width}\raisebox{\Height}{$3$}}% % +\special{pa 1181 -0}\special{pa 1181 39}% +\special{fp}% \settowidth{\Width}{$4$}\setlength{\Width}{-0.5\Width}% \settoheight{\Height}{$4$}\settodepth{\Depth}{$4$}\setlength{\Height}{-\Height}% -\put(4.0000,-0.1500){\hspace*{\Width}\raisebox{\Height}{$4$}}% -% +\put(4.0000000,-0.1500000){\hspace*{\Width}\raisebox{\Height}{$4$}}% % +\special{pa 1575 -0}\special{pa 1575 39}% +\special{fp}% \settowidth{\Width}{$5$}\setlength{\Width}{-0.5\Width}% \settoheight{\Height}{$5$}\settodepth{\Depth}{$5$}\setlength{\Height}{-\Height}% -\put(5.0000,-0.1500){\hspace*{\Width}\raisebox{\Height}{$5$}}% -% +\put(5.0000000,-0.1500000){\hspace*{\Width}\raisebox{\Height}{$5$}}% % +\special{pa 1969 -0}\special{pa 1969 39}% +\special{fp}% \settowidth{\Width}{$6$}\setlength{\Width}{-0.5\Width}% \settoheight{\Height}{$6$}\settodepth{\Depth}{$6$}\setlength{\Height}{-\Height}% -\put(6.0000,-0.1500){\hspace*{\Width}\raisebox{\Height}{$6$}}% -% +\put(6.0000000,-0.1500000){\hspace*{\Width}\raisebox{\Height}{$6$}}% % +\special{pa 2362 -0}\special{pa 2362 39}% +\special{fp}% \settowidth{\Width}{$7$}\setlength{\Width}{-0.5\Width}% \settoheight{\Height}{$7$}\settodepth{\Depth}{$7$}\setlength{\Height}{-\Height}% -\put(7.0000,-0.1500){\hspace*{\Width}\raisebox{\Height}{$7$}}% -% -% -\settowidth{\Width}{$8$}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{$8$}\settodepth{\Depth}{$8$}\setlength{\Height}{-\Height}% -\put(8.0000,-0.1500){\hspace*{\Width}\raisebox{\Height}{$8$}}% -% -% -\settowidth{\Width}{$9$}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{$9$}\settodepth{\Depth}{$9$}\setlength{\Height}{-\Height}% -\put(9.0000,-0.1500){\hspace*{\Width}\raisebox{\Height}{$9$}}% -% -% -\settowidth{\Width}{$10$}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{$10$}\settodepth{\Depth}{$10$}\setlength{\Height}{-\Height}% -\put(10.0000,-0.1500){\hspace*{\Width}\raisebox{\Height}{$10$}}% -% +\put(7.0000000,-0.1500000){\hspace*{\Width}\raisebox{\Height}{$7$}}% % +\special{pa 2756 -0}\special{pa 2756 39}% +\special{fp}% \settowidth{\Width}{$1$}\setlength{\Width}{-1\Width}% \settoheight{\Height}{$1$}\settodepth{\Depth}{$1$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(-0.1500,1.0000){\hspace*{\Width}\raisebox{\Height}{$1$}}% -% +\put(-0.1500000,1.0000000){\hspace*{\Width}\raisebox{\Height}{$1$}}% % +\special{pa 0 -394}\special{pa -39 -394}% +\special{fp}% \settowidth{\Width}{$2$}\setlength{\Width}{-1\Width}% \settoheight{\Height}{$2$}\settodepth{\Depth}{$2$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(-0.1500,2.0000){\hspace*{\Width}\raisebox{\Height}{$2$}}% -% +\put(-0.1500000,2.0000000){\hspace*{\Width}\raisebox{\Height}{$2$}}% % +\special{pa 0 -787}\special{pa -39 -787}% +\special{fp}% \settowidth{\Width}{$3$}\setlength{\Width}{-1\Width}% \settoheight{\Height}{$3$}\settodepth{\Depth}{$3$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(-0.1500,3.0000){\hspace*{\Width}\raisebox{\Height}{$3$}}% -% +\put(-0.1500000,3.0000000){\hspace*{\Width}\raisebox{\Height}{$3$}}% % +\special{pa 0 -1181}\special{pa -39 -1181}% +\special{fp}% \settowidth{\Width}{$4$}\setlength{\Width}{-1\Width}% \settoheight{\Height}{$4$}\settodepth{\Depth}{$4$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(-0.1500,4.0000){\hspace*{\Width}\raisebox{\Height}{$4$}}% -% +\put(-0.1500000,4.0000000){\hspace*{\Width}\raisebox{\Height}{$4$}}% % +\special{pa 0 -1575}\special{pa -39 -1575}% +\special{fp}% \settowidth{\Width}{$5$}\setlength{\Width}{-1\Width}% \settoheight{\Height}{$5$}\settodepth{\Depth}{$5$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(-0.1500,5.0000){\hspace*{\Width}\raisebox{\Height}{$5$}}% -% +\put(-0.1500000,5.0000000){\hspace*{\Width}\raisebox{\Height}{$5$}}% % +\special{pa 0 -1969}\special{pa -39 -1969}% +\special{fp}% \settowidth{\Width}{$6$}\setlength{\Width}{-1\Width}% \settoheight{\Height}{$6$}\settodepth{\Depth}{$6$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(-0.1500,6.0000){\hspace*{\Width}\raisebox{\Height}{$6$}}% -% +\put(-0.1500000,6.0000000){\hspace*{\Width}\raisebox{\Height}{$6$}}% % +\special{pa 0 -2362}\special{pa -39 -2362}% +\special{fp}% \settowidth{\Width}{$7$}\setlength{\Width}{-1\Width}% \settoheight{\Height}{$7$}\settodepth{\Depth}{$7$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(-0.1500,7.0000){\hspace*{\Width}\raisebox{\Height}{$7$}}% -% -% -\settowidth{\Width}{$8$}\setlength{\Width}{-1\Width}% -\settoheight{\Height}{$8$}\settodepth{\Depth}{$8$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(-0.1500,8.0000){\hspace*{\Width}\raisebox{\Height}{$8$}}% -% -% -\settowidth{\Width}{$9$}\setlength{\Width}{-1\Width}% -\settoheight{\Height}{$9$}\settodepth{\Depth}{$9$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(-0.1500,9.0000){\hspace*{\Width}\raisebox{\Height}{$9$}}% -% -% -\settowidth{\Width}{$10$}\setlength{\Width}{-1\Width}% -\settoheight{\Height}{$10$}\settodepth{\Depth}{$10$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(-0.1500,10.0000){\hspace*{\Width}\raisebox{\Height}{$10$}}% -% +\put(-0.1500000,7.0000000){\hspace*{\Width}\raisebox{\Height}{$7$}}% % +\special{pa 0 -2756}\special{pa -39 -2756}% +\special{fp}% \end{picture}}%
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\ No newline at end of file diff --git a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/setwindow.pdf b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/setwindow.pdf Binary files differnew file mode 100644 index 00000000000..38d007daf7c --- /dev/null +++ b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/setwindow.pdf diff --git a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig3d/sf3ddata3.tex b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/sf3ddata3.tex index a2585b3117b..a2585b3117b 100644 --- a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig3d/sf3ddata3.tex +++ b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/sf3ddata3.tex diff --git a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig3d/sf3ddata4.tex b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/sf3ddata4.tex index 7c4fa9d6f42..7c4fa9d6f42 100644 --- 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b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/sfbdpara03.tex index 15121319fe4..15121319fe4 100644 --- a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig3d/sfbdpara03.tex +++ b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/sfbdpara03.tex diff --git a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig3d/sfbdpara04.tex b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/sfbdpara04.tex index 4ea7e247a6a..4ea7e247a6a 100644 --- a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig3d/sfbdpara04.tex +++ b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/sfbdpara04.tex diff --git a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/shade01.tex b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/shade01.tex index 079d9c663aa..056b4ffd7eb 100644 --- a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/shade01.tex +++ b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/shade01.tex 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273 -1575}\special{fp}% +\special{pa 312 -1575}\special{pa 351 -1575}\special{fp}\special{pa 390 -1575}\special{pa 429 -1575}\special{fp}% +\special{pa 469 -1575}\special{pa 508 -1575}\special{fp}\special{pa 547 -1575}\special{pa 586 -1575}\special{fp}% +\special{pa 625 -1575}\special{pa 664 -1575}\special{fp}\special{pa 703 -1575}\special{pa 742 -1575}\special{fp}% +\special{pa 781 -1575}\special{pa 820 -1575}\special{fp}\special{pa 859 -1575}\special{pa 898 -1575}\special{fp}% +\special{pa 937 -1575}\special{pa 976 -1575}\special{fp}\special{pa 1015 -1575}\special{pa 1054 -1575}\special{fp}% +\special{pa 1093 -1575}\special{pa 1132 -1575}\special{fp}\special{pa 1171 -1575}\special{pa 1210 -1575}\special{fp}% +\special{pa 1249 -1575}\special{pa 1288 -1575}\special{fp}\special{pa 1328 -1575}\special{pa 1367 -1575}\special{fp}% +\special{pa 1406 -1575}\special{pa 1445 -1575}\special{fp}\special{pa 1484 -1575}\special{pa 1523 -1575}\special{fp}% +\special{pa 1562 -1575}\special{pa 1601 -1575}\special{fp}\special{pa 1640 -1575}\special{pa 1679 -1575}\special{fp}% +\special{pa 1718 -1575}\special{pa 1757 -1575}\special{fp}\special{pa 1796 -1575}\special{pa 1835 -1575}\special{fp}% +\special{pa 1874 -1575}\special{pa 1913 -1575}\special{fp}\special{pa 1952 -1575}\special{pa 1991 -1575}\special{fp}% +\special{pa 2030 -1575}\special{pa 2069 -1575}\special{fp}\special{pa 2108 -1575}\special{pa 2147 -1575}\special{fp}% +\special{pa 2187 -1575}\special{pa 2226 -1575}\special{fp}\special{pa 2265 -1575}\special{pa 2304 -1575}\special{fp}% +\special{pa 2343 -1575}\special{pa 2382 -1575}\special{fp}\special{pa 2421 -1575}\special{pa 2460 -1575}\special{fp}% +\special{pa 2499 -1575}\special{pa 2538 -1575}\special{fp}\special{pa 2577 -1575}\special{pa 2616 -1575}\special{fp}% +\special{pa 2655 -1575}\special{pa 2694 -1575}\special{fp}\special{pa 2733 -1575}\special{pa 2772 -1575}\special{fp}% +\special{pa 2811 -1575}\special{pa 2850 -1575}\special{fp}\special{pa 2889 -1575}\special{pa 2928 -1575}\special{fp}% +\special{pa 2967 -1575}\special{pa 3006 -1575}\special{fp}\special{pa 3045 -1575}\special{pa 3085 -1575}\special{fp}% +\special{pa 3124 -1575}\special{pa 3163 -1575}\special{fp}\special{pa 3202 -1575}\special{pa 3241 -1575}\special{fp}% +\special{pa 3280 -1575}\special{pa 3319 -1575}\special{fp}\special{pa 3358 -1575}\special{pa 3397 -1575}\special{fp}% +\special{pa 3436 -1575}\special{pa 3475 -1575}\special{fp}\special{pa 3514 -1575}\special{pa 3553 -1575}\special{fp}% +\special{pa 3592 -1575}\special{pa 3631 -1575}\special{fp}\special{pa 3670 -1575}\special{pa 3709 -1575}\special{fp}% +\special{pa 3748 -1575}\special{pa 3787 -1575}\special{fp}\special{pa 3826 -1575}\special{pa 3865 -1575}\special{fp}% +\special{pa 3904 -1575}\special{pa 3944 -1575}\special{fp}\special{pa 3983 -1575}\special{pa 4022 -1575}\special{fp}% +\special{pa 4061 -1575}\special{pa 4100 -1575}\special{fp}\special{pa 4139 -1575}\special{pa 4178 -1575}\special{fp}% +\special{pa 4217 -1575}\special{pa 4256 -1575}\special{fp}\special{pa 4295 -1575}\special{pa 4334 -1575}\special{fp}% +\special{pa 4373 -1575}\special{pa 4412 -1575}\special{fp}\special{pa 4451 -1575}\special{pa 4490 -1575}\special{fp}% +\special{pa 4529 -1575}\special{pa 4568 -1575}\special{fp}\special{pa 4607 -1575}\special{pa 4646 -1575}\special{fp}% +\special{pa 4685 -1575}\special{pa 4724 -1575}\special{fp}% +% +\special{pa 197 -1083}\special{pa 220 -1013}\special{pa 244 -947}\special{pa 268 -883}% +\special{pa 291 -822}\special{pa 315 -764}\special{pa 339 -709}\special{pa 362 -656}% +\special{pa 386 -606}\special{pa 409 -560}\special{pa 433 -516}\special{pa 457 -475}% +\special{pa 480 -436}\special{pa 504 -401}\special{pa 528 -368}\special{pa 551 -339}% +\special{pa 575 -312}\special{pa 598 -288}\special{pa 622 -266}\special{pa 646 -248}% +\special{pa 669 -232}\special{pa 693 -220}\special{pa 717 -210}\special{pa 740 -203}% +\special{pa 764 -198}\special{pa 787 -197}\special{pa 811 -198}\special{pa 835 -203}% +\special{pa 858 -210}\special{pa 882 -220}\special{pa 906 -232}\special{pa 929 -248}% +\special{pa 953 -266}\special{pa 976 -288}\special{pa 1000 -312}\special{pa 1024 -339}% +\special{pa 1047 -368}\special{pa 1071 -401}\special{pa 1094 -436}\special{pa 1118 -475}% +\special{pa 1142 -516}\special{pa 1165 -560}\special{pa 1189 -606}\special{pa 1213 -656}% +\special{pa 1236 -709}\special{pa 1260 -764}\special{pa 1283 -822}\special{pa 1307 -883}% +\special{pa 1331 -947}\special{pa 1354 -1013}\special{pa 1378 -1083}% \special{fp}% -\special{pn 8}% -\special{pn 16}% -\special{pa 2362 -1378}\special{pa 2362 -1102}% +\special{pa 1772 -1280}\special{pa 1795 -1210}\special{pa 1819 -1143}\special{pa 1843 -1080}% +\special{pa 1866 -1019}\special{pa 1890 -961}\special{pa 1913 -905}\special{pa 1937 -853}% +\special{pa 1961 -803}\special{pa 1984 -757}\special{pa 2008 -713}\special{pa 2031 -671}% +\special{pa 2055 -633}\special{pa 2079 -598}\special{pa 2102 -565}\special{pa 2126 -535}% +\special{pa 2150 -509}\special{pa 2173 -484}\special{pa 2197 -463}\special{pa 2220 -445}% +\special{pa 2244 -429}\special{pa 2268 -416}\special{pa 2291 -406}\special{pa 2315 -399}% +\special{pa 2339 -395}\special{pa 2362 -394}\special{pa 2386 -395}\special{pa 2409 -399}% +\special{pa 2433 -406}\special{pa 2457 -416}\special{pa 2480 -429}\special{pa 2504 -445}% +\special{pa 2528 -463}\special{pa 2551 -484}\special{pa 2575 -509}\special{pa 2598 -535}% +\special{pa 2622 -565}\special{pa 2646 -598}\special{pa 2669 -633}\special{pa 2693 -671}% +\special{pa 2717 -713}\special{pa 2740 -757}\special{pa 2764 -803}\special{pa 2787 -853}% +\special{pa 2811 -905}\special{pa 2835 -961}\special{pa 2858 -1019}\special{pa 2882 -1080}% +\special{pa 2906 -1143}\special{pa 2929 -1210}\special{pa 2953 -1280}% \special{fp}% -\special{pn 8}% -\special{pn 16}% -\special{pa 2362 -1102}\special{pa 2362 0}% +\special{pa 3346 -1476}\special{pa 3370 -1407}\special{pa 3394 -1340}\special{pa 3417 -1277}% +\special{pa 3441 -1216}\special{pa 3465 -1157}\special{pa 3488 -1102}\special{pa 3512 -1050}% +\special{pa 3535 -1000}\special{pa 3559 -953}\special{pa 3583 -909}\special{pa 3606 -868}% +\special{pa 3630 -830}\special{pa 3654 -795}\special{pa 3677 -762}\special{pa 3701 -732}% +\special{pa 3724 -705}\special{pa 3748 -681}\special{pa 3772 -660}\special{pa 3795 -642}% +\special{pa 3819 -626}\special{pa 3843 -613}\special{pa 3866 -603}\special{pa 3890 -596}% +\special{pa 3913 -592}\special{pa 3937 -591}\special{pa 3961 -592}\special{pa 3984 -596}% +\special{pa 4008 -603}\special{pa 4031 -613}\special{pa 4055 -626}\special{pa 4079 -642}% +\special{pa 4102 -660}\special{pa 4126 -681}\special{pa 4150 -705}\special{pa 4173 -732}% +\special{pa 4197 -762}\special{pa 4220 -795}\special{pa 4244 -830}\special{pa 4268 -868}% +\special{pa 4291 -909}\special{pa 4315 -953}\special{pa 4339 -1000}\special{pa 4362 -1050}% +\special{pa 4386 -1102}\special{pa 4409 -1157}\special{pa 4433 -1216}\special{pa 4457 -1277}% +\special{pa 4480 -1340}\special{pa 4504 -1407}\special{pa 4528 -1476}% \special{fp}% -\special{pn 8}% -\special{pa 0 -1378}\special{pa 2362 -1378}% +\special{pa 197 -591}\special{pa 1378 -591}% +\special{fp}% +\special{pa 1772 -591}\special{pa 2953 -591}% +\special{fp}% +\special{pa 3346 -591}\special{pa 4528 -591}% \special{fp}% -\special{pa 0 -1102}\special{pa 39 -1102}\special{fp}\special{pa 77 -1102}\special{pa 116 -1102}\special{fp}% -\special{pa 155 -1102}\special{pa 194 -1102}\special{fp}\special{pa 232 -1102}\special{pa 271 -1102}\special{fp}% -\special{pa 310 -1102}\special{pa 349 -1102}\special{fp}\special{pa 387 -1102}\special{pa 426 -1102}\special{fp}% -\special{pa 465 -1102}\special{pa 503 -1102}\special{fp}\special{pa 542 -1102}\special{pa 581 -1102}\special{fp}% -\special{pa 620 -1102}\special{pa 658 -1102}\special{fp}\special{pa 697 -1102}\special{pa 736 -1102}\special{fp}% -\special{pa 774 -1102}\special{pa 813 -1102}\special{fp}\special{pa 852 -1102}\special{pa 891 -1102}\special{fp}% -\special{pa 929 -1102}\special{pa 968 -1102}\special{fp}\special{pa 1007 -1102}\special{pa 1046 -1102}\special{fp}% -\special{pa 1084 -1102}\special{pa 1123 -1102}\special{fp}\special{pa 1162 -1102}\special{pa 1200 -1102}\special{fp}% -\special{pa 1239 -1102}\special{pa 1278 -1102}\special{fp}\special{pa 1317 -1102}\special{pa 1355 -1102}\special{fp}% -\special{pa 1394 -1102}\special{pa 1433 -1102}\special{fp}\special{pa 1472 -1102}\special{pa 1510 -1102}\special{fp}% -\special{pa 1549 -1102}\special{pa 1588 -1102}\special{fp}\special{pa 1626 -1102}\special{pa 1665 -1102}\special{fp}% -\special{pa 1704 -1102}\special{pa 1743 -1102}\special{fp}\special{pa 1781 -1102}\special{pa 1820 -1102}\special{fp}% -\special{pa 1859 -1102}\special{pa 1898 -1102}\special{fp}\special{pa 1936 -1102}\special{pa 1975 -1102}\special{fp}% -\special{pa 2014 -1102}\special{pa 2052 -1102}\special{fp}\special{pa 2091 -1102}\special{pa 2130 -1102}\special{fp}% -\special{pa 2169 -1102}\special{pa 2207 -1102}\special{fp}\special{pa 2246 -1102}\special{pa 2285 -1102}\special{fp}% -\special{pa 2323 -1102}\special{pa 2362 -1102}\special{fp}% -% \settowidth{\Width}{$D>0$}\setlength{\Width}{-0.5\Width}% \settoheight{\Height}{$D>0$}\settodepth{\Depth}{$D>0$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(2.0000,8.0000){\hspace*{\Width}\raisebox{\Height}{$D>0$}}% -% +\put(2.0000000,5.5000000){\hspace*{\Width}\raisebox{\Height}{$D>0$}}% % \settowidth{\Width}{$D=0$}\setlength{\Width}{-0.5\Width}% \settoheight{\Height}{$D=0$}\settodepth{\Depth}{$D=0$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(6.0000,8.0000){\hspace*{\Width}\raisebox{\Height}{$D=0$}}% -% +\put(6.0000000,5.5000000){\hspace*{\Width}\raisebox{\Height}{$D=0$}}% % \settowidth{\Width}{$D<0$}\setlength{\Width}{-0.5\Width}% \settoheight{\Height}{$D<0$}\settodepth{\Depth}{$D<0$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.0000,8.0000){\hspace*{\Width}\raisebox{\Height}{$D<0$}}% -% -% -\settowidth{\Width}{2点で交わる}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{2点で交わる}\settodepth{\Depth}{2点で交わる}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(2.0000,6.3000){\hspace*{\Width}\raisebox{\Height}{2点で交わる}}% +\put(10.0000000,5.5000000){\hspace*{\Width}\raisebox{\Height}{$D<0$}}% % +\settowidth{\Width}{2 点で交わる}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{2 点で交わる}\settodepth{\Depth}{2 点で交わる}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(2.0000000,4.5000000){\hspace*{\Width}\raisebox{\Height}{2 点で交わる}}% % \settowidth{\Width}{接する}\setlength{\Width}{-0.5\Width}% \settoheight{\Height}{接する}\settodepth{\Depth}{接する}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(6.0000,6.3000){\hspace*{\Width}\raisebox{\Height}{接する}}% -% +\put(6.0000000,4.5000000){\hspace*{\Width}\raisebox{\Height}{接する}}% % \settowidth{\Width}{共有点なし}\setlength{\Width}{-0.5\Width}% \settoheight{\Height}{共有点なし}\settodepth{\Depth}{共有点なし}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(10.0000,6.3000){\hspace*{\Width}\raisebox{\Height}{共有点なし}}% -% -% -\settowidth{\Width}{判別式と$x$軸の交点}\setlength{\Width}{-0.5\Width}% -\settoheight{\Height}{判別式と$x$軸の交点}\settodepth{\Depth}{判別式と$x$軸の交点}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% -\put(4.0000,10.0000){\hspace*{\Width}\raisebox{\Height}{判別式と$x$軸の交点}}% -% +\put(10.0000000,4.5000000){\hspace*{\Width}\raisebox{\Height}{共有点なし}}% % -\special{pa 98 -738}\special{pa 110 -703}\special{pa 123 -669}\special{pa 135 -636}% -\special{pa 147 -605}\special{pa 159 -576}\special{pa 171 -548}\special{pa 183 -521}% -\special{pa 195 -496}\special{pa 207 -473}\special{pa 219 -450}\special{pa 231 -430}% -\special{pa 243 -411}\special{pa 255 -393}\special{pa 267 -377}\special{pa 279 -362}% -\special{pa 291 -349}\special{pa 303 -337}\special{pa 315 -326}\special{pa 327 -318}% -\special{pa 339 -310}\special{pa 352 -304}\special{pa 364 -300}\special{pa 376 -297}% -\special{pa 388 -295}\special{pa 400 -295}\special{pa 412 -297}\special{pa 424 -300}% -\special{pa 436 -304}\special{pa 448 -310}\special{pa 460 -318}\special{pa 472 -326}% -\special{pa 484 -337}\special{pa 496 -349}\special{pa 508 -362}\special{pa 520 -377}% -\special{pa 532 -393}\special{pa 544 -411}\special{pa 556 -430}\special{pa 568 -450}% -\special{pa 581 -473}\special{pa 593 -496}\special{pa 605 -521}\special{pa 617 -548}% -\special{pa 629 -576}\special{pa 641 -605}\special{pa 653 -636}\special{pa 665 -669}% -\special{pa 677 -703}\special{pa 689 -738}% -\special{fp}% -\special{pa 886 -837}\special{pa 898 -801}\special{pa 910 -767}\special{pa 922 -735}% -\special{pa 934 -704}\special{pa 946 -674}\special{pa 958 -646}\special{pa 970 -620}% -\special{pa 982 -595}\special{pa 994 -571}\special{pa 1006 -549}\special{pa 1018 -528}% -\special{pa 1030 -509}\special{pa 1043 -491}\special{pa 1055 -475}\special{pa 1067 -460}% -\special{pa 1079 -447}\special{pa 1091 -435}\special{pa 1103 -425}\special{pa 1115 -416}% -\special{pa 1127 -409}\special{pa 1139 -403}\special{pa 1151 -398}\special{pa 1163 -395}% -\special{pa 1175 -394}\special{pa 1187 -394}\special{pa 1199 -395}\special{pa 1211 -398}% -\special{pa 1223 -403}\special{pa 1235 -409}\special{pa 1247 -416}\special{pa 1259 -425}% -\special{pa 1271 -435}\special{pa 1284 -447}\special{pa 1296 -460}\special{pa 1308 -475}% -\special{pa 1320 -491}\special{pa 1332 -509}\special{pa 1344 -528}\special{pa 1356 -549}% -\special{pa 1368 -571}\special{pa 1380 -595}\special{pa 1392 -620}\special{pa 1404 -646}% -\special{pa 1416 -674}\special{pa 1428 -704}\special{pa 1440 -735}\special{pa 1452 -767}% -\special{pa 1464 -801}\special{pa 1476 -837}% -\special{fp}% -\special{pa 1673 -935}\special{pa 1685 -900}\special{pa 1697 -866}\special{pa 1709 -833}% -\special{pa 1721 -802}\special{pa 1733 -773}\special{pa 1746 -745}\special{pa 1758 -718}% -\special{pa 1770 -693}\special{pa 1782 -669}\special{pa 1794 -647}\special{pa 1806 -627}% -\special{pa 1818 -607}\special{pa 1830 -590}\special{pa 1842 -573}\special{pa 1854 -559}% -\special{pa 1866 -545}\special{pa 1878 -534}\special{pa 1890 -523}\special{pa 1902 -514}% -\special{pa 1914 -507}\special{pa 1926 -501}\special{pa 1938 -497}\special{pa 1950 -494}% -\special{pa 1962 -492}\special{pa 1975 -492}\special{pa 1987 -494}\special{pa 1999 -497}% -\special{pa 2011 -501}\special{pa 2023 -507}\special{pa 2035 -514}\special{pa 2047 -523}% -\special{pa 2059 -534}\special{pa 2071 -545}\special{pa 2083 -559}\special{pa 2095 -573}% -\special{pa 2107 -590}\special{pa 2119 -607}\special{pa 2131 -627}\special{pa 2143 -647}% -\special{pa 2155 -669}\special{pa 2167 -693}\special{pa 2179 -718}\special{pa 2191 -745}% -\special{pa 2204 -773}\special{pa 2216 -802}\special{pa 2228 -833}\special{pa 2240 -866}% -\special{pa 2252 -900}\special{pa 2264 -935}% -\special{fp}% -\special{pa 197 -394}\special{pa 591 -394}% -\special{fp}% -\special{pa 984 -394}\special{pa 1378 -394}% -\special{fp}% -\special{pa 1772 -394}\special{pa 2165 -394}% -\special{fp}% \end{picture}}%
\ No newline at end of file diff --git a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/tablesample1E.tex b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/tablesample1E.tex new file mode 100644 index 00000000000..0a78dad4db2 --- /dev/null +++ b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/tablesample1E.tex @@ -0,0 +1,184 @@ +%%% fig.tex 2014-12-18 15:16 +%%% fig.sce 2014-12-18 15:16 +{\unitlength=5mm% +\begin{picture}% +( 12.00000, 9.00000)( -0.00000, -0.00000)% +\special{pn 8}% +% +\special{pn 16}% +\special{pa 0 -1772}\special{pa 787 -1772}% +\special{fp}% +\special{pn 8}% +\special{pn 16}% +\special{pa 787 -1772}\special{pa 1575 -1772}% +\special{fp}% +\special{pn 8}% +\special{pn 16}% +\special{pa 1575 -1772}\special{pa 2362 -1772}% +\special{fp}% +\special{pn 8}% +\special{pn 16}% +\special{pa 0 0}\special{pa 787 0}% +\special{fp}% +\special{pn 8}% +\special{pn 16}% +\special{pa 787 0}\special{pa 1575 0}% +\special{fp}% +\special{pn 8}% +\special{pn 16}% +\special{pa 1575 0}\special{pa 2362 0}% +\special{fp}% +\special{pn 8}% +\special{pn 16}% +\special{pa 0 -1772}\special{pa 0 -1378}% +\special{fp}% +\special{pn 8}% +\special{pn 16}% +\special{pa 0 -1378}\special{pa 0 -1102}% +\special{fp}% +\special{pn 8}% +\special{pn 16}% +\special{pa 0 -1102}\special{pa 0 0}% +\special{fp}% +\special{pn 8}% +\special{pn 16}% +\special{pa 787 -1772}\special{pa 787 -1378}% +\special{fp}% +\special{pn 8}% +\special{pn 16}% +\special{pa 787 -1378}\special{pa 787 -1102}% +\special{fp}% +\special{pn 8}% +\special{pn 16}% +\special{pa 787 -1102}\special{pa 787 0}% +\special{fp}% +\special{pn 8}% +\special{pn 16}% +\special{pa 1575 -1772}\special{pa 1575 -1378}% +\special{fp}% +\special{pn 8}% +\special{pn 16}% +\special{pa 1575 -1378}\special{pa 1575 -1102}% +\special{fp}% +\special{pn 8}% +\special{pn 16}% +\special{pa 1575 -1102}\special{pa 1575 0}% +\special{fp}% +\special{pn 8}% +\special{pn 16}% +\special{pa 2362 -1772}\special{pa 2362 -1378}% +\special{fp}% +\special{pn 8}% +\special{pn 16}% +\special{pa 2362 -1378}\special{pa 2362 -1102}% +\special{fp}% +\special{pn 8}% +\special{pn 16}% +\special{pa 2362 -1102}\special{pa 2362 0}% +\special{fp}% +\special{pn 8}% +\special{pa 0 -1378}\special{pa 2362 -1378}% +\special{fp}% +\special{pa 0 -1102}\special{pa 39 -1102}\special{fp}\special{pa 77 -1102}\special{pa 116 -1102}\special{fp}% +\special{pa 155 -1102}\special{pa 194 -1102}\special{fp}\special{pa 232 -1102}\special{pa 271 -1102}\special{fp}% +\special{pa 310 -1102}\special{pa 349 -1102}\special{fp}\special{pa 387 -1102}\special{pa 426 -1102}\special{fp}% +\special{pa 465 -1102}\special{pa 503 -1102}\special{fp}\special{pa 542 -1102}\special{pa 581 -1102}\special{fp}% +\special{pa 620 -1102}\special{pa 658 -1102}\special{fp}\special{pa 697 -1102}\special{pa 736 -1102}\special{fp}% +\special{pa 774 -1102}\special{pa 813 -1102}\special{fp}\special{pa 852 -1102}\special{pa 891 -1102}\special{fp}% +\special{pa 929 -1102}\special{pa 968 -1102}\special{fp}\special{pa 1007 -1102}\special{pa 1046 -1102}\special{fp}% +\special{pa 1084 -1102}\special{pa 1123 -1102}\special{fp}\special{pa 1162 -1102}\special{pa 1200 -1102}\special{fp}% +\special{pa 1239 -1102}\special{pa 1278 -1102}\special{fp}\special{pa 1317 -1102}\special{pa 1355 -1102}\special{fp}% +\special{pa 1394 -1102}\special{pa 1433 -1102}\special{fp}\special{pa 1472 -1102}\special{pa 1510 -1102}\special{fp}% +\special{pa 1549 -1102}\special{pa 1588 -1102}\special{fp}\special{pa 1626 -1102}\special{pa 1665 -1102}\special{fp}% +\special{pa 1704 -1102}\special{pa 1743 -1102}\special{fp}\special{pa 1781 -1102}\special{pa 1820 -1102}\special{fp}% +\special{pa 1859 -1102}\special{pa 1898 -1102}\special{fp}\special{pa 1936 -1102}\special{pa 1975 -1102}\special{fp}% +\special{pa 2014 -1102}\special{pa 2052 -1102}\special{fp}\special{pa 2091 -1102}\special{pa 2130 -1102}\special{fp}% +\special{pa 2169 -1102}\special{pa 2207 -1102}\special{fp}\special{pa 2246 -1102}\special{pa 2285 -1102}\special{fp}% +\special{pa 2323 -1102}\special{pa 2362 -1102}\special{fp}% +% +\settowidth{\Width}{$D>0$}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{$D>0$}\settodepth{\Depth}{$D>0$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(2.0000,8.0000){\hspace*{\Width}\raisebox{\Height}{$D>0$}}% +% +% +\settowidth{\Width}{$D=0$}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{$D=0$}\settodepth{\Depth}{$D=0$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(6.0000,8.0000){\hspace*{\Width}\raisebox{\Height}{$D=0$}}% +% +% +\settowidth{\Width}{$D<0$}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{$D<0$}\settodepth{\Depth}{$D<0$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(10.0000,8.0000){\hspace*{\Width}\raisebox{\Height}{$D<0$}}% +% +% +\settowidth{\Width}{2}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{2}\settodepth{\Depth}{2}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(2.0000,6.3000){\hspace*{\Width}\raisebox{\Height}{2}}% +% +% +\settowidth{\Width}{1}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{1}\settodepth{\Depth}{1}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(6.0000,6.3000){\hspace*{\Width}\raisebox{\Height}{1}}% +% +% +\settowidth{\Width}{0}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{0}\settodepth{\Depth}{The discriminant and the number of intersections}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(10.0000,6.3000){\hspace*{\Width}\raisebox{\Height}{0}}% + +% +% +\settowidth{\Width}{The discriminant and the number of intersections}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{The discriminant and the number of intersections}\settodepth{\Depth}{The discriminant and the number of intersections}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +%\put(4.0000,10.0000){\hspace*{\Width}\raisebox{\Height}{The discriminant and the number of intersections}}% +\put(6.0000,10.0000){\hspace*{\Width}\raisebox{\Height}{The discriminant and the number of intersections}}% +% +% +\special{pa 98 -738}\special{pa 110 -703}\special{pa 123 -669}\special{pa 135 -636}% +\special{pa 147 -605}\special{pa 159 -576}\special{pa 171 -548}\special{pa 183 -521}% +\special{pa 195 -496}\special{pa 207 -473}\special{pa 219 -450}\special{pa 231 -430}% +\special{pa 243 -411}\special{pa 255 -393}\special{pa 267 -377}\special{pa 279 -362}% +\special{pa 291 -349}\special{pa 303 -337}\special{pa 315 -326}\special{pa 327 -318}% +\special{pa 339 -310}\special{pa 352 -304}\special{pa 364 -300}\special{pa 376 -297}% +\special{pa 388 -295}\special{pa 400 -295}\special{pa 412 -297}\special{pa 424 -300}% +\special{pa 436 -304}\special{pa 448 -310}\special{pa 460 -318}\special{pa 472 -326}% +\special{pa 484 -337}\special{pa 496 -349}\special{pa 508 -362}\special{pa 520 -377}% +\special{pa 532 -393}\special{pa 544 -411}\special{pa 556 -430}\special{pa 568 -450}% +\special{pa 581 -473}\special{pa 593 -496}\special{pa 605 -521}\special{pa 617 -548}% +\special{pa 629 -576}\special{pa 641 -605}\special{pa 653 -636}\special{pa 665 -669}% +\special{pa 677 -703}\special{pa 689 -738}% +\special{fp}% +\special{pa 886 -837}\special{pa 898 -801}\special{pa 910 -767}\special{pa 922 -735}% +\special{pa 934 -704}\special{pa 946 -674}\special{pa 958 -646}\special{pa 970 -620}% +\special{pa 982 -595}\special{pa 994 -571}\special{pa 1006 -549}\special{pa 1018 -528}% +\special{pa 1030 -509}\special{pa 1043 -491}\special{pa 1055 -475}\special{pa 1067 -460}% +\special{pa 1079 -447}\special{pa 1091 -435}\special{pa 1103 -425}\special{pa 1115 -416}% +\special{pa 1127 -409}\special{pa 1139 -403}\special{pa 1151 -398}\special{pa 1163 -395}% +\special{pa 1175 -394}\special{pa 1187 -394}\special{pa 1199 -395}\special{pa 1211 -398}% +\special{pa 1223 -403}\special{pa 1235 -409}\special{pa 1247 -416}\special{pa 1259 -425}% +\special{pa 1271 -435}\special{pa 1284 -447}\special{pa 1296 -460}\special{pa 1308 -475}% +\special{pa 1320 -491}\special{pa 1332 -509}\special{pa 1344 -528}\special{pa 1356 -549}% +\special{pa 1368 -571}\special{pa 1380 -595}\special{pa 1392 -620}\special{pa 1404 -646}% +\special{pa 1416 -674}\special{pa 1428 -704}\special{pa 1440 -735}\special{pa 1452 -767}% +\special{pa 1464 -801}\special{pa 1476 -837}% +\special{fp}% +\special{pa 1673 -935}\special{pa 1685 -900}\special{pa 1697 -866}\special{pa 1709 -833}% +\special{pa 1721 -802}\special{pa 1733 -773}\special{pa 1746 -745}\special{pa 1758 -718}% +\special{pa 1770 -693}\special{pa 1782 -669}\special{pa 1794 -647}\special{pa 1806 -627}% +\special{pa 1818 -607}\special{pa 1830 -590}\special{pa 1842 -573}\special{pa 1854 -559}% +\special{pa 1866 -545}\special{pa 1878 -534}\special{pa 1890 -523}\special{pa 1902 -514}% +\special{pa 1914 -507}\special{pa 1926 -501}\special{pa 1938 -497}\special{pa 1950 -494}% +\special{pa 1962 -492}\special{pa 1975 -492}\special{pa 1987 -494}\special{pa 1999 -497}% +\special{pa 2011 -501}\special{pa 2023 -507}\special{pa 2035 -514}\special{pa 2047 -523}% +\special{pa 2059 -534}\special{pa 2071 -545}\special{pa 2083 -559}\special{pa 2095 -573}% +\special{pa 2107 -590}\special{pa 2119 -607}\special{pa 2131 -627}\special{pa 2143 -647}% +\special{pa 2155 -669}\special{pa 2167 -693}\special{pa 2179 -718}\special{pa 2191 -745}% +\special{pa 2204 -773}\special{pa 2216 -802}\special{pa 2228 -833}\special{pa 2240 -866}% +\special{pa 2252 -900}\special{pa 2264 -935}% +\special{fp}% +\special{pa 197 -394}\special{pa 591 -394}% +\special{fp}% +\special{pa 984 -394}\special{pa 1378 -394}% +\special{fp}% +\special{pa 1772 -394}\special{pa 2165 -394}% +\special{fp}% +\end{picture}}%
\ No newline at end of file diff --git a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/tablesample2E.tex b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/tablesample2E.tex new file mode 100644 index 00000000000..a3a602c2c2f --- /dev/null +++ b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/Fig/tablesample2E.tex @@ -0,0 +1,258 @@ +%%% test.tex 2014-11-26 12:54 +%%% test.sce 2014-11-26 12:54 +{\unitlength=1cm% +\begin{picture}% +( 8.50000, 5.00000)( 0.00000, 0.00000)% +\special{pn 8}% +% +\special{pa 0 -1969}\special{pa 236 -1969}% +\special{fp}% +\special{pa 236 -1969}\special{pa 472 -1969}% +\special{fp}% +\special{pa 472 -1969}\special{pa 866 -1969}% +\special{fp}% +\special{pa 866 -1969}\special{pa 1102 -1969}% +\special{fp}% +\special{pa 1102 -1969}\special{pa 1496 -1969}% +\special{fp}% +\special{pa 1496 -1969}\special{pa 1732 -1969}% +\special{fp}% +\special{pa 1732 -1969}\special{pa 3346 -1969}% +\special{fp}% +\special{pa 0 -709}\special{pa 236 -709}% +\special{fp}% +\special{pa 236 -709}\special{pa 472 -709}% +\special{fp}% +\special{pa 472 -709}\special{pa 866 -709}% +\special{fp}% +\special{pa 866 -709}\special{pa 1102 -709}% +\special{fp}% +\special{pa 1102 -709}\special{pa 1496 -709}% +\special{fp}% +\special{pa 1496 -709}\special{pa 1732 -709}% +\special{fp}% +\special{pa 0 -472}\special{pa 236 -472}% +\special{fp}% +\special{pa 236 -472}\special{pa 472 -472}% +\special{fp}% +\special{pa 472 -472}\special{pa 866 -472}% +\special{fp}% +\special{pa 866 -472}\special{pa 1102 -472}% +\special{fp}% +\special{pa 1102 -472}\special{pa 1496 -472}% +\special{fp}% +\special{pa 1496 -472}\special{pa 1732 -472}% +\special{fp}% +\special{pa 0 -236}\special{pa 236 -236}% +\special{fp}% +\special{pa 236 -236}\special{pa 472 -236}% +\special{fp}% +\special{pa 472 -236}\special{pa 866 -236}% +\special{fp}% +\special{pa 866 -236}\special{pa 1102 -236}% +\special{fp}% +\special{pa 1102 -236}\special{pa 1496 -236}% +\special{fp}% 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+\special{pa 3346 -236}\special{pa 3346 0}% +\special{fp}% +\settowidth{\Width}{$x$}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{$x$}\settodepth{\Depth}{$x$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(0.3000,1.5000){\hspace*{\Width}\raisebox{\Height}{$x$}}% +% +% +\settowidth{\Width}{$0$}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{$0$}\settodepth{\Depth}{$0$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(0.9000,1.5000){\hspace*{\Width}\raisebox{\Height}{$0$}}% +% +% +\settowidth{\Width}{$\cdots$}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{$\cdots$}\settodepth{\Depth}{$\cdots$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(1.7000,1.5000){\hspace*{\Width}\raisebox{\Height}{$\cdots$}}% +% +% +\settowidth{\Width}{$\tfrac{1}{4}$}\setlength{\Width}{-0.5\Width}% 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+\put(4.9000,4.1000){\hspace*{\Width}\raisebox{\Height}{\small{$y$}}}% +% +% +\settowidth{\Width}{\small O}\setlength{\Width}{-1\Width}% +\settoheight{\Height}{\small O}\settodepth{\Depth}{\small O}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(4.8000,1.0000){\hspace*{\Width}\raisebox{\Height}{\small O}}% +% +% +\settowidth{\Width}{$y=x-\sqrt{x}$}\setlength{\Width}{-1\Width}% +\settoheight{\Height}{$y=x-\sqrt{x}$}\settodepth{\Depth}{$y=x-\sqrt{x}$}\setlength{\Height}{\Depth}% +\put(7.9500,2.3200){\hspace*{\Width}\raisebox{\Height}{$y=x-\sqrt{x}$}}% +% +% +\special{pa 236 -472}\special{pa 472 -236}% +\special{fp}% +\special{pa 236 -236}\special{pa 472 -472}% +\special{fp}% +\end{picture}}%
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\ No newline at end of file diff --git a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/KeTCindyReferenceE.tex b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/KeTCindyReferenceE.tex new file mode 100644 index 00000000000..c43602753fb --- /dev/null +++ b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/KeTCindyReferenceE.tex @@ -0,0 +1,5416 @@ +\documentclass[papersize,a4paper,12pt]{article} +\usepackage{ketpic,ketlayer} +\usepackage{amsmath} +% \usepackage{amsmath,newtxmath} +%\usepackage[dvipdfmx]{graphicx,color} +\usepackage{graphicx,color} +\usepackage{wrapfig} +%\usepackage[dvipdfmx,bookmarks=false,colorlinks=true,linkcolor=blue]{hyperref} +\usepackage[bookmarks=false,colorlinks=true,linkcolor=blue]{hyperref} +\setmargin{20}{20}{15}{25} +\usepackage{setspace} +\usepackage{comment} +\usepackage{bm,enumerate} + +%\newcommand{\cmd}[1]{ +%\begin{center}{\bf\large #1}\end{center} +%\hypertarget{#1}{} +%} + +\newenvironment{cmd}[2]{ +\hypertarget{#2}{} +\begin{center}{\bf\large #1}\end{center} +\begin{description} +}{ +\end{description} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$Command List}\end{flushright} +} + +% item command for this documentation +\newcommand{\itemket}[1]{ +\item[\Ltab{27mm}{#1}] +} + + +\begin{document} +\title{\ketcindy\ Command Reference} +\author{\ketcindy\ Project Team} +\maketitle + +\begin{center} - ver.3.2 -\end{center} + +\hypertarget{index}{} +\tableofcontents + +\newpage + +%===== Plane Figure ===================== + +\section{Plane figure} +%========= Setting and Defining =========== +\subsection{Setting and Defining} + +%========= Setting environment =========== +\subsubsection{Setting environment} + +%----------Ketinit---------------------------------- +\begin{cmd}{Ketinit}{ketinit} +\itemket{Usage}Ketinit(); +\itemket{Description}Generic function to initialize \ketcindy. +\itemket{Examples}\mbox{} + +\verb|Ketinit();|\ \ The work sub folder is set to \verb|"fig"| in the folder of the cindy file.\\ +\verb|Ketinit("");|\ \ The work folder is set to the folder of the cindy file. + +\itemket{Details}\mbox{}\\ +This function should be written at the first line on Draw slot page. In case of space figure (KeTCindy's 3D-mode), write it in the initialization slot page \verb|ketlib|. +\end{cmd} + +%-----------Setfiles--------------------------------- +\begin{cmd}{Setfiles}{setfiles} +\itemket{Usage}Setfiles(filename) +\itemket{Description}Generic function to set the name of texfile. +\itemket{Details}Default file name is working Cinderella file name. +\itemket{Examples}\mbox{} + +If working Cinderella file name is "triangle.cdy" then default files name are "triangle.tex". + +By \verb|Setfiles("grav");| output files name are "grav.tex".\\ + +\end{cmd} + +%----------Setparent---------------------------------- +\begin{cmd}{Setparent}{setparent} +\itemket{Usage}Setparent(filename) +\itemket{Description}Generic function to set the name of texfile by using the Parent push button. +\itemket{Details}There is no default file name when we use the Figpdf() function and the Parent push button, so we have to define the name of output texfile. +\itemket{Examples}\mbox{} + +If working Cinderella file name is "triangle.cdy" , by \verb|Setparent("grav");| +output files name are "triangle.tex" and "grav.tex". PDF name is "grav.pdf". +\end{cmd} + +%-----------Changework--------------------------------- +\begin{cmd}{Changework}{changework} +\itemket{Usage}Changework(name of pass) +\itemket{Description}Generic function to change the working directory(folder). + +Default working directory is "fig". + +\end{cmd} + +%--------Addpackage------------------------------------ +\begin{cmd}{Addpackage}{addpackage} +\itemket{Usage}Addpackage(list of style fies) +\itemket{Description}Generic function to add packages of \TeX\ to the main file for previewing. +\itemket{Details}Basically, \verb|ketpic,ketlayer,amsmath,amssymb,graphicx,color| are used. +\itemket{Examples}\mbox{} + +\verb|Addpackage(["[dvipdfmx]{media9}","[dvipdfmx]{animate}","ketmedia"]);| + +\end{cmd} + +%--------Usegraphics------------------------------------ +\begin{cmd}{Usegraphics}{usegraphics} +\itemket{Usage}Usegraphics("pict2e") +\itemket{Description}This function changes the graphics package to \verb|"pict2e"|. +\itemket{Details}The defaut package is \verb|"tpic"|. +\itemket{Examples}\mbox{}\\ +\verb|Usegraphics("pict2e");| +\end{cmd} + +%========= Drawing and defining =========== +\subsubsection{Drawing and defining} + +%-------Addax------------------------------------- +\begin{cmd}{Addax}{addax} + +\itemket{Usage}Addax(1/0); +\itemket{Description}Generic function to decide axis are drawn or not. +\itemket{Details}If argument is 1, axis are output in the TeX file (default) but there are no axis on the Euclidean view. +\itemket{Examples} \mbox{} + +To draw a triangle. + +\verb| Listplot([B,A,C]);|\\ +\verb| Letter([A,"ne","A",B,"se","B",C,"se","C"]);| + +\begin{center} +\input{Fig/addax1} +\end{center} + +Hide coordinate axes. + +\verb| Addax(0);|\\ +\verb| Listplot([B,A,C,B]);|\\ +\verb| Letter([A,"ne","A",B,"sw","B",C,"se","C"]);| + +\begin{center} +\input{Fig/FigE} +\end{center} +\end{cmd} + +%----------Setax---------------------------------- +\begin{cmd}{Setax}{setax} +\itemket{Usage}Setax(a list of parameters); +\itemket{Description}Generic function to set the style of axis. +\itemket{Details}Parameters are:\\ +1. Style of axis ("l'' ; line(default), "a'' : arrow)\\ +2. Name of horizontal ax ( default is x)\\ +3. Posion of horizontal name (default is "e'')\\ +4. Name of horizontal ax ( default is y)\\ +5. Posion of horizontal name (default is "n'')\\ +6. Name of origin (default is O)\\ +7. Position of origin (default is "sw'') +\itemket{Examples}\mbox{} + +\verb|Setax(["a","","","","","","nw"]);|\\ +\verb|Setax([7,"nw"]);|\\ +\verb|Setax(["a","\theta","","x","w"]);| + +\begin{center} +\input{Fig/setax(theta)} +\end{center} + +\end{cmd} + +%-----------Drwxy--------------------------------- +\begin{cmd}{Drwxy}{drwxy} +\itemket{Usage}Drwxy(), Drwxy(options) +\itemket{Description}Generic function to draw axis in the \TeX\ figure. +\itemket{Details}\mbox{}\\ +By default the axes are drawn last. Use this function when axis should be drawn in the middle of commands. There are no axis on the Euclidean view. + +Options is a list of ["Origin=", "Xrng=", "Yrng="]. +\itemket{Examples}\mbox{} + +To draw a point in the void mode. + +\verb|Setax([7,"se"]);|\\ +\verb|Setpt(8);|\\ +\verb|Drwpt([-pi,0],0);|\\ +\verb|Drwxy();|\\ +\verb|Plotdata("1","sin(x)","x",["dr","Num=300"]);|\\ +\verb|Drwpt([pi,0],0);| + +\begin{center} +\input{Fig/drwxy} +\end{center} +\end{cmd} + +%-----------Definecolor--------------------------------- +\begin{cmd}{Definecolor}{definecolor} +\itemket{Usage}Definecolor(name of a color,colorcode) +\itemket{Description}Generic function to define the name of colorcode in the \TeX\ figure. +\itemket{Examples}\mbox{} + +\verb|Definecolor("darkmaz",[0.8,0,0.8]);|\\ +\verb|Setcolor("darkmaz");| + +\end{cmd} + +%---------Setcolor----------------------------------- +\begin{cmd}{Setcolor}{setcolor} +\itemket{Usage}Setcolor(color,options) +\itemket{Description}Generic function to set the color of figures and characters in the \TeX\ figure. +\itemket{Examples}\mbox{} + +\verb|Setcolor([1,0,0]);|\\ +\verb|Circledata([A,D],["Rng=[0,pi/3]"]);|\\ +\verb|Arrowhead(E,[-1,0.8],[2,1]);| + +\verb|Setcolor("red",opacity);|\\ +\hspace*{20mm} opacity is real number from 0 to 1 + +\itemket{Remark}You can also use color option in each command of drawing. + +\verb|Circledata([A,D],["Rng=[0,pi/3]","Color=[1,0,0]"]);|\\ +\verb|Arrowhead(E,[-1,0.8],[2,1],"Color=[1,0,0]");| + +\begin{center} +\includegraphics[bb=0 0 161 134,width=35mm]{Fig/setcolor.pdf} +\end{center} + +Refer to Color table on Appendix. + +\end{cmd} + +%----------Deffun---------------------------------- +\begin{cmd}{Deffun}{deffun} +\itemket{Usage}Deffun(name of a function,a list of commands); +\itemket{Description}Generic function to define a function common to both Cindyscript and R. +\itemket{Examples}\mbox{} + +$f(x)=\dfrac{1}{x^2+1}$ + +\vspace{\baselineskip} +\verb|Deffun("f(x)",["regional(y)","y=1/(x^2+1)","y"]);|\\ +\verb|Plotdata("1","f(x)","x");| + +\vspace{\baselineskip} +\hspace{20mm}\input{Fig/deffun01} + +$f(x)=\left\{\begin{array}{l}1 (x\geq 0)\\ -1 (x<0)\\ \end{array}\right.$ + +\vspace{\baselineskip} +\verb|Deffun("f(x)",["regional(y)","if(x>=0,y=1,y=-1)","y"]);|\\ +\verb|Plotdata("1","f(x)","x",["Dis=1","Num=100"]);| + +\vspace{\baselineskip} +\hspace{20mm}\input{Fig/deffun02} + +"If" command can be nesting. + +\vspace{\baselineskip} +\verb|Deffun("f(x)",["regional y","if(x>1,y=1,if(x>-1,y=x,y=-1))","y"]);| + +\vspace{\baselineskip} +\hspace{20mm}\input{Fig/deffun03} + +\end{cmd} + +%----------Defvar---------------------------------- +\begin{cmd}{Defvar}{defvar} +\itemket{Usage}Defvar([name,value,...]); +\itemket{Description}Generic function to define variables common to both Cindyscript and R. +\itemket{Examples}\mbox{} + +\begin{tabbing} +123456789012345678901234\=\kill +\verb|Defvar(["const",3]);| \> //const=3;\\ +\verb|Defvar(["a",3,"b",1]);| \> //a=3;b=1; +\end{tabbing} + +\end{cmd} + +%-----------Fontsize--------------------------------- +\begin{cmd}{Fontsize}{fontsize} +\itemket{Usage}Fontsize(size symbol) +\itemket{Description}Generic function to define the font size in the \TeX\ figure. +\itemket{Details}The symbol is \verb|"t", "ss", "f", "s", "n", "la", "La", "LA", "h", "H"|. +\itemket{Examples}\mbox{} + +\verb|Ptsize(2);|\\ +\verb|Drawpoint([A,B,C,D,E,F,G]);|\\ +\verb|Fontsize("t"); Letter([A,"s2","A"]);|\\ +\verb|Fontsize("ss"); Letter([B,"s2","B"]);|\\ +\verb|Fontsize("s"); Letter([C,"s2","C"]);|\\ +\verb|Fontsize("la"); Letter([D,"s2","D"]);|\\ +\verb|Fontsize("La"); Letter([E,"s2","E"]);|\\ +\verb|Fontsize("h"); Letter([F,"s2","F"]);|\\ +\verb|Fontsize("H"); Letter([G,"s2","G"]);| + +\begin{center} +\input{Fig/fontsize} +\end{center} + +\end{cmd} + +%-----------Ptsize--------------------------------- +\begin{cmd}{Ptsize}{ptsize} +\itemket{Usage}Ptsize(ratio); +\itemket{Description}Generic funtion to set the size of points. +\itemket{Details}This function is same as Setpt().\\ +\end{cmd} + +%-----------Setpt--------------------------------- +\begin{cmd}{Setpt}{setpt} +\itemket{Usage}Setpt(ratio); +\itemket{Description}Generic funtion to set the size of points. +\itemket{Details}''ratio'' is the ratio from the standard size.\\ +Size can be change as a option of ``Pointdata''. +\itemket{Examples}\mbox{} + +\verb|Pointdata("1",A,["Size=1"]);|\\ +\verb|Pointdata("2",B,["Size=2"]);|\\ +\verb|Pointdata("3",C,["Size=3"]);|\\ +\verb|Pointdata("4",D,["Size=4"]);| + +\hspace{20mm}\input{Fig/pointsize} + +\end{cmd} + +%------------Setmarklen-------------------------------- +\begin{cmd}{Setmarklen}{setmarklen} +\itemket{Usage}Setmarklen(real number) +\itemket{Description}Generic function to set the length of tickmarks on the axsis. +\itemket{Details}Set the length of tickmarks on the axsis when we use the functions \hyperlink{htickmark}{Htickmark()} and Vtickmark().\\ +\end{cmd} + +%-------------Setorigin------------------------------- +\begin{cmd}{Setorigin}{setorigin} +\itemket{Usage}Setorigin(coordinate) +\itemket{Description}Generic function to set or transtate the coordinate of apparent origin. +\itemket{Examples}\mbox{} + +\verb|Setorigin([3,2]);|\\ +if A is identification name of some point, +\verb|Setorigin(A);|\\ +\itemket{Remark} Coordinate system is not changed as the following examples.\\ +\itemket{Examples}\mbox{} + +The coordinate of apparent origin is $(3,2)$ but we use the original coordinate system in the script.\\ +\verb| Setorigin([3,2]);|\\ +\verb| Listplot([A,B,C,A]);|\\ +\verb| Ptsize(3);|\\ +\verb| Drawpoint([1,1]);|\\ +\verb| Letter([[1,1],"s2","P"]);|\\ + + Left figure is Euclidean view, right figure is the result of \TeX. + +\begin{center} +\includegraphics[bb=0 0 227 205 , width=4cm]{Fig/setorigin.pdf}\hspace{10mm}% +\input{Fig/setorigin} +\end{center} + +\end{cmd} + +%------------Setpen-------------------------------- +\begin{cmd}{Setpen}{setpen} +\itemket{Usage}Setpen(real number) +\itemket{Description}Generic function to set the thickness of lines. + +\end{cmd} + +%------------Setscaling-------------------------------- +\begin{cmd}{Setscaling}{setscaling} +\itemket{Usage}Setscaling(scale) +\itemket{Description}Generic function to set the scale of vertical direction. +Argument is real number or list. If it is a real number, vertical scaling. If the list [a, b], scaling a in the horizontal direction and b in the vertical direction. +\itemket{Examples}\mbox{} + +\verb|Setscaling(0.5);|\\ +\verb|Plotdata("1","-2*x^2+10*x","x");|\\ +\verb|p1=[5/2,0]; p2=[5/2,25/2]; p3=[0,25/2];|\\ +\verb|Listplot(``1'',[p1,p2,p3],["da"]);|\\ +\verb|Expr([[5,0],"s2w","5",p3,"w2","\frac{25}{2}",p1,"s4","\frac{5}{2}"]);| + +\begin{center} +\input{Fig/setscaling} +\end{center} +\end{cmd} + +%-----------Setunitlen--------------------------------- +\begin{cmd}{Setunitlen}{setunitlen} +\itemket{Usage}Setunitlen(scale); +\itemket{Description}Generic function to set the scale of unit length. (default is 1cm)\\ +It is recommended to put this function to the beginning of a script. +\itemket{Examples}\mbox{} + +\verb|Setunitlen("8mm");|\\ +\end{cmd} + +%--------------Setwindow------------------------------ +\begin{cmd}{Setwindow}{setwindow} +\itemket{Usage}Setwindow(range of x , range of y); +\itemket{Description}Generic function to set a output area on a Euclidean view. +\itemket{Details}A output area is normally specified by a rectangle with SW and NE as diagonal two vertices. (i.e range of x is [XMIN,XMAX] and range of y is [YMIN,YMAX]) By dragging these two vertices on a Euclidean view, we can change the output area. This command is used to set the window manually and fix it. +\itemket{Examples}\mbox{} + +\verb|Setwindow([-5,5],[-1,3]);| + +\vspace{\baselineskip} +\hspace{20mm}\includegraphics[bb=0.00 0.00 415.02 199.01,width=8cm]{Fig/setwindow.pdf} +\end{cmd} + + +%======== Commands for Drawing ============ +\subsection{Commands for Drawing} + +\subsubsection{Options of drawing command} + +\begin{cmd}{Options of drawing command}{options} + +\item Line type + +\begin{tabbing} +1234\=5678901234567\=\kill + \> "dr, n" \>solid line\\ + \> \> n : thickness\\ + \> "da(,m,n)" \>broken line \\ + \> \> m : length, n : gap \\ + \> \>m,n option are not draw Euclidean view and can be omitted.\\ + \> "id(,m,n)" \>broken line start gap.\\ + \> "do(,m,n)" \>dot line\\ + \> \>m : gap, n : thickness +\end{tabbing} + +\item Color + +\hspace{10mm}"Color=col" : col: RGB or CMYK or color name + +\item Num + +\hspace{10mm}"Num=n" : Number of divisions of plotting data + +\vspace{\baselineskip} +\hspace{5mm} Example + +\hspace{10mm} \verb|Plotdata("1","x^2","x",["Color=red","do,2,3","Num=100"]);| + +\item Output +\begin{tabbing} + 1234\=56789012345\=\kill + \> "notex" \>not output to \TeX.\\ + \> "nodisp" \>not output to \TeX and Euclidean view but make PD.\\ + \> "Size=n" \> size of point and thin of line\\ + \> "Num=n" \>Number of PD +\end{tabbing} + +\item Direction + +The direction is represented by e(east : right), w(west: left), n(north : upper), s(south:lower) and c(center). The distance from the specified position can also be given as a numerical value. For example, ''e2'' and ''e3'' are placed twice and three times of the slightly unit distance away from ''e'', respectively. + +\begin{center}\input{Fig/ewns} \end{center} + +\item Others + +In addition, there are options specific to each function. + +\end{cmd} + +%========= Point , line ====================== +\subsubsection{Point, line } + +%---------Pointdata----------------------------------- +\begin{cmd}{Pointdata}{pointdata} +\itemket{Usage}Pointdata(name, point list, options) +\itemket{Description}Generic function to make a point data. +\itemket{Detailse}Options are "Size=", "Color=", "notex/nodisp". +\itemket{Examples}\mbox{} + +\verb|Pointdata("1",[[1,2],[-2,3]]); | // make 2 points (1,2),(-2,3)\\ +\verb|Pointdata("2",[A,B]); | // A and B are draw by drawing tool.\\ +\verb|Pointdata("3",A,["size=4"]); | // size of point A is 4.\\ +\verb|Pointdata("4",[A,B],[0]); | // white circles\\ +\verb|Pointdata("5",[[3,4],[5,6]],["notex"]); | //not draw in the \TeX file.\\ +\verb|Pointdata("6",[[3,4],[5,6]],["nodisp"]);| //not draw \TeX file and Euclidean view.\\ + +Draw node of tree. + +\verb|Ptsize(3);|\\ +\verb|Pointdata("1",[[1,2],[3,4],[5,2]]);|\\ +\verb|Listplot("1",[[0,0],[1,2],[3,4],[5,2],[4,0]]);|\\ +\verb|Listplot("2",[[1,2],[2,0]]);|\\ +\verb|Listplot("3",[[5,2],[6,0]]);|\\ + +\hspace{20mm} \input{Fig/pointdata} + +\itemket{Remark} \hyperlink{mkpttable}{Comparative chart of drawing of points} + +\end{cmd} + +%---------Drwpt ----------------------------------- +\begin{cmd}{Drwpt}{drwpt} +\itemket{Usage}Drwpt(point, option) or Drawpoint(point, options) +\itemket{Description}Draw a point. +\itemket{Details} +The position of point is specified via its coordinate or the name of geometric object. +When the point is to be displayed not only on \TeX\ final output but also on the Euclidean view, you should generate geometric point on the screen. +Also \verb|Pointdata()| or \verb|Putpoint()| can be used. +When several points are to be generated, +the list of them should be given as the argument. +When 0 is input as the option, the point is displayed in a solid-white manner. +\itemket{Examples}\mbox{} + +Draw the points $(1,1)$ and $(4,3)$. + +\verb| Drwpt([[1,1],[4,3]]);|\\ + +After generating points A, B, and C on the Euclidean view, display their image on \TeX\ document. + +\verb| Drwpt([A,B,C]);|\\ + +The endpoint B of segment AB in a solid-white manner. + +\verb| Ptsize(5);|\\ +\verb| Listplot([A,B]);|\\ +\verb| Drawpoint(B,0);| +\begin{center} +\input{Fig/drawpoint} +\end{center} + +\itemket{Remark} \hyperlink{mkpttable}{Comparative chart of drawing of points} + +\end{cmd} + +%--------------Putpoint------------------------------ +\begin{cmd}{Putpoint}{putpoint} +\itemket{Usage}Putpoint(name of point, A, B); +\itemket{Description}Generic function to put a point. +\itemket{Details}Put a point at A. If there already exists a point at A, it is put at B. +\itemket{Examples}\mbox{} + +\verb|Putpoint("P",[1,1]); | // P is fixed point.\\ +\verb|Putpoint("P",[1,1],[P.x,P.y]); | // for a movable point. + +\itemket{Remark} \hyperlink{mkpttable}{Comparative chart of drawing of points} + +\end{cmd} + +%-------------Putintersect------------------------------- +\begin{cmd}{Putintersect}{putintersect} +\itemket{Usage}Putintersect(name of point, PD1 ,PD2, [Number] ) +\itemket{Description}Generic function to make a intersection point of two curves. +\itemket{Details}PD1 and PD2 are plotting data names of two curves. Only one intersection point exists inside the drawing range, we have the point. If there exist many intersection points inside the drawing range then we have the list of coordinates for the points and the message:"Choose point number" on the console. The "Number" argument is this point number. We have to use the function Pointdata() when we need the figure of points in the output \TeX file. +\itemket{Examples}\mbox{} + +In the following example We have three intersection points for a cubic curve and a line. + +\begin{layer}{150}{0} +\putnotese{90}{5}{\input{Fig/putintersect}} +\end{layer} + +\verb|Plotdata("1","x^3-4*x","x",["Num=200"]);|\\ +\verb|Plotdata("2","1/2*x+1","x");|\\ +\verb|Putintersect("P","gr1","gr2",1);|\\ +\verb|Putintersect("Q","gr1","gr2",2);|\\ +\verb|Putintersect("R","gr1","gr2",3);|\\ +\verb|Pointdata("1",[P,Q,R],["size=4"]);| + +If there exist no such points, we have the message:"No intersect point" on the console. + +\end{cmd} + +%-------------PutonCurve------------------------------- +\begin{cmd}{PutonCurve}{putoncurve} +\itemket{Usage}PutonCurve(name of point, PD, options); +\itemket{Description}Generic function to put a point on the curve. +\itemket{Details}Put a point on the curve of PD. +\itemket{Examples}\mbox{} + +\verb|Paramplot("1","[2*cos(t)^3,2*sin(t)^3]","t=[0,2*pi]");|\\ +\verb|PutonCurve("P","gp1",[-1,1]);|\\ +This Point P on the asteroid can be move along the curve on the Euclidean view. + + \begin{center} \input{Fig/putoncurve.tex} \end{center} +\end{cmd} + +%------------PutonLine-------------------------------- +\begin{cmd}{PutonLine}{putonline} +\itemket{Usage}PutonLine(name of point, A, B); +\itemket{Description}Generic function to put a point on the line. +\itemket{Details}Put a point on the straight line through the two points A and B. +\itemket{Examples}\mbox{} + +\verb|PutonLine("P",A,B);| +\end{cmd} + +%--------------PutonSeg------------------------------ +\begin{cmd}{PutonSeg}{putonseg} +\itemket{Usage}PutonSeg(name of point, A, B); +\itemket{Description}Generic function to put a point on the segment. +\itemket{Details}Put a point on the line segment AB. +\itemket{Examples}\mbox{} + +\verb|PutonSeg("P",A,B);| +\end{cmd} + + +%-------------Reflectpoint------------------------------- +\begin{cmd}{Reflectpoint}{reflectpoint} +\item[Usage]Reflectpoint(a point, center or axis of symmetry); +\itemket{Description}Generic function do return the reflect point. +\itemket{Examples}\mbox{} + +\verb|C.xy=Reflectpoint(A,B);|\\ +\verb|D.xy=Reflectpoint(A,[[2,3]]);|\\ +\verb|E.xy=Reflectpoint([-1,1],[[1,0]]);|\\ +\verb|F.xy=Reflectpoint(A,[C,E]);|\\ +\verb|Lineplot([C,E],["do"]);| + +\begin{center} +\input{Fig/reflectpoint} +\end{center} +\end{cmd} + +%-----------Rotatepoint--------------------------------- +\begin{cmd}{Rotatepoint}{rotatepoint} +\itemket{Usage}Rotatepoint(point, angle(degree), center); +\itemket{Description}Generic function to rotate a point. +\itemket{Examples}\mbox{} + +\verb|C.xy=Rotatepoint(A,2*pi/3,B);|\\ +\verb|D.xy=Rotatepoint((5,2),pi/3,B);|\\ +\verb|E.xy=Rotatepoint([3,0],-pi/4,A);| + +\begin{center} +\input{Fig/rotatepoint} +\end{center} +\end{cmd} + +%-----------Scalepoint--------------------------------- +\begin{cmd}{Scalepoint}{scalepoint} +\itemket{Usage}Scalepoint(point, scale, center): +\itemket{Description}Generic function to scale a point. +\itemket{Examples}\mbox{} + +\verb| D.xy=Scalepoint(A,[3,2],[0,0]);|\\ +\verb| E.xy=Scalepoint(A,[3,2],B);|\\ +\verb| F.xy=Scalepoint(A,C.xy,[0,0]);|\\ +\verb| Arrowdata("1",[[0,0],C]);|\\ +\verb| Pointdata("1",[A,B,C,D,E,F],["size=2"]);|\\ +\verb| Letter([A,"e2","A("+A.x+","+A.y+")"]);|\\ +\verb| Letter([B,"e2","B("+B.x+","+B.y+")"]);|\\ +\verb| Letter([C,"e2","C("+C.x+","+C.y+")"]);|\\ +\verb| Letter([D,"e2","D("+D.x+","+D.y+")"]);|\\ +\verb| Letter([E,"e2","E("+E.x+","+E.y+")"]);|\\ +\verb| Letter([F,"e2","F("+F.x+","+F.y+")"]);|\\ + +\begin{center} +\input{Fig/scalepoint} +\end{center} +\end{cmd} + +%-------------Translatepoint------------------------------- +\begin{cmd}{Translatepoint}{translatepoint} +\itemket{Usage}Translatepoint(point, vector); +\itemket{Description}Generic function to translate a point. +\itemket{Examples}\mbox{} + +\verb|C.xy=Translatepoint(A,[2,3]);|\\ +\verb|D.xy=Translatepoint(A,B.xy);| + +\begin{center} +\input{Fig/translatepoint} +\end{center} +\end{cmd} + +%------------Arrowdata-------------------------------- +\begin{cmd}{Arrowdata}{arrow data} +\itemket{Usage}Arrowdata(name,[starting point, ending point] , options) +\itemket{Description}draw an arrow line between two points. + +Options : arrowhead size, arrowhead angle,position,line type,line color.\\ +All options do not always reflect on Euclidean view. +\itemket{Examples}\mbox{} + +\verb|Arrowdata([A,B]);|\\ +\verb|Arrowdata("1",[[2,0],[4,3]],[1,45,0.5]); | //(2,0) to (4,3) , angle : 45$^\circ$\\ +\verb|Arrowdata([C,D],[2,1,1,"dr,2"]);|\\ +\verb|Arrowdata([E,F],["da,0.5"]);|\\ +\verb|Arrowdata([G,H],[2,1,"do,2,3","Color=[1,0,0]"]);| \\% + +\begin{center} +\input{Fig/arrowdata} +\end{center} +\end{cmd} + +%--------------Arrowhead------------------------------ +\begin{cmd}{Arrowhead}{arrowhead} +\itemket{Usage}Arrowhead(point, direction , options) , Arrowhead(point, PD, options) +\itemket{Description}draw an arrowhead with specified direction at a designated point.\\ +Options are: arrowhead size, arrowhead angle,position,shape,position.\\ +\itemket{Examples}\mbox{} + +\begin{layer}{150}{0} +\putnotese{0}{2}{When A is in the position} +\putnotese{0}{9}{as shown below.} +\putnotese{10}{18}{\input{Fig/ForRef-Arrowhead-1}} +\putnotese{60}{9}{(a) \tt Arrowhead(A,[-1,1]);} +\putnotese{60}{16}{(b) \tt Arrowhead([1,1],[-1,1],[2,60]);} +\putnotese{60}{23}{(c) \tt Arrowhead(A,[-1,1],[2,30,"b"]);} +\putnotese{60}{30}{(d) \tt Arrowhead([1,1],[-1,1],[2,20,"lc"]);} +\end{layer} + +\vspace{7mm} + +%\hspace{6mm} +\begin{layer}{150}{0} +\putnotese{17}{32}{(a)} +\putnotese{47}{32}{(b)} +\putnotese{77}{32}{(c)} +\putnotese{107}{32}{(d)} +\putnotese{15}{40}{\input{Fig/ForRef-Arrowhead-2}} +\putnotese{45}{40}{\input{Fig/ForRef-Arrowhead-3}} +\putnotese{75}{40}{\input{Fig/ForRef-Arrowhead-4}} +\putnotese{105}{40}{\input{Fig/ForRef-Arrowhead-5}} +\end{layer} + +\vspace{70mm} + +\vspace{50mm} + +\hspace{7mm} +\begin{layer}{150}{0} +\putnotese{-10}{0}{When D is on the curve crBC } +\putnotese{-10}{5}{as shown below.} +\putnotese{0}{7}{\input{Fig/ForRef-Arrowhead-6}} +\putnotese{16}{22}{crBC} +\putnotese{50}{0}{(e) \tt Arrowhead(D,"crBC");} +\putnotese{50}{7}{(f) \tt Arrowhead(D,"crBC",[2]);} +\putnotese{50}{14}{(g) \tt Arrowhead(D,"crBC",[2,30,"l"]);} +\putnotese{50}{21}{(h) \tt Arrowhead(D,"Invert(crBC)");} +\end{layer} + +\vspace{3mm} +\hspace{6mm} +\begin{layer}{150}{0} +\putnotese{12}{27}{(e)} +\putnotese{42}{27}{(f)} +\putnotese{72}{27}{(g)} +\putnotese{102}{27}{(h)} +\putnotese{10}{28}{\input{Fig/ForRef-Arrowhead-7}} +\putnotese{40}{28}{\input{Fig/ForRef-Arrowhead-8}} +\putnotese{70}{28}{\input{Fig/ForRef-Arrowhead-9}} +\putnotese{100}{28}{\input{Fig/ForRef-Arrowhead-10}} +\end{layer} +\vspace*{6cm} +\end{cmd} + + +%---------Lineplot----------------------------------- +\begin{cmd}{Lineplot}{lineplot} +\itemket{Usage}Lineplot(name, [A, B], options) +\itemket{Description}Draw the straight line through the two points A, B. +\itemket{Details} +The list of two points is given by the coordinates or the geometric elements. \\ +If the list of points is given by geometric elements, "name" can be omitted. \\ +options : "+" means drawing a half straight line. \\ +Both the line type and "+" can be specified as a list. \\ +\item[Example]\mbox{} + +Draw a straight line connecting the coordinates. + +\hspace{5mm}\verb|Lineplot("1",[[0,0],[1,2]]);| + +Draw the two points A, B in the Cinderella main screen and draw a straight line AB. + +\hspace{5mm}\verb|Lineplot([A,B]);| + +Some examples of options. + +\hspace{5mm}\verb|Lineplot([A,B],["dr,0.5","+"]);| // Draw a half line with A as the end point. + +\hspace{5mm}\verb|Lineplot([C,D],["dr,2"]); | // Draw the straight line CD with double thickness. + +\hspace{5mm}\verb|Lineplot([E,F],["da"]); | // Draw the straight line EF as a broken line. + +\hspace{5mm}\verb|Lineplot([G,H],["do"]); | // Draw the straight line GH as a dotted line. + +The results are shown in order from the top left of the next figure. + +\begin{center} +\input{Fig/lineplot} +\end{center} +\end{cmd} + +%-----------Listplot--------------------------------- +\begin{cmd}{Listplot}{listplot} +\itemket{Usage}Listplot(name, a list of points, options) +\itemket{Description}Connect points by line segments. +\itemket{Details} +The list of two points is given by the names of the coordinates or the geometric elements. \\ +If the list of points is given by geometric element names, the name of the plotting data can be omitted. \\ +\item[Example1]\mbox{} +Line style + +\hspace{10mm} \verb|Listplot([A,B]);| + +\hspace{10mm} \verb|Listplot([C,D],["dr,2"]); | + +\hspace{10mm} \verb|Listplot([E,F],["da"]); | + +\hspace{10mm} \verb|Listplot([G,H],["da,3,1"]);| + +\hspace{10mm} \verb|Listplot([K,L],["da,1,3"]);| + +\hspace{10mm} \verb|Listplot([M,N],["do"]); | + +\hspace{10mm} \verb|Listplot([O,P],["do,3"]); | + +\hspace{10mm} \verb|Listplot([Q,R],["do,3,3"]);| + +\hspace{20mm} \includegraphics[bb=0.00 0.00 328.02 157.01,width=8cm]{Fig/listplot3view.pdf} + +\hspace{20mm} \input{Fig/listplot3} + +\item[Example2]\mbox{} +Draw a triangle. \\ +Draw the triangle ABC or simply creating 3 points A, B, C with the Euclidean view. + +\hspace{10mm}\verb|Addax(0);| + +\hspace{10mm}\verb|Listplot([A,B,C,A]);| + +\hspace{20mm}\input{Fig/listplot1} + +The position of the points can be specified by coordinates. +In this case "name" is necessary. + +\hspace{10mm}\verb|Listplot("1",[[0,0],[2,0],[1,2],[0,0]]);| + +\item[Example3]\mbox{} +Expansion of finite Fourier series + +\hspace{20mm}$\displaystyle{\cfrac{\pi}{2}+\sum_{n=0}^{30} \cfrac{1-(-1)^n}{n}\sin nx}$ + +The plotting data is a list of the coordinates of points. Therefore, define the function in Cindyscript as follows, create plotting data \verb|pd| and pass it as argument. \\ + +\verb|f(x):=(|\\ +\verb| s=pi/2;|\\ +\verb# repeat(30,n,s=s+(1-(-1)^n)/n*sin(n*x));#\\ +\verb|);|\\ +\verb|pd=apply(0..200,t,|\\ +\verb| x=-2*pi+t*4*pi/200;|\\ +\verb| [x,f(x)];|\\ +\verb|);|\\ +\verb|Listplot("1",pd);|\\ +\verb|Expr([[-2*pi,-0.5],"s","-2\pi",[-pi,-0.5],"s","-\pi",[pi,-0.5],"s",|\\ +\verb| "\pi",[2*pi,-0.5],"s","2\pi",[0,pi],"w2","\pi"]);|\\ +\begin{center} +\input{Fig/fourier} +\end{center} +There is a limit on the length of the list, so it is impossible to use a long list or to use it many times. +For example, in the Shellpinski gasket using Turtle Graphics, the next size is possible, but in the growth model of plants there are many branches so it can not be a big figure. +We devise a script and divide it into lists of about 200. \\ +\begin{center} +\input{Fig/listplot2} +\end{center} +\end{cmd} + +%--------------Mksegments------------------------------ +\begin{cmd}{Mksegments}{mksegments} +\itemket{Usage}Mksegments() +\itemket{Description}Create plotting data of all geometric segments. +\itemket{Details} +All the line segments drawn by the "Add line segment" tool in the Euclidean view are used as plotting data as they are. +For example, if the line segment AB is created, plotting data \verb|sgAB| is created. +After that, if you change the identification name of point B (for example to Q) in the inspector of the Euclidean view, the plotting data name is also changed. +Even if the line segmen has already been drawn, it can be changed. \\ + +\item[Example]\mbox{} +Examples of geometric progression\\ +Draw a figure of a geometric progression that makes triangles by connecting the midpoints of each edge of a triangle one after another. \\ +First draw the triangle ABC with the "Add line segment" tool in the Euclidean view. \\ +Take the midpoint of each edge with the "Add midpoint" tool in the Euclidean view and connect the midpoints with the "Add line segment" tool in the Euclidean view. \\ +Repeat this process. +If you write \verb|Mksegments();|, you can obtain the data of the figure at the completion of drawing, without writing \verb|Listplot ([A, B, C]);|. \\ +\begin{center} +\includegraphics[bb=0.00 0.00 438.00 327.00,width=5cm]{Fig/gpro01.pdf}\hspace{10mm}\input{Fig/gpro02} +\end{center} +\end{cmd} + +%---------Framedata----------------------------------- + +\begin{cmd}{Framedata}{framedata} +\itemket{Usage}Framedata(name,expr,options) +\itemket{Description}Generic function to draw a rectangle. +\itemket{Details} + +expr type1 : [center,lx,ly] : lx and ly are a half of the horizontal and vertical length. + +expr type2 : [p1, p2] : if p1 and p2 are name of point, 1st argument can be omitted. + +options : usual options and "center"/"corner" (type2). + +\hspace{10mm} If "center", p1 is center, p2 is apex of rectangle. (Default) + +\hspace{10mm} If "corner", p1 and p2 are diagonal point of rectangle. + +\itemket{Examples}\mbox{} + +\verb|Framedata("1"); | // same as \verb|Framedata([SW,NE],["corner"]);|\\ +\verb|Framedata("2",[[0,0],2,2]);|\\ +\verb|Framedata("3",[A,1.5,1.2]); | // left figure\\ +\verb|Framedata([B,C]); | // center figure\\ +\verb|Framedata([D,E],["corner"]); | // right figure +\begin{center}\includegraphics[bb=0.00 0.00 348.15 106.16,width=12cm]{Fig/Framedata.pdf}\end{center} +\itemket{Reference} \hyperlink{ovaldata}{Ovaldata}. +\end{cmd} + + +%------------Polygonplot-------------------------------- +\begin{cmd}{Polygonplot}{polygonplot} +\itemket{Usage}Polygonplot(name, point list, integer, options) +\itemket{Description}Generic function to draw a polygon inscribed inside the circle. +\itemket{Details}If the point list is [A,B] then the center is A and the radius is AB for the circle. Corresponding circle is not drawing. Two points A,B allowed to be coordinates. + +option : If A and B are geometric point , make geometric apex by "Geo=y". + +\itemket{Examples}\mbox{} + +\verb| Addax(0); |\\ +\verb| Polygonplot("1",[[-4,1],[-4,3]],7); |\\ +\verb| Polygonplot("2",[A,B],7); |\\ +\verb| Polygonplot("3",[C,D],7,["Geo=y"]); |\\ + +\hspace{10mm}\includegraphics[bb=0.00 0.00 541.03 175.01,width=10cm]{Fig/polygonplot2.pdf} + +\hspace{10mm}\input{Fig/polygonplot1} + +We can draw the regular polygon whose one side is the line segment AB. + +\verb| n=5;|\\ +\verb| pti=[complex(A),complex(B)];|\\ +\verb| th=2*pi/n;|\\ +\verb| repeat(n-2,s,|\\ +\verb| z1=pti_s;|\\ +\verb| z2=pti_(s+1);|\\ +\verb| z=z2+(z2-z1)*(cos(th)+i*sin(th));|\\ +\verb| pti=append(pti,z);|\\ +\verb| );|\\ +\verb| pt=apply(pti,gauss(#));|\\ +\verb| pt=append(pt,A.xy);|\\ +\verb| Listplot("1",pt);|\\ + +\verb|pti| is the list of complex numbers correspond to each vertex, +\verb|pt| is the list of coordinates of vertexes. + +\end{cmd} + +%=============- Curves line ============ +\subsubsection{Curved line} + +%----------Bezier---------------------------------- +\begin{cmd}{Bezier}{bezier} +\itemket{Usage}Bezier(name,nodes of curve, control points, options) +\itemket{Description}Draw a bezier curve.\\ +For each interval, control points are given in two lists for 3rd-order and one list for 2nd-order Bezier curve.\\ +You can specify the number of division among nodes (default value is 10). + +\itemket{Examples}\mbox{} + +\begin{layer}{150}{0} +\putnotese{50}{15}{bz1} +\putnotese{58}{-10}{\input{Fig/checkbe1}} +\end{layer} + +2nd-order Bezier curve\\ +\verb|Bezier("1",[A,B],[C]);|\\ + +\vspace{15mm} + +\begin{layer}{150}{0} +\putnotese{63}{17}{bzc} +\putnotese{70}{-5}{\input{Fig/checkbe2}} +\end{layer} + +3rd-order Bezier curve\\ +\verb|Bezier("c",[A,B],[C,D]);|\\ + +\vspace{15mm} + +\begin{layer}{150}{0} +\putnotese{65}{20}{bz3} +\putnotese{75}{-5}{\input{Fig/checkbe3}} +\end{layer} + +Connecting two curves,\\ +\verb|Bezier("3",[A,B,C],[[D],[E,F]]);|\\ + +\vspace{20mm} + +\begin{layer}{150}{0} +\putnotese{70}{20}{bzS} +\putnotese{80}{10}{\input{Fig/checkbe4}} +\end{layer} + +Taking D,B,E on a straight line, it connects smoothly.\\ +\verb|Bezier("S",[A,B,C],[[D],[E,F]]);|\\ + +\vspace{25mm} + +\vspace{50mm} + +\begin{layer}{150}{0} +\putnotese{20}{27}{bzname} +\putnotese{25}{10}{\input{Fig/checkbe7}} +\end{layer} + +\verb|Bezier("name",[A,B,C,D],[E,F,G,H,K,L] );|\\ + +\vspace{30mm} + +\begin{layer}{150}{0} +\putnotese{35}{25}{bz1a} +\putnotese{50}{10}{\input{Fig/checkbe5}} +\end{layer} + +\verb|Bezier("1a",[A,B,C],[[D],[E,F]],["Num=3"]);|\\ + +\vspace{30mm} + +\begin{layer}{150}{0} +\putnotese{35}{20}{bzd5e} +\putnotese{50}{10}{\input{Fig/checkbe6}} +\end{layer} + +\verb|Bezier("d5e",[A,B,C],[[D],[E,F]],["Num=200","da"]);|\\ + +\vspace{40mm} + +\begin{layer}{150}{0} +\putnotese{20}{30}{bz1} +\putnotese{20}{13}{\input{Fig/checkbe8}} +\end{layer} + +\verb|Bezier("1",[A,B,C,D],[E,F,G,H,K,L],["Num=[2,3,4]"]);|\\ +\vspace{30mm} +\end{cmd} + +%------------Beziersmooth-------------------------------- +\begin{cmd}{Beziersmooth}{beziersmooth} +\itemket{Usage}Beziersmooth(name, a list of nodes, options); +\itemket{Description}Generic function to draw a smooth B\'ezier curve. +\itemket{Details}Control points are added to keep smoothness. +\itemket{Examples}\mbox{} + +\verb|Beziersmooth("1",[A,B,C,D]);| + +\begin{center} +\input{Fig/checksm1} +\end{center} + +\itemket{Remark}Control points are movable. + +\begin{center} +\input{Fig/checksm2} +\end{center} +\end{cmd} + +%-----------Beziersym--------------------------------- +\begin{cmd}{Beziersym}{beziersym} +\itemket{Usage}Beziersym(name, a list of nodes, options); +\itemket{Description}Generic function to draw a smooth B\'ezier curve. +\itemket{Details}Control points are added to be symmetric with respect to each node. +\itemket{Examples}\mbox{} + +\begin{center} +\input{Fig/checksy1} +\end{center} + +\itemket{Remark}Some control points are movable. + +\begin{center} +\input{Fig/checksy2} +\end{center} +\end{cmd} + +%------------Mkbeziercrv-------------------------------- +\begin{cmd}{Mkbeziercrv}{mkbeziercrv} +\itemket{Usage}Mkbeziercrv(name, [nodes, control points], options) +\itemket{Description}Draw some B\'ezier curves. +\itemket{Details} +In the case of a single B\'ezier curve, \verb|[ ]| outside the list can be omitted. \\ +Mkbeziercrv(name, [nodes, control points], options) is same as Bezier(name, [nodes, control points], options). \\ +\verb|Mkbeziercrv("n",[[A,B,C],[[D],[E,F]]])| is same as \verb|Bezier("n",[A,B,C],|\\ +\verb|[[D],[E,F]])|. +The name of the plotting data is ''bz''. +\item[Example1]\mbox{} + +\verb|Mkbeziercrv("5",[[[A,B,C],[[D],[E,F]]],[[G,H,K,L],[[M],[N,O],[P]]]]);| +\begin{center} +\input{Fig/checkmc1} +\end{center} + +\end{cmd} + +%---------Mkbezierptcrv----------------------------------- +\begin{cmd}{Mkbezierptcrv}{mkbezierptcrv} +\itemket{Usage}Mkbezierptcrv(a list of points, options) +\itemket{Description}Draw a B\'ezier curve. +\itemket{Details} +Arrange the control points automatically. +After that, move the nodes and the control points and correct the B\'ezier curve to what you want to draw. \\ +In the case of multiple curves, \verb|[ ptlist1, ptlist2.... ]|\\ +The name is automatically attached in order from A. \\ +The options are as follows:\\ +"Deg=...”\hspace{5mm}You can specify the degree (Default is 3rd order). \\ +"Num=..."\hspace{5mm}You can specify the partition number ($\mathrm{the\ partition\ point\ number}-1$) for each section (Default is 10). \\ +\item[Example]\mbox{} + +\verb|Mkbezierptcrv([A,B,C]);| + +\hspace{20mm}\input{Fig/checkb8} + +After that, move the nodes and the control points and correct the B\'ezier curve to what you want to draw. \\ + +\hspace{20mm}\input{Fig/checkb11} + + +\verb|Mkbezierptcrv([A,B,C],["Deg=2"]);|\\ +If Deg = 2, it is the B\'ezier curve of 2nd order. \\ +One control point can be set for each section. \\ + +\hspace{20mm}\input{Fig/checkb9} + +In the case of multiple curves, \verb|[ ptlist1, ptlist2.... ]|\\ +\verb|Mkbezierptcrv([[A,B,C],[D,E,F,G]]);|\\ + +\hspace{10mm}\input{Fig/checkb10} + +\end{cmd} + + +%--------------Bspline------------------------------ +\begin{cmd}{Bspline}{bspline} +\itemket{Usage}Bspline(name ,list of control points, options) +\itemket{Description}Draw second degree B-spline curve. +\itemket{Details}Though not displayed, nodal points are calculated automatically. +\itemket{Examples}\mbox{} + +\verb|Bspline("1",[A,B,C,D,E]);|($=$\verb|Bezier("1",[A,(B+C)/2,(C+D)/2,E],[B,C,D]);|)\\ +The name becomes \verb|bzb1| instead of \verb|bz1|. +Endpoints can be moved instead of control points. +\begin{center} +\input{Fig/checkbs1} +\end{center} + +\verb|Bspline("1",[A,B,C,D,A]);|\\ +The generated curve becomes closed when the first component of the list +is the same as the last one. +\begin{center} +\input{Fig/checkbs2} +\end{center} +\end{cmd} + +%-------CRspline------------------------------------- +\begin{cmd}{CRspline}{crspline} +\itemket{Usage}CRspline(name, list of node points, options) +\itemket{Description}Draw single Catmull-Rom spline curve. +\itemket{Details} +Only node points are free and control points cannot be moved.\\ +Extra options is :\\ +\verb|"size->"| specifies the thickness of line on the Euclidean view. \\ +\itemket{Examples}\mbox{} + +\verb|CRspline("1",[A,B,C,D]);| +\begin{center} +\input{Fig/checkCR} +\end{center} +\end{cmd} + +%----------Ospline---------------------------------- +\begin{cmd}{Ospline}{ospline} + +\itemket{Usage}Ospline(name, a list of control points, options); +\itemket{Description}Generic function to draw a spline curve of Oshima. +%\itemket{Details}If the beginning and end of the list are the same, it is a closed curve. +\itemket{Examples} \mbox{} + +\verb| Ospline("1",[A,B,C,D,E]);| \\ +\verb| Ospline("1",[A,B,C,D,A]);| + + \hspace{20mm} \input{Fig/ospline1} \hspace{10mm} \input{Fig/ospline2} + +\itemket{Reference} \hyperlink{bspline}{Bspline}. +\end{cmd} + +%---------Circledata----------------------------------- +\begin{cmd}{Circledata}{circledata} +\itemket{Usage}Circledata(name, list, options) +\itemket{Description}Draw a circle or polygon. +\itemket{Details} +The list consists of the central point and some point on the circle. +It is also permitted that three points on the circle are given in the list. +The name can be omitted when the central point and a point on the circle +are given with the names of their geometric components.\\ +Options :\\ +\verb|"Rng=[|$\theta_1,\theta_2$\verb|]"| specifies the range of argument +in which the circle is drawn.\\ +\verb|"Num=number of division"| specifies the number of dividing points +used to draw circle. +When this number is small, the corresponding polygon is drawn. + +\itemket{Examples}\mbox{} + +The circle with center \verb|[0,0]| or A and radius 2 ( draw A by drawing tool) + +\verb| Circledata("1",[[0,0],[2,0]]);|\\ +\verb| Circledata("1",[A,A+[2,0]]);|\\ + +The circle with center A and radius AB + +\verb| Circledata([A,B]);|\\ + +The circle which passes through three points A, B, and C + +\verb| Circledata([A,B,C]);|\\ + +When we use \verb|Circledata([A,B,C])|, +the central point of the circle can be drawn by the following command. + +\verb|Pointdata("1",[crABCcenter]);|\\ + +When we add options \verb|"dr,2"|, \verb|"da"|, \verb|"do"|, +the following figures are generated respectively. +\begin{center} +\input{Fig/circledata1} +\end{center} + +The circular arc with center A, radius AB, +and the range of argument $\displaystyle \left[0,\frac{\pi}{3}\right]$ + +\verb|Circledata([A,B],["Rng=[0,pi/3]"]);|\\ + +The sector. + +Draw A, B , C by drawing tool. + +\verb| th=arctan2(B-A);| \\ +\verb| C.xy=Rotatepoint(B,pi/3,A);|\\ +\verb| Circledata([A,B],[Assign("Rng=[th,th+pi/3]","th",th)]);|\\ +\verb| Listplot([B,A,C]);|\\ +\verb| Letter([A,"s","A",B,"e","B",C,"nw","C"]);| + +\begin{center} +\includegraphics[bb=0.00 0.00 180.01 177.01,width=4cm"] {Fig/circledata3.pdf}\hspace{12mm} \input{Fig/circledata2} +\end{center} + +The circle with center A and radius AB, together with the inscribed equilateral hexagon (left figure) + +\verb| Circledata("1",[A,B]);|\\ +\verb| Circledata("2",[A,B],["Num=6"]);|\\ + +The position of vertices can be changed via the option \verb|"Rng="|. (right figure) + +\verb| Circledata("2",[A,B],["Num=6","Rng=[pi/6,13/6*pi]"]);| + +\begin{center} +\input{Fig/circledata4} \hspace{20mm}\input{Fig/circledata5} +\end{center} + +\end{cmd} + +%-------------Mkcircles------------------------------- +\begin{cmd}{Mkcircles}{mkcircles} +\itemket{Usage}Mkcircles() +\itemket{Description}Create plotting data of all geometric circles. +\itemket{Details} +All circles drawn by the "add circle" tool (any one of three types) in the Euclidean view are used as plotting data as they are. +For example, if you create a circle with the center A and the point on the circumference as B, the plotting data \verb|crAB| is created. +After that, if you change the identification name of point B (for example to Q) in the inspector of the Euclidean view, the geometric point name is also changed. +Even if the circle has already been drawn, it can be changed. \\ +\end{cmd} + +%---------Ellipseplot----------------------------------- +\begin{cmd}{Ellipseplot}{ellipseplot} +\itemket{Usage}Ellipseplot(name, [F1,F2,A/a], range, options) +\itemket{Description}Generic function to draw ellipse. +%\itemket{Details} +\itemket{Examples}\mbox{} + +F1,F2 are focus points, A is a point on the ellipse, a is the length F1-A-F2.\\ +Default of the range is [-5,5]. +\itemket{Examples}\mbox{} + +\verb|Ellipseplot("1",[A,B,4]); | //sum of distance from Focus is 4.\\ +\verb|Ellipseplot("1",[A,B,C],"[0,pi]");| //half of ellipse. + +\vspace{\baselineskip} +Now draw tangent and normal. Draw figures by draw tool on Euclidean view. Put point D on tangent and E on normal. + +\verb| Ellipseplot("1",[A,B,C]);|\\ +\verb| Lineplot([C,D]);|\\ +\verb| Lineplot([C,E]);|\\ +\verb| Arrowdata([A,C]);|\\ +\verb| Arrowdata([C,B]);|\\ +\verb| Anglemark([A,C,B]);|\\ +\verb| Expr([A,"s2","F_1",B,"s2","F_2"]);| + +\begin{center} +\includegraphics[bb=0 0 272.01 240.01, width=5cm]{Fig/ellipsecindy.pdf}\hspace{10mm} +\input{Fig/ellipseplot1} +\end{center} + +Now draw point D and E on ellipse. + +\verb| Ellipseplot("1",[A,B,C]);|\\ +\verb| Listplot([A,C,B]);|\\ +\verb| Listplot([A,D,B]);|\\ +\verb| Listplot([A,E,B]);|\\ +\verb| Expr([A,"s2","F_1",B,"s2","F_2"]);| + +\begin{center} +\input{Fig/ellipseplot2} +\end{center} +\end{cmd} + +%----------Hyperbolaplot---------------------------------- +\begin{cmd}{Hyperbolaplot}{hyperbolaplot} +\itemket{Usage}Hyperbolaplot(name,[F1,F2,A], range, options) +\itemket{Description}Generic function to draw a hyperbola. +\itemket{Details}Option is as usual except "Asy=line style".This option is for drawing asymptotes. +\itemket{Reference} \hyperlink{ellipseplot}{Ellipseplot} and \hyperlink{parabolaplot}{Parabolaplot}. +\itemket{Examples}\mbox{} + +\verb|Hyperbolaplot("1",[A,B,C]);|\\ +\verb|Hyperbolaplot("1",[A,B,2]);|\\ +\verb|Hyperbolaplot("1",[A,B,C],["Asy=do"]);| + +\begin{center} +\input{Fig/hyper1} +\end{center} +\end{cmd} + +%--------Parabolaplot------------------------------------ +\begin{cmd}{Parabolaplot}{parabolaplot} + +\itemket{Usage}Parabolaplot(name, [A, B, C], range, options); +\itemket{Description}Generic function to draws a parabola.% determined by the focus and the directrix indicated by the list [A, B, C] of points. +\itemket{Details}A is the focus point, BC is the directrix. +Default of the range is $[-5, 5]$. + +\itemket{Examples} \mbox{} + +\verb|Parabolaplot("1",[A,B,C]); | + +\verb|Parabolaplot("1",[A,B,C],"[-4,4]"); | //range is [-4,4] + +\verb|Parabolaplot("1",[[0,1],[-1,-1],[1,-1]]);| // coordinate + +\vspace{\baselineskip} +Area enclosed by parabola and tangent + +\verb|Parabolaplot("1",[A,B,C]);|\\ +\verb|Putoncurve("D","gr1para");|\\ +\verb|Putoncurve("E","gr1para");|\\ +\verb|Tangentplot("1","gr1para","x="+D.x);|\\ +\verb|Tangentplot("2","gr1para","x="+E.x);|\\ +\verb|pts=Intersectcurves("lntn1","lntn2");|\\ +\verb|Listplot("1",[E,pts_1,D]);|\\ +\verb|Hatchdata("1",["ii"],[["gr1para","s"],["sg1","n"]]);| + +\begin{center} +\input{Fig/parabolaplotE} +\end{center} +\end{cmd} + +%-----------Ovaldata--------------------------------- +\begin{cmd}{Ovaldata}{ovaldata} + +\itemket{Usage}Ovaldata(name, [A, B], options); +\itemket{Description}Generic function to draw a rectangle with rounded corners. +\itemket{Details}A is the center, B is a diagonal point. + +option : ratio of the roundness ( default is 0.2) . + +\itemket{Examples} \mbox{} + +\verb| Ovaldata("1", [A,B]);| \\ +\verb| Ovaldata("2", [C,D],[0]);| \\ +\verb| Ovaldata("3", [E,F],[1,"dr,3"]);| \\ +\verb| Ovaldata("4", [G,H],[1.5,"da"]);| + +\begin{center} +\input{Fig/ovaldata} +\end{center} +\end{cmd} + +%=========== Graph of function ============ +\subsubsection{Graph of function} + +%--------Plotdata------------------------------------ +\begin{cmd}{Plotdata}{plotdata} +\itemket{Usage}Plotdata(name, function, variable and range, options) +\itemket{Description}Generic function to draw the graph of function. +\itemket{Details} +Options : next options and usual options. + +\hspace{20mm} "Dis=real number": discontinuity + +\hspace{20mm} "Exc=list of real numbers": exclusion points + +\hspace{20mm} "Exc=function": exclude the zero points of the function + +\itemket{Examples}\mbox{} + +\verb| Plotdata("1","x^2-2*x","x");|\\ + +\hspace{20mm} \input{Fig/plotdata1}\\ + +Draw in red. + +\verb| Plotdata("1","x^2-2*x","x",["Color=[1,0,0]"]);|\\ + +\verb| Plotdata("3","2*sin(2*x-pi/4)","x=[0,2*pi]");|\\ + +\hspace{20mm} \input{Fig/plotdata2}\\ + +\verb| Plotdata("1","sin(x)","x",["do"]);|\\ +\verb| Plotdata("2","sin(x)+1","x",["da"]);|\\ +\verb| Plotdata("3","sin(x)+2","x",["dr,2"]);|\\ +\verb| Plotdata("4","sin(x)+3","x");|\\ + +\hspace{20mm} \input{Fig/plotdata3}\\ + +Draw smoothly by "Num=n" option. + +Left figure: "Num=50"(default),\quad +Right figure: "Num=200"\\ + +\hspace{20mm}\input{Fig/plotdata4}\\ + +Draw discontinuity accurately by "Dis" option. + +\verb| Plotdata("1","tan(x)","x",["Num=200"]); | // left figure \\ +\verb| Plotdata("1","tan(x)","x",["Num=200","Dis=50"]); | // right figure \\ + +\hspace{20mm}\input{Fig/plotdatatan1}\hspace{20mm}\input{Fig/plotdatatan2} + +\vspace{\baselineskip} +Draw floor function. + +\verb| Plotdata("1","floor(x)","x",["Num=100","Dis=0.9"]); |\\ +\verb| Ptsize(3); |\\ +\verb| Drwxy(); |\\ +\verb| repeat(7,s,start -> -2, |\\ +\verb| Drwpt([s+1,s],0); |\\ +\verb| ); | + +\vspace{\baselineskip} +\hspace{40mm} \input{Fig/plotdata5}\\ + +Assign a value to the letter "b".\\ +\verb| repeat(50,t,|\\ +\verb| cb=t/5-5;|\\ +\verb| Plotdata(text(t),Assign("b*x-b^2","b",cb),"x");|\\ +\verb| );|\\ + +\hspace{40mm} \input{Fig/assign}\\ + +\end{cmd} + +%----------Implicitplot---------------------------------- +\begin{cmd}{Implicitplot}{implicitplot} +\itemket{Usage}Implicitplot(name,functionstring,range of x, range of y, options); +\itemket{Usage}Generic function to draw the graph of a implicit function. +\itemket{Examples}\mbox{} + +\verb| Implicitplot("1","x^2-x*y+2*y^2=4","x=[-3,3]","y=[-2,2]");| + +\begin{center} +\input{Fig/implicit1} +\end{center} + +\verb|Implicitplot("1","x^2+2*y^2=4","x=[-2,2]","y=[-2,2]");|\\ +\verb|Hatchdata("1",["i"],[["imp1"]]);| + +\begin{center} +\input{Fig/implicit} +\end{center} + +\end{cmd} + +%-------Deqplot------------------------------------- +\begin{cmd}{Deqplot}{deqplot} +\itemket{Usage}Deqplot(name, expression, names of variations, options) +\itemket{Description}Draw the solution curve of a differential equation. +\itemket{Details} +The differential equation and its initial conditions should be specified as arguments. +\itemket{Examples}\mbox{} + +The solution curve of the equation $y''=-y$ with initial conditions $y(0)=1,y'(0)=0$ + +\verb|Deqplot("1","y``=-y","x",0, [1,0]);|\\ +\begin{center} +\input{Fig/deqplot1} +\end{center} +\itemket{Remark} Derivative symbol \verb|y`| is a backquate, not a single quote.\\ + +The solution curve of the equation $y'=y*(1-y)$ with initial condition $y(0)=0.5$ + +\verb|Deqplot("2","y`=y*(1-y)","x",0, 0.5,["Num=100"]);|\\ +\begin{center} +\input{Fig/deqplot2} +\end{center} + +The solution curve of the equation $[x,y]'=[x(1-y),0.3y(x-1)]$ of variable $t$ +with initial conditions $x(0)=1, y(0)=0.5$ + +\verb|Deqplot("3","[x,y]`=[x*(1-y),0.3*y*(x-1)]","t=[0,20]",[1,0.5],["Num=200"]);|\\ +\begin{center} +\input{Fig/deqplot3} +\end{center} +\end{cmd} + +%----------Paramplot---------------------------------- +\begin{cmd}{Paramplot}{paramplot} + +\itemket{Usage}Paramaplot(name, expression, variable and domain, options); +\itemket{Description}Generic function to draw a curve of parametric representation.% The head of the plotting data is gp. +%\itemket{Details} +\itemket{Examples} \mbox{} + +Draw a cycloid curve. + +\verb| Paramplot("1","[t-sin(t),1-cos(t)]","t=[0,2*pi]");|\\ + +\begin{center} +\input{Fig//paramplot1} +\end{center} + +Draw ellipses with options.\\ + +\verb| Paramplot("1","[2*cos(t)-5,sin(t)]","t=[0,2*pi]");| \\ +\verb| Paramplot("2","[2*cos(t),sin(t)]","t=[0,2*pi]",["dr,2"]);| \\ +\verb| Paramplot("3","[2*cos(t)+5,sin(t)]","t=[0,2*pi]",["da"]);| \\ +\verb| Paramplot("4","[2*cos(t)+10,sin(t)]","t=[0,2*pi]",["do"]);| + +\begin{center} +\input{Fig//paramplot2} +\end{center} +\end{cmd} + +%----------Polarplot---------------------------------- +\begin{cmd}{Polarplot}{polarplot} + +\itemket{Usage}Polarplot(name, expression, variable and domain, options); +\itemket{Description}This function draws a curve of polar equation. +%\itemket{Details} +\itemket{Examples} To draw a cardioid. + +\verb| Polarplot("1","2*(1+cos(t))","t=[0,2*pi]",["Num=200"]);|\\ + +\begin{center} +\input{Fig//cardioid1} +\end{center} + +\end{cmd} + +%------Periodfun-------------------------------------- +\begin{cmd}{Periodfun}{periodfun} +\itemket{Usage}Periodfun(defL,repeat,options) +\itemket{Description}Function to draw the graph of a periodic function. +\itemket{Details} +\verb|defL| is a list of fun(str),interval,division number.\\ +The options are "Con=n/do, Color=name'' for discontinuous parts. + +ex. "Con=do,Color=red" , " Con=n". Default is broken line and draw. + +Repeat count is a count number or a list of count numbers of left side and right side. + +The return value are a list of function in Maxima format and the period. +\itemket{Remark}The functions should be defined on the symmetrical interval [-a,a]. +\itemket{Examples} \mbox{} + +\verb| defL=["0",[-1,0],1,"1",[0,1],1];|\\ +\verb| Periodfun(defL, 2,["dr,2"]);|\\ +\verb| memori=apply(-5..5,x,[x,text(x)]);|\\ +\verb| memori=flatten(remove(memori,[[0,"0"]]));|\\ +\verb| Htickmark(memori);|\\ +\verb| Vtickmark([1,"1"]);| + +\hspace{20mm}\input{Fig/periodfun.tex} + +\vspace{\baselineskip} +\verb| defL=["0",[-1,0],1,"x^2",[0,1],50];|\\ +\verb| Periodfun(defL, 2, ["Con=n","dr,2"]);|\\ +\verb| memori=apply(-5..5,x,[x,text(x)]);|\\ +\verb| memori=flatten(remove(memori,[[0,"0"]]));|\\ +\verb| Htickmark(memori);|\\ +\verb| Vtickmark([1,"1"]);| + +\hspace{20mm}\input{Fig/periodfun2.tex} + +\end{cmd} + + +%--------Fourierseries------------------------------------ +\begin{cmd}{Fourierseries}{fourierseries} +\itemket{Usage}Fourierseries(name,coeff,period,terms) +\itemket{Description}Function to draw the graph of a fourier series. +\itemket{Details} +$a_0+\displaystyle{\sum _{n=1} ^{\infty}(a_n \cos nx + b_n \sin nx)}$ + +\verb|coeff| is a list of [$a_0, a_n, b_n$]. Each element are string.\\ +\verb|term| is a number of terms. +\itemket{Examples} \mbox{} + +\verb|Fourierseries("1",["1/2","0","(1-(-1)^n)/(pi*n)"],2,6,["Num=200"]);| + +\hspace{20mm}\input{Fig/fourierseries.tex} + +\end{cmd} + + +%-----------Tangentplot--------------------------------- +\begin{cmd}{Tangentplot}{tangentplot} +\itemket{Usage}Tangentplot(name,PD, pointinfo, options); +\itemket{Description}Generic funtion to draw a tangent line of a plotting data. +\itemket{Details} +The pointinfo is one of "x=xvalue","y=yvalue", [point, parameter].\\ +The option "nth" is used to set the number when plotting data has multi intersects. + +\itemket{Examples}\mbox{} + +\verb|Plotdata(`"1","x^2","x")|\\ +\verb|Tangentplot("1","gr1","x=2");|\\ +\verb|Tangentplot("2","gr1","y=1",["Color=red"]);|\\ +\verb|Tangentplot("3","gr1","y=1",[2,"Color=blue"])|\\ + +\begin{center} +\input{Fig/tangent} +\end{center} + +\itemket{Reference} \hyperlink{derivative}{Derivative}. +\end{cmd} + +%==========- Letter ================= +\subsubsection{Letter} + +%-----------Letter--------------------------------- +\begin{cmd}{Letter}{letter} +\itemket{Usage}Letter([position, direction, string]) +\itemket{Description}Display the string. +\itemket{Details} +Write the string at the position specified by position (or coordinates) and direction. \\ +The position (or coordinates) can also be specified by the geometric point name. \\ +The direction is "e", "w", "n", "s", "c". +The distance from the specified position can also be given as a numerical value. For example, ''e2'' and ''e3'' are placed twice and three times of the slightly unit distance away from ''e'', respectively. \\ +Multiple strings can be passed in the form of a list. \\ +\itemket{Remark}\mbox{} +The derivative symbol $'$ uses \$ $'$ \$ (single quart) in mathematical mode (interleaved with two \$ s). +\item[Example]\mbox{} + +\verb|Letter([[2,1] ,"se","P"]); | // Display P in the southeast of the coordinates (2, 1). \\ +\verb|Letter([C ,"c", "C"]); | // Display C with the point C as the center. \\ +\verb|Letter([A,"sw","A",E,"s","$ f(x)=\frac{1}{4} x^2 $"]);| + +\hspace{5mm} //Display A in the southwest of point A and $ f(x)=\frac{1}{4} x^2 $ in the south of the point E. \\ + +\end{cmd} + +%-------Letterrot------------------------------------- +\begin{cmd}{Letterrot}{letterrot} +\itemket{Usage}Letterrot([pos, dir, move, string]) +\itemket{Description}Rotate a string and display it. +\itemket{Details} +At the position of the coordinates, rotate to the direction specified by the direction vector and write the string.\\ +The third argument is a minute movement amount and can be abbreviated.\\ +\item[Example]\mbox{} + +\hspace{10mm}\verb|Letterrot(C,B-A,"t2n5","AB");| + +It is also possible to write as follows, abbreviated for the amount of movement. + +\hspace{10mm}\verb|Letterrot(C,B-A,"AB");| + +\itemket{Reference} \hyperlink{exprrot}{Exprrot}. + +\end{cmd} + +%--------Expr ------------------------------------ +\begin{cmd}{Expr}{expr} +\itemket{Usage}Expr([pos, dir, string]); +\itemket{Description}Generic function to write an expression in \TeX style. +\itemket{Details}pos : position + +\hspace{14mm} dir : direction(e,w,s,n,ne,nw,se,sw,c) + +\hspace{14mm} string : expression\\ + +\hspace{14mm}Also see \hyperlink{letter}{Letter} + +\itemket{Examples}\mbox{} + +\verb|Expr([[-3,3],"e","f(x)=\frac{1}{4}x^2"]);|\\ +\verb|Expr([[3,1.5],"s2e2","f‘(x)=\frac{1}{2}x",[2,0],"s","2",[0,1],"w","1"]);| + +\begin{center} +\input{Fig/expr} +\end{center} + +\verb|Arrowdata(Q,P);|\\ +\verb|Expr([Q,"ne2","\displaystyle\int_a^b \log x\,dx="|\\ +\verb| +text(L.x*(log(L.x)-1)-G.x*(log(G.x)-1))]);| + +\vspace{5mm} + +\begin{center} +\input{Fig/intlog} +\end{center} +\end{cmd} + +%------ Exprrot ------------------------------------- +\begin{cmd}{Exprrot}{exprrot} +\itemket{Usage}Exprrot([pos, dir,[move(optional)], string); +\itemket{Description}Generic function to write a rotated expression in \TeX style. +\itemket{Details}pos : position : coordinate or name + +\hspace{15mm} dir : direction vector : coordinate or name + +\hspace{15mm} move: "t'':tangent , "n":normal + +\hspace{15mm} string : expression +\itemket{Examples}\mbox{} + +\verb|Exprrot(C,B-A,"\frac{2}{3}");|\\ +\verb|Exprrot([3,2],[2,-1],"t0n1","\sqrt{3}");| + +\vspace{\baselineskip} +\vspace{\baselineskip} +\hspace{10mm}\includegraphics[bb=0.00 0.00 181.01 131.01,width=4cm]{Fig/exprrot.pdf} \hspace{10mm} \input{Fig/exprrot} + +\end{cmd} + +%============== Marking ================ +\subsubsection{Marking} + +%------------Anglemark-------------------------------- +\begin{cmd}{Anglemark}{anglemark} +\itemket{Usage}Anglemark( a list of points, options); +\itemket{Description}draw an angle mark with an arc at the angle determined by [A,B,C] + +\hspace{10mm} Options : + +\hspace{15mm} numerical value size of mark (default is 1) + +\hspace{15mm} draw text \verb|"Expr=n,str"| + +\itemket{Examples}\mbox{} + +draw an angle mark at interior angles of a triangle, write characters.\\ +\verb| Listplot([A,B,C,A]);|\\ +\verb| Letter([A,"n1","A",B,"w1","B",C,"e1","C"]);|\\ +\verb| Anglemark([B,A,C]);|\\ +\verb| Anglemark([C,B,A],["Expr=\theta"]);|\\ +\verb| Anglemark([A,C,B],[2,"dr,3","Expr=2,\alpha"]);|\\ + +\begin{center} +\input{Fig/anglemark} +\end{center} +\item{Remark} You can draw an angle mark with a parallelogram. +Refer to \hyperlink{paramark}{Paramark} . +\end{cmd} + +%--------Paramark------------------------------------ +\begin{cmd}{Paramark}{paramark} + +\itemket{Usage}Paramark([A, B, C], options); +\itemket{Description}Generic function to draw an angle mark with a parallelogram at the angle determined by [A,B,C].\\ +Options : numerical value size of mark (default is 1) and usual options. +\itemket{Examples} + +Draw an angle mark at interior angles of a triangle, write characters.\\%\mbox{} + +\verb| Listplot([A,B,C,A]);| \\ +\verb| Paramark([A,B,C]); |\\ +\verb| Paramark([C,A,B],[3,"Expr=\alpha"]); |\\ +\verb| Paramark([B,C,A],["dr,2","Expr=2,\theta"]);| \\ + +\begin{center} +\input{Fig/paramark} +\end{center} + +\itemket{Reference} \hyperlink{anglemark}{Anglemark}. +\end{cmd} + +%------------Bowdata-------------------------------- +\begin{cmd}{Bowdata}{bowdata} +\itemket{Usage}Bowdata(a list of points, options); +\itemket{Description}draw the shape of bow connecting two points in the list counterclockwise +\itemket{Details} + +Options :\\ +curvature (default is 1)\\ +size of the blank space in the middle of bow\\ +expression located at the blank space \verb|"Expr=expressions"|\\ +The location of expressions can be modified via \verb|"Expr=tn, expressions"| where +\verb|t| specifies the movement in the direction of segment and +\verb|n| specifies that of normal direction. +Both positive and negative numbers are permitted.\\ +line type \verb|"dr,n" , "da,m,n" , "do,m,n"| +\itemket{Examples}\mbox{} + +draw the shapes of bow along with the edges of triangle ABC and add marks.\\ +\verb| Listplot([A,B,C,A]);|\\ +\verb| Letter([A,"n1","A",B,"w1","B",C,"e1","C"]);|\\ +\verb| Bowdata([A,B]);|\\ +\verb| Bowdata([B,C],[1,"Expr=t0n3,a"]);|\\ +\verb| Bowdata([C,A],[2,1.2,"Expr=10","da"]);| +\begin{center} +\input{Fig/bowdata} +\end{center} + +Expressions can be displayed in rotated manner +via \verb|"Exprrot=tn,expressions"| +though the Euclidean view does not correspond to this modification. +Adding \verb|r| to \verb|tn| results in the turning round. +\itemket{Examples}\mbox{} + +\verb| Bowdata([B,A],[1,1,"Exprrot=a"]);|\\ +\verb| Bowdata([D,C],[1,1,"Exprrot=t3n0,a"]);|\\ +\verb| Bowdata([F,E],[1,1,"Exprrot=t-3n0,a"]);|\\ +\verb| Bowdata([H,G],[1,1,"Exprrot=t0n3,a"]);|\\ +\verb| Bowdata([L,K],[1,1,"Exprrot=t0n0r,a"]);|\\ +\verb| Bowdata([N,M],[1,1,"Exprrot=t3n0r,a"]);| +\begin{center} +\input{Fig/bowdata2} +\end{center} +\end{cmd} + +%------Drawsegmark-------------------------------------- +\begin{cmd}{Drawsegmark}{drawsegmark} +\itemket{Usage}Drawsegmark(name, list, options) or Segmark(name, list, options) +\itemket{Description}Add a mark to a segment. +\itemket{Details} +Add a mark to the segment determined by the end points specified in the list. +Four kinds of marks can be used.\\ +Extra options :\\ +\verb|"Type=n"| (n=1,2,3,4) specifies the kind of mark.\\ +\verb|"Width="| specifies the distance between two segments of the mark +(in case when $n=2$). +\itemket{Examples}\mbox{} + +\verb|Listplot([A,B,C,D,A]);|\\ +\verb|Segmark("1",[A,B],["Type=1"]);|\\ +\verb|Segmark("2",[B,C],["Type=2","Width=1.5"]);| //width of two lines\\ +\verb|Segmark("3",[C,D],["Type=3"]);|\\ +\verb|Segmark("4",[D,A],["Type=4"]);| +\begin{center} +\input{Fig/segmark} +\end{center} +\end{cmd} + +%--------Htickmark------------------------------------ +\begin{cmd}{Htickmark}{htickmark} +\itemket{Usage}Htickmark([x-coord,[direction(optional)],expression,...]); +\itemket{Description}Generic function to tick on the horizontal axis. +\itemket{Details}Default of direction is \verb|"s1"|. Minor adjustments are not displayed on the Euclidean view, you have to check the results on the PDF file. The length of tickmarks can be set by the function \hyperlink{setmarklen}{Setmarklen()}. +\itemket{Examples}\mbox{} + +\verb|Htickmark([1,"1",2,"n1","2",3,"se","3",4,"4"]);| + +\begin{center} +\input{Fig/htickmark01} +\end{center} + +\verb|ticks=apply(-5..5,x,[x,text(x)]);| // ticks is [ [-5,"5"],...,[5,"5"] ]\\ +\verb|ticks=remove(ticks,[[0,"0"]]); | // [0,"0"] is removed\\ +\verb|ticks=flatten(ticks); | // ticks becomes [-5,"5'',...,5,"5'']\\ +\verb|Htickmark(ticks);| + +\begin{center} +\input{Fig/htickmark} +\end{center} + +\itemket{Reference} \hyperlink{vtickmark}{Vtickmark}. +\end{cmd} + +%------------Vtickmark-------------------------------- +\begin{cmd}{Vtickmark}{vtickmark} +\itemket{Usage}Vtickmark([y-coord,[direction(optional)],expression,...]); +\itemket{Description}Generic function to tick on the vertical axis. +\itemket{Details}Default of direction is \verb|"w1"|. +\itemket{Examples}\mbox{} + +\verb|Vtickmark([1,"1",2,"2"]);| + +\itemket{Reference} \hyperlink{htickmark}{Htickmark}. +\end{cmd} + +%--------------Rulerscale------------------------------ +\begin{cmd}{Rulerscale}{rulerscale} +\itemket{Usage}Rulerscale(starting point, horizontal marks, vertical marks); +\itemket{Description}Generic functio to put ruler marks. +\itemket{Details} + +The marks are give as a list.\\ +\verb|["r",a,b,c,d]| to put marks from \verb|a| to \verb|b| with intervals \verb|c|, scales \verb|d|.\\ +\verb|["f",n1,"str",n2,"str",・・] | to put marks as the same format as Htickmark. +\itemket{Examples1}\mbox{} + +\verb|Listplot("1",[[2,1],[9,1]]);|\\ +\verb|Rulerscale([2,1],["r",2,9,1,10],[]);| + +\begin{center}\input{Fig/ruler1}\end{center} + +\itemket{Examples2}\mbox{} + +\verb|Framedata("1",[A,B],["corner"]);|\\ +\verb|Rulerscale(A,["r",0,5,1],["f",1,"d1",3,"d2"]);| + +\begin{center}\input{Fig/ruler}\end{center} + +\end{cmd} + +%========== Using plotting data =============== +\subsection{Using plotting data} + +%--------------Changestyle------------------------------ +\begin{cmd}{Changestyle}{changestyle} +\itemket{Usage}Changestyle(list of PD, options) +\itemket{Description}Change the option for drawing. +\itemket{Details} +Change the option for drawing several shapes altogether. +\itemket{Examples}\mbox{} + +Draw segment AB and Circle AB with broken line on the Euclidean view +and keep them from being drawn on \TeX\ final output. + +\verb| Listplot([A,B]);|\\ +\verb| Circledata([A,B]);|\\ +\verb| Changestyle(["sgAB","crAB"],["da","notex"]);| + +\end{cmd} + +%--------AddGraph ------------------------------------ +\begin{cmd}{AddGraph}{addgraph} + +\itemket{Usage}AddGraph(name,List of PD,options) +\itemket{Description}Manipulate more than one PD all together. +\itemket{Remark} PD name should be passed as a character string, for example, pass "cr1"' for PD name cr1. + +%\itemket{Details} +\itemket{Examples}\mbox{} +After manipulating PDs of a circle and a point on the circle by AddGraph, you can translate or rotate them together.\\ + +\verb|Setpt(3); |\\ +\verb|Circledata("1",[[0,1],[0,0]]); |\\ +\verb|Pointdata("1",[0,0]); |\\ +\verb|AddGraph("1",["[pt1]","cr1"],["nodisp"]); |\\ +\verb|nn=32; |\\ +\verb|forall(1..nn, |\\ +\verb| t=2*pi/nn*#; |\\ +\verb| Rotatedata(text(#),"ad1",-t,[[0,1],"nodisp"]); |\\ +\verb| Translatedata(text(#),"rt"+text(#),[t,0],["dr,0.3"]); |\\ +\verb|); | + +\begin{center} + \input{Fig/addgraph} +\end{center} + +\end{cmd} + +%------------Invert-------------------------------- +\begin{cmd}{Invert}{invert} +\itemket{Usage}Invert(PD) +\itemket{Description}Rearrange plotting data in the reverse order. +\itemket{Examples}\mbox{} + +See the examples in \hyperlink{shade}{Shade} + +\end{cmd} + +%-------------Joincrvs------------------------------- +\begin{cmd}{Joincrvs}{joincrvs} +\itemket{Usage}Joincrvs(name, list of PDs, options) +\itemket{Description}Create a plotting data of one curve by connecting a list of plotting data of adjacent curves. +\itemket{Details} +The list of curves is specified in the adjacent order. \\ +Options is line type. + +\itemket{Examples}\mbox{} + +Draw the closed curve obtained from the line segment $y=x\ (-\sqrt{2} \leq x \leq \sqrt{2})$ and the half circle, and paint the interior of the closed curve using the yellow color.\\ +Put the point A at the origin and the point B in the appropriate place.\\ +\verb|Plotdata("1","x","x=[-sqrt(2),sqrt(2)]");|\\ +\verb|B.xy=[sqrt(2),sqrt(2)];|\\ +\verb|Circledata("2",[A,B],["Rng=[pi/4,pi/4*5]"]);|\\ +\verb|Joincrvs("1",["gr1","cr2"]);|\\ +\verb|Shade(["join1"],["Color=yellow"]);|\\ +\begin{center} +\input{Fig/joincrvs.tex} +\end{center} +\end{cmd} + + +%--------Partcrv------------------------------------ +\begin{cmd}{Partcrv}{partcrv} +\itemket{Usage}Partcrv(name, A, B, PD, options) +\itemket{Description}Generic function to make a piece of curve from the PD between the points A and B. +\itemket{Details}The order of two points A, B must be same as the direction of the curve.\\ +Options are "dr, n", "da,m,n" or "do,m,n"\\ +\itemket{Examples}\mbox{} + +In the following example We draw a parabola with dotted line and draw a piece of curve with real line.\\ +\verb| Plotdata("1","x^2","x",["do"]);|\\ +\verb| Partcrv("1", [0,0], [1,1], "gr1");| + +\begin{center} +\input{Fig/partcrv1} +\end{center} + +In the next example we draw a piece of circle with real line. The direction of a circle is counterclockwise direction.\\ +\verb| Circledata([A,B], ["do"]);|\\ +\verb| Plotdata("1","x^2","x",["do"]);|\\ +\verb| tmp=Intersectcrvs("crAB","gr1");|\\ +\verb| P.xy=tmp_1;|\\ +\verb| Q.xy=tmp_2;|\\ +\verb| Partcrv("1", P, Q, "crAB");|\\ +\verb| Partcrv("2", Q, P, "crAB");| +\vspace{5mm} + +\begin{center} +\begin{minipage}{45mm} +\begin{center} +\input{Fig/partcrv3}\\ +figure of part1 +\end{center} +\end{minipage} +\hspace{10mm} +\begin{minipage}{45mm} +\begin{center} +\input{Fig/partcrv4}\\ +figure of part2 +\end{center} +\end{minipage} +\end{center} + +In the last example we draw the pice of parabola:$y=x^2$ which is cut off by the circle.\\ +\verb| Circledata("1",[[0,2],[0,0]],["da"]);|\\ +\verb| Plotdata("1","x^2","x",["do"]);|\\ +\verb| tmp=Intersectcrvs("cr1","gr1");|\\ +\verb| Partcrv("2",tmp_2,tmp_1,"gr1",["dr,2"]);| + +\begin{center} +\input{Fig/partcrv} +\end{center} + +\end{cmd} + +%-------- Enclosing ------------------------------------ +\begin{cmd}{Enclosing}{enclosing} +\item[Usage]Enclosing(name, a list of plotdata, options); +\item[Description]This function makes a closed curve form the list of plotdata. +\item[Details]Options are:\\ +near point from start position : Set in case where the first curve and the last curve have multi intersects.\\ +\verb|"dr","da", "do","`notex","nodisp",''Color= "| : as usual. +\item[Examples]\mbox{} + +\verb|Plotdata("1","x^2","x");|\\ +\verb|Lineplot("1",[[0,0],[1,0]]);|\\ +\verb|Lineplot("2",[[2,0],[2,1]]);|\\ +\verb|Enclosing("1",["Invert(gr1)","ln1","ln2"],["nodisp"]);|\\ +\verb|Shade(["en1"],["Color=red"]);| + +\begin{center} +\input{Fig/enclosing} +\end{center} + +\item{Remark}The followings have the opposite direction. + +\verb|Enclosing("1",["ln1","ln2","Invert(gr1)"]);|\\ +\verb|Enclosing("1",["gr1","Invert(ln2)","Invert(ln1)"]);| +\end{cmd} + + +%---------Hatchdata----------------------------------- +\begin{cmd}{Hatchdata}{hatchdata} +\itemket{Usage}Hatchdata(name, a list of "i" or "o" , a list of a list of PD , options) +\itemket{Description}Generic function to draw hatch lines in the close curve. +\itemket{Details}Options are:\\ +\hspace*{5mm}angle(degree,45), interval(ratio,1) of hatches, \\ +\hspace*{5mm}\verb|"Max=(default:20)"| maximum of the number of hatches.\\ +\hspace*{5mm}\verb|"Out=y/n(default:n)"| whether it uses R and make the data file or not. +\itemket{Examples}\mbox{} + + +\verb|Circledata([A,B],["dr"]);|\\ +\verb|Hatchdata("1",["i"],[["crAB"]],["dr,0.7"]);| + +\verb|Circledata([A,B],["dr"]);|\\ +\verb|Paramplot("1","[4*cos(t),2*sin(t)]","t=[0,2*pi]");|\\ +\verb|Paramplot("2","[2*cos(t),4*sin(t)]","t=[0,2*pi]");|\\ +\verb|Hatchdata("1",["ioi"],[["crAB"],["gp1"],["gp2"]],["dr,0.7"]);|\\ +\verb|Hatchdata("2",["iio"],[["crAB"],["gp1"],["gp2"]],["dr,0.7"]);| + +\begin{center} +\input{Fig/hatch1}\hspace{10mm}\input{Fig/hatch2} +\end{center} + +\verb|Plotdata("1","2*sin(x)","x=[-pi,3*pi]",["Num=100"]);|\\ +\verb|Listplot([A,B]);|\\ +\verb|Listplot([A,C]);|\\ +\verb|Hatchdata("1",["ii"],[["sgAB","n"],["gr1","s"]],["dr,0.7"]);|\\ +\verb|Hatchdata("2",["ii"],[["sgAC","s"],["gr1","n"]],["dr,0.7"]);| + +\begin{center} +\input{Fig/hatch3} +\end{center} + +\verb|Plotdata("1","2*sin(x)","x=[-pi,3*pi]",["Num=100"]);|\\ +\verb|Listplot([A,B]);|\\ +\verb|Listplot([A,C]);|\\ +\verb|Hatchdata("1",["iio"],[["sgAB","s"],["sgAC","n"],["gr1","n"]]);| + +\begin{center} +\input{Fig/hatch4} +\end{center} + +\verb|Deffun("f(x)",["regional(y)","y=x^3-2*x","y"]);|\\ +\verb|Plotdata("1","f(x)","x",["Num=100"]);|\\ +\verb|Putoncurve("A","gr1");|\\ +\verb|coef=Derivative("f(x)","x",A.x);|\\ +\verb|Defvar(["coef",coef]);|\\ +\verb|Deffun("g(x)",["regional(y)","y=coef*(x-A.x)+A.y","y"]);|\\ +\verb|Plotdata("2","g(x)","x",["Num=1"]);|\\ +\verb|if(!Ptselected(), // if any point is not selected|\\ +\verb| Enclosing("1",["gr2","Invert(gr1)"],[A,"nodisp"]);|\\ +\verb| Hatchdata("1",["i"],[["en1"]]);|\\ +\verb|);| + +\begin{center} +\input{Fig/hatch5} +\end{center} + +\verb|Circledata([A,B]);|\\ +\verb|Hatchdata("1",["i"],[["crAB"]]);|\\ +\verb|Hatchdata("2",["i"],[["crAB"]],[-40,2]);|// $\mbox{angle}=-40^{\circ}, \mbox{interval}=\times 2$|\\ +\verb|Hatchdata("3",["i"],[["crAB"]],["dr,0.5"]);|\\ +\verb|Hatchdata("4",["i"],[["crAB"]],[-45,2,"dr,0.5"]);| + +\begin{center} +\input{Fig/HatchZuKita1.tex} +\end{center} + +\verb|Lineplot("1",[A,B]);// name of this data is ln1|\\ +\verb|Lineplot("2",[A,C]);|\\ +\verb|Hatchdata("5",["iii"],[["crAB"],["ln1","n"],["ln2","n"]]);|\\ +\verb|Hatchdata("6",["ioo"],[["crAB"],["ln1","n"],["ln2","n"]]);| + +\begin{center} +\input{Fig/HatchZuKita5E.tex}\hspace{10mm}\input{Fig/HatchZuKita6E.tex} +\end{center} + +\verb|Circledata([A,B],["nodisp"]);|\\ +\verb|Hatchdata("7",["i"],[["crAB"]]);|\\ +\verb|Circledata([A,B],["da"]);|\\ +\verb|Hatchdata("8",["i"],[["crAB"]]);| + +\begin{center} +\input{Fig/HatchZuKita7E.tex}\hspace{10mm}\input{Fig/HatchZuKita8.tex} +\end{center} + +%\verb|Hatchdata("9a",["iii"],[["crAB"],["ln1","n"],["ln2","n"]]);|\\ +%\verb|Hatchdata("9b",["ioo"],[["crAB"],["ln1","n"],["ln2","n"]],[90,2]);| +\end{cmd} + +%---------Dotfilldata----------------------------------- +\begin{cmd}{Dotfilldata}{dotfilldata} +\itemket{Usage}Dotfilldata(name, list of the dotted sides "i" or "o", list of PD, option) +\itemket{Description}Fill a domain with dots. +\itemket{Details} +R is called to generate the data. Arguments are the same as Hatchdata. \\ +Option is the density of dots from 0.1 to 0.8 (default is 0.3). +\itemket{Examples}\mbox{} + +A pie chart\\ +After making closed curve via \verb|Partcrv()| and \verb|Enclosing()|, +the surrounded region is filled with dots. + +\verb| r=3;|\\ +\verb| p0=r*[cos(pi/2),sin(pi/2)];|\\ +\verb| p1=r*[cos(-pi/6),sin(-pi/6)];|\\ +\verb| p2=r*[cos(-3*pi/4),sin(-3*pi/4)];|\\ +\verb| Circledata("1",[[0,0],[r,0]]);|\\ +\verb| Listplot("1",[[0,0],p0]);|\\ +\verb| Listplot("2",[[0,0],p1]);|\\ +\verb| Listplot("3",[[0,0],p2]);|\\ +\verb| Partcrv("1",p1,p0,"cr1");|\\ +\verb| Enclosing("1",["sg2","part1","Invert(sg1)"],[[0,0]]);|\\ +\verb| Partcrv("2",p2,p1,"cr1");|\\ +\verb| Enclosing("2",["sg3","part2","Invert(sg2)"],[[0,0]]);|\\ +\verb| Dotfilldata("1",["i"],[["en1"]]);|\\ +\verb| Dotfilldata("2",["i"],[["en2"]],[0.1]);| +\begin{center} +\input{Fig/dotfill} +\end{center} +\end{cmd} + +%-----------Shade--------------------------------- +\begin{cmd}{Shade}{shade} +\itemket{Usage}Shade(("name"),list of PD, options); +\itemket{Description}This function fills a domain surrounded by a closed curve. +\itemket{Details}\mbox{}\\ +If "Invert" is used in some PD, \verb|Enclosing| is used, if not, \verb|Joincrvs| is used as default. +The options are use of enclosing("Enc=y/n") and color. +\itemket{Examples}\mbox{}\\ +\verb|Setax([7,"nw"]);|\\ +\verb|Plotdata("1","2*sin(x)","x",["Num=100"]);|\\ +\verb|Lineplot("1",[[0,1],[1,1]]);|\\ +\verb|Shade(["ln1","Invert(gr1)"],[[2.5,1],"Color=0.2*[0,0,0,1]"]);| + +\begin{center} +\input{Fig/shade} +\end{center} + +\verb|Plotdata("1","x^2-1","x=[-3,3]");|\\ +\verb|Plotdata("2","x^2/2","x=[-3,3]");|\\ +\verb|Shade("1",["gr2","Invert(gr1)"],[[-1.5,1],"Color=[1,0,0]","alpha->0.4"]);| + +\begin{center} +\input{Fig/shade01E} +\end{center} + +\verb|r1=2;|\\ +\verb|r2=1.5;|\\ +\verb|Circledata("1",[A,A+[r1,0]]);|\\ +\verb|Circledata("2",[A,A+[r2,0]]);|\\ +\verb|Listplot("1",[A+[r1,0],A+[r2,0]],["nodisp"]);|\\ +\verb|Shade(["cr1","sg1","Invert(cr2)","Invert(sg1)"],["Enc=n","Color=green"]);| + +\begin{center} +\input{Fig/greenring} +\end{center} + +\itemket{Reference} \hyperlink{joincrvs}{Joincrvs}. +\end{cmd} + +%--------------Reflectdata------------------------------ +\begin{cmd}{Reflectdata}{reflectdata} +\itemket{Usage}Reflectdata(name, PD, center or axis of symmetry, options); +\itemket{Description}Generic function to draw a reflective curve. +\itemket{Details}axis of symmzetry is defined as a list of 2 points. +\itemket{Examples}\mbox{} + +\verb|Circledata([A,B]);|\\ +\verb|Reflectdata("1","crAB",[C]);|\\ +\verb|Reflectdata("2","crAB",[[-1,2]],["dr,2"]);|\\ +\verb|Reflectdata("3","crAB",[D,E],["da"]);| + +\begin{center} +\input{Fig/reflectdata} +\end{center} +\end{cmd} + +%------------Rotatedata-------------------------------- +\begin{cmd}{Rotatedata}{rotatedata} +\itemket{Usage}Rotatedata(name, (a list of )PD, angle(degree), options); +\itemket{Description}Generic function to rotate plotting data. +\itemket{Details}Options are center, and as usual. The default of center is [0,0].\\ +\itemket{Examples}\mbox{} + +\verb|Circledata([A,B]);|\\ +\verb|Rotatedata("1","crAB",pi/2,[C]);|\\ +\verb|Rotatedata("2","crAB",pi/3,[[1,5],"dr,2"]);|\\ +\verb|Rotatedata("3","crAB",-pi/3,[D,"da"]);| + +\begin{center} +\input{Fig/rotatedata} +\end{center} +\end{cmd} + +%---------Scaledata----------------------------------- +\begin{cmd}{Scaledata}{scaledata} +\itemket{Usage}Scaledata(name, list of PD, horizontal ratio, vertical ration, [options]); +\itemket{Description}Generic function to scale plotting data. +\itemket{Details}Options are Center, and as usual. The default of center is [0,0].\\ +\itemket{Examples}\mbox{} + +\verb|Circledata([A,B]);|\\ +\verb|Scaledata("1","crAB",3,2,[[0,0]]);|\\ +\verb|Scaledata("2","crAB",3,2,[C,"dr,2"]);|\\ +\verb|Scaledata("3","crAB",D.x,D.y,[[0,0],"da"]);| + +\begin{center} +\input{Fig/scaledata} +\end{center} +\end{cmd} + +%------------Translatedata-------------------------------- +\begin{cmd}{Translatedata}{translatedata} +\itemket{Usage}Translatedata(name, list of PD, vector, options); +\itemket{Description}Generic function to translate plotting data. +\itemket{Details}Options are Center, and as usual. The default of center is [0,0].\\ +\itemket{Examples}\mbox{} + +\verb|Circledata([A,B]);|\\ +\verb|Translatedata("1","crAB",[2,3]);|\\ +\verb|Translatedata("2","crAB",C,["dr,2"]);|\\ +\verb|Translatedata("3","crAB",D,["da"]);| + +\begin{center} +\input{Fig/translatedata} +\end{center} +\end{cmd} + +%=====Calculus and I/O ============================ +\subsection{Calculus and I/O} + +%-------Derivative------------------------------------- +\begin{cmd}{Derivative}{derivative} +\itemket{Usage}\mbox{}\\ +Derivative(function(string), variable(string), value);\\ +Derivative(PD(string), pointinfo, ([nth of intersects])); +\itemket{Description}Generic funtion to find the derivative of a function or a plotting data. +\itemket{Details} +The pointinfo is one of "x=xvalue","y=yvalue", [point, parameter].\\ +The option of nth is used to set the number when plotting data has multi intersects. + +\itemket{Examples}\mbox{} + +\verb|Deffun("f(x)",["regional(y)","y=x^3-4*x","y"]);|\\ +\verb|coef=Derivative("f(x)","x",A.x);|\\ +\verb|A.y=f(A.x);|\\ +\verb|B.y=coef*(B.x-A.x)+A.y;|\\ +\verb|Plotdata("1","f(x)","x",["Num=200"]);|\\ +\verb|Lineplot([A,B]);|\\ +\verb|Letter([A,"ne","A"]);| + +\begin{center} +\input{Fig/derivative} +\end{center} + +\itemket{Reference} \hyperlink{tangentplot}{Tangentplot}. +\end{cmd} + +%---------Integrate----------------------------------- +\begin{cmd}{Integrate}{integrate} +\itemket{Usage}\mbox{}\\ +Integrate(function or name of PD, "varname=range", [options]); +\itemket{Description}Generic funtion to find the value of numerical integration. +\itemket{Details}Oshima's Bezier formula is used. +\itemket{Examples}\mbox{} + +\verb|f(x):=x^3-2*x^2+2;|\\ +\verb|val=Integrate("f(x)","x=[0,3]");|\\ +\verb|println(val);| // 8.25 will be displyed. + +\verb|plotting data("1","x^3-2*x^2+2","x");|\\ +\verb|println(Integrate("gr1",[0,3]));| +\end{cmd} + +%------------Inversefun-------------------------------- +\begin{cmd}{Inversefun}{inversefun} +\itemket{Usage}Inversefun(function(string), range, value); +\itemket{Description}Generic function to find the value of the inversefunction. +\itemket{Details}The value is found in the range. +\itemket{Examples}\mbox{} + +\verb|x=Inversefun("sin(x)","x=[0,pi/2]",0.5);|\\ +\hspace*{20mm}The value of x is $0.5236$. +\end{cmd} + +%------------Crossprod-------------------------------- +\begin{cmd}{Crossprod}{crossprod} +\itemket{Usage}Crossprod(vec1, vec2); +\itemket{Description}Generic function to return the cross product of 2 vectors. +\itemket{Details}The vectors are a list with length 3 or 2. +\itemket{Examples}\mbox{} + +\verb|v=Crossprod([1,0,0],[1,1,1]);| // The result is v=[0,-1,1]. + +\end{cmd} + +%-----------Dotprod--------------------------------- +\begin{cmd}{Dotprod}{dotprod} +\itemket{Usage}Dotprod(vec1, vec2); +\itemket{Description}Generic function to return the dot product of 2 vectors. +\itemket{Examples}\mbox{} + +\verb|v=Dotprod([1,2,3],[1,-1,1]);| // The result is v=2. +\end{cmd} + +%------------Findarea-------------------------------- +\begin{cmd}{Findarea}{findarea} +\itemket{Usage}Findarea(plotting data( or string of pd )); +\itemket{Description}Generic function to return the area enclosed with a close curve. +\itemket{Details}Oshima's B\'ezier formula is used. +\itemket{Examples}\mbox{} + +\verb|Paramplot("1","[3*cos(t),2*sin(t)]","t=[0,2*pi]");|\\ +\verb|area=Findarea("gp1");|\\ +\verb|println(Sprintf(area,6));| // The result is 18.849536. + +\end{cmd} + +%-----------Findlength--------------------------------- +\begin{cmd}{Findlength}{findlength} +\itemket{Usage}Findlength(plotting data( or string of pd )); +\itemket{Description}Generic function to return the length of a curve. +\itemket{Details}Oshima's B\'ezier formula is used. +\itemket{Examples}\mbox{} + +\verb|Circledata("1",[[0,0],[2,0]]);|\\ +\verb|len=Findlength("cr1");|\\ +\verb|println(Sprintf(len,6));| // The result is 12.558097. +\end{cmd} + + +%-----------Intersectcurves--------------------------------- +\begin{cmd}{Intersectcurves}{intersectcurves} +\itemket{Usage}Intersectcrvs(plotting data1(string), plotting data2(string)); +\itemket{Description}Generic funtion to return a list of intersects of 2 plotting data. +\itemket{Examples}\mbox{} + +\verb|Plotdata("1", "sin(x)", "x", ["Num=100"]);|\\ +\verb|Circledata([A, B]);|\\ +\verb|tmp=Intersectcrvs("gr1","crAB");|\\ +\verb|pP=tmp_1;|\\ +\verb|pQ=tmp_2;| + +\begin{center} +\input{Fig/Intersectcrvs1} +\end{center} +\end{cmd} + +%------------IntersectcurvesPp-------------------------------- +\begin{cmd}{IntersectcurvesPp}{intersectcurvesPp} +\itemket{Usage}IntersectcrvsPp(plotting data1(string), plotting data2(string)); +\itemket{Description}Generic funtion to return a list of intersects with parameters of 2 plotting data. +\itemket{Details}Parameters are positons of the intersect. +\end{cmd} + +%-------------Nearestpt------------------------------- +\begin{cmd}{Nearestpt}{nearestpt} +\itemket{Usage}Nearestpt(plotting data1, plotting data2); +\itemket{Description}Generic funtion to return the nearest point with the parameter and the distance. +\itemket{Examples}\mbox{} + +\verb|Plotdata("1", "x^2+2", "x=[-2,2]");|\\ +\verb|Plotdata("2", "-(x-2)^2+1","x=[0,4]");|\\ +\verb|plist=Nearestpt("gr1","gr2");|\\ +\verb|Listplot("1",plist_1,plist_3);|\\ +\verb|pB=plist_3;| +\itemket{Remark}The returned list is [[0.4,2.16],31,[1.58,0.82],20.73,1.78]. + +\begin{center} +\input{Fig/nearestpt} +\end{center} +\end{cmd} + +%--------------Nearestptcrv------------------------------ +\begin{cmd}{Nearestptcrv}{nearestptcrv} +\itemket{Usage}Nearestptcrv(point1, PD); +\itemket{Description}Generic funtion to return the nearest point on the PD from the point1. +\itemket{Examples}\mbox{} + +\verb|Plotdata("1", "x^2", "x");|\\ +\verb|tmp=Nearestptcrv(A,"gr1");| //Tjhe coordnates will be returned.\\ +\verb|Putpoint("B",tmp);|\\ +\verb|Listplot([A,B],["do"]);| + +\begin{center} +\input{Fig/nearestpt1} +\end{center} + +\itemket{Remark}The return value is [[0.4,2.16],31,[1.58,0.82],20.73,1.78]. +\end{cmd} + +%-------------Numptcrv------------------------------- +\begin{cmd}{Numptcrv}{numptcrv} +\itemket{Usage}Numptcrv (PD) +\itemket{Description}Generic function to return the number of PD. +\itemket{Details}This is the same as \verb|length(PD)|. +\itemket{Examples}\mbox{} + +Compare the order of PD, Implicit() and Paramplot(). ( on Euclidean view ) + +\verb|Slider("A-C-B",[0,-2],[6,-2]); |\\ +\verb|Implicitplot("1","x^2+4*y^2=4","x=[-2,2]","y=[-2,2]",["do"]); |\\ +\verb|Paramplot("1","[2*cos(t)+5,sin(t)]","t=[0,2*pi]",["do","Num=140"]); |\\ +\verb|println([Numptcrv(imp1),Numptcrv(gp1)]);| //display number of PD on console\\ +\verb|n=floor(C.x*2); |\\ +\verb|repeat(n,s,start->0, |\\ +\verb| t=s*10+1; |\\ +\verb| draw(imp1_t,color->hue(s/10)); |\\ +\verb| draw(gp1_t,color->hue(s/10)); |\\ +\verb|); | + +\begin{center} +\includegraphics[bb=0.00 0.00 305.02 133.01,width=8cm]{Fig/numptcrv.pdf} +\end{center} + +\end{cmd} + +%-----------Paramoncurve--------------------------------- +\begin{cmd}{Paramoncurve}{paramoncurve} +\itemket{Usage}Paramoncurve(point, PD) +\itemket{Description}Generic function to return the parameter value of the point on the curve. +\itemket{Details}The integer part is the number of the segment on which the point lies, the fractional part is the position on the segment. +\itemket{Examples}\mbox{} + +\verb|Listplot([A,B,C,A]);|\\ +\verb|Putonseg("D",[B,C]);|\\ +\verb|tmp=Paramoncurve(D,"sgABCA");|\\ +\verb|println(tmp);| // for example display \verb|2.35| on console. + +%\begin{center} +%\input{Fig/paramoncrv} +%\end{center} +\end{cmd} + +%---------Pointoncurve----------------------------------- +\begin{cmd}{Pointoncurve}{pointoncurve} +\itemket{Usage}Pointoncrv(parameter value, plotting data); +\itemket{Description}Generic function to return the point which has the parameter value +\itemket{Examples}\mbox{} + +\verb|Circledata("1",[[0,0],[2,0]],["Num=5","Rng=[0,pi]"]);|\\ +\verb|tmp=Pointoncurve(4.5,"cr1");|\\ +\verb|Pointdata("1",tmp,["Size=3"]);|\\ +\verb|Letter(tmp,"nw","A");| + +\begin{center} +\input{Fig/pointoncrv} +\end{center} +\end{cmd} + +%-----------Ptcrv--------------------------------- +\begin{cmd}{Ptcrv}{ptcrv} +\itemket{Usage}Ptcrv(n,PD); +\itemket{Description}Returns n-th point from PD. +\itemket{Details}Same as \verb|PD_n| of Cindyscript. +\itemket{Examples}\mbox{}\\ +\verb| Circledata([O,P],["do","Num=100","notex"]); |\\ +\verb| Scaledata("1","crOP",4/3,1); |\\ +\verb| F.xy=[-sqrt(7),0]; |\\ +\verb| A=Ptcrv(9,sc1); |\\ +\verb| B=Ptcrv(16,sc1); |\\ +\verb| Listplot("1",[A,F,B],["da"]); |\\ +\verb| Partcrv("1",A,B,"sc1",["dr,3"]); |\\ +\verb| Shade(["part1","sg1"],0.1); |\\ +\verb| Arrowhead(B,"sc1",[1.5]); |\\ +\verb| Letter([A,"ne","A",B,"ne","B",F,"s2","F"]); |\\ +\begin{center}\input{Fig/ptcrv}\end{center} +\end{cmd} + +%-------------Ptstart, Ptend------------------------------- +\begin{cmd}{Ptstart, Ptend}{ptstart, ptend} +\itemket{Usage}Ptstart(PD) , Ptend(PD) +\itemket{Description}Returns start point and end point of PD. respectively. +\itemket{Details} It returns coodinates of point. +\itemket{Examples} +Gets the points at both ends of the graph with limited domain and draw the line segments.\\ +\verb| Deffun("f(x)",["regional(y)","y=x^2","y"]); |\\ +\verb| Plotdata("1","f(x)","x",["do"]); |\\ +\verb| Plotdata("2","f(x)","x=[-1,2]"); |\\ +\verb| Lineplot("1",[Ptstart(gr2),Ptend(gr2)],["do"]); |\\ +\verb| Listplot("1",[Ptstart(gr2),Ptend(gr2)]); |\\ +\verb| Letter([A,"w2","A",B,"e2","B"]); |\\ +\begin{center} \input{Fig/ptstart} \end{center} +\end{cmd} + +%----------ReadOutData---------------------------------- +\begin{cmd}{ReadOutData}{readoutdata} +\itemket{Usage}ReadOutdata(filename); +\itemket{Description}Generic function to read external data of \ketcindy\ format. +\itemket{Details}If the data is outside the working directory, add the path name as the first argument. For example, + +\verb|ReadOutdata("/datafolder","file.txt");| + +\vspace{\baselineskip} +\ketcindy\ format data is next style. + +\verb|variable name// |\\ +\verb|start // | : start of list \\ +\verb|[ , , ], .... // | : coordinates ( 2 or 3 dimension )\\ +\verb|....|\\ +\verb|end// | : end of list\\ +\verb|start// | : start of next list\\ +\verb|....|\\ +\verb|end// |\\ +\verb|variable name// |\\ +\verb|start// |\\ +\verb|… |\\ +\verb|end//// |\\ + +%\itemket{Examples}\mbox{} + + +\itemket{Reference} \hyperlink{writeoutdata}{WriteOutData}. +\end{cmd} + +%------------WriteOutData-------------------------------- +\begin{cmd}{WriteOutData}{writeoutdata} +\itemket{Usage}WriteOutdata(filename, a list of varname and value); +\itemket{Description}Function to write out data in \ketcindy\ format. +\itemket{Details}The file is available commonly from \ketcindy,\ R and C. +\itemket{Examples}\mbox{} + +Write out the plotting data of the parabola and the circle. + +\vspace{\baselineskip} +\verb|Plotdata("1", "x^2","x");|\\ +\verb|Circledata("1",[[0,0],[1,0]]);|\\ +\verb|WriteOutData("figdata.txt",["gr1",gr1,"cr1",cr1]);| + +\vspace{\baselineskip} +The written data is as follows. + +\verb| gr1//|\\ +\verb| start// [[-2.68843,7.22765],[-2.51807,6.34067],・・,[-2.00698,4.02798]]// |\\ +\verb| [[-1.83662,3.37318],[-1.66626,2.77642],・・,[-1.15518,1.33443]]// | + +\hspace{20mm} and so on + +\verb| [[5.82965,33.98479]]//|\\ +\verb| end//|\\ +\verb| cr1//|\\ +\verb| start// [[1,0],[0.99211,0.12533],[0.96858,0.24869],・・,[0.80902,0.58779]]//| + +\hspace{20mm} and so on + +\verb| [[0.87631,-0.48175],[0.92978,-0.36812],・・,[1,0]]//|\\ +\verb| end////| + +\itemket{Reference} See \hyperlink{readoutdata}{ReadOutData}. + +\end{cmd} + +%---------------Extractdata----------------------------- +\begin{cmd}{Extractdata}{extractdata} +\itemket{Usage}Extractdata(dataname,options); +\itemket{Description}Function to add properties to a data. +\itemket{Details}The default properties are ["dr"]. +\itemket{Examples}\mbox{} + +\verb|ReadOutData("figdata.txt");|\\ +\verb|Extractdata("gr1",["da"]);|\\ +\itemket{Reference} See \hyperlink{writeoutdata}{WriteOutData} and \hyperlink{readoutdata}{ReadOutData}. +\end{cmd} + +%========Making Tables========================== +\subsection{Making Tables} + +%------------Tabledata-------------------------------- +\begin{cmd}{Tabledata}{tabledata} +\itemket{Usage}Tabledata("",a list of widths, a list of height,a list of removals,[options]); +\item[Descritption]Table function to draw rules of a table. +\itemket{Details} +The lower left is the origin.\\ +The options are "Rng=y/n"(if "n", command setwindow is not executed) and as usual.\\ +The unit of length is 1/10 of the grid of Euclidean view. The default is 1mm.\\ +Control points are put on the row and column. The names are r0,r1,... and c0,c1,....\\ +The points are movable. +\itemket{Remark}See \verb|Tabledatalight| +\itemket{Examples}\mbox{} + +\verb|xL=[20,20,20,20];|\\ +\verb|yL=[10,10,10,10,10];|\\ +\verb|Tabledata("",xL,yL,[]);| + +\begin{center} +\includegraphics[bb=0.00 0.00 403.52 249.51,height=30mm]{Fig/table01.pdf}\hspace{10mm}\input{Fig/table02} +\end{center} + +\verb|Rmv=["r1c0c1","c3r0r1","c3r3r5","r4c2c4"];|\\ +\verb|Tabledata("",xL,yL,Rmv);| + +\begin{center} +\includegraphics[bb=0.00 0.00 392.02 251.51, height=36mm]{Fig/table03.pdf} +\end{center} +\end{cmd} + +%--------------Tabledatalight------------------------------ +\begin{cmd}{Tabledatalight}{tabledatalight} +\itemket{Usage}Tabledata("",a list of widths, a list of height,a list of removals,[options]); +\itemket{Description}Table function to make a table without geometric points. +\itemket{Details}interval option decides to put names par each interval. +\itemket{Examples}\mbox{} + +\verb|xL=[20,20,20,20];|\\ +\verb|yL=[10,10,10,10,10];|\\ +\verb|Tabledatalight("",xL,yL,[],[2]);|\\ +\end{cmd} + +%--------Changetablestyle------------------------------------ +\begin{cmd}{Changetablestyle}{changetablestyle} +\itemket{Usage}ChangeTablestyle(a list of Rules, [changed style]); +\itemket{Description}Table function to change line styles of rules. +\itemket{Examples}\mbox{} + +\verb|Tabledatalight("",[10,20,10,20],[10,10,10],[]);|\\ +\verb|ChangeTablestyle(["r1c0c4"],["da"]);|\\ +\verb|ChangeTablestyle(["r2c0c2","c1r0r3"],["nodisp"]);| + +\begin{center} +\includegraphics[bb=0.00 0.00 324.00 174.00,height=50mm]{Fig/changetable.pdf} +\end{center} +\end{cmd} + +%-----------Findcell--------------------------------- +\begin{cmd}{Findcell}{findcell} +\itemket{Usage}Findcell(grid name of upper left, grid name of lower right); +\itemket{Description}Table function to return the information of a cell. +\itemket{Details} + +The grid name is, for example, "c0r1".\\ +The result is a list of center, half of width, half of height. + +\itemket{Examples}\mbox{} + +\verb|Tabledatalight("",[10,20,10,20],[10,10,10],[]);|\\ +\verb|tmp=Findcell("c2r0","c3r1");| The return is [[3.5,2.5],0.5,0.5].\\ +\verb|tmp=Findcell("c0r1","c2r3");| The return is [[1.5,1],1.5,1] . +\end{cmd} + +%------------Putcell-------------------------------- +\begin{cmd}{Putcell}{putcell} +\itemket{Usage}Putcell(grid name of upper left, grid name of lower right, postion, a string); +\itemket{Description}Table function to put a string at the cell. +\itemket{Details} +The position is one of \verb|c, r, l, t, b| (center, right, left, top, bottom).\\ +Minute movements can be added. + +\itemket{Examples}\mbox{} + +\verb|xL=apply(1..5,20);|\\ +\verb|yL=apply(1..2,20);|\\ +\verb|rL=["c2r2r3","c5r2r3"];|\\ +\verb|Tabledatalight("",xL,yL,rL);|\\ +\verb|Putcell("c0r0","c1r1","c","A");|\\ +\verb|Putcell("c1r0","c3r1","l2","B");|\\ +\verb|Putcell("c0r1","c2r2","rt","C");|\\ +\verb|Putcell("c3r1","c5r2","lb","D");|\\ + +\begin{center} +\input{Fig/putcellE} +\end{center} +\end{cmd} + +%----------PutcoL---------------------------------- +\begin{cmd}{PutcoL}{putcoL} +\itemket{Usage}PutcoL (column number, position, a list of strings); +\itemket{Description}Table function to put strings to a column. +\itemket{Details} +The position is as \verb|Putcell|.\\ +It's unnecessary to enclose with double quotes in case of numbers.\\ +Null string is available. +\itemket{Reference} \hyperlink{putrow}{Putrow}. +\end{cmd} + +%--------------PutcoLexpr------------------------------ +\begin{cmd}{PutcoLexpr}{putcoLexpr} +\itemket{Usage}PutcoLexpr (column number, position, a list of mathematical expressions); +\itemket{Description}Table function to put strings to a column. +\itemket{Reference} \hyperlink{putrowexpr}{Putrowexpr}. +\end{cmd} + +%-------------Putrow------------------------------- +\begin{cmd}{Putrow}{putrow} +\itemket{Usage}Putrow (row number, position, a list of strings); +\itemket{Description}Table function to put strings to a row. +\itemket{Reference} \hyperlink{putcoL}{PutcoL}. +\end{cmd} + +%--------------Putrowexpr------------------------------ +\begin{cmd}{Putrowexpr}{putrowexpr} +\itemket{Usage}Putrowexpr(row number, position, a list of strings); +\itemket{Description}Table function to put strings to a row. +\itemket{Examples} + +In PutcoLexpr (), Putrowexpr (), formulas and general \TeX sentences can be entered. + +\verb|Tabledata("",5,3,100,45,["c1r1r2","r1c2c3","r2c2c3"]);|\\ +\verb|PutcoL(3,"c",["A","B","C"]);|\\ +\verb|PutcoLexpr(4,"l",["x^2","y=\sqrt{x^3}"]);|\\ +\verb|Putrow(1,"c",[1,"two"]);|\\ +\verb|Putrowexpr(3,"c",["","\frac{\pi}{2}","","","\sum{x^2}"]);|\\ + +\begin{center} +\input{Fig/putcolE} +\end{center} + +\itemket{Remark} r0, c0, ... are numbers displayed on the screen. +\itemket{Examples} + +The graphs can be placed in the cells of the table. These are drawn at the position of the cell. + +\verb|Tabledata("",3,3,120,90,["dr,2"]);|\\ +\verb|ChangeTablestyle(["r1c0c3"],["dr"]);|\\ +\verb|ChangeTablestyle(["r2c0c3"],["da"]);|\\ +\verb|Plotdata("1","(x-2)^2+1.5","x=[0.5,3.5]");|\\ +\verb|Plotdata("2","(x-6)^2+2","x=[4.5,7.5]");|\\ +\verb|Plotdata("3","(x-10)^2+2.5","x=[8.5,11.5]");|\\ +\verb|Listplot([A,B]);|\\ +\verb|Listplot([C,D]);|\\ +\verb|Listplot([E,F]);|\\ +\verb|Putrowexpr(1,"c",["D>0","D=0","D<0"]);|\\ +\verb|Putrow(2,"c",["2","1","0"]);|\\ +\verb|Letter(G,"c","The discriminant and the number of intersections");|\\ + +\begin{center} +\input{Fig/tablesample1E} +\end{center} + +\itemket{Examples}\mbox{} + +\verb|Column=[6,6,10,6,10,6,40];|\\ +\verb|Row=[30,6,6,6];|\\ +\verb|Rmv=["c1r0r1","c2r0r1","c3r0r1","c4r0r1","c5r0r1", "r1c6c7","r2c6c7","r3c6c7"];|\\ +\verb|Tabledata("",Column,Row,Rmv,["dr"]);|\\ +\verb|Tlistplot("23d",["c1r2","c2r3"]);|\\ +\verb|Tlistplot("23u",["c1r3","c2r2"]);|\\ +\verb|Putrowexpr(2,"c",["x",0,"\cdots","\tfrac{1}{4}","\cdots",4]);|\\ +\verb|Putrowexpr(3,"c",["y`","","-",0,"+"]);|\\ +\verb|Putrowexpr(4,"c",["y",0,"\searrow","-\tfrac{1}{4}","\nearrow",2]);|\\ +\verb|Putcell(1,1,"l2t2","{\small\begin{minipage}{44mm}$y=x-\sqrt{x}$\\$y`=|\\ +\verb|\dfrac{2\sqrt{x}-1}{2\sqrt{x}}=0$\vspace{1mm}\\\hspace*{5mm}$x=|\\ +\verb|\dfrac{1}{4}$\vspace{1mm}The following table is obtained.\\\end{minipage}}" );|\\ +\verb|Plotdata("1","x-sqrt(x)","x=[0,3]",["do","notex"]);|\\ +\verb|Listplot("2",[[0,0],[3,0]],["do","notex"]);|\\ +\verb|Listplot("3",[[0,-0.5],[0,3]],["do","notex"]);|\\ +\verb|Translatedata("1","gr1",[4.9,1],["dr"]);|\\ +\verb|Translatedata("2","sg2",[4.9,1],["dr"]);|\\ +\verb|Translatedata("3","sg3",[4.9,1],["dr"]);|\\ +\verb|Letter(Ptend(tr2),"e1","\small{$x$}");|\\ +\verb|Letter(Ptend(tr3),"n1","\small{$y$}");|\\ +\verb|Letter(Ptstart(tr2),"w1","\small O");|\\ +\verb|Expr(Ptend(tr1),"nw-2","y=x-\sqrt{x}");|\\ + +\begin{center} +\input{Fig/tablesample2E} +\end{center} + +\itemket{Examples}\mbox{} + +\verb|Tabledata("",8,4,80,40,[]);|\\ +\verb|Putrowexpr(1,c,["x","\cdots","-1","\cdots","0","\cdots","1","\cdots"]);|\\ +\verb|Putrowexpr(2,c,["y`","+","+","+","0","-","-","-"]);|\\ +\verb|Putrowexpr(3,c,["y``","+","0","-","-","-","0","+"]);|\\ +\verb|Putrowexpr(4,c,["y","\nelarrow","\frac{1}{\sqrt{e}}","\nerarrow",|\\ +\verb|"1","\serarrow","\frac{1}{\sqrt{e}}","\selarrow"]);|\\ + +\begin{center} +\input{Fig/zogen3} +\end{center} + +\itemket{Remark} The arrows here are defined in ketpic.sty.\\ +nelarrow, nerarrow, selarrow, serarrow, NELarrow, NERarrow, SELarrow, SERrarrow\\ +The first ne and se represent northeast and southeast (upper right and lower right), respectively. The next r and l represent the direction of rotation (r: right: counterclockwise, l: left: clockwise).\\ +The straight arrows are NEarrow, SEarrrow. +Since these arrows do not exist in Cindy\TeX, they are not displayed on the drawing surface of Cinderella. +\end{cmd} + +%------------Tgrid-------------------------------- +\begin{cmd}{Tgrid}{tgrid} +\itemket{Usage}Tgrid(grid name); +\itemket{Description}Table function to return the coordinates of the grid name. +\end{cmd} + +%-------------Tlistplot------------------------------- +\begin{cmd}{Tlistplot}{tlistplotgrid} +\itemket{Usage}Tlistplot(grid name, grid name); +\itemket{Description}Table function to connect two lattice points by line segments. +\itemket{Examples} \mbox{} + +\verb|Tlistplot(["c0r1","c1r2"]);| +\end{cmd} + +%=========Data Processing========================= +\subsection{Data Processing} + +This section describes data processing by \ketcindy . Cooperation with spreadsheet software enables efficient data processing. + +%------------Tab2list-------------------------------- +\begin{cmd}{Tab2list}{tab2list} +\itemket{Usage}Tab2list(string data, option); +\itemket{Description}Sheet function to convert contents of string data to list. +\item[Ditails]The options are as follows.\\ +\verb|"Blank=a"| : translate cells that is NULL to ``a''\\ +\verb|"Sep=b"| : separators of the string are ``b''. The default separators are Tab code. +\itemket{Examples} \mbox{} + +In the Cindyscrpt editor, prepare a local variable, for example "data". +\begin{center} +\includegraphics[bb=0.00 0.00 261.01 139.01,width=6cm]{Fig/tab2list02E.pdf} +\end{center} + +Copy the data on the spreadsheet to the clipboard. +\begin{center} +\includegraphics[bb=0.00 0.00 449.02 164.01,width=8cm]{Fig/tab2list01E.pdf} +\end{center} + +Paste it during double quotes. +\begin{center} +\includegraphics[bb=0.00 0.00 465.02 140.01,width=8cm]{Fig/tab2list001E.pdf} +\end{center} + +By executing \verb|"Tab2list(data)"| get a list of matrix form. +\begin{center} +\includegraphics[bb=0.00 0.00 482.02 134.01,width=10cm]{Fig/tab2list03E.pdf} +\end{center} + +If it contains a null character cell (NULL), it defaults to null character.Therefore, if you want to set NULL to 0 for questionnaire processing etc., use option \verb|Blank|. + +\hspace{20mm}\verb|dlist=Tab2list(data,["Blank=0"];| + +When CSV format data is copied from the file, the option is set to \verb|sep|. + +\hspace{20mm}\verb|dlist=Tab2list(data,["Sep=,"];| + + +\end{cmd} + +%-------------Dispmat------------------------------- +\begin{cmd}{Dispmat}{dispmat} +\itemket{Usage}Dispmat(list); +\itemket{Description}Display the list to matrix form in the console. +\itemket{Examples}In the example of Tab2list, put the obtained data in a matrix format. + +\begin{center} +\includegraphics[bb=0.00 0.00 422.52 178.01,width=8cm]{Fig/tab2list04E.pdf} +\end{center} +You can copy this directly to spreadsheet. + +\end{cmd} + +%--------------Writecsv------------------------------ +\begin{cmd}{Writecsv}{writecsv} +\itemket{Usage}Writecsv(namelist, data, filename, option); +\itemket{Description}Make a CSV file consisting of the contents of data. +\item[Ditails]namelist is item name added to the first line of the CSV file. If the namelist omitted, the item names "c1, c2, ..." are appended. + +The filename is the name of CSV file. + +option : \verb|"Col=nn"| : Specify the number of columns in the CSV file as a natural number \verb|nn|. + +When specifying the number of columns is omitted, if data is a matrix, use that number of columns, and if data is a vector, use the number of items in namelist. + +\itemket{Examples}\mbox{}\\ +%(1)\\ +Let \verb|data=[13,25,17,22,14,26] , name2=["aa","ab"] , name3=["ba","bb","bc"]|\\ + +\verb|Writecsv(name2,data,"aaa");|\\ +makes the file "aaa.csv" consists of\\ +aa,ab\\ +13,25\\ +17,22\\ +14,26\\ + +%(2)\\ +\verb|Writecsv(name3,data,"aaa");|\\ +makes the file "aaa.csv" consists of\\ +ba,bb,bc\\ +13,25,17\\ +22,14,26\\ + +%(3)\\ +\verb|Writecsv(,data,"aaa",["Col=3"]);|\\ +makes the file "aaa.csv" consists of\\ +c1,c2,c3\\ +13,25,17\\ +22,14,26\\ +\end{cmd} + +\newpage + + +% =====the others=========================== +\subsection{Others} + +%-------Assign------------------------------------- +\begin{cmd}{Assign}{assign} +\itemket{Usage}Assign(string0, string1, number) +\itemket{Description}Generic function to replace the string1 in the string0 with the number. Number is real number or string of real number. +\itemket{Examples}\mbox{} + +\verb|Assign("x^2+a*x","a","1.3"); | // \verb|a*x| $\to$ \verb|1.3*x|\\ +\verb|Assign("x^2+a*x","a",1.3); | //same as above\\ + +\verb|repeat(50,t,|\\ +\verb| cb=t/5-5;|\\ +\verb| Plotdata(text(t),Assign("b*x-b^2","b",cb),"x");|\\ +\verb|);|\\ + +\hspace{40mm} \input{Fig/assign} + +Perform multiple replacements by list. + +\verb|Assign("a*x^2+b*x",["a",1,"b",2]);| \hspace{10mm}// \verb|a| $\to$ \verb|1 and b| $\to$ \verb|2| +\end{cmd} + + +%-----------BBdata--------------------------------- +\begin{cmd}{BBdata}{bbdata} +\itemket{Usage}BBdata(file name, options); +\itemket{Description}Generic function to return the size of an image file. +\itemket{Details}In the \TeX document, find the BB size when pasting the image with the inputgraphics command. +Create BB data from an image file using extractbb of \TeX processing system and write it as a text file to the working directory. +Read this and write the ingludegarphics command to the console.\\ +Options : specifies width and height. "w=" : width, "h=" : height + +The value of bb is not an integer value, and it is indicated by rounding off the high definition value to two decimal places.\\ +The image files are PDF, PNG, JPG, and so on.\\ + +\itemket{Examples} \mbox{} + +\includegraphics[bb=0.00 0.00 562.03 124.01,width=12cm]{Fig/bbdata.pdf} + +\end{cmd} + +%---------Colorcode----------------------------------- +\begin{cmd}{Colorcode}{colorcode} +\itemket{Usage}Colorcode(colortype1,colortype2,colorcode) +\itemket{Description}Generic function to change colorcode from colortype1 to colortype2. +\itemket{Details}Return value is changed color code. + +Color type is one of "rgb'',"cmyk",''hsv''. +\item[Example]\mbox{} + +RGB to CMYK + +\hspace{10mm} \verb|col=Colorcode("rgb","cmyk",[1,0,0]); | + +CMYK to RGB + +\hspace{10mm} \verb|col=Colorcode("cmyk","rgb",[0,1,1,0]);| + +RGB to HSV + +\hspace{10mm} \verb|col=Colorcode("rgb","hsv",[1,0,0]);| + +\end{cmd} + +%----------Dqq---------------------------------- +\begin{cmd}{Dqq}{dqq} +\itemket{Usage}Dqq(string); +\itemket{Description}This function returns a string surrounded by double quotes. +\itemket{Exaample}\mbox{}\\ +\verb|parse("a");| // The value of variable \verb|a| is returned.\\ +\verb|parse(Dqq("a"));| // String \verb|"a"| is returned.\\ +\end{cmd} + +%----------Factorial---------------------------------- +\begin{cmd}{Factorial}{factorial} +\itemket{Usage}Factorial(n); +\itemket{Description}This function returns the factorial of \verb|n|. +\itemket[Details]\verb|n| should be a positive integer. +\itemket{Exaample}\verb|x=Factorial(5); // x is 120.| +\end{cmd} + +%----------Figpdf---------------------------------- +\begin{cmd}{Figpdf}{Figpdf} +\itemket{Usage}Figpdf(option) +\itemket{Description}Generic function to make a pdf with the same size of figure. +\itemket{Details}Option is a list of margin and the amount of translation. + +(1) Set the output file name with the command \verb|Setparent("filename")|. + +(2) Push the "Parent" button. + +"figure.tex" and "filename.tex" is created in fig folder. ( use "figure.cdy") filename.tex creates filename.pdf using figure.tex. +\itemket{Examples}\mbox{} +\begin{tabbing} +1234678901234567890123456789012\=\kill +\verb|Figpdf();| \> : default\\ +\verb|Figpdf([5,5,10,10]);| \> : left and right margins are 5mm\\ + \> : top and bottom margins are 10mm.\\ +\verb|Figpdf([[5,10]]);| \> : translation to right 5mm and to down 10mm. \\ +\verb|Figpdf([5,8,10,10,[5,-5]]);| \> : margin and translation +\end{tabbing} +We have to take the right margin at least 3mm to draw the axis name. +\end{cmd} + +%------------Cindyname-------------------------------- +\begin{cmd}{Cindyname}{cindyname} +\itemket{Usage}Cindyname(); +\itemket{Description}Generic function to return the name of a current file without ".cdy". +\itemket{Examples}\mbox{} + +\verb|name=Cindyname();| // If cuurent file is "sample.cdy", name="sample". +\end{cmd} + +%------------Indexall-------------------------------- +\begin{cmd}{Indexall}{indexall} +\itemket{Usage}Indexall(string1,string2); +\itemket{Description}Generic function to return all positions of string2 in string1. +\itemket{Examples}\mbox{} + +\verb|str="abcadeaf"|\\ +\verb|pos=Indexall(str,"a");|// Result is [1,4,7]. + +\item[Remarks]This command is an extension of "indexof" which is a command of CindyScript. +\end{cmd} + +%-----------Help--------------------------------- +\begin{cmd}{Help}{help} +\itemket{Usage}Help(string) +\itemket{Description}Generic function to display usages of the function. +\itemket{Examples}\mbox{} + +\verb|Help("L");| then we have the following result in console. + +\vspace{\baselineskip} +\verb|Letter([C,"c","Graph of $f(x)$"]);|\\ +\verb|Letter([C,"c","xy"],["size->30"]);|\\ +\verb|Letterrot(C,B-A,"AB");|\\ +\verb|Letterrot(C,B-A,"t0n5","AB");|\\ +\verb|Letterrot(C,B-A,0,5,"AB");|\\ +$\cdots\cdots\cdots$ + +\end{cmd} + +%-------------Norm------------------------------- +\begin{cmd}{Norm}{norm} +\itemket{Usage}Norm(vector); +\itemket{Description}This function returns the norm of the vector. +\itemket{Details}\mbox{} +The vector is 2D or 3D.\\ + If two vectors \verb|v1|, \verb|v2| are given, the value of \verb|Norm(v2-v1)| is returned. +\itemket{Examples}\verb|Norm([1,1,2]);| // $\sqrt{6}$ is returned. +\end{cmd} + +%-------------Op------------------------------- +\begin{cmd}{Op}{op} +\itemket{Usage}Op(number, list or string); +\itemket{Description}Generic function to return the n-th element of a list or a string. +\itemket{Examples}\mbox{} + +\verb|str="abcde"|\\ +\verb|list=[3,1,2,5];|\\ +\verb|s=Op(2,str); |// Result is "b".\\ +\verb|x=Op(3,list); |// Result is 2. +\end{cmd} + +%---------Ptselected----------------------------------- +\begin{cmd}{Ptselected}{ptselected} +\itemket{Usage}Ptselected(name of points) +\itemket{Description}Generic function to returns "true" if a point is selected. +\itemket{Details}Commands such as \verb|Hachdata| take time to execute, so interactive operations slow down the reaction. Therefore, while interactively operating, you can use this command to stop drawing. +\itemket{Examples}\mbox{} + +Draw the point A near the origin. + +\verb| Deffun("f(x)",["regional(y)","y=x^3-2*x","y"]);|\\ +\verb| Plotdata("1","f(x)","x",["Num=100"]);|\\ +\verb| Putoncurve("A","gr1");|\\ +\verb| coef=Derivative("f(x)","x",A.x);|\\ +\verb| Defvar(["coef",coef]);|\\ +\verb| Deffun("g(x)",["regional(y)","y=coef*(x-A.x)+A.y","y"]);|\\ +\verb| Plotdata("2","g(x)","x",["Num=1"]);|\\ +\verb| if(!Ptselected(A),|\\ +\verb| Enclosing("1",["gr2","Invert(gr1)"],[A,"nodisp"]);|\\ +\verb| Hatchdata("1",["i"],[["en1"]]);|\\ +\verb| );| + +\vspace{\baselineskip} +\hspace{20mm} Dragging point A (select) \hspace{5mm} Unselected + +\hspace{20mm}\includegraphics[bb=0.00 0.00 218.01 204.51,width=40mm]{Fig/ptselected01.pdf} +\hspace{10mm}\includegraphics[bb=0.00 0.00 219.01 204.51,width=40mm]{Fig/ptselected02.pdf} + +\end{cmd} + +%-------------Slider------------------------------- +\begin{cmd}{Slider}{slider} +\itemket{Usage}Slider("endpoint1-pt-endpoint2'',endpoint1,endpoint2); +\itemket{Description}Generic function to make a slider on a Euclidean view.\\ +\itemket{Examples}\mbox{} + +\verb|Slider("A-C-B",[-5,-2],[5,-2]); | // \verb|C| is movable.\\ +\verb|Slider("D-F-E",[-6,-2],[-6,2]); | // \verb|F| is movable.\\ +\verb|Plotdata("1",Assign("y=a*sin(x-b)",["a",F.y,"b",C.x]),"x"); | + +\vspace{\baselineskip} +\hspace{15mm} +\includegraphics[bb=0.00 0.00 445.02 193.01,height=40mm]{Fig/slider.pdf} + +\end{cmd} + +%-----------Sprintf--------------------------------- +\begin{cmd}{Sprintf}{sprintf} +\itemket{Usage}Sprintf(value,number); +\itemket{Description}Converts a real number to a string. +\itemket{Details}\hspace{9mm} Convert a real value to a string to the specified number of digits after the decimal point. +\itemket{Examples}\mbox{} + +\verb|Sprintf(pi,2);| // returns "3.14''.\\ +\verb|Sprintf(pi,7);| // returns "3.1415927''.\\ + +\verb|Remark| : \verb|pi| is a reserved variable in Cindyscript, representing the number $\pi$. + +\itemket{Reference} See \hyperlink{textformat}{Textformat}. +\end{cmd} + +%------------Strsplit-------------------------------- +\begin{cmd}{Strsplit}{strsplit} +\itemket{Usage}Strsplit(string,char); +\itemket{Description}Generic function to return the list of strings separated by \verb|char|. +\itemket{Examples}\mbox{} + +\verb|str="abcadeaf"|\\ +\verb|strL=Strsplit(str,"a"); |// Result is ["","bc","de","f"]. +\end{cmd} + +%\newpage + + +%----------Texcom---------------------------------- +\begin{cmd}{Texcom}{texcom} +\itemket{Usage}Texcom(command); +\itemket{Description}Generic function to add the command in the \TeX file. +\itemket{Details}Command is a \TeX command in string. +\itemket{Examples}\mbox{} + +\verb|Texcommand("{");|\\ +\verb|Texcommand("}");| +\end{cmd} + +%-------------Textformat}------------------------------- +\begin{cmd}{Textformat}{textformat} +\itemket{Usage}Textformat(value,number); +\itemket{Description}Converts a real number to a string. +\itemket{Details}\hspace{9mm}Convert a real value to a string up to the specified number of digits after the decimal point. "value" is can be list. + +Cindyscript has a function \verb|format(value, number)|, like as Textformat. +\itemket{Examples}\mbox{} + +\verb| Textformat(1/6,4);| // return value is string "0.1667'' \\ +\verb| format(1/6,4); | // return value is string "0.1667'' + +\verb| dt=[1/6,0.5];|\\ +\verb| Textformat(dt,4); | // return valu is string "[ 0.1667 , 0.5 ]" \\ +\verb| format(dt,4); | // return value is list ["0.1667" , "0.5" ]\\ +\verb| Sprintf(dt,4); | // return value is list ["0.1667","0.5000"] + +\itemket{Reference} See \hyperlink{sprintf}{Sprintf}. + +\end{cmd} + +%----------Toupper---------------------------------- +\begin{cmd}{Toupper}{toupper} +\itemket{Usage}Toupper(string); +\itemket{Description}This function returns the upper case letters of the string. +\itemket{Examples}\verb|Toupper("aBc123'');| // "ABC123" is returned. + +%\verb|Windispg();| +\end{cmd} + +%----------Windispg---------------------------------- +\begin{cmd}{Windispg}{windispg} +\itemket{Usage}Windispg(); +\itemket{Description}Generic function to display all graphs on Euclidean view. +\itemket{Remark}This command must be put on the final line. +%\itemket{Examples}\mbox{} + +%\verb|Windispg();| +\end{cmd} + +\newpage +%==== Calling Other Softwares ========= +\section{Calling Other Softwares} +\subsection{R} + +%--------------Rfun------------------------------ +\begin{cmd}{Rfun}{rfun} +\itemket{Usage}Rfun(name, ommand,list of arguments,options) +\itemket{Description}This function executes a R command and returns the. +\itemket{Examples}\verb|Rfun("1","rnorm",[10]);| // The result will be assigned to "R1". +\itemket{Remark}Option "Cat=n" supresses display of the result in the console. +\end{cmd} + +%--------------CalcbyR------------------------------ +\begin{cmd}{CalcbyR}{calcbyr} +\itemket{Usage}CalcbyR(var,command,options) +\itemket{Description}executes R commands and returns the execution result to Cinderella. +\itemket{Details}exchange data with R through a batch file (kc.bat) or a shell file (kc.shell). +\itemket{Examples} \mbox{} + +Generate 10 random samples from the standard normal distribution by R and return the result (data) to Cinderella.\\ +\verb| cmdL=[|\\ +\verb| "dt=rnorm",[10,50,5],|\\ +\verb| "m=mean(dt)",[],|\\ +\verb| "u=var(dt)",[],|\\ +\verb| "dt::m::u",[]|\\ +\verb| ]|\\ +\verb| CalcbyR("ans",cmdL);| + +\verb| println("Data : "+ans_1);|\\ +\verb| println("Mean : "+format(ans_2,4));|\\ +\verb| println("UD : "+format(ans_3,4));|\\ + +%\begin{center} +%\includegraphics[bb=0.00 0.00 532.53 249.51,width=12cm]{Fig/calcbyr01.pdf} +%\end{center} + +generate 200 random samples from the Poisson distribution with mean 5 and calculate the sample mean and the unbiased variance of the data.\\ +\verb| cmdL=[|\\ +\verb| "tmp1=rpois",[200,5],|\\ +\verb| "tmp2=mean",["tmp1"],|\\ +\verb| "tmp3=var",["tmp1"],|\\ +\verb| "tmp2::tmp3::tmp1",[]|\\ +\verb| ];|\\ +\verb| CalcbyR("rd",cmdL);|\\ +\verb| dt=rd_(3..length(rd));|\\ +\verb| nn=length(dt);|\\ +\verb| mx=rd_1;|\\ +\verb| vx=rd_2*(nn-1)/nn;|\\ +\verb| sx=sqrt(vx);|\\ +\verb| println(dt);|\\ +\verb| println(["m="+format(mx,4),"v="+format(vx,4)]);|\\ +\verb| Setscaling(1/5);| + +create a histogram for the data, \verb|Breaks=seq(0,14,1)| specifies the bin size.\\ +\verb| Histplot("1",dt,["Breaks=seq(0,14,1)","dr,0.5"]);|\\ + +\begin{center} +\input{Fig/poison01} +\end{center} + +generate 2000 random samples from the Poisson distribution and calculate 200 sample means in 10 samples.\\ +\verb| cmdL=[|\\ +\verb| "tmp1=rpois",[2000,5],|\\ +\verb| "tmp2=c()",[],|\\ +\verb| "for(k in 1:200){",[],|\\ +\verb| " tmp=tmp1[(10*(k-1)+1):(10*k)]",[],|\\ +\verb| " tmp2=c(tmp2,mean(tmp))",[],|\\ +\verb| "}",[],|\\ +\verb| "=tmp2",[]|\\ +\verb| ];|\\ +\verb| CalcbyR("rd2",cmdL);|\\ +\verb| Setscaling(1/10);|\\ +\verb| Histplot("2",rd2);|\\ + +\end{cmd} + +%-------------Boxplot------------------------------- +\begin{cmd}{Boxplot}{boxplot} +\itemket{Usage}Boxplot(name, data, vertical position, height of box,options); +\itemket{Description}draw boxplots +\itemket{Examples}\mbox{} + +draw a boxplot of 100 uniform random numbers less than 5. + +\verb| dt1=apply(1..100,5*random());|\\ +\verb| Boxplot("1",dt1,1,1/2);| + +\begin{center} \input{Fig/boxplot01} \end{center} + +read an external data file in csv format and draw a boxplot of the data. + +\verb| Boxplot("2","datafile.csv",3,1/2);| + +You can read a csv file with more than one column using \verb|Readcsv|. +The csv flie should be stored in current working folder (defalut is fig folder). +Using \verb|Framedata| and \verb|Rulerscale| together, you can mark with a scale. +Before you use \verb|Framedata|, you need to take two diagonal points of the drawing area on the Euclidean view. + +\verb| data=Readcsv("datafile.csv");|\\ +\verb| dt1=apply(data,#_1);|\\ +\verb| dt2=apply(data,#_2);|\\ +\verb| Boxplot("1",dt1/20,1,1/2);|\\ +\verb| Boxplot("2",dt2/20,3,1/2);|\\ +\verb| Framedata("1",[A,B],["corner"]);|\\ +\verb| Rulerscale(A,["r",0,6,1],["f",1,"\mbox{dt1}",3,"\mbox{dt2}"]);| + +\begin{center} \input{Fig/boxplot} \end{center} + +\end{cmd} + +%-------------Histplot------------------------------- +%\newpage + +\begin{cmd}{Histplot}{histplot} + +\itemket{Usage}Histplot(name,data,options) +\itemket{Description}create histograms. +\itemket{Details}data is given in a list or read an external data file in csv format.\\ +You can specify the breaks as a vector of points to get exactly what is wanted, for example\\ +\hspace{20mm} \verb|''Breaks=[0,10,20,30,40,50,60]''| .\\ +The Sturges algorithm is the default.\\ +Other options:\\ +\verb|''Rel=yes/no''| : draw a histogram of proportions or frequencies (default is no)\\ + +\itemket{Examples} \mbox{} + +Read the data file in csv format (datafile.csv) and create a histogram of the data in a frame with a scale.\\ +\verb| Addax(0);|\\ +\verb| Setscaling(5);|\\ +\verb| Setunitlen("0.6mm");|\\ +\verb| data=Readcsv("datafile.csv");|\\ +\verb| Histplot("1",data,[""]);|\\ +\verb| Framedata("1",[A,B],["corner"]);|\\ +\verb| Rulerscale(A,["r",0,100,10],["r",0,15,5]);|\\ + +\begin{center} +\input{Fig/histgram} +\end{center} + +\end{cmd} +%------------PlotdataR-------------------------------- +\begin{cmd}{PlotdataR}{plotdatar} + +\itemket{Usage}PlotdataR(name,formula,var) +\itemket{Description}Draw graph of R's statistical probability function. +\itemket{Details}Draw graphs of functions not built-in Cindyscript. +\itemket{Examples} \mbox{} + +Example1\\ +draw graphs of the probability density function (p.d.f.) and the cummulative distribution function of $N(5,2^2)$.\\ +\verb| PlotdataR(“1”, “dnorm(x,5,2)”, ”x=[0,10]”); |\\ +\verb| PlotdataR(“2”, ”pnorm(x,5,2)”, ”x=[0,10]”);| + +%\vspace{\baselineskip} +\begin{center} +\input{Fig/plotdatar1} +\end{center} + +Example2\\ +1. draw a graph of the p.d.f. of standard normal distribution.\\ +2. shade the region under the graph and above x-axis to the left of \verb|A.x|.\\ +3. find the area of the shaded region.\\ +\verb| PlotdataR("1","dnorm(x)","x=[-5,5]",["Num=100"]); |\\ +\verb| Putpoint("A",[0,0],[A.x,0]); |\\ +\verb| Lineplot("1",[A,A+[0,1]],["nodisp"]); |\\ +\verb| Putintersect("B","grR1","ln1"); |\\ +\verb| Listplot("1",[A,B]); |\\ +\verb| Listplot("2",[[-5,0],[5,0]],"nodisp"); |\\ +\verb| Enclosing("1",["Invert(grR1)","sg2","sg1"],[B,"notex"]); |\\ +\verb| Shade(["en1"],["Color=[0.2,0,0,0]"]); |\\ +\verb| tmp=0.5+Integrate("grR1",[0,A.x]); |\\ +\verb| Expr([A,"s",text(A.x),C,"e","P="+text(tmp)]); | + +%\vspace{\baselineskip} +\begin{center} +\input{Fig/rshade} +\end{center} + +\end{cmd} +%--------------PlotdiscR------------------------------ +\begin{cmd}{PlotdiscR}{plotdiscr} + +\itemket{Usage}PlotdiscR(name,fromaula,var) +\itemket{Description}draw graphs of discrete distributions by calling R’s built-in functions. +\itemket{Details}The ''d'' functions in R to draw graphs of discrete distributions:\\ +dbinom (binomial distribution), dpois (poisson distribution), dgeom (geometric distribution), etc. +\itemket{Examples} \mbox{} + +The normal distribution with the same mean and standard deviation as the binomial distribution\\ +\verb| Setscaling(20);|\\ +\verb| PlotdiscR("1","dbinom(k,10,0.4)","k=[0,10]");|\\ +\verb| PlotdataR("1","dnorm(x,10*0.4,sqrt(10*0.4*0.6))","x=[0,10]",["do"]);| + +\begin{center} +\input{Fig/binvsnormal} +\end{center} + +Example2 + +\verb| PlotdiscR("2","dpois(k,4)","k=[0,10]");|\\ +\verb| PlotdiscR("3","dgeom(k,0.3)","k=[0,10]");| + +\end{cmd} +%------------Readcsv-------------------------------- +\begin{cmd}{Readcsv}{readcsv} + +\itemket{Usage}Readcsv(path,filename,option) +\itemket{Description}read an external data file in csv format. The return value is a list of the data. +\itemket{Details}The first argument sets a path to the current working folder where the data file is (the default is fig). +If you put the data file in fig folder, the pathname can be omitted. Otherwise a full pathname is required.\\ +option: By the argument "Flat=y", you can flatten a list of the data (the default is "Flat=n" ). +\itemket{Examples} \mbox{} +Examples can be found in the command Boxplot(). +\end{cmd} +%------------Scatterplot-------------------------------- +\begin{cmd}{Scatterplot}{scatterplot} + +\itemket{Usage}Scatterplot(name,filename/datalist,options1,options2) +\itemket{Description}This command draw scatter plot reading a csv file. +\itemket{Details} Datafile is next style csv format. +\begin{verbatim} + 2.3, 4.5 (LF) + 3.2, 7 (LF) + 2.0, 6.8 (LF) +\end{verbatim} +If 2nd argment is datalist, next format. +\begin{verbatim} + data=[[2.3,4.5],[3.2,7],[2.0,6.8], ・・・ ]; +\end{verbatim} + +Options1 are switch of draw the regression line or no , style of point.\\ +\verb|"Reg=yes(no:default)"| to decide whether to draw the regression line.\\ +Options2 are position of drawing the regression line and style of line.\\ +Position is coordinate or name of point. +\itemket{Examples}\mbox{} + +\verb| Scatterplot("1","data.csv",["Size=4","Color=blue"],[A,"Color=green"]);|\\ +\verb| Listplot("1",[[0,7],[0,0],[7,0]]);|\\ +\verb| Rulerscale([0,0],["r",0,7,1],["r",1,7,1]);| + +\begin{center} +\input{Fig/scatter} +\end{center} +\end{cmd} + +%\newpage + +%========= Maxima ======= +\subsection{Maxima} +%------------CalcbyM-------------------------------- +\begin{cmd}{CalcbyM}{calcbym} + +\itemket{Usage}CalcbyM(name, command,options) +\itemket{Description}Maxima's script execution +\itemket{Details}The second argument is a command to be executed by Maxima.\\ +Create a list (eg. cmdL) consisting of a repetition of commands and argument lists, and execute at once.\\ +There is no return value. +For the result (of undefined value), the value of the variable of the command list last described (argument is the empty list) is assigned to the variable specified by ''name''. +When you want to return more than one result, if you describe it by separating it with ''::'', it will be substituted into the list. +\itemket{Examples} \mbox{} + +Example1: derivative + +\verb| cmdL=[ |\\ +\verb| "f:sin(x)", [], |\\ +\verb| "df:diff",["sin(x)","x"], |\\ +\verb| "f::df",[] |\\ +\verb| ]; |\\ +\verb| CalcbyM("fdf",cmdL); |\\ +\verb| println(fdf); |\\ + +Example2: solution of quadratic equation + +\verb| cmdL=[ |\\ +\verb| "ans:solve",["x^2-x-4","x"], |\\ +\verb| "ans",[] |\\ +\verb| ]; |\\ +\verb| CalcbyM("ans",cmdL); |\\ +\verb| println("ans="+ans); |\\ + +Example3: + + +\verb| fx="(exp(x)+exp(-x))/2"; |\\ +\verb| cmdL=[ |\\ +\verb| "df:diff",[fx,"x"], |\\ +\verb| "c:ev",["df","x=a"], |\\ +\verb| "b:ev",[fx,"x=a"], |\\ +\verb| "eq:c*(x-a)+b",[], |\\ +\verb| "eq",[] |\\ +\verb| ]; |\\ +\verb| CalcbyM("tn1",cmdL); |\\ +\verb| tn1=Assign(tn1,["%e^a","exp(a)","%e^-a","exp(-a)"]); |\\ +\verb| Plotdata("1",fx,"x"); |\\ +\verb| PutonCurve("A","gr1"); |\\ +\verb| tmp=Assign(tn1,["a",A.x]); |\\ +\verb| plotting data("2",tmp,"x",["Num=2"]); |\\ +\verb| Letter([A,"se","A"]);| + +%\newpage +Example4: Parametric + +\verb| fn="3*cos(t)^2*[cos(t),sin(t)]";|\\ +\verb| cmdL=[|\\ +\verb| "f:",[fn], |\\ +\verb| "df:diff",["f","t"], |\\ +\verb| "df:trigsimp",["df"], |\\ +\verb| "tn:f+s*df",[], |\\ +\verb| "tn",[] |\\ +\verb| ]; |\\ +\verb| CalcbyM("tn2",cmdL); |\\ +\verb| Paramplot("1",fn,"t=[0,2*pi]",["Num=100"]); |\\ +\verb| gn=Assign(tn2,["t",A.x]); |\\ +\verb| Paramplot("2",gn,"s=[-3,3]"); |\\ + +\begin{minipage}{65mm} +\begin{center} +\input{Fig/maxfun01}\\ +Example3 +\end{center} +\end{minipage} +\begin{minipage}{65mm} +\begin{center} +\vspace*{5mm} + +\input{Fig/maxfun02}\vspace{10mm}\\ +Example4 +\end{center} +\end{minipage} + +\end{cmd} +%-------------Mxbatch------------------------------- +\begin{cmd}{Mxbatch}{mxbatch} + +\itemket{Usage}Mxbatch(filename) +\itemket{Description}Creation command to execute Maxima file +\itemket{Details}Create a command for CalcbyM to execute the file in ketcindy/ketlib/maximaL. +ketcindy/ketlib/maximaL contains three files: fourier\_sec.max, matoperation.max and poincare.mac. +For example, when dealing with Fourier series, use fourier\_sec.max. +\itemket{Examples} \mbox{} + +\verb| Setax(["a"]); |\\ +\verb| Slider("A-C-B",[-5.5,-1.5],[4.5,-1.5]); |\\ +\verb| defL=["1",[-3,-2],1,"0",[-2,-1],1,"-x",[-1,1],1,"0",[1,2],1,"-1",[2,3],1]; |\\ +\verb| Drwxy(); |\\ +\verb| tmp=Periodfun(defL,1,["dr,2","Color=red"]); |\\ +\verb| fun=tmp_1; |\\ +\verb| per=tmp_2; |\\ +\verb| Htickmark([1,"n","1",2,"n","2",3,"nw","3"]); |\\ +\verb| Htickmark([-1,"-1",-2,"-2",-3,"-3"]); |\\ +\verb| cmdL=Concat(Mxbatch("fourier_sec"),[ |\\ +\verb| "Ffun(x):="+fun,[], |\\ +\verb| "c:fourier_sec_coeff",["Ffun(x)","x"], |\\ +\verb| "c[1]::c[2]::c[3]",[] |\\ +\verb| ]); |\\ +\verb| CalcbyM("ans",cmdL,[]); |\\ +\verb| nterm=round(4*(C.x-A.x)); |\\ +\verb| Fourierseries("1",ans,per,nterm,["Num=400"]); |\\ +\verb| Mxtex("2",ans_3); |\\ +\verb| Expr([[-5,-2],"e","s_n="+tx2,[4,-2],"e","n="+text(nterm)]); | + +%\vspace{\baselineskip} +%\hspace{20mm}\input{Fig/mxbatch}\vspace*{12mm} + +\begin{center} +\input{Fig/mxbatch}\vspace{3mm} +\end{center} + +\end{cmd} +%-------------Mxfun------------------------------- +\begin{cmd}{Mxfun}{mxfun} + +\itemket{Usage}Mxfun(name,formula,list,options) +\itemket{Description}Execution of Maxima's function +\itemket{Details}The second argument "formula" is Maxima's function name. +The third argument "list" is a list of arguments to pass to the function. \\ +The return value is a string if there is at least one character in the expression of the second argument. +In the case of all numbers (including +, -, .), it becomes a number if it is 16 or less digits, and it becomes a string if it is more than 16 digits. +Also, the return value is also assigned to the variable "mxname".\\ +If "Disp = no" is added to the option, the result is not displayed on the console. +\itemket{Examples} \mbox{} + +\verb| Mxfun("1","taylor",["sin(x)","x",0,7],[""]); |\\ +\verb| Plotdata("1","sin(x)","x",["da"]); |\\ +\verb| Plotdata("2",mx1,"x"); | + +\vspace{\baselineskip} +\hspace{20mm} \input{Fig/taylor}\\ + +\end{cmd} +%------------Mxtex-------------------------------- +\begin{cmd}{Mxtex}{mxtex} + +\itemket{Usage}Mxtex(name, formula) +\itemket{Description}Conversion of expression to TeX format +\itemket{Details}The second argument "formula" is the expression directly written or the return value of Mxfun. +Convert it to TeX format.\\ +The return value is also assigned to the variable "txname". +\itemket{Examples} \mbox{} + +Example1 + +\verb| fx="x^3/((x+1)*(x+2))"; |\\ +\verb| pfx=Mxfun("1","partfrac",[fx,"x"]); |\\ +\verb| form=Mxtex("1",fx)+"="+Mxtex("2",pfx); |\\ +\verb| dform=Assign(form,["frac","dfrac"]); |\\ +\verb| Expr([0,3],"e",form); |\\ +\verb| Expr([0,1],"e",dform); |\\ + +\includegraphics[bb=0.00 0.00 240.01 115.51,width=70mm]{Fig/mxtex01E.pdf} +\input{Fig/mxtex02} + +\vspace{\baselineskip} +Example2 + +\begin{layer}{150}{0} +\putnotese{70}{50}{ \input{Fig/mxtex03}} +\end{layer} + +\verb| fx="x^2-x-3"; |\\ +\verb| cmdL=[ |\\ +\verb| "ans:solve",[fx,"x"], |\\ +\verb| "ans",[] |\\ +\verb| ]; |\\ +\verb| CalcbyM("ans",cmdL); |\\ +\verb| p1=indexof(ans,"["); |\\ +\verb| p2=indexof(ans,","); |\\ +\verb| p3=indexof(ans,"]"); |\\ +\verb| s1=substring(ans,p1,p2-1); |\\ +\verb| s2=substring(ans,p2,p3-1); |\\ +\verb| s1=replace(s1,"x =",""); |\\ +\verb| s2=replace(s2,"x =",""); |\\ +\verb| Mxtex("1",s1); |\\ +\verb| Mxtex("2",s2); |\\ +\verb| Plotdata("1",fx,"x"); |\\ +\verb| Expr([-2,-0.5],"e",tx1); |\\ +\verb| Expr([2,-0.5],"e",tx2); |\\ + +\end{cmd} + +%========= Risa/Asir ======= +\subsection{Risa/Asir} + +%------------CalcbyA-------------------------------- +\begin{cmd}{CalcbyA}{calcbya} + +\itemket{Usage}CalcbyA(name, command,options) +\itemket{Description}Risa/Asir's script execution +\itemket{Details}The second argument is a command to be executed by Risa/Asir.\\ +Create a list (eg. cmdL) consisting of a repetition of commands and argument lists, and execute at once.\\ +There is no return value. +The result (of undefined value) is assigned to the variable specified by "name", the value of the variable of the command list last described (argument is the empty list). +If you want to return more than one result, if you describe it by separating it with "::", it will be substituted into the list. +%\itemket{Examples} \mbox{} + +\end{cmd} +%-------------Asirfun------------------------------- +\begin{cmd}{Asirfun}{asirfun} + +\itemket{Usage}Asirfun(name, formula, list,options) +\itemket{Description}Execution of Risa/Asir's function +\itemket{Details}The second argument "formula" is the function name of Risa/Asir. +The third argument "list" is a list of arguments to pass to the function.\\ +The return value is a string if there is at least one character in the expression of the first argument. +In case of all numbers (including +, -, .), it becomes a number if it is 16 digits or less, and it becomes a string if it is more than 16 digits. +Also, the return value is also assigned to the variable "asname".\\ +If "Disp = no" is added to the option, the result is not displayed on the console. +%\itemket{Examples} \mbox{} + +\end{cmd} +%========= MeshLab ======= +\subsection{MeshLab} + +Write next script in Initialization slot for use \ketcindy\ 3D. + \\ +\verb| Ketinit();|\\ +\verb| Ketinit3d();| + +%--------------Mkobjcmd------------------------------ +\begin{cmd}{Mkobjcmd}{mkobjcmd} + +\itemket{Usage}Mkobjcmd(name,formula,option) +\itemket{Description}generate commands for obj formatted files of surfaces without thickness. +%%\itemket{Details} +\itemket{Examples} \mbox{} + +\verb| fd=[ "z=x^2-y^2","x=[-1,1]","y=[-1,1]"," "]; |\\ +\verb| Sf3data("1",fd); |\\ +\verb| Windispg(); |\\ +\verb| Mkobjcmd("1",fd,[40,40,"-"]); |\\ +\verb| Meshlab():=( |\\ +\verb| Mkviewobj("saddle",oc1, ["m","v"]); |\\ +\verb| ); | + +Option ``$+$" is for the left figure, and ``$-$" for the right. + +\hspace{10mm} \includegraphics[bb=0 0 679.53 263.51 , width=12cm]{Fig/meshlab01.pdf} +\end{cmd} +%-------------Mkobjcrvcmd------------------------------- +\begin{cmd}{Mkobjcrvcmd}{mkobjcrvcmd} + +\itemket{Usage}Mkobjcrvcmd(name,PD,option) +\itemket{Description}generate commands for obj formatted files of spatial curves. +%%\itemket{Details} +\itemket{Examples} \mbox{} + +\verb| Spacecurve("1","[(6*pi-t)/(6*pi)*cos(t),(6*pi-t)/(6*pi)*sin(t),0.1*t]", |\\ +\verb| "t=[0,6*pi]",["Num=200"]); |\\ +\verb| Windispg(); |\\ +\verb| Mkobjcrvcmd("1","sc3d1",[0.1,8,"yz"]); |\\ +\verb| Meshlab():=( |\\ +\verb| Mkviewobj("spiral",oc1,["m","v"]); |\\ +\verb| ); | + +\hspace{10mm} \includegraphics[bb=0 0 614.53 236.51 , width=12cm]{Fig/meshlab02.pdf} + +\end{cmd} +%--------------Mkobjnrm------------------------------ +\begin{cmd}{Mkobjnrm}{mkobjnrm} + +\itemket{Usage}Mkobjnrm(name,formula) +\itemket{Description}calculate normal vector of surface. +\itemket{Details}Normal vector is calculated using the formula of surface. +\itemket{Examples} \mbox{} + +\verb| Mkobjnrm("1","[x,y,x*y/sqrt(x^2+y^2)],x,y"); |\\ + +\end{cmd} +%--------------Mkobjplatecmd------------------------------ +\begin{cmd}{Mkobjplatecmd}{mkobjplatecmd} + +\itemket{Usage}Mkobjplatecmd(name,facedata,options) +\itemket{Description}generate commands for obj formatted files of plates. +%%\itemket{Details} +\itemket{Examples} \mbox{} + +\begin{layer}{150}{0} +\putnotese{80}{13}{ \includegraphics[bb=0 0 287.01 228.01 , width=3cm]{Fig/meshlab03.pdf} } +\end{layer} + +\verb| Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]"); |\\ +\verb| p1=[2,0,0]; |\\ +\verb| p2=[0,2,0]; |\\ +\verb| p3=[0,0,2]; |\\ +\verb| plane=[[p1,p2,p3],[[1,2,3]]]; |\\ +\verb| Mkobjplatecmd("1",plane,[0.05]); |\\ +\verb| Mkobjcrvcmd("2","ax3d"); |\\ +\verb| Mkviewobj("plane",Concatcmd([oc1,oc2]),["m","v"]); | + +\end{cmd} +%-------------Mkobjpolycmd------------------------------- +\begin{cmd}{Mkobjpolycmd}{mkobjpolycmd} + +\itemket{Usage}Mkobjpolycmd(name,PD,options) +\itemket{Description}generate commands for obj formatted files of polyhedra. +%%\itemket{Details} +\itemket{Examples} \mbox{} + +\verb| Setdirectory(Dirhead+"/data/polyhedrons_obj"); |\\ +\verb| polydt=Readobj("r01.obj",["size=-3.5"]); |\\ +\verb| Setdirectory(Dirwork); |\\ +\verb| pd=VertexEdgeFace("1",polydt,["Pt=fix","Edg=nogeo"]); |\\ +\verb| Mkobjpolycmd("1",pd,[[0,0,0]]); |\\ +\verb| Mkviewobj("plane",oc1,["m","v"]); | +%% Setobj(Fhead,["m","v"]); + +The polyhedron obj data is downroaded from\\ +\hspace*{20mm}\url{http://mitani.cs.tsukuba.ac.jp/polyhedron/} + + +\end{cmd} +%--------------Mkobjsymbcmd------------------------------ +\begin{cmd}{Mkobjsymbcmd}{mkobjsymbcmd} + +\itemket{Usage}Mkobjsymbcmd(PD,real,real,vector,vector) +\itemket{Description}generate commands for obj formatted files of some characters. +\itemket{Details}Ploting data are available for characters $x$, $y$, $z$, $t$, $n$, P, Q, and R. +The arguments are their siizes, angles of rotations, directions of the viewpoints, positions. +\itemket{Examples} \mbox{} + + +\verb| Mkobjsymbcmd("P",0.5,pi/3,[0,-1,0],[0,0,6]); |\\ +\verb| Mkobjsymbcmd("x",0.5,0,[0,-1,0],[6,0,0]); |\\ +\verb| Circledata("1",[[0,0],[1,0]],["nodisp"]); |\\ +\verb| Mkobjsymbcmd("cr1",0.5,0,[0,-1,0],[0,5,0]); | + +\end{cmd} +%-------------Mkobjthickcmd------------------------------- +\begin{cmd}{Mkobjthickcmd}{mkobjthickcmd} + +\itemket{Usage}Mkobjthickcmd(name,formula) +\itemket{Description}generate commands for obj formatted files of surfaces with thickness. +%%\itemket{Details} +\itemket{Examples} \mbox{} + +This function use Maxima. + +\begin{layer}{150}{0} +\putnotese{70}{0}{ \includegraphics[bb=0 0 287.01 189.01 , width=4cm]{Fig/meshlab06.pdf}} +\end{layer} + +\verb| fd=[ |\\ +\verb| "z=(x^2+y^2)",|\\ +\verb| "x=R*cos(T)","y=R*sin(T)",|\\ +\verb| "R=[0,2]","T=[0,2*pi]","e"|\\ +\verb| ];|\\ +\verb| Mkobjthickcmd("1",fd,[40,40,0.2,"+n+s-e-w+","assume(R>0)"]);|\\ +\verb| Mkviewobj("pala",oc1,["m","v","Wait=5"]); |\\ + + +\end{cmd} +%---------------Mkviewobj----------------------------- +\begin{cmd}{Mkviewobj}{mkviewobj} + +\itemket{Usage} Mkviewobj(name,PD,options) +\itemket{Description}generate obj formatted files. +\itemket{Details}options +\begin{tabbing} +12345678901234567890\=\kill + "m" or "make" \> for generating data \\ + "v" or "view" \> for starting meshlab and viewing\\ + "W=n" or "Wait=n" \> for setting culculate time\\ + "Unit=mm" \> for setting unit of length \\ + \>\\ +\end{tabbing} +%\itemket{Examples} \mbox{} + +\end{cmd} +\newpage +%=========== Animation =============== +\section{Animation} + +\vspace{\baselineskip} + \hspace{10mm} \includegraphics[bb=0 0 732.04 376.02 , width=12cm]{Fig/mvgaiyou01.pdf} + +Operation of Buttons. + +\begin{tabbing} +1234\=12345678\=1234567897890123456\=\kill + \> Figure \> Viewtex(); \> Making figure.tex\\ + \> Parent \> same code \>Making figure.pdf by Figpdf() \\ + \> ParaF \> Parafolder(); \> Making data folder of animation data\\ + \> Anime \> Mkanimation(); \> Making flip animation\\ + \> Flip \> Mkflipanime(); \>Making animation +\end{tabbing} + +%---------------Setpara----------------------------- +\begin{cmd}{Setpara}{setpara} + +\itemket{Usage}Setpara(fname,funcstr,range,options1,options2) +\itemket{Description}Set up the animation control system. +\itemket{Details}"fname" is the name of output file. "funcstr" is the name of animation function. "range" is the range of parameter.\\ + +options1 + +\begin{tabbing} +1234567890123\=90123456789012345678\=\kill +m/r \> Remake the new data file / Reread the existing data file (default=r)\\ +Div=n \> Total number of frames (default n=25). +\end{tabbing} + +options2 + +\begin{tabbing} +1234567890123\=90123456789012345678\=\kill +Frate=n \> Number of frames per second (default n=20)\\ +Title=str \> Title\\ +Scale=n \> Magnification factor of the figures\\ +opA \> option for animate.sty\\ + \> loop: loop, controls: Show control button, buttonsize\\ + \> step: Mode of frame feed/frame retrun\\ + \> Default is \verb|"OpA=[loop,controls,buttonsize=3mm]"|\\ + \> Use "+" then you can add a mode, for example \verb|"OpA=+step"| then we have\\ + \> \verb|"OpA=[loop,controls,buttonsize=3mm,step]"| +\end{tabbing} + +\itemket{Examples} \mbox{} + +\verb| Slider("A-C-B",[0,YMIN-1],[2*pi,YMIN-1]); |\\ +\verb| Setax(["","","sw","","sw"]); |\\ +\verb| Circledata("1",[[0,0],[0,2]]); |\\ +\verb| mf(t):=( |\\ +\verb| pt=2*[cos(t),sin(t)]; |\\ +\verb| mp=(pt+[4,0])/2; |\\ +\verb| Listplot("1",[[4,0],pt]); |\\ +\verb| Pointdata("1",[mp,pt],["Size=2"]); |\\ +\verb| if(t==0, |\\ +\verb| ptlist=[mp]; |\\ +\verb| , |\\ +\verb| ptlist=append(ptlist,mp); |\\ +\verb| ); |\\ +\verb| Pointdata("2",ptlist,["Size=2","Color=red"]); |\\ +\verb| Letter([[4,0],"s","A",pt,"en","P",mp,"ne","Q"]); |\\ +\verb| ); |\\ +\verb| Setpara("middle","mf(t)","t=[0,4*pi]"); |\\ +\verb| mf(C.x); | + +\vspace{\baselineskip} +\hspace{20mm} \includegraphics[bb=0.00 0.00 608.03 367.02,width=8cm]{Fig/moviedata01.pdf} + +When we make the animation, comment out \verb|//mf(C.x);| and click the Anime button. The following figure is the first page of the animatemiddle.pdf file. + +\hspace{30mm}\includegraphics[bb=0.00 0.00 470.02 394.02,width=6cm]{Fig/moviedata02.pdf} + +The animation is continued for 5 seconds with the following options.\\ + \verb| Setpara("middle","mf(t)","t=[0,4*pi]",["Div=30"],["Frate=6"]);|\\ +A smooth-looking animation is achieved with the options: \verb|["Div=150"],["Frage=30"]|. +\end{cmd} + +\newpage +%============== Slide ================== +\section{\ketcindy\ Slide} + +%------------Setslidebody-------------------------------- +\begin{cmd}{Setslidebody}{setslidebody} +\itemket{Usage}Setslidebody(bodycolor,bodystyle,density) +\itemket{Description}Set up the color and density of the letters in slide body.\\ +\itemket{Details}Meanings and defaults of options are\\ +\Ltab{25mm}{bodycolor}\Ltab{50mm}{color of letters}\verb|"blue"|\\ +\Ltab{25mm}{bodystyle}\Ltab{50mm}{style of letters}\verb|"\Large\bf\boldmath"|\\ +\Ltab{25mm}{density}\Ltab{50mm}{density of thin letters}\verb|0.1|\ (The range is from 0 to 1).\\ +\hspace{10mm}Remark : density can be changed by \verb|\setthin{density}| in the text file. +\end{cmd} + +%------------Setslidehyper------------------------------- +\begin{cmd}{Setslidehyper}{setslidehyper} +\itemket{Usage}Setslidehyper("dvipdfmx",options) +\itemket{Description}Use \verb|hyperref.sty|. +\itemket{Details}if the 1st argument is null, it will be replaced with "dvipdfmx".\\ +options : \verb|["cl=true,lc=blue,fc=blue","Pos=[125,73]","Size=1"]|\\ +Meanings and defaults of options are\\ +\\ +\Ltab{25mm}{"cl=..."}\Ltab{50mm}{colorlinks}\verb|cl=true|\\ +\Ltab{25mm}{"lc=..."}\Ltab{50mm}{linkcolor}\verb|lc=blue|\\ +\Ltab{25mm}{"fc=..."}\Ltab{50mm}{filecolor}\verb|fc=blue|\\ +\Ltab{25mm}{"Pos=..."}\Ltab{50mm}{start position of buttons}\verb|"Pos=[125,73]"|\\ +\Ltab{25mm}{"Size=..."}\Ltab{50mm}{size of buttons}\verb|"Size=1"|.\\ +\end{cmd} + +%------------Setslidemain------------------------------- +\begin{cmd}{Setslidemain}{setslidemain} +\itemket{Usage}Setslidemain([letterc,boxc,framec,xpos,size]); +\itemket{Description}Set up the main slide (a section delimiter). +\itemket{Details}Meanings and defaults of options are\\ +\Ltab{25mm}{letterc}\Ltab{50mm}{color of letters}\verb|[0.98,0.13,0,0.43]|\\ +\Ltab{25mm}{boxc}\Ltab{50mm}{color of box}\verb|[0,0.32,0.52,0]|\\ +\Ltab{25mm}{framec}\Ltab{50mm}{color of frame}\verb|[0,0.32,0.52,0]|\\ +\Ltab{25mm}{xpos}\Ltab{50mm}{horizontal position of title}\verb|62|\\ +\Ltab{25mm}{size}\Ltab{50mm}{magnification of title}\verb|2|. +\itemket{Remark}If some arguments are null, the defaul is used.\\ +\hspace*{10mm}\verb|Setslidemain([,,,,3]);| +\end{cmd} + +%------------Setslidepage------------------------------ +\begin{cmd}{Setslidepage}{setslidepage} +\itemket{Usage}Setslidepage([letterc,boxc,framec,shadowc,xpos,size]); +\itemket{Description}Set up each page of slides. +\itemket{Details}Meanings and defaults of options are\\ +\Ltab{25mm}{letterc}\Ltab{50mm}{color of letters}\verb|[0.98,0.13,0,0.43]|\\ +\Ltab{25mm}{boxc}\Ltab{50mm}{color of box}\verb|[0,0.32,0.52,0]|\\ +\Ltab{25mm}{framec}\Ltab{50mm}{color of frame}\verb|[0,0.32,0.52,0]|\\ +\Ltab{25mm}{shadowc}\Ltab{50mm}{color of shadow}\verb|[0,0,0,0.5]|\\ +\Ltab{25mm}{xpos}\Ltab{50mm}{horizontal position of title}\verb|6|\\ +\Ltab{25mm}{size}\Ltab{50mm}{magnification of title}\verb|1.3|. +\itemket{Remark}If some arguments are null, the defaul is used.\\ +\hspace*{10mm}\verb|Setslidepage([,"red"]);| +\end{cmd} + +%------------Setslidemargin----------------------------- +\begin{cmd}{Setslidemargin}{setslidemargin} +\itemket{Usage}Setslidepage([leftmarginchange,topmarginchange]); +\itemket{Description}This function changes the margin of slides from the default. +\itemket{Example}Setslidemargin([+5,-10]); +\end{cmd} + +%------------Settitle------------------------------ +\begin{cmd}{Settitle}{settitle} +\itemket{Usage}Settitle(list of title components,options) +\itemket{Description}Make a title slide. +\itemket{Details}Meanings and defaults of options are\\ +\Ltab{25mm}{"Title=..."}\Ltab{50mm}{name of the title file}\verb|"Title=slide0"|\\ +\Ltab{25mm}{"Layery=..."}\Ltab{50mm}{starting vertical position}\verb|"Layery=0"|\\ +\Ltab{25mm}{"Color=..."}\Ltab{50mm}{color of letters}\verb|"Color=blue"|. + +\itemket{Examples} \mbox{}\\ +\hspace{10mm}\verb| Settitle([ |\\ +\hspace{10mm}\verb| "s{60}{20}{Main Title}", |\\ +\hspace{10mm}\verb| "s{60}{50}{Name}", |\\ +\hspace{10mm}\verb| "s{60}{60}{Affiliation}", |\\ +\hspace{10mm}\verb| "s{60}{70}{Info}" |\\ +\hspace{10mm}\verb| ],|\\ +\hspace{10mm}\verb| ["Title=SlideA","Color=[1,1,0,0]"]|\\ +\hspace{10mm}\verb| );| +\end{cmd} + +\newpage +%=== 3D ========= +\section{\ketcindy 3D} + + +%==================================== +\subsection{Setting and Defining} +%------------Ketinit3d-------------------------------- +\begin{cmd}{Ketinit3d}{ketinit3D} +\itemket{Usage}Ketinit3d() +\itemket{Description}Declare the use of KeTCindy3D +\itemket{Details}Euclidean view of Cinderella becomes 3D mode. Two sliders are created to indicate the viewing angle TH($\theta$), FI($\phi$). The initial values are $\mathrm{TH}=0$ and $\mathrm{FI}=0$.\\ +\textcolor{red}{Caution} + This funcition and Ketinit() have to write on Initializaiton slot. +\itemket{Remark}If \verb|Ketinit3d(0)| is used, the subscreen is not displayed. +\end{cmd} + +%------------Start3d-------------------------------- + +\begin{cmd}{Start3d}{start3d} +\itemket{Usage}Start3d(option) +\itemket{Description}3d function to initialize limited variables. +\itemket{Details} +This funcition should be written at the beginning of Draw slot.\\ +The option is a list of geometric points which are not regarded as 3D points. +\itemket{Example}\mbox{}\\ +\verb|Start3d([A,B,C]);|\\ +\verb|Slider("A-C-B");| // A,C,B should not be 3D points. +\end{cmd} + +%--------------Startsurf------------------------------ + +\begin{cmd}{Startsurf}{startsurf} +\itemket{Usage}Startsurf(options) +\itemket{Description}Defines values related to surface rendering. +\itemket{Details}Values are number to divide, size of C, limit of error. +Omitted options selects [50,50],[1500,500,200],[0.01,0.1].\\ +Drawing of a curved surface with hidden line processing is performed in the following procedure.\\ +(1) Startsurf();\\ +(2) Making data wtih draw function.\\ +(3) Draws shapes in batch in C language using function ExeccmdC();. +%\itemket{Examples} \mbox{} +\end{cmd} + +%--------------Isangle------------------------------ +\begin{cmd}{Isangle}{isangle} + +\itemket{Usage}Isangle() +\itemket{Description}Decide the selection of the angle slider. +\itemket{Details}Returns ``true'' if select slider, and ``false'' if not.\\ +In drawing including hidden line processing, reaction is bad when recalculating while moving the viewpoint. With this function, you can write code that does not recalculate while moving the viewpoint. + +\itemket{Examples} \mbox{} + +\verb| fd=[ |\\ +\verb| "z=4-(x^2+y^2)",|\\ +\verb| "x=R*cos(T)","y=R*sin(T)",|\\ +\verb| "R=[0,2]","T=[0,2*pi]","e" \verb| ];|\\ +\verb| if(Isangle(),|\\ +\verb| Sf3data("1",fd);|\\ +\verb| ,|\\ +\verb| Startsurf();|\\ +\verb| Sfbdparadata("1",fd);|\\ +\verb| Crvsfparadata("1","ax3d","sfbd3d1",fd);|\\ +\verb| ExeccmdC("1");|\\ +\verb| );| + + +\end{cmd} + +\subsection{Command for Drawing} +%-------------Bezier3d}------------------------------- + +\begin{cmd}{Bezier3d}{bezier3d} + +\itemket{Usage}Bezier3d(name,list1,list2) +\itemket{Description}Draw a Cubic B\'ezier curve. +\itemket{Details}list1 is list of anchor points, and list2 is list of handle points +\itemket{Examples} \mbox{} + +\verb|Bezier3d("1",["A","B","C"],["D","E","F","G"]);| + +\begin{center} \input{Fig/bezier3d1} \end{center} + +\end{cmd} +%----------Changestyle3d---------------------------------- + +\begin{cmd}{Changestyle3d}{changestyle3d} +\itemket{Usage} Changestyle3d(PD,option) +\itemket{Description}Change the attribute of PD. +\itemket{Details}Change the attribute of PD to one with option specification. PD is a plotting data or a list of plotting data. +\itemket{Examples} \mbox{} + +Make a tetrahedron by four points of space.\\ +\verb|Spaceline("1",[A,B]);|\\ +\verb|Spaceline("2",[A,C]);|\\ +\verb|Spaceline("3",[B,C]);|\\ +\verb|Spaceline("4",[A,D]);|\\ +\verb|Spaceline("5",[B,D]);|\\ +\verb|Spaceline("6",[C,D]);|\\ +then\\ +\verb|Changestyle3d("sl3d1",["dr,3"]);| // one edge become thick.\\ +or\\ +\verb|edges=apply(1..6,"sl3d"+text(#));|\\ +\verb|Changestyle3d(edges,["notex"]);| // all edges become ``notex''.\\ +\end{cmd} +%------------Concatobj-------------------------------- + +\begin{cmd}{Concatobj}{concatobj} +\itemket{Usage}Concatobj(list,options) +\itemket{Description}Concatenates several objects. +%\itemket{Details} +\itemket{Examples} \mbox{} + +A tetrahedron by four vertecies A,B,C,D.\\ +The tetrahedron consists of four planes $\triangle\mathrm{ABC}$, $\triangle\mathrm{ABD}$, $\triangle\mathrm{ACD}$, $\triangle\mathrm{BCD}$.\\ +\begin{center} \input{Fig/concatobj} \end{center} +\verb|Concatobj([[A,B,C],[A,B,D],[A,C,D],[B,C,D]]);|\\ +makes [[A,B,C,D],[[1,2,3],[1,2,4],[1,3,4],[2,3,4]]] +This data is used to drawing tetrahedron. +For example code, see \hyperlink{vertexedgeface}{VertexEdgeFace()}. +\end{cmd} + +%-------------Crvsfparadata------------------------------- + +\begin{cmd}{Crvsfparadata}{crvsfparadata} +\itemket{Usage}Crvsfparadata(name,PD1,PD2,formula) +\itemket{Description}Remove curves hidden by curved face. +%\itemket{Details} +\itemket{Examples} \mbox{} + +For example code, see \hyperlink{execcmdc}{ExeccmdC()}. +\end{cmd} + +%--------------Datalist2d------------------------------ + +\begin{cmd}{Datalist2d}{datalist2d} + +\itemket{Usage}Datalist2d() +\itemket{Description} Generic function to get a list of 2D-plotting data on the screen. +\itemket{Examples} \mbox{} + +We execute the following program then the computer will display "PD=[ax2d,AB2d]" on the console.\\ + +\verb| Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]"); |\\ +\verb| Putpoint3d(["A",[0,-3,0],"B",[0,3,3]],"fix"); |\\ +\verb| Spaceline("1",[A,B]); |\\ +\verb| println("PD="+Datalist2d());| + +\end{cmd} +%--------------Datalist3d------------------------------ + +\begin{cmd}{Datalist3d}{datalist3d} + +\itemket{Usage}Datalist3d() +\itemket{Details}Generic function to get a list of 3D-plotting data. +\itemket{Examples} \mbox{} + +We execute the following program then the computer will display "PD=[ax3d,AB3d]" on the console.\\ + +\verb| Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]"); |\\ +\verb| Putpoint3d(["A",[0,-3,0],"B",[0,3,3]],"fix"); |\\ +\verb| Spaceline("1",[A,B]); |\\ +\verb| println("PD="+Datalist3d()); | + +\end{cmd} +%--------------Dist3d------------------------------ + +\begin{cmd}{Dist3d}{dist3d} + +\itemket{Usage}Dist3d(a1,a2) +\itemket{Description}Generic function to get the 3D-distance of two points. +\itemket{Examples} \mbox{} + +Following three programs return the same result.\\ + +\verb| Dist3d("A","B"); |\\ +\verb| Dist3d(A,B); |\\ +\verb| Dist3d(A3d,B3d); | + +\end{cmd} +%--------------Drawpoint3d------------------------------ + +\begin{cmd}{Drawpoint3d}{drawpoint3d} + +\itemket{Usage}Drawpoint3d(list of coordinates) +\itemket{Description}Generic function to draw 3D-points. +\itemket{Details}These points are not geometric point. +To convert the geometric point, use \hyperlink{putpoint3d}{Putpoint3d()}. +To output in the \TeX file, use \hyperlink{pointdata}{Pointdata()} or \hyperlink{drwpt}{Drawpoint()}. +\itemket{Examples} \mbox{} + +\verb| Drawpoint3d([1,1,1]); |\\ +\verb| Drawpoint3d([[1,1,1],[0,1,0]]); | + +\itemket{Remark} \hyperlink{mkpttable}{Comparative chart of drawing of points} + +\end{cmd} +%--------------ExeccmdC------------------------------ + +\begin{cmd}{ExeccmdC}{execcmdc} + +\itemket{Usage}ExeccmdC(name,options1,options2) +\itemket{Description}Generic function to draw 3D-surface. The return value is the list of processed plot data. +\itemket{Details}options1=no option or " "(space) or "r" or "m" and "Wait=integer" , line type. Default value of Wait is 20.\\ +No option or " "(space) means\\ +(1) If there exist no deta then it make a new data file.\\ +(2) If there exist deta then it read the data file.\\ +"m" means that it remake the new data file.\\ +"r" means that it reread the existing data file.\\ + +option2="nodisp" or line type of hidden line. Default is "do".\\ + +If we specify only option2 then we denote that option1 is empty list:[]. +\itemket{Examples} \mbox{} + +left figure + +\verb| Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]"); |\\ +\verb| Putpoint3d(["A",[0,-3,0],"B",[0,3,3]],"fix"); |\\ +\verb| Spaceline([A,B]); |\\ +\verb| fd=["z=4-(x^2+y^2)","x=R*cos(T)","y=R*sin(T)","R=[0,2]","T=[0,2*pi]","e"]; |\\ +\verb| Startsurf(); |\\ +\verb| Sfbdparadata("1",fd); |\\ +\verb| Crvsfparadata("1","AB3d","sfbd3d1",fd); |\\ +\verb| Crvsfparadata("2","ax3d","sfbd3d1",fd); |\\ +\verb| ExeccmdC("1"); | + +right figure + +\verb| ExeccmdC("1",[],["nodisp"]);| + +\hspace{20mm}\input{Fig/crvsfparadata2} \hspace{20mm} \input{Fig/crvsfparadata1} + +By using the return value, you can change the hidden line style (line style, color). +The same as the return value is displayed as "readoutdata from template3D1.txt:" on the console, so you can decide the operation target by looking at it. For example, in the left diagram above, the hidden line of line AB is the fourth crvsfh3d1 in the list, so you can make it a red dashed line as follows. + +\verb| ret=ExeccmdC("1");|\\ +\verb| Changestyle3d(ret_4,["da","Color=red"]);|\\ + +\hspace{20mm} \input{Fig/execcmdc1} + +In addition, please refer to the next. \hyperlink{sfbdparadata}{Sfbdparadata()},\hyperlink{wireparadata}{Wireparadata()} + +\end{cmd} +%--------------Embed------------------------------ + +\begin{cmd}{Embed}{embed} +\itemket{Usage}Embed(name,PDlist,formula,varlist) +\itemket{Description}Embed plotting data of 2D in plane of 3D. +\itemket{Details}PDlist is list of plotting data of 2D. Plane of 3D is given by formula and varlist. +\itemket{Examples} \mbox{} + +Embed an equilateral triangle and its circumscribed circle in a plane in 3D space. + +(1) \verb|vo|, \verb|vx|, \verb|vy| are defined with function {\tt \hyperlink{defvar}{Defvar}} that uses R.\\ +\verb|Xyzax3data("","x=[-5,4]","y=[-10,4]","z=[-5,5]",["a","O"]);|\\ +\verb|Spaceline("1",[[3,0,0],[3,6,0],[3,6,6],[3,0,6],[3,0,0]]);|\\ +\verb|Defvar("vo=[3,3,3]");| // Defined in R\\ +\verb|Defvar("vx=[0,1,0]");| // Defined in R\\ +\verb|Defvar("vy=[0,0,1]");| // Defined in R\\ +\verb|Putpoint3d(["A",[3,3,3]],"fix");|\\ +\verb|Circledata("1",[[0,0],[2,0]],["nodisp"]);|\\ +\verb|Listplot("1",[[0,2],[-sqrt(3),-1],[sqrt(3),-1],[0,2]],["nodisp"]);|\\ +\verb|Embed("1",["cr1","sg1"],"vo+x*vx+y*vy","[x,y]");|\\ +\verb|Ptsize(3);|\\ +\verb|Drawpoint(A);| + +Following view is as \verb|TH|=75,\verb|FI|=70. + \begin{center} \input{Fig/embed01} \end{center} + +(2) A, B, and C are defined instead of vo, vx, vy defined by Defvar. But, in this case, points B and C are not drawn in the plane. So, the figure may be difficult to understand.\\ +\verb|Putpoint3d(["A",[3,3,3],"B",[0,1,0],"C",[0,0,1]],"fix");|\\ +\verb|Embed("1",["cr1","sg1"],"A3d+x*B3d+y*C3d","[x,y]");|\\ +\begin{center} +\includegraphics[bb=0.00 0.00 477.02 383.02,width=8cm]{Fig/embed03.pdf} +\end{center} +To draw the B and C on the embedded figure, code changes as follows. + +\verb|Putpoint3d(["A",[3,3,3],"B",[3,4,3],"C",[3,3,4]],"fix");|\\ +\verb|Embed("1",["cr1","sg1"],"A3d+x*B3d+y*C3d","[x,y]");|\\ + +(3) The function {\tt \hyperlink{perpplane}{Perpplane}} is used in next.\\ +\verb|Xyzax3data("","x=[-5,5]","y=[-8,5]","z=[-5,5]");|\\ +\verb|Putpoint3d(["O",[0,0,0],"P",[1,1,2]],"fix");|\\ +\verb|Perpplane("E-F","P",P3d-O3d,"put");|\\ +\verb|vec1=3*(E3d-P3d);|\\ +\verb|vec2=3*(F3d-P3d);|\\ +\verb|Putpoint3d(["A",P3d+vec1+vec2],"fix");|\\ +\verb|Putpoint3d(["B",P3d+vec1-vec2],"fix");|\\ +\verb|Putpoint3d(["C",P3d-vec1-vec2],"fix");|\\ +\verb|Putpoint3d(["D",P3d-vec1+vec2],"fix");|\\ +\verb|Spaceline("1",[A,B,C,D,A]);|\\ +\verb|Circledata("1",[[0,0],[2,0]],["nodisp"]);|\\ +\verb|Listplot("1",[[0,2],[-sqrt(3),-1],[sqrt(3),-1],[0,2]],["nodisp"]);|\\ +\verb|Embed("1",["cr1","sg1"],"P3d+x*(E3d-P3d)+y*(F3d-P3d)","[x,y]");|\\ +\verb|Ptsize(3);|\\ +\verb|Drawpoint(P);|\\ +\verb|Skeletonparadata("1");| + \begin{center} \input{Fig/embed02} \end{center} +\end{cmd} + +%------------Intersectcrvsf-------------------------------- + +\begin{cmd}{Intersectcrvsf}{intersectcrvsf} +\itemket{Usage}Intersectcrvsf(name,PD,formula) +\itemket{Description}Returns a list of intersects of a curve and curved face. +\itemket{Details}PD is plotting data of curve. Curved face is given by formula. +\itemket{Examples} \mbox{} + +\verb|Putpoint3d(["A",[0,-3,0],"B",[0,3,2]],"fix");|\\ +\verb|Spaceline("1",[A,B]);|\\ +\verb|fd=[|\\ +\verb| "z=4-(x^2+y^2)","x=R*cos(T)","y=R*sin(T)",|\\ +\verb| "R=[0,2]","T=[0,2*pi]","e"|\\ +\verb|];|\\ +\verb|Startsurf();|\\ +\verb|Sfbdparadata("1",fd);|\\ +\verb|Intersectcrvsf("1","sl3d1",fd);|// The result [[0,1.57,1.52],[0,-1.91,0.36]] will be shown in the console.\\ +\verb|ExeccmdC("1",[""]);|\\ +\verb|println("Intersect="+intercrvsf1);|\\ +\verb|Drawpoint3d(intercrvsf1); |\\ +\verb|Letter(Parapt(intercrvsf1_1),"ne","P1");|\\ +\verb|Letter(Parapt(intercrvsf1_2),"ne","P2");|\\ + +\hspace{30mm}\includegraphics[bb=0.00 0.00 325.55 292.54,width=8cm]{Fig/Intersectcurvsf.pdf} +\end{cmd} + +%-------------IntersectsgpL------------------------------- + +\begin{cmd}{IntersectsgpL}{intersectsgpL} +\itemket{Usage}IntersectsgpL(name,segment,plane,option) +\itemket{Description}Returns a intersection of a line segment and plane. +\itemket{Details}Specify a line segment with two endpoints. Specify the plane as three points that it contains. Options are ``put'' or ``draw'', and if omitted select ``draw''.\\ +Following two programs return the same result.\\ +\verb| IntersectsgpL("P","A-B","C-D-E"); |\\ +\verb| IntersectsgpL("P",[A3d,B3d],[C3d,D3d,E3d]); | + +% \verb|IntersectsgpL("P",[p1,p2],[p3,p4,p5],"draw");| +\itemket{Examples} \mbox{} + +cutcube + +\verb| Hn=3; |\\ +\verb| Putaxes3d(Hn); |\\ +\verb| Putpoint3d("A",[Hn,Hn,0],"fix"); |\\ +\verb| Putpoint3d("B",[Hn,0,Hn],"fix"); |\\ +\verb| Putpoint3d("C",[Hn,Hn,Hn],"fix"); |\\ +\verb| Putpoint3d("D",[0,Hn,Hn],"fix"); |\\ +\verb| Putonseg3d("E",X,B); |\\ +\verb| Putonseg3d("F",Z,B); |\\ +\verb| Putonseg3d("G",Z,D); |\\ +\verb| IntersectsgpL("M","A-C","E-F-G","put"); |\\ +\verb| IntersectsgpL("N","D-Y","E-F-G","put"); |\\ +\verb| phd=Concatobj([[O,X,A,Y],[X,A,M,E],[A,Y,N,M],[Y,N,G,Z,O], |\\ +\verb| [O,Z,F,E,X],[Z,F,G],[E,M,N,G,F]]); |\\ +\verb| VertexEdgeFace("1",phd,["Edg=nogeo"]); |\\ +\verb| Nohiddenbyfaces("1","phf3d1"); | + +\hspace{20mm}\includegraphics[bb=0.00 0.00 713.04 327.02,width=10cm]{Fig/IntersectsgpL0.pdf} + +add next script (right figure) + +\verb| Spaceline("1",[E,B,F],["do"]); |\\ +\verb| Spaceline("2",[B,C,M],["do"]); |\\ +\verb| Spaceline("3",[C,D,N],["do"]); |\\ +\verb| Spaceline("4",[D,G],["do"]); |\\ + +\begin{center} \input{Fig/IntersectsgpL1} \input{Fig/IntersectsgpL2} \end{center} + +\end{cmd} +%-------------Invparapt------------------------------- + +\begin{cmd}{Invparapt}{invparapt} +\itemket{Usage}Invparapt(coordinate,PD) +\itemket{Description}Returns the point on the curve that is corresponding to the coordinates on the Euclidean view. +\itemket{Details}Returns the 3D-coordinates of the point on the curve(\verb|PD|) from the \verb|coordinate| on the Euclidean view. +\itemket{Examples} \mbox{} + +Find on the screen (not in the space) intersection points (\verb|tmp_1|, \verb|tmp_2|, $\dots$) of the spiral curve and the space line. Draw a part of the spiral whose end points (\verb|p1| and \verb|p2|) are selected from the intersection points.\\ +\verb| Spaceline("1",[[-1,-1,-1],[1,2,3]]); |\\ +\verb| Spacecurve("1","[2*cos(t),2*sin(t),0.2*t]","t=[0,4*pi]",["do"]);|\\ +\verb| tmp=Intersectcrvs("sl2d1","sc2d1");|\\ +\verb| p1=Invparapt(tmp_1,"sc3d1");|\\ +\verb| p2=Invparapt(tmp_2,"sc3d1");|\\ +\verb| Partcrv3d("1",p1,p2,"sc3d1"); |\\ +\begin{center} \input{Fig/invparapt} \end{center} +\end{cmd} + +%---------Mkbezierptcrv3d----------------------------------- +\begin{cmd}{Mkbezierptcrv3d}{mkbezierptcrv3d} +\itemket{Usage}Mkbezierptcrv3d(list) +\itemket{Description}Draw a cubic B\'ezier curve from nodes. +\itemket{Details}Arrange the control points automatically. +After that, move the nodes and the control points and correct the cubic B\'ezier curve to what you want to draw. See the function {\tt \hyperlink{bezier}{Bezier3d}}. +\itemket{Examples} \mbox{} + +\verb|Mkbezierptcrv3d(["A","B","C","D"]);| +\end{cmd} + +%--------------Nohiddenbyfaces------------------------------ +\begin{cmd}{Nohiddenbyfaces}{nohiddenbyfaces} + +\itemket{Usage}Nohiddenbyfaces(name,PD1,PD2,option1,option2) +\itemket{Description}Generic function to draw hidden lines by the surfaces. +\itemket{Details}PD1 are hidden lines, PD2 are surfaces.\\ +If we omit PD1 then all lines are processing objects.\\ +By default, hidden lines are drawn with dotted lines.\\ +Option1=line type of PD2 and option2=line type of hidden lines.\\ +If we specify only option2 then option1 must be null list:[].\\ +\itemket{Examples} \mbox{} + +\begin{verbatim} +Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,4]"); +Putpoint3d("A",2*[-1,-1/sqrt(3),0],"fix"); +Putpoint3d("B",2*[1,-1/sqrt(3),0],"fix"); +Putpoint3d("C",2*[0,sqrt(3)-1/sqrt(3),0],"fix"); +Putpoint3d("D",2*[0,0,2*sqrt(6)/3],"fix"); +phd=Concatobj([[A,B,C],[A,B,D],[A,C,D],[B,C,D]]); +VertexEdgeFace("1",phd,["Edg=nogeo"]); +Nohiddenbyfaces("1","phf3d1"); +\end{verbatim} +(left figure) + +\verb|Nohiddenbyfaces("1","phe3d1","phf3d1",["dr,2"],["da"]); | +(right figure) + +\begin{center} \input{Fig/nohiddenbyfaces1} \input{Fig/nohiddenbyfaces2} \end{center} + +We draw hidden axes with broken line in the following example.\\ +\verb|Nohiddenbyfaces("1","ax3d","phf3d1",[],["da"]);| + +\end{cmd} +%-------------Parapt------------------------------- +\begin{cmd}{Parapt}{parapt(coordinate)} + +\itemket{Usage}Parapt(3D-coordinate) +\itemket{Description}Generic function to return the 2D-coordinate on the plane of projection for the 3D-point. +\itemket{Examples} \mbox{} + +\verb|println(Parapt([2,1,5]));| +\end{cmd} +%--------------Perpplane------------------------------ +\begin{cmd}{Perpplane}{perpplane} + +\itemket{Usage}Perpplane(name, point, vector, option) +\itemket{Description}Generic function to return the two points on the plane which is passing through the point and orthogonal to the vector. +\itemket{Details}The name is the two points name such as the form "A-B".\\ +Point is the name or the coordinate of the point through which the plane is passing.\\ +The vector is the normal of the plane.\\ +If option is "put" then the function draw two geometric points. +\itemket{Examples} \mbox{} + +Return the points A,B on the plane which is passing through the point P and orthogonal to the vector [1,1,1]\\. +\verb|Perpplane("A-B","P",[1,1,1],"put");|\\ + +Return the points A,B on the plane which is passing through the point P and orthogonal to the line segment OP. In this situation PA and PB is orthogonal and length of PA and PB are 1.\\. +\verb|Perpplane("A-B","P",P3d-O3d);|\\ + +Draw point A,B,C,D by draw tool of Cinderella. + +\begin{layer}{120}{0} +\putnotese{100}{20}{ \input{Fig/perpplane}} +\end{layer} + +\verb| Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,4]"); |\\ +\verb| Putpoint3d(["O",[0,0,0]],"fix"); |\\ +\verb| Putpoint3d(["P",[1,1,1]],"fix"); |\\ +\verb| Perpplane("E-F","P",P3d-O3d,"put"); |\\ +\verb| vec1=2*(E3d-P3d); |\\ +\verb| vec2=2*(F3d-P3d); |\\ +\verb| Putpoint3d(["A",P3d+vec1+vec2],"fix"); |\\ +\verb| Putpoint3d(["B",P3d+vec1-vec2],"fix"); |\\ +\verb| Putpoint3d(["C",P3d-vec1-vec2],"fix"); |\\ +\verb| Putpoint3d(["D",P3d-vec1+vec2],"fix"); |\\ +\verb| Spaceline("1",[A,B,C,D,A]); |\\ +\verb| Arrowdata([O,P],["dr,2"]); |\\ +\verb| Letter([P,"w","P",A,"ne","A",B,"e","B",C,"ws","C",D,"nw","D",]); |\\ +\verb| Skeletonparadata("1"); |\\ + +\end{cmd} +%-------------Perppt------------------------------- +\begin{cmd}{Perppt}{perppt} + +\itemket{Usage}Perppt(name, point, list of points, option) +\itemket{Description}Generic function to get the foot of a perpendicular for the plane from the point. +\itemket{Details}We specify the plane by the list of points.\\ +Option is the following.\\ +"draw": draw the point, don't make the geometric point(default).\\ +"put" : make the geometric point.\\ +"none": only make the data and don't draw. +\itemket{Examples} \mbox{} + +We get the coordinate of the point H in the variable H3d for the following examples.\\ +\verb|Perppt("H","O","A-B-C","none");|\\ +\verb|Perppt("H","O","A-B-C");|\\ +\verb|Perppt("H","O","A-B-C","put");|\\ + +Example + +\verb|Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,4]"); |\\ +\verb|Putpoint3d("O",[0,0,0],"fix"); |\\ +\verb|Putpoint3d("A",[3,0,0],"fix"); |\\ +\verb|Putpoint3d("B",[0,3,0],"fix"); |\\ +\verb|Putpoint3d("C",[0,0,3],"fix"); |\\ +\verb|Perppt("H","O","A-B-C","put"); |\\ +\verb|Spaceline("1",[A,B,C,A]); |\\ +\verb|Spaceline("2",[O,H]); |\\ +\verb|Letter([A,"nw","A",B,"ne","B",C,"ne","C",O,"nw","O",H,"ne","H"]); |\\ + +\begin{center} \input{Fig/perppt} \end{center} + +\end{cmd} +%--------------Partcrv3d------------------------------ +\begin{cmd}{Partcrv3d}{partcrv3d} + +\itemket{Usage}Partcrv3d(name, start point, end point, PD) +\itemket{Description}Generic function to draw the part curve of the curve PD. +\itemket{Examples} \mbox{} + +\verb| Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,4]"); |\\ +\verb| Spacecurve("1","[2*cos(t),2*sin(t),0.2*t]","t=[0,4*pi]",["Num=100"]); |\\ +\verb| PutonCurve3d("C","sc3d1"); |\\ +\verb| PutonCurve3d("D","sc3d1"); |\\ +\verb| Partcrv3d("1",C,D,"sc3d1",["dr,3"]); |\\ +\verb| Letter([C,"n2","C",D,"n2","D"]); |\\ + +\begin{center} \input{Fig/partcrv3d1} \end{center} + +\verb|Spacecurve("1","[2*cos(t),2*sin(t),0.2*t]","t=[0,4*pi]",["Num=10","do"]);|\\ +\verb|Partcrv3d("1",3.3,8.5,"sc3d1");| // 3.3 and 8.5 are plotting data number of the points. +\begin{center} \input{Fig/partcrv3d2} \end{center} + +\end{cmd} + +%--------------Phparadata------------------------------ +\begin{cmd}{Phparadata}{phparadata} + +\itemket{Usage}Phparadata(name, name2, list of options) +\itemket{Description}Generic function to draw the polyhedron by performing hidden line processing. +\itemket{Details}Name2 is the plotting data of polyhedron which we get form the function VertexEdgeFace(). +\itemket{Examples} \mbox{} + +\verb|Setdirectory( Dirhead+"/data/polyhedrons_obj");| //Many polyhedron data exist in this directory.\\ +\verb|phd=Readobj("s06.obj",["size=3"]);| //"s06" is the name of truncated icosahedron data.\\ +\verb|Setdirectory(Dirwork);| //Chage work space.\\ +\verb|VertexEdgeFace("s06",phd,["Edg=nogeo"]);|\\ +\verb|Phparadata("1","s06");| //default usage, left figure\\ + +The last two lines we can write the following.\\ +\verb|VertexEdgeFace("1",phd,["Edg=nogeo"]);|\\ +\verb|Phparadata("1","1");| +\begin{center} + \includegraphics[bb=0 0 1452 730 , width=10cm]{Fig/phparadata01.pdf} +\end{center} + +\verb|Phparadata("1","s06",["dr,2","Hidden=do"]);| //right figure + \begin{center} \input{Fig/phparadata02} \input{Fig/phparadata03} \end{center} +\end{cmd} + +%--------------Phparadata------------------------------ +\begin{cmd}{Pointdata3d}{pointdata3d} + +\itemket{Usage}Pointdata3d(name, point list, options) +\itemket{Description}Generic function to generate data of the point list. +\itemket{Details}Options are "Size=","Color=". +\itemket{Examples} \verb|Pointdata3d("1",[[0,1,0],[1,1,2]],["Size=2","Color=red"]);| +\end{cmd} + +%---------------Projcoordpara----------------------------- +\begin{cmd}{Projcoordpara}{projcoordpara} + +\itemket{Usage}Projcoordpara(3D-coordinate) +\itemket{Description}Generic function to get the projection coordinate on the Euclidean view coordinate system. +\itemket{Examples} \mbox{} + +\verb|println(Projcoordpara([3,1,2]));| //printed value is such as [-0.65, 1.7, 3.27] where the third element means the (signed) distance from the projection plane. +\end{cmd} +%-----------------Putaxes3d--------------------------- +\begin{cmd}{Putaxes3d}{putaxes3d} + +\itemket{Usage}Putaxes3d([x,y,z]) +\itemket{Description}Generic function to make the geometric points on the coordinate axis. +\itemket{Details}For the argument [x,y,x] we get the four geometric points X(x,0,0), Y(0,y,0), Z(0,0,z) and O(0,0,0). +\itemket{Examples} \mbox{} + +\verb|Putaxes3d([1,2,3]);|\\ +\verb|Putaxes3d(a);| //this equals to \verb|Putaxes3d([a,a,a]);| + +\end{cmd} +%--------------PutonCurve3d------------------------------ +\begin{cmd}{PutonCurve3d}{putonCurve3d} + +\itemket{Usage} PutonCurve3d(name, PD) +\itemket{Description}Generic function to make the geometric point on the 3D-curve. +\itemket{Details}This point moves along the curve by mouse dragging. +\itemket{Examples} \mbox{} + +Make reference to \hyperlink{partcrv3d}{Partcrv3d()} +\end{cmd} +%----------------Putonseg3d---------------------------- +\begin{cmd}{Putonseg3d}{putonseg3d} + +\itemket{Usage}Putonseg3d(name, point1, point2) +\itemket{Description}Generic function to make the geometric point on the 3D-segment. +\itemket{Details}We get the middle point between the two points. This point moves along the segment by mouse dragging. +\itemket{Examples} \mbox{} + +\verb|Putonseg3d("C",A,B);| //Put C on the center of A and B.\\ +\verb|Putonseg3d("C",[A,B]);| //same as above +\end{cmd} +%---------------Putpoint3d----------------------------- +\begin{cmd}{Putpoint3d}{putpoint3d} + +\itemket{Usage}Putpoint3d(list of 3D-points, option) +\itemket{Description}Generic function to draw the geometric point in the space. +\itemket{Details}Option is "fix" or "free"(default). +\itemket{Examples} \mbox{} + +\verb|Putpoint3d(["A",[2,1,3]]);|\\ +\verb|Putpoint3d(["A",[2,1,3]],"free");| //same as above\\ +\verb|Putpoint3d(["A",[1,1,1],"C",[1,0,1]],"fix");|\\ + +These points don't output in the \TeX file. To output in the \TeX file use the following \hyperlink{pointdata}{Pointdata()} or \hyperlink{drwpt}{Drawpoint()} + +In the 3D-drawings the coordinate of the point name A is A3d. + +\itemket{Remark} \hyperlink{mkpttable}{Comparative chart of drawing of points} + +\end{cmd} +%-------------Readobj------------------------------- +\begin{cmd}{Readobj}{readobj} + +\itemket{Usage}Readobj(filename, option) +\itemket{Description}Read in the polyhedron data in the folder name \verb|polyhedrons_obj| +\itemket{Details}Option is ["size=n"] then we get the magnification of n times. If n is negative value then we have the image of vertical inversion. +\itemket{Examples} \mbox{} + +\verb|Setdirectory( Dirhead+"/data/polyhedrons_obj");| //Many polyhedron data exist in this directory.\\ +\verb|polydt=Readobj("r02.obj",["size=2"]);| //"r02" is the name of regular octahedron data.\\ +\verb|Setdirectory(Dirwork);| //Chage work space.\\ +\verb|VertexEdgeFace("1",polydt,["Edg=nogeo"]);| //output data name is phf3d1\\ +\verb|Nohiddenbyfaces("1","phf3d1");| +\begin{center} \input{Fig/readobj} \end{center} + +\begin{center} \input{Fig/readobj} \end{center} + +The main polyhedral data is as follows. + + \input{Fig/kobayashiE} + +Besides this, there are facing convex polyhedrons from n01 to n92. + +cf.http://mitani.cs.tsukuba.ac.jp/polyhedron/ + +\end{cmd} + + +%---------------Reflectdata3d----------------------------- +\begin{cmd}{Reflectdata3d}{reflectdata3d} + +\itemket{Usage}Reflectdata3d(name, list of PD, list, options) +\itemket{Description}Generic function to draw the reflection of plotting data. +%\itemket{Details} +\itemket{Examples}\mbox{} + +\verb| Putpoint3d(["A",[0,-2,0],"B",[2,-2,0],"C",[1,-2,2],"D",[1,0,1], |\\ +\verb| "E",[1,0,0]],"fix"); |\\ +\verb| Spaceline("1",[A,B,C,A]); |\\ + +Reflection on the point D + +\verb| Reflectdata3d("1",["sl3d1"],[D3d],["Color=blue","dr,2"]);|\\ + +\begin{center}\input{Fig/reflectdata3d01}\end{center} + +Reflection on the straight line DE + +\verb| Reflectdata3d("1",["sl3d1"],[D3d,E3d],["Color=blue","dr,2"]);|\\ + +\begin{center}\input{Fig/reflectdata3d02}\end{center} + +Reflection on the plane BDE + +\verb| Reflectdata3d("1",["sl3d1"],[D3d,E3d,B3d],["Color=blue","dr,2"]);|\\ + +\begin{center}\input{Fig/reflectdata3d03}\end{center} + +\end{cmd} + +%---------------Reflectpoint3d----------------------------- +\begin{cmd}{Reflectpoint3d}{reflectpoint3d} + +\itemket{Usage}Reflectpoint3d(coordinate,list) +\itemket{Description}Return the coordinate of the reflect point. +\itemket{Details}Argument "list" is the list of 3D-coordinate of the points. The following examples are the details. +\itemket{Examples} \mbox{} + +\verb|Reflectpoint3d(A3d,[B3d]); | // reflection of the point A on the point B\\ +\verb|Reflectpoint3d(A3d,[B3d,C3d]); | // reflection of the point A on the line BC\\ +\verb|Reflectpoint3d(A3d,[B3d,C3d,D3d]);| // reflection of the point A on the plane BCD +\end{cmd} + +%---------------Rotatedata3d----------------------------- +\begin{cmd}{Rotatedata3d}{rotatedata3d} + +\itemket{Usage}Rotatedata3d(name, list of PD, vec, angle, options) +\itemket{Description}Generic function to rotate plotting data around the vector vec starting from the origin. +\itemket{Details}The options are the center point (the starting point of vec) and so on. +\itemket{Examples} \mbox{} + +\verb|Xyzax3data("","x=[-5,4]","y=[-5,5]","z=[-5,4]",["a","O"]); |\\ +\verb|Putpoint3d(["A",[0,-2,0],"B",[2,-2,0],"C",[1,-2,2],"D",[1,-2,3]],"fix"); |\\ +\verb|Spaceline("1",[A,B,C,A]); |\\ +\verb|Spaceline("2",[C,D]); |\\ +\verb|Rotatedata3d("1",["sl3d1","CD3d"],[0,0,1],pi/2,["dr,2"]); |\\ +\verb|Letter([A,"s","A",B,"w","B",C,"ne","C",D,"ne","D"]); | + +\begin{center} +\input{Fig/rotatedata3d01} +\end{center} + +\verb|Rotatedata3d("1",["sl3d1","CD3d"],[0,0,1],pi/2,[[1,0,0],"dr,2"]);|\\ +\begin{center} +\input{Fig/rotatedata3d02} +\end{center} + +\end{cmd} + +%--------------Rotatepoint3d------------------------------ +\begin{cmd}{Rotatepoint3d}{rotatepoint3d} + +\itemket{Usage}Rotatepoint3d(coordinate,vec,angle,center) +\itemket{Description}Return the coordinate of the rotate point. +\itemket{Details}"vec"(3D-vector) represents the axis of rotation and "center" means the start point of 3D-vector. Default value of center is the origin (of the coordinate axes). +\itemket{Examples} \mbox{} + +\verb| Putpoint3d("A",[0,-1,0]);| \\ +\verb| Rotatepoint3d(A3d,[0,0,1],pi/2); | // return value is [1,0,0].\\ +\verb| Rotatepoint3d(A3d,[0,0,1],pi/2,[1,1,1]);| // return value is [3,0,0]. + +\end{cmd} + +%---------Scaledata3d----------------------------------- +\begin{cmd}{Scaledata3d}{scaledata3d} + +\itemket{Usage}Scaledata3d(name, list of PD, vec, [options]) +\itemket{Description}Generic function to scale plotting data. +\itemket{Details}Vec is a three-dimensional vector to express ratio. The center and options are given in a list. +\itemket{Examples}\mbox{} + +\verb|Putpoint3d(["A",[0,-2,0],"B",[2,-2,0],"C",[1,-2,2]],"fix");|\\ +\verb|Spaceline("1",[A,B,C,A]);|\\ +\verb|Spacecurve("1","[cos(t)+1,sin(t)+1,1]","t=[0,2*pi]",["Num=100"]);|\\ +\verb|Scaledata3d("1",["sl3d1","sc3d1"],[2,2,2],[[0,0,0],"dr,2"]);|\\ + +\begin{center} +\input{Fig/scaledata3d} +\end{center} +\end{cmd} + +%--------------Scalepoint3d------------------------------ +\begin{cmd}{Scalepoint3d}{scalepoint3d} + +\itemket{Usage}Scalepoint3d(point,vector,center) +\itemket{Description}Execute scale transformation for the coordinate of the point. +\itemket{Details}$\text{Scalepoint3d}([a_i],[v_i],[c_i])=[(a_i-c_i)v_i+c_i]$ +\itemket{Examples} \mbox{} + +\verb|Putpoint3d(["A",[2,-1,2]],"fix");|\\ +\verb|pt=Scalepoint3d(A3d,[3,2,4],[1,1,1]); //pt=[4,-3,5]|\\ +\verb|Putpoint3d(["B",pt],"fix");| + +\end{cmd} + +%--------------Sf3data------------------------------ +\begin{cmd}{Sf3data}{sf3data} + +\itemket{Usage}Sf3data(name, list, list of options) +\itemket{Description}Generic function to draw the wire frame model of the surface. +\itemket{Details}Second argument is the list of equations and ranges. \\ +Options are the followings.\\ +"Num=[a,b]": x- and y-division number, default(or initial values) are a=b=25.\\ +"Wire=[a,b]": x- and y-wire number, default(or initial values) are a=b=20.\\ +"ewsn": From east to south, this indicates the boundary. +\itemket{Examples} \mbox{} + +\verb|Sf3data("1",["z=x^2-y^2","x=[-2,2]","y=[-2,2]"]);|\\ +\ \ //This is the first expression of the equation for the surface. Second argument is the list of equation, x-range and y-range. +\begin{center} \input{Fig/saddle1} \end{center} + +\verb|fd=["z=4-(x^2+y^2)","x=R*cos(T)","y=R*sin(T)","R=[0,2]","T=[0,2*pi]"];|\\ +\verb|Sf3data("1",fd);| //fd is the second argument.\\ +(left figure)\\ + +\verb|fd=["z=sin(sqrt(abs(x^2+y^2)))","x=r*cos(t)","y=r*sin(t)",|\\ +\verb|"r=[0,3]","t=[0,2*pi]"];|\\ +\verb|Sf3data("1",fd);|\\ +(right figure) +\begin{center} \input{Fig/parabola} \input{Fig/sf3ddata3} \end{center} + +\verb|fd=["p","x=2*sin(u)*cos(v)","y=2*sin(u)*sin(v)","z=2*cos(u)",|\\ +\verb|"u=[0,pi]","v=[0,2*pi]"];| //"p" indicates the 3D-parameter expression.\\ +\verb|Sf3data("1",fd);| +\begin{center} \input{Fig/sf3ddata4} \end{center} + +\end{cmd} + +%-------------Sfbdparadata------------------------------- +\begin{cmd}{Sfbdparadata}{sfbdparadata} + +\itemket{Usage}Sfbdparadata(name, list, list of options) +\itemket{Description}Generic function to make the surface by performing hidden line processing. +\itemket{Details}Second argument is the list of equations and ranges same as the function "Sf3data". \\ +options1=no option or " "(space) or "r" or "m" and "Wait=integer". Default value of Wait is 20.\\ +No option or " "(space) means\\ +(1) If there exist no deta then it make a new data file.\\ +(2) If there exist deta then it read the data file.\\ +"m" means that it remake the new data file.\\ +"r" means that it reread the existing data file.\\ + +option2="nodisp" or line type of hidden line. Default is "nodisp".\\ + +If we specify only option2 then we denote that option1 is empty list:[]. +\itemket{Examples} \mbox{} + +\verb|fd=["x=x^2-y^2","x=[-2,2]","y=[-2,2]"];|\\ +\verb|if(Isangle(),| //selecting the slider point, draw wire frame surfaces.\\ +\verb| Sf3data("1",fd);|\\ +\verb| ,|\\ +\verb| Startsurf();|\\ +\verb| Sfbdparadata("1",fd);|\\ +\verb| ExeccmdC("1",[],["nodisp"]);| //draw the surface\\ +\verb|);|\\ +(left figure)\\ + +\verb|ExeccmdC("1",["dr,2"],["do"]);| //the surface with thick line, hidden line with dotted line.\\ +(right figure) +\begin{center} \input{Fig/sfbdpara01} \input{Fig/sfbdpara02}\end{center} + +\verb|fd=["z=4-(x^2+y^2)","x=R*cos(T)","y=R*sin(T)","R=[0,2]","T=[0,2*pi]","e"];|\\ +\ \ //"e"=east indicate the boundary line $R=2$, $0 < T < 2\pi$.\\ + +\begin{center} \input{Fig/sfbdpara03} \input{Fig/sfbdpara04} \end{center} + +\end{cmd} +%-------------Skeletonparadata------------------------------- +\begin{cmd}{Skeletonparadata}{skeletonparadata} + +\itemket{Usage}Skeletonparadata(name, PDlist, PDlist, option) +\itemket{Description}Generic function to draw the lines by performing hidden line processing. +\itemket{Details}This function draw the second argument(the list of the lines) by performing hidden line processing which are hidden by the third argument(the list of the lines). If both arguments are omitted the function draw all lines by performing hidden line processing. +\itemket{Examples} \mbox{} + +\verb| Xyzax3data("","x=[-5,5]","y=[-5,4]","z=[-5,3]");| //Data name is "ax3d".\\ +\verb| Putpoint3d(["A",[0,-2,-2]],"fix");|\\ +\verb| Putpoint3d(["B",[-1,1,3]],"fix");|\\ +\verb| Spaceline([A,B]);| //Data name is "AB3d".\\ +\verb| Spacecurve("1","[2*cos(t),2*sin(t),0.2*t]","t=[0,4*pi]",["Num=100"]);| //Data name is "sc3d1".\\ + +\verb|Skeletonparadata("1");| //(left figure)\\ +\verb|Skeletonparadata("1",[2]);| //option\verb|=[2]|: gap of lines\verb|=2| (center figure)\\ +\verb|Skeletonparadata("1",["AB3d","ax3d"],["sc3d1"]);| //(right figure) +\begin{center} \input{Fig/skeletonparadata01} \input{Fig/skeletonparadata02} + \input{Fig/skeletonparadata03} \end{center} + +\end{cmd} +%-------------Spacecurve------------------------------- +\begin{cmd}{Spacecurve}{spacecurve} + +\itemket{Usage}Spacecurve(name, formula, domain, options) +\itemket{Description}Generic function to draw the space curve. +\itemket{Examples} \mbox{} +\verb|Spacecurve("1","[2*cos(t),2*sin(t),0.2*t]","t=[0,4*pi]",["Num=100"]);|\\ +option=["Num=100"]: division number of the interval "t=[0,4*pi]" + \begin{center} \input{Fig/rasen} \end{center} +\end{cmd} +%--------------Spaceline------------------------------ +\begin{cmd}{Spaceline}{spaceline} + +\itemket{Usage} Spaceline(name, list) +\itemket{Description}Generic function to draw the space polygonal lines. +\itemket{Details}Options are line type: "dr" or "da" or "do". +\itemket{Examples} \mbox{} + +\verb|Spaceline("1",[[2,5,1],[4,2,3]]);| //draw the line between two points\\ +\verb|Spaceline("2",[A,B,C,A]);| //draw the triangle ABC\\ + +\begin{layer}{150}{0} +\putnotese{100}{-5}{ \input{Fig/oresenex01}} +\end{layer} + +\verb|pt=[[2,0,0],[2,0,2],[2,2,2],[0,2,2],[0,4,2],[0,4,4]]; |\\ +\verb|Spaceline("1",pt); |\\ +\verb|Pointdata3d("1",pt,["Size=3"]);| + +\vspace{30mm} +\end{cmd} + +%---------------Translatedata3d----------------------------- +\begin{cmd}{Translatedata3d}{translatedata3d} + +\itemket{Usage}Translatedata3d(name, PD, vector) +\itemket{Description}Generic function to translate plotting data. +%\itemket{Details} +\itemket{Examples} \mbox{} + +The curve sc3d1 is translated by 2 in the y axis direction. +As a result, two curves parallel to the original curves are drawn. + +\verb|Translatedata3d("1",["sc3d1"],[0,2,0]);|\\ + +Since polygons drawn with VertexEdgeFace() can not be translated by this function, parallel movement is performed by directly manipulating the surface data. For example, to draw a regular octahedron using the polyhedron data obj of Kobayashi, Suzuki, and Mitani, do the following. This is the case of parallel movement by 2 in the y axis direction. + +\verb|Setdirectory( Dirhead+"/data/polyhedrons_obj"); |\\ +\verb|phd=Readobj("r02.obj",["size=2"]); |\\ +\verb|Setdirectory(Dirwork); |\\ +\verb|dn=length(phd_1); |\\ +\verb|repeat(dn,s,phd_1_s=phd_1_s+[0,2,0]); |\\ +\verb|VertexEdgeFace("1",phd,["Edg=nogeo"]); |\\ + +\begin{center} +\input{Fig/translate01} +\end{center} + +\end{cmd} +%-------------Translatepoint3d------------------------------- +\begin{cmd}{Translatepoint3d}{translatepoint3d} + +\itemket{Usage}Translatepoint3d(coordinate,vector) +\itemket{Description}Return the translated coordinate for the point. +\itemket{Details}$\text{Translatepoint3d}([a_i],[v_i])=[a_i+v_i]$ +\itemket{Examples} \mbox{} + +\verb|Putpoint3d(["A",[1,0,0]],"fix"); |\\ +\verb|pt=Translatepoint3d(A3d,[-1,1,1]); |\\ +\verb|Putpoint3d(["B",pt],"fix"); | + +\end{cmd} + +%-------------Vertexedgeface------------------------------- +\begin{cmd}{Vertexedgeface}{vertexedgeface} + +\itemket{Usage} VertexEdgeFace(name, list, options) +\itemket{Description}Generic function to draw the polyhedron. +\itemket{Details}We use the faces data of the polyhedron.\\ +The second argument is the list of vertexes list and the faces list.\\ +For example, the faces data of the tetrahedron is [[A,B,C,D],[[1,2,3],[1,2,4],[1,3,4],[2,3,4]]].\\ +Option is the following.\\ +no option: output edges as the geometric elements but don't to \TeX file.\\ +\verb|["Edg=nogeo"]|: output data to \TeX file.\\ +\verb|["Pt=free"]|: Vertexes are free geometric points. +\itemket{Examples} \mbox{} + +\verb| Putpoint3d("A",2*[-1,-1/sqrt(3),0],"fix"); |\\ +\verb| Putpoint3d("B",2*[1,-1/sqrt(3),0],"fix"); |\\ +\verb| Putpoint3d("C",2*[0,sqrt(3)-1/sqrt(3),0],"fix"); |\\ +\verb| Putpoint3d("D",2*[0,0,sqrt(3)],"fix"); |\\ +\verb| phd=Concatobj([[A,B,C],[A,B,D],[A,C,D],[B,C,D]]); |\\ +\verb| VertexEdgeFace("1",phd,["Edg=nogeo"]); |\\ + //Three data lists are made, phv3d1:vertex, phe3d1:edge and phf3d1:face. + \begin{center} \input{Fig/vertex01} \end{center} +\end{cmd} +%-------------Wireparadata------------------------------- +\begin{cmd}{Wireparadata}{wireparadata} + +\itemket{Usage} Wireparadata(name, PD, formula, integer, integer, options) +\itemket{Description}Generic function to draw the surface by wire frame data with performing hidden line processing. +\itemket{Details}The second argument PD is the surface data made by Sfbdparadata function.\\ +options=no option or " "(space) or "r" or "m" and "Wait=integer". Default value of Wait is 30.\\ +No option or " "(space) means\\ +(1) If there exist no deta then it make a new data file.\\ +(2) If there exist deta then it read the data file.\\ +"m" means that it remake the new data file.\\ +"r" means that it reread the existing data file.\\ + +\itemket{Examples} \mbox{} + +\verb|fd=["z=x^2-y^2","x=[-2,2]","y=[-2,2]"]; |\\ +\verb|if(Isangle(), |\\ +\verb| Sf3data("1",fd); |\\ +\verb| , |\\ +\verb| Startsurf(); |\\ +\verb| Sfbdparadata("1",fd); | //We get the data named as "sfbd3d1".\\ +\verb| Wireparadata("1","sfbd3d1",fd,4,5,[""]); | //number of wires are 4 and 5.\\ +\verb| ExeccmdC("1"); | //draw the wires\\ +\verb|); | + +\begin{center} +\input{Fig/wirepara1} +\end{center} + +Change the following code. + +\verb|fd=["z=4-(x^2+y^2)","x=r*cos(t)","y=r*sin(t)","r=[0,2]","t=[0,2*pi]","e"];|\\ +\verb|Wireparadata("1","sfbd3d1",fd,5,7,[""]);| + +\begin{center} +\input{Fig/wirepara2} +\end{center} + +\verb|fd=["p","x=2*sin(u)*cos(v)","y=2*sin(u)*sin(v)","z=2*cos(u)","u=[0,pi]", |\\ +\verb| "v=[0,2*pi]","s"]; |\\ +\verb|Wireparadata("1","sfbd3d1",fd,12,12,[""]); | + +\begin{center} +\input{Fig/wirepara3} +\end{center} + +\begin{layer}{150}{0} +\putnotese{90}{15}{ \input{Fig/wirepara4}} +\end{layer} + +\verb|fd=["p","x=2*sin(u)*cos(v)","y=2*sin(u)*sin(v)","z=2*cos(u)","u=[0,pi]",|\\ +\verb| "v=[0,2*pi]","s"];|\\ +\verb|if(Isangle(),|\\ +\verb| Sf3data("1",fd);|\\ +\verb| ,|\\ +\verb| Startsurf();|\\ +\verb| Sfbdparadata("1",fd);|\\ +\verb| Wireparadata("1","sfbd3d1",fd,12,12,[""]);|\\ +\verb| Crvsfparadata("1","ax3d","sfbd3d1",fd);|\\ +\verb| ret=ExeccmdC("1");|\\ +\verb| forall(1..length(ret),|\\ +\verb| if(indexof(ret_#,"wireh")>0,|\\ +\verb| Changestyle3d([ret_#],["nodisp"]);|\\ +\verb| );|\\ +\verb| );|\\ +\verb|);| + +\vspace{\baselineskip} +\verb|fd=["p","x=(2+cos(u))*cos(v)","y=(2+cos(u))*sin(v)","z=sin(u)",|\\ +\verb| "u=[0,2*pi]","v=[0,2*pi]","s"];|\\ +\verb|Sfbdparadata("1",fd);|\\ +\verb|Wireparadata("1","sfbd3d1",fd,12,12,[""]); | + +\begin{center} \input{Fig/wirepara5} \end{center} + +\end{cmd} +%-------------Xyzax3data------------------------------- +\begin{cmd}{Xyzax3data}{xyzax3data} + +\itemket{Usage} Xyzax3data(name, range of x, range of y, range of z, options) +\itemket{Description}Generic function to draw the coordinate axis. +\itemket{Details}Name can be null string.\\ +Options are the followings.\\ +"an": arrowhead, n is size.\\ +"Onesw": origin and its position. +\itemket{Examples} \mbox{} + +\verb|Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]");|\\ +\verb|Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]","a");| //arrowhead\\ +\verb|Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]",["a2"]);| //big arrowhead\\ +\verb|Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]",["O"]);|\\ +\verb|Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]",["a","Oe2n2"]);| //set origin upper right + +\end{cmd} +%------------Xyzcoord-------------------------------- +\begin{cmd}{Xyzcoord}{xyzcoord} + +\itemket{Usage}\hspace{10mm} Xyzcoord(P.x, P.y, Pz.y) +\itemket{Description}Generic function to return the 3D-coordinate of the point P. +\itemket{Details}(P.x, P.y) is the coordinate of P in the mainarea and Pz.y is the y-coordinate of P in the subarea. +\itemket{Examples} \mbox{} + +\verb|println(Xyzcoord(A.x,A.y,Az.y));| //print the 3D-coordinate of point A on the console. +\end{cmd} + + +\newpage +%-==Appendix ======================== +\section{Appendix} + +\subsection{Color table} + +\begin{center} +%\scalebox{0.9}{\input{Fig/colortable}} +\input{Fig/colortable} +\end{center} +\newpage + +%-----------Comparative chart of drawing of points--------- +\hypertarget{mkpttable}{} +\subsection{Comparative chart of drawing of points} +\begin{tabbing} +123456789012345\=1234567890\=\kill + \> return \>: use return value\\ + \> draw \>: draw Euclidean view\\ + \> geo \>: make geometric point on Euclidean view\\ + \> Tex \>: output Tex file +\end{tabbing} + +\begin{center} +\input{Fig/mkpttableE} +\end{center} + +\hspace{20mm} $\triangle$ : use PD + +\newpage +%-==Command List ======================== +\hypertarget{functionlist}{} +\section{Command List} +\hyperlink{index}{To index} + +\begin{tabbing} +12345678901234567890\=\kill +{\bf Setting and Defining} \> \\ +\hyperlink{addax}{Addax} \> decide axis are drawn or not.\\ +\hyperlink{addpackage}{Addpackage} \> add packages of \TeX to the main file for previewing.\\ +\hyperlink{assign}{Assign} \> replace the string1 in the string0 with the string2.\\ +\hyperlink{changework}{Changework} \> change the working directory.\\ +\hyperlink{deffun}{Deffun} \> define a function common to both Cindy and R.\\ +\hyperlink{definecolor}{Definecolor} \> define the name of colorcode in the \TeX\ figure.\\ +\hyperlink{defvar}{Defvar} \> define variables common to both Cindy and R.\\ +\hyperlink{drwxy}{Drwxy} \> draw axis in the \TeX\ figure.\\ +\hyperlink{fontsize}{Fontsize} \> define the font size in the \TeX\ figure.\\ +\hyperlink{ketinit}{Ketinit} \> initialize \ketcindy.\\ +\hyperlink{ptsize}{Ptsize} \> set the size of points.\\ +\hyperlink{setax}{Setax} \> set the style of axis.\\ +\hyperlink{setcolor}{Setcolor} \> set the color of figures and characters in the \TeX\ figure.\\ +\hyperlink{setfiles}{Setfiles} \> set the name of texfile.\\ +\hyperlink{setparent}{Setparent} \> set the name of texfile by using the Parent push button.\\ +\hyperlink{setmarklen}{Setmarklen} \> set the length of tickmarks on the axsis.\\ +\hyperlink{setorigin}{Setorigin} \> set or transtate the coordinate of apparent origin.\\ +\hyperlink{setpen}{Setpen} \> set the thickness of lines.\\ +\hyperlink{setpt}{Setpt} \> set the size of points.\\ +\hyperlink{setscaling}{Setscaling} \> set the scale of vertical direction.\\ +\hyperlink{setunitlen}{Setunitlen} \> set the scale of unit length. (default is 1cm)\\ +\hyperlink{setwindow}{Setwindow} \> set a drawing area on a Euclidean view.\\ +\hyperlink{strsplit}{Strsplit} \> return the list of strings separated by a string.\\ +\hyperlink{usegraphics}{Usegraphics} \> change to pict2e.\\ + +{\bf Drawing} \> \\ +\hyperlink{addgraph}{AddGraph} \> manipulate more than one PD all together.\\ +\hyperlink{anglemark}{Anglemark} \> draw an angle mark.\\ +\hyperlink{arrowdata}{Arrowdata} \> draw an arrow line between two points.\\ +\hyperlink{arrowhead}{Arrowhead} \>draw an arrowhead with specified direction at a designated point.\\ +\hyperlink{bezier}{Bezier} \> draw a Bezier curve.\\ +\hyperlink{beziersmooth}{Beziersmooth} \> draw a smooth Bezier curve.\\\hyperlink{beziersym}{Beziersym} \> draw a smooth Bezier curve.\\ +\hyperlink{bowdata}{Bowdata} \> draw the shape of bow connecting two points.\\ +\hyperlink{bspline}{Bspline} \> draw second degree B-spline curve. \\ +\hyperlink{changestyle}{Changestyle} \> change the option for drawing. \\ +\hyperlink{circledata}{Circledata} \> draw a circle or polygon. \\ +\hyperlink{crspline}{CRspline} \> draw single Catmull-Rom spline curve. \\ +\hyperlink{deqplot}{Deqplot} \> draw the solution curve of a differential equation.\\ +\hyperlink{dotfilldata}{Dotfilldata} \> fill a domain with dots.\\ +\hyperlink{drwpt}{Drawppoint} \> draw a point. \\ +\hyperlink{drwpt}{Drwpt} \> draw a point. \\ +\hyperlink{drawsegmark}{Drawsegmark} \> Add a mark to a segment. \\ +\hyperlink{ellipseplot}{Ellipseplot} \> draw ellipse.\\ +\hyperlink{enclosing}{Enclosing} \> make a closed curve form the list of plotting data.\\ +\hyperlink{expr}{Expr} \> write an expression in \TeX style.\\ +\hyperlink{exprrot}{Exprrot} \> write a rotated expression in \TeX style.\\ +\hyperlink{fourierseries}{Fourierseries} \> draw the graph of a fourier series.\\ +\hyperlink{framedata}{Framedata} \> draw a rectangle.\\ +\hyperlink{hatchdata}{Hatchdata} \> draw hatch lines in the close curve.\\ +\hyperlink{htickmark}{Htickmark} \> tick on the horizontal ax.\\ +\hyperlink{hyperbolaplot}{Hyperbolaplot} \> draw a hyperbola.\\ +\hyperlink{implicitplot}{Implicitplot} \> draw the graph of a implicit function.\\ +\hyperlink{invert}{Invert} \> rearrange plotting data in the reverse order.\\ +\hyperlink{joincrvs}{Joincrvs} \> create a plotting data of connecting in list of plotting data.\\ +\hyperlink{letter}{Letter} \> display the string.\\ +\hyperlink{letterrot}{Letterrot} \> rotate a string and display it.\\ +\hyperlink{lineplot}{Lineplot} \> draw the straight line through the two points.\\ +\hyperlink{listplot}{Listplot} \> connect points by line segments.\\ +\hyperlink{mkbeziercrv}{Mkbeziercrv} \> draw some bezier curves.\\ +\hyperlink{mkbezierptcrv}{Mkbezierptcrv} \> draw a bezier curve.\\ +\hyperlink{mkcircles}{Mkcircles} \> create plotting data of all geometric circles.\\ +\hyperlink{mksegments}{Mksegments} \> create plotting data of all geometric segments.\\ +\hyperlink{ospline}{Ospline} \> draw a spline curve of Oshima.\\ +\hyperlink{ovaldata}{Ovaldata} \> draw a rectangle with rounded corners.\\ +\hyperlink{parabolaplot}{Parabolaplot} \> draws a parabola.\\ +\hyperlink{paramark}{Paramark} \> draw an angle mark with a parallelogram.\\ +\hyperlink{paramplot}{Paramplot} \> draw a curve of parametric representation.\\ +\hyperlink{polarplot}{Polarplot}\> draw a curve of polar equation.\\ +\hyperlink{partcrv}{Partcrv} \> make a piece of curve from the PD.\\ +\hyperlink{periodfun}{Periodfun} \> draw the graph of a periodic function.\\ +\hyperlink{plotdata}{Plotdata} \> draw the graph of function.\\ +\hyperlink{pointdata}{Pointdata} \> make a point data.\\ +\hyperlink{polygonplot}{Polygonplot} \> draw a polygon inscribed inside the circle.\\ +\hyperlink{putintersect}{Putintersect} \> make a intersection point of two curves.\\ +\hyperlink{putoncurve}{PutonCurve} \> put a point on the curve.\\ +\hyperlink{putonline}{PutonLine} \> put a point on the line.\\ +\hyperlink{putonSeg}{Putonseg} \> put a point on the segment.\\ +\hyperlink{putpoint}{Putpoint} \> put a point.\\ +\hyperlink{reflectdata}{Reflectdata} \> draw a reflective curve.\\ +\hyperlink{reflectpoint}{Reflectpoint} \> return the reflect point.\\ +\hyperlink{rotatedata}{Rotatedata} \> rotate plotting data.\\ +\hyperlink{rotatepoint}{Rotatepoint} \> rotate a point.\\ +\hyperlink{rulerscale}{Rulerscale} \> put ruler marks.\\ +\hyperlink{scaledata}{Scaledata} \> scale plotting data.\\ +\hyperlink{scalepoint}{Scalepoint} \> scale a point.\\ +\hyperlink{segmark}{Segmark} \> add a mark to a segment.\\ +\hyperlink{shade}{Shade} \> fill a domain surrounded by a closed curve.\\ +\hyperlink{tangentplot}{Tangentplot} \> draw a tangent line of a plotting data.\\ +\hyperlink{translatedata}{Translatedata} \> translate plotting data.\\ +\hyperlink{translatepoint}{Transelatepoint} \> translate a point.\\ +\hyperlink{vtickmark}{Vtickmark} \> tick on the vertical ax.\\ + +{\bf Calculus and I/O} \> \\ +\hyperlink{crossprod}{Crossprod} \> return the cross product of 2 vectors.\\ +\hyperlink{derivative}{Derivative} \> find the derivative of a function or a plotting data.\\ +\hyperlink{dotprod}{Dotprod} \> return the dot product of 2 vectors.\\ +\hyperlink{extractdata}{Extractdata} \> add properties to a data.\\ +\hyperlink{findarea}{Findarea} \> return the area enclosed with a close curve.\\ +\hyperlink{findlength}{Findlength} \> return the length of a curve.\\ +\hyperlink{integrate}{Integrate} \> find the value of numerical integration.\\ +\hyperlink{intersectcurves}{Intersectcurves} \> return a list of intersects of 2 plotting data.\\ +\hyperlink{intersectcurvesPp}{IntersectcurvesPp} \> return a list of intersects with parameters of 2 plotting data.\\ +\hyperlink{inversefun}{Inversefun} \> find the value of the inversefunction.\\ +\hyperlink{nearestpt}{Nearestpt} \> return the nearest point with the parameter and the distance.\\ +\hyperlink{nearestptcrv}{Nearestptcrv} \> return the nearest point on the plotting data from the point1.\\ +\hyperlink{numptcrv}{Numptcrv} \> return the number of plotting data.\\ +\hyperlink{paramoncurve}{Paramoncurve} \> return the parameter value of the point on the curve.\\ +\hyperlink{pointoncurve}{Pointoncurve} \> point which has the parameter value\\ +\hyperlink{ptstart, ptend}{Ptstart, Ptend} \> returns start point and end point of PD.\\ +\hyperlink{ptcrv}{Ptcrv} \> Returns n-th point from PD.\\ +\hyperlink{readoutdata}{ReadOutData} \> read external data.\\ +\hyperlink{writeoutdata}{WriteOutData} \> write out data in \ketcindy\ format.\\ + +{\bf Making Table} \> \\ +\hyperlink{changetablestyle}{Changetablestyle} \> change line styles of rules.\\ +\hyperlink{findcell}{Findcell} \> return the information of a cell.\\ +\hyperlink{putcell}{Putcell} \> put a string at the cell.\\ +\hyperlink{putcoL}{PutcoL} \> put strings to a column.\\ +\hyperlink{putcoLexpr}{PutcoLexpr} \> put strings to a column.\\ +\hyperlink{putrow}{Putrow} \> put strings to a row.\\ +\hyperlink{putrowexpr}{Putrowexpr} \> put strings to a row.\\ +\hyperlink{tabledata}{Tabledata} \> draw rules of a table.\\ +\hyperlink{tabledatalight}{Tabledatalight} \> make a table without geometric points.\\ +\hyperlink{tgrid}{Tgrid} \> return the coordinates of the grid name.\\ +\hyperlink{tlistplot}{Tlistplot} \> connect two lattice points by line segments.\\ + +{\bf Data Processing}\\ +\hyperlink{dispmat}{Dispmat} \> display the list in the console matrix.\\ +\hyperlink{tab2list}{Tab2list} \> convert contents of string data to list.\\ +\hyperlink{writecsv}{Writecsv} \> make a CSV file consisting of the contents of data.\\ + +{\bf Others} \> \\ +\hyperlink{assign}{Assign} \> replace the string1 in the string0 with the string2.\\ +\hyperlink{bbdata}{BBdata} \> return the size of an image file.\\ +\hyperlink{cindyname}{Cindyname} \> return the name of a current file.\\ +\hyperlink{colorcode}{Colorcode} \> change colorcode from colortype1 to colortype2.\\ +\hyperlink{dqq}{Dqq} \> return the string surrounded by double quotes.\\ +\hyperlink{factorial}{Factorial} \> return the factorial.\\ +\hyperlink{figpdf}{Figpdf} \> make a pdf file with the same size of figure.\\ +\hyperlink{help}{Help} \> display usages of the function.\\ +\hyperlink{indexall}{Indexall} \>return all positions of string2 in string1.\\ +\hyperlink{norml}{Norm} \> return the norm of a vector.\\ +\hyperlink{opl}{Op} \> return the n-th element of a list or a string.\\ +\hyperlink{ptselected}{Ptselected} \> tests whether the point is selected.\\ +\hyperlink{slider}{Slider} \> make a slider on a Euclidean view.\\ +\hyperlink{sprintf}{Sprintf} \> converts a real number to a string.\\ +\hyperlink{texcom}{Texcom} \> add the command in the \TeX file.\\ +\hyperlink{textformat}{Textformat} \> converts a real number to a string.\\ +\hyperlink{toupper}{Toupper} \> return the upper case letters of a string.\\ +\hyperlink{windispg}{Windispg} \> display all graphs on Euclidean view.\\ + +{\bf R} \> \\ +\hyperlink{boxplot}{Boxplot} \> draw boxplots.\\ +\hyperlink{calcbyr}{CalcbyR} \> executes R commands and returns the execution result to Cinderella.\\ +\hyperlink{histplot}{Histplot} \> create histograms.\\ +\hyperlink{plotdatar}{PlotdataR} \>draw graph of R's statistical probability function.\\ +\hyperlink{rfun}{Rfun} \>execute a R command.\\ + +{\bf Maxima} \> \\ +\hyperlink{calcbym}{CalcbyM} \> execute Maxima's script. \\ +\hyperlink{mxbatch}{Mxbatch} \> make a command to execute the Maxima file. \\ +\hyperlink{mxfun}{Mxfun} \> execute Maxima's function. \\ +\hyperlink{mxtex}{Mxtex} \> convert expression to TeX format. \\ + +{\bf Risa/Asir} \> \\ +\hyperlink{calcbya}{CalcbyA} \> execute Risa/Asir's script. \\ +\hyperlink{asirfun}{Asirfun} \> execute Risa/Asir's function. \\ + +{\bf MeshLab} \> \\ +\hyperlink{mkobjcmd}{Mkobjcmd} \> obj formatted files of surfaces without thickness.\\ +\hyperlink{mkobjcrvcmd}{Mkobjcrvcmd} \> obj formatted files of spatial curves.\\ +\hyperlink{mkobjnrm}{Mkobjnrm} \> calculate normal vector of surface.\\ +\hyperlink{mkobjplatecmd}{Mkobjplatecmd} \> obj formatted files of plates.\\ +\hyperlink{mkobjpolycmd}{Mkobjpolycmd} \> obj formatted files of polyhedra.\\ +\hyperlink{mkobjsymbcmd}{Mkobjsymbcmd} \> generate commands for obj formatted files of some characters.\\ +\hyperlink{mkobjthickcmd}{Mkobjthickcmd} \> generate commands for obj formatted files of surfaces with thickness.\\ +\hyperlink{mkviewobj}{Mkviewobj} \> generate obj formatted files.\\ +{\bf Animation} \> \\ +\hyperlink{setpara}{Setpara} \> set up the animation control system.\\ + +{\bf \ketcindy\ Slide} \> \\ +\hyperlink{setslidebody}{Setslidebody} \> set up the color and density of the letters in slide body.\\ +\hyperlink{setslidehyper}{Setslidehyper} \> use \verb|hyperref.sty|.\\ +\hyperlink{setslidemain}{Setslidemain} \> set up the main slide.\\ +\hyperlink{setslidepage}{Setslidepage} \> set up each page of slides.\\ +\hyperlink{setslidemargin}{Setslidemargin} \> change the margin of slides.\\ +\hyperlink{settitle}{Settitle} \> make a title slide.\\ + +{\bf \ketcindy 3D} \> \\ +\hyperlink{bezier3d}{Bezier3d} \> draw a Cubic Bézier curve.\\ +\hyperlink{changestyle3d}{Changestyle3d} \> change the attribute of PD.\\ +\hyperlink{concatobj}{Concatobj} \> concatenates several objects.\\ +\hyperlink{crvsfparadata}{Crvsfparadata} \> remove curves hidden by curved face.\\ +\hyperlink{datalist2d}{Datalist2d} \> get a list of 2D-plotting data on the screen.\\ +\hyperlink{datalist3d}{Datalist3d} \> get a list of 3D-plotting data.\\ +\hyperlink{dist3d}{Dist3d} \> get the 3D-distance of two points.\\ +\hyperlink{drawpoint3d}{Drawpoint3d} \> draw 3D-points.\\ +\hyperlink{embed}{Embed} \> embed plotting data of 2D in plane of 3D.\\ +\hyperlink{execcmdc}{ExeccmdC} \> draw 3D-surface.\\ +\hyperlink{intersectcrvsf}{Intersectcrvsf} \> return a list of intersects of a curve and curved face.\\ +\hyperlink{intersectsgpL}{IntersectsgpL} \>return a intersection of a line segment and plane.\\ +\hyperlink{invparapt}{Invparapt} \> return the point on the curve.\\ +\hyperlink{ketinit3d}{Ketinit3d} \> declare the use of KeTCindy3D\\ +\hyperlink{mkbezierptcrv3d}{Mkbezierptcrv3d} \> draw a cubic Bezier curve from nodes.\\ +\hyperlink{nohiddenbyfaces}{Nohiddenbyfaces} \> draw hidden lines by the surfaces.\\ +\hyperlink{parapt}{Parapt} \> return the 2D-coodinate on the plane.\\ +\hyperlink{partcrv3d}{Partcrv3d} \> draw the part curve of the curve PD.\\ +\hyperlink{perpplane}{Perpplane} \> return the two points which is passing through the point and\\ +\>orthogonal to the vector.\\ +\hyperlink{perppt}{Perppt} \> get the foot of a perpendicular for the plane from the point.\\ +\hyperlink{phparadata}{Phparadata} \> draw the polyhedron by performing hidden line processing.\\ +\hyperlink{pointdata3d}{Pointdata3d} \> generate data of point list.\\ +\hyperlink{projcoordpara}{Projcoordpara} \> get the projection coordinate.\\ +\hyperlink{putaxes3d}{Putaxes3d} \> make the geometric points on the coordinate axis. \\ +\hyperlink{putonCurve3d}{PutonCurve3d} \> make the geometric point on the 3D-curve.\\ +\hyperlink{putonseg3d}{Putonseg3d} \> make the geometric point on the 3D-segment.\\ +\hyperlink{putpoint3d}{Putpoint3d} \> draw the geometric point in the space.\\ +\hyperlink{readobj}{Readobj} \> read in the polyhedron data in the folder name \verb|polyhedrons_obj|\\ +\hyperlink{reflectdata3d}{Reflectdata3d} \> draw the reflection of plotting data.\\ +\hyperlink{reflectpoint3d}{Reflectpoint3d} \> return the coordinate of the reflect point.\\ +\hyperlink{rotatedata3d}{Rotatedata3d} \> rotate plotting data around the vector\\ +\hyperlink{rotatepoint3d}{Rotatepoint3d} \> return the coordinate of the rotate point.\\ +\hyperlink{scaledata3d}{Scaledata3d} \>scale plotting data \\ +\hyperlink{scalepoint3d}{Scalepoint3d} \> execute scale transformation for the coordinate of the point.\\ +\hyperlink{sf3data}{Sf3data} \> draw the wire frame model of the surface.\\ +\hyperlink{sfbdparadata}{Sfbdparadata} \> draw the surface by performing hidden line processing.\\ +\hyperlink{skeletonparadata}{Skeletonparadata} \> draw the lines by performing hidden line processing.\\ +\hyperlink{spacecurve}{Spacecurve} \> draw the space curve.\\ +\hyperlink{spaceline}{Spaceline} \> draw the space polygonal lines.\\ +\hyperlink{start3d}{Start3d} \> creates subarea, and recognize 3D points.\\ +\hyperlink{startsurf}{Startsurf} \> defines values related to surface rendering.\\ +\hyperlink{translatedata3d}{Translatedata3d} \> translate plotting data\\ +\hyperlink{translatepoint3d}{Translatepoint3d} \> return the translated coordinate for the point.\\\hyperlink{vertexedgeface}{Vertexedgeface} \> draw the polyhedron.\\ +\hyperlink{wireparadata}{Wireparadata} \> draw the surface by wire frame data with performing hidden line processing.\\ +\hyperlink{xyzax3data}{Xyzax3data} \> draw the coordinate axis.\\ +\hyperlink{xyzcoord}{Xyzcoord} \> return the 3D-coordinate of the point P.\\ + +\end{tabbing} + +\end{document} diff --git a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/KeTCindyReferenceJ.tex b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/KeTCindyReferenceJ.tex index 58a7dfdd22e..937c5a10cc1 100644 --- a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/KeTCindyReferenceJ.tex +++ b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/KeTCindyReferenceJ.tex @@ -7,4210 +7,5234 @@ \usepackage[dvipdfmx,bookmarks=false,colorlinks=true,linkcolor=blue]{hyperref} \setmargin{20}{20}{15}{25} \usepackage{setspace} - +\usepackage{comment} +\setcounter{tocdepth}{3} \begin{document} -\title{\ketcindy リファレンスマニュアル} +\title{\ketcindy 関数リファレンス} \author{\ketcindy\ Project Team} \maketitle +\begin{center} - 第3.2版 -\end{center} +\hypertarget{index}{} \tableofcontents \newpage +\section{平面の図形とグラフ} -\section{\ketcindy について} -\subsection{システムの構成} -\ketcindy は，Cinderella での作図データをScilab版 \ketpic に渡し，\LaTeX ファイルを作成するためのスクリプトライブラリである。Cinderella によるインタラクティブな作図機能と，CindyScript によるプログラミングにより，\LaTeX 文書の挿入図を効率よく作成することができる。また，R,Maxima,Risa/Asirなどの数式処理ソフトと連携して計算を行うことができる。 +%設定・定義 ================================== -\input{Fig/concept} +\subsection{設定・定義} - Cinderellaで作図した図のデータは，Scilabのファイル（拡張子 sci）に書き出される。これをScilabで処理して\TeX ファイルを作成する（ Scilab版 \ketpic）。できた\TeX ファイルを，本文中に inputコマンド で挿入すれば図が表示される。\\ - CinderellaとScilabやその他のソフトウェアとの連携には，バッチファイル（Macではシェルファイル）を用いている。(概念図の両方向矢印) バッチファイルは kc.bat，シェルファイルは kc.sh で，KeTCindy が目的に応じてこれらのファイルを書き出し，プラグイン KetCindyPlugin.jar でそれらを実行する手順になっている。\\ - \\ -\subsection{Cindyscriptのスロットの概念} -CindyscriptはCinderellaのプログラミング言語で，スクリプトエディタで記述する。スクリプトエディタは，「スクリプト」メニューの「Cindyscript」を選択して開くか，Ctrl+9 (Windows) / ⌘＋9 (Mac) で開く。\\ - スクリプトエディタの左方に並んでいるフォルダアイコンのメニュー風のものを「スロット」といい，Cindyscriptの実行タイミングによりスクリプトを書き分けることができる。通常は Initialzation スロットと Draw スロットを使う。\\ - Initialzation スロットは，スクリプトを実行すると最初に一度だけ実行される。従って，関数定義や変数の初期設定などを書く。ひな形やサンプルの cdy ファイルではここに KETlib というページがあり，パス名の設定やライブラリの読み込みなど，KeTCindyの初期設定に関する記述がある。\\ - Draw スロットは，Cinderellaの画面上でなにか操作が行われるたびに実行される。通常はここにスクリプトを書く。ひな形のcdyファイルでは，Ketinit() などが記述された figures ページが用意されている。\\ - \\ - \includegraphics[bb=0 0 1076 392 , width=10cm]{Fig/slot.png}\\ - \\ - １つのスロットに複数のページを作ることができる。KETlib以外に初期設定のスクリプトを書く場合は，Initialzation スロットに新しいページを作るのがよい。\\ +\subsubsection{環境設定} +\begin{description} -\subsection{プロットデータ} -プロットデータ(Plot Data) とは，関数のグラフや幾何要素を描くデータのことであり，KeTCindyの処理の中核をなしている。本マニュアルでは PD と略すことがある。たとえば曲線は，描画範囲を分割して線分の集まりとして描画しており，このときのプロットデータはそれらの線分の端点のリストである。\\ - プロットデータの名称はKeTCindyが自動的に命名する。その命名規則は次の通りである。\\ -\\ -・名称の頭部は，プロットデータを作成する関数ごとに決まっている。\\ -・第１引数に name が与えられる場合，name を頭部に付加する。\\ - 例：\verb|Listplot("1",[[0,0],[1,2]]);| のとき，sg1\\ -・関数によっては，第１引数の name を略すことができる。この場合，引数で用いられた点の名前を頭部に付加する。\\ - 例：\verb|Listplot([A,B,C]);| のとき，sgABC\\ - \\ - プロットデータを生成したときは，Cindyscriptエディタのコンソールにその名称を表示する。上の例では，\\ - \verb|generate Listplot sgABC|\\ -と表示される。プロットデータを操作する関数では，このPDの名称を用いる。\\ - プロットデータの内容を知りたい場合は，Cindyscriptの\\ - println(プロットデータ名)\\ -でコンソールに表示することができる。\\ - プロットデータは，Cindyscriptによるプログラムで作成してそれをKeTCindyで利用することもできる。Listplot()の例を参照のこと。ただし，要素の数が大きいとScilabでエラーとなるので，１つのプロットデータの要素は200程度とするのがよい。これより多い場合は分割する。\\ +\vspace{\baselineskip} +\hypertarget{ketinit}{} +\item[関数] Ketinit(options) +\item[機能] \ketcindy を初期化する。平面図形ではDrawスロットに，空間図形ではInitialization スロットの冒頭に記述する必要がある。 +\item[説明] option 作業サブフォルダ，縦方向の倍率と描画領域を設定する。\\ +\phantom{option }通常は不要で，\verb|Ketinit()| だけでよい。\\ -\subsection{Cinderellaの作図ツール} - \\ -\includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/move.png} 動かすモード（選択モード）にする：標準状態\\ -\includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/single-add.png} 点を加える\\ -\includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/multi-add-line.png} 直線を加える\\ -\includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/segment.png} 線分を加える\\ -\includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/middle.png} 中点を加える\\ -\includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/intersection.png} 交点を加える\\ -\includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/multi-add-parallel.png} 平行線を加える\\ -\includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/multi-add-perp.png} 垂線を加える\\ -\includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/bisector.png} 角の二等分線を加える\\ -\includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/multi-add-circle.png} 円を加える\\ -\includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/circle-by-radius.png} 半径つき円を加える\\ -\includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/ellipse-by-foci.png} 焦点と通る点で決まる楕円\\ -\includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/hyperbola-by-foci.png} 焦点と通る点で決まる双曲線\\ -\includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/parabola-by-foci.png} 焦点と準線で決まる放物線\\ -\includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/polygon.png} 多角形を加える\\ -\includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/angle-mark.png} 角に印をつける\\ -\includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/angle.png} 角度を測る\\ -\includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/delete.png} 選択した要素を消去する\\ -\includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/select-points.png} 点をまとめて選択する\\ -\includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/select-lines.png} 線分をまとめて選択する\\ - \\ -設定メニューから「上のツールバーのカスタマイズ」を選び，「すべて表示」にすると現れるツール\\ -\includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/mirror.png} 鏡映\\ -\includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/polar-of-point.png} 点の極線を描く\\ - \\ -画面ツール（下のツールバー）\\ -\includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/translate-view.png} 原点を移動する\\ -\includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/zoom-in.png} 矩形領域を画面サイズに拡大\\ -\includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/zoom-out.png} 画面を矩形領域サイズに縮小\\ -\includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/snap.png} 軸と方眼を表示し格子点にスナップする\\ +【例】 -\subsection{用語解説} -インシデント\\ - 点が曲線上に乗っている状態を表す。\\ -インスペクタ\\ - 幾何要素の属性などを管理するウィンドウ。\\ -幾何要素 \\ - Cinderellaの作図ツールで作図した点や直線などの要素\\ -幾何点 \\ - 幾何要素としての点。マウスドラッグで動かすことができる。\\ -固定点\\ - マウスドラッグで移動することのできない点\\ -コンソール\\ - スクリプトエディタの右下のエリア。\\ -自由点\\ - マウスドラッグで任意に動かすことのできる点。\\ -スロット \\ - Cindyscriptで，スクリプトを書くとき，実行タイミングによりに分類するもの\\ -スナップ \\ - マウスポイントが格子点の近くに来ると格子点上にぴったり移動する。\\ - Cinderellaの画面の下方ツールのうち，磁石アイコンによりこのモードになる。\\ +\verb|Ketinit()| ：サブフォルダ\verb|"fig"|，倍率１，描画領域 $-5 \leq x \leq 5 , -5 \leq y \leq 5$ -\newpage -%======================= -\section{定数と変数} -KeTCindy は Cindyscript で記述されている。CindyScriptでは，変数名は大文字と小文字を区別するが，関数名は大文字小文字を区別しない。Cindyscriptのマニュアルでは組み込み関数名はすべて小文字で表記されている。例示されたスクリプトでは，変数も小文字である。そこで，KeTCindyでは，組み込みの変数名・関数名と区別しやすいように，次の規則により名前を付けている。\\ - \\ - ・グローバルな変数はすべて大文字か，大文字で始まるものとする。\\ - ・局所変数は小文字で，関数定義の冒頭で regional() により局所変数として宣言する。\\ - ・関数名は大文字で始まる。\\ - \\ - なお，CindyScriptは関数型プログラミング言語であり，命令はすべて関数を用いて行われるが，本マニュアルでは，文脈により「コマンド」という表現も用いる。\\ - \\ -{\bf 定数} \\ - つぎのものがCindyScriptに予約されており，小文字で表されている。\\ +\verb|Ketinit("")| ： サブフォルダはcindyファイルと同じ -\begin{tabbing} -12345678\=\kill - pi \>：円周率。Scilabには \% pi で書き出される。\\ - i \> ：虚数単位。Scilabには \% i で書き出される。\\ -\end{tabbing} - 一般のプログラミングでは変数 i をループ変数としてよく使うが，CindyScript では i は予約定数と考え，変数として用いないことを勧める。ただし，変数としてまったく使えないわけではなく，変数として用いた後，必要があれば \verb|i=complex([0,1])| を実行することにより虚数単位として再定義することができる。\\ - \\ -{\bf 予約変数}\\ - KeTCindy が内部的に使用する予約変数がある。そのうち次のものはユーザーが値を変更または設定することができる。設定は Initalization スロットの「KETlib」ページでおこなうが，Fhead とTexparent は Draw スロットでもよい。\\ -\begin{tabbing} -1234567890123\=45678989012345678901234567890123\=\kill - Fhead \>書き出されるファイル名の頭部\\ - Texparent \>親プロセスのファイル名\\ - Dirhead \>パスの頭部\\ - Dirlib \>ライブラリ ketlib のパス\\ - Dirbin \>ketbin のパス\\ - Dirwork \>作業ディレクトリのパス\\ - Shellfile \>シェルファイル名\\ -\end{tabbing} - 以下の予約変数は，ライブラリが使用するグローバル変数であるので，ユーザーはこれらの変数名を使ってはいけない。なお，変数は大文字小文字を区別するので，小文字で書く分には支障はない。したがって，ユーザーが作るプログラムでは，すべて小文字か，先頭だけが大文字の変数を使うことを勧める。\\ - \\ -ADDAXES， ArrowlineNumber， ArrowheadNumber， BezierNumber，\\ -COM0thlist， COM1stlist， COM2ndlist， Dq， FUNLIST，\\ -Fnamesc ，Fnamescibody，Fnameout，Fnametex，GDATALIST，\\ -GLIST， GCLIST， GOUTLIST， KCOLOR， KETPICCOUNT， \\ -KETPICLAYER， LETTERlist， LFmark， MilliIn， PenThick， \\ -PenThickInit， POUTLIST， SCALEX， SCALEY， SCIRELIST， \\ -SCIWRLIST， TenSize， TenSizeInit， ULEN， XMAX， XMIN， YaSize，\\ -YaThick， YMAX， YMIN， VLIST +\verb|Ketinit(2)| ： 倍率2，描画領域 $-5 \leq x \leq 5 , -5 \leq y \leq 5$ -\newpage +\verb|Ketinit(2,[-2,3],[-2,4])| ： 倍率2，描画領域 $-2 \leq x \leq 3 , -2 \leq y \leq 4$ -%設定・定義 ================================== -\section{関数リファレンス} -\subsection{設定・定義} +\vspace{\baselineskip} +描画領域(TeXに出力する領域)は制御点SW（左下）とNE（右上）を対角とする矩形領域。描画領域を指定すると，制御点がなければその位置に作り，すでに存在する場合は何もしない。作成された制御点はドラッグして描画領域を変更することができる。倍率は，Setscaling(倍率)を実行するのと同じ。ただし，Cinderellaで作図した幾何要素に対しては無効。(\hyperlink{setscaling}{Setscaling()}の項参照) -\begin{description} +%\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\hypertarget{addax}{} -\item[関数] Addax(0または1) -\item[機能] 座標軸を書くかどうかを定める -\item[説明] ScilabのClosefile() の引数に対応する。\\ - 引数が0のとき座標軸を書かない（デフォルトは1） -\begin{verbatim} - Listplot([B,A,C]); - Letter([A,"ne","A",B,"se","B",C,"se","C"]); -\end{verbatim} - \\ - \input{Fig/addax1} -\begin{verbatim} - Listplot([B,A,C,B]); - Letter([A,"ne","A",B,"sw","B",C,"se","C"]); - Addax(0); -\end{verbatim} - \input{Fig/addax2}\\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} - \\ -\hypertarget{addcolor}{} -\item[関数] Addcolor(描画コマンド , カラーコード) -\item[機能] 描画コマンドで描かれる線を指定色で描く -\item[説明] 描画コマンドはダブルクウォートでくくって文字列とする。描画コマンド内にダブルクウォートがある場合は，シングルクウォートにする。optionのある描画コマンドでoptionを指定しない場合は，必ず空リストをoptionとして書く。描画色は，RGBまたはCMYK。描画色は画面と図版の両方に有効。\\ - \\ - 例：\verb|Addcolor("Plotdata('2','x^2','x',[])",[1,1,0]);|\\ - \\ - \\ -\hypertarget{colorcode}{} -\item[関数] Colorcode(文字1,文字2, カラーコード) -\item[機能] 文字１から文字２へカラーコードを変換する。戻り値は変換されたコード。 -\item[説明] 文字は，"rgb","cmyk","hsv"のいずれか。\\ - \\ -例：\verb|Colorcode("rgb","cmyk",[1,0,0]); |\\ - RGBコードの[1,0,0]をCMYKに変換したコードを返す\\ - \verb|Colorcode("cmyk","rgb",[0,1,1,0]);|\\ - CMYKコードの[0,1,1,0]をRGBに変換したコードを返す\\ - \verb|Colorcode("rgb","hsv",[1,0,0]);|\\ - RGBコードの[1,0,0]をHSVに変換したコードを返す\\ - \\ - \\ -\hypertarget{deffun}{} -\item[関数] Deffun(関数名 , 定義のリスト) -\item[機能] 関数を定義する -\item[説明] 関数定義は，CindyScript の関数定義 f(x):=式 でもできるが，Deffun()を使うことにより，Scilab 側に渡すファイルに\\ - function 定義式 endfunction;\\ - が記述されるので，Scilab側でこの関数を利用することができる。目的に応じて使い分けるとよい。\\ - 式のリストには if文を用いた場合分けの関数式を記述することもできる。\\ - \\ -例：$f(x)=\dfrac{1}{x^2+1}$ を定義し，グラフを描いてx=1 における微分係数を求める。 +\vspace{\baselineskip} +\hypertarget{setfiles}{} +\item[関数] Setfiles(filename） +\item[機能] 出力するファイル名の設定 +\item[説明] 出力するTexのファイル名を指定する。 + +出力するファイル名は 初期設定では，作図しているCinderellaのファイル名。 + +たとえば，triangle.cdy で作図して出力すると，triangle.tex ができる。 + +これに対し，triangle.cdy で作図しているときに，grav.tex で出力したい場合は + +\hspace{10mm} \verb|Setfiles("grav");| + +とすると，grav.tex ができる。 + +\vspace{\baselineskip} +\hypertarget{setparent}{} +\item[関数] Setparent(filename） +\item[機能] Parent ボタンで出力するファイル名の設定 +\item[説明] Figpdf() を使ってParent ボタンで出力するTexのファイル名を指定する。 + +Parent ボタンで出力するファイル名は 初期設定がないので，指定する必要がある。 + +たとえば，triangle.cdy で作図しているときに，図サイズの grav.pdf を作る場合， + +\hspace{10mm} \verb|Setparent("grav");| + +とすると，図のTeXファイル triangle.tex と PDFを作る grav.tex ができ，ここから grav.pdf ができる。 + +\vspace{\baselineskip} +\hypertarget{changework}{} +\item[関数] Changework(パス名） +\item[機能] 作業ディレクトリを指定（変更）する +\item[説明] 作業ディレクトリは， 初期設定では，現在作図しているファイルのあるフォルダ（ディレクトリ）の fig フォルダである。これを変更する。 + +\vspace{\baselineskip} +\hypertarget{addpackage}{} +\item[関数] Addpackage(パッケージ名) +\item[機能] TeXのパッケージを追加する +\item[説明] プレビュー用のTeXソースにパッケージを追加する。 + +\vspace{\baselineskip} + 【例】emath パッケージを追加する。 + +\hspace{10mm} \verb|Addpackage("emath"); | + + または + +\hspace{10mm} \verb|Addpackage(["emath"]); | + + により， + プレビュー用のTeXのプリアンブルに + +\hspace{10mm} \verb| \usepackage{emath}| + +が追加されて，emath のコマンドが利用できる。 + +\vspace{\baselineskip} +注）初期設定では，次のパッケージを利用している。 \begin{verbatim} - Deffun("f(x)",["regional(y)","y=1/(x^2+1)","y"]); - Plotdata("1","f(x)","x"); - coeff=Derivative("f(x)","x",1); -\end{verbatim} - 点Aを作図しておくと，点Aをドラッグしたとき常に曲線上に乗せ，その点での\\ - 接線を引くことができる。 + ketpic, ketlayer, amsmath, amssymb, graphicx, color + \end{verbatim} + +\vspace{\baselineskip} +\hypertarget{usegraphics}{} +\item[関数] Usegraphics("pict2e") +\item[機能] TeXのグラフィクスパッケージを \verb|"pict2e"| に変更する +\item[説明] デフォルトのパッケージは \verb|"tpic"| であるが，これを\verb|"pict2e"| に変更する。 + + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\end{description} +\newpage +%-----------------描画設定・定義-------------------------------------- +\subsubsection{描画設定・定義} + +\vspace{\baselineskip} +\begin{description} +\hypertarget{addax}{} +\item[関数] Addax(0または1) +\item[機能] 座標軸の表示 +\item[説明] 引数が1のとき座標軸を描き，0のとき描かない。ただし，描画面には座標軸は表示されない。 +初期設定は1で，座標軸を描かない場合のみ \verb|Addax(0)| とすればよい。 + +\vspace{\baselineskip} +【例】三角形を描く + +左図が 初期設定（座標軸表示） Addax(0) をつけると右図になる。 + \begin{verbatim} - A.xy=[A.x,f(A.x)]; - coeff=Derivative("f(x)","x",A.x); - Lineplot("1",[A,[A.x+1,A.y+coeff]]); + Listplot([B,A,C]); + Letter([A,"ne","A",B,"se","B",C,"se","C"]); \end{verbatim} - \input{Fig/deffun}\\ - 例：$f(x)=\left\{\begin{array}{l}1 (x\geq 0)\\ -1 (x<0)\\ \end{array}\right.$ を定義する。 +\vspace{\baselineskip} +\hspace{10mm} \input{Fig/addax1} \input{Fig/FigE} + + +\hypertarget{setax}{} +\item[関数] Setax() +\item[機能] 座標軸の書式を設定する。 +\item[説明] Cinderellaの描画面には反映されない。（座標軸は描かれない） + +引数はリストで与え，要素は順番に + +1. 軸の形状（直線は "l" ，矢印は "a"） 初期設定は直線 + +2. 横軸名 初期設定は $x$ + +3. 横軸名の位置 + +4. 縦軸名 初期設定は$y$ + +5. 縦軸名の位置 + +6. 原点名 初期設定はO + +7. 原点名の位置 + +それぞれダブルクウォートでくくる。 + +7つの引数のうちn番目だけを指定する場合は，[n,"内容"]で指定できる。 + +また，後方は 初期設定なら省略できる。 + +\vspace{\baselineskip} +【例】座標軸の先端を矢印にし，原点の北西にOを書く。 + +\hspace{10mm} \verb|Setax(["a","","","","","","nw"]);| + +【例】原点の北西にOを書く。 + +\hspace{10mm} \verb|Setax([7,"nw"]);| + +【例】先端を矢印にし，横軸を$\theta$，縦軸を$x$にして矢じりの左側に書く。 + +\hspace{10mm} \verb|Setax(["a","\theta","","x","w"]);| + +\vspace{\baselineskip} +\hspace{10mm}\input{Fig/setax(theta)} + + +\vspace{\baselineskip} +\hypertarget{drwxy}{} +\item[関数] Drwxy(), Drwxy(options) +\item[機能] 指定する手順で座標軸を描く +\item[説明] 座標軸は 初期設定では最後に描かれるが，座標軸上に白抜きの点を表示するなど，先に描くことが必要な場合に用いる。描画面には座標軸は表示されない。 + +options は次のリストである。\\ +\hspace*{10mm}["Origin=",\ "Xrng=",\ "Yrng="] + +【例】点$(-\pi,\ 0)$と$(\pi,\ 0)$を白抜きの点で表示する。 \begin{verbatim} - Deffun("f(x)",["regional(y)","if(x>=0,y=1,y=-1)","y"]); + Setax([7,"se"]); + Setpt(5); + Drwpt([-pi,0],0); + Drwxy(); + Plotdata("1","sin(x)","x",["dr","Num=200"]); + Drwpt([pi,0],0); \end{verbatim} - if 文はネストすることができる。 + + このスクリプトでは，Drwpt([-pi,0],0); を実行したのち座標軸を描き，次に，$y=\sin x$ のグラフを描いてから Drwpt([pi,0],0);を実行するので，点($-\pi$,0) の上を座標軸が通り，点($\pi$,0)は座標軸とグラフの上を通るので白抜きになる。\\ + +\begin{center} \input{Fig/drwxy}\end{center} + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\vspace{\baselineskip} +\hypertarget{definecolor}{} +\item[関数] Definecolor(色名 , 定義のリスト) +\item[機能] 色名を定義する +\item[説明] ユーザー命名の色名を定義する。定義リストは RGBまたはCMYKのリスト + +各色０〜１の範囲で指定する。定義した色名は，Setcolor(color,options) で使うことができる。 + +なお，\ketcindy では，68色を色名で使うことができる。色の名称は\hyperlink{colorcodelist}{カラーコード一覧} 参照。 + +\vspace{\baselineskip} + 【例】暗い紫色を darkmaz の名称で定義して使う。 \begin{verbatim} - Deffun("f(x)",["regional y","if(x>1,y=1, - if(x>-1,y=x,y=-1))","y"]); + Definecolor("darkmaz",[0.8,0,0.8]); + Setcolor("darkmaz"); \end{verbatim} - \\ -\hypertarget{defvar}{} -\item[関数] Defvar(文字列) -\item[機能] 変数を定義する -\item[説明] 変数の定義をScilabと共有する。また，ScilabのAssignリストに追加する。\\ - \\ - 例：\verb|Defvar("const=3");|\\ - \\ - 複数の変数を定義するときはリストにする。\\ - \\ - 例：\verb|Defvar([“a”,3,”b”,1]);|\\ - \\ -\hypertarget{drwxy}{} -\item[関数] Drwxy() -\item[機能] 座標軸を描く -\item[説明] 座標軸はデフォルトでは最後に描かれるが，座標軸上に白抜きの点を表示するなど，先に描くことが必要な場合に用いる。\\ +\vspace{\baselineskip} +\hypertarget{setcolor}{} +\item[関数] Setcolor(color,options） +\item[機能] 描画色の設定 +\item[説明] 引数colorはカラーコードまたは色の名称。 + +カラーコードはRGBまたはCMYKをリストで与える。各色０〜１。 + +色の名称は\hyperlink{colorcodelist}{カラーコード一覧} の68色が指定できる。 -例：点$(-\pi,\ 0)$と$(\pi,\ 0)$を白抜きの点で表示する。 + +\vspace{\baselineskip} +【例】 Cinderellaの描画ツールとCindyScriptで線分AB,ACを60°の角をなすように描いておき，点DとEを弧の両端になるように設定して \begin{verbatim} - Setax([7,"se"]); - Setpt(8); - Drwpt([-pi,0],0); - Drwxy(); - Plotdata("1","sin(x)","x",["dr","Num=300"]); - Drwpt([[pi,0],0]); + Setcolor([1,0,0]); + Circledata([A,D],["Rng=[0,pi/3]"]); + Arrowhead(E,[-1,0.8],[2,1]); \end{verbatim} +を実行すると，矢じりつきの弧を赤で表示することができる。 + +１行目は，\verb|Setcolor("red");| でもよい。 +座標軸を描く場合は，このあと \verb|Setcolor("black")| で黒に戻しておかないと，座標軸が赤で表示されてしまうので要注意。 - このスクリプトでは，Drwpt([-pi,0],0); を実行したのち座標軸を描き，次に，$y=\sin x$ のグラフを描いてから Drwpt([pi,0],0);を実行するので，点($-\pi$,0) の上を座標軸が通り，点($\pi$,0)は座標軸とグラフの上を通るので白抜きになる。\\ -\input{Fig/drwxy} - \\ - \\ -\hypertarget{fontsize}{} -\item[関数] Fontsize(記号) -\item[機能] フォントサイズを設定する -\item[説明] 次に Fontsize() を実行するまで有効\\ - 記号は，"t" , "ss" , "f", "s" , "n" , "la", "La", "LA", "h" , "H"\\ - -例:小さい方からいくつか表示する。 -\begin{verbatim} - Ptsize(2); - Drawpoint([A,B,C,D,E,F,G]); - Fontsize("t"); Letter([A,"s2","A"]); - Fontsize("ss"); Letter([B,"s2","B"]); - Fontsize("s"); Letter([C,"s2","C"]); - Fontsize("la"); Letter([D,"s2","D"]); - Fontsize("La"); Letter([E,"s2","E"]); - Fontsize("h"); Letter([F,"s2","F"]); - Fontsize("H"); Letter([G,"s2","G"]); -\end{verbatim} - \input{Fig/fontsize} - -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\newpage -\hypertarget{ketinit}{} -\item[関数] Ketinit(options) -\item[機能] \ketcindy を初期化する -\item[説明] opution 縦方向の倍率と描画領域を設定\\ +\vspace{\baselineskip} +\hspace{20mm} \includegraphics[width=3.5cm,bb=0 0 161 134]{Fig/setcolor.pdf} - 例：\verb|Ketinit()| ：倍率１，描画領域 $-5 \leq x \leq 5 , -5 \leq y \leq 5$（デフォルト）\\ - \verb|Ketinit(2)| ： 倍率２，描画領域 $-5 \leq x \leq 5 , -5 \leq y \leq 5$\\ - \verb|Ketinit(2,[-2,3],[-2,4])| ： 倍率２，描画領域 $-2 \leq x \leq 3 , -2 \leq y \leq 4$\\ +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} - 描画領域(TeXに出力する領域)は制御点SW（左下）とNE（右上）を対角とする矩形領域。描画領域を指定すると，制御点がなければその位置に作り，すでに存在する場合は何もしない。作成された制御点はドラッグして描画領域を変更することができる。\\ - 倍率は，Setscaling(倍率)を実行するのと同じ。ただし，Cinderellaで作図した幾何要素に対しては無効。(Setscaling()の項参照)\\ +\vspace{\baselineskip} +\hypertarget{deffun}{} +\item[関数] Deffun(関数名 , 定義のリスト) +\item[機能] 関数を定義する +\item[説明] 関数定義は，CindyScript の関数定義 f(x):=式 でもできるが，Deffun()を使うことにより，Rでこの関数を利用することができる。目的に応じて使い分けるとよい。 -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +式のリストには if文を用いた場合分けの関数式を記述することもできる。 -\hypertarget{ptsie}{} -\item[関数] Ptsize(n) , Setpt(n) -\item[機能] 表示する点の大きさを設定する。 -\item[説明] Ptsize() と Setpt() は同じである。デフォルトは１\\ - Ptsize()はCindyScript風の語法，Setpt() は \ketpic 風の語法\\ - 全体の点の大きさを設定する。点の大きさを個々に変えたい場合は，sizeオプションを用いる。\\ +\vspace{\baselineskip} +【例】 +$f(x)=\dfrac{1}{x^2+1}$ を定義し，グラフを描く。 -例：１から４までの点の大きさ\\ - あらかじめ，Cinderellaの作図ツールで点A,B,C,Dを作図しておく。 \begin{verbatim} - Pointdata("1",A,["size=1"]); - Pointdata("2",B,["size=2"]); - Pointdata("3",C,["size=3"]); - Pointdata("4",D,["size=4"]); +Deffun("f(x)",["regional(y)","y=1/(x^2+1)","y"]); +Plotdata("1","f(x)","x"); \end{verbatim} -\input{Fig/pointsize}\\ +\vspace{\baselineskip} +\hspace{20mm}\scalebox{0.9}{\input{Fig/deffun01}} + + +\vspace{\baselineskip} + 【例】$f(x)=\left\{\begin{array}{l}1 (x\geq 0)\\ -1 (x<0)\\ \end{array}\right.$ を定義してグラフを描く。 -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\newpage -\hypertarget{setax}{} -\item[関数] Setax() -\item[機能] 座標軸の書式を設定する。 -\item[説明] Scilabのみで実行する。Cinderellaの描画面に反映されない。\\ -引数は順番に\\ - 1. 軸の形状（直線は "l" ，矢印は "a"）デフォルトは直線\\ - 2. 横軸名 デフォルトは $x$ \\ - 3. 横軸名の位置\\ - 4. 縦軸名 デフォルトは$y$\\ - 5. 縦軸名の位置\\ - 6. 原点名 デフォルトはO\\ - 7. 原点名の位置\\ -それぞれダブルクウォートでくくる。\\ -７つの引数のうちn番目だけを指定する場合は，[n,"内容"]で指定できる。\\ -また，後方はデフォルトなら省略できる。\\ - - 例：座標軸の先端を矢印にし，原点の北西にOを書く。\\ - \verb|Setax(["a","","","","","","nw"]);|\\ - - 例：原点の北西にOを書く。\\ - \verb|Setax([7,"nw"]);|\\ - - 例：先端を矢印にし，横軸をθ，縦軸を$x$にして矢じりの左側に書く。\\ - \verb|Setax(["a","θ","","x","w"]);|\\ - \\ - \input{Fig/setax_theta} - \\ - -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\newpage -\hypertarget{definecolor}{} -\item[関数] Definecolor(色名 , 定義のリスト) -\item[機能] 色名を定義する -\item[説明] ユーザー命名の色名を定義する。定義リストは RGBまたはCMYKのリスト\\ - 各色０〜１の範囲で指定する。定義した色名は，Setcolor(color,options) で使うことができる。なお，KeTCindyでは，68色を色名で使うことができる。次の Setcolor(color,options) 参照）\\ - \\ - 例：暗い紫色を darkmaz の名称で定義して使う。 \begin{verbatim} - Definecolor("darkmaz",[0.8,0,0.8]); - Setcolor("darkmaz"); + Deffun("f(x)",["regional(y)","if(x>=0,y=1,y=-1)","y"]); + Plotdata("1","f(x)","x",["Dis=1","Num=100"]; \end{verbatim} -\hypertarget{setcolor}{} - \\ - \\ -\item[関数] Setcolor(color,options） -\item[機能] 描画色の設定 -\item[説明] 引数colorはカラーコードまたは色の名称。\\ - カラーコードはRGBまたはCMYKをリストで与える。各色０〜１。\\ - 色の名称は次頁の68色が指定できる。ただし，Cinderellaの画面には色は反映されない。\\ - colorに色の名称を用いた場合は，option として，透明度を０〜１の数で指定できる。１が最も濃く，０は結果として色塗りをしない。\\ - \\ -例 Cinderellaの描画ツールとCindyScriptで線分AB,ACを60°の角をなすように描いておき，点DとEを弧の両端になるように設定して -\begin{verbatim} - Setcolor([1,0,0]); - Circledata([A,D],["Rng=[0,pi/3]"]); - Arrowhead(E,[-1,0.8],[2,1]); -\end{verbatim} - を実行すると，矢じりつきの弧を赤で表示することができる。\\ - １行目は，\verb|Setcolor("red");| でもよい。\\ - ただし，Cinderellaの描画面では着色されない。\\ - 描画面でも着色したい場合は，オプション \verb|"Color=[R,G,B]"| を用いる。\\ - 上の例の場合， -\begin{verbatim} - Circledata([A,D],["Rng=[0,pi/3]","Color=[1,0,0]"]); - Arrowhead(E,[-1,0.8],[2,1,"Color=[1,0,0]"]); -\end{verbatim} - とすれば，描画面でも赤で表示される。\\ - - \includegraphics[width=3.5cm,bb=0 0 161 134]{Fig/setcolor.pdf} - \\ - \\ -\scalebox{0.9}{\input{Fig/colortable1-34}} -\newpage - \\ - \\ - \\ -\scalebox{0.9}{\input{Fig/colortable35-68}} - \\ - \\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\newpage +\vspace{\baselineskip} +\hspace{20mm}\scalebox{0.9}{\input{Fig/deffun02}} + + if 文はネストすることができる。 +\begin{verbatim} + Deffun("f(x)",["regional y","if(x>1,y=1,if(x>-1,y=x,y=-1))","y"]); +\end{verbatim} + +\vspace{\baselineskip} +\hspace{20mm}\scalebox{0.9}{\input{Fig/deffun03}} + + +\vspace{\baselineskip} +\hypertarget{defvar}{} +\item[関数] Defvar(文字列) +\item[機能] 変数を定義する +\item[説明] 変数の定義をRと共有する。 + +【例】 \verb|Defvar("const=3");| + +\vspace{\baselineskip} + 複数の変数を定義するときはリストにする。 + +【例】 \verb|Defvar([“a”,3,”b”,1]);| + +\vspace{\baselineskip} +\hypertarget{fontsize}{} +\item[関数] Fontsize(記号) +\item[機能] フォントサイズを設定する +\item[説明] 次に Fontsize() を実行するまで有効\\ + 記号は，"t" , "ss" , "f", "s" , "n" , "la", "La", "LA", "h" , "H"\\ + +【例】作図ツールの「点を加える」で，A〜Gの点をとっておく。小さい方からいくつか表示する。 +\begin{verbatim} + Ptsize(2); + Drawpoint([A,B,C,D,E,F,G]); + Fontsize("t"); Letter([A,"s2","A"]); + Fontsize("ss"); Letter([B,"s2","B"]); + Fontsize("s"); Letter([C,"s2","C"]); + Fontsize("la"); Letter([D,"s2","D"]); + Fontsize("La"); Letter([E,"s2","E"]); + Fontsize("h"); Letter([F,"s2","F"]); + Fontsize("H"); Letter([G,"s2","G"]); +\end{verbatim} +\input{Fig/fontsize} + +\vspace{\baselineskip} +\hypertarget{setpt}{} +\hypertarget{ptsize}{} +\item[関数] Ptsize(n) , Setpt(n) +\item[機能] 表示する点の大きさを設定する。 +\item[説明] Ptsize() と Setpt() は同じである。 初期設定は１ + +全体の点の大きさを設定する。点の大きさを個々に変えたい場合は，sizeオプションを用いる。 + +\vspace{\baselineskip} +【例】１から4までの点の大きさ + +あらかじめ，Cinderellaの作図ツールで点A,B,C,Dを作図しておく。 +\begin{verbatim} + Pointdata("1",A,["Size=1"]); + Pointdata("2",B,["Size=2"]); + Pointdata("3",C,["Size=3"]); + Pointdata("4",D,["Size=4"]); +\end{verbatim} +\hspace{10mm}\input{Fig/pointsize} + \hypertarget{setmarklen}{} -\item[関数] Setmarklen(数) -\item[機能] 座標軸の目盛の長さを設定する -\item[説明] Htickmark() , Vtickmark() で座標軸に目盛を入れるとき，その長さを設定する。 \\ - ⇒ \hyperlink{htickmark}{Htickmark([横座標 , 方向 , 文字])}\\ +\item[関数] Setmarklen(数) +\item[機能] 座標軸の目盛の長さを設定する +\item[説明] \hyperlink{htickmark}{Htickmark()} , Vtickmark() で座標軸に目盛を入れるとき，その長さを設定する。 +\vspace{\baselineskip} \hypertarget{setorigin}{} -\item[関数] Setorigin(座標） -\item[機能] 描画する座標軸の原点を設定（移動）する -\item[説明] 描画する座標軸の原点を引数の座標とする。座標は点の識別名でもよい。\\ +\item[関数] Setorigin(座標） +\item[機能] 描画する座標軸の原点を設定（移動）する。座標系は変化しない。 +\item[説明] 描画する座標軸の原点を引数の座標とする。座標は点の識別名でもよい。 + +\vspace{\baselineskip} +【例】原点を (3,2) として座標軸を描く。 - 例：原点を (3,2) として座標軸を描く。\\ - \verb|Setorigin([3,2]);|\\ - 原点を点Aの位置にして座標軸を描く。\\ - \verb|Setorigin(A);| \\ +\hspace{10mm} \verb|Setorigin([3,2]);| - 注意：座標軸とともに，原点のO，軸名なども移動するが，座標系が変更される\\ - わけではない。\\ +原点を点Aの位置にして座標軸を描く。 - 例：原点は(3,2)に移動するが，スクリプトではもとの座標系を使う。 +\hspace{10mm} \verb|Setorigin(A);| + +\vspace{\baselineskip} + 【例】原点は(3,2)に移動するが，スクリプトではもとの座標系を使う。 \begin{verbatim} - Setorigin([3,2]); - Listplot([A,B,C,A]); - Ptsize(3); - Drawpoint([1,1]); - Letter([[1,1],"s2","P"]); + Setorigin([3,2]); + Listplot([A,B,C,A]); + Ptsize(3); + Drawpoint([1,1]); + Letter([[1,1],"s2","P"]); \end{verbatim} - 左が実行時のCinderellaの画面，右が\TeX の結果。\\ + 左が実行時のCinderellaの画面，右が\TeX の結果。\\ + +\hspace{10mm} \includegraphics[bb=0 0 227 205 , width=4cm]{Fig/setorigin.pdf} \input{Fig/setorigin} - \includegraphics[bb=0 0 227 205 , width=4cm]{Fig/setorigin.png} \input{Fig/setorigin}\\ - \\ +\vspace{\baselineskip} \hypertarget{setpen}{} -\item[関数] Setpen(数） -\item[機能] 線の太さを設定する\\ - \\[-5mm] -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} - \\ -\hypertarget{setpt}{} -\item[関数] Setpt(数) -\item[機能] 表示する点の大きさを設定する\\ +\item[関数] Setpen(数） +\item[機能] 線の太さの初期値を設定する + +\verb|Listplot()| などの描画関数のオプション \verb|dr| で，個々の太さは指定できる。 +\vspace{\baselineskip} \hypertarget{setscaling}{} -\item[関数] Setscaling(倍率) -\item[機能] 縦方向の倍率を設定する -\item[説明] ２次関数の応用問題などでは，グラフが縦に大きくなる場合があり，$y$軸方向のスケーリングを変えることがよくある。次のスクリプトは，$f(x)=-x^2+10x$ のグラフを縦軸方向を半分にして描くものである。\\ +\item[関数] Setscaling(倍率) +\item[機能] 縦方向の倍率を設定する。倍率は実数またはリスト。実数の場合は縦方向，リストの場合は[横方向，縦方向]の指定となる。 +\item[説明] 2次関数の応用問題などでは，グラフが縦に大きくなる場合があり，$y$軸方向のスケーリングを変えたいことがよくある。次のスクリプトは，$f(x)=-x^2+10x$ のグラフを縦軸方向を半分にして描くものである。 + \begin{layer}{150}{0} -\putnotese{80}{0}{\input{Fig/setscaling}} +\putnotese{80}{5}{\input{Fig/setscaling}} \end{layer} - \\ -\begin{verbatim} - Setscaling(0.5); - A.xy=[0,25/4]; - B.xy=[5/2,25/4]; - C.xy=[5/2,0]; - Listplot([A,B],["do"]); - Listplot([C,B],["do"]); - Plotdata("1","-2*x^2+10*x","x"); - Letter([[5,0],"s2w","5",[0,25/2],"w2", - "$\frac{25}{2}$",C,"s4","$\frac{5}{2}$"]); -\end{verbatim} -% \input{Fig/setscaling}\\ - ここで，点A,Bの座標が -\begin{verbatim} - A.xy=[0,25/4]; - B.xy=[5/2,25/4]; -\end{verbatim} -となっていることに注意されたい。$y$座標をあらかじめ半分にしている。すなわち，Cinderellaで作図した幾何要素に対してはSetscalingは無効である。これは，Putpoint関数を用いて点の位置を決めても同じである。\\ - たとえば，次のスクリプトでは，Cinderellaの画面上では２本の線分が点Bでつながるが，書き出された\TeX の図では離れてしまう。 -\begin{verbatim} - Setscaling(0.5); - Putpoint("A",[0,2]); - Putpoint("B",[2,2]); - Listplot([A,B]); - Listplot("1",[[0,0],[2,2]]); -\end{verbatim} - \\ - \\ -%\newpage +\begin{verbatim} + Setscaling(0.5); + A.xy=[0,25/4]; + B.xy=[5/2,25/4]; + C.xy=[5/2,0]; + Listplot([A,B],["do"]); + Listplot([C,B],["do"]); + Plotdata("1","-2*x^2+10*x","x"); + Letter([[5,0],"s2w","5",[0,25/2],"w2", + "$\frac{25}{2}$",C,"s4","$\frac{5}{2}$"]); +\end{verbatim} + ここで，点A,Bの座標が +\begin{verbatim} + A.xy=[0,25/4]; + B.xy=[5/2,25/4]; +\end{verbatim} +となっていることに注意されたい。$y$座標をあらかじめ半分にしている。すなわち，Cinderellaで作図した幾何要素に対してはSetscalingは無効である。これは，Putpoint関数を用いて点の位置を決めても同じである。 + +たとえば，次のスクリプトでは，Cinderellaの画面上では2本の線分が点Bでつながるが，書き出された\TeX の図では離れてしまう。 +\begin{verbatim} + Setscaling(0.5); + Putpoint("A",[0,2]); + Putpoint("B",[2,2]); + Listplot([A,B]); + Listplot("1",[[0,0],[2,2]]); +\end{verbatim} + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\vspace{\baselineskip} \hypertarget{setunitlen}{} -\item[関数] Setunitlen(文字列) -\item[機能] 単位長を設定する。デフォルトは 1cm\\ - この関数は，スクリプトの初めの方に書くのがよい。\\ - \\ +\item[関数] Setunitlen(文字列) +\item[機能] 単位長を設定する。 初期設定は 1cm。 + +この関数は，スクリプトの初めの方に書くのがよい。 + +【例】Setunitlen("8mm") + +\vspace{\baselineskip} \hypertarget{setwindow}{} -\item[関数] Setwindow(） -\item[機能] 出力する描画領域を設定する\\ -\item[説明] 出力する描画領域は，通常は２点SWとNEを対角とする矩形領域である。 -この２点をドラッグすることによりビジュアルに描画領域を決められる。\\ -しかし，これとは別に出力範囲を設定したい場合にこの関数を用いる。\\ -また，表を作成したときは，表の範囲が出力範囲として優先される（Tabledata()を実行したとき）ので，表外に図を描いた場合は，最後にこの関数で出力範囲を指定して書き出す。\\ - \\ +\item[関数] Setwindow(） +\item[機能] 出力する描画領域を設定する +\item[説明] 出力する描画領域は，通常は2点SWとNEを対角とする矩形領域である。 -\hypertarget{slider}{} -\item[関数] Slider(名称，位置1,位置2) -\item[機能] スライダを作成する -\item[説明] 名称は "A-C-B" の形で，端点をA,B，スライダ点をCとしたスライダを作る。\\ - 端点A,Bの位置を，位置1，位置2で指定する。 +この2点をドラッグすることによりビジュアルに描画領域を決められる。 + +しかし，これとは別に出力範囲を設定したい場合にこの関数を用いる。 + +また，表を作成したときは，表の範囲が出力範囲として優先される（Tabledata()を実行したとき）ので，表外に図を描いた場合は，最後にこの関数で出力範囲を指定して書き出す。 + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -例：端点をA,Bとし，スライダの点をCとして，Aの位置を[0,2]，Bの位置を[8,2]としてスライダを作る。 -\begin{verbatim} - Slider("A-C-B",[0,2],[8,2]); -\end{verbatim} - スライダにより取得したい値は，点Cの座標（たとえば C.x）を利用する。 - \\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} \end{description} \newpage -%第５節＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝ +%＝＝＝＝＝＝＝＝＝＝＝ 描画 ＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝ \subsection{描画} +\subsubsection{書式とオプション} + +描画関数は曲線などを作図する関数である。 + +基本的な書式は + +\hspace{20mm} 関数名(name , 点リストなど , options); + +である。 + +nameは，プロットデータの名称で，関数ごとに決められた頭部のあとに付けられる。たとえば，線分を描く Listplot() でできるプロットデータは，頭部が"sg"であり，nameを"1"とすれば，"sg1" という名称のプロットデータができる。name指定は不要の場合もあり，その場合は \ketcindy が自動的に名称を作成する。 + +点リストなどには，点の座標，点の識別名，複数の点のリスト，複数の点を示す文字列などがあり，関数によって異なる。点はCinderellaで作図した幾何要素の点を利用できる。 + +optionsは，線種・表示する文字列・解像度・出力の有無などを指定するオプション群。 + + 線種はつぎの4通り。 初期設定は実線。 -描画関数は曲線などを作図する関数である。\\ - 基本的な書式は\\ - 関数名(name , 点リストなど , options);\\ -であるが，nameの不要なものもある。\\ - nameは，プロットデータの名称を指定するもので，関数ごとに決められた頭部のあとに付けられる。nameが不要の場合は \ketcindy が自動的に名称を作成する。\\ - 点リストなどは，点の座標，点の識別名，複数の点のリスト，複数の点を示す文字列などがあり，関数によって異なる。点はCinderellaで作図した幾何要素の点を利用できる。\\ - \\ - optionsは，線種・表示する文字列・解像度・出力の有無などを指定するオプション群。 \begin{tabbing} -1234567890123\=\kill - 線種はつぎの４通り。デフォルトは実線。\\ - "dr, n" \>太さnの実線で描く。Scilab のファイルに Drwline() を出力する。\\ - "da,m,n" \>破線を描く。Scilab のファイルに Dashline() を出力する。\\ - \> mは破線の長さ，nは破線の間隔 (m,nは省略可)\\ - \>m,n オプションはCinderellaの描画面には反映されない。\\ - "id,m,n" \>ギャップからはじまる破線を描く。Scilab のファイルに Invdashline() を出力する。\\ - "do,m,n" \>点線で描く。Scilab のファイルに Dottedline() を出力する。\\ - \>mは点の間隔，nは太さ (m,nは省略可)\\ - 描画色指定は，RGBまたはCMYKのリストで指定するか，色名を用いる。\\ - 例：\verb|"Color=[0,0.7,0]"| で暗い緑になる。\\ - 出力の有無は\\ - "notex" \>Cinderella画面上で補助線として用いた図形をScilabに出力しない\\ - "nodisp" \>Cinderella画面上にも出力しない\\ - - "nodisp"は画面上にも，Scilabへのデータにも出力されないが，プロットデータは作成され，\\ - それを戻り値とするので，プロットデータだけを利用したい場合に有効である。\\ - 例 \verb|pdata=Circledata([A,B],["nodisp"]);|\\ - として，プロットデータ pdata を処理する。\\ +1234\=5678901234567\=\kill + \> "dr, n" \>太さnの実線で描く。\\ + \> "da,m,n" \>破線を描く。\\ + \> \> mは破線の長さ，nは破線の間隔 (m,nは省略可)\\ + \> \>m,n オプションはCinderellaの描画面には反映されない。\\ + \> "id,m,n" \>ギャップからはじまる破線を描く。\\ + \> "do,m,n" \>点線で描く。\\ + \> \>mは点の間隔，nは太さ (m,nは省略可) \end{tabbing} -\newpage +描画色指定は，RGBまたはCMYKのリストで指定するか，色名を用いる。 + +\hspace{10mm}【例】\verb|"Color=[0,0.7,0]"| で暗い緑になる。 + +出力の有無は +\begin{tabbing} + 1234\=567890123\=\kill + \> "notex" \>Cinderella画面上の図形を出力しない\\ + \> "nodisp" \>Cinderella画面上にも出力しない + \end{tabbing} + + "nodisp"は画面上にも，Ｒへのデータにも出力されないが，プロットデータは作成されるので，プロットデータだけを利用したい場合に有効である。 + +\hspace{10mm}【例】 \verb|pdata=Circledata([A,B],["nodisp"]);| + +として，後にプロットデータ pdata を利用する。 + +その他，次のようなオプションがある。 +\begin{tabbing} + 1234\=567890123\=\kill + \> "Size=n" \>点の大きさ，線の太さの指定\\ + \> "Num=n" \>曲線の場合の分割数（プロットデータの個数+1）\\ +\end{tabbing} + +%＝＝＝＝＝＝＝＝＝＝＝ 点・直線 ＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝ +\subsubsection{点・線分・直線} \begin{description} -\hypertarget{anglemark}{} -\item[関数] Anglemark(点リスト , options) -\item[機能] 点リスト[A,B,C]で示された角に弧の形状の角の印をつける。 -\item[説明] optionsは次の通り。\\ - 数値 角の印の大きさ。デフォルトは１\\ - 線種 "dr, n" , "da,m,n" , "do,m,n"\\ - "Expr=文字" : 文字を入れる\\ - "Expr=位置 , 文字" : 位置を指定して文字を入れる。位置は頂点からの距離。\\ +\vspace{\baselineskip} +\hypertarget{pointdata}{} +\item[関数] Pointdata(name , 点リスト , options) +\item[機能] 点のデータを作成する。 +\item[説明] 与えられた座標の点データを作成する。オプションは"Size=","Color="。 + +\vspace{\baselineskip} +【例】 -例：三角形の内角に印をいれ，文字を書き込む。 +(1) 座標指定で2つの点データを作る。 + +\hspace{10mm} \verb|Pointdata("1",[[1,2],[-2,3]]);| + +(2) 作図した点A,Bについて，点データを作る。 + +\hspace{10mm} \verb|Pointdata("1",[A,B]);| + +\hspace{5mm}A,Bが作図されていない場合は作成されない。 + +\hspace{5mm}Cinderellaの描画面上では既存の点A,Bに黒の点が重なって表示される。 + +(3) Aの位置に大きさ4で点を作る。 + +\hspace{10mm} \verb|Pointdata("1",A,["size=4"]);| + +(4) 点データを作り，TeXにオプション0（白抜き）で描く + +\hspace{10mm} \verb|Pointdata("1",[A,B],[0]);| + +(5) 点データを作るが，TeXには出力しない + +\hspace{10mm} \verb|Pointdata("1",[[3,4],[5,6]],["notex"]);| + +(6) 点データを作るが，TeXには出力せず画面上にも表示しない。 + +\hspace{10mm} \verb|Pointdata("1",[[3,4],[5,6]],["nodisp"]);| + +(7) 節点を明示した木を描く \begin{verbatim} - Listplot([A,B,C,A]); - Letter([A,"n1","A",B,"w1","B",C,"e1","C"]); - Anglemark([B,A,C]); - Anglemark([C,B,A],["Expr=\theta"]); - Anglemark([A,C,B],[2,"dr,3","Expr=2,\alpha"]); + Ptsize(3); + Pointdata("1",[[1,2],[3,4],[5,2]]); + Listplot("1",[[0,0],[1,2],[3,4],[5,2],[4,0]]); + Listplot("2",[[1,2],[2,0]]); + Listplot("3",[[5,2],[6,0]]); \end{verbatim} - \input{Fig/anglemark} + + \begin{center} \input{Fig/pointdata} \end{center} -※角の印には平行四辺形の形状のものもある。Paramark() を参照のこと。\\ +注) 幾何点の有無など，付録の「\hyperlink{mkpttable}{点の作図についての比較表}」を参照のこと。 -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +%\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\hypertarget{arrowdata}{} -\item[関数] Arrowdata(name,[始点 , 終点] , options) -\item[機能] 2点間を結ぶ矢線を描く。プロットデータ名の頭部は ar -\item[説明] name は，座標を数値で与えるときに必要。幾何要素の識別名で与えるときはなくてもよい。\\ - optionsは矢じりの形状などの指定で\\ - [ 矢じりの大きさ, 開き角, 矢じり位置, 線種,線の表示色] - のリストで与える。\\ - 開き角は60分法で与える。ただし，° はつけない。5未満の時は18°の倍数指定とする。\\ - 矢じり位置は，線分の長さを１とした始点からの距離。\\ - ただし，Cinderellaの画面上には全ては反映されない。たとえば，太さ指定をしても太さは同じ。\\ - - 例：線分ABを矢線にする。\\ - \verb|Arrowdata([A,B]);|\\ - 始点が(2,0) , 終点が(4,3) ，開き角45°，EFの中点に矢じりの先端\\ - \verb|Arrowdata("1",[[2,0],[4,3]],[1,45,0.5]);|\\ - 大きさ２，太さ２\\ - \verb|Arrowdata([C,D],[2,1,1,"dr,2"]);|\\ - 破線で太さ0.5\\ - \verb|Arrowdata([E,F],["da,0.5"]);|\\ - 少し間が空いて太い点線で，Cinderellaの画面上では赤で表示する。\\ - \verb|Arrowdata([G,H],[2,1,"do,2,3","color-$>$[1,0,0]"]);| \\ - - \input{Fig/arrowdata}\\ -\\ +\vspace{\baselineskip} +\hypertarget{drwpt}{} +\item[関数] Drwpt(点,option）, Drawpoint(点,options) +\item[機能] 点を表示する +\item[説明] 座標または幾何点の識別名を与えて点を表示する。これだけではCinderellaの描画面には描かれないので，描画面にも表示するにはCinderellaの作図ツールで作図するか，Pointdata() または Putpoint() を用いる。 -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +複数の点の場合は座標または識別名はリストで与える。 + +optionに数字 0 を入れると，白抜きで表示する。なお白抜きの場合は，Ptsize()で点の大きさを少し大きめにとるとよい。 + +可読性を高めるときはDrawpointを推奨する。 + +\vspace{\baselineskip} +【例】座標(1,1)と(4,3)に点を表示する。Cinderellaの描画面には描かれない。 + +\hspace{10mm} \verb|Drwpt([[1,1],[4,3]]);| + +\vspace{\baselineskip} +【例】Cinderellaで点A,B,Cを作図しておき，\TeX で表示する。 + +\hspace{10mm} \verb|Drwpt([A,B,C]); | + +\vspace{\baselineskip} +【例】線分ABの右端（B）を白抜きで表示する -\hypertarget{arrowhead}{} -\item[関数] Arrowhead(点 , 方向 , options) , Arrowhead(点 , プロットデータ,options) -\item[機能] 点に矢じりだけを描く -\item[説明] 指定された位置に，指定された方向を向いた矢じりだけを描く。\\ - 点は座標または幾何要素名。方向は原点から見て座標[a,b]の方向。\\ - optionsは [大きさ，矢じりの開き角，形状と位置] のリスト。\\ - 矢じりの開き角は60分法で片側半分の角。\\ - 形状は， "f" ：塗りつぶしの三角形（デフォルト）または " l " ： ラインのみ。\\ - 位置は，"t"（デフォルト）または "c" , "b"\\ - "t" は矢じりの先端が終点に一致，"c" は三角形の中心が終点と一致，"b" は終点が矢じりの底辺にのる。\\ - プロットデータを指定したときは，曲線上の点に矢じりをつける。\\ - 曲線には向きがあり，それによって矢じりの向きが決まる。" Invert(プロットデータ) " とすると反対向きの矢じりになる。\\ - 曲線の向きとは，曲線を描くときの順序で，プロットデータの順序でもある。invert() はこのプロットデータを逆順にするものである。\\ - -例： - -\vspace{-8mm} -\hspace{6mm} \begin{layer}{150}{0} -\putnotese{0}{0}{点 A が下図の位置のとき} -\putnotese{0}{8}{\input{Fig/ForRef-Arrowhead-1}} -\putnotese{40}{0}{(ア) Arrowhead(A,[-1,1]);} -\putnotese{40}{7}{(イ) Arrowhead([1,1],[-1,1],[2,60]);} -\putnotese{40}{14}{(ウ) Arrowhead(A,[-1,1],[2,30,"b"]);} -\putnotese{40}{21}{(エ) Arrowhead([1,1],[-1,1],[2,20,"lc"]);} +\putnotese{50}{8}{ \input{Fig/drawpoint}} \end{layer} +\begin{verbatim} + Ptsize(5); + Listplot([A,B]); + Drawpoint(B,0); +\end{verbatim} + +※ Drawpoint([A,B],0); とすれば，両端が白抜きになる。 + +\vspace{\baselineskip} +{\bf 点の表示方法} + +点を表示する関数はいくつかある。Cinderellaの描画面上に単に点を表示するもの，幾何点を作るもの，TeXに出力するためのもの，と少しずつ意味が異なる。 + +付録の「\hyperlink{mkpttable}{点の作図についての比較表}」を参照のこと。 + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\vspace{\baselineskip} +\hypertarget{putpoint}{} +\item[関数] Putpoint(点名 , 座標１ ,座標2 ) +\item[機能] 点を作る +\item[説明] 識別名が点名の点を，既存でなければ座標１に作る。既存ならば座標2に移動する。Texには出力されない。 + +\vspace{\baselineskip} +【例】点Aを作る。 + +(1,1) に固定点Aを作る。 この点は動かすことができない。 + +\hspace{10mm} \verb|Putpoint("A",[1,1]);| + + (1,1)に自由点を作るには次のようにする。 + +\hspace{10mm} \verb|Putpoint("A",[1,1],[A.x,A.y]);| + + この点は座標2の効果により，自由点となり，ドラッグして動かすことができる。 + +\vspace{\baselineskip} +注）点名は半角アルファベットとする。数字や漢字でもCinderellaでは点ができるが，Rでエラーとなる。 + +\vspace{\baselineskip} +\hypertarget{putintersect}{} +\item[関数] Putintersect(点名 , PD1 , PD2 , [No] ) +\item[機能] 2曲線の交点を作る +\item[説明] PD1,PD2は2曲線のプロットデータ名。作成される点は幾何点。 + +描画範囲に交点が１つだけのとき，第4引数がなくても交点が作られる。 + +描画範囲に2つ以上の交点がある場合，第4引数を省略するとコンソールに交点の座標のリストと，「Choose point number 」というガイドが表示される。そこで，引数のNoとして，その番号を指定すると，その点が作られる。この関数で作成されるのは幾何点だけなので，\TeX の図に点として明示するためにはPointdata()で書き出す。 + +次の例は，3次曲線と直線の交点を3つとも取ったものである。 -\vspace{2mm} -\hspace{6mm} \begin{layer}{150}{0} -\putnotese{0}{0}{\input{Fig/ForRef-Arrowhead-ya1}} -\putnotese{95}{55}{D の座標がわかれ} -\putnotese{95}{60}{ば，それでもよい} -\putnotese{12}{27}{(ア)} -\putnotese{42}{27}{(イ)} -\putnotese{72}{27}{(ウ)} -\putnotese{102}{27}{(エ)} -\putnotese{0}{30}{\input{Fig/ForRef-Arrowhead-2}} -\putnotese{30}{30}{\input{Fig/ForRef-Arrowhead-3}} -\putnotese{60}{30}{\input{Fig/ForRef-Arrowhead-4}} -\putnotese{90}{30}{\input{Fig/ForRef-Arrowhead-5}} +\putnotese{80}{5}{ \input{Fig/putintersect}} \end{layer} -\vspace{56mm} -\hspace{6mm} +\begin{verbatim} + Plotdata("1","x^3-4*x","x",["Num=200"]); + Plotdata("2","1/2*x+1","x"); + Putintersect("P","gr1","gr2",1); + Putintersect("Q","gr1","gr2",2); + Putintersect("R","gr1","gr2",3); + Pointdata("1",[P,Q,R],["size=4"]); +\end{verbatim} + 交点が存在しない場合は，「No intersect point」がコンソールに表示される。 + +\vspace{\baselineskip} +\hypertarget{putoncurve}{} +\item[関数] PutonCurve(点の名前, プロットデータ, options) +\item[機能] 曲線上に点を乗せる。 +\item[説明] 点が存在しない場合は新たに作る。すでにその点が存在する場合は，その点の$x$座標を使う。初期値の$x$座標の 初期設定は 0。 + +optionsは，$x$座標の範囲をリストで与える。 + +\vspace{\baselineskip} +【例】アステロイド上の動点P をとる。 +\begin{verbatim} + Paramplot("1","[2*cos(t)^3,2*sin(t)^3]","t=[0,2*pi]"); + PutonCurve("P","gp1",[-1,1]); +\end{verbatim} +点Pがアステロイド上にでき，この点はドラッグするとアステロイド上を $-1 \leq x\leq 1$ の範囲で動かすことができる。ただし，-1,1の付近はy座標の判断の関係でぴったりはいかない。 + + \begin{center} \input{Fig/putoncurve.tex} \end{center} + +%\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\vspace{\baselineskip} +\hypertarget{putonline}{} +\item[関数] PutonLine(点名 , 座標１ ,座標2 ) +\item[機能] 直線上に点を作る +\item[説明] 座標１，座標2を通る直線上に点名の点を作る。できた点は直線に対してインシデントとなる。 + +\vspace{\baselineskip} +【例】 点A,\ Bを通る直線上に点Pをとる。 + + \verb|PutonLine("P",A,B);| + +\vspace{\baselineskip} +\hypertarget{putonseg}{} +\item[関数] PutonSeg(点名 , 座標１ ,座標2 ) +\item[機能] 線分上に点を作る +\item[説明] 座標１，座標2を通る線分上に点名の点を作る。できた点は線分に対してインシデントとなる。 + +\vspace{\baselineskip} +【例】 点A,\ Bを通る線分上に点Pをとる。 + + \verb|PutonSeg("P",A,B);| + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\vspace{\baselineskip} +\hypertarget{reflectpoint}{} +\item[関数] Reflectpoint(点，対称点または対称軸) +\item[機能] 点の鏡映の座標を返す。 +\item[説明] 点を指定された点または軸に関して対称移動した点の座標を返す。対称軸は[ 点1, 点2 ]で指定 + +\vspace{\baselineskip} +【例】点A〜Fを作図しておき，C〜FをAの鏡映の位置に配置する。 + \begin{layer}{150}{0} -\putnotese{0}{0}{曲線 crBC 上の点 D が} -\putnotese{0}{5}{下図のようなとき} -\putnotese{0}{7}{\input{Fig/ForRef-Arrowhead-6}} -\putnotese{16}{22}{crBC} -\putnotese{40}{0}{(オ) Arrowhead(D,"crBC");} -\putnotese{40}{7}{(カ) Arrowhead(D,"crBC",[2]);} -\putnotese{40}{14}{(キ) Arrowhead(D,"crBC",[2,30,"l"]);} -\putnotese{40}{21}{(ク) Arrowhead(D,"Invert(crBC)");} +\putnotese{70}{10}{ \input{Fig/reflectpoint}} \end{layer} -\vspace{3mm} -\hspace{6mm} +\hspace{5mm} ＣはBに関してAと対称な点 + +\hspace{5mm} Ｄは点(2,3)に関してAと対称な点 + +\hspace{5mm} Eは点(1,0) に関して (-1,1) と対称な点 + +\hspace{5mm} Fは直線CEに関してAと対称な点 + +\begin{verbatim} + C.xy=Reflectpoint(A,B); + D.xy=Reflectpoint(A,[[2,3]]); + E.xy=Reflectpoint([-1,1],[[1,0]]); + F.xy=Reflectpoint(A,[C,E]); + Lineplot([C,E],["do"]); +\end{verbatim} + +\vspace{\baselineskip} +注）鏡映はCinderellaの作図ツールでも作成することができる。場合によってはCinderellaで作図する方が簡明である。 + +%\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\vspace{\baselineskip} +\hypertarget{rotatepoint}{} +\item[関数] Rotatepoint(点 ，角度 , 中心) +\item[機能] 点の位置を回転する +\item[説明] 点を，中心で示された点の周りに回転した座標を返す。角度は弧度法で与える + +\vspace{\baselineskip} +【例】点A〜Eは作図しておき，C〜Eをそれぞれの位置に配置する。 + \begin{layer}{150}{0} -\putnotese{12}{27}{(オ)} -\putnotese{42}{27}{(カ)} -\putnotese{72}{27}{(キ)} -\putnotese{102}{27}{(ク)} -\putnotese{0}{28}{\input{Fig/ForRef-Arrowhead-7}} -\putnotese{30}{28}{\input{Fig/ForRef-Arrowhead-8}} -\putnotese{60}{28}{\input{Fig/ForRef-Arrowhead-9}} -\putnotese{90}{28}{\input{Fig/ForRef-Arrowhead-10}} +\putnotese{75}{10}{ \input{Fig/rotatepoint}} \end{layer} +\begin{spacing}{1.5} +点CはAを，Ｂに関して$\dfrac{2}{3}\pi $だけ回転した点 + +点Dは点(5,2)を，Ｂに関して$\dfrac{\pi}{3}$ だけ回転した点 +\end{spacing} +点Eは点(3,0)をAに関して $-\dfrac{\pi}{4} $だけ回転した点 -\vspace{70mm} -\hypertarget{bezier}{} -\item[関数] Bezier(名前，節点リスト，制御点リスト，[オプション] ) -\item[機能] 単独のベジエ曲線を描く -\item[説明] 制御点は，各区間に対して，３次の場合２個，２次の場合１個のリストで与える。 +\begin{verbatim} + C.xy=Rotatepoint(A,2*pi/3,B); + D.xy=Rotatepoint((5,2),pi/3,B); + E.xy=Rotatepoint([3,0],-pi/4,A); +\end{verbatim} +注）図の点線は位置関係を示すためのもの。 - [ [F,G] , [H], ... ] +点名や座標は，実際にはLetter()関数で記述する。 -オプション +\vspace{\baselineskip} +\hypertarget{scalepoint}{} +\item[関数] Scalepoint(点，比率ベクトル，中心) +\item[機能] 点の位置の拡大・縮小を行う +\item[説明] 点を，指定された中心を原点とする座標系で，比率ベクトルの分だけ拡大・縮小した位置の座標を返す。 -"Num=..." : 節点間の分割数（分点数 $-1$）を指定できる。（デフォルトは10） +\vspace{\baselineskip} +【例】点A〜Fは作図ツールで適当な位置にとっておく。 -\vspace{5mm} +点Dを，点Aを原点を中心に横に3倍，縦に2倍した位置に置く。 + +点Eを，点Aを点Bを中心に横に3倍，縦に2倍した位置に置く。 + +点Fを，点Aを原点を中心にベクトル$\overrightarrow{OC} $で示された比率の位置に置く。 +\begin{verbatim} + D.xy=Scalepoint(A,[3,2],[0,0]); + E.xy=Scalepoint(A,[3,2],B); + F.xy=Scalepoint(A,C.xy,[0,0]); + Arrowdata("1",[[0,0],C]); + Pointdata("1",[A,B,C,D,E,F],["size=2"]); + Letter([A,"e2","A("+A.x+","+A.y+")"]); + Letter([B,"e2","B("+B.x+","+B.y+")"]); + Letter([C,"e2","C("+C.x+","+C.y+")"]); + Letter([D,"e2","D("+D.x+","+D.y+")"]); + Letter([E,"e2","E("+E.x+","+E.y+")"]); + Letter([F,"e2","F("+F.x+","+F.y+")"]); +\end{verbatim} +\vspace{\baselineskip} +\begin{center} \input{Fig/scalepoint} \end{center} + +点A,B,Cをドラッグすると，インタラクティブにD,E,F の位置が変わる。 + +\vspace{\baselineskip} +\hypertarget{translatepoint}{} +\item[関数] Translatepoint(点 , 移動ベクトル) +\item[機能] 点を平行移動する +\item[説明] 点を移動ベクトルで示された分だけ平行移動した点の座標を返す + +\vspace{\baselineskip} +【例】点A〜Dは作図しておく。 + +点Cを点Aを$x$軸方向に2 , $y$軸方向に3 + +だけ平行移動した点にする。 + +点Dを点Aをベクトル$\overrightarrow{OB} $だけ + +平行移動した点にする。 +\begin{verbatim} + C.xy=Translatepoint(A,[2,3]); + D.xy=Translatepoint(A,B.xy); +\end{verbatim} + +\hspace{20mm} \input{Fig/translatepoint} + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\hypertarget{arrowdata}{} +\item[関数] Arrowdata(name,[始点 , 終点] , options) +\item[機能] 2点間を結ぶ矢線を描く。 +\item[説明] name は，座標を数値で与えるときに必要。幾何要素の識別名で与えるときはなくてもよい。 + +optionsは矢じりの形状などの指定で + +\hspace{10mm} [ 矢じりの大きさ, 開き角, 矢じり位置, 線種,線の表示色] -例： +のリストで与える。 + +開き角は60分法で与える。ただし，° はつけない。5未満の時は18°の倍数指定とする。 + + 矢じり位置は，線分の長さを１とした始点からの距離。 + +ただし，Cinderellaの画面上には全ては反映されない。たとえば，太さ指定をしても画面上では太さは同じ。 + + トリミング : "Cutend=m" または "Cutend=[m,n]" +右辺が数のときは両端をmだけカットする。リストのときは始点をm,終点をnだけカットする。 + +\vspace{\baselineskip} +【例】線分ABを矢線にする。 + +\hspace{10mm} \verb|Arrowdata([A,B]);| + +始点が(2,0) , 終点が(4,3) ，開き角45°，EFの中点に矢じりの先端 + +\hspace{10mm} \verb|Arrowdata("1",[[2,0],[4,3]],[1,45,0.5]);| + +大きさ2，太さ2 + +\hspace{10mm} \verb|Arrowdata([C,D],[2,1,1,"dr,2"]);| + +破線で太さ0.5 + +\hspace{10mm} \verb|Arrowdata([E,F],["da,0.5"]);| + + 少し間が空いて太い点線で，Cinderellaの画面上では赤で表示する。 + +\hspace{10mm} \verb|Arrowdata([G,H],[2,1,"do,2,3","Color=[1,0,0]"]);| + +\hspace{20mm} \input{Fig/arrowdata} + +【例】２つの円を矢線で結ぶ。 + \begin{layer}{150}{0} -\putnotese{50}{15}{bz1} -\putnotese{60}{-15}{\input{Fig/checkbe1}} +\putnotese{75}{0}{ \input{Fig/trimarrow}} \end{layer} +\hspace{20mm} + +\begin{verbatim} + Circledata("1",[A,A.xy+[0.5,0]]); + Circledata("2",[B,B.xy+[0.7,0]]); + Arrowdata([A,B],["Cutend=[0.5,0.7]"]); + Letter([A,"c","A",B,"c","B"]); +\end{verbatim} + Cinderellaの作図ツールで２点ABをとっておく。 -２次ベジエ曲線 +円A,Bの半径が同じ（たとえば0.5）であれば，\verb|Arrowdata([A,B],["Cutend=0.5"]);| でよい。 -Bezier("1",[A,B],[C]); +%\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\vspace{\baselineskip} +\hypertarget{arrowhead}{} +\item[関数] Arrowhead(点 , 方向 , options) , Arrowhead(点 , プロットデータ,options) +\item[機能] 点に矢じりだけを描く +\item[説明] 指定された位置に，指定された方向を向いた矢じりだけを描く。 -\vspace{20mm} +点は座標または幾何要素名。方向は原点から見て座標[a,b]の方向。 + +optionsは [大きさ，矢じりの開き角，形状と位置] のリスト。 + +矢じりの開き角は60分法で片側半分の角。 + +形状は， "f" ：塗りつぶしの三角形（ 初期設定）または " l " ： ラインのみ。 + +ただし，塗りつぶし矢じりは画面上では塗りつぶしにならない。 +位置は，"t"（ 初期設定）または "c" , "b" +\begin{tabbing} +1234\=567890123\=\kill + \>"t" は矢じりの先端が終点に一致\\ + \>"c" は三角形の中心が終点と一致\\ + \>"b" は終点が矢じりの底辺にのる。 +\end{tabbing} +プロットデータを指定したときは，曲線上の点に矢じりをつける。 + +曲線には向きがあり，それによって矢じりの向きが決まる。" Invert(PD) " とすると反対向きの矢じりになる。 + +曲線の向きとは，曲線を描くときの順序で，プロットデータの順序でもある。invert() はこのプロットデータを逆順にするものである。 + +\vspace{\baselineskip} + +【例】 + +\vspace{\baselineskip} +%\hspace{6mm} +\begin{layer}{150}{0} +\putnotese{0}{0}{点 A が右図の位置のとき} +\putnotese{80}{8}{\input{Fig/ForRef-Arrowhead-1}} +\putnotese{0}{7}{(ア) Arrowhead(A,[-1,1]);} +\putnotese{0}{14}{(イ) Arrowhead([1,1],[-1,1],[2,60]);} +\putnotese{0}{21}{(ウ) Arrowhead(A,[-1,1],[2,30,"b"]);} +\putnotese{0}{28}{(エ) Arrowhead([1,1],[-1,1],[2,20,"lc"]);} +\putnotese{0}{38}{(ア)} +\putnotese{30}{38}{(イ)} +\putnotese{60}{38}{(ウ)} +\putnotese{90}{38}{(エ)} +\putnotese{0}{45}{ \input{Fig/ForRef-Arrowhead-2}} +\putnotese{30}{45}{ \input{Fig/ForRef-Arrowhead-3}} +\putnotese{60}{45}{ \input{Fig/ForRef-Arrowhead-4}} +\putnotese{90}{45}{ \input{Fig/ForRef-Arrowhead-5}} +\end{layer} + +\vspace{75mm} +%\hspace{6mm} \begin{layer}{150}{0} -\putnotese{50}{20}{bzc} -\putnotese{60}{-10}{\input{Fig/checkbe2}} +\putnotese{0}{0}{曲線 crBC 上の点 D が右図のようなとき} +\putnotese{80}{8}{ \input{Fig/ForRef-Arrowhead-6}} +\putnotese{96}{22}{crBC} +\putnotese{0}{7}{(オ) Arrowhead(D,"crBC");} +\putnotese{0}{14}{(カ) Arrowhead(D,"crBC",[2]);} +\putnotese{0}{21}{(キ) Arrowhead(D,"crBC",[2,30,"l"]);} +\putnotese{0}{28}{(ク) Arrowhead(D,"Invert(crBC)");} +\putnotese{0}{38}{(オ)} +\putnotese{30}{38}{(カ)} +\putnotese{60}{38}{(キ)} +\putnotese{90}{38}{(ク)} +\putnotese{0}{45}{ \input{Fig/ForRef-Arrowhead-7}} +\putnotese{30}{45}{ \input{Fig/ForRef-Arrowhead-8}} +\putnotese{60}{45}{ \input{Fig/ForRef-Arrowhead-9}} +\putnotese{90}{45}{ \input{Fig/ForRef-Arrowhead-10}} \end{layer} -３次ベジエ曲線 +\vspace{70mm} -Bezier("c",[A,B],[C,D]); +\vspace{\baselineskip} +\hypertarget{lineplot}{} +\item[関数] Lineplot（name , 2点のリスト , options) +\item[機能] 2点のリストで示された点を結ぶ直線を描く。 +\item[説明] 2点のリストは座標または幾何要素の名前で与える。 -\vspace{20mm} +options は次の通り。 + +線種 "dr, n" , "da,m,n" , "do,m,n" + + "+" 半直線を描く。 + +"dr" , "da" , "do" と "+" はリストにして両方指定することができる。 + +点のリストが，座標ではなく幾何要素名のリストの場合は，nameは省略できる。 + +いくつか例を示す。 + +\vspace{\baselineskip} +各座標を結ぶ直線を引く + +\hspace{5mm} \verb|Lineplot("1",[[0,0],[1,2]])| + +Cinderellaの描画ツールで2点A,Bをとっておき，直線ABを引く + +\hspace{5mm} \verb|Lineplot([A,B]);| + +optionの働きの例 +\begin{tabbing} +1234\=56789012345678901234567890123456789\=\kill + \> \verb|Lineplot([A,B],["dr,0.5","+"]);| \>Aを端点とする半直線を引く\\ + \> \verb|Lineplot([C,D],["dr,2"]);| \>直線CDを太さ2で描く\\ + \> \verb|Lineplot([E,F],["da"]);| \>直線EFを破線で描く\\ + \> \verb|Lineplot([G,H],["do"]);| \>直線GHを点線で描く +\end{tabbing} +結果は，次図左上から。 + +\vspace{\baselineskip} +\hspace{20mm} \input{Fig/lineplot} + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\vspace{\baselineskip} +\hypertarget{listplot}{} +\item[関数] Listplot（name , 点のリスト , options) +\item[機能] 点のリストで示された点を結ぶ。 +\item[説明] 点のリストは座標または幾何要素名のリストで与える。点が，座標ではなく幾何要素名の場合は，nameは省略可 + +プロットデータの名前は，"sg" に引数の name を付加したものとなる。 + + options は次の通り。 + +線種 "dr, n" , "da,m,n" , "do,m,n" + +トリミング : "Cutend=m" または "Cutend=[m,n]" + +数のときは両端をmだけカットする。リストのときは始点をm,終点をnだけカットする。 + +\begin{tabbing} +1234567890123456789012345678901234\=\kill + optionsの使用例\\ + \verb|Listplot([A,B]);| \>線分ABを描く。太さは 初期設定。\\ + \verb|Listplot([C,D],["dr,2"]);| \>線分CDを描く。太さ2\\ + \verb|Listplot([E,F],["da"]);| \>線分EFを破線で描く\\ + \verb|Listplot([G,H],["da,3,1"]);| \>線分GHを破線で描く。線を長く\\ + \verb|Listplot([K,L],["da,1,3"]);| \>線分KLを破線で描く。間隔を空ける\\ + \verb|Listplot([M,N],["do"]);| \>線分MNを点線で描く。\\ + \verb|Listplot([O,P],["do,3"]);| \>線分OPを点線で描く。間隔を空ける\\ + \verb|Listplot([Q,R],["do,3,3"]);| \>線分QRを点線で描く。間隔を空けて太く\\ +結果は次図左から。 +\end{tabbing} + \begin{center} \input{Fig/listplot3}\end{center} + +【例】三角形を描く。 + + Cinderellaの作図ツールで三角形ABCを描いておく。あるいは，単に3点A,B,Cをとるだけでもよい。 \begin{layer}{150}{0} -\putnotese{50}{20}{bz3} -\putnotese{60}{-10}{\input{Fig/checkbe3}} +\putnotese{75}{0}{ \input{Fig/listplot1}} \end{layer} +\hspace{20mm} -つなげる +\begin{verbatim} + Addax(0); + Listplot([A,B,C,A]); +\end{verbatim} -Bezier("3",[A,B,C],[[D],[E,F]]); +点の位置は座標で指定してもよい。 -\vspace{20mm} +その場合は name が必要。 +\hspace{10mm} \verb|Listplot("1",[[0,0],[2,0],[1,2],[0,0]]);| + +\vspace{\baselineskip} +【例】２つの円を線分で結ぶ。 + \begin{layer}{150}{0} -\putnotese{50}{20}{bzS} -\putnotese{60}{5}{\input{Fig/checkbe4}} +\putnotese{75}{0}{ \input{Fig/trimseg}} \end{layer} +\hspace{20mm} + +\begin{verbatim} + Circledata("1",[A,A.xy+[0.5,0]]); + Circledata("2",[B,B.xy+[0.7,0]]); + Listplot([A,B],["Cutend=[0.5,0.7]"]); + Letter([A,"c","A",B,"c","B"]); +\end{verbatim} + Cinderellaの作図ツールで２点ABをとっておく。 -D,B,E を１直線上にとると，滑らかにつながる +円A,Bの半径が同じであれば，\verb|Listplot([A,B],["Cutend=0.5"]);| でよい。 -Bezier("S",[A,B,C],[[D],[E,F]]); +\vspace{\baselineskip} +プロットデータは点の座標のリストである。したがって，プロットデータを自作してListplot()で表示することができる。 -\vspace{25mm} +\vspace{\baselineskip} +【例】有限フーリエ級数展開 + \[\cfrac{\pi}{2}+\sum_{n=0}^{30} \cfrac{1-(-1)^n}{n}\sin nx\] + +次のようにCindyscriptで関数を定義し，プロットデータpd を作って引数に渡す。 +\begin{verbatim} + f(x):=( + s=pi/2; + repeat(30,n,s=s+(1-(-1)|^n)/n*sin(n*x)); + ); + pd=apply(0..200,t, + x=-2*pi+t*4*pi/200; + [x,f(x)]; + ); + Listplot("1",pd); + Expr([[-2*pi,-0.5],"s","-2\pi",[-pi,-0.5],"s","-\pi",[pi,-0.5],"s", + "\pi",[2*pi,-0.5],"s","2\pi",[0,pi],"w2","\pi"]); +\end{verbatim} + +\vspace{\baselineskip} +\hspace{20mm}\input{Fig/fourier} + +\vspace{\baselineskip} + リストの長さには制限がある。たとえば，タートルグラフィクスを用いたシェルピンスキーのギャスケットでは200くらいずつのリストに分割する。 + + \hspace{20mm}\scalebox{0.9}{ \input{Fig/listplot2}} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\vspace{\baselineskip} +\hypertarget{mksegments}{} +\item[関数] Mksegments() +\item[機能] すべての幾何線分のPD を作成 +\item[説明] Cinderellaの「線分を加える」ツールで描いたすべての線分をそのままプロットデータとする。たとえば，線分ABを作ると，プロットデータsgABが作成される。その後，インスペクタで点Bの識別名を変更（たとえばQに）すると，プロットデータ名も変更される。線分はすでに描かれていてもよい。 + +\vspace{\baselineskip} +【例】等比数列の例題 + +三角形の各辺の中点を結んでできる三角形を次々に作っていく，等比数列の図を描く。 + +まず「線分を加える」ツールで三角形ABCを描く。 + +「中点を加える」ツールで各辺の中点を取り，「線分を加える」ツールで中点を結ぶ。 + +これを繰り返す。\verb|Mksegments()| を書いておけば，\verb|Listplot([A,B,C]| などを書かなくても，作図ができた時点で，図のデータができる。 + +\includegraphics[bb=0.00 0.00 438.02 327.02,width=5cm]{Fig/gpro01.pdf} \input{Fig/gpro02} + +\vspace{\baselineskip} +\hypertarget{framedata}{} +\item[関数] Framedata(name , リスト,options) +\item[機能] 矩形を描く +\item[説明] リストの形は2通り。 + +その1：[中心 ,横 , 縦] で，矩形を描く。横，縦は中心からの距離。 + +その2：2点のリスト。点が座標でなく名称のときはnameは省略できる。 + +点の座標は点の名前でもよい。点を座標で与える場合はnameは省略できない。 + +リストを省略した場合は，描画範囲と同一の矩形を描く。 + +その2のタイプでは，option として，"center" または "corner" がある。"center" のときは，中心と対角点（ 初期設定），"corner" のときは2点を対角点として解釈する。 + +以下にいくつか例を示す +\begin{tabbing} +1234567890123456789012345678901234\=\kill + \verb|Framedata("1");| \> 描画範囲(SW,NE)と同一の矩形を描く\\ + \verb|Framedata("2",[[0,0],2,2]);| \> 原点を中心とする縦横幅4の正方形を描く\\ + \verb|Framedata("3",[A,1.5,1.2]);| \> 点Aを中心とする横3，縦2.4の矩形を描く。(図左)\\ + \verb|Framedata([B,C]);| \> 点Bを中心,点Cを頂点とする矩形を描く。(図中央)\\ + \verb|Framedata([D,E],["corner"]); | \> 点D,Eを対角点とする矩形を描く。(図右) + \end{tabbing} +\begin{center}\includegraphics[bb=0.00 0.00 348.15 106.16,width=12cm]{Fig/Framedata.pdf}\end{center} + +矩形の角を丸めたい場合は，Framedata()ではなく，\hyperlink{ovaldata}{Ovaldata()}を使うとよい。 + +\vspace{\baselineskip} +\hypertarget{polygonplot}{} +\item[関数] Polygonplot(name , 点リスト , 整数,options) +\item[機能] 2点を半径とする円に内接する正多角形を描く。 +\item[説明] 点リストを[A,B] とすると，Aを中心とする半径ABの円周上に点をとって正多角形を描く。ただし円は描かない。A,B は座標でもよい。 + +点リストが座標ではなく作図してある点の名称のとき，オプションに "Geo=y" をつけると，頂点の幾何点を作る。幾何点の名称はBに番号を付けたものとなる。整数でない数を指定した場合は，きちんと閉じない折れ線が描かれる。 + +\vspace{\baselineskip} +【例】点リストとoptionの違いによる作図と，TeXの図を示す。 + +\begin{verbatim} + Addax(0); + Polygonplot("1",[[-4,1],[-4,3]],7); + Polygonplot("2",[A,B],7); + Polygonplot("3",[C,D],7,["Geo=y"]); +\end{verbatim} + +\hspace{10mm}\includegraphics[bb=0.00 0.00 541.03 175.01,width=10cm]{Fig/polygonplot2.pdf} + +\hspace{10mm}\input{Fig/polygonplot1} + + +円に内接する形でなく，与えられた線分ABを１辺とする正多角形を描くには次のようにする。 + +線分ABは，Cinderellaの作図ツールなどで描かれているものとする。ただし，線分でなく，両端の点が与えられているだけでもよい。Cindyscriptで点A,Bが複素平面上にあるものとして，多角形の頂点の位置を計算する。 + +\vspace{\baselineskip} +【例】ABを1辺とする正五角形を描く。 + +\begin{verbatim} + n=5; + pti=[complex(A),complex(B)]; + th=2*pi/n; + repeat(n-2,s, + z1=pti_s; + z2=pti_(s+1); + z=z2+(z2-z1)*(cos(th)+i*sin(th)); + pti=append(pti,z); + ); + pt=apply(pti,gauss(#)); + pt=append(pt,A.xy); + Listplot("1",pt); +\end{verbatim} +ptiは，各頂点に対応する複素数のリスト，ptが各頂点の座標のリストである。 + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\end{description} +\newpage +% ====== 曲線 ============== +\subsubsection{曲線} +\begin{description} + +\hypertarget{bezier}{} +\item[関数] Bezier(名前，節点リスト，制御点リスト，[オプション] ) +\item[機能] ベジェ曲線を描く +\item[説明] 制御点は，各区間に対して，3次の場合2個，2次の場合1個のリストで与える。 + +オプションは + +"Num=n" : 節点間の分割数（分点数 $-1$）を指定できる。 ベジェ曲線とスプライト曲線の関数は節点間が短い場合が多いので初期設定は10になっている。Plotdata()などと違い，大きい数（200など）を指定すると，全体の分割数が増大して描画時間がかかるようになってしまうので注意。 + +\vspace{\baselineskip} +【例】 \begin{layer}{150}{0} -\putnotese{16}{27}{bzname} -\putnotese{15}{10}{\input{Fig/checkbe7}} +\putnotese{60}{-10}{\scalebox{0.9}{ \input{Fig/checkbe1}}} \end{layer} -全て同じ次数の場合，次のようにしてもよい． +2次ベジェ曲線 -Bezier("name", [A,B,C,D], [E,F,G,H,K,L] ); +Bezier("1",[A,B],[C]); -\vspace{30mm} +\vspace{20mm} \begin{layer}{150}{0} -\putnotese{50}{20}{bz1a} -\putnotese{60}{5}{\input{Fig/checkbe5}} +\putnotese{60}{-10}{\scalebox{0.9}{\input{Fig/checkbe2}}} \end{layer} -オプション +3次ベジェ曲線 -Bezier("1a",[A,B,C],[[D],[E,F]],["Num=3"]); +Bezier("2",[A,B],[C,D]); -\vspace{30mm} +\vspace{20mm} \begin{layer}{150}{0} -\putnotese{50}{20}{bzd5e} -\putnotese{60}{5}{\input{Fig/checkbe6}} +\putnotese{60}{-10}{\scalebox{0.9}{ \input{Fig/checkbe3}}} \end{layer} -Bezier("d5e",[A,B,C],[[D],[E,F]],["Num=200","da"]); +%ベジェ曲線をつなげる -\vspace{35mm} +%Bezier("3",[A,B,C],[[D],[E,F]]); + +%\vspace{20mm} +%\begin{layer}{150}{0} +%\putnotese{60}{5}{ \input{Fig/checkbe4}} +%\end{layer} + +%D,B,E を１直線上にとると，滑らかにつながる +節点を増やす。2次と3次。 + +Bezier("3",[A,B,C],[[D],[E,F]]); + +\vspace{20mm} + +全て同じ次数の場合，次のようにしてもよい． + +Bezier("4", [A,B,C,D], [E,F,G,H,K,L] ); \begin{layer}{150}{0} -\putnotese{20}{32}{bz1} -\putnotese{15}{15}{\input{Fig/checkbe8}} +\putnotese{20}{2}{\input{Fig/checkbe7}} \end{layer} +\vspace{35mm} + +オプションの例 + +Bezier("5",[A,B,C],[[D],[E,F]],["Num=3"]); + +\hspace{20mm}\input{Fig/checkbe5} + +Bezier("6",[A,B,C],[[D],[E,F]],["Num=40","da"]); + +\hspace{20mm}\input{Fig/checkbe6} + Numを（ベクトルとして）区間ごとに与えることもできる。 Bezier("1", [A,B,C,D], [E,F,G,H,K,L] , [ "Num=[2,3,4]"]); -\vspace{30mm} - -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\hspace{10mm} \input{Fig/checkbe8} +%\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\vspace{\baselineskip} \hypertarget{beziersmooth}{} -\item[関数] Beziersmooth(名前，節点リスト，[オプション] ) -\item[機能] 節点間を３次ベジエ曲線でスムーズに結んだ曲線を描く -\item[説明] 節点をはさむ制御点は１直線上にとる（したがって，１つは半自由点で，直線上しか動けない）。 +\item[関数] Beziersmooth(名前，節点リスト，[オプション] ) +\item[機能] 節点間を3次ベジェ曲線でスムーズに結んだ曲線を描く +\item[説明] 節点をはさむ制御点は１直線上にとる（したがって，１つは半自由点で，直線上しか動けない）。 制御点は自動的に配置される。その後，節点や制御点を動かして，描きたいものにする。 -例： +\vspace{\baselineskip} +【例】 \begin{layer}{150}{0} \putnotese{70}{25}{bz1} -\putnotese{40}{-5}{\input{Fig/checksm1}} +\putnotese{40}{-5}{ \input{Fig/checksm1}} \end{layer} Beziersmooth("1",[A,B,C,D]); \vspace{20mm} +その後，節点や制御点を動かして，描きたいものにする。ただし，C2p は C1q と B を通る直線上しか動けない。C3p は C2q と C を通る直線上しか動けない。 \begin{layer}{150}{0} \putnotese{70}{35}{bz1} -\putnotese{40}{10}{\input{Fig/checksm2}} +\putnotese{40}{10}{ \input{Fig/checksm2}} \end{layer} -その後，節点や制御点\\ -を動かして，描きたい\\ -ものにする。ただし，\\ -C2p は C1q と B を通\\ -る直線上しか動けない。\\ -C3p は C2q と C を通\\ -る直線上しか動けない。 - -\vspace{10mm} - +\vspace{40mm} +\vspace{\baselineskip} \hypertarget{beziersym}{} -\item[関数] Beziersym(名前，節点リスト，[オプション] ) -\item[機能] 節点間を３次ベジエ曲線でスムーズに結んだ曲線を描く -\item[説明] 節点をはさむ制御点は節点に関し対称（片方は表示されず，動かせない）。 +\item[関数] Beziersym(名前，節点リスト，[オプション] ) +\item[機能] 節点間を3次ベジェ曲線でスムーズに結んだ曲線を描く +\item[説明] 節点をはさむ制御点は節点に関し対称（片方は表示されず，動かせない）。 制御点は自動的に配置される。その後，節点や制御点を動かして描きたいものにする。 -例： +【例】 \begin{layer}{150}{0} \putnotese{70}{20}{bz1} -\putnotese{40}{-5}{\input{Fig/checksy1}} +\putnotese{40}{10}{ \input{Fig/checksy1}} +\putnotese{0}{5}{Beziersym("1",[A,B,C,D]);} +\putnotese{0}{15}{C2p と C3p は表示されない} \end{layer} -Beziersym("1",[A,B,C,D]);\\ -C2p と C3p は表示され\\ -ない。 +\vspace{50mm} -\vspace{10mm} +その後，節点や制御点を動かして，描きたいものにする。 + +C2p と C3p は表示されず，動かせない。 +\begin{center} \input{Fig/checksy2} \end{center} + +\vspace{\baselineskip} +\hypertarget{mkbeziercrv}{} +\item[関数] Mkbeziercrv(名前, [節点リスト,制御点リスト] のリスト,options ) +\item[機能] 複数のベジェ曲線を描く +\item[説明] [節点リスト,制御点リスト] が１つの場合は，Bezier()と同じ。 + +\vspace{\baselineskip} +【例】ベジェ曲線を2つ描く。 + +\verb|Mkbeziercrv("5",[[[A,B,C],[[D],[E,F]]],[[G,H,K,L],[[M],[N,O],[P]]]]);| + + \input{Fig/checkmc1} + +%\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\vspace{\baselineskip} +\hypertarget{mkbezierptcrv}{} +\item[関数] Mkbezierptcrv(節点リストptlist，[オプション] ) +\item[機能] ベジェ曲線を描く +\item[説明] 制御点は，自動的に配置される。 + +複数の場合は [ ptlist1, ptlist2.... ] + +名前は，A から順に自動的につける。 + +オプション + +"Deg=...” 次数指定ができる。（ 初期設定は3次） + +"Num=..." 各区間の区間数（分点数ー１）を指定できる。（ 初期設定は10） + +\vspace{5mm} + +【例】 \begin{layer}{150}{0} -\putnotese{70}{30}{bz1} -\putnotese{40}{0}{\input{Fig/checksy2}} +\putnotese{50}{15}{bzA} +\putnotese{50}{-5}{ \input{Fig/checkb8}} \end{layer} -その後，節点や制御点\\ -を動かして，描きたい\\ -ものにする。\\ -C2p と C3p は表示さ\\れず，動かせない。 - \\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\verb|Mkbezierptcrv([A,B,C]);| -\hypertarget{bowdata}{} -\item[関数] Bowdata(点リスト , options) -\item[機能] 弓形を描く -\item[説明] 点リストで与えられた２点を結ぶ弓形を描く。\\ - ２点を反時計回りに回る方向に弓形を描く。\\ - optionsは，[曲がり , 空白サイズ , 文字, 線種]\\ - 曲がり は弧の曲がり具合の指定。デフォルトは１\\ - 空白サイズ は中央にあける空白の大きさ\\ - 文字は，"Expr=文字" \\ - また，"Expr=位置 , 文字" で位置を指定して文字を入れる。位置はe,w,n,s,c\\ - -例 三角形ABCの各辺に弓形マークをつけ記号を入れる。 -\begin{verbatim} - Listplot([A,B,C,A]); - Letter([A,"n1","A",B,"w1","B",C,"e1","C"]); - Bowdata([A,B]); - Bowdata([B,C],[1,"Expr=s3,a"]); - Bowdata([C,A],[2,1.2,"Expr=10","da"]); -\end{verbatim} - \input{Fig/bowdata}\\ - - 以上が基本。これに加え，文字を回転して表示する方法がある。\\ - ただし，Cinderellaの画面には反映されない。\\ - 文字をを回転するには次のように書く。\\ - "Exprrot=微小移動 , 文字"\\ - 微小移動は t , n ,u \\ - t は線分方向の微小移動。移動量は数字をつける。正負が可。\\ - n は線分と垂直方向の微小移動\\ - u は上下反転\\ - t , n , u は組み合わせることができる。 - 以下にいくつか例を示す。 -\begin{verbatim} - Bowdata([B,A],[1,1,"Exprrot=a"]); - Bowdata([D,C],[1,1,"Exprrot=t3,a"]); - Bowdata([F,E],[1,1,"Exprrot=t-3,a"]); - Bowdata([H,G],[1,1,"Exprrot=n3,a"]); - Bowdata([L,K],[1,1,"Exprrot=u,a"]); - Bowdata([N,M],[1,1,"Exprrot=t3u,a"]); -\end{verbatim} - \input{Fig/bowdata2}\\ - - -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\vspace{25mm} + +\begin{layer}{150}{0} +\putnotese{50}{15}{bzA} +\putnotese{60}{-10}{ \input{Fig/checkb11}} +\end{layer} + +その後，節点や制御点を動かして， + +描きたいものにする。 + +\vspace{30mm} + +\begin{layer}{150}{0} +\putnotese{80}{25}{bzA} +\putnotese{50}{-5}{\input{Fig/checkb9}} +\end{layer} + +\verb|Mkbezierptcrv([A,B,C],["Deg=2"]);| +Deg=2 とすると2次になる。 + +制御点は各区間に１個ずつできる。 + +\vspace{20mm} + +\begin{layer}{150}{0} +\putnotese{20}{45}{bzA} +\putnotese{80}{45}{bzB} +\putnotese{0}{10}{ \input{Fig/checkb10}} +\end{layer} + +複数の場合は [ ptlist1, ptlist2.... ] + +\verb|Mkbezierptcrv([[A,B,C],[D,E,F,G]]);| + +\vspace{40mm} + + \vspace{\baselineskip} \hypertarget{bspline}{} -\item[関数] Bspline(名前，制御点リスト，[オプション] ) -\item[機能] ２次B-spline曲線を描く -\item[説明] 節点は自動的に計算され，表示されない\\ +\item[関数] Bspline(名前，制御点リスト，[オプション] ) +\item[機能] 2次B-spline曲線を描く +\item[説明] 節点は自動的に計算され，表示されない + + \vspace{\baselineskip} +【例】\verb|Bspline("1",[A,B,C,D,E])| + +これは， \verb|Bezier("1",[A,(B+C)/2,(C+D)/2,E],[B,C,D])| と同じ。曲線の名前が bz1 ではなくbzb1 となる。 +通常のB-spline曲線の端の制御点の代わりに，端点を動かせるようにしている。 -例：\verb|Bspline("1",[A,B,C,D,E]);|\\ - \verb|Bezier("1",[A,(B+C)/2,(C+D)/2,E],[B,C,D]);|\\ - と同じ。曲線の名前が bz1 ではなくbzb1 となる。\\ - 通常のB-spline曲線の端の制御点の代わりに，端点を動かせるようにしている。\\ - \input{Fig/checkbs1} + \begin{center} \input{Fig/checkbs1}\end{center} +【例】\verb|Bspline("1",[A,B,C,D,A]);| -例：\verb|Bspline("1",[A,B,C,D,A]);|\\ - リストの最初と最後が同じ場合は閉曲線になる。\\ - \verb|Bezier("1",[(D+A)/2,(A+B)/2,(B+C)/2,(C+D)/2,(D+A)/2],[A,B,C,D]);| と同じ。\\ - \\ - \input{Fig/checkbs2} - \\ - 参照：\hyperlink{ospline}{Ospline：大島のスプラインを描く} \\ +リストの最初と最後が同じ場合は閉曲線になる。 + + \verb|Bezier("1",[(D+A)/2,(A+B)/2,(B+C)/2,(C+D)/2,(D+A)/2],[A,B,C,D]);| + + と同じ。 + + \begin{center} \input{Fig/checkbs2}\end{center} +参照：\hyperlink{ospline}{Ospline：大島のスプラインを描く} + +\vspace{\baselineskip} \hypertarget{crspline}{} -\item[関数] CRspline(名前，節点リスト，[オプション] ) -\item[機能] 単独のCatmull-Rom スプライン曲線を描く +\item[関数] CRspline(名前，節点リスト，[オプション] ) +\item[機能] 単独のCatmull-Rom スプライン曲線を描く \item[説明] - 自由点は，節点のみで，制御点は節点から作られ移動はできない。\\ - オプションに，通常のオプションのほか，次の２つが使える。\\ - "size-$>$n" 画面上での線の太さを指定する。\\ - "pointsize-$>$n" 制御点の大きさを指定する。0のとき非表示となる。\\ - -例：\verb|CRspline("3",[A,B,C,D]);|\\ - \input{Fig/checkCR} - \\ +自由点は，節点のみで，制御点は節点から作られ移動はできない。 + +オプションに，通常のオプションのほか，次が使える。 + +\verb|size ->n| : 画面上での線の太さを指定する。 + +【例】\verb|CRspline("1",[A,B,C,D]);| + +\hspace{20mm} \input{Fig/checkCR} + +\vspace{\baselineskip} +\hypertarget{ospline}{} +\item[関数] Ospline(名前，制御点リスト，[オプション] ) +\item[機能] 大島のspline曲線を描く +\item[説明] 制御点を通るスプライン曲線を描く + +リストの最初と最後が同じ場合は閉曲線になる。 + +\vspace{\baselineskip} +【例】\verb|Ospline("1",[A,B,C,D,E]);| \verb|Ospline("1",[A,B,C,D,A]);| + + \input{Fig/ospline1} \input{Fig/ospline2} + +\vspace{\baselineskip} + スプライン曲線については次も参照されたい：\hyperlink{bspline}{Bspline：Ｂスプラインを描く} + + +\vspace{\baselineskip} \hypertarget{circledata}{} -\item[関数] Circledata(name,リスト,options) -\item[機能] 円または多角形を描く。 -\item[説明] 中心の点と，円周上の1点，または３点をリストで与えて円を描く。\\ - プロットデータの名前は，"cr" に引数の name を付加したものとなる。\\ - 中心と円周上の点を，座標ではなく幾何要素名で指定する場合は name は省略可。\\ - optionsは以下のものをリストで与える。省略した場合は実線で円が描かれる。 +\item[関数] Circledata(name,リスト,options) +\item[機能] 円または多角形を描く。 +\item[説明] 中心の点と，円周上の1点，または3点をリストで与えて円を描く。 + +中心と円周上の点を，座標ではなく幾何要素名で指定する場合は name は省略可。 + +optionsは以下のものをリストで与える。省略した場合は実線で円が描かれる。 \begin{tabbing} -1234567890123456789012\=\kill - "Rng=[$θ_1,θ_2$]" \>角$θ_1$から$θ_2$の範囲の弧を描く。角は弧度法で与える。\\ - "Num=分割数" \>円を描くときの分割数。値が小さい場合は多角形になる。\\ - 線種 \>"dr, n" , "da,m,n" , "do,m,n"\\ +1234\=567890123456789012\=\kill + \> "Rng=[$\theta_1,\theta_2$]" \>角$\theta_1$から$\theta_2$の範囲の弧を描く。角は弧度法で与える。\\ + \> "Num=分割数" \>円を描くときの分割数。値が小さい場合は多角形になる。\\ + \> 線種 \>"dr, n" , "da,m,n" , "do,m,n" +\end{tabbing} +\begin{tabbing} +1234\=56789012345678901234567890\=\kill + +【例】いろいろな円を描く。\\ + \>原点中心，半径2の円 \> \verb|Circledata("1",[[0,0],[2,0]]);|\\ + \>A中心，半径ABの円 \> \verb|Circledata([A,B]);|\\ + \>A中心，半径2の円 \> \verb|Circledata("1",[A,A+[2,0]]);|\\ + \>3点A,B,Cを通る円 \> \verb|Circledata([A,B,C]);|\\ + \>下図左より，オプションに "dr,2" , "da" , "do" をつけた場合。 +\end{tabbing} +\hspace{10mm} \input{Fig/circledata1} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + + \verb|Circledata([A,B,C]);| で，3点A,B,Cを通る円を描いたとき，できた円の中心は \verb|Pointdata("1",[crABCcenter]);| で作図できる。 + +\vspace{\baselineskip} +【例】A中心，半径AB，中心角60°の弧を描く。 + +\hspace{10mm} \verb|Circledata([A,B],["Rng=[0,pi/3]"]); | + +\vspace{\baselineskip} +【例】A中心，半径AB，中心角60°の扇型を描く。点A,B,Cを適当に取っておく。 + +\begin{verbatim} + th=arctan2(B-A); + C.xy=Rotatepoint(B,pi/3,A); + Circledata([A,B],[Assign("Rng=[th,th+pi/3]","th",th)]); + Listplot([B,A,C]); + Letter([A,"s","A",B,"e","B",C,"nw","C"]); +\end{verbatim} + +\begin{center} +\includegraphics[bb=0.00 0.00 180.01 177.01,width=4cm"] {Fig/circledata3.pdf}\hspace{12mm} \input{Fig/circledata2} +\end{center} + +１行目は，ABが$x$軸となす角を arctan2 関数 によって求めている。 + +\vspace{\baselineskip} +【例】弧を太く描く + + \verb|Circledata([C,D],["dr,3","Rng=[0,pi/3]"]);| + + 円はNが大きな値の正N多角形として描いている。optionの ["Num=数値"] によってその細かさを指定できる。Nの値が小さければ正多角形が描けることになる。 + +\vspace{\baselineskip} +【例】A中心，半径ABの円と，その円に内接する正六角形 +\begin{verbatim} + Circledata("1",[A,B]); + Circledata("2",[A,B],["Num=6"]); +\end{verbatim} +ここで，同じ[A,B]を使うため，nameを付与して区別する必要がある。(下図左) + +また，頂点の位置を変えるのであれば，Rng= オプションを使う。（下図右） + + \verb|Circledata("2",[A,B],["Num=6","Rng=[pi/6,13/6*pi]"]);| + +\hspace{10mm} \input{Fig/circledata4} +\hspace{5mm} \input{Fig/circledata5} + +%\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\vspace{\baselineskip} +\hypertarget{mkcircles}{} +\item[関数] Mkcircles() +\item[機能] すべての幾何円のPD を作成 +\item[説明] Cinderellaの「円を加える」ツール（3種類いずれでも）で描いたすべての円をそのままプロットデータとする。たとえば，中心A，円周上の点をBとした円を作ると，プロットデータcrABが作成される。その後，インスペクタで点Bの識別名を変更（たとえばQに）すると，プロットデータ名も変更される。円はすでに描かれていてもよい。 + +\vspace{\baselineskip} +\hypertarget{ellipseplot}{} +\item[関数] Ellipseplot(name,点リスト ,定義域, options) +\item[機能] 焦点と通る点を与えて楕円を描く。 +\item[説明] 点リストで2つの焦点と通る点を与える。点はCinderellaの幾何点が使える。 + + また，通る点のかわりに，焦点からの距離の和を実数で与えることもできる。 + + 実際には，媒介変数表示$x=a \cos \theta,y=b \sin \theta$ を，回転・平行移動して描いている。定義域はこのときの$t$の定義域で，省略も可能。省略したときの初期値は[-5,5] + +\vspace{\baselineskip} +【例】点A,Bを焦点とする楕円を描く。 + +\verb|Ellipseplot("1",[A,B,C]);| 点Cを通る楕円を描く。 + +\verb|Ellipseplot("1",[A,B,4]);| 焦点からの距離の和が4である楕円を描く。 + +\verb|Ellipseplot("1",[A,B,C],"[0,pi]");| 楕円の半分を描く。 + +\vspace{\baselineskip} +【例】Cinderellaの作図ツールを使う + +作図ツールに，焦点と通る点で楕円を描くもの，点の極線を描くツールがある。（モードメニュー / 直線 / 点の極線）これを利用すると，楕円上にとった点をインシデントにできるので，インタラクティブに図を変更することができる。このCinderellaの作図機能と合わせて，一方の焦点から出た光が楕円上で反射して他方の焦点に至る，という図を次のようにして描くことができる。 + +まず，3つの点，焦点A,Bと通る点Cを適当な位置に作図する。次に「焦点と通る点で決まる楕円」ツールを選び，点A,B,Cを順に指定すると，楕円が描かれる。 + +モードメニューの「直線」から「点の極線」を選び，点Cと楕円を順に指定すると接線が引かれる。 + +「垂線を加える」ツールを用いて，点Cで垂線，すなわち法線を引く。（下図） + +「点を加える」ツールを用いて，接線，法線上に適当に点を取る。(D,Eとなったとする) + +次のスクリプトを書いて実行すると，楕円に関して入射角と反射角が等しくなるように光が反射する様子を図にすることができる。 + +\vspace{\baselineskip} +\begin{layer}{150}{0} +\putnotese{75}{5}{ \includegraphics[bb=0 0 272.01 240.01, width=5cm]{Fig/ellipsecindy.pdf}} +\end{layer} +\hspace{50mm} + +\begin{verbatim} + Ellipseplot("1",[A,B,C]); + Lineplot([C,D]); + Lineplot([C,E]); + Arrowdata([A,C]); + Arrowdata([C,B]); + Anglemark([A,C,B]); + Expr([A,"s2","F_1",B,"s2","F_2"]); +\end{verbatim} +\vspace{\baselineskip} + \begin{center} \input{Fig/ellipseplot1}\end{center} + + また，接線，法線を描かず，この楕円上に点D,E,・・をとり（個数は任意）次のスクリプトを書けば，何本かの光線が一方の焦点を出て他方の焦点に集まる様子を描くことができる。 + +\begin{layer}{150}{0} + \putnotese{70}{0}{\scalebox{0.9}{ \input{Fig/ellipseplot2}}} +\end{layer} +\begin{verbatim} + Ellipseplot("1",[A,B,C]); + Listplot([A,C,B]); + Listplot([A,D,B]); + Listplot([A,E,B]); + Expr([A,"s2","F_1",B,"s2","F_2"]); +\end{verbatim} +\vspace{10mm} + +\hypertarget{hyperbolaplot}{} +\item[関数] Hyperbolaplot(name,点リスト ,定義域, options) +\item[機能] 焦点と通る点を与えて双曲線を描く。 +\item[説明] 点リストで2つの焦点と通る点を与える。点はCinderellaの幾何点が使える。 + +また，通る点のかわりに，焦点からの距離の差を実数で与えることもできる。 + +実際には，ハイパボリック関数を用いた媒介変数表示 $x=\cosh t,y=\sinh t$を回転・平行移動している。 + +optionとして，"Asy=線種" を与えると，漸近線を指定した線種で表示する。 初期設定では漸近線は非表示。 + +\vspace{\baselineskip} +【例】点A,Bを焦点とする双曲線を描く。 + +\verb|Hyperbolaplot("1",[A,B,C]);| 点Cを通る双曲線を描く。 + +\verb|Hyperbolaplot("1",[A,B,2]);| 焦点からの距離の差が2の双曲線を描く。 + +\verb|Hyperbolaplot("1",[A,B,C],["Asy=do"]);| 漸近線を点線で描く。 + +\vspace{\baselineskip} +\hspace{20mm} \scalebox{0.9}{\input{Fig/hyper1}} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\vspace{\baselineskip} +\hypertarget{parabolaplot}{} +\item[関数] Parabolaplot(name，点リスト ,定義域, options) +\item[機能] 点リスト[A,B,C]で示された焦点，準線で決まる放物線を描く。 +\item[説明] 焦点Aと準線BCで決定する放物線を描く。 + + 実際には，2次関数 $y=x^2$のグラフを回転・平行移動して描いており，定義域は，$y=x^2$での定義域と考えてよい。定義域は省略することもできる。省略したときの初期値は[-5,5] + +\vspace{\baselineskip} +【例】点Aを焦点，直線BCを準線とする放物線を描く + +\hspace{10mm}\verb|Parabolaplot("1",[A,B,C]); | + +定義域を $-4 \leq x \leq 4$ とする。 + +\hspace{10mm} \verb|Parabolaplot("1",[A,B,C],"[-4,4]");| + +点(0,1)を焦点，直線$y=-1$を準線とする放物線を描く + +\hspace{10mm} \verb|Parabolaplot("1",[[0,1],[-1,-1],[1,-1]]);| + +\vspace{\baselineskip} +【例】放物線上の2点で引かれた接線と放物線で囲まれた領域を斜線で描く。 + +Cinderellaの作図ツールに，焦点と準線で放物線を描くものがある。また，点の極線を描くツールがある。（モードメニュー / 直線 / 点の極線）これを利用すると，放物線上にとった点をインシデントにできるので，インタラクティブに図を変更することができる。このCinderellaの作図機能と合わせて，次の手順で図を描く。 + +まず，焦点A(0,1)と準線$y=-1$：BCを作図する。次に「焦点と準線で決まる放物線」ツールを選び，点Aと直線BCを指定すると，放物線が描かれる。方程式では$y=\dfrac{1}{4}x^2$の放物線である。 + +次に，放物線上に点D,Eをとる。Cinderellaの作図機能を用いているので，この2点は放物線上だけを動かすことができる。（インシデント） + +モードメニューの「直線」から「点の極線」を選び，点Dと放物線，点Eと放物線を順に指定すると接線が引かれる。その交点に点を取る。 + +\vspace{\baselineskip} +\begin{center} \includegraphics[bb=0 0 482.02 413.02 , width=6cm]{Fig/parabolaplot.pdf} \end{center} + +\vspace{\baselineskip} + 以上で作図ができたので，次のスクリプトを書いて実行する。 +\begin{verbatim} + Parabolaplot("1",[A,B,C]); + Lineplot([D,F]); + Lineplot([E,F]); + Hatchdata("1",["iii"],[["gr1para","s"],["lnEF","n"],["lnDF","n"]]); +\end{verbatim} + +これで，次図ができる。このあと，文字などは適当に追加する。 + +\vspace{\baselineskip} +\begin{center} \input{Fig/parabolaplot}\end{center} + +なお，Cinderellaの作図ツールで放物線を描かず，焦点Aと準線上の点B,Cだけを用意して，次のスクリプトで描くこともできる。 +\begin{verbatim} + Parabolaplot("1",[A,B,C]); + Putoncurve("D","gr1para"); + Putoncurve("E","gr1para"); + Tangentplot("1","gr1para","x="+D.x); + Tangentplot("2","gr1para","x="+E.x); + Hatchdata("1",["iii"],[["gr1para","s"],["lntn1","n"],["lntn2","n"]]); +\end{verbatim} + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +%\vspace{\baselineskip} +\hypertarget{ovaldata}{} +\item[関数] Ovaldata(name, 点リスト,options) +\item[機能] 角を丸くした矩形を描く +\item[説明] 中心と対角の１点を指定し，角を丸くした矩形を描く + +optionsは，角の落とし具合と線種など。 初期設定は0.2 + +\vspace{\baselineskip} +【例】いくつかの例を示す。 +\begin{verbatim} + Ovaldata("1", [A,B]); + Ovaldata("2", [C,D],[0]); + Ovaldata("3", [E,F],[1,"dr,3"]); + Ovaldata("4", [G,H],[1.5,"da"]); +\end{verbatim} +\begin{center} \input{Fig/ovaldata}\end{center} + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +%\newpage +\end{description} +% ====== 関数のグラフ ============== +\subsubsection{関数のグラフ} +\begin{description} + +\vspace{\baselineskip} +\hypertarget{plotdata}{} +\item[関数] Plotdata(name , 式 , 変数と定義域 , options) +\item[機能] 関数のグラフを描く。プロットデータの名前は，gr +\item[説明] 式で表された関数のグラフを，指定された定義域で描く。 + +式，定義域は " " でくくって文字列とする。定義域はx=に続いてリストで指定。 + +options は次の通り。 +\begin{tabbing} +12345678901234567890123\=\kill + 線種 \>"dr, n" , "da,m,n" , "do,m,n"\\ + "Num=数値" \>描画時の分割数\\ + "Dis=数値" \>値が指定数値以上ジャンプする場合は不連続点とみなす。\\ + "Exc=数値リスト \>リストで示された点は除外する。\\ + "Exc=関数" \>関数の零点は除外する。\\ + "Color=RGB" \>色指定。RGBはCMYKでもよい。 \end{tabbing} -例：原点中心，半径２の円を描く \verb|Circledata("1",[[0,0],[2,0]]);|\\ - A中心，半径ABの円 を描く \verb|Circledata([A,B]);|\\ - A中心，半径２の円 を描く \verb|Circledata([A,A+[2,0]]);|\\ - ３点A,B,Cを通る円を描く \verb|Circledata([A,B,C]);|\\ - この場合，できた円の中心を \verb|Pointdata("1",[crABCcenter]);| で\\ - 作図できる。\\ - 下図左より，A中心，半径ABの円 を\\ - 太さ２の実線で描く \verb|Circledata([A,B],["dr,2"]);|\\ - 破線で描く \verb|Circledata([A,B],["da"]);|\\ - 点線で描く \verb|Circledata([A,B],["do"]);|\\ - \\ -\input{Fig/circledata1} - \\ -例：A中心，半径AB，中心角60°の弧を描く。\\ - \verb|Circledata([A,B],["Rng=[0,pi/3]"]); |\\ - このとき，扇型を描くのであれば，2本の半径を引く必要がある。そのためには，Aが原点，Bがx軸上にあれば，点A,B以外にもうひとつ点Cをとり，その位置を CindyScript を用いて -\begin{verbatim} - C.xy=|A,B|*[cos(pi/3),sin(pi/3)] -\end{verbatim} - で指定し，扇型ができたのを確かめてから，\verb|Listplot([B,A,C])| を付加すればよい。\\ -\\ - \input{Fig/circledata2}\\ -\\ - 辺ABが$x$軸と平行でない場合は，角の範囲は０からではなく，ABが$x$軸となす角から始める必要があり，ちょっとした工夫が必要である。中心Aが原点でない場合も含め，次のようなスクリプトで実現できる。\begin{verbatim} - th=arctan2(B.xy-A.xy); - str="Rng=["+text(th+0)+","+text(th+pi/3)+"]"; - C.xy=A.xy+|A,B|*[cos(th+pi/3),sin(th+pi/3)]; - Circledata([A,B],[str]); - Listplot([B,A,C]); -\end{verbatim} -１行目は，ABが$x$軸となす角を arctan2 関数 によって求めている。\\ -２行目は引数の文字列を作っている。th+0 , th+pi/3 により弧度法にしている。ここで，+0 が必要である。\\ -\\ - \input{Fig/circledata3}\\ -\\ -複数のオプションをリストで与えることもできる。\\ + 【例】2次関数 $f(x)=x^2-2x$ のグラフを定義域指定なしで描く。 + +\hspace{10mm} \verb|Plotdata("1","x^2-2*x","x");| -例：弧を太く描く\\ - \verb|Circledata([C,D],["dr,3","Rng=[0,pi/3]"]);|\\ +\vspace{\baselineskip} +\hspace{20mm} \scalebox{0.9}{\input{Fig/plotdata1}} - 円はNが大きな値の正N多角形として描いている。optionの ["Num=数値"] によってその細かさを指定できる。Nの値が小さければ正多角形が描けることになる。\\ -例：A中心，半径ABの円と，その円に内接する正六角形 + \verb|Plotdata("1","x^2-2*x","x",["Color=[1,0,0]"]);| + +とすると赤で描かれる。 + +\vspace{\baselineskip} + 【例】三角関数 $2\sin \left(2x-\dfrac{\pi}{4} \right)$ のグラフを，定義域 $0 \leq x \leq 2 \pi$で描く。 + +\hspace{10mm} \verb|Plotdata("3","2*sin(2*x-pi/4)","x=[0,2*pi]");| + +\vspace{\baselineskip} +\hspace{20mm} \input{Fig/plotdata2} + +%\vspace{\baselineskip} + CindyScript では，plot( 式 , 定義域 ); で描くが， \ketcindy を用いるときは，CindyScript のplot 関数のかわりに，このPlotdata を使えばよい。 + +軸に数字を入れるのであれば，Letter() を用いる。 + +\vspace{\baselineskip} +optionsの使用例 +\begin{tabbing} +1234\=567890123456789012345678901234567890123456\=\kill + \> \verb|Plotdata("1","sin(x)+3","x");| \> 初期設定\\ + \> \verb|Plotdata("2","sin(x)+2","x",["dr,2"]);| \> 同じく，太さ2で描く\\ + \> \verb|Plotdata("3","sin(x)+1","x",["da"]);| \> 同じく，破線で描く\\ + \> \verb|Plotdata("4","sin(x)","x",["do"]);| \> 同じく，点線で描く + \end{tabbing} +結果は次図上から。 + +\vspace{\baselineskip} +\hspace{20mm} \scalebox{0.9}{\input{Fig/plotdata3}} + +Num=分割数の指定 + +グラフの描画は，区間を分割して関数値をとり，各点を結ぶという通常の方法によっている。Nの指定はこの分割数の指定である。 初期設定は50。思うような結果が得られない場合はこの値を大きく指定するとよい。下図左は 初期設定，右は Num=200。 + +\vspace{\baselineskip} +\hspace{20mm}\scalebox{0.8}{ \input{Fig/plotdata4}} + +不連続点の指定 + +Dis オプションにより，値がジャンプする不連続点を線で結ばないようにする。Numオプションと合わせて使うと効果が上がる。 + +\vspace{\baselineskip} + 【例】$f(x)=$tan$x$ のグラフは，そのままではあたかも漸近線が描かれたようになるが，これは，不連続点の前後をそのまま結んでいるためである。（下図左） \begin{verbatim} - Circledata("1",[A,B]); - Circledata("2",[A,B],["Num=6"]); + Plotdata("1","tan(x)","x",["Num=200","Dis=50"]); \end{verbatim} - \input{Fig/circledata4}\\ -ここで，同じ[A,B]を使うため，nameを付与して区別する必要がある。\\ -また，頂点の位置を変えるのであれば，Rng= オプションを使う。\\ - \verb|Circledata("2",[A,B],["Num=6","Rng=[pi/6,13/6*pi]"]);|\\ - \input{Fig/circledata5}\\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +のように，"Dis" オプションを使えば余分な線が描かれなくなる。（下図右） -\hypertarget{crosspoint}{} -\item[関数] Crosspoint(name , PD1 ,PD2 , 範囲) -\item[機能] 2曲線の交点を作る -\item[説明] 曲線1と曲線2の範囲にある交点を作る。曲線１と曲線２はプロットデータの名称。\\ -範囲は，交点が存在する範囲を指定する。\\ +\vspace{\baselineskip} +\hspace{20mm} \input{Fig/plotdatatan1}\hspace{20mm} \input{Fig/plotdatatan2} -例：3次曲線の接線がその曲線と交わる点を求める。\\ -２点A,Bを作図ツールで適当なところにとり，次のスクリプトで3次曲線を描く。 +\vspace{\baselineskip} +【例】ガウス記号 [$x$] で表される関数（床関数 : floor()）のグラフ。 \begin{verbatim} - f(x):=x^3-4*x; - g(x):=d(f(#),A.x)*(x-A.x)+A.y; - A.y=f(A.x); - B.y=g(B.x); - Plotdata("1","f(x)","x"); - Lineplot([A,B]); + Plotdata("1","floor(x)","x",["Num=100","Dis=0.9"]); + Ptsize(3); + Drwxy(); + repeat(7,s,start -> -2, + Drwpt([s+1,s],0); + ); \end{verbatim} -１行目と２行目で3次曲線とその接線を定義し，点A,Bをその上に乗せている。\\ -Plotdata() と Lineplot() により，3次曲線と接線のプロットデータができる。\\ -それぞれの名称はコンソールに出力される。3次曲線は gr1 , 接線は lnAB である。\\ -また，図を見て，交点のある場所を確認して範囲を決める。\\ -プロットデータ名と範囲を用いて次のスクリプトを追加する。\\ - \verb|Crosspoint("C",gr1,lnAB,[1,2]);|\\ +\hspace{40mm}\input{Fig/plotdata5} -これで，交点Ｃが新たに作られる。\\ -必要に応じ，Letter関数で点の名前を表示すると次のようになる。\\ -\\ - \input{Fig/crosspoint}\\ - \\ -交点が存在しない場合，PD1の端点に点が作られる。\\ -２曲線の交点を作るのに，\hyperlink{putintersect}{Putintersect(点名,PD1,PD2)} 関数を用いることもできる。\\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\vspace{\baselineskip} + 関数に文字係数がついており，文字係数の値を変化させながらグラフを描くには，Assign を使うか，Defvar で変数を定義する。 + +\vspace{\baselineskip} + 【例】直線 $y=bx-b^2$ の係数$b$を変化させて描き，包絡線をうかびあがらせる。 +\begin{verbatim} + repeat(50,t, + cb=t/5-5; + Plotdata(text(t),Assign("b*x-b^2","b",cb),"x"); + ); +\end{verbatim} +\begin{layer}{150}{0} +\putnotese{80}{0}{\input{Fig/assign}} +\end{layer} + +または +\begin{verbatim} + Defvar("b"); + repeat(50,t, + b=t/5-5; + Plotdata(text(t),"b*x-b^2","x"); + ); +\end{verbatim} + +\vspace{\baselineskip} +\hypertarget{implicitplot}{} +\item[関数] Implicitplot(name,式,xの定義域,yの定義域, options) +\item[機能] 陰関数のグラフを描く。 +\item[説明] 陰関数の式を与えてグラフを描く。式，定義域とも文字列。 + +options は，"r","m","Wait=n" が指定できる。Wait の初期値は10。 + +"r","m"に関しては，オプションなしのとき + + i) データファイルがなければ，新しく作る + + ii) データファイルが既にあればそれを読み込む + +"m" のとき，強制的にデータファイルを作り直す。 + +"r" のとき，すでにあるデータファイルを読み込む。 + +\vspace{\baselineskip} +【例】楕円を描く。 +\begin{verbatim} + Implicitplot("1","x^2-x*y+2*y^2=4","x=[-3,3]","y=[-2,2]"); +\end{verbatim} + +\vspace{\baselineskip} +\hspace{20mm}\input{Fig/implicit1} + +\vspace{\baselineskip} \hypertarget{deqplot}{} -\item[関数] Deqplot(name,式，変数名，初期値，options) -\item[機能] 微分方程式の解曲線を描く -\item[説明] 微分方程式と初期値を与えて解曲線を描く。\\ - \\ -例：$y''=-y$で，初期値が$x=0$のとき$y=1,y'=0$ の解曲線\\ +\item[関数] Deqplot(name,式，変数名，初期値，options) +\item[機能] 微分方程式の解曲線を描く +\item[説明] 微分方程式と初期値を与えて解曲線を描く。 - \verb|Deqplot("1","y``=-y","x",0, [1,0]); |\\ +\vspace{\baselineskip} +【例】$y''=-y$で，初期値が$x=0$のとき$y=1,y'=0$ の解曲線 - \input{Fig/deqplot1}\\ + \verb|Deqplot("1","y``=-y","x",0, [1,0]); | + +注） \verb|`| はバッククウォート。ここからカットアンドペーストするときは注意。 -例：$y'=y*(1-y)$で，$x=0$のとき，$y=0.5$の解曲線\\ +\vspace{\baselineskip} +\hspace{20mm} \input{Fig/deqplot1} - \verb|Deqplot("2","y`=y*(1-y)","x",0, 0.5,["Num=100"]);| \\ +\vspace{\baselineskip} +【例】$y'=y*(1-y)$で，$x=0$のとき，$y=0.5$の解曲線 + + \verb|Deqplot("2","y`=y*(1-y)","x",0, 0.5,["Num=100"]);| + +\vspace{\baselineskip} +\hspace{20mm} \input{Fig/deqplot2} - \input{Fig/deqplot2}\\ +\vspace{\baselineskip} -例：$[x,y]'=[x(1-y),0.3y(x-1)]$で，変数は$t$，$t=0$（区間の左端）のときの$x, y$の値が1と0.5 であるときの解曲線 +【例】$[x,y]'=[x(1-y),0.3y(x-1)]$で，変数は$t$，$t=0$（区間の左端）のときの$x, y$の値が1と0.5 であるときの解曲線 \begin{verbatim} - Deqplot("3","[x,y]`=[x*(1-y),0.3*y*(x-1)]","t=[0,20]", - [1,0.5],["Num=200"]); + Deqplot("3","[x,y]`=[x*(1-y),0.3*y*(x-1)]","t=[0,20]", + [1,0.5],["Num=200"]); \end{verbatim} - \\ - \input{Fig/deqplot3}\\ - \\ - なお，この例では，Cinderellaの画面上の図は誤差が大きくて正確な図にはならないが，\TeX に出力する図は正確な図になる。解像度を上げる(Numの数を大きくする)ことにより，Cinderellaの画面上の図も正確な図に近づく。\\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\vspace{\baselineskip} +\hspace{20mm} \input{Fig/deqplot3} -\hypertarget{drwpt}{} -\item[関数] Drwpt(点,option）, Drawpoint(点,options) -\item[機能] 点を表示する -\item[説明] 座標または幾何点の識別名を与えて点を表示する。これだけではCinderellaの描画面には描かれないので，描画面にも表示するにはCinderellaの作図ツールで作図するか，Pointdata() または Putpoint() を用いる。\\ - 複数の点の場合は座標または識別名はリストで与える。\\ - optionに数字 0 を入れると，白抜きで表示する。なお白抜きの場合は，Ptsize()で点の大きさを少し大きめにとるとよい。\\ - 可読性を高めるときはDrawpointを推奨する。\\ +\vspace{\baselineskip} +\hypertarget{paramplot}{} +\item[関数] Paramplot(name , 式 , 変数と定義域,options) +\item[機能] 媒介変数表示の曲線を描く。 +\item[説明] 式は""でくくった媒介変数表示のリストで与える。 + +定義域も " " でくくって文字列とし，t=に続いてリストで指定する。 + +options は線種が有効 -例：座標(1,1)と(4,3)に点を表示する。Cinderellaの描画面には描かれない。\\ - \verb|Drwpt([[1,1],[4,3]]);|\\ +\vspace{\baselineskip} +【例】サイクロイド曲線を描く。 -例：Cinderellaで点A,B,Cを作図しておき，\TeX で表示する。\\ - \verb|Drwpt([A,B,C]); |\\ +\hspace{10mm} \verb|Paramplot("1","[t-sin(t),1-cos(t)]","t=[0,2*pi]");| -例：線分ABの右端（B）を白抜きで表示する +\vspace{\baselineskip} +\hspace{20mm} \input{Fig/paramplot1} + +\vspace{\baselineskip} +【例】optionsの使用例。左から， 初期設定，太線，破線，点線の楕円 \begin{verbatim} - Ptsize(5); - Listplot([A,B]); - Drawpoint(B,0); + Paramplot("1","[2*cos(t)-5,sin(t)]","t=[0,2*pi]"); + Paramplot("2","[2*cos(t),sin(t)]","t=[0,2*pi]",["dr,2"]); + Paramplot("3","[2*cos(t)+5,sin(t)]","t=[0,2*pi]",["da"]); + Paramplot("4","[2*cos(t)+10,sin(t)]","t=[0,2*pi]",["do"]); \end{verbatim} - \\ - \input{Fig/drawpoint}\\ -※ Drawpoint([A,B],0); とすれば，両端が白抜きになる。\\ -\\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\begin{center} \input{Fig/paramplot2} \end{center} + +%\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\vspace{\baselineskip} +\hypertarget{polarplot}{} +\item[関数] Polarplot(name , 式 , 変数と定義域,options) +\item[機能] 極座標表示$r=f(\theta)$の曲線を描く。 + +\vspace{\baselineskip} +【例】カージオイド曲線を描く。 + +\hspace{20mm}\verb|Polarplot("1","2*(1+cos(t))","t=[0,2*pi]",["Num=200"]);| + +\vspace{\baselineskip} +\begin{center}\scalebox{0.9}{\input{Fig/cardioid1}}\end{center} + +\vspace{\baselineskip} +\hypertarget{periodfun}{} +\item[関数] Periodfun(定義式,周期,options) +\item[機能] 周期関数のグラフを描く。戻り値はMaxima形式の式とperiodのリスト。 +\item[説明] 周期関数の式を定義してグラフを描く。 +定義式は，関数式（文字列），区間，分割数のリスト。 + +この関数固有のオプションは "Con=" で，不連続点を線で結ぶか否かと，その時の色。 + 初期設定は破線。結ばない場合は "Con=n"，色指定は線種に続いてコンマで区切って指定する。たとえば，"Con=do,Color=red"。 + +周期（描画回数）は，数またはリストで指定する。周期がmのとき，2m+1周期分描かれる。 + + +注意）関数は左右対称な定義域 [-a,a] で定義すること。 + +\vspace{\baselineskip} +【例】矩形関数のグラフ -\hypertarget{drawsegmark}{} -\item[関数] Drawsegmark(name,リスト,options）または Segmark(name,リスト,options） -\item[機能] 線分に印をつける -\item[説明] リストで与えられた２点を端点とする線分に印をつける。印には４種類がある。\\ - optionsは，\\ - Type=n：n=1〜4：印の種類\\ - Width：二本線のときの線の幅\\ - 例：Listplot()で四角形ABCDを描き線分に印をつけた。 \begin{verbatim} - Segmark("1",[A,B],["Type=1"]); - Segmark("2",[B,C],["Type=2","Width=1.5"]); - Segmark("3",[C,D],["Type=3"]); - Segmark("4",[D,A],["Type=4"]); + defL=["0",[-1,0],1,"1",[0,1],1]; + Periodfun(defL, 2,["dr,2"]); + memori=apply(-5..5,x,[x,text(x)]); + memori=flatten(remove(memori,[[0,"0"]])); + Htickmark(memori); + Vtickmark([1,"1"]); \end{verbatim} - \input{Fig/segmark} -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\hspace{20mm}\input{Fig/periodfun.tex} -\hypertarget{expr}{} -\item[関数] Expr([座標 , 位置 , 文字列]) -\item[機能] \TeX 記法の文字列を与えて数式を書く。 -\item[説明] Letterで文字列の前後に\$ \$をおくのと同じ。\\ - 導関数の記号（シングルクウォート）$'$は，Scilab でのシングルクウォートの使用とぶつかるので，$`$（バッククウォート）を用いる。\\ - 複数の箇所に文字を書く場合は，Letter() と同様，引数をリストにして与える。\\ +\vspace{\baselineskip} +一方を放物線にした場合 +\begin{verbatim} + defL=["0",[-1,0],1,"x^2",[0,1],50]; + Periodfun(defL, 2, ["Con=n","dr,2"]); + memori=apply(-5..5,x,[x,text(x)]); + memori=flatten(remove(memori,[[0,"0"]])); + Htickmark(memori); + Vtickmark([1,"1"]); +\end{verbatim} -例 $f(x)=\dfrac{1}{4} x^2$ とその導関数 $f'(x)=\dfrac{1}{2} x$ の式，軸上に必要な数を入れる。 +\hspace{20mm}\input{Fig/periodfun2.tex} + +\vspace{\baselineskip} +\hypertarget{fourierseries}{} +\item[関数] Fourierseries(name,係数,周期,項数) +\item[機能] フーリエ級数のグラフを描く。 +\item[説明] $a_0+\displaystyle{\sum _{n=1} ^{\infty}(a_n \cos nx + b_n \sin nx)}$ を描く。 +係数は $a_0,a_n,b_n$ のリストで，それぞれの要素は文字列とする。 + +この関数固有のオプションは "Con=y/n" で，不連続点を破線で結ぶか否か。 初期設定は y。 + +矩形波のフーリエ近似のような場合は，オプションとして，["Num=200"]（100以上の値を指定）をつけるとよい。 + +\vspace{\baselineskip} +【例】矩形波のフーリエ近似 \begin{verbatim} - Expr([[-3,3],"e","f(x)=\frac{1}{4} x^2",[3,1.5],"s2e2", - "f‘(x)=\frac{1}{2}x",[2,0],"s","2",[0,1],"w","1"]); + Fourierseries("1",["1/2","0","(1-(-1)^n)/(pi*n)"],2,6,["Num=200"]); \end{verbatim} - \\ - \input{Fig/expr}\\ - ※原点Oが線と重なっている。位置をずらすには，Setax() の項を参照のこと。\\ +\begin{center} +\input{Fig/fourierseries.tex} +\end{center} + +\vspace{\baselineskip} +\hypertarget{tangentplot}{} +\item[関数] Tangentplot(name , PD , 位置 , options) +\item[機能] 接線を描く。プロットデータの名前は，lntn +\item[説明] 曲線PDの指定した位置での接線を描く。位置は "x=n" で指定する。 + +使用例は\hyperlink{parabolaplot}{Parabolaplot}の例を参照。 + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -例 対数関数の定積分の記号および積分値を図に書き込む。\\ - 下図で，定積分の表示の部分は矢線をPQとして， +\end{description} +%\newpage +% ====== 文字 ============== +\subsubsection{文字} +\begin{description} + +\vspace{\baselineskip} +\hypertarget{expr}{} +\item[関数] Expr([座標 , 位置 , 文字列]) +\item[機能] \TeX 記法の文字列を与えて数式を書く。 +\item[説明] Letterで文字列の前後に\$ \$をおくのと同じ。 + +導関数の記号は，$'$（シングルクウォート）を用いる。 + +複数の箇所に文字を書く場合は，Letter() と同様，引数をリストにして与える。 + +\vspace{\baselineskip} +【例】 $f(x)=\dfrac{1}{4} x^2$ とその導関数 $f'(x)=\dfrac{1}{2} x$ の式，軸上に必要な数を入れる。 \begin{verbatim} - Arrowdata(Q,P); - Expr([Q+[0.2,0],"ne","\displaystyle \int_a^b \log x\,dx="+ - text(L.x*(log(L.x)-1)-G.x*(log(G.x)-1)) ]); + Expr([[-3,3],"e","f(x)=\frac{1}{4} x^2",[3,1.5],"s2e2", + "f‘(x)=\frac{1}{2}x",[2,0],"s","2",[0,1],"w","1"]); \end{verbatim} - で表示している。\\ - \verb|L.x*(log(L.x)-1)-G.x*(log(G.x)-1)| は，点L,G(図の$a,b$)をドラッグして\\ - 積分範囲を決めるようにしているので，そこから計算した値。\\ -\\ +\vspace{\baselineskip} + \begin{center} \input{Fig/expr}\end{center} - \input{Fig/intlog} +【例】 対数関数の定積分の記号および積分値を図に書き込む。 +\begin{verbatim} + Expr([Q+[0.2,0],"ne","\displaystyle \int_a^b \log x\,dx="+ + text(L.x*(log(L.x)-1)-G.x*(log(G.x)-1)) ]); +\end{verbatim} + + \verb|L.x*(log(L.x)-1)-G.x*(log(G.x)-1)| は，点L,G(図の$a,b$)をドラッグして + + 積分範囲を決めるようにしているので，そこから計算した値。 + + 矢線は \verb| Arrowdata(Q,P); | で表示している。矢線の始点がQ +\vspace{\baselineskip} +\begin{center} \input{Fig/intlog}\end{center} + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\vspace{\baselineskip} \hypertarget{exprrot}{} -\item[関数] Exprrot([座標 , 向き , 文字列]) -\item[機能] \TeX 記法の文字列を与えて傾いた数式を書く。 -\item[説明] 「座標」の位置に，指定された向きで数式を書く。\\ - 向きはベクトルで与える。\\ - 座標，向きとも，Cinderellaで作図した幾何点を用いることができる。\\ - A(1,1),B(3,2),C(0,2) のとき，次の２つのスクリプトは同じ結果になる。 +\item[関数] Exprrot([座標 , 向き , 方向，文字列]) +\item[機能] \TeX 記法の文字列を与えて傾いた数式を書く。 +\item[説明] 「座標」の位置に，指定された向きで数式を書く。 + +向きはベクトルで与える。 + +方向はオプションで， t (ベクトルと同じ向き) と n（ベクトルと垂直な向き） の両方を数字つきで与える。ただし，方向はオプション。 + +座標，向きとも，Cinderellaで作図した幾何点を用いることができる。 + \begin{verbatim} - Exprrot(C,B-A,"\sqrt{3}"); - Exprrot([0,2],[2,1],"\sqrt{3}"); + Exprrot([3,2],[2,-1],"t0n1","\sqrt{3}"); + Exprrot(C,B-A,"\frac{2}{3}"); \end{verbatim} - \\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\vspace{\baselineskip} +\hspace{10mm}\includegraphics[bb=0.00 0.00 181.01 131.01,width=4cm]{Fig/exprrot.pdf} \hspace{10mm} \input{Fig/exprrot} -\hypertarget{ellipseplot}{} -\item[関数] Ellipseplot(name,点リスト ,定義域, options) -\item[機能] 焦点と通る点を与えて楕円を描く。 -\item[説明] 点リストで２つの焦点と通る点を与える。点はCinderellaの幾何点が使える。\\ - また，通る点のかわりに，焦点からの距離の和を実数で与えることもできる。\\ - 実際には，媒介変数表示$x=a \cos \theta,x=b \sin \theta$ を，回転・平行移動して描いている。定義域はこのときの$t$の定義域で，省略も可能。省略したときの初期値は[-5,5]\\ - -例：点A,Bを焦点とする楕円を描く。\\ - \verb|Ellipseplot("1",[A,B,C]);| 点Cを通る楕円を描く。\\ - \verb|Ellipseplot("1",[A,B,4]);| 焦点からの距離の和が４である楕円を描く。\\ - \verb|Ellipseplot("1",[A,B,C],"[0,pi]");| 楕円の半分を描く。\\ - \\ -例：Cinderellaの作図ツールに，焦点と通る点で楕円を描くものがある。また，点の極線を描くツールがある。これを利用すると，楕円上にとった点をインシデントにできるので，インタラクティブに図を変更することができる。このCinderellaの作図機能と合わせて，一方の焦点から出た光が楕円上で反射して他方の焦点に至る，という図を次のようにして描くことができる。\\ - まず，３つの点A,B,Cを作図する。次に「焦点と通る点で決まる楕円」ツールを選び，点A,B,Cを順に指定すると，楕円が描かれる。\\ - - モードメニューの「直線」から「点の極線」を選び，点Cと楕円を順に指定すると接線が引かれる。\\ - 「垂線を加える」ツールを用いて，点Cで垂線，すなわち法線を引く。\\ - 「点を加える」ツールを用いて，接線，法線上に適当に点を取る。(D,Eとなったとする)\\ - 次のスクリプトを書いて実行すると，楕円に関して入射角と反射角が等しくなるように光が反射する様子を図にすることができる。 -\begin{verbatim} - Ellipseplot("1",[A,B,C]); - Lineplot([C,D]); - Lineplot([C,E]); - Arrowdata([A,C]); - Arrowdata([C,B]); - Anglemark([A,C,B]); - Expr([A,"s2","F_1",B,"s2","F_2"]); -\end{verbatim} - \\ - \input{Fig/ellipseplot1}\\ - - また，接線，法線を描かず，この楕円上に点D,E,・・をとり（個数は任意）次のスクリプトを書けば，何本かの光線が一方の焦点を出て他方の焦点に集まる様子を描くことができる。 -\begin{verbatim} - Ellipseplot("1",[A,B,C]); - Listplot([A,C,B]); - Listplot([A,D,B]); - Listplot([A,E,B]); - Expr([A,"s2","F_1",B,"s2","F_2"]); -\end{verbatim} - \\ - \input{Fig/ellipseplot2}\\ - \\ +\vspace{\baselineskip} +\hypertarget{letter}{}\item[関数] Letter([位置, 方向, 文字列]) +\item[機能] 文字列を表示する +\item[説明] 「位置（座標）」と方向で指定された場所に文字を書き込む。 -\hypertarget{framedata}{} -\item[関数] Framedata(name , リスト) -\item[関数] Framedata2(name ,[P1,P2]) -\item[機能] 矩形を描く -\item[説明] 中心の座標，横，縦をリスト[中心 ,横 , 縦]で与え，矩形を描く。横，縦は中心からの距離。\\ - 中心の座標は点の名前でもよい。\\ - 中心を座標で与える場合はnameは省略できない。\\ - 横，縦は，矩形の頂点を示す点にすることもできる。\\ - 中心，横，縦を省略した場合は，描画範囲と同一の矩形を描く\\ - Framedata2() では，対角点（左下P1と右上P2）をリストで与える。\\ - 以下にいくつか例を示す\\ - \verb|Framedata("1");| 描画範囲と同一の矩形を描く\\ - \verb|Framedata("2",[[0,0],2,2]);| 原点を中心とする縦横幅４の正方形を描く\\ - \verb|Framedata("3",[A,3,2]);| 点Aを中心とする横６，縦４の矩形を描く\\ - \verb|Framedata([A,3,2]);| 中心が点の名称の場合はnameは省略できる。\\ - \verb|Framedata([A,B]);| 点Aを中心，点Bを頂点のひとつとする矩形を描く\\ - 矩形の角を丸めたい場合は，Ovaldata(name, 点リスト,options)を使う。\\ - \verb|Framedata2("1",[A,B]);| 点A，Bを対角点とする矩形を描く\\ - \\ +位置（座標）は点の名前で指定することもできる。 -\hypertarget{hyperbolaplot}{} -\item[関数] Hyperbolaplot(name,点リスト ,定義域, options) -\item[機能] 焦点と通る点を与えて双曲線を描く。 -\item[説明] 点リストで２つの焦点と通る点を与える。点はCinderellaの幾何点が使える。また，通る点のかわりに，焦点からの距離の差を実数で与えることもできる。\\ - 実際には，ハイパボリック関数を用いた媒介変数表示 $x=\cosh t,y=\sinh t$を回転・平行移動している。 - optionとして，"Asy=線種" を与えると，漸近線を指定した線種で表示する。デフォルトでは漸近線は非表示。\\ +場所は上下左右を東西南北で表し， n/s/w/e/c の方向で表す。cは中央。 -例：点A,Bを焦点とする双曲線を描く。\\ - \verb|Hyperbolaplot("1",[A,B,C]);| 点Cを通る双曲線を描く。\\ - \verb|Hyperbolaplot("1",[A,B,2]);| 焦点からの距離の差が2の双曲線を描く。\\ - \verb|Hyperbolaplot("1",[A,B,C],["Asy=do"]);| 漸近線を点線で描く。\\ +% \begin{center} \input{Fig/letter4} +指定位置からの距離を，数値で与えることもでき，e2, e3 は e より少し離して置く。 - \input{Fig/hyper1}\\ +複数の文字列をリストの形にして渡すことができる。 -\hypertarget{ospline}{} -\item[関数] Ospline(名前，制御点リスト，[オプション] ) -\item[機能] 大島のspline曲線を描く -\item[説明] 制御点を通るスプライン曲線を描く\\ - リストの最初と最後が同じ場合は閉曲線になる。\\ + 注）導関数の記号$'$は，数式モード（\$ ではさむ）で$'$（シングルクウォート）を用いる。 +\vspace{\baselineskip} +【例】 -例：\verb|Ospline("1",[A,B,C,D,E]);| \verb|Ospline("1",[A,B,C,D,A]);|\\ - \input{Fig/ospline1} \input{Fig/ospline2} - \\ - 参照：\hyperlink{bspline}{Bspline：Ｂスプラインを描く} \\ +座標 (2,1) の南東にＰを表示 -\hypertarget{parabolaplot}{} -\item[関数] Parabolaplot(name，点リスト ,定義域, options) -\item[機能] 点リスト[A,B,C]で示された焦点，準線で決まる放物線を描く。 -\item[説明] 焦点Aと準線BCで決定する放物線を描く。\\ - 実際には，２次関数 $y=x^2$のグラフを回転・平行移動して描いており，定義域は，$y=x^2$での定義域と考えてよい。定義域は省略することもできる。省略したときの初期値は[-5,5]\\ - -例：点Aを焦点，直線BCを準線とする放物線を描く\\ - \verb|Parabolaplot("1",[A,B,C]); |\\ - \verb|Parabolaplot("1",[A,B,C],"[-5,5]");| 定義域を $-5 \leq x \leq 5$ とする。\\ - 点(0,1)を焦点，直線$y=-1$を準線とする放物線を描く\\ - \verb|Parabolaplot("1",[[0,1],[-1,-1],[1,-1]]);|\\ - \\ -例：放物線上の２点で引かれた接線と放物線で囲まれた領域を斜線で描く。\\ - Cinderellaの作図ツールに，焦点と準線で放物線を描くものがある。また，点の極線を描くツールがある。これを利用すると，放物線上にとった点をインシデントにできるので，インタラクティブに図を変更することができる。このCinderellaの作図機能と合わせて，次の手順で図を描く。\\ - まず，焦点A(0,1)と準線$y=1$：BCを作図する。次に「焦点と準線で決まる放物線」ツールを選び，点Aと直線BCを指定すると，放物線が描かれる。方程式では$y=\dfrac{1}{4}x^2$の放物線である。\\ - 次に，放物線上に点D,Eをとる。Cinderellaの作図機能を用いているので，この２点は放物線上だけを動かすことができる。（インシデント）\\ - モードメニューの「直線」から「点の極線」を選び，点Dと放物線，点Eと放物線を順に指定すると接線が引かれる。その交点に点を取る。\\ - \\ - \includegraphics[bb=0 0 964 826 , width=6cm]{Fig/parabolaplot.png}\\ - \\ - 以上で作図ができたので，次のスクリプトを書いて実行する。 -\begin{verbatim} - Parabolaplot("1",[A,B,C]); - Lineplot([D,F]); - Lineplot([E,F]); - Listplot([E,F,D]); - Hatchdata("1",["ii"],[["gr1para","s"],["sgEFD","n"]]); -\end{verbatim} - \\ - これで，次図ができる。このあと，文字などは適当に追加する。\\ - \\ - \input{Fig/parabolaplot} - \\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} - \\ -\hypertarget{ovaldata}{} -\item[関数] Ovaldata(name, 点リスト,options) -\item[機能] 角を丸くした矩形を描く -\item[説明] 中心と対角の１点を指定し，角を丸くした矩形を描く\\ - optionsは，角の落とし具合と線種など。デフォルトは0.2 \\ +\hspace{10mm} \verb|Letter([[2,1] ,"se","P"]);| + +点Ｃを中央としてＣを表示 + +\hspace{10mm} \verb|Letter([C ,"c", "C"]);| + +点Aの南西にA，Eの南に数式を表示 + +\hspace{10mm} \verb|Letter([A,"sw","A",E,"s","$ f(x)=\frac{1}{4} x^2 $"]);| + +\vspace{\baselineskip} +\hypertarget{letterrot}{}\item[関数] Letterrot(座標, 方向ベクトル,移動量, 文字列) +\item[機能] 文字列を回転して表示する +\item[説明] 座標で示された位置に，方向ベクトルで指定された向きに回転して文字を書き込む。 + +第3引数は微小移動量で，略すこともできる。 -例：いくつかの例を示す。 \begin{verbatim} - Ovaldata("1", [A,B]); - Ovaldata("2", [C,D],[0]); - Ovaldata("3", [E,F],[1,"dr,3"]); - Ovaldata("4", [G,H],[1.5,"da"]); + Letterrot(C,B-A,"t2n5","AB"); \end{verbatim} - \input{Fig/ovaldata}\\ - \\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\hypertarget{htickmark}{} -\item[関数] Htickmark([横座標 , 方向 , 文字]) -\item[機能] 横軸に目盛を書く。 -\item[説明] Scilabのみで実行する。Cinderellaの描画面には反映されない。引数は位置（横座標），方向，文字。複数点の情報を[ ]内にまとめて記入できる。\\ +移動量を略して + +\hspace{10mm} \verb|Letterrot(C,B-A,"AB");| -例 点$(2,\ 0)$の南西側に$2$を表示する。\\ - \verb|Htickmark([2,"sw","2"]);|\\ +とすることもできる。この場合は，微小な移動はされない。 -例 -5から5までの目盛を打つ。\\ - Cindyscriptのリスト処理を使って，次のように引数のリストを作って渡す。 +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\newpage +\end{description} +% ====== マーキング ============== +\subsubsection{マーキング} +\begin{description} + +\hypertarget{anglemark}{} +\item[関数] Anglemark(name,点リスト , options) +\item[機能] 点リストで示された角に弧の形状の角の印をつける。 +\item[説明] Listplot() などと同様，点リストが点名の場合はnameは省略できる。 + +optionsは次の通り。 + +数値 角の印の大きさ。 初期設定は１ + +線種 "dr, n" , "da,m,n" , "do,m,n" + +"Expr=文字" : 文字を入れる + +"Expr=位置 , 文字" : 位置を指定して文字を入れる。位置は頂点からの距離。 + +\vspace{\baselineskip} +【例】三角形の内角に印をいれ，文字を書き込む。 \begin{verbatim} - memori=apply(-5..5,x,[x,"s",text(x)]); - memori=flatten(remove(memori,[[0,"s","0"]])); - Htickmark(memori); + Listplot([A,B,C,A]); + Letter([A,"n1","A",B,"w1","B",C,"e1","C"]); + Anglemark([B,A,C]); + Anglemark([C,B,A],["Expr=\theta"]); + Anglemark([A,C,B],[2,"dr,3","Expr=2,\alpha"]); \end{verbatim} - １行目，apply のカッコ内の -5..5 でリスト[-5,-4,-3,-2,-1,0,1,2,3,4,5] ができる。\\ - それを用いて，applyで[数, "s",数の文字] からなるリストができる。text(x) はxを文字にする関数。\\ - ２行目で，このリストから，[0,"s","0"]を除き，リストを平滑化する。\\ - 結果は次のようになる。\\ -\input{Fig/htickmark}\\ +\hspace{20mm}\input{Fig/anglemark} -\hypertarget{vtickmark}{} -\item[関数] Vtickmark([横座標 , 方向 , 文字]) -\item[機能] 縦軸に目盛を書く。 -\item[説明] Htickmarkと同様。縦軸に目盛を書く。\\ +※角の印には平行四辺形の形状のものもある。\hyperlink{paramark}{Paramark()}を参照のこと。 -例：点$(0,\ 1),\ (0,\ 2)$の西側に$1,\ 2$を表示する。\\ - \verb|Htickmark([1,"w","1",2,"w","2"]);|\\ -\\ +\vspace{\baselineskip} +\hypertarget{paramark}{} +\item[関数] Paramark(name,点リスト , options) +\item[機能] 点リストで示された角に平行四辺形の形状の角の印をつける。 +\item[説明] Listplot() などと同様，点リストが点名の場合はnameは省略できる。 -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +optionsは次の通り。 -\hypertarget{implicitplot}{} -\item[関数] Implicitplot(name,式,xの定義域,yの定義域, options) -\item[機能] 陰関数のグラフを描く。 -\item[説明] 陰関数の式を与えてグラフを描く。式，定義域とも文字列。\\ - options は，"r","m","Wait=n" が指定できる。Wait の初期値は10。\\ - "r","m"に関しては，オプションなしまたは，”” のとき\\ - i) データファイルがなければ，新しく作る\\ - ii) データファイルが既にあればそれを読み込む\\ - "m" のとき，強制的にデータファイルを作り直す。\\ - "r" のとき，すでにあるデータファイルを読み込む。\\ - -例：楕円を描いて，中にハッチをかける。 -\begin{verbatim} - Implicitplot("1","x^2+2*y^2=4","x=[-2,2]","y=[-2,2]"); - Hatchdata("1","i",["imp1"]); -\end{verbatim} - 注）ここで，yの定義域は実際より広くとってある。"y=[-1,1]" とすると，上下が欠けた楕円になる。曲線だけならそれでよいが，その場合，閉曲線ではないのでHatchdata() で無用に時間がかかってしまうので要注意。\\ - \\ - -\hypertarget{letter}{}\item[関数] Letter([位置, 方向, 文字列]) -\item[機能] 文字列を表示する -\item[説明] 「位置（座標）」と方向で指定された場所に文字を書き込む。\\ - 位置（座標）は点の名前で指定することもできる。場所は上下左右中央（ n/s/w/e/c )の方向で表す。（n/s/w/e は東西南北の記号）\\ - \\ - \input{Fig/letter4}\\ - 指定位置からの距離を，数値で与えることもでき，e2, e3 は e より少し離して置く。\\ - 複数の文字列をリストの形にして渡すことができる。\\ - 注）導関数の記号$'$は，数式モード（\$ ではさむ）で$`$（バッククウォート）を用いる。\\ - -例：座標 (2,1) の南東にＰを表示\\ - \verb|Letter([2,1] ,"se","P");|\\ - 点Ｃを中央としてＣを表示\\ - \verb|Letter(C ,"c", "C");|\\ - 点Aの南西にA，Eの南に数式を表示\\ - \verb|Letter([A,"sw","A",E,"s","$ f(x)=\frac{1}{4} x^2 $"]);| \\ - \\ -%\input{Fig/letter3} - -\hypertarget{letterrot}{}\item[関数] Letterrot(座標, 方向ベクトル,移動量, 文字列) -\item[機能] 文字列を回転して表示する -\item[説明] 座標で示された位置に，方向ベクトルで指定された向きに回転して文字を書き込む。\\ - 第３引数は微小移動量で，略すこともできる。\\ - A(1,1),B(3,2),C(0,2) のとき，次のスクリプトは同じ結果になる。 -\begin{verbatim} - Letterrot([0,2],[2,1],2,5,"AB"); - Letterrot([0,2],B-A,2,5,"AB"); - Letterrot(C,B-A,2,5,"AB"); - Letterrot(C,B-A,"t2n5","AB"); -\end{verbatim} - 移動量を略して\\ - \verb|Letterrot(C,B-A,"AB");|\\ - とすることもできる。この場合は，微小な移動はされない。\\ - - -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +数値 角の印の大きさ。 初期設定は1 -\hypertarget{lineplot}{} -\item[関数] Lineplot（name , 2点のリスト , options) -\item[機能] ２点のリストで示された点を結ぶ直線を描く。プロットデータ名の頭部は ln -\item[説明] ２点のリストは座標または幾何要素の名前で与える。\\ - options は次の通り。\\ - 線種 "dr, n" , "da,m,n" , "do,m,n"\\ - "+" 半直線を描く。\\ - "dr" , "da" , "do" と "+" はリストにして両方指定することができる。\\ - 点のリストが，座標ではなく幾何要素名のリストの場合は，nameは省略できる。\\ - いくつか例を示す。\\ - 各座標を結ぶ直線を引く\\ - \verb|Lineplot("1",[[0,0],[1,2]])| \\ - Cinderellaの描画ツールで２点A,Bをとっておき，直線ABを引く\\ - \verb|Lineplot([A,B]);| \\ - optionの働きの例\\ - \verb|Lineplot([A,B],["dr,0.5","+"]);| Aを端点とする半直線を引く\\ - \verb|Lineplot([C,D],["dr,2"]);| 直線CDを太さ2で描く\\ - \verb|Lineplot([E,F],["da"]);| 直線EFを破線で描く\\ - \verb|Lineplot([G,H],["do"]);| 直線GHを点線で描く\\ - 結果は，次図左上から。\\ - - \input{Fig/lineplot}\\ - -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\newpage +線種 "dr, n" , "da,m,n" , "do,m,n" -\hypertarget{listplot}{} -\item[関数] Listplot（name , 点のリスト , options) -\item[機能] 点のリストで示された点を結ぶ。プロットデータ名の頭部は sg -\item[説明] 点のリストは座標または幾何要素名のリストで与える。点が，座標ではなく幾何要素名の場合は，nameは省略可 \\ - プロットデータの名前は，"sg" に引数の name を付加したものとなる。\\ - options は次の通り。\\ - 線種 "dr, n" , "da,m,n" , "do,m,n" +"Expr=文字" : 文字を入れる + +"Expr=位置 , 文字" : 位置を指定して文字を入れる。位置は頂点からの距離。 + +\vspace{\baselineskip} +\begin{layer}{150}{0} +\putnotese{85}{0}{ \input{Fig/paramark}} +\end{layer} + + +【例】三角形の内角に印をいれ，文字を書き込む。 + +\begin{verbatim} + Listplot([A,B,C,A]); + Paramark([A,B,C]); + Paramark([C,A,B],[3,"Expr=\alpha"]); + Paramark([B,C,A],["dr,2","Expr=2,\theta"]); + +\end{verbatim} + +※角の印には弧の形状のものもある。\hyperlink{anglemark}{Anglemark()} を参照のこと。\\ + +\vspace{\baselineskip} +\hypertarget{bowdata}{} +\item[関数] Bowdata(name,点リスト , options) +\item[機能] 弓形を描く +\item[説明] 点リストで与えられた2点を結ぶ弓形を描く。Listplot() などと同様，点リストが点名の場合はnameは省略できる。 + +2点を反時計回りに回る方向に弓形を描く。 + +optionsは，[曲がり , 空白サイズ , 文字, 線種] + +曲がり は弧の曲がり具合の指定。 初期設定は1 + +空白サイズ は中央にあける空白の大きさ + +文字は，"Expr=文字" + +また，"Expr=微小移動 , 文字" で位置を指定して文字を入れる。 + +微小移動は t n + + t は線分方向の微小移動。移動量は数字をつける。正負が可。 + + n は線分と垂直方向の微小移動 + +\vspace{\baselineskip} + \begin{layer}{150}{0} +\putnotese{85}{5}{ \input{Fig/bowdata}} + \end{layer} + +【例】 三角形ABCの各辺に弓形マークをつけ記号を入れる。 +\begin{verbatim} + Listplot([A,B,C,A]); + Letter([A,"n1","A",B,"w1","B",C,"e1","C"]); + Bowdata([A,B]); + Bowdata([B,C],[1,"Expr=t0n3,a"]); + Bowdata([C,A],[2,1.2,"Expr=10","da"]); +\end{verbatim} + +\vspace{\baselineskip} +これに加え，文字を回転して表示する方法がある。ただし，Cinderellaの画面には反映されない。文字をを回転するには次のように書く。 + +\hspace{10mm}"Exprrot=微小移動 , 文字" + + 微小移動の最後にr をつけると，上下反転する。 + +以下にいくつか例を示す。 +\begin{verbatim} + Bowdata([B,A],[1,1,"Exprrot=a"]); + Bowdata([D,C],[1,1,"Exprrot=t3n0,a"]); + Bowdata([F,E],[1,1,"Exprrot=t-3n0,a"]); + Bowdata([H,G],[1,1,"Exprrot=t0n3,a"]); + Bowdata([L,K],[1,1,"Exprrot=t0n0r,a"]); + Bowdata([N,M],[1,1,"Exprrot=t3n0r,a"]); +\end{verbatim} +\hspace{10mm} \input{Fig/bowdata2} + +%\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\hypertarget{drawsegmark}{} +\item[関数] Drawsegmark(name,リスト,options）または Segmark(name,リスト,options） +\item[機能] 線分に印をつける +\item[説明] リストで与えられた2点を端点とする線分に印をつける。印には4種類がある。 + +optionsは \begin{tabbing} -1234567890123456789012345678901234\=\kill - optionsの使用例\\ - \verb|Listplot([A,B]);| \>線分ABを描く。太さはデフォルト。\\ - \verb|Listplot([C,D],["dr,2"]);| \>線分CDを描く。太さ２\\ - \verb|Listplot([E,F],["da"]);| \>線分EFを破線で描く\\ - \verb|Listplot([G,H],["da,3,1"]);| \>線分GHを破線で描く。線を長く\\ - \verb|Listplot([K,L],["da,1,3"]);| \>線分KLを破線で描く。間隔を空ける\\ - \verb|Listplot([M,N],["do"]);| \>線分MNを点線で描く。\\ - \verb|Listplot([O,P],["do,3"]);| \>線分OPを点線で描く。間隔を空ける\\ - \verb|Listplot([Q,R],["do,3,3"]);| \>線分QRを点線で描く。間隔を空けて太く\\ - 結果は次図左から。 +1234\=56789012\=345678901234567890\=\kill + \> Type=n \>：印の種類 n=1〜4\\ + \> Width \>：二本線のときの線の幅 \end{tabbing} - \input{Fig/listplot3} - 例 : Cinderellaの作図ツールで三角形ABCを描いておく。 + 【例】四角形ABCDを描き線分に印をつける。 + +\begin{layer}{150}{0} +\putnotese{90}{5}{ \input{Fig/segmark}} +\end{layer} +\hspace{50mm} \begin{verbatim} - Listplot([A,B,C,A]); - Addax(0); + Listplot([A,B,C,D,A]); + Segmark("1",[A,B],["Type=1"]); + Segmark("2",[B,C],["Type=2","Width=1.5"]); + Segmark("3",[C,D],["Type=3"]); + Segmark("4",[D,A],["Type=4"]); \end{verbatim} - \input{Fig/listplot1}\\ - 各座標を頂点とする三角形を描く\\ - \verb|Listplot("1",[[0,0],[2,0],[1,2],[0,0]]);| -\\ - プロットデータは点の座標のリストである。したがって，プロットデータを自作してListplot()で表示することができる。\\ - \\ -例：有限フーリエ級数展開\\ - \[\cfrac{\pi}{2}+\sum_{n=0}^{30} \cfrac{1-(-1)^n}{n}\sin nx\] -次のようにCindyscriptで関数を定義し，プロットデータpd を作って引数に渡す。 -\begin{verbatim} - f(x):=( - s=pi/2; - repeat(30,n,s=s+(1-(-1)|^n)/n*sin(n*x)); - ); - pd=apply(0..200,t, - x=-2*pi+t*4*pi/200; - [x,f(x)]; - ); - Listplot("1",pd); - Expr([[-2*pi,-0.5],"s","-2\pi",[-pi,-0.5],"s","-\pi",[pi,-0.5],"s", - "\pi",[2*pi,-0.5],"s","2\pi",[0,pi],"w2","\pi"]); -\end{verbatim} - \\ + +\vspace{\baselineskip} +\hypertarget{htickmark}{} +\item[関数] Htickmark([横座標 , 方向 , 文字]) +\item[機能] 横軸に目盛と文字を書く。 +\item[説明] 引数は位置（横座標），方向，文字。複数点の情報を[ ]内にまとめて記入できる。方向を省略すると "s1"になる。微調整は描画面には反映されないので，PDFにして確認する。 +目盛の長さは \hyperlink{setmarklen}{Setmarklen()} で設定できる。 + +\vspace{\baselineskip} +【例】 方向指定の例 + +\hspace{10mm} \verb|Htickmark([1,"1",2,"n1","2",3,"se","3",4,"4"]);| + +\vspace{\baselineskip} \begin{center} -\input{Fig/fourier} +\input{Fig/htickmark01} \end{center} - \\ - リストの長さには制限があるため，あまり長いリストを用いたり，何度も用いたりすることができない。たとえば，タートルグラフィクスを用いたシェルピンスキーのギャスケットでは，次のサイズくらいは可能だが，植物の成長モデルでは分岐が多いためあまり大きな図はできない。スクリプトを工夫して，200くらいずつのリストに分割する。\\ - \input{Fig/listplot2} - \\ - \\ -\hypertarget{mesegmets}{} -\item[関数] Mksegments() -\item[機能] 幾何線分のすべてのPD を作成 -\item[説明] Ketinit() の直後に置くことにより，Cinderellaの作図ツールで描いたすべての線分をそのままプロットデータとする。たとえば，線分ABを作ると，プロットデータsgABが作成される。その後，インスペクタで点Bの識別名を変更（たとえばQに）すると，プロットデータ名も変更される。線分はすでに描かれていてもよい。\\ - -\hypertarget{mkcircle}{} -\item[関数] Mkcircles() -\item[機能] 幾何円のすべてのPD を作成 -\item[説明] Ketinit() の直後に置くことにより，Cinderellaの作図ツールの「円を加える」で描いたすべての円をそのままプロットデータとする。たとえば，中心A，円周上の点をBとした円を作ると，プロットデータcrABが作成される。その後，インスペクタで点Bの識別名を変更（たとえばQに）すると，プロットデータ名も変更される。円はすでに描かれていてもよい。\\ -\\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +%\vspace{\baselineskip} +【例】 -5から5までの目盛を打つ。 + Cindyscriptのリスト処理を使って，次のように引数のリストを作って渡す。 +\begin{verbatim} + memori=apply(-5..5,x,[x,text(x)]); + memori=flatten(remove(memori,[[0,"0"]])); + Htickmark(memori); +\end{verbatim} +１行目，apply のカッコ内の -5..5 でリスト[-5,-4,-3,-2,-1,0,1,2,3,4,5] ができる。それを用いて，applyで[数, 数の文字] からなるリストができる。text(x) はxを文字にする関数。2行目で，このリストから，[0,"0"]を除き，リストを平滑化する。 結果は次のようになる。 -\hypertarget{mkbeziercrv}{} -\item[関数] Mkbeziercrv(名前,[[節点リスト,制御点リスト],[節点リスト,制御点リスト],...],\\ -\hfill[オプション] ) -\item[機能] 複数のベジエ曲線を描く -\item[説明] 単独のベジエ曲線の場合はリストの外側の[ ]はなくてもよい。\\ -Mkbeziercrv|(名前，[節点リスト，制御点リスト]，[オプション] ) は\\ -Bezier(名前，節点リスト，制御点リスト，[オプション] ) と同じ。 +\begin{center} \scalebox{0.9}{\input{Fig/htickmark}}\end{center} +\hypertarget{vtickmark}{} +\item[関数] Vtickmark([横座標 , 方向 , 文字]) +\item[機能] 縦軸に目盛と文字を書く。 +\item[説明] Htickmarkと同様。縦軸に目盛を書く。方向を省略すると "w1"になる。 -\vspace{2mm} +\vspace{\baselineskip} +【例】点$(0,\ 1),\ (0,\ 2)$の西側に$1,\ 2$を表示する。 -例：\verb|Mkbeziercrv("n",[[A,B,C],[[D],[E,F]]]);| は\\ - \verb|Bezier("n",[A,B,C],[[D],[E,F]]);| と同じ。\\ - 曲線の名前が bzn ではなく bzn1 となる。 +\hspace{10mm} \verb|Vtickmark([1,"1",2,"2"]);| -\vspace{2mm} +\vspace{\baselineskip} +\hypertarget{rulerscale}{} +\item[関数] Rulerscale(始点 ，横軸目盛 , 縦軸目盛) +\item[機能] 目盛を打つ +\item[説明] 始点の位置を縦横の起点として目盛りを打つ。目盛はリストで与える。 + ["r",a,b,c,d] の形式では，aからbまでc間隔で，倍率dの目盛を打つ。 + ["f",n1,"str",n2,"str",・・] の形式では，nと"str"がセットで，nの位置に"str"を書く。ただし，位置はCinderellaの描画面の原点を0とする。 + + Listplot() とともに用いると，座標軸とは異なる線分に目盛を打つことができる。 + + Framedata() とともに用いると矩形に目盛を打つことができる。 + +\vspace{\baselineskip} +【例】x軸上の (2,1) から (9,1) まで線分を引き，1目盛を10として目盛を打つ。 +\begin{verbatim} + Listplot("1",[[2,1],[9,1]]); + Rulerscale([2,1],["r",2,9,1,10],[]); +\end{verbatim} + \begin{center} \input{Fig/ruler1} \end{center} +\vspace{\baselineskip} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\begin{layer}{150}{0} -\putnotese{30}{45}{bz51} -\putnotese{90}{45}{bz52} -\putnotese{0}{5}{\input{Fig/checkmc1}} -\end{layer} +【例】Aを原点に置いた矩形枠を描き，横に0,1,2,3,4,5，縦に d1，d2 の目盛を打つ。 +\begin{verbatim} + Framedata("1",[A,B],["corner"]); + Rulerscale(A,["r",0,5,1],["f",1,"d1",3,"d2"]); +\end{verbatim} + \begin{center} \input{Fig/ruler} \end{center} +\vspace{\baselineskip} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -複数の場合は，\verb|[ [ptlist1,ctrlist1], [ptlist2,ctrlist2],... ]| +\end{description} +\newpage +% ＝＝プロットデータの操作＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝ +\subsection{プロットデータの操作} +\begin{description} -\verb|Mkbeziercrv("5",[[[A,B,C],[[D],[E,F]]],[[G,H,K,L],[[M],[N,O],[P]]]]);| +\hypertarget{addgraph}{} +\item[関数] AddGraph(name ,プロットデータのリスト,option) +\item[機能] 複数のプロットデータをまとめる +\item[説明] 複数のプロットデータをまとめて扱う。たとえば，円と，円周上の点の2つのプロットデータをまとめて扱えば，平行移動や回転で，それらのプロットデータをまとめて平行移動や回転ができる。Joincrvs()では，プロットデータをつなげて１つのプロットデータにするが，AddGraph()では，それぞれのプロットデータからなるリスト（リストのリスト）にする。（プロットデータは座標のリストである） -\vspace{40mm} +引数には，プロットデータ名を文字列化して渡す。たとえば，円のプロットデータが cr1 のとき，"cr1" とする。 + +\vspace{\baselineskip} +【例】サイクロイドの図を描く。 \begin{verbatim} -ptlist1=[A,B,C];ctrlist1=[[D],[E,F]];list1=[ptlist1,ctrlist1]; -ptlist2=[G,H,K,L];ctrlist2=[[M],[N,O],[P]];list2=[ptlist2,ctrlist2]; -list=[list1,list2]; -Mkbeziercrv("5",list); + Setpt(3); + Circledata("1",[[0,1],[0,0]]); + Pointdata("1",[0,0]); + AddGraph("1",["[pt1]","cr1"],["nodisp"]); + nn=32; + forall(1..nn, + t=2*pi/nn*#; + Rotatedata(text(#),"ad1",-t,[[0,1],"nodisp"]); + Translatedata(text(#),"rt"+text(#),[t,0],["dr,0.3"]); + ); \end{verbatim} -などとしても同じ。 - \\ - \\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\hypertarget{mkbezierptcrv}{} -\item[関数] Mkbezierptcrv(節点リストptlist，[オプション] ) -\item[機能] ベジエ曲線を描く -\item[説明] 制御点は，自動的に配置される。その後，節点や制御点を動かして， -描きたいものにする。 +\vspace{\baselineskip} +\hspace{20mm} \input{Fig/addgraph} -複数の場合は [ ptlist1, ptlist2.... ] +ここで，AddGraph()の引数に与えるプロットデータのリストで，点のプロットデータ pt1 を"[pt1]" としていることに注意。円のプロットデータが，点の座標のリストであるのに対し，点のプロットデータは一つの座標だけなので，このようにしてリスト化して渡す。 -名前は，A から順に自動的につける。 +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -オプション +\hypertarget{changestyle}{} +\item[関数] Changestyle(PDリスト, options) +\item[機能] 描画オプションを変更する +\item[説明] 複数の図形の描画オプションを一括して変更する。 -"Deg=...” 次数指定ができる。（デフォルトは３次） +\vspace{\baselineskip} +【例】線分AB，円ABの線を破線にして\TeX に書き出さないようにする。 -"Num=..." 各区間の区間数（分点数ー１）を指定できる。（デフォルトは10） +\hspace{10mm} \verb|Changestyle(["sgAB","crAB"],["da","notex"]);| + -\vspace{5mm} +\vspace{\baselineskip} +\hypertarget{invert}{} +\item[関数] Invert(PD) +\item[機能] プロットデータを逆順にする + +\vspace{\baselineskip} +\hypertarget{joincrvs}{} +\item[関数] Joincrvs(name, プロットデータのリスト, options) +\item[機能] 隣接する曲線プロットデータ のリストを繋いで1本の曲線を作る。 +\item[説明] 曲線のリストは隣接する順番で指定する。 + +optionsは線種 "dr, n" , "da,m,n" , "do,m,n" -例： +\vspace{\baselineskip} +【例】線分$y=x\ (-\sqrt{2} \leq x \leq \sqrt{2})$と半円で得られる閉曲線を描いて黄色で塗る。 + +点Aは原点に，点Bは適当なところに作図しておく。 \begin{layer}{150}{0} -\putnotese{50}{15}{bzA} -\putnotese{50}{-5}{\input{Fig/checkb8}} +\putnotese{80}{5}{ \input{Fig/joincrvs}} \end{layer} -\verb|Mkbezierptcrv([A,B,C]);| +\begin{verbatim} + Plotdata("1","x","x=[-sqrt(2),sqrt(2)]"); + B.xy=[sqrt(2),sqrt(2)]; + Circledata("2",[A,B],["Rng=[pi/4,pi/4*5]"]); + Joincrvs("1",["gr1","cr2"]); + Shade(["join1"],["Color=yellow"]); +\end{verbatim} +\vspace{5mm} +%\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\vspace{\baselineskip} +\hypertarget{partcrv}{} +\item[関数] Partcrv(name, A, B, プロットデータ, options) +\item[機能] 曲線プロットデータ上の点A, B の間の部分曲線を描く。 +\item[説明] 2点A, Bの順序は曲線の向きと同一であること。曲線の向きは，$y=f(x)$のグラフではx座標が増加する向き。 -\vspace{25mm} +optionsは線種 "dr, n" , "da,m,n" , "do,m,n" -\begin{layer}{150}{0} -\putnotese{50}{15}{bzA} -\putnotese{60}{-10}{\input{Fig/checkb11}} -\end{layer} +\vspace{\baselineskip} +【例】放物線を点線で描き，一部を実線で描く。 + + \verb|Plotdata("1", "x^2", "x", ["do"]);| （プロットデータの名前はgr1となる） + + \verb|Partcrv("1", [0,0], [1,1], "gr1");| -その後，節点や制御点を動かして， +\begin{center} \input{Fig/partcrv1} \end{center} -描きたいものにする。 +【例】円の一部を実線で描く。円のプロットデータは指定した円周上の点から反時計回りの順にできる。点Aは円の中心，Bは円周上の点とする。点P,Qは適当な位置に作図しておく。 +\begin{verbatim} + Circledata([A,B], ["do"]); + Plotdata("1", "x^2", "x", ["do"]); + tmp=Intersectcrvs("crAB","gr1"); + P.xy=tmp_1; + Q.xy=tmp_2; + Partcrv("1", P, Q, "crAB"); + Partcrv("2", Q, P, "crAB"); +\end{verbatim} +\vspace{\baselineskip} +\hspace{10mm} \input{Fig/partcrv3} \hspace{10mm} \input{Fig/partcrv4} + +\hspace{25mm}part1 の図\hspace{45mm}part2 の図 -\vspace{30mm} +\vspace{\baselineskip} +【例】放物線$y=x^2$が円で切り取られる部分を実線で描く。 \begin{layer}{150}{0} -\putnotese{80}{25}{bzA} -\putnotese{50}{-5}{\input{Fig/checkb9}} +\putnotese{85}{0}{\input{Fig/partcrv}} \end{layer} +\begin{verbatim} + Circledata("1",[[0,2],[0,0]],["da"]); + Plotdata("1","x^2","x",["do"]); + tmp=Intersectcrvs("cr1","gr1"); + Partcrv("2",tmp_2,tmp_1,"gr1",["dr,2"]); + +\end{verbatim} -\verb|Mkbezierptcrv([A,B,C],["Deg=2"]);| +\vspace{\baselineskip} -Deg=2 とすると２次になる。 +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -制御点は各区間に１個ずつできる。 +%\vspace{\baselineskip} +\hypertarget{enclosing}{} +\item[関数] Enclosing(name , PDリスト , [開始位置, 交点計算の許容限界1, 2]) +\item[機能] 複数の曲線から閉曲線を作る。 +\item[説明] 開始位置は，最初と最後の曲線の交点が複数あるときに指定する。 -\vspace{20mm} +開始点は近くに取ればよい。許容限界は，通常は指定しなくてよい。 -\begin{layer}{150}{0} -\putnotese{20}{45}{bzA} -\putnotese{80}{45}{bzB} -\putnotese{0}{10}{\input{Fig/checkb10}} -\end{layer} +\vspace{\baselineskip} +【例】放物線と直線で囲まれる領域に色を塗るために Shade() を使う。 +\begin{verbatim} + Plotdata("1","x^2","x"); + Lineplot("1",[[0,0],[1,0]]); // axis x + Lineplot("2",[[2,0],[2,1]]); + Enclosing("1",["Invert(gr1)","ln1","ln2"],["nodisp"]); + Shade(["en1"],["Color=red"]); +\end{verbatim} +\vspace{\baselineskip} + \begin{center} \input{Fig/enclosing} \end{center} -複数の場合は [ ptlist1, ptlist2.... ] +\vspace{\baselineskip} +注）閉曲線のとりかたでは，出発点を原点にした反時計回りまたは時計回りにすると -\verb|Mkbezierptcrv([[A,B,C],[D,E,F,G]]);| + 反時計回りで \verb|Enclosing("1",["ln1","ln2","Invert(gr1)"]);| -\vspace{25mm} - \\ + 時計回りで \verb|Enclosing("1",["gr1","Invert(ln2)","Invert(ln1)"]);| +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\hypertarget{paramark}{} -\item[関数] Paramark(点リスト , options) -\item[機能] 点リスト[A,B,C]で示された角に平行四辺形の形状の角の印をつける。 -\item[説明] optionsは次の通り。\\ - 数値 角の印の大きさ。デフォルトは１\\ - 線種 "dr, n" , "da,m,n" , "do,m,n"\\ - "Expr=文字" : 文字を入れる\\ - "Expr=位置 , 文字" : 位置を指定して文字を入れる。位置は頂点からの距離。\\ +\vspace{\baselineskip} +\hypertarget{hatchdata}{} +\item[関数] Hatchdata(name , 方向リスト , プロットデータ , options) +\item[機能] 閉曲線の内部に斜線を引く。 +\item[説明] 引数は，曲線名，内部外部のパターンを与える''i''，''o''の文字列，閉曲線を与える曲線と領域の内部を定める方向のリストとオプション。\\ +オプション（カッコ内はデフォルト値）\\ + 角度(45)，間隔(1)，\verb|"Max=(20)"| 斜線の最大本数，\\ + \verb|"Out=y/n (n)"| Rを呼び出して外部ファイルを作るか + +\vspace{\baselineskip} +【例】円の内部。(次図左) +\begin{verbatim} + Circledata([A,B],["dr"]); + Hatchdata("1",["i"],[["crAB"]],["dr,0.7"]); +\end{verbatim} -例：三角形の内角に印をいれ，文字を書き込む。 +【例】3つの閉曲線の内側・外側のパターンが同一である領域（次図右） \begin{verbatim} - Paramark([B,A,C]); - Paramark([C,B,A],[3,"Expr=B"]); - Paramark([A,C,B],["dr,2","Expr=2,C"]); + Circledata([A,B],["dr"]); + Paramplot("1","[4*cos(t),2*sin(t)]","t=[0,2*pi]"); + Paramplot("2","[2*cos(t),4*sin(t)]","t=[0,2*pi]"); + Hatchdata("1",["ioi"],[["crAB"],["gp1"],["gp2"]],["dr,0.7"]); + Hatchdata("2",["iio"],[["crAB"],["gp1"],["gp2"]],["dr,0.7"]); \end{verbatim} - \input{Fig/paramark}\\ +\vspace{\baselineskip} +\hspace{5mm} \input{Fig/hatch1} \hspace{5mm} \input{Fig/hatch2} -※角の印には弧の形状のものもある。Anglemark() を参照のこと。\\ +【例】複数の領域。 +\begin{verbatim} + Plotdata("1","2*sin(x)","x=[-pi,3*pi]",["Num=100"]); + Listplot([A,B]); + Listplot([A,C]); + Hatchdata("1",["ii"],[["sgAB","n"],["gr1","s"]],["dr,0.7"]); + Hatchdata("2",["ii"],[["sgAC","s"],["gr1","n"]],["dr,0.7"]); +\end{verbatim} +\begin{center} +\begin{center} \input{Fig/hatch3} \end{center} +\end{center} -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +【例】複数の領域 その2。 +\begin{verbatim} + Plotdata("1","2*sin(x)","x=[-pi,3*pi]",["Num=100"]); + Listplot([A,B]); + Listplot([A,C]); + Hatchdata("1",["iio"],[["sgAB","s"],["sgAC","n"],["gr1","n"]]); +\end{verbatim} +\begin{center} +\begin{center} \input{Fig/hatch4} \end{center} +\end{center} -\hypertarget{paramplot}{} -\item[関数] Paramplot(name , 式 , 変数と定義域,options) -\item[機能] 媒介変数表示の曲線を描く。プロットデータの頭部は gp -\item[説明] 式は""でくくった媒介変数表示のリストで与える。\\ - 定義域も " " でくくって文字列とし，t=に続いてリストで指定する。\\ - options は線種が有効\\ -例：サイクロイド曲線を描く。\\ - \verb|Paramplot("1","[t-sin(t),1-cos(t)]","t=[0,2*pi]");|\\ +【例】3次曲線と接線で囲まれた領域 -\input{Fig/paramplot1}\\ + 点Aを原点付近に作図しておく。 \begin{verbatim} - Deffun("fx(t)", ["regional(x)","x=t-sin(t)","x"]); - Deffun("fy(t)", ["regional(y)","y=1-cos(t)","y"]); - Paramplot("1","[fx(t),fy(t)]","t=[0,2*pi]"); + Deffun("f(x)",["regional(y)","y=x^3-2*x","y"]); + Plotdata("1","f(x)","x",["Num=100"]); + Putoncurve("A","gr1"); + coef=Derivative("f(x)","x",A.x); + Defvar(["coef",coef]); + Deffun("g(x)",["regional(y)","y=coef*(x-A.x)+A.y","y"]); + Plotdata("2","g(x)","x",["Num=1"]); + if(!Isptselected(A), + Enclosing("1",["gr2","Invert(gr1)"],[A,"nodisp"]); + Hatchdata("1",["i"],[["en1"]]); + ); + \end{verbatim} -とすれば，関数定義も Scilab に引き継がれる。\\ - \\ -optionsの使用例。左から，デフォルト，太線，破線，点線の楕円 +\begin{layer}{150}{0} +\putnotese{80}{0}{\input{Fig/hatch5}} +\end{layer} + +点Aをドラッグして曲線上を動かすと， + +\verb|if(!Isptselected(A),・・・| の効果により， + +その間は領域の斜線は引かれない。 + +点A以外の画面上の適当な位置をクリックして， + +点Aが選択状態でなくなると斜線が引かれる。 + +引かれる斜線の向きや間隔を変えることもできる。 + +間隔は実数で指定できる。 + +\vspace{\baselineskip} +【例】円の内部または円と直線で区切られた図形 + +\verb|Circledata([A,B]);| のプロットデータ crAB を用いて，下図左から + +\verb|Hatchdata("1",["i"],[["crAB"]]);| 円内に傾き$45^{\circ}$の斜線を引く + +\verb|Hatchdata("2",["i"],[["crAB"]],[-40,2]);| 傾き$-40^{\circ}$，間隔を2倍に + +\verb|Hatchdata("3",["i"],[["crAB"]],["dr,0.5"]);| 線の太さを0.3倍に + +\verb|Hatchdata("4",["i"],[["crAB"]],[-45,2,"dr,0.3"]);| + +\input{Fig/HatchZuKita1.tex} + +円のオプションに "notex"をつけた場合と，破線で描いた場合。 +\begin{verbatim} + Circledata([A,B],["notex"]); + Circledata([A,B],["da"]); + \end{verbatim} + +\hspace{10mm} \input{Fig/HatchZuKita7.tex} \input{Fig/HatchZuKita8.tex} + +直線で分けられた領域を作り，対角の上下にハッチをかける。線を描き分ける。 \begin{verbatim} - Paramplot("1","[2*cos(t),sin(t)]","t=[0,2*pi]"); - Paramplot("2","[2*cos(t)+5,sin(t)]","t=[0,2*pi]",["dr,2"]); - Paramplot("3","[2*cos(t),sin(t)+3]","t=[0,2*pi]",["da"]); - Paramplot("4","[2*cos(t)+5,sin(t)+3]","t=[0,2*pi]",["do"]); + Circledata([A,B]); + Lineplot("1",[A,B]); + Lineplot("2",[A,C]); + Hatchdata("1",["iii"],[["crAB"],["ln1","n"],["ln2","n"]]); + Hatchdata("2",["iii"],[["crAB"],["ln1","s"],["ln2","s"]],[90,0.5]); \end{verbatim} -\input{Fig/paramplot2} -\\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\hspace{40mm} \input{Fig/HatchZuKita9.tex} -\hypertarget{plotdata}{} -\item[関数] Plotdata(name , 式 , 変数と定義域 , options) -\item[機能] 関数のグラフを描く。プロットデータの名前は，gr -\item[説明] 式で表された関数のグラフを，指定された定義域で描く。\\ - 式，定義域は " " でくくって文字列とする。定義域はx=に続いてリストで指定。\\ - options は次の通り。 -\begin{tabbing} -12345678901234567890123\=\kill - 線種 \>"dr, n" , "da,m,n" , "do,m,n"\\ - "Num=数値" \>描画時の分割数\\ - "Dis=数値" \>値が指定数値以上ジャンプする場合は不連続点とみなす。\\ - "Exc=数値リスト \>リストで示された点は除外する。\\ - "Exc=関数" \>関数の零点は除外する。\\ - "Color=RGB" \>色指定。RGBはCMYKでもよい。\\ -\end{tabbing} - 例：２次関数 $f(x)=x^2-2x$ のグラフを定義域指定なしで描く。\\ - \verb|Plotdata("1","x^2-2*x","x");|\\ - \\ - \input{Fig/plotdata1} - \\ - \verb|Plotdata("1","x^2-2*x","x",["Color=[0,0,1]"]);|\\ - \\ - とすると赤で描かれる。\\ - \\ - 例：三角関数 $2\sin \left(2x-\dfrac{\pi}{4} \right)$ のグラフを，定義域 $0 \leq x \leq 2 \pi$で描く。\\ - \verb|Plotdata("3","2*sin(2*x-pi/4)","x=[0,2*pi]");|\\ - \\ - \input{Fig/plotdata2} - \\ - CindyScript では，plot( 式 , 定義域 ); で描くが， \ketcindy を用いるときは，CindyScript のplot 関数のかわりに，このPlotdata を使えばよい。\\ - 軸に数字を入れるのであれば，Letter() を用いる。\\ +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -optionsの使用例\\ - \verb|Plotdata("1","sin(x)","x");| $f(x)=$sin$x$ のグラフを描く（デフォルト）\\ - \verb|Plotdata("2","sin(x)+1","x",["dr,2"]);| 同じく，太さ２で描く\\ - \verb|Plotdata("3","sin(x)+2","x",["da"]);| 同じく，破線で描く\\ - \verb|Plotdata("4","sin(x)+3","x",["do"]);| 同じく，点線で描く\\ -結果は次図上から。\\ - \\ - \input{Fig/plotdata3}\\ +\vspace{\baselineskip} +\hypertarget{dotfilldata}{} +\item[関数] Dotfilldata(name , 方向リスト , プロットデータ , options) +\item[機能] 領域を点で敷き詰める。 +\item[説明] Rとデータの授受をおこなって描画する。書式はHatchdata()と同様。 - Num=分割数の指定\\ - グラフの描画は，区間を分割して関数値をとり，各点を結ぶという通常の方法によっている。Nの指定はこの分割数の指定である。デフォルトは50。思うような結果が得られない場合はこの値を大きく指定するとよい。\\ - 下図左はデフォルト，右は Num=200 とした。\\ +オプションは，ドットの密度で 0.1〜0.8 程度。 初期設定は0.3。 - \input{Fig/plotdata4}\\ +\vspace{\baselineskip} +【例】円グラフ - 不連続点の指定\\ - Dis オプションにより，値がジャンプする不連続点を線で結ばないようにする。Numオプションと合わせて使うと効果が上がる。\\ +Partcrv() と Enclosing() で閉曲線を作って点を敷き詰める。 - 例：$f(x)=$tan$x$ のグラフは，そのままではあたかも漸近線が描かれたようになるが，これは，不連続点をそのまま結んでいるためである。 +\begin{layer}{150}{0} +\putnotese{75}{5}{ \input{Fig/dotfill}} +\end{layer} \begin{verbatim} - Plotdata("1","tan(x)","x",["Num=200","Dis=50"]); + r=3; + p0=r*[cos(pi/2),sin(pi/2)]; + p1=r*[cos(-pi/6),sin(-pi/6)]; + p2=r*[cos(-3*pi/4),sin(-3*pi/4)]; + Circledata("1",[[0,0],[r,0]]); + Listplot("1",[[0,0],p0]); + Listplot("2",[[0,0],p1]); + Listplot("3",[[0,0],p2]); + Partcrv("1",p1,p0,"cr1"); + Enclosing("1",["sg2","part1","Invert(sg1)"],[[0,0]]); + Partcrv("2",p2,p1,"cr1"); + Enclosing("2",["sg3","part2","Invert(sg2)"],[[0,0]]); + Dotfilldata("1",["i"],[["en1"]]); + Dotfilldata("2",["i"],[["en2"]],[0.1]); +\end{verbatim} + +\vspace{\baselineskip} +\hypertarget{shade}{} +\item[関数] Shade(("名前"), プロットデータのリスト , options) +\item[機能] 閉曲線で囲まれた領域を塗りつぶす。 +\item[説明] 第１引数には，閉曲線を与える曲線分のプロットデータ名を並べる。 + +デフォルトでは，Joincrvsを使って閉曲線を作っている。ただし，プロットデータのリストに +"Invert()"が入っていれば，Enclosingを使う。 + +optionの Color は，Cinderellaの画面上での描画色をリストで与える。濃さを指定したい場合は色名やRGBではなくCMYKにする。 + +optionsには，他に，「Enclosingを使うか（''Enc=y/n'')」，Enclosingのときの開始点，描画色 がある。 + +複数のShadeを使うときは，名前をつける。 + +\vspace{\baselineskip} +【例】$y=2\sin x$のグラフと直線$y=1$ とで囲まれた部分に黒0.2の濃さで色を塗る。 +\begin{verbatim} + Setax([7,"nw"]); + Plotdata("1","2*sin(x)","x",["Num=100"]); + Lineplot("1",[[0,1],[1,1]]); + Enclosing("1",["ln1","Invert(gr1)"],[[2,1],"nodisp"]); + Shade(["en1"],["Color=[0,0,0,0.2]"]); \end{verbatim} -で漸近線が描かれなくなる。\\ +\begin{center} \input{Fig/shade} \end{center} - 例：ガウス記号 [$x$] で表される関数のグラフは，不連続な階段状になる。この関数は天井関数 floor()であるので， +正弦曲線と直線の交点は簡単に計算できるので，次のように Partcrv() で部分曲線を求め，Enclosingで閉曲線を求めずにShadeを使ってもよい。 \begin{verbatim} - Plotdata("1","floor(x)","x",["Num=100","Dis=0.9"]); + Plotdata("1","2*sin(x)","x",["Num=100"]); + Lineplot("1",[[0,1],[1,1]]); + Partcrv("1",[5*pi/6,1],[13*pi/6,1],"gr1"); + Shade(["ln1","Invert(part1)"],[[2.5,1],"Color=0.2*[1,0,0,1]"]); \end{verbatim} -できれいに描ける。\\ - \input{Fig/plotdata5}\\ - 関数に文字係数がついており，文字係数の値を変化させながらグラフを描くには，Assign を使う。\\ - \\ - 例：直線 $y=bx-b^2$ の係数$b$を変化させて描き，包絡線をうかびあがらせる。 +\vspace{\baselineskip} +【例】2つの放物線で囲まれた部分を赤で塗る。 \begin{verbatim} - repeat(50,t, - cb=t/5-5; - Plotdata(text(t),Assign("b*x-b\verb|^|2","b",cb),"x");\\ - ); + Plotdata("1","x^2-1","x=[-3,3]"); + Plotdata("2","x^2/2","x=[-3,3]"); + Shade(["gr2","Invert(gr1)"],[[-1.5,1],"Color=[1,0,0]","alpha->0.4"]); \end{verbatim} - \\ - \input{Fig/assign}\\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +ここで，\verb|alpha->0.4| は画面上の色濃度指定。 + +\vspace{\baselineskip} +\begin{center} \input{Fig/shade01} \end{center} + +%\vspace{\baselineskip} +【例】同心円をリング状に塗る。 + + 下図右のように，同心円をリング状に塗るが，円2つだけでは閉曲線はできない。そこで，左図のように，円の描き始めを線分で結んで閉曲線を作る。このとき，向きを考えて，Joincrvsで結ぶように，''Enc=n''をつける。線分は非表示にしたいので，\verb|"nodisp"|オプションをつけておく。なお，点Aを適当な位置に作図しておく。 -\hypertarget{pointdata}{} -\item[関数] Pointdata(name , 点リスト , optionss) -\item[機能] 点を作ってScilabに点のリスト Pointdata(list)を出力する。 -\item[説明] 点データを作成する。この点は，幾何要素ではない。プロットデータの頭部は pt\\ - 例：\verb|Pointdata("1",[[1,2],[-2,3]]);|\\ - ２つの点データを作る。Cinderellaの描画面では緑の点で表示される。\\ - \verb|Pointdata("1",[A,B]);|\\ - 作図した点A,Bについて，点データを作る。\\ - Cinderellaの描画面上では既存の点A,Bに緑の点が重なって表示される。\\ - \verb|Pointdata("1",A,["size=4"]);|\\ - Aの位置に大きさ４で点を作る。Ptsize(Setpt) の項を参照のこと。\\ - \verb|Pointdata("1",[A,B],[0]);|\\ - 点データを作り，TeXにオプション0（白抜き）で描く\\ - \verb|Pointdata("1",[[3,4],[5,6]],["notex"]);|\\ - 点データを作るが，TeXには描かない\\ - \verb|Pointdata("1",[A,B],["nodisp"]);|\\ - 点データを作らない．（戻り値として返す）\\ - - 生成されるリストは，座標のリストがネストした形になっている。\\ - その内容は，println()を用いてコンソールに表示することができる。たとえば - \begin{verbatim} - Pointdata("1",[[1,2],[3,4],[6,2]]); - println(pt1); -\end{verbatim} - で，コンソールに次のように表示される。 \begin{verbatim} - generate pointdata pt1 - [[[1,2]],[[3,4]],[[6,2]]] + r1=2; + r2=1.5; + Circledata("1",[A,A+[r1,0]]); + Circledata("2",[A,A+[r2,0]]); + Listplot("1",[A+[r1,0],A+[r2,0]],["nodisp"]); + Shade(["cr1","sg1","Invert(cr2)","Invert(sg1)"],["Enc=n","Color=green"]); \end{verbatim} - ネストされたリストは，Cindyscriptの flatten() 関数を利用して平滑化（ネストを解除）することにより，Listplot()で利用することができる。\\ - \\ - 例：\verb|Ptsize(3);|\\ - \verb|Pointdata("1",[[1,2],[3,4],[6,2]]);|\\ - \verb|Listplot("1",flatten(pt1));|\\ - これで，節点を明示した折れ線が描ける。（下図左）\\ - \verb|Listplot("1",[[1,2],[3,4],[6,2]]);|\\ - では線分のみが描かれる。（下図右）\\ - \input{Fig/pointdata}\\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\begin{center} \input{Fig/greenring} \end{center} -\hypertarget{polygonplot}{} -\item[関数] Polygonplot(name , 点リスト , 整数,optionss) -\item[機能] ２点を指定して正多角形を描く。 -\item[説明] 円に内接する正多角形を描き，頂点の幾何点を作る。\\ - 例：\verb|Polygonplot("1",[A,B],12);|\\ - 点Aを中心とし，半径ABの円周上に，点Bからスタートして正十二角形の頂点B1〜B11を反時計回りに作り，これを結んだ正多角形を描く。頂点は幾何点。\\ - 整数でない数を指定した場合は，きちんと閉じない折れ線が描かれる。\\ +その他，\hyperlink{joincrvs}{Joincrvs() の例}も参照のこと +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\hypertarget{putintersect}{} -\item[関数] Putintersect(点名 , PD1 ,PD2,[No] ) -\item[機能] ２曲線の交点を作る -\item[説明] ２曲線はプロットデータ名で指定する。指定した点名で交点を作る。この点は幾何点。\\ - 交点が２つ以上ある場合でも，描画範囲にそのうち１つだけが存在するなら，その点となる。描画範囲に２つ以上の交点がある場合は，それらのうちいずれかになる。このとき，コンソールに交点の座標のリストと，「Choose point number 」というガイドが表示される。引数のNoとして，その番号を指定すると，その点が採用される。\\ - この関数で作成されるのは幾何点だけなので，\TeX の図に点として明示するためにはPointdata()で書き出す必要がある。\\ - 次の例は，３次曲線と直線の交点を３つとも取ったものである。 -\begin{verbatim} - Plotdata("1","x^3-4*x","x",["Num=200"]); - Plotdata("2","1/2*x+1","x"); - Putintersect("P","gr1","gr2",1); - Putintersect("Q","gr1","gr2",2); - Putintersect("R","gr1","gr2",3); - Pointdata("1",[P,Q,R],["size=4"]); -\end{verbatim} - \\ - \input{Fig/putintersect}\\ - \\ - 交点が存在しない場合は，「No intersect point」がコンソールに表示される。\\ - ２曲線の交点を作るのに，\hyperlink{crosspoint}{Crosspoint()} 関数を用いることもできる。\\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\vspace{\baselineskip} +\hypertarget{reflectdata}{} +\item[関数] Reflectdata(name , プロットデータ , 対称点または対称軸,options) +\item[機能] プロットデータの鏡映を作成 +\item[説明] プロットデータを指定された点または軸に関して対称移動する。 + 対称点は座標または，点の識別名。ただし，対称点を座標で示すときは要素がひとつのリストにする。 + + 対称軸はリスト[ 点1, 点2 ] で指定。 -\hypertarget{putpoint}{} -\item[関数] Putpoint(点名 , 座標１ ,座標２ ) -\item[機能] 点を作る -\item[説明] 識別名が点名の点を，既存でなければ座標１に作る。既存ならば座標２に移動する。Texには出力されない。\\ +\vspace{\baselineskip} +【例】中心A , 半径ABの円を描き，そのプロットデータを用いて鏡映を描く。 -例：(1,1) に固定点Aを作る。 この点は動かすことができない。\\ - \verb|Putpoint("A",[1,1]);|\\ - (1,1)に自由点を作る。\\ - \verb|Putpoint("A",[1,1],[A.x,A.y]);|\\ - この点は座標２の効果により，自由点となり，ドラッグして動かすことができる。\\ +点Cに関して対称な円を実線 -実際には，Cinderellaの作図ツールで点を取り，インスペクタで名前を変更すればよいわけだが，この形でとればスクリプトの可読性が増す意味がある。\\ -注）点名は半角アルファベットとする。数字や漢字でもCinderellaでは点ができるが，Scilabでエラーとなる。\\ +点(-1,2)に関して対称な円を太い実線 -\hypertarget{putonline}{} -\item[関数] PutonLine(点名 , 座標１ ,座標２ ) -\item[機能] 直線上に点を作る -\item[説明] 座標１，座標２を通る直線上に点名の点を作る。できた点は直線に対してインシデントとなる。\\ -例 点A,Bを通る直線上に点Pをとる。\\ - \verb|PutonSeg("P",A,P);|\\ +直線DEに関して対称な円を破線 -\hypertarget{putonseg}{} -\item[関数] PutonSeg(点名 , 座標１ ,座標２ ) -\item[機能] 線分上に点を作る -\item[説明] 座標１，座標２を通る線分上に点名の点を作る。できた点は線分に対してインシデントとなる。\\ -例 点A,Bを通る線分上に点Pをとる。\\ - \verb|PutonSeg("P",A,P);|\\ - -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} - -\hypertarget{reflextpoint}{} -\item[関数] Reflectpoint(点，対称点または対称軸) -\item[機能] 点の鏡映を作成 -\item[説明] 点を指定された点または軸に関して対称移動する。対称軸は[ 点1, 点2 ]で指定\\ - \\ -例：ＣはBに関してAと対称な点\\ - Ｄは点(2,3)に関してAと対称な点\\ - Eは点(1,0) に関して (-1,1) と対称な点\\ - Fは直線CEに関してAと対称な点\\ -\begin{verbatim} - C.xy=Reflectpoint(A,B); - D.xy=Reflectpoint(A,[[2,3]]); - E.xy=Reflectpoint([-1,1],[[1,0]]); - F.xy=Reflectpoint(A,[C,E]); - Lineplot([C,E],["do"]); -\end{verbatim} - \\ - \input{Fig/reflectpoint}\\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\begin{verbatim} + Circledata([A,B]); + Reflectdata("1","crAB",[C]); + Reflectdata("2","crAB",[[-1,2]],["dr,2"]); + Reflectdata("3","crAB",[D,E],["da"]); +\end{verbatim} +\vspace{\baselineskip} + \begin{center} \input{Fig/reflectdata} \end{center} + +%\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\vspace{\baselineskip} +\hypertarget{rotatedata}{} +\item[関数] Rotatedata(name , プロットデータ ，角度 , [中心 , options]) +\item[機能] プロットデータの位置を回転する +\item[説明] 図形を，中心で示された点の周りに回転する。角度は弧度法で与える + + 中心とoptionsはまとめてリストで与える。 -\hypertarget{rotatepoint}{} -\item[関数] Rotatepoint(点 ，角度 , 中心) -\item[機能] 点の位置を回転する -\item[説明] 点を，中心で示された点の周りに回転する。角度は弧度法で与える\\ \begin{spacing}{1.5} -例：点CはAを，Ｂに関して$\dfrac{2}{3}\pi $だけ回転した点\\ - 点Dは点(5,2)を，Ｂに関して$\dfrac{\pi}{3}$ だけ回転した点\\ - 点Eは点(3,0)をAに関して $-\dfrac{\pi}{4} $だけ回転した点 +【例】中心A , 半径ABの円を描き，次のように回転して線種を変えて描く。 + + 点Cを中心に$\dfrac{\pi}{2} $，点(1,5)を中心に$\dfrac{\pi}{3}$ ， 点Dを中心に $-\dfrac{\pi}{3} $ \end{spacing} \begin{verbatim} - C.xy=Rotatepoint(A,2*pi/3,B); - D.xy=Rotatepoint((5,2),pi/3,B); - E.xy=Rotatepoint([3,0],-pi/4,A); + Circledata([A,B]); + Rotatedata("1","crAB",pi/2,[C]); + Rotatedata("2","crAB",pi/3,[[1,5],"dr,2"]); + Rotatedata("3","crAB",-pi/3,[D,"da"]); \end{verbatim} - \\ - \input{Fig/rotatepoint}\\ - \\ -%\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\vspace{\baselineskip} +\begin{center}\scalebox{0.9}{ \input{Fig/rotatedata} }\end{center} + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\hypertarget{rulerscale}{} -\item[関数] Rulerscale(始点 ，横軸目盛 , 縦軸目盛) -\item[機能] 目盛を打つ -\item[説明] 始点の位置を縦横の起点として目盛りを打つ。\\ - 目盛はリストで与える。\\ - ["r",a,b,c] の形式では，aからbまでc間隔で目盛を打つ。\\ - ["f",n1,"str",n2,"str",・・] の形式では，nと"str"がセットで，nの位置に"str"を書く。ただし，位置はCinderellaの描画面の原点を0とする。\\ - Framedata() または Framedata2() とともに用いると矩形に目盛を打つことができる。\\ - \\ -例：Aを原点に置いた矩形枠を描き，横に0,1,2,3,4,5，縦に d1，d2 の目盛を打つ。 -\begin{verbatim} - Framedata2("1",[A,B]); - Rulerscale(A,["r",0,5,1],["f",1,"d1",3,"d2"]); -\end{verbatim} - \input{Fig/ruler}\\ - \\ +\vspace{\baselineskip} +\hypertarget{scaledata}{} +\item[関数] Scaledata(name , プロットデータ，x方向比率 , y方向比率 , [中心 , options]) +\item[機能] 図形の位置を拡大・縮小する +\item[説明] 図形の位置をプロットデータを用いて指定された比率で拡大・縮小する -\hypertarget{scalepoint}{} -\item[関数] Scalepoint(点，比率ベクトル，中心) -\item[機能] 点の位置を拡大・縮小する -\item[説明] 点を，指定された中心を原点とする座標系で，比率ベクトルの分だけ拡大・縮小した位置に置く。\\ + 比率は [x方向比率 , y方向比率] のリストで与えてもよい。 + + 中心とoptionsはまとめてリストで与える。optionsは線種 + +\vspace{\baselineskip} +【例】点A(2,1)，B(1,1)，C(-1,-1)，D(3,-1) を作図しておく。 -例：点Cを，点Aを原点中心に横に３倍，縦に２倍した位置に置く。\\ - 点Dを，点Aを点B中心に横に３倍，縦に２倍した位置に置く。\\ - 点Fを，点Aを原点中心にベクトル$\overrightarrow{OE} $で示された比率の位置に置く。 + Aを中心とする半径ABの円のプロットデータを作り， + +原点中心に$x$軸方向に3，$y$軸方向に2拡大する。 + +Ｃを中心に$x$軸方向に3，$y$軸方向に2拡大し，実線で太く描く。 + +原点中心にベクトル$\overrightarrow{OD} $だけ拡大し，破線で描く。 \begin{verbatim} - C.xy=Scalepoint(A,[3,2],[0,0]); - D.xy=Scalepoint(A,[3,2],B); - F.xy=Scalepoint(A,E.xy,[0,0]); + Circledata([A,B]); + Scaledata("1","crAB",3,2,[[0,0]]); + Scaledata("2","crAB",3,2,[C,"dr,2"]); + Scaledata("3","crAB",[D.x,D.y],[[0,0],"da"]); \end{verbatim} - \input{Fig/scalepoint}\\ - \\ + \begin{center} \input{Fig/scaledata} \end{center} -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\hypertarget{translatepoint}{} -\item[関数] Translatepoint(点 , 移動ベクトル) -\item[機能] 点を平行移動する -\item[説明] 点を移動ベクトルで示された分だけ平行移動する。\\ -\\ -例：点Cは点Aを$x$軸方向に2 , $y$軸方向に３だけ平行移動した点\\ - 点Dは点Aをベクトル$\overrightarrow{OB} $だけ平行移動した点 +\vspace{\baselineskip} +\hypertarget{translatedata}{} +\item[関数] Translatedata(name , プロットデータ , 移動ベクトル , options) +\item[機能] プロットデータを平行移動する +\item[説明] プロットデータを移動ベクトルで示された分だけ平行移動する。 + +\vspace{\baselineskip} +【例】点A,B,C,Dを作図ツールでとっておく。 + + \verb|Circledata([A,B]);| でできる円（crAB）を + + x軸方向に2，y軸方向に3だけ平行移動して実線で描く。 + +ベクトル$\overrightarrow{OC} $だけ平行移動し，実線で太く描く。 + +ベクトル$\overrightarrow{OD} $だけ平行移動し，破線で描く。 + \begin{verbatim} - C.xy=Translatepoint(A,[2,3]); - D.xy=Translatepoint(A,B.xy); + Circledata([A,B]); + Translatedata("1","crAB",[2,3]); + Translatedata("2","crAB",C,["dr,2"]); + Translatedata("3","crAB",D,["da"]); \end{verbatim} - \\ - \input{Fig/translatepoint} -\end{description} - \\ +\vspace{\baselineskip} + \begin{center} \input{Fig/translatedata} \end{center} -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\newpage -% ＝＝プロットデータの操作＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝ -\subsection{プロットデータの操作} -% 描画関数で作成されたプロットデータを用いて描画をおこなう。なお，本節では，該当する図形のことを「プロットデータ」と表記する場合がある。\\ +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\begin{description} +\vspace{\baselineskip} +\hypertarget{intersectcrvs}{} +\item[関数] Intersectcrvs(プロットデータ1, プロットデータ2) +\item[機能] 2曲線の交点リストを取得する。 +\item[説明] オプションとして，共有点があるかどうかを判断するための限界値があるが，通常は使わない。 -\hypertarget{changestyple}{} -\item[関数] Changestyle(PDリスト, optionss) -\item[機能] 描画オプションを変更する -\item[説明] 複数の図形の描画オプションを一括して変更する。\\ +\vspace{\baselineskip} +【例】円と曲線の交点をP,Qとする。 -例：線分AB，円ABの線を破線にして\TeX に書き出さないようにする。\\ - \verb|Changestyle(["sgAB","crAB"],["da","notex"]);|\\ - \\ +\begin{layer}{150}{0} +\putnotese{80}{5}{ \input{Fig/Intersectcrvs1}} +\end{layer} -\hypertarget{enclosing}{} -\item[関数] Enclosing(name , PDリスト , [位置，方向，数式]) -\item[機能] 複数の曲線から閉曲線を描く。 -\item[説明] 引数の位置，方向，数式は，複数点の情報を[ ]内にまとめて -記入できる。以下は一例。 \begin{verbatim} - Circledata([A,B],["do"]); - Scaledata("1","crAB",1.5,1/1.5,["do"]); - Scaledata("2","crAB",1/1.5,1.5,["do"]); - Tmp1=Intersectcrvs(sc2,crAB); - Putpoint("C",Tmp1\_1); - Enclosing("1",["sc2","crAB","sc2","Invert(sc1)"],[C]); - Hatchdata("1","i",[["en1"]],["dr,0.5"]); -\end{verbatim} - \input{Fig/enclosing} + Plotdata("1", "sin(x)", "x", ["Num=100"]); + Circledata([A, B]); + tmp=Intersectcrvs("gr1","crAB"); + P.xy=tmp_1; + Q.xy=tmp_2; + \end{verbatim} -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} - \\ +この関数は，交点のデータのリストを返すので，tmp＝[ [ -0.37, -0.36 ], [ 2.13, 0.85 ] ] のように値が返ってくる。交点の順序は PD1, PD2 の順序と曲線の向きによって決まる。曲線の向きは，$y=f(x)$のグラフではx座標が増加する向きで，パラメーター表示曲線ではパラメータの増加する向き。また，PD1 上から探し始めて PD2 との交点を拾っていく。 -\hypertarget{addgraph}{} -\item[関数] AddGraph(name ,プロットデータのリスト,option) -\item[機能] 複数のプロットデータをまとめる -\item[説明] 複数のプロットデータをまとめて扱う。たとえば，円と，円周上の点の２つのプロットデータをまとめて扱えば，スライダを用いたり動画にするときに，個々に移動や回転をしなくてすむ。Joincrvs()では，プロットデータをつなげて１つのプロットデータにするが，AddGraph()では，プロットデータをリスト化して扱うという違いがある。\\ - プロットデータのリストは，プロットデータ名を文字列化して渡す。たとえば，円のプロットデータが cr1 のとき，"cr1" とする。\\ - \\ -例：サイクロイドの図を描く。 -\begin{verbatim} - Setpt(3); - Circledata("1",[[0,1],[0,0]]); - Pointdata("1",[0,0]); - AddGraph("1",["[pt1]","cr1"],["nodisp"]); - nn=32; - forall(1..nn, - t=2*pi/nn*#; - Rotatedata(text(#),"ad1",-t,[[0,1],"nodisp"]); - Translatedata(text(#),"rt"+text(#),[t,0],["dr,0.3"]); - ); -\end{verbatim} +交点がひとつの場合も tmp＝[ [ 2.45, 0.63 ] ] と2重のリストに入っているので，点として取出すには \verb|P.xy=tmp_1; | とする。 -\begin{center} -\input{Fig/addgraph} -\end{center} - ここで，AddGraph()の引数で与えるプロットデータのリストで，点のプロットデータ pt1 を"[pt1]" としていることに注意。円のプロットデータが，点の座標のリストであるのに対し，点のプロットデータは一つの座標だけなので，このようにしてリスト化して渡す。\\ - \\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} - \\ +\vspace{\baselineskip} +注）交点の算出は，数式処理によるのではなく，プロットデータからの数値探索のアルゴリズムによっている。 -\hypertarget{hatchdata}{} -\item[関数] Hatchdata(name , 方向リスト , プロットデータ , optionss) -\item[機能] 閉曲線の内部に斜線を引く。 -\item[説明] 引数は，曲線名，内部外部のパターンを与える''i''，''o''の文字列，閉曲線を与える曲線分と領域の内部を定める方向のリストとオプション。\\ - Scilabでハッチデータを作成して読み込む。同じ名前のハッチデータがすでにある場合，"m"をつけるとハッチデータを強制的に更新することができる。\\ - \\ -例：円の内部。(下図左) +\vspace{\baselineskip} +\hypertarget{intersectcrvspp}{} +\item[関数] IntersectcrvsPp(プロットデータ1, プロットデータ2) +\item[機能] 2曲線の交点のパラメータリストを取得する。 +\item[説明] 2曲線の交点の座標とパラメータのリストを返す。 + +Intersectcrvs() との違いは，パラメータがあるかどうかである。 + +\vspace{\baselineskip} +【例】放物線と直線の交点のパラメータを求める。 + +2点A(-1,1),B(2.4) を作図しておく。 \begin{verbatim} - Circledata([A,B],["dr"]); - Hatchdata("1",["i"],[["crAB"]],["dr,0.7","out"]); + Plotdata("1","x^2","x"); + Lineplot([A,B]); + p1=Intersectcrvs("gr1","lnAB"); + p2=IntersectcrvsPp("gr1","lnAB"); + println("p1="+p1); + println("p2="+p2); \end{verbatim} +とすると，コンソールには +\begin{verbatim} + p1=[[-1,1],[2,4]] + p2=[[[-1,1],17.68,1],[[2,4],42.66,1]] +\end{verbatim} +と表示される。 +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\vspace{\baselineskip} +\hypertarget{nearestpt}{} +\item[関数] Nearestpt(PD1，PD2) +\item[機能] 2曲線に対し，最も近い点とそのパラメータ，距離のリストを返す +\item[説明] 戻り値は，それぞれの曲線上の点の座標とプロットデータ中の位置，その距離からなるリスト。 + +\vspace{\baselineskip} +【例】2つの放物線上の点の最短距離とその位置を求める。 + +点A,Bを作図ツールでとっておく。 + +\begin{layer}{150}{0} +\putnotese{80}{5}{ \input{Fig/nearestpt}} +\end{layer} -例：３つの閉曲線の内側・外側のパターンが同一である領域（下図右） \begin{verbatim} - Circledata([A,B],["dr"]); - Paramplot("1","[4*cos(t),2*sin(t)]","t=[0,2*pi]"); - Paramplot("2","[2*cos(t),4*sin(t)]","t=[0,2*pi]"); - Hatchdata("1",["ioi"],[["crAB"],["gp1"],["gp2"]],["dr,0.7","out"]); - Hatchdata("2",["iio"],[["crAB"],["gp1"],["gp2"]],["dr,0.7","out"]); + Plotdata("1", "x^2+2", "x=[-2,2]"); + Plotdata("2", "-(x-2)^2+1","x=[0,4]"); + plist=Nearestpt("gr1","gr2"); + A.xy=plist_1; + B.xy=plist_3; + Listplot([A,B],["do"]); + Ptsize(2); + Drwpt([A,B]); + Letter([A,"n2w","A",B,"s2e","B",(A+B)/2,"e",text(plist_5)]); \end{verbatim} - \\ - \input{Fig/hatch1} \input{Fig/hatch2} -\newpage -例：複数のパターンに分かれた領域。 +ここで plistに代入されたリストは次のようになっている。 + +\hspace{10mm} [[0.4,2.16],31,[1.58,0.82],20.73,1.78] + +なお，距離 1.78 は小数点以下第3位を四捨五入して表示されている。 + +\vspace{\baselineskip} +\hypertarget{nearestptcrv}{} +\item[関数] Nearestptcrv(座標, プロットデータ) +\item[機能] 点に最も近いプロットデータの点を求める +\item[説明] 第１引数の座標に最も近い曲線プロットデータ上の点の座標を返す。 + +\vspace{\baselineskip} +【例】点(3,0)に最も近い $y=x^2$ 上の点を求める。 + +点Aは(3,0)に，点Bは適当な位置に作図しておき，次のスクリプトを実行すると点Bが求める点となる。 + +\begin{layer}{150}{0} +\putnotese{80}{0}{ \input{Fig/Nearestpt1}} +\end{layer} + \begin{verbatim} - Plotdata("1","2*sin(x)","x=[-pi,3*pi]",["Num=100"]); - Listplot([A,B]); - Listplot([A,C]); - io="out"; - Hatchdata("1",["ii"],[["sAB","n"],["gr1","s"]],["dr,0.7",io]); - Hatchdata("2",["ii"],[["sAC","s"],["gr1","n"]],["dr,0.7",io]); + Plotdata("1", "x^2", "x"); + B.xy=Nearestptcrv(A.xy,"gr1"); + Listplot([A,B],["do"]); + Ptsize(2); + Pointdata("1",[A,B]); + Letter([A,"ne","A",B,"nw","B"]); \end{verbatim} -\begin{center} -\input{Fig/hatch3} -\end{center} -複数領域の斜線塗の場合，それらの領域をまとめて出力するか， -まとめてCinderellaに読み込む場合が多く，そのような場合には -4行目のような指定の仕方もある。\\ +注）第１引数は座標なので，\verb|A| ではなく \verb|A.xy| としなければならない。 + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\vspace{\baselineskip} +\hypertarget{numptcrv}{} +\item[関数] Numptcrv (プロットデータ) +\item[機能] プロットデータの個数を返す +\item[説明] Cindyscript で length(PD)とするのと同じ + +\vspace{\baselineskip} +【例】 Implicit() と Paramplot() でそれぞれ楕円を描いたときのプロットデータの順序を比較する。 + ただし，TeXには書き出さない。 -例：描画範囲とあわせて閉領域となる場合。 \begin{verbatim} - Plotdata("1","2*sin(x)","x=[-pi,3*pi]",["Num=100"]) - Listplot([A,B]); - Listplot([A,C]); - Hatchdata("1",["iio"],[["sAB","s"],["sAC","n"],["gr1","[0,2]"]], - ["dr,0.7","out"]); + Slider("A-C-B",[0,-2],[6,-2]); + Implicitplot("1","x^2+4*y^2=4","x=[-2,2]","y=[-2,2]",["do"]); + Paramplot("1","[2*cos(t)+5,sin(t)]","t=[0,2*pi]",["do","Num=140"]); + println([Numptcrv(imp1),Numptcrv(gp1)]); + n=floor(C.x*2); + repeat(n,s,start->0, + t=s*10+1; + draw(imp1_t,color->hue(s/10)); + draw(gp1_t,color->hue(s/10)); + ); \end{verbatim} + \begin{center} -\input{Fig/hatch4} +\includegraphics[bb=0.00 0.00 305.02 133.01,width=8cm]{Fig/numptcrv.pdf} \end{center} -\newpage +4行目で，２つのプロットデータの個数が同じであることを確かめている。 + +スライダを動かすと，10個おきのプロットデータに対応する点が描かれる。 + +\vspace{\baselineskip} +\hypertarget{paramoncrv}{} +\item[関数] Paramoncrv(点の座標, 曲線の名前) +\item[機能] 曲線上の点のパラメータ値を返す。 +\item[説明] 曲線は折れ線として描かれ，曲線上の各点はこの折れ線の節点を基準としたパラメータ値を持つ。パラメータ値は整数部分が節点の番号，小数部分が節間の位置を表す。 + +\vspace{\baselineskip} +【例】図のような点PからQに至る円周上の5等分点を節点とする折れ線cr1において，$n$番目の線分上の点は$n\leq t\leq n+1$の範囲のパラメータ値を持つ。 + +たとえば，図の点$\mathrm{A}$は2番目の線分上にあり，この値は + +\begin{layer}{150}{0} +\putnotese{80}{0}{ \input{Fig/paramoncrv}} +\end{layer} -例：接線で囲まれた領域の場合。 \begin{verbatim} - Deffun("f(x)",["regional(y)","y=x＾2*(x-3)","y"]); - Plotdata("1","f(x)","x"); - PutonCurve("A",gr1,-1); - coef=Derivative("f(x)","x","A.x"); - Defvar("DC=coef"); - Deffun("g(x)",["regional(y)","y=DC*(x-A.x)+A.y","y"]); - Plotdata("2","g(x)","x"); - Tmp=Intersectcrvs(gr1,gr2); - Partcrv("1",A,Tmp＿3,"gr1"); - Partcrv("2",A,Tmp＿3,"gr2"); - Hatchdata("1",["ii"],[["part1","n"],["part2","s"]],["dr,0.7","out"]); + println(Paramoncrv(A.xy,"cr1")); +\end{verbatim} + +によってコンソールに表示される。（たとえば2.45）。 + +点Aの位置を動かすとパラメータ値は変わる。 + +\vspace{20mm} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + + +\vspace{\baselineskip} +\hypertarget{pointoncrv}{} +\item[関数] Pointoncrv(点のパラメータ値, PD) +\item[機能] 曲線上のパラメータ値を持つ点の座標を返す。 +\item[説明] 曲線（折れ線）上の節点を基準としたパラメータ値により点の位置が定まる。 + +\vspace{\baselineskip} +【例】図のような点$\mathrm{P}$から$\mathrm{Q}$に至る半円周上の5等分点を節点とする折れ線cr1において，パラメータ値$4.5$を持つ点$\mathrm{A}$は4番目の線分の中点である。したがって + +\begin{verbatim} + Circledata("0",[[0,0],[2,0]],["do"]); + Circledata("1",[[0,0],[2,0]],["Num=5","Rng=[0,pi]"]); + tmp=Pointoncurve(4.5,"cr1"); + Pointdata("1",tmp,["Size=3"]); + Letter([tmp,"nw","A",[2,0],"se","P",[-2,0],"sw","Q"]); \end{verbatim} -\begin{center} -\input{Fig/hatch5} -\end{center} - \\ -斜線の向きや間隔を変えることもできる。\\ - -\noindent -%￥Ltab{10mm}{文} -例：円の内部または円と直線で区切られた図形\\ -\verb|Circledata([A,B]);| で円データの名前が crABとなる。これを用いて\\ -\verb|Hatchdata("1",["i"],[["crAB"]]);| -円内に傾き$45^{\circ}$の斜線を引く（下図ha1）\\ -\verb|Hatchdata("2",["i"],[["crAB"]],[-40,2]);| 傾き$-40^{\circ}$，間隔を2倍に（ha2）\\ - （間隔は実数で指定できる）\\ -\verb|Hatchdata("3",["i"],[["crAB"]],["dr,0.5"]);| 線の太さを0.5倍に（ha3）\\ -\verb|Hatchdata("4",["i"],[["crAB"]],[-45,2,"dr,0.5"]);| （ha4）\\ - - \input{Fig/HatchZuKita1.tex} \input{Fig/HatchZuKita2.tex}\\ - 図ha1 図ha2\\ - \input{Fig/HatchZuKita3.tex} \input{Fig/HatchZuKita4.tex}\\ - 図ha3 図ha4\\ - \\ - -この円に直線を加え領域を分ける。\\ - \verb|Lineplot("1",[A,B]);| 直線データの名前は ln1\\ - \verb|Lineplot("2",[A,C]);| 直線データの名前は ln2\\ -円の内部で右上（ln1とln2の北側）（下図ha5）\\ - \verb|Hatchdata("5",["iii"],[["crAB"],["ln1","n"],["ln2","n"]]);|\\ -円の内部で右上と左下（下図ha6）\\ -\verb|Hatchdata("6",["iii","ioo"],[["crAB"],["ln1","n"],["ln2","n"]]);|\\ - - \input{Fig/HatchZuKita5.tex} \input{Fig/HatchZuKita6.tex}\\ - 図ha5 図ha6\\ - \\ -円データcrABを作るが描かなければ境界線が含まれない。（下図ha7）\\ - \verb|Circledata([A,B],["notex"]);|\\ - \verb|Hatchdata("7",["i"],[["crAB"]]);|\\ -境界線を破線で描くと開集合のようになる（下図ha8）\\ - \verb|Circledata([A,B],["da"]);|\\ - \verb|Hatchdata("8",["i"],[["crAB"]]);|\\ - - \input{Fig/HatchZuKita7.tex} \input{Fig/HatchZuKita8.tex}\\ - 図ha7 図ha8\\ - -問題：次図のように上と下で斜線の描き分けをするには？ 答は図の後に\\ - - \input{Fig/HatchZuKita9.tex}\\ - \\ -問題の答：次のように2つのデータを作り両方描く -\begin{verbatim} - Hatchdata("9a",["iii"],[["crAB"],["ln1","n"],["ln2","n"]]); - Hatchdata("9b",["ioo"],[["crAB"],["ln1","n"],["ln2","n"]],[90,2]); -\end{verbatim} - （この答は図ha7と図ha8との関係と同じ） - \\ -\hypertarget{dotfilldata}{} -\item[関数] Dotfilldata(name , 方向リスト , プロットデータ , optionss) -\item[機能] 領域を点で敷き詰める。 -\item[説明] Scilabとデータの授受をおこなって描画する。書式はHatchdata()と同じ\\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} - \\ + +によって，点Aを中点に置くことができる。 -\hypertarget{joincrvs}{} -\item[関数] Joincrvs(name, プロットデータのリスト, options) -\item[機能] 隣接する曲線プロットデータ のリストを繋いで1本の曲線を作る。 -\item[説明] 曲線のリストは隣接する順番で指定する。プロットデータ名の頭部はjoin。\\ -optionsは線種 "dr, n" , "da,m,n" , "do,m,n"\\ - \\ -例：線分$y=x\ (-\sqrt{2} \leq x \leq \sqrt{2})$と半円を繋いで得られる閉曲線を描く。\\ -\begin{verbatim} - Plotdata("1","x","x=[-sqrt(2),sqrt(2)]"); - Putpoint("B",[sqrt(2),sqrt(2)]); - Circledata("2",[A,B],["Rng=[pi/4,pi/4*5]"]); - Joincrvs("3",["gr1","cr2"]); -\end{verbatim} - \\ - \input{Fig/joincrvs.tex} - -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} - \\ -\hypertarget{partcrv}{} -\item[関数] Partcrv(name, A, B, プロットデータ, options) -\item[機能] 曲線プロットデータ上の点A, B の間の部分曲線を描く。 -\item[説明] プロットデータ名の頭部はpart。\\ -optionsは線種 "dr, n" , "da,m,n" , "do,m,n"\\ - -例1：2点A, Bの順序と曲線の向きによって部分曲線が決まる。 -曲線の向きは，$y=f(x)$のグラフではx座標が増加する向き。ここで，PDname="gr1"のように""で囲むことが必要。\\ - \verb|Plotdata("1", "x^2", "x", ["do"]);| （放物線の名前はgr1）\\ - \verb|Partcrv("1", [0,0], [1,1], "gr1");| （部分曲線の名前はpart1）\\ - \verb|Partcrv("2", [1,1], [0,0], "gr1");| （部分曲線の名前はpart2）\\ - -\begin{minipage}{35mm} -\begin{center} -\input{Fig/partcrv1}\\ -part1 の図 -\end{center} -\end{minipage} -\hspace{10mm} -\begin{minipage}{35mm} -\begin{center} -\input{Fig/partcrv2}\\ -part2 の図 -\end{center} -\end{minipage} -\vspace{5mm} +\vspace{\baselineskip} + \begin{center} \scalebox{0.9}{\input{Fig/pointoncrv}} \end{center} + +%\vspace{\baselineskip} +\hypertarget{ptcrv}{} +\item[関数] Ptcrv(n,プロットデータ) +\item[機能] 曲線プロットデータのn 番目の節点を返す +\item[説明] Cindyscript の PD\_n と同じ + +\vspace{\baselineskip} +【例】楕円上の点で分割する。あからじめ必要な点を作図しておく。 -例2：閉曲線の例．パラメータ表示曲線はパラメータの増える向きをもつ。 +\begin{layer}{150}{0} +\putnotese{70}{10}{ \input{Fig/ptcrv}} +\end{layer} \begin{verbatim} - Circledata([A,B], ["do"]); - Plotdata("1", "x^2", "x", ["do"]); - tmp=Intersectcrvs(crAB, gr1); - P.xy=tmp_1; - Q.xy=tmp_2; - Partcrv("1", P, Q, "crAB"); - Partcrv("2", Q, P, "crAB"); + Circledata([O,P],["do","Num=100","notex"]); + Scaledata("1","crOP",4/3,1); + F.xy=[-sqrt(7),0]; + A=Ptcrv(9,sc1); + B=Ptcrv(16,sc1); + Listplot("1",[A,F,B],["da"]); + Partcrv("1",A,B,"sc1",["dr,3"]); + Shade(["part1","sg1"],0.1); + Arrowhead(B,"sc1",[1.5]); + Letter([A,"ne","A",B,"ne","B",F,"s2","F"]); \end{verbatim} -\vspace{5mm} + +%\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\begin{minipage}{45mm} -\begin{center} -\input{Fig/partcrv3}\\ -part1 の図 -\end{center} -\end{minipage} -\hspace{10mm} -\begin{minipage}{45mm} -\begin{center} -\input{Fig/partcrv4}\\ -part2 の図 -\end{center} -\end{minipage} -\\ -\\ +\vspace{\baselineskip} +\hypertarget{ptstart}{} +\item[関数] Ptstart(プロットデータ) , Ptend(プロットデータ) +\item[機能] プロットデータの最初の点，最後の点を取得する。 +\item[説明] プロットデータの最初の点，最後の点の座標を返す。 -例3：放物線$y=x^2$が円で切り取られる部分を描く。 +\vspace{\baselineskip} +【例】定義域を限定したグラフの両端の点を取得し線分ABを引く。 \begin{verbatim} - Circledata([A,B]); - Plotdata("1","x^2","x",["do"]); - tmp3=Intersectcrvs("crAB","gr1"); - Partcrv("2",tmp3_2,tmp3_1,"gr1",["dr,2"]); + Deffun("f(x)",["regional(y)","y=x^2","y"]); + Plotdata("1","f(x)","x",["do"]); + Plotdata("2","f(x)","x=[-1,2]"); + Lineplot("1",[Ptstart(gr2),Ptend(gr2)],["do"]); + Listplot("1",[Ptstart(gr2),Ptend(gr2)]); + Letter([A,"w2","A",B,"e2","B"]); \end{verbatim} -\input{Fig/partcrv} +\vspace{\baselineskip} +\begin{center} \input{Fig/ptstart} \end{center} -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\vspace{\baselineskip} +\hypertarget{readoutdata}{} +\item[関数] ReadOutData(ファイル名） +\item[機能] 外部データをプロットデータとして読み込む +\item[説明] CやRなどで作成したKeTCindy形式のデータファイルを読み込む。 +引数を省略した場合は，Fheadで定義したファイル名のテキストファイルから読み込む。 -\hypertarget{putoncurve}{} -\item[関数] PutonCurve(点の名前, プロットデータ, options) -\item[機能] 曲線上に点を乗せる。 -\item[説明] 点が存在しない場合は新たに作る。すでにその点が存在する場合は，その点の$x$座標を使う。初期値の$x$座標のデフォルトは 0。\\ -optionsは[$x$座標の範囲]。\\ +ファイル名にはコンマで区切ってパスを与えることができる。たとえば， + +\verb|ReadOutData("/datafolder","file.txt"); | + +KeTCindy形式のデータとは + + 変数名// \\ + start// （リストの始まり） \\ + [ , , ], …. // （個々のデータ２か３次元） \\ + … \\ + end// （リストの終わり） \\ + start// （次のリストの始まり） \\ + … \\ + end// \\ + 変数名// \\ + start// \\ + … \\ + end// \\ + +の形式のテキストファイル。 + +\vspace{\baselineskip} +\hypertarget{writeoutdata}{} +\item[関数] WriteOutData(ファイル名,PDリスト） +\item[機能] 外部データに書き出す +\item[説明] プロットデータをKeTCindy形式のデータファイルに書き出す。出力先の 初期設定は作業フォルダ。 + +【例】 放物線と円のプロットデータを書き出す。 -例：アステロイド上の動点P をとる。 \begin{verbatim} - Paramplot("1","[2*cos(t)^3,2*sin(t)^3]","t=[0,2*pi]"); - PutonCurve("P","gp1",[-1,1]); + Plotdata("1", "x^2","x"); + Circledata("1",[[0,0],[1,0]]); + WriteOutData("figdata.txt",["gr1",gr1,"cr1",cr1]); \end{verbatim} -点Pがアステロイド上にでき，この点はドラッグするとアステロイド上を $-1 \leq x\leq 1$ の範囲で動かすことができる。\\ - \input{Fig/putoncurve.tex} +書き出されたファイルの中身は次のようになっている。 - \\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\begin{verbatim} +gr1// +start// +[[-2.68843,7.22765],[-2.51807,6.34067],・・,[-2.00698,4.02798]]// +[[-1.83662,3.37318],[-1.66626,2.77642],・・,[-1.15518,1.33443]]// + 以下，同様にプロットデータが続く +[[5.82965,33.98479]]// +end// +cr1// +start// +[[1,0],[0.99211,0.12533],[0.96858,0.24869],・・,[0.80902,0.58779]]// + 以下，同様にプロットデータが続く +[[0.87631,-0.48175],[0.92978,-0.36812],・・,[1,0]]// +end//// +\end{verbatim} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\hypertarget{reflextdata}{} -\item[関数] Reflectdata(name , プロットデータ , 対称点または対称軸,options) -\item[機能] プロットデータの鏡映を作成 -\item[説明] プロットデータを指定された点または軸に関して対称移動する。\\ - 対称点は座標または，点の識別名。ただし，対称点を座標で示すときは要素がひとつのリストにする。\\ - 対称軸はリスト[ 点1, 点2 ] で指定\\ - optionsは線種\\ -\\ -例：中心A , 半径ABの円を描き，そのプロットデータを用いて，\\ - 点Cに関して対称な円を\\ - 点(-1,2)に関して対称な円を太い実線で\\ - 直線DEに関して対称な円を破線で\\ - それぞれ描く。\\ - 作成されるプロットデータの名称を rf1 ,rf2 ,rf3 とする。 +\vspace{\baselineskip} +\hypertarget{extractdata}{} +\item[関数] Extractdata(データ名,属性） +\item[機能] ReadOutData() で読み込んだデータに属性をつける。 +\item[説明] ReadOutData() で読み込んだデータには，線種などの属性がついていないので，そのままでは表示されない。そこで，この関数により属性をつけて表示する。 \begin{verbatim} - Circledata([A,B]);\\ - Reflectdata("1","crAB",[C]);\\ - Reflectdata("2","crAB",[[-1,2]],["dr,2"]);\\ - Reflectdata("3","crAB",[D,E],["da"]);\\ + ReadOutData("figdata.txt"); + Extractdata("gr1",["da"]); \end{verbatim} - \\ - \input{Fig/reflectdata} -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\end{description} +%\newpage +% ======== 計算 ======================= +\subsection{計算} -\hypertarget{rotatedata}{} -\item[関数] Rotatedata(name , プロットデータ ，角度 , [中心 , options]) -\item[機能] プロットデータの位置を回転する -\item[説明] 図形を，中心で示された点の周りに回転する。角度は弧度法で与える\\ - 中心とoptionsはまとめてリストで与える。optionsは線種\\ +\begin{description} -\begin{spacing}{1.5} -例：中心A , 半径ABの円のプロットデータを描き，\\ - 点Cを中心に$\dfrac{\pi}{2} $だけ回転した円\\ - 点(1,5)を中心に$\dfrac{\pi}{3}$ だけ回転し，線を太くした円\\ - 点Dを中心に $-\dfrac{\pi}{3} $だけ回転し，破線にした円\\ - をそれぞれ描く。\\ - 作成されるプロットデータの名称を rt1 ,rt2 ,rt3 とする。 -\end{spacing} +\hypertarget{derivative}{} +\item[関数] Derivative(関数式 , 変数 , 値) +\item[機能] 関数の微分係数を求める +\item[説明] 関数式で与えられた関数の，「変数＝値」における微分係数を求める。 + +値は，点の座標を用いることができる。点Aのx座標であれば， A.x とする。 + +\vspace{\baselineskip} +【例】3次曲線上の点Aで接線を引く。点A,Bは作図ツールで適当にとっておく。 \begin{verbatim} - Circledata([A,B]);\\ - Rotatedata("1","crAB",pi/2,[C]);\\ - Rotatedata("2","crAB",pi/3,[[1,5],"dr,2"]);\\ - Rotatedata("3","crAB",-pi/3,[D,"da"]);\\ + Deffun("f(x)",["regional(y)","y=x^3-4*x","y"]); + coef=Derivative("f(x)","x",A.x); + A.y=f(A.x); + B.y=coef*(B.x-A.x)+A.y; + Plotdata("1","f(x)","x",["Num=200"]); + Lineplot([A,B]); + Letter([A,"ne","A"]); \end{verbatim} - \\ - \input{Fig/rotatedata} +%\vspace{\baselineskip} + \begin{center} \input{Fig/derivative} \end{center} +%\vspace{\baselineskip} -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\hypertarget{scaledata}{} -\item[関数] Scaledata(name , プロットデータ，x方向比率 , y方向比率 , [中心 , options]) -\item[機能] 図形の位置を拡大・縮小する -\item[説明] 図形の位置をプロットデータを用いて指定された比率で拡大・縮小する\\ - 中心とoptionsはまとめてリストで与える。optionsは線種\\ - -例：中心A,半径ABの円を描いておく。プロットデータ名は crABとなる。\\ - この円を\\ - 原点中心に$x$軸方向に３，$y$軸方向に２だけ平行移動する。\\ - Ｃを中心に$x$軸方向に３，$y$軸方向に２だけ平行移動し，実線で太く描く。\\ - 原点中心にベクトル$\overrightarrow{OD} $だけ平行移動し，破線で描く。 -\begin{verbatim} - Circledata([A,B]); - Scaledata("1","crAB",3,2,[[0,0]]); - Scaledata("2","crAB",3,2,[C,"dr,2"]); - Scaledata("3","crAB",D.x,D.y,[[0,0],"da"]); -\end{verbatim} - \input{Fig/scaledata}\\ - \\ -%\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\hypertarget{shade}{} -\item[関数] Shade(プロットデータのリスト , optionss) -\item[機能] 閉曲線で囲まれた領域を塗りつぶす。 -\item[説明] 第１引数には，閉曲線を与える曲線分のリストを並べる。\\ - optionssは，Cinderellaの画面上での描画色，濃さをリストで与える。\\ +なお，曲線のプロットデータを用いて，微分係数を求めることもできる。 + +書式は，Derivative(PD , 値) で，次のように使う。（上の例と同じ図ができる） -例：$y=2\sin x$のグラフと直線$y=1$（直線ABの一部）とで囲まれた部分に0.5の濃さで色を塗る。 \begin{verbatim} - Setax([7,"nw"]); - Plotdata("1","2*sin(x)","x",["Num=100"]); - Plotdata("2","2*sin(x)","x=[5*pi/6,13*pi/6]",["Num=100"]); - Lineplot("1",[[0,1],[1,1]]); - Listplot("1",[[5*pi/6,1],[13*pi/6,1]]); - Shade(["gr2","sg1"],[0.5]); + Deffun("f(x)",["regional(y)","y=x^3-4*x","y"]); + Plotdata("1","f(x)","x",["Num=200"]); + coef=Derivative("gr1","x="+A.x); + A.y=f(A.x); + B.y=coef*(B.x-A.x)+A.y; + Lineplot([A,B]); + Letter([A,"ne","A"]); \end{verbatim} -\begin{center} -\input{Fig/shade} -\end{center} -例：２つの放物線で囲まれた部分に0.2の濃さで色を塗る。Cinderellaの画面では赤で少し薄く塗る。 +また，曲線の接線については，\hyperlink{tangentplot}{Tangentplot}も参照されたい。 + +%\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\vspace{\baselineskip} +\hypertarget{integrate}{} +\item[関数] integrate(関数式 , 変数$=$範囲 , options) +\item[関数] integrate(PD , 範囲 , options) +\item[機能] 関数式またはプロットデータで与えられた関数（データ）の数値積分の値を求める。 +\item[説明] optionsは次の通り。 + + "Rule=s" ： シンプソン法による。 初期設定は大島ベジェ公式。 + + "Num=数値" ： 分割数の指定。初期値は 100 + +\vspace{\baselineskip} +【例】$f(x)=x^3-2x^2+2$ について，0から3までの定積分の値を求める。 \begin{verbatim} - Plotdata("1","x^2-1","x=[-sqrt(2),sqrt(2)]",["Num=100"]); - Plotdata("2","x^2/2","x=[-sqrt(2),sqrt(2)]",["Num=100"]); - Shade(["gr2","gr1"],[0.2,"Color=[1,0,0]","alpha->0.4"]); + f(x):=x^3-2*x^2+2; + val=Integrate("f(x)","x=[0,3]"); + println(val); //8.25が表示される \end{verbatim} -\begin{center} -\input{Fig/shade01} -\end{center} - -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\newpage -\hypertarget{translatedata}{} -\item[関数] Translatedata(name , プロットデータ , 移動ベクトル , options) -\item[機能] プロットデータを平行移動する -\item[説明] プロットデータを移動ベクトルで示された分だけ平行移動する。\\ - nameはこれによってつくるプロットデータの名称を設定。単なる番号は不可。\\ - optionsは線種\\ -\\ -例：中心A,半径ABの円を描いておく。プロットデータ名は crABとなる。\\ - この円を\\ - x軸方向に２，y軸方向に３だけ平行移動する。\\ - ベクトル$\overrightarrow{OC} $だけ平行移動し，実線で太く描く。\\ - ベクトル$\overrightarrow{OD} $だけ平行移動し，破線で描く。\\ - 作成されるプロットデータの名称を tr1 , tr2 , tr3 とする。 +\vspace{\baselineskip} +【例】上の例と同じ関数をプロットデータで指定する。 \begin{verbatim} - Circledata([A,B]); - Translatedata("tr1","crAB",[2,3]); - Translatedata("tr2","crAB",C,["dr,2"]); - Translatedata("tr3","crAB",D,["da"]); + plotdata("1","x^3-2*x^2+2","x"); + println(Integrate("gr1",[0,3])); \end{verbatim} - \\ - \input{Fig/translatedata} + +\vspace{\baselineskip} +\hypertarget{inversefun}{} +\item[関数] Inversefun(関数 , 範囲 , 値) +\item[機能] 関数の逆関数値を求める +\item[説明] 関数は文字列で，関数式もしくは定義された関数名とする。\\ + 指定された範囲の中で逆関数値を求める。存在しない場合は一方の端点を戻り値とし，コンソールに「not found」と表示される。 + +数式処理ではなく数値探索のアルゴリズムを使っているので，単調関数でない場合は範囲をできるだけ狭くとるとよい。値が複数ある場合は，小さいほうが返される。 + + +\vspace{\baselineskip} +【例】\verb|x=Inversefun("sin(x)","x=[0,pi/2]",0.5);| + +実行すると $x=0.5236$ となる。 +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} \end{description} -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} \newpage -% =============================== -\subsection{微積分など} +%==========値の取得と入出力========================= +\subsection{値の取得と入出力} + + 計算値やプロットデータの値を取得したり，R用とのデータのやりとりをする。 \begin{description} +\hypertarget{bbdata}{} +\item[関数] BBdata(ファイル名,option） +\item[機能] 画像ファイルのサイズを求める +\item[説明] TeX文書において，inputgraphics コマンドで画像を貼り込むときのBBサイズを求める。 +TeX処理系の extractbb を用いて画像ファイルからBBデータを作り，テキストファイルとして作業ディレクトリに書き出す。これを読んで，コンソールに ingludegarphics のコマンドを書き出す。これをそのままコピーすればよい。 なお，bbの値は整数値ではなく，高精細の値を小数点以下2桁に四捨五入して示される。 画像ファイルは，PDFに限らず，PNG，JPGなどでもよい。 + +optionは，幅または高さの指定。 -\hypertarget{derivative}{} -\item[関数] Derivative(関数式 , 変数 , 値) -\item[機能] 関数の微分係数を求める -\item[説明] 関数式で与えられた関数の，「変数＝値」における微分係数を求める。\\ -値は，点の座標を用いることができる。点Aのx座標であれば， A.x とする。\\ - -例：3次曲線上の点Aで接線を引く。点A,Bは作図ツールでとっておく。 -\begin{verbatim} - Deffun("f(x)",["regional(y)","y=x^3-4*x","y"]); - coef=Derivative("f(x)","x",A.x); - A.y=f(A.x); - B.y=coef*(B.x-A.x)+A.y; - Plotdata("1","f(x)","x",["Num=200"]); - Lineplot([A,B]); - Letter([A,"ne","A"]); -\end{verbatim} - \\ - \input{Fig/derivative}\\ - \\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +"w=40mm" で width=40mm が，"h=40mm" で height=40mm が付加される。 -\hypertarget{integrate}{} -\item[関数] integrate(関数式 , 変数 , 範囲 , options) -\item[関数] integrate(PD , 範囲 , options) -\item[機能] 関数式またはプロットデータで与えられた曲線の積分値を求める -\item[説明] 関数式またはプロットデータで与えられた曲線の，指定された範囲の定積分の値を求める。\\ -関数を与えたときのoptionsは次の通り。\\ - "Rule=s" ： シンプソン法による。デフォルトは台形公式。\\ - "R=s"と略記できる。\\ - "Num=数値" ： 分割数の指定。初期値は 100 \\ - 一般にはシンプソン法の方が精度がよいが，そうではない場合もある。\\ - \\ -例：$f(x)=x^3-2x^2+2$ について，0から3までの定積分の値を求める。\\ - CindyScriptでは，guess()関数を用いると，可能な場合は値を分数表記にする。 -\begin{verbatim} - f(x):=x^3-2*x^2+2; - println(guess(Integrate("f(x)","x",[0,3],["Num=200"]))); - println(guess(Integrate("f(x)","x",[0,3],["Num=5","Rule=s"]))); -\end{verbatim} -を実行すると，コンソールに結果が表示される。シンプソン法では 33/4 と表示される。 -整関数の場合，シンプソン法では分割数がかなり少なくても高い精度が得られる。\\ -整関数でない場合，分割数を区間幅の10の整数倍にするとよい精度になる。\\ -たとえば，$f(x)=\sqrt{x} $の場合，区間が [2,9] であれば，Num=100 よりも Num=70 の方が精度がよい。\\ - \\ - プロットデータを与えたときは，アルゴリズムが異なるので上記オプションは無効。\\ -例：上の例と同じ関数をプロットデータで指定する。 -\begin{verbatim} - plotdata("1","x^3-2*x^2+2","x"); - println(Integrate("gr1",[0,3])); -\end{verbatim} - \\ - プロットデータで与える方法は，Rを利用して正規分布曲線を描いたときなどに記述が楽になる。\hyperlink{plotdatar}{PlotdataR()} の項を参照のこと。\\ - \\ - -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\newpage -\hypertarget{invesefun}{} -\item[関数] Inversefun(関数 , 範囲 , 値) -\item[機能] 関数の逆関数値を求める -\item[説明] 関数は文字列で，関数式もしくは定義された関数名とする。\\ - 指定された範囲の中で逆関数値を求める。存在しない場合は一方の端点を戻り値とし，コンソールに「not found」と表示される。\\ - 数式処理ではなく数値探索のアルゴリズムを使っているので，単調関数でない場合は範囲をできるだけ狭くとるとよい。値が複数ある場合は，小さいほうが返される。\\ - -例：\verb|x=Inversefun("sin(x)","x=[0,pi/2]",0.5);|\\ - 実行すると $x=\dfrac{\pi}{6}$ となる。 -\begin{verbatim} - Deffun("f(x)", ["regional(y)","y=sin(x)","y"]); - x=Inversefun("f(x)","x=[0,pi/2]",0.5); -\end{verbatim} - でも同じ結果が返される。\\ - \verb|x=Inversefun("f(x)","x=[pi/3,pi]",0.97);|\\ - は区間設定が不適切で正しい結果が得られない。\\ - \\ -例：アステロイド上に点Pをとり，Pの$x$座標から，逆関数値$t$を求めて接線を引く。\\ - できた点Pはドラッグしてアステロイド上を動かすことができる。 -\begin{verbatim} - Deffun("fx(t)", ["regional(x)","x=2*cos(t)^3","x"]); - Deffun("fy(t)", ["regional(y)","y=2*sin(t)^3","y"]); - Paramplot("1","[fx(t),fy(t)]","t=[0,2*pi]"); - PutonCurve("P",gp1,1); - if(P.y>=0,range="t=[0,pi]",range="t=[pi,2*pi]"); - t0=Inversefun("fx(t)",range,P.x); - dx=Derivative("fx(t)","t",t0); dy=Derivative("fy(t)","t",t0); - Putpoint("Q",[0,0],P.xy+[dx,dy]); - Lineplot([P,Q]); - Drawpoint(P); - Letter(P,"ne","P"); -\end{verbatim} - \input{Fig/inversefun} +\vspace{\baselineskip} +【例】 + +\vspace{\baselineskip} +\includegraphics[bb=0.00 0.00 562.03 124.01,width=10cm]{Fig/bbdata.pdf} + + +\vspace{\baselineskip} +\hypertarget{cindyname}{} +\item[関数] Cindyname() +\item[機能] 作図中のファイル名を取得する。 +\item[説明] たとえば，現在作図しているファイル名が 「polygon.cdy」のとき，"polygon" を返す。 + +\vspace{\baselineskip} +\hypertarget{crossprod}{} +\item[関数] Crossprod(リスト，リスト) +\item[機能] 2つのベクトルの外積を求める。 +\item[説明] Cindyscriptの組み込み関数 cross(リスト，リスト)と同じ。 + +\vspace{\baselineskip} +【例】\verb|Crossprod([1,0,0],[1,1,1]);| + + 結果は [0,-1,1]\\ + +\vspace{\baselineskip} +\hypertarget{dotprod}{} +\item[関数] Dotprod(リスト，リスト) +\item[機能] 2つのベクトルの内積を求める。 +\item[説明] Cindyscriptでは，積の演算で内積が求められる。 + +\vspace{\baselineskip} + 【例】\verb|Dotprod([1,2,3],[1,-1,1]);| + + 結果は 2 + + [1,2,3]*[1,-1,1] でも同じ結果を得る。 + +\vspace{\baselineskip} +\hypertarget{findarea}{} +\item[関数] Findarea(プロットデータ) +\item[機能] プロットデータで囲まれる部分の面積を求める。 +\item[説明] 閉曲線をなすプロットデータで囲まれる部分の面積を求める。大島のベジェ公式を用いている。 + +\vspace{\baselineskip} +【例】楕円の面積を求めて表示する。 +\begin{verbatim} + Paramplot("1","[3*cos(t),2*sin(t)]","t=[0,2*pi]"); + area=Findarea("gp1"); + println(Sprintf(area,6)); +\end{verbatim} + +コンソールに面積 18.849536 が表示される。 + +\vspace{\baselineskip} +\hypertarget{findlength}{} +\item[関数] Findlength(プロットデータ) +\item[機能] プロットデータの曲線の長さを求める。 +\item[説明] プロットデータが描く曲線の長さを求める。大島のベジェ公式を用いている。 + +\vspace{\baselineskip} +【例】円周の長さを求めて表示する。 +\begin{verbatim} + Circledata("1",[[0,0],[2,0]]); + len=Findlength("cr1"); + println(Sprintf(len,6)); +\end{verbatim} + +コンソールに 12.558097 が表示される。 + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} \end{description} \newpage -%=================================== +%==============作表===================== \subsection{作表} \begin{description} \hypertarget{tabledata}{} -\item[関数] Tabledata(name , 縦横データ, 除外線 , options) -\item[機能] 表の枠を作成し，表のデータlist を返す -\item[説明] Cinderellaの描画面上に左下を原点とする表を作成する。\\ - 他の関数との引数の整合性，\ketpic のコマンドとの整合性などから，先頭にnameの引数をつけるが，実際にはあまり利用しないので，空文字""でもよい。\\ - optionsは線種と"notex"など，および "Rng=n"。\\ - "Rng=n" をつけると，NE,SWによる出力領域指定が有効になる。つけない場合は，表の部分だけが出力される。\\ - 縦横データには，次の２通りの書式がある。\\ - \\ -(1) 横のセル数 , 縦のセル数 , 表の横幅 , 表の縦幅 を指定する。\\ - 例： \verb|Tabledata("",4,5,80,50,[]);|\\ -(2) 横と縦の幅を指定したリストを使う\\ - 例： \verb|Yoko=[20,20,20,20];|\\ - \verb|Tate=[10,10,10,10,10];|\\ - \verb|Tabledata("",Yoko,Tate,[]);|\\ - 上の２つのスクリプトは同じ表を作成する。幅はCinderellaの描画面の0.1を単位とする。\\ - 作成された表には，行，列の制御点がつく。画面上では，横罫線の番号 r0,r1,・・・ 縦罫線の番号 c1,c2,・・・と見ることもできる。また，縦幅，横幅が数字で示される。ただし，これらは\TeX には出力されない。\\ - また，作表はCinderellaの描画面上では座標平面上に置かれるが，\TeX への出力は座標平面上には置かないことが多いので，座標軸は非表示としている。\\ - -\includegraphics[bb=0 0 807 499 , width=6cm]{Fig/table01.png} → -\input{Fig/table02}\\ - - 表のサイズ，行幅，列幅は，作成後にそれぞれの制御点をドラッグすることにより任意に変えることができる。\\ - - 除外線は，除外するセルの罫線を，rとc で位置指定する。\\ - 横罫線の場合，横罫線の番号，範囲（から，まで）\\ - 縦罫線の場合，縦罫線の番号，範囲（から，まで）\\ -とする。\\ - - 例：\verb|Rmv=["r1c0c1","c3r0r1","c3r3r5","r4c2c4"];|\\ - \verb|Tabledata("",4,5,80,50,Rmv);|\\ - で，次の表ができる。\\ - \\ - \includegraphics[bb=0 0 784 503 , width=6cm]{Fig/table03.png}\\ - 除外する罫線がない場合は，空リストとする。\\ - - 例：\verb|Tabledata("",Yoko,Tate,[]);|\\ -\\ - Tabledata()関数は，制御点r0,r1,・・・,c0,c1,・・・ がなければ新しく作り，すでに存在する場合はそのままとする。したがって，一度表を作成したのち，行数・列数を修正して作り直す場合は，一度既存の点を消去する必要がある。そのためには，「すべての点を選択する」ツールをクリックして点を消去するのがよい。クリックすると，消去後すぐに新規作成される。(誤って「すべての要素のを選択する」を選ばないこと)\\ - 他の点が描画されている場合は，表の部分だけドラッグで選択するか，表示メニューの「式による表示」で一覧表を出して，制御点を選択して消去する。\\ - ただし，行数，列数が多すぎた場合は，必ずしも作り直す必要はない。Settable() 関数により，実際に書き出す表の範囲を指定できる。\\ +\item[関数] Tabledata(name , 縦横データ, 除外線 , options) +\item[機能] 表の枠を作成し，表のデータlist を返す +\item[説明] Cinderellaの描画面上に左下を原点とする表を作成する。 + +他の関数との引数の整合性，\ketpic のコマンドとの整合性などから，先頭にnameの引数をつけるが，実際にはあまり利用しないので，空文字""でもよい。 + +除外線がない場合は空リストを指定する。（必須） + +optionsは線種と"notex"など，および "Rng=n"。 + +"Rng=n" をつけると，NE,SWによる出力領域指定が有効になり，NE,SWをドラッグして出力領域を変更できる。（初期状態は，表の右上と左下）つけない場合は，表の部分だけが出力される。 + +縦横データには，次の2通りの書式がある。いずれも同じ表を作成する。 + +\vspace{\baselineskip} +(1) 横のセル数 , 縦のセル数 , 表の横幅 , 表の縦幅 を指定する。除外線なし。 + +\begin{verbatim} + Tabledata("",4,5,80,50,[]); +\end{verbatim} + +(2) 横と縦の幅を指定したリストを使う +\begin{verbatim} + Yoko=[20,20,20,20]; + Tate=[10,10,10,10,10]; + Tabledata("",Yoko,Tate,[]); + \end{verbatim} + +幅はCinderellaの描画面の0.1を単位とする。 + +作成された表には，行，列の制御点がつく。画面上では，横罫線の番号 r0,r1,・・・ 縦罫線の番号 c0,c1,・・・と見ることもできる。また，縦幅，横幅が数字で示される。ただし，これらは\TeX には出力されない。 +また，作表はCinderellaの描画面上では座標平面上に置かれるが，\TeX への出力は座標平面上には置かないことが多いので，座標軸は非表示としている。 + +\hspace{25mm} 描画面 \hspace{45mm} TeX + +\hspace{5mm}\includegraphics[bb=0 0 403.52 249.51 , width=5cm]{Fig/table01.pdf} \hspace{10mm} \input{Fig/table02} + -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + 表のサイズ・行幅・列幅は，作成後にそれぞれの制御点をドラッグすることにより任意に変えることができる。 +\vspace{\baselineskip} +除外線は，除外するセルの罫線を，rとc で位置指定する。 + +\hspace{10mm} 横罫線の場合，横罫線の番号，範囲（から，まで） + +\hspace{10mm} 縦罫線の場合，縦罫線の番号，範囲（から，まで） + +とする。 + +\vspace{\baselineskip} +【例】4つの罫線を非表示にする +\begin{verbatim} + Rmv=["r1c0c1","c3r0r1","c3r3r5","r4c2c4"]; + Tabledata("",4,5,80,50,Rmv); +\end{verbatim} + +で，次の表ができる。 + +\vspace{\baselineskip} +\hspace{20mm} \includegraphics[bb=0 0 392.02 251.51 , width=6cm]{Fig/table03.pdf} + +\vspace{\baselineskip} +＜補足＞ + +Tabledata()関数は，制御点r0,r1,・・・,c0,c1,・・・ がなければ新しく作り，すでに存在する場合はそのままとする。したがって，一度表を作成したのち，行数・列数を修正して作り直す場合は，一度既存の点を消去する必要がある。そのためには，「すべての点を選択する」ツールをクリックして点を消去するのがよい。クリックすると，消去後すぐに新規作成される。(誤って「すべての要素を選択する」を選ばないこと) + +他の点が描画されている場合は，表の部分だけドラッグで選択するか，表示メニューの「式による表示」で一覧表を出して，制御点を選択して消去する。 + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\vspace{\baselineskip} \hypertarget{tabledatalight}{} -\item[関数] Tabledatalight(name , 縦横データ, 除外線 , options) -\item[機能] 幾何点を持たない表の枠を作成し，表のデータlist を返す -\item[説明] Tabledata()がCinderellaの幾何点を生成するのに対し，こちらは幾何点を生成しない。\\ - 幾何点を作成しないメリットは，スクリプトだけで縦横幅を変更できること。デメリットはインタラクティブな微調整ができないこと。\\ - optionとして，ラベルのスキップ値（スキップするところは表示されない）を指定することができる。ただし，ラベルはCinderellaの画面上だけの問題。\\ - \\ - 例： \verb|Yoko=[20,20,20,20];|\\ - \verb|Tate=[10,10,10,10,10];|\\ - \verb|Tabledatalight("",Yoko,Tate,[],[2]);|\\ - とすると，r1,r3,c1,c2 が非表示となる。\\ - - -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} - -%\hypertarget{tableseg}{} -%\item[関数] Tableseg( 罫線リスト, 線種) -%\item[機能] 罫線の線種を指定する -%\item[説明] 罫線リストを与えて線種を指定する\\ -% 罫線リストは，["r1c0c1","r4c2c4"] のように与える。\\ -% 破線・点線にする場合は，Tabledata()であらかじめ除外しておく。\\ - -% 例： \verb|Rmv=["r1c0c1","c3r0r1","c3r3r5","r4c2c4"];|\\ -% \verb|Tabledata("",4,5,80,50,Rmv);|\\ -% \verb|Tableseg(["r1c0c1","r4c2c4"],["da"]);|\\ -% -% \input{Fig/tableseg}\\ -% -% 注）R0,C0,・・は実際には表示されない\\ -% \\ +\item[関数] Tabledatalight(name , 縦横データ, 除外線 , options) +\item[機能] 幾何点を持たない表の枠を作成し，表のデータlist を返す +\item[説明] Tabledata()がCinderellaの幾何点を生成するのに対し，Tabledatalight()は幾何点を生成しない。 + +幾何点を作成しないメリットは，スクリプトだけで全体の縦横幅を変更できること。デメリットはインタラクティブな微調整ができないこと。 + +optionとして，ラベルのスキップ値（スキップするところは表示されない）を指定することができる。ただし，ラベルはCinderellaの画面上だけの問題。 + +\vspace{\baselineskip} + 【例】１つおきにスキップして，r1,r3,c1,c2 を非表示とする。 +\begin{verbatim} + Yoko=[20,20,20,20]; + Tate=[10,10,10,10,10]; + Tabledatalight("",Yoko,Tate,[],[2]); +\end{verbatim} + +\vspace{\baselineskip} \hypertarget{changetablestyle}{} -\item[関数] ChangeTablestyle(罫線リスト, 変更オプション) -\item[機能] Table の罫線の描画オプションを変更 -\item[説明] 罫線の部分的に指定して描画オプションを変更できる。\\ - \\ -例：\verb|ChangeTablestyle(["r0c0c3"],["da"]);| \\ - の実行により、r0の位置の横線がc0からc3まで破線に変わる。\\ - \verb|ChangeTablestyle(["c1r0r2"],["da"]);|\\ - の実行により、c1の位置の縦線がr0からr2まで破線に変わる。\\ - \\ +\item[関数] ChangeTablestyle(罫線リスト, 変更オプション) +\item[機能] Table の罫線の描画オプションを変更 +\item[説明] 罫線の部分的に指定して描画オプションを変更できる。 + +\vspace{\baselineskip} +【例】 + +\verb|Tabledatalight("",[10,20,10,20],[10,10,10],[]);|\\ +\verb|ChangeTablestyle(["r1c0c4"],["da"]);|\\ +\verb|ChangeTablestyle(["r2c0c2","c1r0r3"],["nodisp"]);| + +\vspace{\baselineskip} +\hspace{20mm}\includegraphics[bb=0.00 0.00 324.00 174.00,width=50mm]{Fig/changetable.pdf} + +\vspace{\baselineskip} \hypertarget{findcell}{} -\item[関数] Findcell(列番号, 行番号) -\item[機能] セルの情報list（中心，横幅／２，縦幅／２）を返す -\item[説明] 列番号，行番号は左上のセルを１列１行として数える。 \\ +\item[関数] Findcell(列番号, 行番号) +\item[機能] セルの情報list（中心，横幅／2，縦幅／2）を返す +\item[説明] 列番号，行番号は左上のセルを１列１行として数える。 -例：\verb|Tabledata(4,5,80,50,[]);|\\ - \verb|println(Findcell(tb,2,1));|\\ - とすると，２列１行のセルの中心の座標と横幅の半分，縦幅の半分の値がリストとしてコンソールに表示される。結果は [[3,4.5],1,0.5]\\ +\vspace{\baselineskip} +【例】\verb|Tabledata(4,5,80,50,[]);| -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + \verb|println(Findcell(tb,2,1));| + + とすると，2列１行のセルの中心の座標と横幅の半分，縦幅の半分の値がリストとしてコンソールに表示される。結果は [[3,4.5],1,0.5] +\vspace{\baselineskip} \hypertarget{putcell}{} -\item[関数] Putcell (列番号, 行番号, 位置, 文字データ) -\item[機能] セルに文字列を入れる -\item[説明] 複数のセルにまたぐ位置指定の場合，列番号，行番号は，セル左上と右下の制御点の名称で指定する。\\ - 位置は c, r, l, t, b （中央center , 右right , 左left , 上top , 下bottom ）\\ - 位置の例を以下に示す。 -\begin{verbatim} - Tabledata("",5,2,100,40,["c1r1r2","c4r1r2"]); - Putcell(1,1,"c","A"); - Putcell(2,1,"r","B"); - Putcell(3,1,"l","C"); - Putcell(4,1,"t","D"); - Putcell(5,1,"b","E"); - Putcell(c0r1,c2r2,"c","F"); - Putcell(c2r1,c3r2,"lb","G"); - Putcell(c3r1,c5r2,"rt","H"); -\end{verbatim} - \\ - \input{Fig/putcell}\\ - ※R0,C0,・・は実際には表示されない\\ - -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\item[関数] Putcell (列番号, 行番号, 位置, 文字データ) +\item[機能] セルに文字列を入れる +\item[説明] 複数のセルにまたぐ位置指定の場合，列番号，行番号は，セル左上と右下の制御点の名称で指定する。 -\hypertarget{putcol}{} -\item[関数] PutcoL (列番号, 文字位置，文字列リスト) -\item[機能] １列に順に文字を書き入れる -\item[説明] 列番号で指定した列に，第１行から順に文字列リストの文字を書き入れる\\ - 数の場合はダブルクウォートでくくらなくてもよい。\\ - セルを飛ばす場合は，ヌル文字列 "" を書く。\\ +位置は c, r, l, t, b （中央center , 右right , 左left , 上top , 下bottom ） + +位置の例を以下に示す。 +\begin{verbatim} + Tabledata("",5,2,100,40,["c1r1r2","c4r1r2"]); + Putcell(1,1,"c","A"); + Putcell(2,1,"r","B"); + Putcell(3,1,"l","C"); + Putcell(4,1,"t","D"); + Putcell(5,1,"b","E"); + Putcell("c0r1","c2r2","c","F"); + Putcell("c2r1","c3r2","lb","G"); + Putcell("c3r1","c5r2","rt","H"); +\end{verbatim} +\vspace{\baselineskip} + \begin{center} \input{Fig/putcell} \end{center} + + ※r0,c0,・・は画面に表示される番号 +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\vspace{\baselineskip} +\hypertarget{putcol}{} +\item[関数] PutcoL (列番号, 文字位置，文字列リスト) +\item[機能] １列に順に文字を書き入れる +\item[説明] 列番号で指定した列に，第１行から順に文字列リストの文字を書き入れる\\ + 数の場合はダブルクウォートでくくらなくてもよい。 + + セルを飛ばす場合は，ヌル文字列 "" を書く。 + +\vspace{\baselineskip} \hypertarget{putcolexpr}{} -\item[関数] PutcoLexpr (列番号, 文字位置，文字列リスト) -\item[機能] １列に順に文字を書き入れる -\item[説明] 文字列に\TeX 書式を使うことができる\\ +\item[関数] PutcoLexpr (列番号, 文字位置，文字列リスト) +\item[機能] １列に順に文字を書き入れる +\item[説明] 文字列に\TeX 書式を使うことができる +\vspace{\baselineskip} \hypertarget{putrow}{} -\item[関数] Putrow (行番号, 文字位置，文字列リスト) -\item[機能] １行に順に文字を書き入れる -\item[説明] 行番号で指定した行に，第１列から順に文字列リストの文字を書き入れる。\\ +\item[関数] Putrow (行番号, 文字位置，文字列リスト) +\item[機能] １行に順に文字を書き入れる +\item[説明] 行番号で指定した行に，第１列から順に文字列リストの文字を書き入れる。 +\vspace{\baselineskip} \hypertarget{putrowexpr}{} -\item[関数] Putrowexpr (行番号, 文字位置，文字列リスト) -\item[機能] １行に順に文字を書き入れる -\item[説明] 文字列に\TeX 書式を使うことができる\\ +\item[関数] Putrowexpr (行番号, 文字位置，文字列リスト) +\item[機能] １行に順に文字を書き入れる +\item[説明] 文字列に\TeX 書式を使うことができる 文字を入れる例を示す。 \begin{verbatim} - Tabledata("",5,3,100,45,["c1r1r2","r1c2c3","r2c2c3"]); - PutcoL(3,"c",["A","B","C"]); - PutcoLexpr(4,"l",["x^2","y=\sqrt{x^3}"]); - Putrow(1,"c",[1,"二"]); - Putrowexpr(3,"c",["","\frac{\pi}{2}","","","\sum{x^2}"]); + Tabledata("",5,3,100,45,["c1r1r2","r1c2c3","r2c2c3"]); + PutcoL(3,"c",["A","B","C"]); + PutcoLexpr(4,"l",["x^2","y=\sqrt{x^3}"]); + Putrow(1,"c",[1,"二"]); + Putrowexpr(3,"c",["","\frac{\pi}{2}","","","\sum{x^2}"]); \end{verbatim} + \vspace{\baselineskip} + \begin{center} \input{Fig/putcol} \end{center} - \input{Fig/putcol}\\ + ※ r0,c0,・・は画面に表示される番号。 - ※ R0,C0,・・は実際には表示されない\\ - また，この例では，C4列の罫線を，制御点C4をドラッグすることにより\\ - 右にずらしている。\\ -\\ +グラフや文を入れた表の作成例 -グラフや文を入れた表の作成例\\ - - PutcoLexpr(),Putrowexpr() では，数式だけでなく，一般の\TeX の文を入れることができる。\\ - また，グラフの位置を適当に合わせて描画することにより，表のセルの中にグラフを入れることができる。\\ - - 例：２次関数のグラフと２次方程式の判別式の関係\\ - セルの中にグラフを描く例。実際には，セルの位置にグラフを描いているだけ。 -\begin{verbatim} - Tabledata("",3,3,120,90,["r1c0c3","r2c0c3"],["dr,2"]); - ChangeTablestyle(["r1c0c3"],["dr"]); - ChangeTablestyle(["r2c0c3"],["da"]); - Plotdata("1","(x-2)^2+1.5","x=[0.5,3.5]"); - Plotdata("2","(x-6)^2+2","x=[4.5,7.5]"); - Plotdata("3","(x-10)^2+2.5","x=[8.5,11.5]"); - Listplot([A,B]); - Listplot([C,D]); - Listplot([E,F]); - Putrowexpr(1,"c",["D>0","D=0","D<0"]); - Putrow(2,"c",["2点で交わる","接する","共有点なし"]); - Letter(G,"c","判別式と$x$軸の交点"); -\end{verbatim} - \\ - \input{Fig/tablesample1}\\ -\\ -注意：この例を実行するとわかるが，セルのサイズと文字サイズの関係などにより，Cinderellaの画面上と\TeX への書き出しは必ずしも同一にはならない。\\ - \\ -例：増減表とグラフ\\ - - 関数の増減表とグラフを１つの表の中に入れた例。 -\begin{verbatim} - Tate=[6,6,10,6,10,6,40]; - Yoko=[30,6,6,6]; - Rmv=["c1r0r1","c2r0r1","c3r0r1","c4r0r1","c5r0r1", "r1c6c7","r2c6c7","r3c6c7"]; - Tabledata("",Tate,Yoko,Rmv,["dr"]); - Tlistplot("23d",["c1r2","c2r3"]); - Tlistplot("23u",["c1r3","c2r2"]); - Putrowexpr(2,"c",["x",0,"\cdots","\tfrac{1}{4}","\cdots",4]); - Putrowexpr(3,"c",["y`","","-",0,"+"]); - Putrowexpr(4,"c",["y",0,"\searrow","-\tfrac{1}{4}","\nearrow",2]); - Putcell(1,1,"l2t2","{\small\begin{minipage}{44mm}$y=x-\sqrt{x}$\\$y`= - \dfrac{2\sqrt{x}-1}{2\sqrt{x}}=0$|より\vspace{1mm}\\\hspace*{2zw}$x= - \dfrac{1}{4}$\vspace{1mm}\\増減表は次のようになる\end{minipage}}" ); - Plotdata("1","x-sqrt(x)","x=[0,3]",["do","notex"]); - Listplot("2",[[0,0],[3,0]],["do","notex"]); - Listplot("3",[[0,-0.5],[0,3]],["do","notex"]); - Translatedata("1","gr1",[4.9,1],["dr"]); - Translatedata("2","sg2",[4.9,1],["dr"]); - Translatedata("3","sg3",[4.9,1],["dr"]); - Letter(Ptend(tr2),"e1","\small{$x$}"); - Letter(Ptend(tr3),"n1","\small{$y$}"); - Letter(Ptstart(tr2),"w1","\small O"); - Expr(Ptend(tr1),"nw-2","y=x-\sqrt{x}"); -\end{verbatim} - \input{Fig/tablesample2} - \\ - - 例：凹凸を含めた増減表 -\begin{verbatim} - Tabledata("",8,4,80,40,[]); - Putrowexpr(1,c,["x","\cdots","-1","\cdots","0","\cdots","1","\cdots"]); - Putrowexpr(2,c,["y`","+","+","+","0","-","-","-"]); - Putrowexpr(3,c,["y``","+","0","-","-","-","0","+"]); - Putrowexpr(4,c,["y","\nelarrow","\frac{1}{\sqrt{e}}","\nerarrow", - "1","\serarrow","\frac{1}{\sqrt{e}}","\selarrow"]); -\end{verbatim} - \input{Fig/zogen3}\\ - \\ - ここで，凹凸を示す矢印は，ketpic.sty で定義されているものである。 - - nelarrow,nerarrow,selarrow,serarrow,NELarrow,NERarrow,SELarrow,SERrarrow がある。\\ - - 先頭の ne,se で北東・南東（右上・右下）次の r,l は回転の向き（r：right：反時計回り，l：left：時計回り）の矢印(arrow)と覚えるとよい。 - - 直線系の矢印は\\ - NEarrow,SEarrrow\\ - 少しずつ違うので試されたい。 - - なお，これらの矢印はCindyTeXにはないので，Cinderellaの描画面には表示されない。 - \\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} - -\hypertarget{settable}{} -\item[関数] Settable((左上) , 右下) -\item[機能] 表データを書き出す -\item[説明] 指定された範囲で表の枠線を書き出す。指定しなければ全体が書き出される。\\ - 表の出力範囲は，NE,SWによる描画範囲にかからわず，全体もしくはSettable()で指定した範囲となる。\\ - 位置は，制御点による位置表示で，c2r3 のように指定する。\\ - c,rは小文字で c,r の順。\\ - 左上を省略すると，デフォルトの c0r0 と解釈される。\\ - -例：\verb|Tabledata("",4,5,80,50,[]);|\\ - \verb|repeat(5,s, Putrow(s,"c",[s*4-3,s*4-2,s*4-1,s*4]));|\\ - \verb|Settable(c4r5);|\\ - - ２行目で各セルに数字を入れている。\\ - 左上と右下（罫線C4とR5の交点）を対角とする範囲，すなわち全体を書き出す。\\ - \verb|Settable(c3r4);|\\ - とすると，左上と右下（罫線C3とR4の交点）を対角とする範囲。\\ - 出力するのは罫線だけなので，セルの中身はそのまま表示される。（下図左）\\ - \verb|Settable(c1r1,c3r4);|\\ - とすると，左上（罫線C1とR1の交点）と右下（罫線C3とR4の交点）を対角とする範囲。\\ - 罫線だけなので，セルの中身はそのまま表示される。（下図右）\\ -\\ - \input{Fig/settable1} \input{Fig/settable2}\\ - \\ - \\ + PutcoLexpr(),Putrowexpr() では，数式だけでなく，一般の\TeX の文を入れることができる。 + また，グラフの位置を適当に合わせて描画することにより，表のセルの中にグラフを入れることができる。 + +\vspace{\baselineskip} + 【例】2次関数のグラフと2次方程式の判別式の関係 + +セルの中にグラフを描く例。実際には，セルの位置にグラフを描く。 + +x軸を描くための点A〜Fは作図ツールでとっておく。 + +スクリプトを実行して表ができたら，制御点をドラッグしてサイズを調整し，点A〜Ｆもドラッグして軸と放物線の共有状況を示すようにする。 + +\vspace{\baselineskip} +\begin{verbatim} + Tabledata("",3,3,120,60,[],["dr,2"]); + ChangeTablestyle(["r1c0c3"],["dr"]); + ChangeTablestyle(["r2c0c3"],["da"]); + Plotdata("1","(x-2)^2+0.5","x=[0.5,3.5]"); + Plotdata("2","(x-6)^2+1","x=[4.5,7.5]"); + Plotdata("3","(x-10)^2+1.5","x=[8.5,11.5]"); + Listplot([A,B]); + Listplot([C,D]); + Listplot([E,F]); + Putrowexpr(1,"c",["D>0","D=0","D<0"]); + Putrow(2,"c",["2点で交わる","接する","共有点なし"]); +\end{verbatim} + +\vspace{\baselineskip} + \begin{center}\scalebox{0.9}{ \input{Fig/tablesample1}} \end{center} + + +\vspace{\baselineskip} +【例】増減表とグラフ + + 関数の増減表とグラフを１つの表の中に入れた例。 +\begin{verbatim} + Tate=[6,6,10,6,10,6,40]; + Yoko=[30,6,6,6]; + Rmv=["c1r0r1","c2r0r1","c3r0r1","c4r0r1","c5r0r1", "r1c6c7", + "r2c6c7","r3c6c7"]; + Tabledata("",Tate,Yoko,Rmv,["dr"]) + Tlistplot("23d",["c1r2","c2r3"]); + Tlistplot("23u",["c1r3","c2r2"]); + Putrowexpr(2,"c",["x",0,"\cdots","\tfrac{1}{4}","\cdots",4]); + Putrowexpr(3,"c",["y`","","-",0,"+"]); + Putrowexpr(4,"c",["y",0,"\searrow","-\tfrac{1}{4}","\nearrow",2]); + Putcell(1,1,"l2t2","{\small\begin{minipage}{44mm}$y=x-\sqrt{x}$\\$y`= + \dfrac{2\sqrt{x}-1}{2\sqrt{x}}=0$|より\vspace{1mm}\\\hspace*{2zw}$x= + \dfrac{1}{4}$\vspace{1mm}\\増減表は次のようになる\end{minipage}}" ); + Plotdata("1","x-sqrt(x)","x=[0,3]",["do","notex"]); + Listplot("2",[[0,0],[3,0]],["do","notex"]); + Listplot("3",[[0,-0.5],[0,3]],["do","notex"]); + Translatedata("1","gr1",[4.9,1],["dr"]); + Translatedata("2","sg2",[4.9,1],["dr"]); + Translatedata("3","sg3",[4.9,1],["dr"]); + Letter(Ptend(tr2),"e1","\small{$x$}"); + Letter(Ptend(tr3),"n1","\small{$y$}"); + Letter(Ptstart(tr2),"w1","\small O"); + Expr(Ptend(tr1),"nw-2","y=x-\sqrt{x}"); +\end{verbatim} +\begin{center} \input{Fig/tablesample2} \end{center} + +\vspace{\baselineskip} + 【例】凹凸を含めた増減表 +\begin{verbatim} + Tabledata("",8,4,80,40,[]); + Putrowexpr(1,c,["x","\cdots","-1","\cdots","0","\cdots","1","\cdots"]); + Putrowexpr(2,c,["y`","+","+","+","0","-","-","-"]); + Putrowexpr(3,c,["y``","+","0","-","-","-","0","+"]); + Putrowexpr(4,c,["y","\nelarrow","\frac{1}{\sqrt{e}}","\nerarrow", + "1","\serarrow","\frac{1}{\sqrt{e}}","\selarrow"]); +\end{verbatim} +\begin{center} \input{Fig/zogen3} \end{center} +%\vspace{\baselineskip} +ここで，凹凸を示す矢印は，ketpic.sty で定義されているものである。 + +nelarrow,nerarrow,selarrow,serarrow,NELarrow,NERarrow,SELarrow,SERrarrow がある。先頭の ne,se で北東・南東（右上・右下）次の r,l は回転の向き（r：right：反時計回り，l：left：時計回り）の矢印(arrow)と覚えるとよい。直線系の矢印は NEarrow,SEarrrow。 少しずつ違うので試されたい。 + +なお，これらの矢印はCindyTeXにはないので，Cinderellaの描画面には表示されない。 + +%\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\vspace{\baselineskip} \hypertarget{tgrid}{} -\item[関数] Tgrid(セルラベル) -\item[機能] 表のセルの座標を返す -\item[説明] 指定されたセルの左上の座標を返す。実際には，セルラベルは罫線を示しているので，指定した罫線の交点（格子点）ということもできる。\\ - \\ +\item[関数] Tgrid(セルラベル) +\item[機能] 表のセルの座標を返す +\item[説明] 指定されたセルの左上の座標を返す。実際には，セルラベルは罫線を示しているので，指定した罫線の交点（格子点）ということもできる。 + +\vspace{\baselineskip} \hypertarget{tlistplot}{} -\item[関数] Tlistplot(セルラベル1,セルラベル2) -\item[機能] 指定された２つの格子点を線分で結ぶ -\item[説明] セルに斜線を引くのに用いる。\\ - 例：\verb|Tlistplot(["c0r1","c1r2"]);| - \\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\item[関数] Tlistplot(セルラベル1,セルラベル2) +\item[機能] 指定された2つの格子点を線分で結ぶ +\item[説明] セルに斜線を引くのに用いる。 -\end{description} +\vspace{\baselineskip} +【例】\verb|Tlistplot(["c0r1","c1r2"]);| + +\vspace{\baselineskip} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\newpage +\end{description} -%=================================== -\subsection{値の取得と入出力} +%=================================================== +\subsection{その他} - 計算値やプロットデータの値を取得したり，Scilab用とのデータのやりとりをする。\\ \begin{description} -\hypertarget{crossprod}{} -\item[関数] Crossprod(リスト，リスト) -\item[機能] ２つのベクトルの外積を求める。 -\item[説明] Cindyscriptの組み込み関数 cross(リスト，リスト)と同じ。\\ - 例：\verb|Crossprod([1,0,0],[1,1,1]);|\\ - 結果は [0,-1,1]\\ +%\vspace{\baselineskip} +%\hypertarget{makeshell}{} +%\item[関数] Makeshell(ファイル名) / Makebat(ファイル名) +%\item[機能] Macの場合はシェルファイル，Windowsの場合はバッチファイルを書き出す。 +%\item[説明] 書き出されるファイルについては，figいったんフォルダを空にしてから確かめられたい。 -\hypertarget{dotprod}{} -\item[関数] Dotprod(リスト，リスト) -\item[機能] ２つのベクトルの内積を求める。 -\item[説明] Cindyscriptでは，積の演算で内積が求められる。\\ - 例：\verb|Dotprod([1,2,3],[1,-1,1]);|\\ - 結果は ２\\ - [1,2,3]*[1,-1,1] でも同じ結果を得る。\\ +\hypertarget{assign}{} +\item[関数] Assign(文字列，文字，文字） +\item[機能] 文字列の中のある文字を他の文字で置き換える +\item[説明] 第１引数の文字列中の第2引数の文字を，第3引数の文字で置き換える。 -\hypertarget{findarea}{} -\item[関数] Findarea(プロットデータ) -\item[機能] プロットデータで囲まれる部分の面積を求める。 -\item[説明] 閉曲線をなすプロットデータで囲まれる部分の面積を求める。\\ -例：ベジェ曲線で囲まれた部分の面積を求めて表示する。\\ - \verb|Bezier("1",[A,B,C],[[D],[E,F]]);|\\ - \verb|drawtext([2,1],Findarea("bz1"));|\\ +第3引数が数値の場合，文字列に変換される。 -\hypertarget{findlength}{} -\item[関数] Findlength(プロットデータ) -\item[機能] プロットデータの曲線の長さを求める。 -\item[説明] プロットデータが描く曲線の長さを求める。\\ -例：ベジェ曲線で描いた曲線の長さを求めて表示する。\\ - \verb|Bezier("1",[A,B,C],[[D],[E,F]]);|\\ - \verb|drawtext([2,1],Findlength("bz1"));|\\ +第2引数と，第3引数をリストにして，複数の置き換えをすることができる。 +\vspace{\baselineskip} + 【例】\verb|a*x| を\verb|1.3*x| とした文字列を返す。次のいずれも同じ結果になる。 +\begin{verbatim} + Assign("x^2+a*x","a","1.3"); + Assign("x^2+a*x","a",1.3); +\end{verbatim} -\hypertarget{intersectcrvs}{} -\item[関数] Intersectcrvs(プロットデータ1, プロットデータ2, optionss) -\item[機能] 2曲線の交点リストを取得する。 -\item[説明] オプションは共有点があるかどうかを判断するための限界値\\ -ただし，オプションは通常は使わないので気にしなくてよい。\\ - \\ -例：円と曲線の交点をP,Qとする。 -\begin{verbatim} - Plotdata("1", "sin(x)", "x", ["Num=100"]); - Circledata([A, B]); - tmp=Intersectcrvs(gr1, crAB); - P.xy=tmp_1; - Q.xy=tmp_2; - \end{verbatim} - - リスト内に2交点のデータが tmp＝[ [ $-0.37$, $-0.36$ ], [ 2.13, 0.85 ] ] のように入っている。交点の順序は PD1, PD2 の順序と曲線の向きによって決まる。曲線の向きは，$y=f(x)$のグラフではx座標が増加する向きで，パラメーター表示曲線ではパラメータの増加する向き。また，PD1 上から探し始めて PD2 との交点を拾ってゆく。\\ - 交点がひとつの場合も tmp＝[ [ 2.45, 0.63 ] ] と2重のリストに入っているので，点として取出すには P=tmp\verb|_|1; とする。\\ -\begin{center} -\input{Fig/Intersectcrvs1}\\ -\end{center} +\vspace{\baselineskip} + 【例】直線 $y=bx-b^2$ の係数$b$を変化させて描き，包絡線をうかびあがらせる。 +\begin{verbatim} + repeat(50,t, + cb=t/5-5; + Plotdata(text(t),Assign("b*x-b^2","b",cb),"x"); + ); +\end{verbatim} +%\vspace{\baselineskip} +\begin{center} \input{Fig/assign} \end{center} +\vspace{\baselineskip} + 【例】文字で表された $x$ と $y$ の係数をまとめて数値で置き換える。 +\begin{verbatim} + Assign("a*x^2+b*x",["a",1,"b",2]); +\end{verbatim} -\hypertarget{invert}{} -\item[関数] Invert(PD) -\item[機能] プロットデータの点を逆順にする（reverseと同じ） -\\ +%\vspace{\baselineskip} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\hypertarget{meetcurve}{} -\item[関数] MeetCurve(曲線,x0, y0) -\item[機能] 曲線上の点を返す。 -\item[説明] x座標がx0で，点(x0, y0)に近い曲線上の点を返す。\\ -注）x0, y0 は文字列でもよい。\\ -\hypertarget{lcrd}{} -\item[関数] Lcrd() -\item[機能] 幾何点，リスト点の論理座標を取得する。 -\\ +% =========== commented to com2th() ========== +\begin{comment} -\hypertarget{pcrd}{} -\item[関数] Pcrd() -\item[機能] 幾何点，リスト点の物理（表示）座標を取得する。 -\\ +\vspace{\baselineskip} +\hypertarget{com0th}{} +\item[関数] Com0th(文字列） +\item[機能] RのOpenfileの前に置くコマンド（文字列）を定義する。 +\item[説明] 【例】\verb|Com0th("Setax('a')");| +Openfileの前の部分の先頭に書き出す。これにより， \ketcindy でサポートされていないR版\ketpic のコマンドを利用することができる。 + +\vspace{\baselineskip} +\hypertarget{com1st}{} +\item[関数] Com1st(文字列） +\item[機能] RのOpenfileの前に置くコマンド（文字列）を定義する。 +\item[説明] 【例】\verb|Com1st("Setax('a')");|\\ + これにより， \ketcindy でサポートされていないR版\ketpic のコマンドを利用することができる。 -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\hypertarget{nearestpt}{} -\item[関数] Nearestpt(PD1，PD2) -\item[機能] ２曲線に対し，最も近い点とそのパラメータ，距離のリストを返す -\item[説明] 戻り値は，それぞれの曲線上の点の座標とプロットデータ中の位置，その距離からなるリスト。\\ -例：２つの放物線上の点の最短距離とその位置を求める。点A,Bを作図ツールでとっておく。 -\begin{verbatim} - Plotdata("1", "x^2+2", "x=[-2,2]"); - Plotdata("2", "-(x-2)^2","x=[0,3]"); - plist=Nearestpt("gr2","gr1"); - B.xy=plist_1; - A.xy=plist_3; - Listplot([A,B],["do"]); - Ptsize(4); - Drwpt([A,B]); - Letter([A,"nw","A",B,"n2e","B",(A+B)/2,"e",text(plist_5)]); -\end{verbatim} - \input{Fig/Nearestpt}\\ -\\ -ここで plistに代入されたリストは次の形である。５番目の要素が２点間の距離，すなわち最短距離。\\ - [[1.68,-0.1],29,[0.32,2.1],30,2.59] \\ - \\ -\hypertarget{nearestptcrv}{} -\item[関数] Nearestptcrv(座標, プロットデータ) -\item[機能] 第１引数の座標に最も近い曲線プロットデータ上の点座標を返す -\item[説明] 次に例示する。中心A，半径ABの円と点C,DはCinderellaで作図しておく。 +\vspace{\baselineskip} +\hypertarget{com2nd}{} +\item[関数] Com2nd(文字列） +\item[機能] RのOpenfileのあとに置くコマンド（文字列）を定義する。 + + +\vspace{\baselineskip} +\hypertarget{com2ndpre}{} +\item[関数] Com2ndpre(文字列） +\item[機能] RのOpenfileのあとに置くコマンド（文字列）を定義する。 + +Openfileの直後（グループの先頭に）書き出す。 +\end{comment} + +% =========== ここまで コメント化 ========== + +\hypertarget{colorcode}{} +\item[関数] Colorcode(種別1,種別2, カラーコード) +\item[機能] 種別1から種別2へカラーコードを変換する。戻り値は変換されたコード。 +\item[説明] 種別は，"rgb","cmyk","hsv"のいずれか。 + +\vspace{\baselineskip} +【例】変換例をいくつか示す。 + +RGBの[1,0,0]をCMYKに変換したコードをコンソールに表示する。 \begin{verbatim} - Circledata([A, B]); - Plotdata("1", "x^2", "x"); - pCr=Nearestptcrv(C.xy, "crAB") - pC1=Nearestptcrv(C.xy, "gr1") - pDr=Nearestptcrv(D.xy, "crAB"); - pD1=Nearestptcrv(D.xy, "gr1"); + col=Colorcode("rgb","cmyk",[1,0,0]); + println(col); \end{verbatim} -ぞれぞれ，点C，点D から最も近い曲線上の点を表す。\\ - \\ - \input{Fig/Nearestpt1}\\ - \\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +CMYKの[0,1,1,0]をRGBに変換したコードをコンソールに表示する。 -\hypertarget{numptcrv}{} -\item[関数] Numptcrv (プロットデータ) -\item[機能] 曲線の節点の個数を返す -\item[説明] Cindyscript の length(PD)と同じ\\ - -例： 曲線上のいくつかの点で分割し破線で図示する。\\ -区間$[-1, 2]$に対する2次関数のグラフを描く\\ - \verb|Deffun("f(x)",["regional(y)","y=-x^2+4","y"]);|\\ - \verb|Plotdata("1","f(x)","x=[-1,2]",["Num=200"]);|\\ -曲線の端点を結ぶ直線を描く\\ - \verb|Lineplot("3",[Ptstart(gr1),Ptend(gr1)],["do"]);|\\ -節点の4分の１で曲線を分割して破線を描く\\ - \verb|Lineplot("4",[Ptstart(gr1),Ptcrv(0.25*Numptcrv(gr1),gr1)],["da"]); |\\ -節点の2等分で曲線を分割して破線を描く\\ - \verb|Lineplot("5",[Ptstart(gr1),Ptcrv(0.5*Numptcrv(gr1),gr1)],["da"]); |\\ -節点の4分の3で曲線を分割して破線を描く\\ - \verb|Lineplot("6",[Ptstart(gr1),Ptcrv(0.75*Numptcrv(gr1),gr1)],["da"]);| \\ -曲線上の点Aの接線を引く。 -\begin{verbatim} - coef=Derivative("f(x)","x",G.x); - Defvar("DC=coef"); - Deffun("g(x)",["regional(y)","y=DC*(x-G.x)+G.y","y"]); - Plotdata("2","g(x)","x",["dr,2"]); -\end{verbatim} - \\ -\input{Fig/numptcrv}\\ - -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\begin{verbatim} + col=Colorcode("cmyk","rgb",[0,1,1,0]); + println(col); +\end{verbatim} + +RGBの[1,0,0]をHSVに変換したコードをコンソールに表示する。 -\hypertarget{paramoncrv}{} -\item[関数] Paramoncrv(点の座標, 曲線の名前) -\item[機能] 曲線上の点のパラメータ値を返す。 -\item[説明] 曲線は折れ線として描かれるが，曲線上の各点はこの折れ線の節点を基準としたパラメータ値を持つ。パラメータ値は整数部分が節点の番号，小数部分が節間の位置を表す。\\ - -例：図のような点PからQに至る円周上の5等分点を節点とする折れ線sg1において， -$n$番目の線分上の点は$n\leq t\leq n+1$の範囲のパラメータ値を持つ。\\ -図の点$\mathrm{A}$は2番目の線分上にあり，パラメータ値は2.45である。この値は\\ - \verb|Paramoncrv(A.xy,"sg1");|\\ -によって得られる。\\ - \\ - \input{Fig/paramoncrv}\\ - -\hypertarget{pointcrv}{} -\item[関数] Pointoncrv(点のパラメータ値, PD) -\item[機能] 曲線上のパラメータ値を持つ点の座標を返す。 -\item[説明] 曲線（折れ線）上の節点を基準としたパラメータ値により点の位置が定まる。\\ - -例：図のような点$\mathrm{P}$から$\mathrm{Q}$に至る半円周上の5等分点を節点とする折れ線sg1において，パラメータ値$4.5$を持つ点$\mathrm{A}$は4番目の線分の中点である。したがって\\ - \verb|A.xy=Pointoncrv(4.5,"cr1");|\\ -によって，点Aを中点に置くことができる。\\ - \\ - \input{Fig/pointoncrv} - -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\newpage -\hypertarget{ptcrv}{} -\item[関数] Ptcrv(n,プロットデータ) -\item[機能] 曲線プロットデータのn 番目の節点を返す -\item[説明] Cindyscript の PD\_n と同じ\\ - -例：楕円上の点で分割する。あからじめ必要な点を作図しておく。 -\begin{verbatim} - Circledata([O,P],["do","Num=100","notex"]); - Scaledata("1","crOP",4/3,1); - F.xy=[-sqrt(7),0]; - A=Ptcrv(9,sc1); - B=Ptcrv(16,sc1); - Listplot("1",[A,F,B],["da"]); - Partcrv("1",A,B,"sc1",["dr,3"]); - Shade(["part1","sg1"],0.1); - Arrowhead(B,"sc1",[1.5]); - Letter([A,"ne","A",B,"ne","B",F,"s2","F"]); -\end{verbatim} - \input{Fig/ptcrv} - -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\begin{verbatim} + col=Colorcode("rgb","hsv",[1,0,0]); + println(col); +\end{verbatim} -\hypertarget{ptstart}{} -\item[関数] Ptstart(プロットデータ) , Ptend(プロットデータ) -\item[機能] プロットデータの最初の点，最後の点を取得する。 -\item[説明] プロットデータの最初の点，最後の点の座標を返す。\\ - \\ -例：定義域を限定したグラフの両端の点を取得し線分ABを引く。\\ +\vspace{\baselineskip} +\hypertarget{dqq}{} +\item[関数] Dqq(文字列) +\item[機能] 文字列の前後に\verb|"|をつける。 \begin{verbatim} - Deffun("f(x)",["regional(y)","y=x^2","y"]); - Plotdata("1","f(x)","x=[-1,2]",["dr"]); - Lineplot("2",[Ptstart(gr1),Ptend(gr1)]); + str="abc"; + str2=Dqq(str); + println([str,str2]); \end{verbatim} - \input{Fig/ptstart}\\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} - \\ +\vspace{\baselineskip} +\hypertarget{factorial}{} +\item[関数] Factorial(n) +\item[機能] 正の整数$n$の階乗を計算する。 -\hypertarget{readoutdata}{} -\item[関数] ReadOutData(ファイル名） -\item[機能] 外部データを読み込む -\item[説明] ScilabのWriteOutDataで作ったプロットデータ列のデータファイルを読み込む。\\ -引数を省略した場合は，Fheadで定義したファイル名のテキストファイルから読み込む。 -ファイル名にはコンマで区切ってパスを与えることができる。たとえば，\\ - \verb|ReadOutData("/datafolder","file.txt"); |\\ - \\ - \\ -\hypertarget{sprintf}{} -\item[関数] Sprintf(実数,長さ) -\item[機能] 小数点以下の長さを固定した文字列に変換 -\item[説明] 実数を，小数点n位までの数とした文字列に変換する\\ - \\ -例 Sprintf(pi,2) は 3.14 を返す\\ - Sprintf(pi,7) は 3.1415927 を返す\\ -注）pi は Cindyscriptの予約変数で，円周率を表す。 \\ - -\hypertarget{writetosci}{} -\item[関数] WritetoSci(引数) ,WritetoScibody(引数) -\item[機能] Scilab用のソースファイルに書き出す -\item[説明] ソースファイルへの書き出し方に３つのタイプがある\\ - -・引数なしの場合\\ - Fheadで定義したファイル名に拡張子 .sci を付加して全体を書き出す。\\ - 末尾にコメントアウトした quit() を付加する。\\ -・WritetoSciの引数に次の数を渡す \\ - \verb|WritetoSci(1)|： WritetoSci() と同じ\\ - \verb|WritetoSci(2)|： 全体を書き出し，末尾に quit() を付加する。\\ - \verb|WritetoSci(3)|： WritetoScibody() と同じ。body部分のみを書き出す。\\ -・ファイル名を引数とする\\ - 引数のファイル名で書き出す。ただし，拡張子 .sci をつける必要がある。\\ -・引数を "sh" とする\\ - WritetoSci(2) と同じ。\\ -・\verb|WritetoSci(filename,"sh")|\\ - 引数のファイル名でshell（bat）コマンド用のファイルを書き出す。\\ -・\verb|WritetoSci(数字 ,filename)| は不可（エラーとなる）\\ -\\ +\vspace{\baselineskip} +\hypertarget{norm}{} +\item[関数] Norm(ベクトル), Norm(ベクトル1, ベクトル2) +\item[機能] ベクトル（2つのベクトルの場合は差の大きさ）の大きさを計算する。 + +\vspace{\baselineskip} +\hypertarget{figpdf}{} +\item[関数] Figpdf(option） +\item[機能] 出力枠サイズのPDFを作る。 +\item[説明] \ketcindy では，通常，出力された fig.tex ファイルを閲覧するPDFをA4サイズで作成する。これに対し，Figpdf()を実行すると，出力サイズのPDFを作成する。閲覧用だけではなくワープロなどにに貼り込むときにそのまま使用できる。ただし，そのための親子プロセスを生成して実行するため，次の手続き(1)(2)が必要となる。 -\hypertarget{makeshell}{} -\item[関数] Makeshell(ファイル名) / Makebat(ファイル名) -\item[機能] Macの場合はシェルファイル，Windowsの場合はバッチファイルを書き出す。 -\item[説明] 書き出されるファイルは次の通り。\\ -・書き出される場所とファイル名は， Shellparent / Batparent で指定したもの。\\ -・内容は，Shellchild / Batchild に，子プロセスの引数として Fhead と引数のファイル名を付加したもの。たとえば，Shellchild="sh ketcindy.sh" で，Fhead="fig" , 引数が "fig2tex" であれば +\vspace{\baselineskip} +(1) Setparent(filename)で，出力するPDF用のファイル名を設定する。 + +(2) 出力は，「Parent」のボタンを押す。 + +\vspace{\baselineskip} +たとえば，fig.cdy で作図しているとき， \begin{verbatim} - #!/bin/sh - cd /Users/Hoge/Desktop/KeTCindy - sh ketcindy.sh fig fig2tex - exit 0 + Setparent("pic"); \end{verbatim} -が書き出される。２行目のディレクトリ（フォルダ）名は，Dirwork で指定したもの。\\ -ただし，上記の fig は fig.sci のことだが，fig.sci は出力されないので，別途 WritetoSci(2) で書き出す必要がある。\\ - \\ +とすると，fig.tex を表示した pic.pdf が作成される。pic.pdf が目的のPDF。 + +このファイル名は 作図しているCinderellaのファイル名，または Setfiles() で指定したファイル名とは異なるものにする。 -\hypertarget{textformat}{} -\item[関数] Textformat(数，桁数) -\item[機能] 小数点以下の桁数を指定して数を文字列化する。 -\item[説明] Cindyscriptの組み込み関数にも，format()という同様の関数があるが，こちらは，数のリストにも対応する。\\ - -例：円周率を小数点以下５位までで文字列化する。\\ - \\ - \verb|Textformat(pi,5);|\\ - \\ - 戻り値は，3.14159\\ - \\ -例：円周率と，ネピア数をリストにして，共に小数点以下５位までで文字列化したリストを返す。\\ - \\ - \verb|Textformat([pi,exp(1)],5);|\\ - \\ - 戻り値は，[3.14159,2.71828] \\ - \\ +optionは，マージン（余白）と平行移動量。指定しない場合は 初期設定値。 -\hypertarget{viewtex}{} -\item[関数] Viewtex() -\item[機能] \TeX のソースファイルを書き出す。引数なし。 -\item[説明] グローバル変数Fheadで定義したファイル名に "main" を付加した\TeX のソースファイルとバッチファイル（Macの場合はシェルファイル）を作成する。\\ -Fhead のほか，ディレクトリ指定などのため，次のグローバル変数に必要事項が代入されていることが条件である。\\ - \\ - Dirwork=作業フォルダのパス\\ - Shellparent=親プロセス (kc.sh / kc.bat )を置くディレクトリのパス\\ - Shellchild=子プロセス名\\ - Libname=Scilabのライブラリ ketpicsciL5 へのパス\\ - \\ -たとえば，Fhead="fig" とすると\\ -・図を表示する fig.sci を Dirwork で指定したフォルダにを生成する。(すでにある場合は上書き)\\ -・Dirwork で指定したフォルダに figmain.tex を生成する。（すでにある場合は上書き）\\ - figmain.tex は \TeX のプリアンブルと \verb|begin{document}| を設定したソースファイルで，中には \verb|input{"fig.tex"}| が書かれており，これをコンパイルすれば作成した図を表示することができる。\\ -・親プロセスの生成（すでにある場合は上書き）\\ - ketcindy.sh (Mac) ketcindy.bat(Windows) を子プロセスとして figmain.tex と fig.tex を引数として実行するプロセス kc.sh(Mac) kc.bat (Windows) を作業ディレクトリに生成する。これを実行すると図を表示するPDFファイルが作られる。\\ - 以上の手続きにより，Viewtex() を実行すれば，デスクトップ上に生成された kc.sh / kc.bat を使って，fig.sci の生成から，fig.tex の作成，\TeX のコンパイルまでの一連の操作を自動実行して，図を表示することができることになる。kc.sh / kc.bat の実行は，kc() で行うことができる。\\ - \\ - - \hypertarget{workprocess}{} -\item[関数] Workprocess(） -\item[機能] 作図の経過を取得する -\item[説明] 作図ツールを用いた作図の経過を取得する。\\ - \verb|println(Workproccess());|\\ - とすると，コンソールに作図手順が表示される。\\ +余白は，左右上下の順に4つの数をコンマで区切る。 -\end{description} +平行移動量は，右方向，下方向をリストで与える。 -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\newpage +余白指定と平行移動指定は同時に行うことができる。 -%=================================================== -\subsection{その他} -\begin{description} +\vspace{\baselineskip} +【例】余白の設定 +\begin{tabbing} +1234\=567890123456789012345678901234\=\kill + \> \verb|Figpdf([5,5,10,10]);| \> 左右に5mm，上下10mmの余白\\ + \> \verb|Figpdf([[5,10]]);| \> 右に5mm，下に10mm平行移動して表示\\ + \> \verb|Figpdf([5,8,10,10,[5,-5]]);| \> 左5mm，右8mm，上下10mmの余白，\\ + \> \> 右に5mm，上に5mm平行移動して表示 +\end{tabbing} + +なお，座標軸を表示する場合，右側は最低3mmの余白を設定しないと軸の文字が入らない。 -\hypertarget{assign}{} -\item[関数] Assign(文字列，文字，文字） -\item[機能] 文字列の中のある文字を他の文字で置き換える -\item[説明] 第１引数の文字列中の第２引数の文字を，第３引数の文字で置き換える。\\ - 第３引数が数値の場合，文字列に変換される。\\ - 第２引数と，第３引数をリストにして，複数の置き換えをすることができる。\\ - \\ - 例：a*x を1.3*x とした文字列を返す。次のいずれも同じ結果になる。 -\begin{verbatim} - Assign("x^2+a*x","a","1.3"); - Assign("x^2+a*x","a",1.3); -\end{verbatim} - \\ - 例：直線 $y=bx-b^2$ の係数$b$を変化させて描き，包絡線をうかびあがらせる。 -\begin{verbatim} - repeat(50,t, - cb=t/5-5; - Plotdata(text(t),Assign("b*x-b^2","b",cb),"x"); - ); -\end{verbatim} - \\ - \input{Fig/assign}\\ - \\ - 例：文字で表された $x$ と $y$ の係数をまとめて数値で置き換える。\\ - \verb|Assign("a*x^2+b*x",["a",1,"b",2]);|\\ - \\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\hypertarget{bbdata}{} -\item[関数] BBdata(ファイル名,option） -\item[機能] 画像ファイルのサイズを求める -\item[説明] TeX文書において，inputgraphics コマンドで画像を貼り込むときのBBサイズを求める。\\ - TeX処理系の extractbb を用いて画像ファイルからBBデータを作り，テキストファイルとして作業ディレクトリに書き出す。これを読んで，コンソールに ingludegarphics のコマンドを書き出す。\\ - optionは，幅または高さの指定。\\ - "w=40mm" で width=40mm が，"h=40mm" で height=40mm が付加される。\\ - \\ -例：pic.pdf のサイズを求める。\\ - \verb|BBdata("pic.pdf")|\\ - を実行すると，コンソールに ingludegarphics のコマンド文\\ - \verb|\includegraphics[bb=・・・・]{pic.pdf} |\\ - が表示される。これをそのままコピーすればよい。\\ - なお，bbの値は整数値ではなく，高精細の値を小数点以下2桁に四捨五入して示される。\\ - 画像ファイルは，PDFに限らず，PNG，JPGなどでもよい。\\ - \\ -例：\verb|BBdata("fig.jpg",["h=40mm"]);|\\ - で\\ - \verb|\includegraphics[bb=0.00 0.00 578.16 592.56,height=40mm]{fig.jpg} |\\ - が表示される。\\ - \\ +\vspace{\baselineskip} +\hypertarget{help}{} +\item[関数] Help(文字列） +\item[機能] 関数の使用例を取得する +\item[説明] 文字列で始まる関数の使用例をコンソールに表示する。 -\hypertarget{changework}{} -\item[関数] Changework(パス名） -\item[機能] 作業ディレクトリを指定（変更）する -\item[説明] 作業ディレクトリは，InitializationスロットのKETlibページに Dirwork= で指定されているが，これを変更する。Drawスロットの，Ketinit() の前に記述することにより，Ketlibページの記述を変更しなくてすむ。\\ - これにより，作成したファイルを他の人とやり取りしやすくなる。\\ +\hspace{10mm} \verb|println(Help("L"));| + + のようにすると，コンソールに，次のように「L」で始まる関数の使用例が表示される。 +\begin{verbatim} + Letter([C,"c","Graph of $f(x)$"]); + Letter([C,"c","xy"],["size->30"]); + 文字を書き込む + Letterrot(C,B-A,"AB"); + Letterrot(C,B-A,"t0n5","AB"); + Letterrot(C,B-A,0,5,"AB"); + 傾いた文字を書き込む + ・・・・ +\end{verbatim} -\hypertarget{com0th}{} -\item[関数] Com0th(文字列） -\item[機能] ScilabのOpenfileの前に置くコマンド（文字列）を定義する。 -\item[説明] 例：\verb|Com0th("Setax('a')");|\\ - Openfileの前の部分の先頭に書き出す。これにより， \ketcindy でサポートされていないScilab版\ketpic のコマンドを利用することができる。\\ - \\ -\hypertarget{com1st}{} -\item[関数] Com1st(文字列） -\item[機能] ScilabのOpenfileの前に置くコマンド（文字列）を定義する。 -\item[説明] 例：\verb|Com1st("Setax('a')");|\\ - これにより， \ketcindy でサポートされていないScilab版\ketpic のコマンドを利用することができる。 -\\ -\hypertarget{com2nd}{} -\item[関数] Com2nd(文字列） -\item[機能] ScilabのOpenfileのあとに置くコマンド（文字列）を定義する。 -\\ +\vspace{\baselineskip} +\hypertarget{helpkey}{} +\item[関数] Helpkey(文字列） +\item[機能] 関数の使用例をキーワードで検索する +\item[説明] 文字列に与えたキーワードで関数の使用例を検索し，コンソールに表示する。 -\hypertarget{com2ndpre}{} -\item[関数] Com2ndpre(文字列） -\item[機能] ScilabのOpenfileのあとに置くコマンド（文字列）を定義する。 - Openfileの直後（グループの先頭に）書き出す。\\ +\vspace{\baselineskip} +【例】\verb|Helpkey("直線");| とすると，コンソールに次のように表示される。 +\begin{verbatim} + IntersectsgpL("",[p1,p2],[p3,p4,p5],"draw"); + IntersectsgpL("R","P-Q","A-B-C"); + IntersectsgpL("R","P-Q","A-B-C","put"); + 空間の直線と平面の交点 + Lineplot("1",[[2,1],[3,3]]); + ・・・・ +\end{verbatim} -\hypertarget{figpdf}{} -\item[関数] Figpdf(option） -\item[機能] 出力枠サイズのPDFを作る。 -\item[説明] KeTCindyでは，通常，出力された fig.tex ファイルを閲覧するPDFをA4サイズで作成する。これに対し，Figpdf()を実行すると，出力サイズのPDFを作成する。閲覧用だけではなくワープロなどにに貼り込むときにそのまま使用できるので便利である。ただし，そのための親子プロセスを生成して実行するため，次の手続き(1)(2)が必要となる。\\ -(1) 変数 Texparent を設定する。\\ - これは，出力するPDFのファイル名の指定である。たとえば， -\begin{verbatim} - Fhead="fig"; - Texparent="pic"; -\end{verbatim} - とすると，fig.tex を表示した pic.pdf が作成される。pic.pdf が目的のPDF。\\ - Texparent は Fhead とは異なるものにする。\\ -(2) 出力は，「Parent」のボタンを押す。\\ - \\ -optionは，マージン（余白）と平行移動量。指定しない場合はデフォルト値。\\ -余白は，左右上下の順に４つの数をコンマで区切る。。\\ -平行移動量は，右方向，下方向をリストで与える。\\ -余白指定と平行移動指定は同時に行うことができる。\\ -例：\verb|Figpdf([5,5,10,10]);| 左右に5mm，上下10mmの余白\\ - \verb|Figpdf([5,10]);| 右に5mm，下に10mm平行移動して表示\\ - \verb|Figpdf([5,8,10,10,[5,-5]]);| 左5mm，右8mm，上下10mmの余白，\\ - 右に5mm，上に5mm平行移動して表示\\ -なお，座標軸を表示する場合，右側は最低3mmの余白を設定しないと軸の文字が入らない。\\ +\vspace{\baselineskip} +\hypertarget{indexall}{} +\item[関数] Indexall(str1,str2); +\item[機能] 文字列 str1 から str2 を検索しその位置をすべて返す +\item[説明] Cindyscriptの indexof() の拡張版。indexof() が最初に見つかった位置を返すのに対し，Indexall()は存在する位置をすべてリストにして返す。 + +\vspace{\baselineskip} +【例】str="abcabcabc" から "b"を検索する。 + +\verb|indexof(str,"b")| では，2 が返る。 + +\verb|Indexall(str,"b")| では，[2,5,8]が返る。 + +\vspace{\baselineskip} +\hypertarget{isptselected}{} +\item[関数] Isptselected(点名）または Ptselected(点名) +\item[機能] 点が選択されていれば true,そうでなければ false を返す。 +\item[説明] 点名はリストで与える。引数はなしにすることも可能で，その場合はすべての点が対象。 + +KeTCindyの関数の中には処理に時間がかかるものがある。その場合，点をドラッグするなど，画面上で操作をするとその都度再計算されるために，動きが非常に遅くなる。そこで，ドラッグする点をこの関数で指定すれば，ドラッグしている間は処理されないようにすることができる。 + +\vspace{\baselineskip} +【例】点Aを原点近くにとっておき，次のスクリプトを実行する。 + +\verb| Deffun("f(x)",["regional(y)","y=x^3-2*x","y"]);|\\ +\verb| Plotdata("1","f(x)","x",["Num=100"]);|\\ +\verb| Putoncurve("A","gr1");|\\ +\verb| coef=Derivative("f(x)","x",A.x);|\\ +\verb| Defvar(["coef",coef]);|\\ +\verb| Deffun("g(x)",["regional(y)","y=coef*(x-A.x)+A.y","y"]);|\\ +\verb| Plotdata("2","g(x)","x",["Num=1"]);|\\ +\verb| if(!Ptselected(A),|\\ +\verb| Enclosing("1",["gr2","Invert(gr1)"],[A,"nodisp"]);|\\ +\verb| Hatchdata("1",["i"],[["en1"]]);|\\ +\verb| );| + +\vspace{\baselineskip} +\hspace{5mm} 点Aをドラッグ中（選択状態）\hspace{5mm} 他の点をクリックして選択状態を解除 + +\hspace{10mm}\includegraphics[bb=0.00 0.00 218.01 204.51,width=40mm]{Fig/ptselected01.pdf} +\hspace{10mm}\includegraphics[bb=0.00 0.00 219.01 204.51,width=40mm]{Fig/ptselected02.pdf} + +\vspace{\baselineskip} +\hypertarget{slider}{} +\item[関数] Slider(名称，位置1,位置2) +\item[機能] スライダを作成する +\item[説明] 名称は "A-C-B" の形で，端点をA,B，スライダ点をCとしたスライダを作る。 + +端点A,Bの位置を，位置1，位置2で指定する。 +スライダにより取得したい値は，点Cの座標（たとえば C.x）を利用する。 + +点A,B,Cはあらかじめ作図しておく必要はない。既にある場合はその点を使う。 + +\vspace{\baselineskip} +【例】2つのスライダを用意し，$y=a\sin(x-b)$ のa,b をインタラクティブに変化させる。 + +\verb|Slider("A-C-B",[-5,-2],[5,-2]); | // \verb|C| is movable.\\ +\verb|Slider("D-F-E",[-6,-2],[-6,2]); | // \verb|F| is movable.\\ +\verb|Plotdata("1",Assign("y=a*sin(x-b)",["a",F.y,"b",C.x]),"x"); | + +\vspace{\baselineskip} +\hspace{15mm} +\includegraphics[bb=0.00 0.00 445.02 193.01,height=40mm]{Fig/slider.pdf} + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\vspace{\baselineskip} +\hypertarget{sprintf}{} +\item[関数] Sprintf(実数,長さ) +\item[機能] 小数点以下の長さを固定した文字列に変換 +\item[説明] 実数を，小数点n位までの数とした文字列に変換する + +\vspace{\baselineskip} +【例】円周率 + + Sprintf(pi,2) は 3.14 を返す + + Sprintf(pi,7) は 3.1415927 を返す + +注）pi は Cindyscriptの予約変数で，円周率を表す。\vspace{\baselineskip} + +\vspace{\baselineskip} +\hypertarget{textformat}{} +\item[関数] Textformat(数，桁数) +\item[機能] 小数点以下の桁数を指定して数を文字列化する。 +\item[説明] 第１引数は数のリストでもよい。数のリストの場合は，戻り値は，対応する数値を指定係数にした後，リストを文字列化する。Cindyscriptの組み込み関数にも，format()という同様の関数があるが，format() は文字列のリストを返す。 + +\vspace{\baselineskip} +【例】円周率を小数点以下5位までで文字列化する。 + +\hspace{10mm} \verb|Textformat(pi,5);| +\hspace{10mm} \verb|format(pi,5);| + +戻り値は，いずれも \verb|"3.14159"| + +\vspace{\baselineskip} +【例】第１引数がリストのときの，format() との戻り値の違い。 + +\hspace{10mm} \verb| dt=[1/6,0.5];|\\ +\hspace{10mm} \verb| Textformat(dt,4); | // 戻り値は "[ 0.1667 , 0.5 ]" \\ +\hspace{10mm} \verb| format(dt,4); | // 戻り値は [ "0.1667" , "0.5" ] \\ + +\vspace{\baselineskip} \hypertarget{texcom}{} -\item[関数] Texcom(\TeX コード） -\item[機能] \TeX のコードを書き出す -\item[説明] 任意の\TeX のコードを書き出す\\ - ScilabのTeXcomにそのまま引き渡しているだけ。\\ +\item[関数] Texcom(\TeX コード） +\item[機能] \TeX のコードを書き出す +\item[説明] 任意の\TeX のコードを書き出す +\vspace{\baselineskip} \hypertarget{windispg}{} -\item[関数] Windispg() または Windisp(データのリスト） -\item[機能] 定義されているプロットデータをCinderella画面に黒線で描く -\item[説明] Windispg()は，スクリプトの最後に置くことで，出力される部分だけが黒で描かれるので，出力図を確認することができる。ただし，Letter()関数で表示した点の名称などがCinderellaで作図したラベルと重なって表示されて見にくくなることもある。この関数を実行しなくても出力には影響しない。\\ - Windisp(データのリスト）は，Scilabから \ketcindy 用に出力されたファイルを ReadOutData()関数で読み込んだときに，必要なプロットデータ列だけを表示するのに用いる。\\ - ReadOutData("filename.txt") でデータを読み込むと，そのデータに含まれるプロットデータ列が，コンソールに\\ -Outdata of filename.txt : [Gfn,Gdfn,Gh] \\ -のように表示される。\\ -このうち，GfnとGhだけを表示するのであれば\\ -Windispg([Gfn,Gh]);\\ - とする。引数なしで\\ -Windispg();\\ -とすればすべてのプロットデータ列が表示される。\\ -なお，いずれの場合も，作図したプロットデータも同時に表示される。\\ - 作図した図を全てではなく選択して表示する場合は，それらのプロットデータ名をリストにして引数とする。\\ - たとえば，sg1, gr1, crABが定義されているとき，\\ - \verb|Windispg(["sg1","gr1"]);| +\item[関数] Windispg() または Windisp(データのリスト） +\item[機能] 定義されているプロットデータをCinderella画面に黒線で描く +\item[説明] Windispg()は，スクリプトの最後に置くことで，出力される部分だけが黒で描かれるので，出力図を確認することができる。ただし，Letter()関数で表示した点の名称などがCinderellaで作図したラベルと重なって表示されて見にくくなることもある。この関数を実行しなくても出力には影響しない。 + +Windisp(データのリスト）は，Rから \ketcindy 用に出力されたファイルを ReadOutData()関数で読み込んだときに，必要なプロットデータ列だけを表示するのに用いる。 + +ReadOutData("filename.txt") でデータを読み込むと，そのデータに含まれるプロットデータ列が，コンソールに + +\hspace{10mm}Outdata of filename.txt : [Gfn,Gdfn,Gh] + +のように表示される。 + +このうち，GfnとGhだけを表示するのであれば + +\hspace{10mm}\verb|Windispg([Gfn,Gh]);| + +とする。引数なしで + +\hspace{10mm}\verb|Windispg();| + +とすればすべてのプロットデータ列が表示される。 + +なお，いずれの場合も，作図したプロットデータも同時に表示される。 + +作図した図を全てではなく選択して表示する場合は，それらのプロットデータ名をリストにして引数とする。 + +たとえば，sg1, gr1, crABが定義されているとき， + +\hspace{10mm}\verb|Windispg(["sg1","gr1"]);| + とすれば，sg1,gr1のみが表示される。 - 次の３つの関数は，プロットデータの操作で，単独で用いることもできるが，描画関数，プロットデータの操作関数のオプションに組み込まれているので，特殊な場合を除いてはほとんど利用しないと思われる。\\ -\hypertarget{drwline}{} -\item[関数] Drwline(プロットデータ） -\item[機能] プロットデータ（文字列）を実線で描く -\item[説明] ScilabのDrwlineを書き出す\\ - 例：\verb|Drwline("sABCA,1");|\\ -\\ +%\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\hypertarget{dashline}{} -\item[関数] Dashline(プロットデータ） -\item[機能] プロットデータ（文字列）を破線で描く -\item[説明] ScilabのDashlineを書き出す\\ - 例：\verb|Dashline("sABCA");|\\ -\\ -\hypertarget{dottedline}{} -\item[関数] Dottedline(プロットデータ） -\item[機能] プロットデータ（文字列）を点線で描く -\item[説明] ScilabのDottedlineを書き出す\\ - 例：\verb|Dottedline("sABCA");|\\ - -\hypertarget{helplist}{} -\item[関数] helplist() -\item[機能] ヘルプデータを作成する -\item[説明] 関数の簡単な説明データを作成する。\\ - この関数は，Initialization スロットに書く。\\ - \\ - -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\hypertarget{help}{} -\item[関数] Help(文字列） -\item[機能] 関数の使用例を取得する -\item[説明] 文字列で始まる関数の使用例をコンソールに表示する。\\ - \verb|println(Help("C"));|\\ - のようにすると，コンソールに，次のように「C」で始まる関数の使用例が表示される。 -\begin{verbatim} - CRspline("1",[A,B,C,A]); - ChangeTablestyle(["r0c0c3"],["da"]);\ - Changestyle("sgAB",["da"]); - Changstyle("geoseg3","ax3d"],["notex"]);\ - Circledata([A,B,C]); - Circledata([A,B],["Rng=[0,pi/2]"]);\ - Com2nd("\color[cmyk]{0,0,0,0.5}");\ - Crossprod(vec1,vec2); \\ -\end{verbatim} - - さらに，\\ - \verb|println(Help("Ci"));| とすると -\begin{verbatim} - Circledata([A,B,C]); - Circledata([A,B],["Rng=[0,pi/2]"]); -\end{verbatim} - だけが表示される。\\ - \verb|println(Help("*"));| - とすると，すべての関数の使用例が表示される。\\ - 引数がない場合は，\verb|Helplist(Dirlib,["+","+3d"],"helpJ”);| とみなされる。+はketcindylibの意味。\\ -\\ +\vspace{\baselineskip} +\hypertarget{viewtex}{} +\item[関数] Viewtex() +\item[機能] \TeX のソースファイルを書き出す。引数なし。 +\item[説明] グローバル変数Fheadで定義したファイル名に "main" を付加した\TeX のソースファイルとバッチファイル（Macの場合はシェルファイル）を作成する。 + +\vspace{\baselineskip} +\hypertarget{workprocess}{} +\item[関数] Workprocess(） +\item[機能] 作図の経過を取得する +\item[説明] 作図ツールを用いた作図の経過を取得する。 -\hypertarget{helpkey}{} -\item[関数] Helpkey(文字列） -\item[機能] 関数の使用例をキーワードで検索する -\item[説明] 文字列に与えたキーワードで関数の使用例を検索し，コンソールに表示する。\\ - 例：\verb|Helpkey("直線");| とすると，コンソールに次のように表示される。 -\begin{verbatim} - IntersectsgpL("",[p1,p2],[p3,p4,p5],"draw"); - IntersectsgpL("R","P-Q","A-B-C"); - IntersectsgpL("R","P-Q","A-B-C","put"); - 空間の直線と平面の交点 - Lineplot("1",[[2,1],[3,3]]); - Lineplot([A,B]); - 直線データを作成 - PtonLine("C",pA,pB); - 直線上に点をとる -\end{verbatim} - \\ -\hypertarget{indexall}{} -\item[関数] Indexall(str1,str2); -\item[機能] 文字列 str1 から str2 を検索しその位置をすべて返す -\item[説明] Cindyscriptの indexof() の拡張版。indexof() が最初に見つかった位置を返すのに対し，Indexall()は存在する位置をすべてリストにして返す。\\ - \\ -例：str="abcabcabc" から "b"を検索する。\\ - \verb|indexof(str,"b")| では，2 が返る。\\ - \verb|Indexall(str,"b")| では，[2,5,8]が返る。\\ - \\ - -\hypertarget{ketcindylogo}{} -\item[関数] Ketcindylogo(） -\item[機能] \ketcindy のロゴを書き出す -\item[説明] \ketcindy のロゴを表示する\TeX のコマンド行を書き出す。\\ - 内容は\\ -\verb|\|def\verb|\|ketcindy\{\{K\verb|\|kern-.20em \verb|\|lower.5ex\verb|\|hbox\{E\}\verb|\|kern-.125em\{TCindy\}\}\}" - \\ +\verb|println(Workproccess());| + + とすると，コンソールに作図手順が表示される。 + +\vspace{\baselineskip} \hypertarget{op}{} -\item[関数] Op(n,list or str) -\item[機能] リストまたは文字列から要素を抜き出す -\item[説明] 第２引数のリストまたは文字列のn番目の要素（文字）を返す。\\ -Cindyscriptの アンダーバーの演算子 (list\_n , str\_n) と同様。Silabとの整合性のため追加\\ - \\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\newpage +\item[関数] Op(n,list or str) +\item[機能] リストまたは文字列から要素を抜き出す +\item[説明] 第2引数のリストまたは文字列のn番目の要素（文字）を返す。 + +Cindyscriptの アンダーバーの演算子 (list\_n , str\_n) と同様。 + +\vspace{\baselineskip} +\hypertarget{strsplit}{} +\item[関数] Strsplit(文字列 , 文字) +\item[機能] 文字列を分解する。 +\item[説明] 第１引数の文字列を第2引数の文字の位置で分解したリストを返す。 + +\vspace{\baselineskip} +【例】文字aで区切って分解する。 + +\verb| str="abcadeaf";| \\ +\verb| strL=Strsplit(str,"a"); | // [” ”,”bc”,”de”,”f”] を返す。 + +同様の関数に，Cindyscriptの tokenize(文字列,文字列)がある。tokenize() の第２引数は文字列や，文字のリストでもよい。 + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + \end{description} \newpage -%第11節 他の数式処理ソフトとの連携 ============================= +%第11節 他の数式処理ソフトとの連携 ============================= \section{他の数式処理ソフトなどとの連携} \subsection{Rとの連携} -Rは主に統計解析のためのソフトウェアで， binorm（二項分布），pois（ポアソン），unif（一様分布），chisq（カイ２乗），f（F分布），t（t分布）など，多くの確率分布をサポートしている。\\ -正規分布（normal distribution）では\\ - dnorm 確率密度関数\\ - pnorm 分布関数\\ - qnorm 分布関数の逆関数\\ - rnorm 乱数発生\\ -というように，分布名の頭にd, p, q, r をつけると上記４つの関数が得られる。\\ - 各分布には，自由度などの引数があり，たとえば，平均m, 標準偏差sの正規分布（の密度関数）は dnorm(x, m ,s ) となる。\\ - \\ - KeTCindyでは，kc.bat/shによってコマンドをRに渡し，結果をテキストファイルで受け取る。このとき，Rとのやりとりで，次のようなファイルが作業ディレクトリに作成される。\\ -拡張子 r ：r用のファイル\\ -拡張子 dat，拡張子 txt：データファイル\\ -このデータのやり取りに関する次のオプションがある。\\ - オプションなしまたは，”” のとき\\ - i) データファイルがなければ，新しく作る\\ - ii) データファイルが既にあればそれを読み込む\\ - "m" のとき，強制的にデータファイルを作り直す。\\ - "r" のとき，すでにあるデータファイルを読み込む。\\ - このとき，ファイルの読み書きで不具合があると，数秒の後「==$>$ file.txt not generated (5 s ) 」のようなエラーメッセージがコンソールに表示される。このような場合は作業ディレクトリの設定などを確認していただきたい。この待ち時間については，Waitオプションで設定することもできる。\\ - \\ + +Rは主に統計解析のためのソフトウェアで， binorm（二項分布），pois（ポアソン），unif（一様分布），chisq（カイ2乗），f（F分布），t（t分布）など，多くの確率分布をサポートしている。 + + \ketcindy では，kc.bat/shによってコマンドをRに渡し，結果をテキストファイルで受け取る。このとき，Rとのやりとりで，次のようなファイルが作業ディレクトリに作成される。 + +拡張子 r ：r用のファイル + +拡張子 dat，拡張子 txt：データファイル + +このデータのやり取りに関する次のオプションがある。 + + オプションなしまたは，”” のとき + + i) データファイルがなければ，新しく作る + + ii) データファイルが既にあればそれを読み込む + + "m" のとき，強制的にデータファイルを作り直す。 + + "r" のとき，すでにあるデータファイルを読み込む。 + +\vspace{\baselineskip} \begin{description} + \hypertarget{boxplot}{} -\item[関数] Boxplot(名前,データ,垂直位置,高さ,option) -\item[機能] 箱ひげ図を描く -\item[説明] データは，直接的に変数で渡す場合とファイルから読み込む場合がある。\\ -例：乱数で作成した５未満の実数のデータを箱ひげ図にする。\\ +\item[関数] Boxplot(名前,データ,垂直位置,箱の高さ,option) +\item[機能] 箱ひげ図を描く +\item[説明] データは，リストで渡す場合とファイル名を渡してファイルから読み込む場合がある。データファイルは csv 形式とする。 + +\vspace{\baselineskip} +【例】乱数で作成した5未満の実数のデータを箱ひげ図にする。 + \begin{verbatim} - dt1=apply(1..100,5*random()); - Boxplot("1",dt1,1,1/2); + dt1=apply(1..100,5*random()); + Boxplot("1",dt1,1,1/2); \end{verbatim} - \\ -例：外部ファイルとして用意したデータを読み込んで箱ひげ図にする。データファイルはcsv形式とする。\\ +\vspace{\baselineskip} +\hspace{20mm} \input{Fig/boxplot01} + +\vspace{\baselineskip} +【例】外部ファイルとして用意したデータを読み込んで箱ひげ図にする。 \begin{verbatim} - Boxplot("2","datafile.csv",3,1/2); - Boxplot("1",dt1,1,1/2); + Boxplot("2","datafile.csv",3,1/2); \end{verbatim} - \\ - 複数列から成るcsvファイルを読み込むには，Readcsvを使う。csvファイルは，ketworkフォルダに入れておく。戻り値は読み込んだファイル。\\ - データの値を画面に入るように調節するには，次のようにリストの計算を利用すればよい。\\ - また，Framedata2()，Rulerscale() を併用することで目盛を入れることができる。Framedata2() のために，表示領域の対角点A,BをCinderellaの作図ツールで作図しておく。\\ + +\vspace{\baselineskip} +複数列から成るcsvファイルを読み込むには，Readcsvを使う。csvファイルは，作業フォルダ（ 初期設定は fig ）に入れておく。戻り値は読み込んだファイル。 + +データの値を画面に入るように調節するには，dt1/20 のようにしてリサイズする。 + +また，Framedata()，Rulerscale() を併用することで目盛を入れることができる。Framedata() のために，表示領域の対角点A,BをCinderellaの作図ツールで作図しておく。 + \begin{verbatim} - data=Readcsv("datafile.csv"); - dt1=apply(data,#_1); - dt2=apply(data,#_2); - Boxplot("1",dt1/20,1,1/2); - Boxplot("2",dt2/20,3,1/2); - Framedata2("1",[A,B]); - Rulerscale(A,["r",0,6,1],["f",1,"\mbox{dt1}",3,"\mbox{dt2}"]); + data=Readcsv("datafile.csv"); + dt1=apply(data,#_1); + dt2=apply(data,#_2); + Boxplot("1",dt1/20,1,1/2); + Boxplot("2",dt2/20,3,1/2); + Framedata("1",[A,B],["corner"]); + Rulerscale(A,["r",0,6,1],["f",1,"\mbox{dt1}",3,"\mbox{dt2}"]); \end{verbatim} - \\ - \input{Fig/boxplot}\\ +%\vspace{\baselineskip} + \begin{center} \input{Fig/boxplot} \end{center} + +注）一度実行した後，データを書き直すと，図が更新されないので，"m" オプションをつけて + Boxplot("1",dt1/20,1,1/2,["m"]); とすると，図が更新される。データを書き出すときは，もう一度 "m" オプションをはずして実行してから Figure ボタンを押す。これは，データの作成タイミングの関係。 -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\hypertarget{rfun}{} +\item[関数] Rfun(name,コマンド, 引数, option) +\item[機能] Rの1つのコマンドを実行して結果を返す +\item[説明] バッチファイル kc.bat / シェルファイル kc.sh を利用してRとデータをやり取りし，計算結果を取得する。結果は，変数 R+name に入り，コンソールにも表示される。 + +\vspace{\baselineskip} +【例】Rを用いて標準正規分布から10個の乱数を発生し，戻り値から平均値と標準偏差を求めてコンソールに表示する。 +\begin{verbatim} + Rfun("1","rnorm",[10]); + nx=length(R1); + mx=sum(R1)/nx; + sx=sqrt(R1*R1/nx-mx^2); + println("平均："+format(mx,4)+" 標準偏差："+format(sx,4)); +\end{verbatim} \hypertarget{calcbyr}{} -\item[関数] CalcbyR(変数名,コマンド列，option) -\item[機能] Rのコマンドを実行して結果を返す -\item[説明] バッチファイル kc.bat / シェルファイル kc.sh を利用してRとデータをやり取りし，計算結果を取得する。\\ - \\ -例：Rを用いて標準正規分布から10個の乱数を発生し，平均値と標準偏差を求めてコンソールに表示する。 -\begin{verbatim} - cmdL=[ "=rnorm",[10] ]; - CalcbyR("dt",cmdL); - nx=length(dt); - mx=sum(dt)/nx; - sx=sqrt(dt*dt/nx-mx^2); - println("データ："+dt); - println("平均："+format(mx,4)+" 標準偏差："+format(sx,4)); -\end{verbatim} -１行目の cmdL=[ "=rnorm",[10] ] で，標準正規分布から10個の乱数を発生するコマンド列を定義。\\ -２行目で，Rで計算した結果がリスト dt に入る。\\ - \\ -例：Rを用いてN(50,$5^2$)から10個の乱数を発生し，平均と不偏分散もRで計算してその結果をコンソールに表示する。 -\begin{verbatim} - cmdL=[ - "tmp1=rnorm",[10,50,5], - "tmp2=mean",["tmp1"], - "tmp3=var",["tmp1"], - "=c(tmp1,tmp2,tmp3)",[] - ]; - CalcbyR("rd",cmdL); - dt=rd_(1..(length(rd)-2)); - mx=rd_(-2); - vx=rd_(-1); - println("データ："+dt); - println("平均："+format(mx,4)+" 不偏分散："+format(vx,4)); -\end{verbatim} - CalcbyR()によって，データと平均，不偏分散からなるリストが作成されるので，mxに平均，vxに不偏分散を代入している。\verb|rd_(-1)| は，リスト rd の末尾の要素。\\ - \\ -例：Ｒでポアソン分布から200個の乱数をとり，標本平均の分布の様子＝分散が小さくなって，正規分布に近づいている様子＝をヒストグラムで見る。 -\begin{verbatim} - cmdL=[ - "tmp1=rpois",[200,5], - "tmp2=mean",["tmp1"], - "tmp3=var",["tmp1"], - "=c(tmp2,tmp3,tmp1)",[] - ]; - CalcbyR("rd",cmdL); - dt=rd_(3..length(rd)); - nn=length(dt); - mx=rd_1; - vx=rd_2*(nn-1)/nn; - sx=sqrt(vx); - println(dt); - println(["m="+format(mx,4),"v="+format(vx,4)]); - Setscaling(1/5); - Histplot("1",dt,["Breaks=seq(0,14,1)","dr,0.5"]); -\end{verbatim} - \\ - \input{Fig/poison01}\\ - \\ -例：ポアソン分布で乱数を2000個発生させ，10個ずつの平均をＲで計算し， -\begin{verbatim} - cmdL=[ - "tmp1=rpois",[2000,5], - "tmp2=c()",[], - "for(k in 1:200){",[], - " tmp=tmp1[(10*(k-1)+1):(10*k)]",[], - " tmp2=c(tmp2,mean(tmp))",[], - "}",[], - "=tmp2",[] - ]; - CalcbyR("rd2",cmdL); - Setscaling(1/10); - Histplot("2",rd2); -\end{verbatim} - -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\item[関数] CalcbyR(変数名,コマンド列，option) +\item[機能] Rのコマンドを実行して結果を返す +\item[説明] バッチファイル kc.bat / シェルファイル kc.sh を利用してRとデータをやり取りし，計算結果を取得する。 + + コマンド列は，"戻り値=コマンド"，[引数] の2つをセットとして並べる。 + + 最後の行の結果が戻り値として第１引数の変数名に代入される。"戻り値1::戻り値2・・",[] の形（戻り値1，戻り値2・・は各コマンドの戻り値）でコマンドを書くと，戻り値1,・・のリストとなる。戻り値が一つの場合は実数。"=値",[] の形の場合，「値」がそのまま戻り値となる。 + +\vspace{\baselineskip} +【例】Rを用いてN(50,$5^2$)から10個の乱数を発生し，平均と不偏分散もRで計算してその結果をコンソールに表示する。 +\begin{verbatim} + cmdL=[ + "tmp1=rnorm",[10,50,5], + "tmp2=mean",["tmp1"], + "tmp3=var",["tmp1"], + "tmp1::tmp2::tmp3",[] + ]; + CalcbyR("rd",cmdL); + dt=rd_1; + mx=rd_2; + vx=rd_3; + println("データ："+dt); + println("平均："+format(mx,4)+" 不偏分散："+format(vx,4)); +\end{verbatim} + CalcbyR()によって，データと平均，不偏分散からなるリストが作成されるので，mxに平均，vxに不偏分散を代入している。\verb|rd_(-1)| は，リスト rd の末尾の要素。 + +\vspace{\baselineskip} +【例】Ｒでポアソン分布から200個の乱数をとり，標本平均の分布の様子＝分散が小さくなって，正規分布に近づいている様子＝をヒストグラムで見る。分散はＲで求めた不偏分散に (n-1)/n をかけて再計算してコンソールに表示する。 +\begin{verbatim} + cmdL=[ + "tmp1=rpois",[200,5], + "tmp2=mean",["tmp1"], + "tmp3=var",["tmp1"], + "=c(tmp2,tmp3,tmp1)",[] + ]; + CalcbyR("rd",cmdL); + dt=rd_(3..length(rd)); + n=length(dt); + mx=rd_1; + vx=rd_2*(n-1)/n; + sx=sqrt(vx); + println(dt); + println(["m="+format(mx,4),"v="+format(vx,4)]); + Setscaling(1/5); + Histplot("1",dt,["Breaks=seq(0,14,1)","dr,0.5"]); +\end{verbatim} +\vspace{\baselineskip} + \begin{center} \input{Fig/poison01} \end{center} +\vspace{\baselineskip} +【例】ポアソン分布で乱数を2000個発生させ，10個ずつの平均をＲで計算し，ヒストグラムを作る。 +\begin{verbatim} + cmdL=[ + "tmp1=rpois",[2000,5], + "tmp2=c()",[], + "for(k in 1:200){",[], + " tmp=tmp1[(10*(k-1)+1):(10*k)]",[], + " tmp2=c(tmp2,mean(tmp))",[], + "}",[], + "=tmp2",[] + ]; + CalcbyR("rd2",cmdL); + Setscaling(1/10); + Histplot("2",rd2); +\end{verbatim} + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} \hypertarget{histplot}{} -\item[関数] Histplot(name,data,option) -\item[機能] Rを利用してヒストグラムを描く -\item[説明] dataはリストにして作成するか，外部ファイルからReadcsv()で読み込む。\\ -階級範囲（ブレークポイント）は，通常スタージェスの公式によるが，オプションで，\\ - "breaks=[0,10,20,30,40,50,60,70,80,90,100]"\\ -などと指定することもできる。\\ - この他のオプションは\\ - "Den=yes/no"：密度の指定（初期値は no）\\ - "Rel=yes/no"：相対度数にする/しない（初期値は no）\\ - \\ -例：csvファイル（datafile.csv）を読み込み，ヒストグラムを作る。Framedata2() と Rulerscale()を併用して，目盛付きの枠の中に表示する。表示枠の対角点A,BはCinderellaの作図ツールで作図しておく。 -\begin{verbatim} - Addax(0); - Setscaling(5); - Setunitlen("0.6mm"); - data=Readcsv("datafile.csv"); - Histplot("1",data,[""]); - Framedata2("1",[A,B]); - Rulerscale(A,["r",0,100,10],["r",0,15,5]); -\end{verbatim} - \input{Fig/histgram}\\ - -２行目と３行目は，データに合わせて縦方向を５倍にし，TeXの単位長を0.6mmにしている。\\ -Den,Rel オプションをyes にしたときは，Setscaling(100)くら いにするのがよい。\\ -csvファイルが複数のデータからなる場合は，\\ - \verb|dt1=apply(rc1,#_1);| -として，リストの第１要素を取得する。第２要素のヒストグラムであれば \verb|#_2| とする。\\ - \\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\item[関数] Histplot(name,data,option) +\item[機能] Rを利用してヒストグラムを描く +\item[説明] dataはリストにして作成するか，外部ファイルからReadcsv()で読み込む。 + +階級境界値（ブレークポイント）は，自動的に設定される（スタージェスの公式による）が，オプションで， + +\verb|"breaks=[0,10,20,30,40,50,60,70,80,90,100]"| + +などと指定することもできる。 + + この他のオプションは + + "Den=yes/no"：密度の指定（初期値は no） + + "Rel=yes/no"：相対度数にする/しない（初期値は no） + +\vspace{\baselineskip} +【例】csvファイル（datafile.csv）を読み込み，ヒストグラムを作る。Framedata() と Rulerscale()を併用して，目盛付きの枠の中に表示する。表示枠の対角点A,BはCinderellaの作図ツールで作図しておく。 +\begin{verbatim} + Addax(0); + Setscaling(5); + Setunitlen("0.6mm"); + data=Readcsv("datafile.csv"); + Histplot("1",data,[""]); + Framedata("1",[A,B],["corner"]); + Rulerscale(A,["r",0,100,10],["r",0,15,5]); +\end{verbatim} + \begin{center} \input{Fig/histgram} \end{center} + +2行目と3行目は，データに合わせて縦方向を5倍にし，TeXの単位長を0.6mmにしている。 + +Den,Rel オプションをyes にしたときは，Setscaling(100)くらいにするのがよい。 + +csvファイルが複数のデータからなる場合は， + + \verb|dt1=data_1;| +として，リストの第１要素を取得する。第2要素のヒストグラムであれば \verb|data_2| とする。 + +\vspace{\baselineskip} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} \hypertarget{plotdatar}{} -\item[関数] PlotdataR(name,式,変数) -\item[機能] Rの関数のグラフを描く -\item[説明] Cindyscriptの組み込み関数にはない関数のグラフをRを利用して描く。\\ +\item[関数] PlotdataR(name,式,変数) +\item[機能] Rの関数のグラフを描く +\item[説明] Cindyscriptの組み込み関数にはない関数のグラフをRを利用して描く。 -例：平均5, 標準偏差2の正規分布の密度関数と分布関数のグラフを描く。 +\vspace{\baselineskip} +【例】平均5, 標準偏差2の正規分布の密度関数と分布関数のグラフを描く。 \begin{verbatim} - PlotdataR(“1”, “dnorm(x,5,2)”, ”x=[0,10]”); - PlotdataR(“2”, ”pnorm(x,5,2)”, ”x=[0,10]”); + PlotdataR(“1”, “dnorm(x,5,2)”, ”x=[0,10]”); + PlotdataR(“2”, ”pnorm(x,5,2)”, ”x=[0,10]”); \end{verbatim} -例：標準正規分布のグラフ上の点とx軸を結んだ線分を描く。\\ +\hspace{20mm} \input{Fig/plotdatar1} + +【例】標準正規分布のグラフ上の点とx軸を結んだ線分を描く。 + 点A,BはCinderellaの作図ツールで作図しておき，点Aをグラフ上のおよその位置に置いてから実行する。 \begin{verbatim} - PlotdataR("1","dnorm(x)","x=[-5,5]"); - Putoncurve("A","grR1",[-3,3]); - Putpoint("B",[A.x,0]); - Listplot("1",[A,B]); -\end{verbatim} -２行目の最後の引数の[-3,3]は，その範囲を動かすことを意味する。\\ -Aはグラフ上を動かすことができて，Bはそれに伴って動く。ただし，少し動かす度に バッチ/シェル ファイルを実行するので，煩雑な場合は，Plotdata() の行をコメント化してから点Aを動かしたあと再実行するとよい。\\ - \\ -例：上と同様で，x軸上の点を自由点Aとし，曲線上にBを置く。 -\begin{verbatim} - PlotdataR("1","dnorm(x)","x=[-5,5]"); - PlotdataR("1","dnorm(x)","x=[-5,5]"); - A.xy=[A.x,0]; - Lineplot("1",[A,A+[0,1]],["nodisp"]); - Putintersect("B","grR1","ln1"); - Listplot("1",[A,B]); -\end{verbatim} - \\ -例：前の例のグラフで，ABの左側にShadeをかけ，Shadeの部分の面積を求める。Pの値を表示する位置に，Cinderellaの作図ツールで点Cをとっておく。 -\begin{verbatim} - tmp1=[0.2,0,0,0]; - tmp2=Colorcmyk2rgb(tmp1); - Setcolor(tmp1); - Setcolor([0.2,0,0,0]); - Shade(["en1"],["Color="+text(tmp2)]); - Setcolor("black"); - PlotdataR("1","dnorm(x)","x=[-5,5]",["Num=100"]); - Putpoint("A",[0,0],[A.x,0]); - Lineplot("1",[A,A+[0,1]],["nodisp"]); - Putintersect("B","grR1","ln1"); - Listplot("1",[A,B]); - Listplot("2",[[-5,0],[5,0]],"nodisp"); - Enclosing("1",["Invert(grR1)","sg2","sg1"],[B,"notex"]); - tmp=0.5+Integrate("grR1",[0,A.x]); - Expr([A,"s",text(A.x),C,"e","P="+text(tmp)]); -\end{verbatim} - \\ - \input{Fig/rshade}\\ - \\ -Shade() はプロットデータを定義しないので，先に書いておくと塗ってから線を描くので，にじみがなくきれいに仕上がる。（"en1"はEnclosing("1"・・)でできるプロットデータ）\\ - \\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + PlotdataR("1","dnorm(x)","x=[-5,5]"); + PutonCurve("A","grR1",[-3,3]); + Putpoint("B",[A.x,0]); + Listplot("1",[A,B]); +\end{verbatim} +2行目の最後の引数の[-3,3]は，その範囲を動かすことを意味する。 -\hypertarget{plotdiscr}{} -\item[関数] PlotdiscR(name,式,変数) -\item[機能] Rを利用して離散型のグラフを描く -\item[説明] dbinom （二項分布），dpois（ポアソン分布），dgeom（幾何分布）など離散型確率分布のグラフを描く。\\ - \\ -例：二項分布のグラフと正規分布のグラフを比較する。 +Aはグラフ上を動かすことができて，Bはそれに伴って動く。ただし，少し動かす度に バッチ/シェル ファイルを実行するので，煩雑な場合は，Plotdata() の行をコメント化してから点Aを動かしたあと再実行するとよい。 + +\vspace{\baselineskip} +【例】上と同様で，x軸上の点を自由点Aとし，曲線上にBを置く。 \begin{verbatim} - Setscaling(20); - PlotdiscR("1","dbinom(k,10,0.4)","k=[0,10]"); - PlotdataR("1","dnorm(x,10*0.4,sqrt(10*0.4*0.6))","x=[0,10]",["do"]); + PlotdataR("1","dnorm(x)","x=[-5,5]"); + PlotdataR("1","dnorm(x)","x=[-5,5]"); + A.xy=[A.x,0]; + Lineplot("1",[A,A+[0,1]],["nodisp"]); + Putintersect("B","grR1","ln1"); + Listplot("1",[A,B]); \end{verbatim} - \\ - \input{Fig/binvsnormal}\\ - \\ -関数部分が長くなるときは，Assign()を利用して次のように書くこともできる。 +\vspace{\baselineskip} +【例】前の例のグラフで，ABの左側にShadeをかけ，Shadeの部分の面積を求める。Pの値を表示する位置に，Cinderellaの作図ツールで点Cをとっておく。 \begin{verbatim} - tmp="dnorm(x,n*p,sqrt(n*p*(1-p)))"; - tmp=Assign(tmp,["n",10,"p",0.4]); - PlotdataR("2",tmp,"x=[0,10]",["do"]); + PlotdataR("1","dnorm(x)","x=[-5,5]",["Num=100"]); + Putpoint("A",[0,0],[A.x,0]); + Lineplot("1",[A,A+[0,1]],["nodisp"]); + Putintersect("B","grR1","ln1"); + Listplot("1",[A,B]); + Listplot("2",[[-5,0],[5,0]],"nodisp"); + Enclosing("1",["Invert(grR1)","sg2","sg1"],[B,"notex"]); + Shade(["en1"],["Color=[0.2,0,0,0]"]); + tmp=0.5+Integrate("grR1",[0,A.x]); + Expr([A,"s",text(A.x),C,"e","P="+text(tmp)]); \end{verbatim} -次は，ポアソン分布および幾何分布のグラフ。 + \begin{center} \input{Fig/rshade} \end{center} + +\vspace{\baselineskip} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\vspace{\baselineskip} +\hypertarget{plotdiscr}{} +\item[関数] PlotdiscR(name,式,変数) +\item[機能] Rを利用して離散型のグラフを描く +\item[説明] dbinom （二項分布），dpois（ポアソン分布），dgeom（幾何分布）など離散型確率分布のグラフを描く。 + +\vspace{\baselineskip} +【例】二項分布のグラフと正規分布のグラフを比較する。 +\begin{verbatim} + Setscaling(20); + PlotdiscR("1","dbinom(k,10,0.4)","k=[0,10]"); + PlotdataR("1","dnorm(x,10*0.4,sqrt(10*0.4*0.6))","x=[0,10]",["do"]); +\end{verbatim} +\vspace{\baselineskip} +\begin{center} \scalebox{0.9}{\input{Fig/binvsnormal}} \end{center} + +【例】ポアソン分布および幾何分布のグラフ。 \begin{verbatim} PlotdiscR("2","dpois(k,4)","k=[0,10]"); PlotdiscR("3","dgeom(k,0.3)","k=[0,10]"); \end{verbatim} - \\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +%\vspace{\baselineskip} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} \hypertarget{readcsv}{} -\item[関数] Readcsv(path,filename,option) -\item[機能] Rを利用してcsvファイルを読む。 -\item[説明] Rを使ってcsvファイルを読みこむ。戻り値は読み込んだデータのリスト。\\ -第１引数の path は，ファイルを ketwork フォルダに置いた場合は省略することができる。そうでない場合は，フルパスで指定する。たとえば，"/Users/Hoge/Desktop"\\ -option は，"Flat=" で，"Flat=y" の場合は，読み込んだデータをリスト化したときに平滑化（１次元のリスト）にする。デフォルトは "Flat=n"\\ -また，Ｒを使わずScilabを使って読み込むこともできる。その場合は，optionに"Use=S" をつけるが，Macで作成したファイルで，改行コードがCRのみの場合はうまく読み込むことができない。Windows標準のCR+LFなら読み込める。 +\item[関数] Readcsv(path,filename,option) +\item[機能] Rを利用してcsvファイルを読む。 +\item[説明] Rを使ってcsvファイルを読みこむ。戻り値は読み込んだデータのリスト。 + +第１引数の path は，ファイルを作業フォルダ（ 初期設定は fig ）に置いた場合は省略することができる。そうでない場合は，フルパスで指定する。たとえば，"/Users/Hoge/Desktop" + +option は，"Flat=" で，"Flat=y" の場合は，読み込んだデータをリスト化したときに平滑化（１次元のリスト）にする。 初期設定は "Flat=n" + +【例】次のようなCSVファイル sample.csvを読み込むとする。 -利用例は Boxplot() などの例を参照のこと。\\ - \\ +\begin{verbatim} + 12,14,15,18,13 + 9,13,17,21 +\end{verbatim} + +つまり，２行分のデータである。 + +\begin{verbatim} + data=Readcsv("sample.csv"); +\end{verbatim} + +とすると， +\begin{verbatim} + data=[[12,14,15,18,13],[9,13,17,21]] +\end{verbatim} +となる。 + +したがって，１行目のデータだけ取り出したい場合は + +\begin{verbatim} + dt1=data_1; +\end{verbatim} + +とする。 + +\vspace{\baselineskip} \hypertarget{scatterplot}{} -\item[関数] Scatterplot(name,filename,option) -\item[機能] ２次元データを読み込み，散布図を描く -\item[説明] 外部ファイル filename（csv形式）を読み，散布図を描く。\\ -オプションは "Reg=no" : 回帰直線を描くかどうか（yes/no) 初期値は yes\\ - A, B 表示枠の対角点（左下と右上の点）（Cinderellaで作図）\\ - C 相関係数と回帰直線の式を表示する点\\ - "Size=n" ：点の大きさ。Cinderellaの描画面には反映されない。\\ - 描画面の点も大きくする場合は，"size-$>$n"オプションを追加する。\\ -例：data.csv を読んで散布図を描き，回帰直線を引く。 -\begin{verbatim} - Scatterplot("1","data.csv",["Reg=yes",A,B,C,"Size=5"]); - Rulerscale(A,["r",0,10,1],["r",1,10,1]); -\end{verbatim} - optionの点A,BはCinderellaの作図ツールでとった表示領域の対角点。（ Aが左下。なお，対角点の名称はA,Bには限らない。）\\ - 回帰直線を描く場合("Reg=yes")は，回帰直線が枠からはみ出すので，AをSW，BをNEに一致させるとよい。\\ - Cは相関係数と回帰直線の式を表示する点としてCinderellaの作図ツールで取る。これも，名称はＣには限らない。\\ - \verb|Rulerscale(A,["r",0,10,1],["r",1,10,1]);|\\ - で表示枠に目盛を打っている。"r" は等幅，"f"は Tickmark と同じ指定。\\ - \\ - \input{Fig/scatter}\\ +\item[関数] Scatterplot(name,filename/datalist,option1,option2) +\item[機能] 2次元データを読み込み，散布図を描く +\item[説明] 外部ファイル filename（csv形式）を読み，散布図を描く。 + +外部ファイルの２次元データとは，次の形のcsvファイル。（行末はLFまたはCR） +\begin{verbatim} + 2.3, 4.5 (LF) + 3.2, 7 (LF) + 2.0, 6.8 (LF) +\end{verbatim} + + +datalistの場合は，次の形。 + +\begin{verbatim} + data=[[2.3,4.5],[3.2,7],[2.0,6.8], ・・・ ]; +\end{verbatim} + + +第１オプションは，回帰直線を描くかどうかと点のスタイル。 + +"Reg=no" : 回帰直線を描くかどうか（yes/no) 初期値は yes + +第２オプションは，相関係数と回帰直線の式を表示する位置と，回帰直線のスタイル。 + +位置は，幾何点の名称でもよい。 + +\vspace{\baselineskip} +【例】data.csv を読んで散布図を描き，回帰直線を引く。 +\begin{verbatim} + Scatterplot("1","data.csv"); +\end{verbatim} + +だけで描ける。オプションをつけた例は次。 + +点Aを相関係数と回帰直線の式を表示する点としてCinderellaの作図ツールで取る。 + +点を青で大きさ2とし，回帰直線を緑で表示する。 + +\begin{verbatim} + Scatterplot("1","data.csv",["Size=4","Color=blue"],[A,"Color=green"]); + Listplot("1",[[0,7],[0,0],[7,0]]); + Rulerscale([0,0],["r",0,7,1],["r",1,7,1]); +\end{verbatim} + +\vspace{\baselineskip} + \begin{center} \input{Fig/scatter} \end{center} + \end{description} \newpage -% Maximaとの連携 ================================== +% Maximaとの連携 ================================== \subsection{Maximaとの連携} -Maximaは数式処理ソフトで，KeTCindyにおいては微積分の計算など，Cindyscriptでは不十分な点を補うことができる。\\ - KeTCindyでは，kc.bat/shによってコマンドをMaximaに渡し，結果をテキストファイルで受け取る。このとき，Maximaとのやりとりで，次のようなファイルが作業ディレクトリに作成される。\\ -拡張子 max ：Maxima用のファイル\\ -拡張子 txt：データファイル\\ -このデータのやり取りに関する次のオプションがある。\\ - オプションなしまたは，”” のとき\\ - i) データファイルがなければ，新しく作る\\ - ii) データファイルが既にあればそれを読み込む\\ - "m" のとき，強制的にデータファイルを作り直す。\\ - "r" のとき，すでにあるデータファイルを読み込む。\\ - このとき，ファイルの読み書きで不具合があると，数秒の後「==$>$ file.txt not generated (5 s ) 」のようなエラーメッセージがコンソールに表示される。このような場合は作業ディレクトリの設定などを確認していただきたい。この待ち時間については，Waitオプションで設定することもできる。\\ +Maximaは数式処理ソフトで，\ketcindy においては微積分の計算など，Cindyscriptでは不十分な点を補うことができる。 + + \ketcindy では，kc.bat/shによってコマンドをMaximaに渡し，結果をテキストファイルで受け取る。このとき，Maximaとのやりとりで，次のようなファイルが作業ディレクトリに作成される。 + +拡張子 max ：Maxima用のファイル +拡張子 txt：データファイル + +このデータのやり取りに関する次のオプションがある。 + + オプションなしまたは，”” のとき + + i) データファイルがなければ，新しく作る + + ii) データファイルが既にあればそれを読み込む + + "m" のとき，強制的にデータファイルを作り直す。 + + "r" のとき，すでにあるデータファイルを読み込む。 + + このとき，ファイルの読み書きで不具合があると，数秒の後「==$>$ file.txt not generated (5 s ) 」のようなエラーメッセージがコンソールに表示される。このような場合は作業ディレクトリの設定などを確認していただきたい。この待ち時間については，Waitオプションで設定することもできる。 + \begin{description} \hypertarget{calcbyM}{} -\item[関数] CalcbyM(name，コマンド，option) -\item[機能] Maximaのスクリプトを実行する -\item[説明] 第２引数はMaximaで実行するコマンド。\\ - コマンドと引数リストの繰り返しからなるリスト（例えばcmdL）を作って，一度に実行する。\\ - 戻り値はない。（未定義値） 結果は，コマンドリストの最後に記述した変数（引数は空リスト）の値がname で指定された変数に代入される。複数の結果を戻すときは，:: で区切って記述するとリストにして代入される。\\ - \\ -例：$\sin x$ とその導関数を表示する。結果は 変数 fdf に f とdf のリストが代入される。 -\begin{verbatim} - cmdL=[ - "f:sin(x)", [], - "df:diff",["sin(x)","x"], - "f::df",[] - ]; - CalcbyM("fdf",cmdL); - println(fdf); -\end{verbatim} - \\ - 実行すると，コンソールに，[sin(x),cos(x)] と表示される。\\ - \\ -例：２次方程式 $x^2-x-4=0$の解を求める。 -\begin{verbatim} - cmdL=[ - "ans:solve",["x^2-x-4","x"], - "ans",[] - ]; - CalcbyM("ans",cmdL); - println("ans="+ans); -\end{verbatim} - コンソールには\\ - ans=[x = -(sqrt(17)-1)/2,x = (sqrt(17)+1)/2] \\ - が表示される。\\ - \\ -{\bf 応用例１：曲線の接線を引く}\\ - \\ - $f(x)=\dfrac{e^x+e^{-x}}{2}$ の，$x=a$における接線の方程式を作る。\\ +\item[関数] CalcbyM(name，コマンド，option) +\item[機能] Maximaのスクリプトを実行する +\item[説明] 第2引数はMaximaで実行するコマンド。 + +コマンドと引数リストの繰り返しからなるリスト（例えばcmdL）を作って，一度に実行する。 + +戻り値はない。（未定義値） 結果は，コマンドリストの最後に記述した変数（引数は空リスト）の値がname で指定された変数に代入される。複数の結果を戻すときは，:: で区切って記述するとリストにして代入される。 + +\vspace{\baselineskip} +【例】$\sin x$ とその導関数を表示する。結果は 変数 fdf に f とdf のリストが代入される。 +\begin{verbatim} + cmdL=[ + "f:sin(x)", [], + "df:diff",["sin(x)","x"], + "f::df",[] + ]; + CalcbyM("fdf",cmdL); + println(fdf); +\end{verbatim} +\vspace{\baselineskip} + 実行すると，コンソールに，[sin(x),cos(x)] と表示される。 + +\vspace{\baselineskip} +【例】2次方程式 $x^2-x-4=0$の解を求める。 +\begin{verbatim} + cmdL=[ + "ans:solve",["x^2-x-4","x"], + "ans",[] + ]; + CalcbyM("ans",cmdL); + println("ans="+ans); +\end{verbatim} + コンソールには + + ans=[x = -(sqrt(17)-1)/2,x = (sqrt(17)+1)/2] + + が表示される。 + +\vspace{\baselineskip} +{\bf 応用例１：曲線の接線を引く} + +\vspace{\baselineskip} + $f(x)=\dfrac{e^x+e^{-x}}{2}$ の，$x=a$における接線の方程式を作る。 + Maximaでその処理を行うコマンドを定義し，CalbyMで実行する。 \begin{verbatim} - fx="(exp(x)+exp(-x))/2"; - cmdL=[ - "df:diff",[fx,"x"], - "c:ev",["df","x=a"], - "b:ev",[fx,"x=a"], - "eq:c*(x-a)+b",[], - "eq",[] - ]; - CalcbyM("tn1",cmdL); - println(tn1); + fx="(exp(x)+exp(-x))/2"; + cmdL=[ + "df:diff",[fx,"x"], + "c:ev",["df","x=a"], + "b:ev",[fx,"x=a"], + "eq:c*(x-a)+b",[], + "eq",[] + ]; + CalcbyM("tn1",cmdL); + println(tn1); \end{verbatim} - コンソールには + コンソールには \begin{verbatim} - (%e^a-%e^-a)*(x-a))/2+(%e^a+%e^-a)/2 + (%e^a-%e^-a)*(x-a))/2+(%e^a+%e^-a)/2 \end{verbatim} が表示される。\\ - この，CalbyMの戻り値 tn1 を用いて，曲線上の１点Aにおける接線のグラフを描く。以下のスクリプトを追加する。なお，点AをCinderellaの作図ツールで適当なところにとっておく。 -\begin{verbatim} - tn1=Assign(tn1,["%e^a","exp(a)","%e^-a","exp(-a)"]); - Plotdata("1",fx,"x"); - Putoncurve("A","gr1"); - tmp=Assign(tn1,["a",A.x]); - plotdata("2",tmp,"x",["Num=2"]); -\end{verbatim} -１行目ではMaximaで作成した式を，Cindyscriptでプロットできる式にしている。\\ - \\ - \input{Fig/maxfun01}\\ - \\ - なお，接線の方程式を求めるだけであれば，Mxfun()を使うこともできる。Mxfun()の解説を参照のこと。\\ - \\ -{\bf 応用例２：パラメトリックの場合の接線}\\ - \\ - 媒介変数の値を決めるために，点AをCinderellaの描画面のx軸上にとっておき，その$x$座標を媒介変数$t$の値とする。スライダを作ってもよい。 -\begin{verbatim} - fn="3*cos(t)^2*[cos(t),sin(t)]"; - cmdL=[ - "f:",[fn], - "df:diff",["f","t"], - "df:trigsimp",["df"], - "tn:f+s*df",[], - "tn",[] - ]; - CalcbyM("tn2",cmdL); - Paramplot("1",fn,"t=[0,2*pi]",["Num=100"]); - gn=Assign(tn2,["t",A.x]); - Paramplot("2",gn,"s=[-3,3]"); -\end{verbatim} - \\ - \input{Fig/maxfun02}\\ - \\ - cmdLで定義しているMaximaのコマンド（trigsimp など）については，Maximaの解説書などを参照されたい。\\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} - \\ -\hypertarget{example}{} -\item[関数] Example("Mxfun",文字) -\item[機能] Mxfunの使用例を表示。文字は "a"，"b"，など。 -\item[説明] たとえば，\verb|Example("Mxfun","a")| とすると，Mxfunの使用例がコンソールに表示される。\\ - \\ + この，CalbyMの戻り値 tn1 を用いて，曲線上の１点Aにおける接線のグラフを描く。以下のスクリプトを追加する。なお，点AをCinderellaの作図ツールで適当なところにとっておく。 +\begin{verbatim} + tn1=Assign(tn1,["%e^a","exp(a)","%e^-a","exp(-a)"]); + Plotdata("1",fx,"x"); + PutonCurve("A","gr1"); + tmp=Assign(tn1,["a",A.x]); + plotdata("2",tmp,"x",["Num=2"]); +\end{verbatim} +１行目ではMaximaで作成した式を，Cindyscriptでプロットできる式にしている。 +\vspace{\baselineskip} + \begin{center} \input{Fig/maxfun01} \end{center} +\vspace{\baselineskip} + なお，接線の方程式を求めるだけであれば，Mxfun()を使うこともできる。Mxfun()の解説を参照のこと。 + +\vspace{\baselineskip} +{\bf 応用例2：パラメトリックの場合の接線} + +\vspace{\baselineskip} + 媒介変数の値を決めるために，点AをCinderellaの描画面のx軸上にとっておき，その$x$座標を媒介変数$t$の値とする。スライダを作ってもよい。 + +\begin{layer}{150}{0} +\putnotese{60}{20}{ \input{Fig/maxfun02}} +\end{layer} +\begin{verbatim} + fn="3*cos(t)^2*[cos(t),sin(t)]"; + cmdL=[ + "f:",[fn], + "df:diff",["f","t"], + "df:trigsimp",["df"], + "tn:f+s*df",[], + "tn",[] + ]; + CalcbyM("tn2",cmdL); + Paramplot("1",fn,"t=[0,2*pi]",["Num=100"]); + gn=Assign(tn2,["t",A.x]); + Paramplot("2",gn,"s=[-3,3]"); +\end{verbatim} + +cmdLで定義しているMaximaのコマンド（trigsimp など）については，Maximaの解説書などを参照されたい。 + +%\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +%\vspace{\baselineskip} +%\hypertarget{example}{} +%\item[関数] Example("Mxfun",文字) +%\item[機能] Mxfunの使用例を表示。文字は "a"，"b"，など。 +%\item[説明] たとえば，\verb|Example("Mxfun","a")| とすると，Mxfunの使用例がコンソールに表示される。 + +\vspace{\baselineskip} \hypertarget{mxbatch}{} -\item[関数] Mxbatch(ファイル名) -\item[機能] Maximaのファイルを実行するコマンド作る -\item[説明] Dirlibで指定されたフォルダの中の maximaL フォルダにあるファイルを実行するための，CalcbyM用のコマンドを作成する。\\ -例：\verb|cmd=Mxbatch("fourier_sec")|\\ - を実行すると，cmdに\\ - \verb|[batch,["/Applications/ketcindy/ketlib/maximaL/fourier_sec.max"]] |\\ - が代入される。そこで，\\ - \verb|CalcbyM("ret",cmd,[]);|\\ - を実行すれば，fourier\_sec.max が実行されて，結果を ret に取得できる。\\ - fourier\_sec.max に続けて，コマンド列 cmd2 を実行することもでき，その場合は -\begin{verbatim} - cmdL=Concat(Mxbatch("fourier_sec"),cmd2); - CalcbyM("ret",cmdL,[]); -\end{verbatim} -とする。（Concat() はリストを結合するCindyscriptの関数）\\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} - \\ +\item[関数] Mxbatch(ファイル名) +\item[機能] Maximaのファイルを実行するコマンドを作る +\item[説明] ketcindy/ketlib/maximaL にあるファイルを実行するための，CalcbyM用のコマンドを作成する。 + +ketcindy/ketlib/maximaL には，fourier\_sec.max , matoperation.max , poincare.mac の3つのファイルが入っている。たとえば，フーリエ級数を扱うときには，fourier\_sec.max を使用する。 + +\vspace{\baselineskip} +【例】\verb|cmd=Mxbatch("fourier_sec")| + を実行すると，cmdに，たとえば + + \verb|[batch,["/Applications/ketcindy/ketlib/maximaL/fourier_sec.max"]] | + + が代入される。（Mac/Windows および KeTCindyの設定によって異なる） + + そこで，次のように利用する。 + +\begin{verbatim} + Setax(["a"]); + Slider("A-C-B",[-5.5,-1.5],[4.5,-1.5]); + defL=["1",[-3,-2],1,"0",[-2,-1],1,"-x",[-1,1],1,"0",[1,2],1,"-1",[2,3],1]; + Drwxy(); + tmp=Periodfun(defL,1,["dr,2","Color=red"]); + fun=tmp_1; + per=tmp_2; + Htickmark([1,"n","1",2,"n","2",3,"nw","3"]); + Htickmark([-1,"-1",-2,"-2",-3,"-3"]); + cmdL=Concat(Mxbatch("fourier_sec"),[ + "Ffun(x):="+fun,[], + "c:fourier_sec_coeff",["Ffun(x)","x"], + "c[1]::c[2]::c[3]",[] + ]); + CalcbyM("ans",cmdL,[]); + nterm=round(4*(C.x-A.x)); + Fourierseries("1",ans,per,nterm,["Num=400"]); + Mxtex("2",ans_3); + Expr([[-5,-2],"e","s_n="+tx2,[4,-2],"e","n="+text(nterm)]); +\end{verbatim} + +\hspace{20mm}\input{Fig/mxbatch} + +%\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\vspace{\baselineskip} \hypertarget{mxfun}{} -\item[関数] Mxfun(name，式，リスト，option) -\item[機能] Maximaの関数を実行する -\item[説明] 第２引数の「式」はMaximaの関数名。第３引数のリストは関数に渡す引数のリスト。\\ - 戻り値は，第１引数の式に１つでも文字があると文字列となる。すべて数字（+,-, . を含む）の場合は -16桁以下であれば数，それ以上の場合は文字列となる。また，戻り値は，変数 mxname にも代入される。\\ -オプションに "Disp=no" をつけると，結果をコンソールに表示しない。\\ - \\ -例：$10!$を求める。\\ - \verb|Mxfun("1","10!",[],[""]);|\\ - を実行すると，コンソールに mx1 is 362880 と表示される。この値は変数 mx1 に代入されているので，\\ - \verb|drawtext([0,1],mx1);|\\ -とすればCinderellaの描画面上に表示される。\\ - また，戻り値を別の変数に代入して使うこともできる。 -\begin{verbatim} - fact10=Mxfun("1","10!",[],[""]); - drawtext([0,1],fact10); -\end{verbatim} - \\ -例：$f(x)=\sin x$ を微分する\\ - \verb|Mxfun("1", "diff",["sin(x)","x"])|\\ - とすると\\ - diff(sin(x),x)\\ - というコマンドをMaximaに渡して，戻り値をCindyの変数mx1に代入する。\\ - \verb|Mxfun("1", "diff(sin(x),x)",[]])|\\ - と，第１引数にまとめても同じ結果になる。ただし，この場合，第２引数は空リストとする。\\ - 文字列を引数とする場合，例えば，文字列を連結するコマンドconcatでは，\\ - concat("a","b")\\ - とするが，Cindyscriptの文字列の処理の関係で，第１引数ではこの形で記述できない。\\ - したがって，このような場合は，第２引数を使って\\ - \verb|Mxfun("1","concat",["a","b"])| - とすればよい。\\ - \\ -{\bf Cindyscriptの微分との違い}\\ - Cindyscriptでも微分はできる。たとえば， -\begin{verbatim} - f(x):=sin(x); - g(x):=d(f(#),x); - plot(g(#)); -\end{verbatim} - とすると，cos(x)のグラフが描かれる。\\ - しかし，Cindyscriptの微分が，微分の定義による数値計算であるのに対し，Maximaでは数式処理として微分ができる。\\ - その意味の違いは，次のスクリプトで確かめられる。 -\begin{verbatim} - f(x):=sin(x); - g(x):=d(f(#),x); - println(g(x)); -\end{verbatim} - では，コンソールに表示されるのは未定義値（\_ \_ \_） である。\\ +\item[関数] Mxfun(name，式，リスト，option) +\item[機能] Maximaの関数を実行する +\item[説明] 第2引数の「式」はMaximaの関数名。第3引数のリストは関数に渡す引数のリスト。 + +戻り値は，第１引数の式に１つでも文字があると文字列となる。すべて数字（+,-, . を含む）の場合は +16桁以下であれば数，それ以上の場合は文字列となる。また，戻り値は，変数 mxname にも代入される。 + +オプションに "Disp=no" をつけると，結果をコンソールに表示しない。 + +\vspace{\baselineskip} +【例】$10!$を求める。 + + \verb|Mxfun("1","10!",[]);| + + を実行すると，コンソールに mx1 is 362880 と表示される。この値は変数 mx1 に代入されているので， + + \verb|drawtext([0,1],mx1);| + +とすればCinderellaの描画面上に表示される。mx1のかわりに，戻り値を変数に代入して使うこともできる。 + +\begin{verbatim} + fact10=Mxfun("1","10!",[]); + drawtext([0,1],fact10); +\end{verbatim} + +\vspace{\baselineskip} +【例】$f(x)=\sin x$ を微分する + + \verb|Mxfun("1", "diff",["sin(x)","x"])| + + とすると + + diff(sin(x),x) + + というコマンドをMaximaに渡して，戻り値をCindyの変数mx1に代入する。 + + \verb|Mxfun("1", "diff(sin(x),x)",[]])| + + と，第１引数にまとめても同じ結果になる。ただし，この場合，第2引数は空リストとする。 + + 文字列を引数とする場合，例えば，文字列を連結するコマンドconcatでは， + + concat("a","b") + + とするが，Cindyscriptの文字列の処理の関係で，第１引数ではこの形で記述できない。 + + したがって，このような場合は，第2引数を使って + + \verb|Mxfun("1","concat",["a","b"])| + + とすればよい。 + +\vspace{\baselineskip} +{\bf Cindyscriptの微分との違い} + + Cindyscriptでも微分はできる。たとえば， +\begin{verbatim} + f(x):=sin(x); + g(x):=d(f(#),x); + plot(g(#)); +\end{verbatim} + とすると，cos(x)のグラフが描かれる。 + + しかし，Cindyscriptの微分が，微分の定義による数値計算であるのに対し，Maximaでは数式処理として微分ができる。 + + その意味の違いは，次のスクリプトで確かめられる。 +\begin{verbatim} + f(x):=sin(x); + g(x):=d(f(#),x); + println(g(x)); +\end{verbatim} + では，コンソールに表示されるのは未定義値（\_ \_ \_） である。 + 一方， \begin{verbatim} - Mxfun("1", "diff",["sin(x)","x"]); - println(mx1); + Mxfun("1", "diff",["sin(x)","x"]); + println(mx1); \end{verbatim} -では，コンソールに \verb|cos(x)| と表示される。\\ +では，コンソールに \verb|cos(x)| と表示される。 + mx1は文字列であるので， \begin{verbatim} - g(x):=parse(mx1); -\end{verbatim} -とすれば，g(x)を導関数とすることができ，\verb|plot(g(#))| でグラフを描くことができる。\\ - また，Cindyscriptの微分では，３階か４階までの導関数が計算上の限度であるのに対し，Maximaなら何階でも微分ができるので，テイラー展開などで有利である。\\ - \\ - \\ -例 $\sin x$ の テイラー展開を行い，グラフを表示する。 -\begin{verbatim} - Mxfun("1","taylor",["sin(x)","x",0,7],[""]); - Plotdata("1","sin(x)","x",["da"]); - Plotdata("2",mx1,"x"); -\end{verbatim} - \\ - \input{Fig/taylor} - \\ -Mxtex() を用いて，Mxfun()の結果の mx1をTeX書式にして表示することもできる。\\ - \verb|Expr([[1,2],"e",Mxtex("1",mx1)]);|\\ -を追加すれば[1,2]の位置に式が表示される。\\ - \\ - \\ -{\bf 応用例：接線の方程式を作る}\\ - \\ - $f(x)=\dfrac{e^x+e^{-x}}{2}$ の，$x=a$における接線の方程式を作る。\\ - 関数式を文字列にしておき，Assign() を用いて変数$x$を$a$に変えれば，$f(a)$の式を作ることができる。導関数についても同様にする。\\ -\begin{verbatim} - fx="(exp(x)+exp(-x))/2"; - gx=Mxfun("1","diff",[fx,"x"]); - fa=Assign(fx,["x","a"]); - ga=Assign(gx,["x","a"]); - tf=ga+"*(x-a)+("+fa+")"; - println(tf); -\end{verbatim} - コンソールには -\begin{verbatim} - (%e^a-%e^-a)/2*(x-a)+((exp(a)+exp(-a))/2) + g(x):=parse(mx1); \end{verbatim} -が表示される。\\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} - \\ +とすれば，g(x)を導関数とすることができ，\verb|plot(g(#))| でグラフを描くことができる。 + + また，Cindyscriptの微分では，3階か4階までの導関数が計算上の限度であるのに対し，Maximaなら何階でも微分ができるので，テイラー展開などで有利である。 + +\vspace{\baselineskip} +\vspace{\baselineskip} +例 $\sin x$ の テイラー展開を行い，グラフを表示する。 +\begin{verbatim} + Mxfun("1","taylor",["sin(x)","x",0,7],[""]); + Plotdata("1","sin(x)","x",["da"]); + Plotdata("2",mx1,"x"); +\end{verbatim} +\vspace{\baselineskip} + \begin{center} \input{Fig/taylor} \end{center} +\vspace{\baselineskip} +Mxtex() を用いて，Mxfun()の結果の mx1をTeX書式にして表示することもできる。 + + \verb|Expr([[1,2],"e",Mxtex("1",mx1)]);| + +を追加すれば[1,2]の位置に式が表示される。 + +\vspace{\baselineskip} +{\bf 応用【例】接線の方程式を作る} + +\vspace{\baselineskip} + $f(x)=\dfrac{e^x+e^{-x}}{2}$ の，$x=a$における接線の方程式を作る。 + + 関数式を文字列にしておき，Assign() を用いて変数$x$を$a$に変えれば，$f(a)$の式を作ることができる。導関数についても同様にする。 + +\begin{verbatim} + fx="(exp(x)+exp(-x))/2"; + gx=Mxfun("1","diff",[fx,"x"]); + fa=Assign(fx,["x","a"]); + ga=Assign(gx,["x","a"]); + tf=ga+"*(x-a)+("+fa+")"; + println(tf); +\end{verbatim} + コンソールには +\begin{verbatim} + (%e^a-%e^-a)/2*(x-a)+((exp(a)+exp(-a))/2) +\end{verbatim} +が表示される。 +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\vspace{\baselineskip} \hypertarget{mxtex}{} -\item[関数] Mxtex(name,式) -\item[機能] 式をTeX書式にする -\item[説明] 第２引数の式は，直接書いた式もしくはMxfunの戻り値。これをTeXの書式にする。\\ -戻り値は，変数 txname にも代入される。\\ - \\ -例：部分分数への分解 +\item[関数] Mxtex(name,式) +\item[機能] 式をTeX書式にする +\item[説明] 第2引数の式は，直接書いた式もしくはMxfunの戻り値。これをTeXの書式にする。 + +戻り値は，変数 txname にも代入される。 + +\vspace{\baselineskip} +【例】部分分数への分解 \begin{spacing}{1.5} - 部分分数$\dfrac{x^3}{(x+1)(x+2)}$の分解をMaximaで行い，その結果をTeX書式にして画面に表示する。画面に表示された結果はそのままKeTCindyで出力できる。 + 部分分数$\dfrac{x^3}{(x+1)(x+2)}$の分解をMaximaで行い，その結果をTeX書式にして画面に表示する。画面に表示された結果はそのまま\ketcindy で出力できる。 \end{spacing} - \begin{verbatim} - Mxfun("1","partfrac",["x^3/((x+1)*(x+2))","x"]); - Mxtex("1",mx1); - Expr([0,1],"e",tx1); -\end{verbatim} - ここで，mx1，tx1はそれぞれMxfun("1",・・) , Mxtex"1",・・) の結果（戻り値）である。mx1，tx1 はコンソールにも表示され，tx1は次のようになっている。 -\begin{verbatim} - \frac{8}{x+2}-\frac{1}{x+1}+x-3 -\end{verbatim} - CindyscriptはTeX書式をサポートしているのでこれで描画面に分数式が表示されるが，Texの文書では，\verb|\frac{}{}| ではなく，\verb|\dfrac{}{}|を使うことが多い。そこで，Assign()を用いて，"frac" を "dfrac" に変えれば，そのままTex文書で使える。ただし，Cindyscriptは \verb|\dfrac{}{}| をサポートしていないので，画面上では分数表記にならない。そのあたりの事情を次のスクリプトで示す。 -\begin{verbatim} - fx="x^3/((x+1)*(x+2))"; - pfx=Mxfun("1","partfrac",[fx,"x"]); - form=Mxtex("1",fx)+"="+Mxtex("2",pfx); - dform=Assign(form,["frac","dfrac"]); - Letter([0,5],"e","部分分数への分解 $"+form+"$"); - Letter([0,3],"e","部分分数への分解 $"+dform+"$"); -\end{verbatim} -Cinderellaの描画面では次のように表示される。\\ - \\ - \includegraphics[bb=0 0 694 232 , width=8cm]{Fig/mxtex01.png}\\ - \\ -出力したTeX挿入図では次のようになる。\\ - \\ - \input{Fig/mxtex02}\\ - \\ -なお，文字列を置換するのに，\verb|Assign(form,["frac","dfrac"])| ではなく，\\ -Cindyscriptの文字列の関数 replace を用いて，\\ - \verb|dform=replace(form,"frac","dfrac");| \\ -としてもよい。\\ - \\ -例：２次関数のグラフを表示し，$x$軸との交点の$x$座標を表示する。 -\begin{verbatim} - fx="x^2-x-3"; - cmdL=[ - "ans:solve",[fx,"x"], - "ans",[] - ]; - CalcbyM("ans",cmdL); - p1=indexof(ans,"["); - p2=indexof(ans,","); - p3=indexof(ans,"]"); - s1=substring(ans,p1,p2-1); - s2=substring(ans,p2,p3-1); - s1=replace(s1,"x =",""); - s2=replace(s2,"x =",""); - Mxtex("1",s1); - Mxtex("2",s2); - Plotdata("1",fx,"x"); - Expr([-2,-0.5],"e",tx1); - Expr([2,-0.5],"e",tx2); -\end{verbatim} - \\ - \input{Fig/mxtex03}\\ - \\ - ここで，\verb|CalcbyM("ans",cmdL);| で得られるansは，次のような文字列である。\\ - \verb|"[x = -(sqrt(13)-1)/2,x = (sqrt(13)+1)/2] "|\\ -そこで，ここから２つの式だけを抽出する作業を行ったのち，Mxtex() でTeXの式を得ている。\\ - さらに応用として，点AをCinderellaの作図ツールで作図し， -\begin{verbatim} - if(A.y<0, - fx="(x-"+text(A.x)+")^2"+guess(A.y), - fx="(x-"+text(A.x)+")^2+"+guess(A.y); - ); -\end{verbatim} -とすると，点Aを頂点とする放物線と軸との交点の座標が描かれる。Maximaとのデータのやり取りをするためのタイムラグがあるが，インタラクティブに放物線の位置を変えることができる。\\ - \\ -＜参考＞\\ - ２次関数のような簡単な関数であれば，Cindyscriptの roots() 関数を用いて２次方程式が解けるので，次のスクリプトでほぼ同じ動作をするものを作ることができる。「ほぼ」というのは点Aの位置によっては，guess()で解釈しきれないことがあるためである。Maximaを使えば数式処理で解を求めるので，Aがどこにあってもきれいに表示できる。 -\begin{verbatim} - fx="x^2-2*A.x*x+A.x^2+A.y"; - cf=[A.x^2+A.y,-2*A.x,1]; - sol=roots(cf); - s1=guess(sol_2); - s2=guess(sol_1); - Mxtex("1",s1); - Mxtex("2",s2); - Plotdata("1",fx,"x"); - Expr([-2,-0.5],"e",tx1); - Expr([2,-0.5],"e",tx2); + Mxfun("1","partfrac",["x^3/((x+1)*(x+2))","x"]); + Mxtex("1",mx1); + Expr([0,1],"e",tx1); +\end{verbatim} + ここで，mx1，tx1はそれぞれMxfun("1",・・) , Mxtex"1",・・) の結果（戻り値）である。mx1，tx1 はコンソールにも表示され，tx1は次のようになっている。 +\begin{verbatim} + \frac{8}{x+2}-\frac{1}{x+1}+x-3 \end{verbatim} + CindyscriptはTeX書式をサポートしているのでこれで描画面に分数式が表示されるが，Texの文書では，\verb|\frac{}{}| ではなく，\verb|\dfrac{}{}|を使うことが多い。そこで，Assign()を用いて，"frac" を "dfrac" に変えれば，そのままTex文書で使える。ただし，Cindyscriptは \verb|\dfrac{}{}| をサポートしていないので，画面上では分数表記にならない。そのあたりの事情を次のスクリプトで示す。 +\begin{verbatim} + fx="x^3/((x+1)*(x+2))"; + pfx=Mxfun("1","partfrac",[fx,"x"]); + form=Mxtex("1",fx)+"="+Mxtex("2",pfx); + dform=Assign(form,["frac","dfrac"]); + Letter([0,5],"e","部分分数への分解 $"+form+"$"); + Letter([0,3],"e","部分分数への分解 $"+dform+"$"); +\end{verbatim} +Cinderellaの描画面では次のように表示される。 -\end{description} +\vspace{\baselineskip} +\hspace{20mm} \includegraphics[bb=0 0 347.02 116.01 , width=8cm]{Fig/mxtex01.pdf} + +\vspace{\baselineskip} +出力したTeX挿入図では次のようになる。 -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\newpage +%\vspace{\baselineskip} +\input{Fig/mxtex02} +なお，文字列を置換するのに，\verb|Assign(form,["frac","dfrac"])| ではなく， -% Scilabとの連携 ================================== -\subsection{Scilabとの連携} - KeTCindyは，もともと Scilab と連携して，Cinderellaからの出力をTeXのテキストとするシステムである。しかし，それだけでなく，Maximaなどとの連携と同様，Scilab の関数を実行して，データをやりとりすることができる。\\ - KeTCindyでは，kc.bat/shによってコマンドをScilabに渡し，結果をテキストファイルで受け取る。このとき，Scilabとのやりとりで，次のようなファイルが作業ディレクトリに作成される。\\ -拡張子 sci ：Scilab用のファイル\\ -拡張子 txt：データファイル\\ -このデータのやり取りに関する次のオプションがある。\\ - オプションなしまたは，”” のとき\\ - i) データファイルがなければ，新しく作る\\ - ii) データファイルが既にあればそれを読み込む\\ - "m" のとき，強制的にデータファイルを作り直す。\\ - "r" のとき，すでにあるデータファイルを読み込む。\\ - このとき，ファイルの読み書きで不具合があると，数秒の後「==$>$ file.txt not generated (5 s ) 」のようなエラーメッセージがコンソールに表示される。このような場合は作業ディレクトリの設定などを確認していただきたい。この待ち時間については，Waitオプションで設定することもできる。\\ +Cindyscriptの文字列の関数 replace を用いて， -\begin{description} +\hspace{10mm} \verb|dform=replace(form,"frac","dfrac");| + +としてもよい。 -\hypertarget{calcbyS}{} -\item[関数] CalcbyS(name，コマンド，option) -\item[機能] Scilabのコマンドスクリプトを実行する -\item[説明] 第２引数はScilabで実行するコマンドのリスト。\\ - \\ -\hypertarget{plotdataS}{} -\item[関数] PlotdataS(name，関数，変数) -\item[機能] Plotdataと同様の書式で，Scilabの関数を実行する -\item[説明] Cindyscriptの組込関数にない関数のグラフを描くことができる。\\ - \\ -例：ベッセル関数のグラフを描く +%\vspace{10mm} + +\vspace{\baselineskip} +【例】2次関数のグラフを表示し，$x$軸との交点の$x$座標を表示する。 + +\begin{layer}{150}{0} +\putnotese{70}{50}{ \input{Fig/mxtex03}} +\end{layer} \begin{verbatim} - PlotdataS("1","besselj(1,x)","x"); + fx="x^2-x-3"; + cmdL=[ + "ans:solve",[fx,"x"], + "ans",[] + ]; + CalcbyM("ans",cmdL); + p1=indexof(ans,"["); + p2=indexof(ans,","); + p3=indexof(ans,"]"); + s1=substring(ans,p1,p2-1); + s2=substring(ans,p2,p3-1); + s1=replace(s1,"x =",""); + s2=replace(s2,"x =",""); + Mxtex("1",s1); + Mxtex("2",s2); + Plotdata("1",fx,"x"); + Expr([-2,-0.5],"e",tx1); + Expr([2,-0.5],"e",tx2); +\end{verbatim} + +ここで，\verb|CalcbyM("ans",cmdL);| で得られるansは，次のような文字列である。 + + \verb|"[x = -(sqrt(13)-1)/2,x = (sqrt(13)+1)/2] "| + +そこで，ここから2つの式だけを抽出する作業を行ったのち，Mxtex() でTeXの式を得ている。 + +さらに応用として，点AをCinderellaの作図ツールで作図し， +\begin{verbatim} + if(A.y<0, + fx="(x-"+text(A.x)+")^2"+guess(A.y), + fx="(x-"+text(A.x)+")^2+"+guess(A.y); + ); +\end{verbatim} +とすると，点Aを頂点とする放物線と軸との交点の座標が描かれる。Maximaとのデータのやり取りをするためのタイムラグがあるが，インタラクティブに放物線の位置を変えることができる。 + +\vspace{\baselineskip} +＜参考＞ + + 2次関数のような簡単な関数であれば，Cindyscriptの roots() 関数を用いて2次方程式が解けるので，次のスクリプトでほぼ同じ動作をするものを作ることができる。「ほぼ」というのは点Aの位置によっては，guess()で解釈しきれないことがあるためである。Maximaを使えば数式処理で解を求めるので，Aがどこにあってもきれいに表示できる。 +\begin{verbatim} + fx="x^2-2*A.x*x+A.x^2+A.y"; + cf=[A.x^2+A.y,-2*A.x,1]; + sol=roots(cf); + s1=guess(sol_2); + s2=guess(sol_1); + Mxtex("1",s1); + Mxtex("2",s2); + Plotdata("1",fx,"x"); + Expr([-2,-0.5],"e",tx1); + Expr([2,-0.5],"e",tx2); \end{verbatim} \end{description} -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} \newpage -% Risa/Asirとの連携 ================================== + + +% Risa/Asirとの連携 ================================== \subsection{Risa/Asirとの連携} \begin{description} \hypertarget{calcbyA}{} -\item[関数] CalcbyA(name，コマンド，option) -\item[機能] Risa/Asirのスクリプトを実行する -\item[説明] 第２引数はRisa/Asirで実行するコマンド。\\ - コマンドと引数リストの繰り返しからなるリスト（例えばcmdL）を作って，一度に実行する。\\ - 戻り値はない。（未定義値） 結果は，コマンドリストの最後に記述した変数（引数は空リスト）の値がname で指定された変数に代入される。複数の結果を戻すときは，:: で区切って記述するとリストにして代入される。\\ +\item[関数] CalcbyA(name，コマンド，option) +\item[機能] Risa/Asirのスクリプトを実行する +\item[説明] 第2引数はRisa/Asirで実行するコマンド。 + + コマンドと引数リストの繰り返しからなるリスト（例えばcmdL）を作って，一度に実行する。 + + 戻り値はない。（未定義値） 結果は，コマンドリストの最後に記述した変数（引数は空リスト）の値がname で指定された変数に代入される。複数の結果を戻すときは，:: で区切って記述するとリストにして代入される。 + +\vspace{\baselineskip} \hypertarget{asirfun}{} -\item[関数] Asirfun(name，式，リスト，option) -\item[機能] Risa/Asirの関数を実行する -\item[説明] 第２引数の「式」はRisa/Asirの関数名。第３引数のリストは関数に渡す引数のリスト。\\ - 戻り値は，第１引数の式に１つでも文字があると文字列となる。すべて数字（+,-, . を含む）の場合は -16桁以下であれば数，それ以上の場合は文字列となる。また，戻り値は，変数 asname にも代入される。\\ -オプションに "Disp=no" をつけると，結果をコンソールに表示しない。\\ +\item[関数] Asirfun(name，式，リスト，option) +\item[機能] Risa/Asirの関数を実行する +\item[説明] 第2引数の「式」はRisa/Asirの関数名。第3引数のリストは関数に渡す引数のリスト。 + +戻り値は，第１引数の式に１つでも文字があると文字列となる。すべて数字（+,-, . を含む）の場合は +16桁以下であれば数，それ以上の場合は文字列となる。また，戻り値は，変数 asname にも代入される。 + +オプションに "Disp=no" をつけると，結果をコンソールに表示しない。 + \end{description} -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} \newpage -% FriCASとの連携 ================================== +% FriCASとの連携 ================================== \subsection{FriCAS(Axiom)との連携} \begin{description} \hypertarget{calcbyF}{} -\item[関数] CalcbyF(name，コマンド，option) -\item[機能] FriCASのスクリプトを実行する -\item[説明] 第２引数はFriCASで実行するコマンド。\\ - コマンドと引数リストの繰り返しからなるリスト（例えばcmdL）を作って，一度に実行する。\\ - 戻り値はない。（未定義値） 結果は，コマンドリストの最後に記述した変数（引数は空リスト）の値がname で指定された変数に代入される。複数の結果を戻すときは，:: で区切って記述するとリストにして代入される。\\ +\item[関数] CalcbyF(name，コマンド，option) +\item[機能] FriCASのスクリプトを実行する +\item[説明] 第2引数はFriCASで実行するコマンド。 + +コマンドと引数リストの繰り返しからなるリスト（例えばcmdL）を作って，一度に実行する。 +戻り値はない。（未定義値） 結果は，コマンドリストの最後に記述した変数（引数は空リスト）の値がname で指定された変数に代入される。複数の結果を戻すときは，:: で区切って記述するとリストにして代入される。 + + +\vspace{\baselineskip} \hypertarget{frfun}{} -\item[関数] Frfun(name，式，リスト，option) -\item[機能] FriCASの関数を実行する -\item[説明] 第２引数の「式」はFriCASの関数名。第３引数のリストは関数に渡す引数のリスト。\\ - 戻り値は，第１引数の式に１つでも文字があると文字列となる。すべて数字（+,-, . を含む）の場合は -16桁以下であれば数，それ以上の場合は文字列となる。また，戻り値は，変数 friname にも代入される。\\ -オプションに "Disp=no" をつけると，結果をコンソールに表示しない。\\ +\item[関数] Frfun(name，式，リスト，option) +\item[機能] FriCASの関数を実行する +\item[説明] 第2引数の「式」はFriCASの関数名。第3引数のリストは関数に渡す引数のリスト。 + +戻り値は，第１引数の式に１つでも文字があると文字列となる。すべて数字（+,-, . を含む）の場合は +16桁以下であれば数，それ以上の場合は文字列となる。また，戻り値は，変数 friname にも代入される。 + +オプションに "Disp=no" をつけると，結果をコンソールに表示しない。 + \end{description} -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} \newpage -% MeshLabとの連携 ================================== +% MeshLabとの連携 ================================== \subsection{MeshLabとの連携} -MeshLabは，3Dデータ（objデータなど）を読み込んでレイトレーシングで表示・編集するソフトウェアである。レイトレーシングで3Dグラフィクスを描くには，Cinderellaと親和性の高い Cindy3D を利用するのがよいが，MeshLabを使うメリットは3Dプリンタ用のSTLファイルを出力できることである。また，KeTCindyで描いた3Dの図がレイトレーシングでどのようになるのかを見ることも比較的簡単にできる。\\ - MeshLabとの連携は，KeTCindyから Obj 形式のデータを書き出すことで行う。Mkobj**() 関数でデータを作り，Mkviewobj() 関数でMeshLabを呼び出して表示を行う。\\ - なお，Mkviewobj() 関数でMeshLabを呼び出して表示を行う場合，これをDrawスロットに書くと頻繁に呼び出しが行われるため非効率となる。そこで，if(1==0,・・・) で・・・の部分にMeshLabの呼び出し関係のスクリプトを書いて，実際に呼び出すときに if(1==1,・・・)とする方法と，呼び出し関係のスクリプトを関数化してボタンに割り当てる方法がある。ketcindyパッケージに含まれる sample にボタンをつけたものがある。\\ - なお，３Dであるので，Initialization スロットに\\ - \verb|Ketinit();| - \verb|Ketinit3d();| +MeshLabは，3Dデータ（objデータなど）を読み込んでレイトレーシングで表示・編集するソフトウェアである。レイトレーシングで3Dグラフィクスを描くには，Cinderellaと親和性の高い Cindy3D を利用するのがよいが，MeshLabを使うメリットは3Dプリンタ用のSTLファイルを出力できることである。また，\ketcindy で描いた3Dの図がレイトレーシングでどのようになるのかを見ることも比較的簡単にできる。 + +MeshLabとの連携は，\ketcindy から Obj 形式のデータを書き出すことで行う。Mkobj**() 関数でデータを作り，Mkviewobj() 関数でMeshLabを呼び出して表示を行う。 + +なお，Mkviewobj() 関数でMeshLabを呼び出して表示を行う場合，これをDrawスロットに書くと頻繁に呼び出しが行われるため非効率となる。そこで，if(1==0,・・・) で・・・の部分にMeshLabの呼び出し関係のスクリプトを書いて，実際に呼び出すときに if(1==1,・・・)とする方法と，呼び出し関係のスクリプトを関数化してボタンに割り当てる方法がある。ketcindyパッケージに含まれる sample にボタンをつけたものがある。 + + なお，3Dであるので，Initialization スロットに + + \verb|Ketinit();| + \verb|Ketinit3d();| を記述しておく。 \begin{description} \hypertarget{mkobjcmd}{} -\item[関数] Mkobjcmd(name，式，option) -\item[機能] 厚みを持たない曲面のobjファイルのためのコマンドを作成する -\item[説明] オプションは [分割数1，分割数2，表側の方向の指定]\\ -表側の方向は，変数に対して，右手系の方向が"+"\\ -作成されるデータは"oc"+name のファイル名の obj データである。この名称は，Mkviewobj() で用いる。（以下，Mkobj**()関数では同様）\\ -\\ +\item[関数] Mkobjcmd(name，式，option) +\item[機能] 厚みを持たない曲面のobjファイルのためのコマンドを作成する +\item[説明] オプションは [分割数1，分割数2，表側の方向の指定] + +表側の方向は，変数に対して，右手系の方向が"+" + +作成されるデータは"oc"+name のファイル名の obj データである。この名称は，Mkviewobj() で用いる。（以下，Mkobj**()関数では同様） + +\vspace{\baselineskip} 【例】：サドル面 \begin{verbatim} - fd=[ "z=x^2-y^2", "x=[-1,1]","y=[-1,1]"," "]; - Sf3data("1",fd); - Windispg(); - Mkobjcmd("1",fd,[40,40,"-"]); - Meshlab():=( - Mkviewobj("saddle",oc1, ["m","v"]); - ); + fd=[ "z=x^2-y^2", "x=[-1,1]","y=[-1,1]"," "]; + Sf3data("1",fd); + Windispg(); + Mkobjcmd("1",fd,[40,40,"-"]); + Meshlab():=( + Mkviewobj("saddle",oc1, ["m","v"]); + ); \end{verbatim} このうち，\verb|Sf3data("1",fd); | はCinderellaの画面に表示するためであって，なくてもよい。 -次図で，左が option + の場合，右が - の場合である。\\ -\includegraphics[bb=0 0 1359 527 , width=12cm]{Fig3d/meshlab01.png} - \\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +次図で，左が option + の場合，右が - の場合である。 + +\includegraphics[bb=0 0 679.53 263.51 , width=12cm]{Fig/meshlab01.pdf} +\vspace{\baselineskip} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\vspace{\baselineskip} \hypertarget{mkobjcrvcmd}{} -\item[関数] Mkobjcrvcmd(name，PD，option) -\item[機能] 空間曲線（直線）のobjファイルのためのコマンドを作成 -\item[説明] オプションは [太さ，断面の形状（正多角形）の辺の数，断面の正面]\\ -曲線は紐のようなもので表す。その断面は正多角形で，デフォルトは正6角形である。断面の正面は"xy","yz","zx"のいずれかで指定する。太くなった時に形状の差が現れる。 +\item[関数] Mkobjcrvcmd(name，PD，option) +\item[機能] 空間曲線（直線）のobjファイルのためのコマンドを作成 +\item[説明] オプションは [太さ，断面の形状（正多角形）の辺の数，断面の正面] + +曲線は紐のようなもので表す。その断面は正多角形で， 初期設定は正6角形である。断面の正面は"xy","yz","zx"のいずれかで指定する。太くなった時に形状の差が現れる。 -例 太さ0.03で螺旋を描く +例 太さ0.03で螺旋を描く \begin{verbatim} - Spacecurve("1","[(6*pi-t)/(6*pi)*cos(t),(6*pi-t)/(6*pi)*sin(t),0.1*t]", - "t=[0,6*pi]",["Num=200"]); - Windispg(); - Mkobjcrvcmd("1","sc3d1",[0.03]); - Meshlab():=( - Mkviewobj("spiral",oc1,["m","v"]); - ); + Spacecurve("1","[(6*pi-t)/(6*pi)*cos(t),(6*pi-t)/(6*pi)*sin(t),0.1*t]", + "t=[0,6*pi]",["Num=200"]); + Windispg(); + Mkobjcrvcmd("1","sc3d1",[0.03]); + Meshlab():=( + Mkviewobj("spiral",oc1,["m","v"]); + ); \end{verbatim} -\verb| Mkobjcrvcmd("1","sc3d1",[0.1,8,"yz"]);| としたのが下図右。\\ +\verb| Mkobjcrvcmd("1","sc3d1",[0.1,8,"yz"]);| としたのが下図右。 - \includegraphics[bb=0 0 1229 473 , width=12cm]{Fig3d/meshlab02.png}\\ -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + \includegraphics[bb=0 0 614.53 236.51 , width=12cm]{Fig/meshlab02.pdf} + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\vspace{\baselineskip} \hypertarget{mkobjnrm}{} -\item[関数] Mkobjnrm(name，式) -\item[機能] 法線ベクトルのデータを作成 -\item[説明] 式は曲面を表す式。これに対し，法線ベクトルを表す式を求める。\\ +\item[関数] Mkobjnrm(name，式) +\item[機能] 法線ベクトルのデータを作成 +\item[説明] 式は曲面を表す式。これに対し，法線ベクトルを表す式を求める。 +\vspace{\baselineskip} \hypertarget{mkobjplatecmd}{} -\item[関数] Mkobjplatecmd(name，面データ，options) -\item[機能] 面を描く -\item[説明] 面データを渡して面を描く。\\ -options は，面の厚みの指定。厚みは中心線に対し，両側につけることができる。\\ -たとえば，[0.05] はプラス側に 0.05 の厚み，[0.05,-0.04] はマイナス側にも0.04の厚みをつける。\\ +\item[関数] Mkobjplatecmd(name，面データ，options) +\item[機能] 面を描く +\item[説明] 面データを渡して面を描く。 + +options は，面の厚みの指定。厚みは中心線に対し，両側につけることができる。 +たとえば，[0.05] はプラス側に 0.05 の厚み，[0.05,-0.04] はマイナス側にも0.04の厚みをつける。 + +\vspace{\baselineskip} 【例】三角形のプレートを描く + +\begin{layer}{150}{0} +\putnotese{80}{15}{ \includegraphics[bb=0 0 287.01 228.01 , width=3cm]{Fig/meshlab03.pdf} } +\end{layer} \begin{verbatim} - Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]"); - p1=[2,0,0]; - p2=[0,2,0]; - p3=[0,0,2]; - plane=[[p1,p2,p3],[[1,2,3]]]; - Mkobjplatecmd("1",plane,[0.05]); - Mkobjcrvcmd("2","ax3d"); - Mkviewobj("plane",Concatcmd([oc1,oc2]),["m","v"]); + Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]"); + p1=[2,0,0]; + p2=[0,2,0]; + p3=[0,0,2]; + plane=[[p1,p2,p3],[[1,2,3]]]; + Mkobjplatecmd("1",plane,[0.05]); + Mkobjcrvcmd("2","ax3d"); + Mkviewobj("plane",Concatcmd([oc1,oc2]),["m","v"]); \end{verbatim} - \includegraphics[bb=0 0 574 456 , width=5cm]{Fig3d/meshlab03.png}\\ - +\vspace{\baselineskip} \hypertarget{mkobjpolycmd}{} -\item[関数] Mkobjpolycmd(name，PD，options) -\item[機能] 多面体を描く -\item[説明] VertexEdgeFace() の戻り値を PDとして渡して多面体を描く。\\ - +\item[関数] Mkobjpolycmd(name，PD，options) +\item[機能] 多面体を描く +\item[説明] VertexEdgeFace() の戻り値を PDとして渡して多面体を描く。 - +\vspace{\baselineskip} \hypertarget{mkobjsymbcmd}{} -\item[関数] Mkobjsymbcmd(PD, 実数，実数，ベクトル, ベクトル) -\item[機能] 文字等のobjデータのためのコマンドを作成 -\item[説明] 引数のPDを描く。第２引数は大きさ，第３引数は回転角，第４引数は正面方向のベクトル，第５引数はPDの中心の位置。\\ -PDは，平面の描画コマンドによるプロットデータが使える。また，PD に半角アルファベットを文字として与えることができる。この場合，文字は n,p,q,r,t,x,y,z で，該当するフォントが data フォルダの fontF フォルダに用意されている。この中にないフォントは使えない。 \\ -【例】軸の名前 x,y,z を表示し，円を描く。\\ -円は Circledata(); でプロットデータを作成する。\\ -\begin{verbatim} -\end{verbatim} +\item[関数] Mkobjsymbcmd(PD, 実数，実数，ベクトル, ベクトル) +\item[機能] 文字等のobjデータのためのコマンドを作成 +\item[説明] 引数のPDを描く。第2引数は大きさ，第3引数は回転角，第4引数は正面方向のベクトル，第5引数はPDの中心の位置。 +PDは，平面の描画コマンドによるプロットデータが使える。また，PD に半角アルファベットを文字として与えることができる。この場合，文字は n,p,q,r,t,x,y,z で，該当するフォントが data フォルダの fontF フォルダに用意されている。この中にないフォントは使えない。 +\vspace{\baselineskip} \hypertarget{mkobjthickcmd}{} -\item[関数] Mkobjthickcmd(name，式) -\item[機能] 厚みを持つ曲面のobjファイルのためのコマンドを作成 -\item[説明] オプションは [分割数1，分割数2，厚み，表側の方向の指定，条件] +\item[関数] Mkobjthickcmd(name，式) +\item[機能] 厚みを持つ曲面のobjファイルのためのコマンドを作成 +\item[説明] オプションは [分割数1，分割数2，厚み，表側の方向の指定，条件] 表側の方向は，変数に対して，右手系の方向が"+"。厚みを持つため，nsew のそれぞれについて， -"+n+s-e-w" のように指定する。\\ -条件として，\verb|"Assume(R>0)"| をつけると，Rが0以下になるための不具合を回避できる。\\ +"+n+s-e-w" のように指定する。 + +条件として，\verb|"Assume(R>0)"| をつけると，Rが0以下になるための不具合を回避できる。 + また，"ratsimp" をつけると有理関数について，"trigsimp"をつけると三角関数について，処理を速くすることができる。 -なお，この関数はMaximaを使うので，Maximaをインストールしていることが前提。\\ + +なお，この関数はMaximaを使うので，Maximaをインストールしていることが前提。 + +\vspace{\baselineskip} 【例】回転放物線 + +\begin{layer}{150}{0} +\putnotese{70}{0}{ \includegraphics[bb=0 0 287.01 189.01 , width=4cm]{Fig/meshlab06.pdf}} +\end{layer} \begin{verbatim} - fd=[ - "z=(x^2+y^2)", - "x=R*cos(T)","y=R*sin(T)", - "R=[0,2]","T=[0,2*pi]","e" - ]; - Mkobjthickcmd("1",fd,[40,40,0.2,"+n+s-e-w+","assume(R>0)"]); - Mkviewobj("pala",oc1,["m","v","Wait=5"]); + fd=[ + "z=(x^2+y^2)", + "x=R*cos(T)","y=R*sin(T)", + "R=[0,2]","T=[0,2*pi]","e" + ]; + Mkobjthickcmd("1",fd,[40,40,0.2,"+n+s-e-w+","assume(R>0)"]); + Mkviewobj("pala",oc1,["m","v","Wait=5"]); \end{verbatim} - \includegraphics[bb=0 0 574 378 , width=5cm]{Fig3d/meshlab06.png}\\ +%\begin{center} \includegraphics[bb=0 0 574 378 , width=5cm]{Fig/meshlab06.pdf}\end{center} + +\vspace{\baselineskip} \hypertarget{mkviewobj}{} -\item[関数] Mkviewobj(name，PD, options) -\item[機能] objファイルを作成。optionにより MeshLab を立ち上げて表示する。 -\item[説明] 第２引数に複数のプロットデータを与えるときは，Concatcmd() により１つにまとめる。 +\item[関数] Mkviewobj(name，PD, options) +\item[機能] objファイルを作成。optionにより MeshLab を立ち上げて表示する。 +\item[説明] 第2引数に複数のプロットデータを与えるときは，Concatcmd() により１つにまとめる。 オプションは \begin{tabbing} 12345678901234567890\=\kill - "m"または"make" \> データを作る（指定しない場合もデータがなければ作る）\\ - "v"または"view" \>MeshLabを立ち上げて表示する\\ - "W=n" \>作成するための待ち時間。ｎ秒。これを過ぎると終了する\\ - "Unit=mm" \>Setunitlen()と連動して３Ｄプリンタの数値の単位をmmで指定する\\ - \>３Dプリンターがインチで認識する場合は "Unit=in" とする。\\ + "m"または"make" \> データを作る（指定しない場合もデータがなければ作る）\\ + "v"または"view" \>MeshLabを立ち上げて表示する\\ + "W=n" \>作成するための待ち時間。ｎ秒。これを過ぎると終了する\\ + "Unit=mm" \>Setunitlen()と連動して3Ｄプリンタの数値の単位をmmで指定する\\ + \>3Dプリンターがインチで認識する場合は "Unit=in" とする。\\ \end{tabbing} \end{description} -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} \newpage -% 表計算ソフトとの連携 ================================== +% 表計算ソフトとの連携 ================================== \subsection{表計算ソフトとの連携} -表計算ソフトでは，複数のセルを選択してコピー（Windowsでは Crtl+ C ，Macでは Command+C）すると，セルの内容はtab区切りのテキストデータとしてクリップボードにコピーされる。これをCindyscriptエディタにペーストすることで表計算ソフトのデータをKeTCindyで利用できる。逆に，Cindyscriptのコンソールへの出力を表計算ソフトのシートにコピーすることもできる。 +表計算ソフトでは，複数のセルを選択してコピー（Windowsでは Crtl+ C ，Macでは Command+C）すると，セルの内容はtab区切りのテキストデータとしてクリップボードにコピーされる。これをCindyscriptエディタにペーストすることで表計算ソフトのデータを\ketcindy で利用できる。逆に，Cindyscriptのコンソールへの出力を表計算ソフトのシートにコピーすることもできる。 また，表計算ソフトから書き出したCSVファイルについても同様にしてCSV形式のデータを扱うことができる。 \begin{description} \hypertarget{tab2list}{} -\item[関数] Tab2list(str，option) -\item[機能] str の内容をリストに変換する -\item[説明] tabやコンマ区切りになっている文字列 str をリストに変換する。\\ - optionは，次の通り。\\ - Blank=a ：NULLのセルをaに置き換える。\\ - Sep=b ：セパレータ（区切り文字）を b とする。デフォルトは tabコード\\ - -次のような手順で表計算ソフトやCSVファイルからデータをKeTCindyに移すことができる。\\ - \\ -(1) Cindyscriptエディタで，適当な文字変数を用意する。\\ - たとえば，data="";\\ - \\ -\includegraphics[bb=0 0 858 298 , width=10cm]{Fig/tab2list02.png}\\ - \\ -(2) 表計算ソフトで，適当な範囲を指定しクリップボードにコピーする。\\ - Windowsなら Ctrl+C，Macなら Command+C\\ - \\ -\includegraphics[bb=0 0 742 308 , width=8cm]{Fig/tab2list01.png}\\ - \\ -(3) data=""; のダブルクウォートの間にペーストする。\\ - 最後の行は右図のように，" の前で改行されていてもよい。\\ - \\ -\includegraphics[bb=0 0 738 236 , width=6cm]{Fig/tab2list00.png} - \includegraphics[bb=0 0 748 276 , width=6cm]{Fig/tab2list001.png}\\ - \\ -(4) この文字変数 data に対し，Tab2list(data) を実行すると，行列を表すリストが返される。\\ - これを適当な変数に代入し，作表コマンドで表にするなど，目的に応じて利用する。\\ - 数値だけなら行列として計算もできる。\\ - \\ -\includegraphics[bb=0 0 1245 457 , width=10cm]{Fig/tab2list03.png}\\ - \\ - 空文字のセル(NULL)が含まれる場合，デフォルトではそのまま空文字になるが，アンケート処理などで無回答を０にしたいような場合は\\ - \\ - \verb|dlist=Tab2list(data,["Blank=0"];|\\ - \\ - とする。\\ +\item[関数] Tab2list(str，option) +\item[機能] str の内容をリストに変換する +\item[説明] tabやコンマ区切りになっている文字列 str をリストに変換する。 + + optionは，次の通り。 - CSVファイルからCSV形式（コンマ区切り）のデータをコピーした場合は\\ - \\ - \verb|dlist=Tab2list(data,["Sep=,"];|\\ - \\ - とする。\\ + Blank=a ：NULLのセルをaに置き換える。 - なお，文字列をセパレータで区切ってリスト化するCindyscriptの関数に tokenize()がある。上の例で，\\ - \verb|dlist=tokenize(data,[unicode("000a"),unicode("0009")]);|\\ - とすると，改行コード(000a)とtabコード(0009)で切り分けてリスト化する。このとき，リストの各要素はつぎのようになる。\\ - 文字列→文字列\\ - 数値形式の文字→実数 例： 14 → 整数14 12.3 → 実数12.3\\ - 計算式の形 → 文字列 例： 437-0023 → 437-0023 (文字列)\\ -これに対し，Tab2list()では，計算式の形の文字列は数値と見なして計算結果を取得する。\\ - 例： 437-0023 → 414 (数値)\\ -したがって，郵便番号や日付(28/12/5)のようなものは計算されてしまうので，tokenize() を用いるのがよい。なお，tokenize()の場合，空行は空リストになるので，最後の行でダブルクウォートの前で改行されていると空リストが入るので注意されたい。\\ +Sep=b ：セパレータ（区切り文字）を b とする。 初期設定は tabコード + +次のような手順で表計算ソフトやCSVファイルからデータを\ketcindy に移すことができる。 + +\vspace{\baselineskip} +(1) Cindyscriptエディタで，適当な文字変数を用意する。 + + たとえば，data=""; + +\vspace{\baselineskip} +\hspace{10mm} \includegraphics[bb=0 0 429.02 149.01 , width=7cm]{Fig/tab2list02.pdf} + +\vspace{\baselineskip} +(2) 表計算ソフトで，適当な範囲を指定しクリップボードにコピーする。 + + Windowsなら Ctrl+C，Macなら Command+C + +\vspace{\baselineskip} +\hspace{10mm} \includegraphics[bb=0 0 371.02 154 , width=7cm]{Fig/tab2list01.pdf} + +\vspace{\baselineskip} +(3) data=""; のダブルクウォートの間にペーストする。 + +最後の行は右図のように，" の前で改行されていてもよい。 + +\vspace{\baselineskip} +\hspace{10mm} \includegraphics[bb=0 0 369.02 118.01 , width=6cm]{Fig/tab2list00.pdf} + +\hspace{10mm} \includegraphics[bb=0 0 374.02 138.01 , width=6cm]{Fig/tab2list001.pdf} + +\vspace{\baselineskip} +(4) この文字変数 data に対し，Tab2list(data) を実行すると，行列を表すリストが返される。 + +これを適当な変数に代入し，作表コマンドで表にするなど，目的に応じて利用する。 + +数値だけなら行列として計算もできる。 + +\vspace{\baselineskip} +\hspace{10mm} \includegraphics[bb=0 0 622.53 228.51 , width=10cm]{Fig/tab2list03.pdf} + +\vspace{\baselineskip} + 空文字のセル(NULL)が含まれる場合， 初期設定ではそのまま空文字になるが，アンケート処理などで無回答を０にしたいような場合は + +\hspace{10mm}\verb|dlist=Tab2list(data,["Blank=0"];| + +とする。 + + CSVファイルからCSV形式（コンマ区切り）のデータをコピーした場合は + +\hspace{10mm} \verb|dlist=Tab2list(data,["Sep=,"];| + +とする。 + +なお，文字列をセパレータで区切ってリスト化するCindyscriptの関数に tokenize()がある。上の例で， + +\hspace{10mm} \verb|dlist=tokenize(data,[unicode("000a"),unicode("0009")]);| + +とすると，改行コード(000a)とtabコード(0009)で切り分けてリスト化する。このとき，リストの各要素はつぎのようになる。 +文字列→文字列 + +数値形式の文字→実数 【例】 14 → 整数14 12.3 → 実数12.3 + +計算式の形 → 文字列 【例】 437-0023 → 437-0023 (文字列) + +これに対し，Tab2list()では，計算式の形の文字列は数値と見なして計算結果を取得する。 + +\vspace{\baselineskip} +【例】 437-0023 → 414 (数値) + +したがって，郵便番号や日付(28/12/5)のようなものは計算されてしまうので，tokenize() を用いるのがよい。なお，tokenize()の場合，空行は空リストになるので，最後の行でダブルクウォートの前で改行されていると空リストが入る。 + +\vspace{\baselineskip} \hypertarget{dispmat}{} -\item[関数] Dispmat(list) -\item[機能] リストを行列の形でtab区切りにしてコンソールに表示する。 -\item[説明] 行列を表すリスト （たとえば dlist) を引数としてDispmat(dlist) を実行すると，コンソールに行列型で内容が表示される。\\ - 実際にはTAB区切りの文字列。（println としなくても直接コンソールに表示される）\\ - これを表計算ソフトのシートにコピーする。\\ - \\ -\includegraphics[bb=0 0 855 395 , width=8cm]{Fig/tab2list04.png}\\ -\\ +\item[関数] Dispmat(list) +\item[機能] リストを行列の形でtab区切りにしてコンソールに表示する。 +\item[説明] 行列を表すリスト （たとえば dlist) を引数としてDispmat(dlist) を実行すると，コンソールに行列型で内容が表示される。 + +実際にはTAB区切りの文字列。（println としなくても直接コンソールに表示される） + +これを表計算ソフトのシートにコピーする。 +\vspace{\baselineskip} +\hspace{10mm} \includegraphics[bb=0 0 427.52 197.51 , width=7cm]{Fig/tab2list04.pdf} + + +\vspace{\baselineskip} \hypertarget{writecsv}{} -\item[関数] Writecsv(namelist, data, filename, option) -\item[機能] data の内容をCSVファイルに出力する -\item[説明] ベクトルまたは行列となっている data を、filenameのファイル名としてCSVファイルに書き出す。\\ - optionは，次の通り。（省略できる）\\ - Col=nn ：自然数nnで指定した列数のCSVファイルとして書き出す。\\ - namelistは，CSVファイルの1行目に追加される項目名。省略すると"C1,C2,..."という項目名が付く。\\ +\item[関数] Writecsv(namelist, data, filename, option) +\item[機能] data の内容をCSVファイルに出力する +\item[説明] ベクトルまたは行列となっている data を、filenameのファイル名としてCSVファイルに書き出す。 + +optionは，次の通り。（省略できる） + +Col=nn ：自然数nnで指定した列数のCSVファイルとして書き出す。 - なお，列数の指定を省略するとdataが行列の場合は、その列数をdataがベクトルの場合はnamelistの項目数を利用する。 +namelistは，CSVファイルの1行目に追加される項目名。省略すると"C1,C2,..."という項目名が付く。 + + +なお，列数の指定を省略するとdataが行列の場合は、その列数をdataがベクトルの場合はnamelistの項目数を利用する。 \end{description} -\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} \newpage -% MeshLabとの連携 ================================== -%\subsection{MeshLabとの連携} -% アニメーション ================================== + +% アニメーション ================================== \section{アニメーションPDF} \subsection{概要} アニメーションのできるPDFを作る。 Cinderellaの作図機能とCindyscriptを用いてアニメーションができるが，PDFにすることでCinderellaがなくてもPDFビュアーがあればアニメーションを実行できるので，プレゼンテーションや教材の受け渡しなどに便利である。 -次の画面は，samplesフォルダにある「s06animation」の「s0601cycloid」のものである。\\ - \\ - \includegraphics[bb=0 0 1581 880 , width=12cm]{Figmv/mvgaiyou01.png} +次の画面は，samplesフォルダにある「s06animation」の「s0601cycloid」のものである。これをひな形として使うのがよい。 -画面上方のボタンには，次のようなスクリプトが割り当てられているので，ボタンを自作することもできる。 +\vspace{\baselineskip} + \includegraphics[bb=0 0 732.04 376.02 , width=12cm]{Fig/mvgaiyou01.pdf} + +画面上方のボタンには，次のようなスクリプトが割り当てられている。 \begin{tabbing} - 12345678\=1234567897890123456\=\kill - Figure \>： Viewtex(); \>現在の画面のPDFデータを作る\\ - Parent \>： \>Figpdf() を使うときに使用する。\\ - ParaF \>： Parafolder(); \>パラパラ動画のデータを作る\\ - Anime \>： Mkanimation(); \>アニメーションPDFを作る\\ - Flip \>： Mkflipanime(); \>パラパラ動画PDFを作る + 12345678\=1234567897890123456\=\kill + Figure \>： Viewtex(); \>現在の画面のPDFデータを作る\\ + Parent \>：複数のスクリプト \>Figpdf() を使うときに使用する。\\ + ParaF \>： Parafolder(); \>アニメーションのデータを作る\\ + Anime \>： Mkanimation(); \>アニメーションPDFを作る\\ + Flip \>： Mkflipanime(); \>パラパラ動画PDFを作る \end{tabbing} アニメーションの作成は，フレームを定義する関数を作成し，Mkanimation() 関数を実行する(Animeボタン)。 %たとえば，Fhead が "hoge" の場合，TeX の文書には\\ -% \verb|\input{hogemoviefigs.tex}|\\ +% \verb|\begin{center} \input{hogemoviefigs.tex}|\\ %で動画を挿入することができる。 %ただし，動画のできるPDFを作成するには，ドキュメントクラスと使用パッケージについて注意が必要である。 @@ -4218,133 +5242,620 @@ Cinderellaの作図機能とCindyscriptを用いてアニメーションがで %ドキュメントクラスは，article または jarticle とする。jsarticle は使えない。 %パッケージは animate に dvipdfmx オプションをつける。\\ -% \verb|\usepackage[dvipdfmx]{animate}| +% \verb|\usepackage[dvipdfmx]{animate}| なお，アニメーションPDFでアニメーションを行うにはAdobe Acrobat Reader など，アニメーションに対応したPDFリーダーが必要である。WindowsのSumatraPDF，Macの プレビューでは動かない。 Flipボタンを押すと，フレームに分割したPDFが生成されて表示される。 -\subsection{設定} -KeTCindymvでは，KeTCindyと若干異なる設定が必要である。 +\subsection{関数} +\begin{description} + +\hypertarget{setpara}{} +\item[関数] Setpara(fname,funcstr,range,options1,options2) +\item[機能] アニメーションの設定をする +\item[説明] fname は出力するファイル名，funcstrは動画関数名，rangeは範囲 + +options1 はアニメーションのデータを作るための設定。 +\begin{tabbing} +1234567890123\=90123456789012345678\=\kill +m/r \> データの作成 / 既存データがある場合の読み込み（ 初期設定は r ）\\ +Div=n \> フレーム数。初期値は25。 +\end{tabbing} +options2 はアニメーションについての設定で，次の通り。 +\begin{tabbing} +1234567890123\=90123456789012345678\=\kill +Frate=n \>１秒間のフレーム数。初期値は20。 \\ +Title=str \> タイトル。\\ +Scale=n \> 図の大きさの拡大率 \\ +opA \> animate.sty のためのオプション。 \\ + \> loop：loopする，controls：ボタンを表示，buttonsize：ボタンのサイズ\\ + \> step：コマ送りモード\\ + \> 初期設定は loop,controls,buttonsize=3mm\\ + \> +をつけるとモードが追加される。たとえば \verb|"OpA=+step"| で\\ + \> \verb|"OpA=[loop,controls,buttonsize=3mm,step]"| となる。 +\end{tabbing} + +\vspace{\baselineskip} +\item[関数] Parafolder(funcstr,fname,range,options) +\item[機能] アニメーションのフレームデータを作成する +\item[説明] funcstrは動画関数名，fname は出力するフォルダ名，rangeは範囲 + +作業フォルダ(fig)内に，フレームデータを格納した fname フォルダを作る。ひな形（s0601cycloid）にある ParaF ボタンに割り当てられており，通常はそのまま使えばよい。 + +\vspace{\baselineskip} +\item[関数] Mkanimation(path,folder) +\item[機能] アニメーションのPDFを作る +\item[説明] 作業フォルダ(fig)内に，フレームデータを格納した fname フォルダを作り，ここからアニメーションのPDFを作る。Setpara() で設定したファイル名を fname とすると，生成する TeX ファイルは，animatefname.tex （PDF作成のTeXファイル）と animfname.tex （動画データ）で，PDFの名称は，animatefname.pdf となる。 + +ひな形（s0601cycloid）にある Anime ボタンに割り当てられており，通常はあらためて設定せずそのまま使えばよい。 + +\vspace{\baselineskip} +\item[関数] Mkflipanime(path,folder) +\item[機能] パラパラ動画のPDFを作る +\item[説明] 作業フォルダ(fig)内に，フレームデータを格納した fname フォルダを作り，ここからパラパラ動画のPDFを作る。Setpara() で設定したファイル名を fname とすると，生成する TeX ファイルは，flipanimefname.tex （PDF作成のTeXファイル）で，PDFの名称は，flipanimefname.pdf となる。 + +ひな形にある Flip ボタンに割り当てられており，通常はあらためて設定せずそのまま使えばよい。 + +\end{description} + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\subsection{制作例} + +%\begin{description} +\vspace{\baselineskip} +【例】定円上を動く点Pと，定点Aを結ぶ線分の中点をQとして動きを見る。 +アニメーションを定義する関数は，時間を $t$ とすれば，時刻 $t$ における図（動くものだけ）を定義する。時刻は単なる媒介変数であるので，$t$ でなく $s$ などでもよい。 + +\begin{verbatim} + Setax(["","","sw","","sw"]); + Slider("A-C-B",[0,YMIN-1],[2*pi,YMIN-1]); + Circledata("1",[[0,0],[0,2]]); + mf(t):=( + pt=2*[cos(t),sin(t)]; + mp=(pt+[4,0])/2; + Listplot("1",[[4,0],pt]); + Pointdata("1",[mp,pt],["Size=2"]); + if(t==0, + ptlist=[mp]; + , + ptlist=append(ptlist,mp); + ); + Letter([[4,0],"s","A",pt,"en","P",mp,"ne","Q"]); + Pointdata("2",ptlist,["Size=2","Color=red"]); + ); + mf(C.x); + Setpara("middle","mf(t)","t=[0,4*pi]"); +\end{verbatim} + +この例の場合，\verb|mf(C.x)| を実行するとスライダを動かすことでインタラクティブに軌跡を表示できる。 +Cinderellaの画面は次のようになる。 + +\vspace{\baselineskip} +\hspace{20mm} \includegraphics[bb=0.00 0.00 608.03 367.02,width=8cm]{Fig/moviedata01.pdf} + +アニメーションを作成するときは \verb|//mf(C.x)| とコメントアウトしてから Anime ボタンをクリックする。次の図は，でき上がった animatemiddle.pdf の始めの画面である。 + +\hspace{30mm}\includegraphics[bb=0.00 0.00 470.02 394.02,width=6cm]{Fig/moviedata02.pdf} + +また，次のようにオプションを指定すると，5秒間のアニメーションとなる。 + + \verb| Setpara("middle","mf(t)","t=[0,4*pi]",["Div=30"],["Frate=6"]);| + +\verb|["Div=150"],["Frage=30"]|とすると，やはり5秒間のアニメーションとなるが，1秒間のフレーム数が多いため，なめらかな動きとなる。これは標準的なビデオのフレームレートである。ただし，ファイルサイズは約5倍となる。 + + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +%\end{description} + +\newpage + + +%==================== Slide =============== +\section{\ketcindy スライド} +\subsection{概要と制作手順} +\ketcindy で作成した図とテキストを統合してプレゼンテーション用のスライドPDFを作成する。必要なファイルは，スライドの内容を記述したテキストファイル（ここではコンテンツファイルと呼ぶ）と，タイトルや図を作成し，コンテンツファイルと統合する \ketcindy のファイルである。この2つのファイルは，拡張子が txt と cdy で，ファイル名は同一とする。たとえば，コンテンツファイルを makeslide.txt ， \ketcindy ファイルを makeslide.cdy としたときの，制作イメージを次の図に示す。 + +\hspace{10mm}\input{Fig/makeslide} + +\hspace{10mm}makeslide.cdy + +\hspace{10mm}\includegraphics[bb=0.00 0.00 881.05 451.02,width=10cm]{Fig/slide01.pdf} + +\vspace{\baselineskip} +ひな形として，サンプルとして提供されている samples フォルダの中の s0701basic.cdy をコピーし，適当にリネームして使うのがよいだろう。必要なボタンと，最低限のスクリプトが記述されている。 + +以下では，\ketcindy のファイルを makeslide.cdy , コンテンツファイルを makeslide.txt として説明を進める。制作手順は次の通り。 + +(1) makeslide.cdy に \verb|Settitle| コマンドでタイトルを書き，「Titile」ボタンで書き出す。 + +タイトルスライドが作業フォルダに，makeslide.txt が makeslide.cdy と同じフォルダに作成される。makeslide.txt がすでにある場合には上書きはされず，タイトルスライドだけが上書きされる。 + +(2) makeslide.txt に，スライドの各ベージごとの内容を記述する。 + +(3) 必要な図やアニメーションのコードを書き，ボタンをクリックしてファイルを作る。 + +\hspace{10mm}Figure : 図を挿入するとき + +\hspace{10mm}ParaF : アニメーションやパラパラスライドを挿入するとき + +(4) Slide ボタンでスライドPDFを作成する。 + +PDFと，関連する中間ファイルは，作業フォルダではなく，makeslide.cdyのあるフォルダに作成される。また，スライドPDFはアニメーションと同様，Adobe Reader で開く必要がある。 + +\subsection{コンテンツファイル} + +コンテンツファイルは次のような構成にする。 + +\begin{tabbing} +1234567890\=12345678912345678901234567890\=\kill + \>title::slide0// \> タイトルスライド。title はコマンド。\\ + \>main::三角比と三角関数// \> セクション1のタイトル。main はコマンド。\\ + \> 直角三角形と三角比// \> 1ページ目の表示内容。\\ + \> ・・・・// \\ + \> new::角の概念の拡張// \> 新しいページとタイトル。new はコマンド。\\ + \> enumerate::[(1)]// \> 2ページ目の表示内容。enumerate はコマンド。\\ + \> ・・・・// \\ + \> new::負の角// \> 新しいページとタイトル。\\ + \> ・・・・// \\ + \>main::三角関数のグラフ// \> セクション2のタイトル。\\ + \> $f(x)=\sin x$// \> \hspace{10mm}以下同様\\ + \> new::振幅と周期// \\ + \> ・・・・// \\ +\end{tabbing} +%あまりスマートな方法ではないが，枠をKeTCindyで作ってレイヤーで表示 +\begin{layer}{150}{0} +\hspace{7mm}\input{Fig/boxframeslide} +\end{layer} + + +・すべての行の末尾には必ず // をつける。 + +\hspace{10mm} 注）urlの指定で // を用いるときは，$||||$ とすれば // に変換される。 + +・ページの内容は，コマンドでレイアウトなどを指定し，表示する文をテキストで書く。 + +\vspace{\baselineskip} +{\bf コマンド} + +コマンドにおいて，各ブロックの引数の区切りは \verb|::| とし，各行の終わりには必ず//をつける。 + +\vspace{\baselineskip} + {\bf 【タイトルと壁紙】} + + タイトルスライドをつけるときは， + + \hspace{10mm}\verb|title::slide0//| + + を１行目に置く。タイトルスライドは makeslide.cdy で作る。slide0は 初期設定のタイトルスライドのファイル名。このファイル名を変更(たとえば "start")したときは，makeslide.cdy で，Settile() のオプションに "Title=start" をつけて，ファイル名が一致するようにしておく。 + + タイトルスライドをつけないときはスライド名をつけないでおく。 + +\hspace{10mm} \verb|title:://| + +注）title コマンドは必須で，これを１行目に書かないとスライドは作成されない。 + +\vspace{\baselineskip} +壁紙（背景）を表示するときは，タイトルコマンドに続けて壁紙ファイル名を書く。 + + \hspace{10mm}\verb|title::slide0::wallpaper//| + +wallpaper は壁紙のファイル名。壁紙ファイルはTeXのファイルで，作業フォルダ（fig）に入れておく。 + +壁紙ファイルの一例 + +\begin{verbatim} + {\color[cmyk]{0.6,0.2,0.8,0}\huge\rm\normalsize + \newpage + \begin{layer}{120}{0} + \lineseg{0}{2}{125}{0} + \lineseg{0}{88}{125}{0} + \putnotese{0}{90}{\ketcindy} + \end{layer} + } +\end{verbatim} + +\vspace{\baselineskip} +{\bf 【セクションタイトル】} + +\hspace{10mm}\verb|main::セクションタイトル名//| + +セクションを分けないときはなくてもよい。 + +\vspace{\baselineskip} + {\bf 【新しいページ】} + +\hspace{10mm}\verb|new(::行下げ)::タイトル((::位置)::読み込みファイル)//| + + 例）\verb|new::[10]::はじめに::{50}{20}::figure//| + +読み込みファイルの表示サイズを変更するときは + + \hspace{10mm}\verb|new::[10]::はじめに::{50}{20}::figure,0.8//| + +のようにする。 + +読み込みファイルがなければ，figure は省略。 + +\vspace{\baselineskip} + {\bf 【箇条書き】} + +番号つき箇条書きは + + \hspace{10mm}\verb|enumerate//| + + で，enumerate環境の始まりを示す。 + +番号にかっこをつけるなど，番号の形式を変えるには， + +\hspace{10mm}\verb|enumerate::[(1)]| + +のように，\verb|::|で区切って形式を示す。 初期設定は，かっこなしの番号。 + +記号つき箇条書きは + +\hspace{10mm}\verb|itemize//| + +で itemize環境の始まりを示す。記号は中黒。 + +enumerate，itemizeのいずれも + +\hspace{10mm}\verb|item::文//| + +で itemを記述する。 + +環境の終わりは， + +\hspace{10mm}\verb|end//| + +で示す。 + +\vspace{\baselineskip} +{\bf 【項目の順表示】} + +1枚のスライド内で，項目を段階的に表示するときは，\verb|new| の次の行に + +\hspace{10mm}\verb| %repeat=m(,para)//| + +を書く。mは段階数で，たとえば，そのスライドの内容を3段階で表示したい場合は + +\hspace{10mm}\verb| %repeat=3//| + +とする。実際には３枚のスライドが作られる。 + +para をつけると，右下にコントローラが表示され，前後に進めやすくなる。 + +\hspace{10mm}\verb| %repeat=3,para//| + +段階的に表示したい行の先頭に，表示する順番を，2番目以降から +\begin{verbatim} + %[2,-]::text// + %[3,-]::text// +\end{verbatim} + +のように書く。 + +番号指定を \verb| [-, 3] | とすると，3番目まで表示する。 + +\verb| [1..3,5 ]| とすると，1番目から３番目までと5番目に表示する。（4番目をスキップ） + +\vspace{\baselineskip} + {\bf 【薄文字】} + + 順表示したい項目の全体像を見せておいて，そのうちの現在までの項目を示すような場合に用いる。番号指定の前に thin をつけ， + + \begin{verbatim} + %thin[2,-]::text// + %thin[3,-]::text// +\end{verbatim} + +のように書くと，現段階の項目よりあとは薄文字で表示される。 + +薄文字の濃さは， + +\hspace{10mm} \verb|\setthin{alpha}//| + +で指定できる。alphaは0から1までの数で， 初期設定は0.1。 + +\verb|\setthin{0}//| のとき，指定段階以降の項目は非表示になる。 + + 初期設定の薄文字の濃さは，makeslide.cdy の Setslidebodyの第３引数で設定できる。たとえば， + +\hspace{10mm}\verb|Setslidebody(["","",0.2]);| -まず，Initialization スロットでは，KeTCindy で\\ - \verb|Shellfile="";|\\ -になっているのを\\ - \verb| Shellfile="mv";|\\ とする。 -次に，Draw スロットでは，次のように \verb|Ketinit();| に加え，\verb|Ketinitmv();| が必要である。また，画面表示のために，\verb|Windispg();| のかわりに \verb|Mvdispg();| を用いる。 +item とともに用いるときは，\verb|%thin[n,-]| を先に書く。 + +\vspace{\baselineskip} +【例】項目の順表示 + +図は，３番目のJavaまで進んだところである。右下にコントローラがある。 + +\begin{layer}{150}{0} +\putnotese{70}{10} {\includegraphics[bb=0.00 0.00 777.04 516.03,width=7cm]{Fig/sliderepeat.pdf} } +\end{layer} \begin{verbatim} - Fhead="templatemv"; - Texparent=""; - Ketinit(); - Ketinitmv(); + new::プログラミング言語 // + %repeat=6,para// + \slidepage// + itemize// + item::Python// + %thin[2,-]::item::Ruby// + %thin[3,-]::item::Java// + %thin[4,-]::item::JavaScript// + %thin[5,-]::item::CindyScript// + %thin[6,-]::item::C// + end// +\end{verbatim} + +\vspace{\baselineskip} + {\bf 【図ファイルの順表示】} + +作業フォルダ（fig）の中にあるサブフォルダ（例えばsubfig）の図ファイルすべてを順に表示する。 + + パラパラ動画のときに用いる。パラパラ動画では，ParaFボタンをクリックすると，作業フォルダ(fig)の中に，動画のフレームファイルが入ったフォルダが作られる。そのフォルダのファイルをアルファベット順に表示する。もちろん，パラパラ動画以外のファイルの順表示に使ってもよい。 + +\verb|new| の次に + +\hspace{10mm} \verb|%repeat=//| + +\hspace{10mm} \verb|%para=subfig:{0}:s{60}{10}:input(:倍率)//| + +を書く。TeXのソースには， + +\hspace{10mm}\verb| layer{120}{0}, \putnotes{60}{10 初期設定put...}| + +の形で書き入れられる。 - ここにスクリプトを書く +また，２行に分けずに - Mvdispg(); +\hspace{10mm} \verb|%repeat=,para=... |と続けて書いてもよい。 + + +\vspace{\baselineskip} +{\bf 【レイヤー】} + +\hspace{10mm}\verb|layer::{範囲}{0}//| + +で layer環境の始まりを示す。layer環境の終わりは + +\hspace{10mm}\verb|end//| + + レイヤーの中に作業フォルダ（fig）にある図を表示するには + +\hspace{10mm}\verb|putnote::方向と位置::読み込みファイル//| + +とする。 + + 例） figure.texを(30,10)の位置の南東（原点は左上）に表示する。 + +\hspace{10mm} \verb|putonote::se{30}{10}::figure//| + + 例） figの中のfigure.texを0.8倍にして表示する。 + +\hspace{10mm} \verb|putonote::se{30}{10}::figure,0.8//| + + + 例）includegraphics で figure.pdf を表示する。 + +\hspace{10mm} \verb|putonote::se{30}{10}::include[width=5cm]::figure.pdf//| + + + 注）\verb|KeTpicStyle.pdf|を参照。文字などは本来の書式を用いて次のように入れる。 + +\hspace{10mm} \verb|\putonotee{30}{10}{文字}//| + +\vspace{\baselineskip} +{\bf 【テキストと動画】} + +コマンド以外のテキストはそのまま \TeX\ に書き出される。行末には // をつける。 +テキストを途中で改行するには，\TeX\ の 強制改行マーク \textbackslash \textbackslash をつける。 + +動画の場合は，動画の設定をして（アニメーションの節を参照）ファイルを作る。 + +パラパラ動画の場合は，ParaFボタンをクリックすると，figフォルダ内に動画のフレームファイルが入ったフォルダ（たとえば sincurve）が作られる。これを， + +\hspace{10mm} \verb|%repeat=//| + +\hspace{10mm} \verb|%para=sincurve:{0}:s{60}{10}:input(:倍率)//| + +で表示する。 + +アニメーションの場合は，スライドのために，makeslide.cdy のスクリプトに， \verb|Addpackage(["[dvipdfmx]{animate}"]);| を追加しておく。 + +Animeボタンをクリックすると，パラパラアニメと同様に動画のフレームファイルが入ったフォルダが作られ，動画用の\TeX\ ファイルができる。Setpara() で設定したファイル名が "sincurve" のとき，動画用の\TeX\ ファイルは "animsincurve.tex" となるので，\verb|%repeat| ではなく \verb|\input{fig/animsincurve}//| で表示する。 + + +\vspace{\baselineskip} +{\bf 【コメント行】} + + コマンドや文をコメントアウトするときは，\verb|%%| とする。 + +\vspace{\baselineskip} +{\bf 【空白行】} + +空白行を入れたいときは，\verb|...//| とする。 + +\vspace{\baselineskip} +{\bf 【タブ】} + +\hspace{10mm}\verb|\Ltab{長さ}{文１}文２| + +とすると，文１が行頭から，文２が長さ分の字下げをした位置から表示される。長さは 20mm のように指定。 + +\vspace{\baselineskip} +{\bf 【ページ番号】} + +page番号を表示するときは次のようにする。 + + mainの場合は \verb|\slidepage[m]//| + +それ以外の場合は \verb|%repeatの後に \slidepage//| + + 注）総ページ数を取得するため，TeXを２度コンパイルすることが必要である。そのため，Slideボタンを２度クリックすると総ページ数が表示される。 + +\vspace{\baselineskip} +{\bf mp3/mp4ファイルの追加} + +makeslide.txtのタイトルコマンドの後に，以下を追加する。 +\begin{verbatim} + title::slide0(::wallpaper) + ::\usepackage{ketmedia} + ::\usepackage[dvipdfmx]{media9}// \end{verbatim} -なお，ひながたの templatemv.cdy ではこの設定がすでにしてある。 -\newpage -\subsection{描画} +mp3ファイルを追加するときは，\verb|\inputsound|または\verb|\inputsoundclick|を用いる。\\ +\hspace{10mm}\verb|\inputsountclik[90]{フォルダ/}{ファイル}|\\ +\verb|\inputsound|は「自動再生」，\verb|\inputsoundclick|は「クリック再生」である。 +最初の引数は，ボタンの水平位置（単位mm）でデフォルトは90である．またフォルダには\verb|/|をつける。\vspace{2mm} + +mp4ファイルを追加するときは，\verb|\inputmovie|を用いる。\\ +\hspace{10mm}\verb|\inputsountclik[90]{1}{0.4}{フォルダ/}{ファイル}|\\ +2番目と3番目の引数は，幅と高さの\verb|\linewidth|からの倍率である。 + +\subsection{関数} +makeslide.cdy で使う，\ketcindy の関数。 + \begin{description} -\hypertarget{moviedata}{} -\item[関数] Moviedata(str1,str2,options) -\item[機能] アニメーションデータを作る -\item[説明] str1 はアニメーションを定義する関数名を文字列とする。str2 は定義域。\\ - optionsは，Cut と Div \\ - Cut ： 1秒のフレーム数。初期値は20。\\ - Div ： 全体のフレーム数。初期値は80。\\ - したがって，初期値では4秒間のアニメーションとなる。\\ - \\ -【例】定円上を動く点Pと，定点Aを結ぶ線分の中点をQとして動きを見る。\\ -まず，定円を，原点中心、半径２として描いておく。\\ -アニメーションを定義する関数は，時間を $t$ とすれば，時刻 $t$ における図（動くものだけ）を定義する。時刻は単なる媒介変数であるので，$t$ でなく $s$ などでもよい。 -\begin{verbatim} - Mf(t):=( - pt=2*[cos(t),sin(t)]; - Listplot("2",[[4,0],pt]); - Pointdata("2",mid(pt,[4,0])); - Letter([[4,0],"s","A",pt,"en","P",mid(pt,[4,0]),"ne","Q"]); - ); -\end{verbatim} -ここで，\verb|Mf(t)| の中で使っているユーザー定義関数\verb|mid()| は，端点を引数として線分の中点を返すもので，\\ - \verb|mid(p1,p2):=(p1+p2)/2;|\\ -として定義しておく。\\ -また，点の大きさを適宜設定しておく。\\ -以上の準備の後，\\ - \verb|Moviedata("Mf(t)","t=[0,2*pi]");|\\ -を実行する。\\ -ここでは，角度を媒介変数としているので，時間の$t$ でなく$s$ として\\ - \verb|Moviedata("Mf(s)","s=[0,2*pi]");|\\ -としてもよい。\\ -次のようにオプションを指定すると，5秒間のアニメーションとなる。\\ - \verb|Moviedata("Mf(s)","s=[0,2*pi]",["Div=50","Cut=10"]);|\\ -\verb|["Div=150","Cut=30"]|とすると，やはり5秒間のアニメーションとなるが，1秒間のフレーム数が多いためなめらかな動きとなる。ビデオのフレームレートである。ただし，ファイルサイズは約３倍となる。\\ -Cinderellaの画面は次のようになる。\\ - \\ - \includegraphics[bb=0 0 1054 706 , width=8cm]{Figmv/moviedata01.png}\\ - \\ -TexMvボタン または TexParaボタンを押すと画面上でもアニメーションが実行される。その後 Exekc ボタンを押すとファイルが作成される。 - -この図では，点が明示されるのは Q だけである。A,Pとも点を明示する場合のスクリプトの全体を示しておく。 -\begin{verbatim} - Fhead="mid"; - Texparent=""; - Ketinit(); - Ketinitmv(); - mid(p1,p2):=(p1+p2)/2; - Circledata("1",[[0,0],[2,0]]); - Ptsize(4); - Pointdata("1",[4,0]); - Mf(t):=( - pt=2*[cos(t),sin(t)]; - Listplot("2",[[4,0],pt]); - Pointdata("2",pt); - Pointdata("3",mid(pt,[4,0])); - Letter([[4,0],"s","A",pt,"en","P",mid(pt,[4,0]),"ne","Q"]); - ); - Moviedata("Mf(s)","s=[0,2*pi]",["Div=30","Cut=10"]); - Mvdispg(); -\end{verbatim} -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +\hypertarget{setslidebody}{} +\item[関数] Setslidebody(bodycolor,bodystyle,density) +\item[機能] 全体の文字スタイルと薄文字の濃さ(0-1)の設定 +\item[説明] 引数の意味は次の通り。 +\begin{tabbing} +1234567890123\=4567890\=\kill +bodycolor \> 文字色 : 初期設定は "blue"\\ +bodystyle \> フォントタイプ : 初期設定は \verb|"\Large\bf\boldmath"|\\ +density \> 薄文字の濃さ : 初期設定は 0.1 +\end{tabbing} -\hypertarget{setpara}{} -\item[関数] Setpara(str) -\item[機能] parapa のタイトルを指定する -\item[説明] パラパラ動画のタイトルを str にする。デフォルトは Fhead。\\ - "" にした場合はタイトルを表示しない。 +引数がない場合や（ \verb|Setslidebody()|）この関数を書かない場合は初期値が使われる。 -\end{description} +ある引数だけを指定したい場合は，それより前は空にする。 -\newpage +【例】\verb|Setslidebody(,"\large")| +\vspace{\baselineskip} +\hypertarget{setslidehyper}{} +\item[関数] Setslidehyper("dvipdfmx",options) +\item[機能] 順表示でページ送りのコントローラを設定する。 +\item[説明] 順表示しないときもこの関数の記述は必須と考えてよい。 -%== 3D =============== -\section{\ketcindy 3D} -\subsection{概要} -\ketcindy 3Dの画面は次のように構成される。 +パッケージ hyperref.styを読み込み，かつ，options の値を与える。 + +\verb|Setslidehyper();| は無効。初期設定で使う場合は \verb|Setslidehyper("");| とする。 + +第１引数は hyperref.sty の第１パラメータ。初期設定は "dvipdfmx" -Cinderellaの描画面に，白の矩形で囲んだ領域が２つできる。NE,SWを対角とする左側の領域を主画面，右側の領域を副画面という。\\ +options は ["cl=bool,lc=col,fc=col","Pos=[x,y]","Size=n"] - \includegraphics[bb=0 0 1776 998 , width=8cm]{Fig3d/3dstart.png}\\ +\begin{tabbing} +12345\=4567890\=\kill +cl \> colorlinks : リンクに色をつけるかどうか。true / false で指定。 初期設定は true\\ +lc \> linkcolor : コントローラの色。色名で指定。 初期設定は blue\\ +fc\> filecolor リンクの色。色名で指定。 初期設定は blue\\ +以上３つは，セットで指定。一部初期値を使う場合は\verb|lc=,| のように右辺を空にする。\\ +Pos \> コントローラの位置。 初期設定は [125,73] （左上が原点）\\ +Size \> コントローラの大きさ。 初期設定は1 +\end{tabbing} -主画面は平面の場合と同様，TeXに出力される範囲を示し，NE,SWの２点をドラッグすることにより変更できる。 -副画面は，Start3d() 関数により作成される。座標軸は，Xyzax3data() 関数によって描くことができる。主画面の下方のスライダで視点が移動でき，主画面上では軸が回転する。副画面は，xy平面上に視点を置いたものと考えればよい。 +\vspace{\baselineskip} +\hypertarget{setslidemain}{} +\item[関数] Setslidemain([letterc,boxc,boxd,framec,xpos,size]) +\item[機能] メインスライド（セクション区切り）の設定 +\item[説明] 引数の一部を 初期設定値とする場合は [,,,,3] や [,"red"] などとする。 +\begin{tabbing} +1234567\=4567890\=\kill +letterc \> 文字の色。 初期設定は CMYKで [0.98,0.13,0,0.43]\\ +boxc \> ボックスの色。 初期設定は [0,0.32,0.52,0] \\ +frame\> フレームの色。 初期設定は [0,0.32,0.52,0]\\ +xpos \> タイトルの水平位置。 初期設定は 62\\ +size \> タイトルの倍率。 初期設定は 2 +\end{tabbing} -主画面上にCinderellaの作図ツールで点や線分を作図すると，Start3d() 関数により副画面に対応する点が作図される。主画面上の点をドラッグするとx,y座標を変更でき，副画面上の点をドラッグするとz座標を変更できる。空間内の点は，Putpoint3d()関数によって座標を指定して作成することもできる。次のような図はCinderellaの作図ツールだけでも作ることができるし，Putpoint3d()関数を用いても作ることができる。\\ - \includegraphics[bb=0 0 1892 840 , width=10cm]{Fig3d/3dscreen.png}\\ +\vspace{\baselineskip} +\hypertarget{setslidepage}{} +\item[関数] Setslidepage([letterc,boxc,boxd,framec,shadowc,xpos,size]) +\item[機能] ページの設定をする。 +\item[説明] 引数の一部を 初期設定値とする場合は [,,,,3] や [,"red"]などとする。 -主画面と副画面の対応する点をドラッグすることにより，インタラクティブに図形を描くことができるが、実際には描画関数を用いて図形を描き，スライダで視点を変えて見やすい図をTeXに出力することになるだろう。 +\begin{tabbing} +1234567\=4567890\=\kill +letterc \> 文字の色。 初期設定は CMYKで [0.98,0.13,0,0.43]\\ +boxc \> ボックスの色。 初期設定は [0,0.32,0.52,0] \\ +frame\> フレームの色。 初期設定は [0,0.32,0.52,0]\\ +shadowc \> 影の色。 初期設定は [0,0,0,0.5]\\ +xpos \> タイトルの水平位置。 初期設定は 6\\ +size \> タイトルの倍率。 初期設定は 1.3 +\end{tabbing} + +\vspace{\baselineskip} +\hypertarget{setslidemargin}{} +\item[関数] Setslidemargin([leftmarginchange,topmarginchange]) +\item[機能] スライドの左上マージンをデフォルトから変更する場合の値。 +\item[説明] Setslidemargin([+5,-10]);（横方向に$+5$mm，縦方向に$-10$mm変更） -KeTCindy3Dでは，点・直線・曲線・面の描画を描画関数を用いて行うことができる。線や面については陰線処理を行い，立体的な図を作成することができる。しかし，陰線処理は処理にかなりの時間がかかるので，CindyscriptではなくScilabで行っているが，それでも相当時間がかかることを覚悟しなければならない。Scilabでの計算は，バッチファイル/シェルファイルで行っているが，Cindyscriptではその計算結果が出るのを待つため一時的に反応がなくなる。したがって，反応がなくなってもハングアップではないので，Cinderellaを強制終了しないように。 +\vspace{\baselineskip} +\hypertarget{settitle}{} +\item[関数] Settitle(タイトルリスト,options) +\item[機能] タイトルスライドを作る +\item[説明] タイトルリストはコンマ区切りで位置と文を文字列で与える。例を参照。 +「Title」ボタンをクリックすると，コンテンツファイルがない場合は新たに作る。すでにある場合は上書きせずタイトルスライドのみを作る。 -一例を示すと，球面をメッシュ入りで座標軸とともに陰線処理して描いた場合，次のような図が画面に表示されるまでの時間は，MacBookPro13' (Late 2013) Core i7 2.8GHz 8GB （OSX 10.11.6） の場合で約124秒であった。スクリプトは \hyperlink{wireparadata}{Wireparadata() } の例を参照されたい。\\ - \input{Fig3d/wirepara4} +Settitleのオプションは次をリストで与える。 + +\begin{tabbing} +123456789012\=4567890\=\kill +"Title=" \> タイトルスライドのファイル名。 初期設定は "slide0"。\\ +"Layery=" \> タイトルの縦位置。 初期設定は0。0でないときは方眼を表示。 \\ +"Color="\> 文字の色。 初期設定は blue。 +\end{tabbing} + +\vspace{\baselineskip} +【例】タイトルの設定 + +\begin{verbatim} + Settitle([ + "s{60}{20}{メインタイトル}", + "s{60}{50}{名前}", + "s{60}{60}{所属}", + "s{60}{70}{情報}" + ] , + ["Title=SlideA","Color=[1,1,0,0]"]); +\end{verbatim} + +出力する \TeX\ ファイルに，\verb|\begin{layer}| の設定をする。 \verb|s| は，東西南北の\verb|s| 。 + +例のように，タイトルリストは改行すると見やすい。 + +\end{description} +\newpage +%================== 3D =============== +\section{\ketcindy 3D} +\subsection{概要} +\ketcindy 3Dの画面は次のように構成される。 + +Cinderellaの描画面に，白の矩形で囲んだ領域が2つできる。NE,SWを対角とする左側の領域を主画面，右側の領域を副画面という。 + +\vspace{\baselineskip} +\begin{center} + \includegraphics[bb=0 0 879.05 447.02 , width=8cm]{Fig/3dstart.pdf} +\end{center} +主画面は平面の場合と同様，TeXに出力される範囲を示し，NE,SWの2点をドラッグすることにより変更できる。主画面の下方のスライダで視点が移動でき，主画面上では軸が回転する。副画面は，xy平面上に視点を置いたものと考えればよい。 + +主画面上にCinderellaの作図ツールで点や線分を作図すると，副画面に対応する点が作図される。主画面上の点をドラッグするとx,y座標を変更でき，副画面上の点をドラッグするとz座標を変更できる。 + +\vspace{\baselineskip} +\begin{center} + \includegraphics[bb=0.00 0.00 863.04 378.52 , width=10cm]{Fig/3dscreen.pdf} +\end{center} + +KeTCindy3Dでは，線や面についての陰線処理を行う。陰線処理はＣ言語との連携により処理を速めている。C言語を使う環境整備が必要であるが，現在はこれを標準としている。C言語が使えない場合はRで計算する関数を用いることになるが，その場合はかなり時間がかかる。（場合にもよるが2分程度） \newpage \subsection{設定・定義} @@ -4352,1683 +5863,1696 @@ KeTCindy3Dでは，点・直線・曲線・面の描画を描画関数を用い \begin{description} \hypertarget{ketinit3d}{} -\item[関数] Ketinit3d() -\item[機能] KeTCindy3Dの使用宣言 -\item[説明] Cinderellaの画面を３Ｄモードにする。\\ - Cinderellaの描画面に，視点移動のための２つのスライダを作る。スライダは初期位置が左端になる。\\ - KeTCindyの使用宣言 Ketinit() とともに用いるが，この関数は一度だけ実行すればよいので，通常は Initialization スロットに置く。Ketinit() も，平面の場合と異なり Initialization スロットに置けばよい。ただし，平面の関数を多用する場合は，Ketinit() は Drawスロットに書いておく。場合によって変数の初期化などが必要なためである。KeTCindy3Dにおける変数の初期化などは，Start3d()で行われる。\\ - \\ +\item[関数] Ketinit3d() +\item[機能] KeTCindy3Dの使用宣言 +\item[説明] Cinderellaの画面を3Ｄモードにする。 +Cinderellaの描画面に，視点移動のための2つのスライダを作る。スライダは初期位置が左端になる。 + +\textcolor{red}{＜重要＞} + + この関数は Initialization スロットに置く。Ketinit() も，平面の場合と異なり Initialization スロットに置く。KeTCindy3Dにおける変数の初期化などを行う，Start3d()はDrawスロットに書く。 + +\vspace{\baselineskip} \hypertarget{start3d}{} -\item[関数] Start3d(option) -\item[機能] ３Ｄの画面設定と空間点の認識 -\item[説明] 副画面を作り，幾何点を３Ｄの点として認識する。この関数は必須で，Drawスロットのはじめの方に置く。\\ - Cinderellaの作図ツールで，点・線分を作図すると，内部関数の Ptseg3data() によってそれらを空間の点として認識し，副画面上に対応する点をとる。ただし，始めはz座標を０とする。点の名前がAであれば，副画面上の点はAzとなる。点をポイントして選択すると副画面の上に座標が表示される。\\ - 作図した点の名称をインスペクタで変更した場合，新しい名称に対応する点を副画面上に作成するが，以前の点は消えないので要注意。たとえば，点Aを作図した後，主画面上の点Aをインスペクタで点Dに変えた場合，副画面上に新たにDzができるが，以前のAzも残る。残ったAzは，選択しておいて作図ツールの消去ボタン \includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/delete.png}で消すことができる。\\ - optionに，除外点のリストを与えると，その点は空間点としない。（始点を移動しても位置は変わらない）\\ -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +\item[関数] Start3d(option) +\item[機能] 3Ｄの画面設定と空間点の認識 +\item[説明] 副画面を作り，幾何点を3Ｄの点として認識する。この関数は必須で，Drawスロットの先頭に書く。 + +Cinderellaの作図ツールで，点・線分を作図すると，内部関数の Ptseg3data() によってそれらを空間の点として認識し，副画面上に対応する点をとる。ただし，始めはz座標を０とする。点の名前がAであれば，副画面上の点はAzとなる。点をポイントして選択すると副画面の上に座標が表示される。 + +作図した点の名称をインスペクタで変更した場合，新しい名称に対応する点を副画面上に作成するが，以前の点は消えないので要注意。たとえば，点Aを作図した後，主画面上の点Aをインスペクタで点Dに変えた場合，副画面上に新たにDzができるが，以前のAzも残る。残ったAzは，選択しておいて作図ツールの消去ボタン \includegraphics[bb=0 0 6.48 5.04 , width=0.6cm]{Fig/delete.pdf}で消すことができる。 + +optionに，除外点のリストを与えると，その点は空間点としない。（始点を移動しても位置は変わらない） + +\vspace{\baselineskip} +\hypertarget{startsurf}{} +\item[関数] Startsurf(options) +\item[機能] 曲面描画の初期化と定数の設定 +\item[説明] options で定数を設定する。定数としては，分割数，Cのサイズ，誤差の限界を設定する。 + +optionsがないときは，以下の 初期設定を用いる。 + + [50,50],[1500,500,200],[0.01,0.1] + +設定後に初期値にリセットするときは，文字列 "reset" を引数に与える。 + +これにより，陰線処理をともなう面の描画の手順は，次のようになる。 + +(1) Startsurf(); で面描画の宣言をする。 + +(2) 描画関数でプロットデータを作る。 + +(3) ExeccmdC(); で，C言語を用いてまとめて描画する。 + + +\vspace{\baselineskip} +\hypertarget{isangle}{} +\item[関数] Isangle() +\item[機能] 角度スライダ（視点スライダ）の選択判断 +\item[説明] 角度スライダを選択しているときは true ，そうでないときは false を返す。 + +曲面の描画・陰線処理には時間がかかるため，角度スライダを動かすと反応が悪くなる。そこで，角度スライダを選択しているときは曲面の描画をしないようにすることで反応がよくなる。 + +\vspace{\baselineskip} +【例】放物面の描画 + +次のようにすると，スライダの点を選んでいる間はワイヤフレームモデルが描かれ，画面上の他の部分をクリックして選択状態が解除されると陰線処理された放物面が描かれる。 +\begin{verbatim} + fd=[ + "z=4-(x^2+y^2)", + "x=R*cos(T)","y=R*sin(T)", + "R=[0,2]","T=[0,2*pi]","e" + ]; + if(Isangle(), + Sf3data("1",fd); + , + Startsurf(); + Sfbdparadata("1",fd); + Crvsfparadata("1","ax3d","sfbd3d1",fd); + ExeccmdC("1"); + ); +\end{verbatim} \end{description} + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + \newpage \subsection{描画} \begin{description} \hypertarget{bezier3d}{} -\item[関数] Bezier3d(name,リスト1,リスト2) -\item[機能] 空間ベジェ曲線を描く -\item[説明] 引数はリスト1が端点リスト，リスト2が制御点リスト\\ - １組の端点につき，２つの制御点を使う。\\ - \\ -【例】いくつかの点をベジェ曲線で結ぶ\\ - 端点A,Bに対し，制御点をD,Eとする。\\ - \verb|Bezier3d("1",["A","B"],["D","E"]);| \\ - 端点A,Bに対し，制御点をD,Eとし，端点BCに対し制御点をE,Fとする。\\ - \verb|Bezier3d("1",["A","B","C"],["D","E","E","F"]);|\\ - 端点A,Bに対し，制御点をD,Eとし，端点BCに対し制御点をF,Gとする。（図）\\ - \verb|Bezier3d("1",["A","B","C"],["D","E","F","G"]);|\\ - \input{Fig3d/bezier3d1} - -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} - -\hypertarget{changstyle3d}{} -\item[関数] Changstyle3d(リスト,リスト) -\item[機能] 3Dプロットデータの属性を変更 -\item[説明] 第１引数のプロットデータの属性を，第２引数に変更する。\\ -たとえば，補助線など，画面には描いてもTeXに書き出さない線を描画するときは，optionに["notex"] をつけるが，これをあとから付加したい場合に利用する。プロットデータはリストにできるので，複数のプロットデータの属性をまとめて変更することができて便利である。\\ - \\ -【例】４つの点で四面体の辺を描き，まとめて notex にする。点A,B,C,Dはとってあるものとする。 -\begin{verbatim} - Spaceline("1",[A,B]); - Spaceline("2",[A,C]); - Spaceline("3",[B,C]); - Spaceline("4",[A,D]); - Spaceline("5",[B,D]); - Spaceline("6",[C,D]); - edges=apply(1..6,"sl3d"+text(#)); - Changestyle3d(edges,["notex"]); -\end{verbatim} - -\hypertarget{concatobj}{} -\item[関数] Concatobj(リスト,option) -\item[機能] いくつかのobjデータを結合する -\item[説明] 多面体の各面の頂点リストから面データ（頂点リストと面リスト）を作る。\\ - \\ -【例】４点A,B,C,Dを頂点とする四面体を描く。\\ - 四面体は４つの面からなっている。頂点をA,B,C,Dとすると，４つの面は\\ - △ABC，△ABD，△ACD，△BCD\\ - である。\\ - \input{Fig3d/concatobj}\\ - そこで\\ - \verb|Concatobj([[A,B,C],[A,B,D],[A,C,D],[B,C,D]]);|\\ - とすると，面データ [[A,B,C,D],[[1,2,3],[1,2,4],[1,3,4],[2,3,4]]] が返される。\\ - この面データを使って四面体を描くことができる。コード例は，\hyperlink{vertexedgeface}{VertexEdgeFace()} を参照のこと。 - -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +\item[関数] Bezier3d(name,リスト1,リスト2) +\item[機能] 空間ベジェ曲線を描く +\item[説明] 引数はリスト1が端点リスト，リスト2が制御点リスト + +１組の端点につき，2つの制御点を使う。 + +\vspace{\baselineskip} +【例】いくつかの点をベジェ曲線で結ぶ + + 端点A,Bに対し，制御点をD,Eとする。 + + \verb|Bezier3d("1",["A","B"],["D","E"]);| \vspace{\baselineskip} + + 端点A,Bに対し，制御点をD,Eとし，端点BCに対し制御点をE,Fとする。 + + \verb|Bezier3d("1",["A","B","C"],["D","E","E","F"]);| + + 端点A,Bに対し，制御点をD,Eとし，端点BCに対し制御点をF,Gとする。（図） + + \verb|Bezier3d("1",["A","B","C"],["D","E","F","G"]);| + + \begin{center} \input{Fig/bezier3d1} \end{center} + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\hypertarget{changestyle3d}{} +\item[関数] Changestyle3d(リスト,リスト) +\item[機能] 3Dプロットデータの属性を変更 +\item[説明] 第１引数のプロットデータの属性を，第2引数に変更する。 + +たとえば，補助線など，画面には描いてもTeXに書き出さない線を描画するときは，optionに["notex"] をつけるが，これをあとから付加したい場合に利用する。プロットデータはリストにできるので，複数のプロットデータの属性をまとめて変更することができて便利である。 + +\vspace{\baselineskip} +【例】4つの点で四面体の辺を描き，まとめて notex にする。点A,B,C,Dはとってあるものとする。 +\begin{verbatim} + Spaceline("1",[A,B]); + Spaceline("2",[A,C]); + Spaceline("3",[B,C]); + Spaceline("4",[A,D]); + Spaceline("5",[B,D]); + Spaceline("6",[C,D]); + edges=apply(1..6,"sl3d"+text(#)); + Changestyle3d(edges,["notex"]); +\end{verbatim} + +\hypertarget{concatobj}{} +\item[関数] Concatobj(リスト,option) +\item[機能] いくつかのobjデータを結合する +\item[説明] 多面体の各面の頂点リストから面データ（頂点リストと面リスト）を作る。 + +\vspace{\baselineskip} +【例】4点A,B,C,Dを頂点とする四面体を描く。 + +四面体は4つの面からなっている。頂点をA,B,C,Dとすると，4つの面は + + △ABC，△ABD，△ACD，△BCD\\ +である。 + + \begin{center} \input{Fig/concatobj} \end{center} + +そこで + + \verb|Concatobj([[A,B,C],[A,B,D],[A,C,D],[B,C,D]]);| + +とすると，面データ [[A,B,C,D],[[1,2,3],[1,2,4],[1,3,4],[2,3,4]]] が返される。 + +この面データを使って四面体を描くことができる。コード例は，\hyperlink{vertexedgeface}{VertexEdgeFace()} を参照のこと。 + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} \hypertarget{crvsfparadata}{} -\item[関数] Crvsfparadata(name,PD1,PD2,式,options1,options2) -\item[機能] 曲線の曲面による陰線処理 -\item[説明] 曲線PD1を表示するにあたり，曲面PD2によって隠れる部分を非表示にする。\\ -通常は曲面PD2も表示するので，Sfbdparadata() も同時に用いることになる。曲面を表示しなければ，曲線だけが陰線処理された状態で表示される。\\ -第4引数の式は，PD2を描くための式。\\ -options1 には"r","m", "Wait=n" が指定できる。Wait の初期値は20\\ - "r","m"に関しては，オプションなしまたは，”” のとき\\ - i) データファイルがなければ，新しく作る\\ - ii) データファイルが既にあればそれを読み込む\\ - "m" のとき，強制的にデータファイルを作り直す。\\ - "r" のとき，すでにあるデータファイルを読み込む。\\ -options2 には 軸の陰線の表示について "nodisp" または線種が指定できる。デフォルトは "nodisp"。\\ -options2だけを指定したい場合は，options1 を空リスト [ ] にする。\\ - \\ -【例】回転放物面と座標軸，線分を描く。\\ -デフォルトでは陰線は非表示である。（下図左） -\begin{verbatim} - Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]"); - Putpoint3d(["A",[0,-3,0],"B",[0,3,3]],"fix"); - Spaceline([A,B]); - fd=["z=4-(x^2+y^2)","x=R*cos(T)","y=R*sin(T)","R=[0,2]","T=[0,2*pi]","e"]; - Sfbdparadata("1",fd); - Crvsfparadata("1","AB3d","sfbd3d1",fd); - Crvsfparadata("2","ax3d","sfbd3d1",fd); -\end{verbatim} -options2に線種指定 ["do"] をつけると，陰線は点線で表示される。（下図右） -\begin{verbatim} -Sfbdparadata("1",fd,[],["do"]); -Crvsfparadata("1","AB3d","sfbd3d1",fd,[],["do"]); -Crvsfparadata("2","ax3d","sfbd3d1",fd,[],["do"]); -\end{verbatim} - - \input{Fig3d/crvsfparadata1} \input{Fig3d/crvsfparadata2} - \\ -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} - -\hypertarget{datalist}{} -\item[関数] Datalist2d() -\item[機能] 画面上のプロットデータのリストを取得する -\item[説明] 画面に描かれているすべてのプロットデータのリストを返す。\\ -空間図形は，Cinderellaの画面上に射影し表示する。そのため，KeTCindy3Dは，空間におけるプロットデータと，画面上に表示するプロットデータの２つを作っている。Datalist2d()では，画面上に表示するプロットデータのリストを返す。\\ - \\ +\item[関数] Crvsfparadata(name,PD1,PD2,式) +\item[機能] 曲面による曲線の陰線処理を行う。 +\item[説明] 曲線PD1を表示するにあたり，曲面PD2によって隠れる部分処理を行う。 + +曲面PD2のプロットデータを作るため，Sfbdparadata() も同時に用いることになる。nameは，Sfbdparadata() と同じものにする。 + +作図例は，\hyperlink{execcmdc}{ExeccmdC()} を参照のこと。 + +C言語が使えない場合は，CrvsfparadataR(name,PD1,PD2,式,options1,options2) を使う。 +options1 は分割数と誤差限界， options2 は陰線の線種。 + +\vspace{\baselineskip} +\hypertarget{datalist}{} +\item[関数] Datalist2d() +\item[機能] 画面上のプロットデータのリストを取得する +\item[説明] 画面に描かれているすべてのプロットデータのリストを返す。 + +空間図形は，Cinderellaの画面上に射影し表示する。そのため，KeTCindy3Dは，空間におけるプロットデータと，画面上に表示するプロットデータの2つを作っている。Datalist2d()では，画面上に表示するプロットデータのリストを返す。 + +\vspace{\baselineskip} 【例】 \begin{verbatim} - Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]"); - Putpoint3d(["A",[0,-3,0],"B",[0,3,3]],"fix"); - Spaceline([A,B]); - println("PD="+Datalist2d()); + Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]"); + Putpoint3d(["A",[0,-3,0],"B",[0,3,3]],"fix"); + Spaceline("1",[A,B]); + println("PD="+Datalist2d()); \end{verbatim} -とすると，コンソールに PD=[ax2d,AB2d] と表示される。ax2dは座標軸のプロットデータ ax3d に，AB2d は線分ABのプロットデータ AB3d に対応している。\\ - \\ +とすると，コンソールに PD=[ax2d,AB2d] と表示される。ax2dは座標軸のプロットデータ ax3d に，AB2d は線分ABのプロットデータ AB3d に対応している。 +\vspace{\baselineskip} \hypertarget{datalist}{} -\item[関数] Datalist3d() -\item[機能] 空間のプロットデータのリストを取得する -\item[説明] 空間に描かれているすべてのプロットデータのリストを返す\\ - \\ +\item[関数] Datalist3d() +\item[機能] 空間のプロットデータのリストを取得する +\item[説明] 空間に描かれているすべてのプロットデータのリストを返す + +\vspace{\baselineskip} 【例】 \begin{verbatim} - Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]"); - Putpoint3d(["A",[0,-3,0],"B",[0,3,3]],"fix"); - Spaceline([A,B]); - println("PD="+Datalist3d()); + Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]"); + Putpoint3d(["A",[0,-3,0],"B",[0,3,3]],"fix"); + Spaceline("1",[A,B]); + println("PD="+Datalist3d()); \end{verbatim} -とすると，コンソールに PD=[ax3d,AB3d] と表示される。\\ +とすると，コンソールに PD=[ax3d,AB3d] と表示される。 -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} \hypertarget{dist3d}{} -\item[関数] Dist3d(a1,a2) -\item[機能] 空間の２点間の距離を返す -\item[説明] 引数a1,a2 は作図点の名称，空間点の名称のいずれでもよい。\\ -次の３通りの記法は同じ結果を返す。混在も可 +\item[関数] Dist3d(a1,a2) +\item[機能] 空間の2点間の距離を返す +\item[説明] 引数a1,a2 は作図点の名称，空間点の名称のいずれでもよい。 + +次の3通りの記法は同じ結果を返す。混在も可 \begin{verbatim} - Dist3d("A","B"); - Dist3d(A,B); - Dist3d(A3d,B3d); + Dist3d("A","B"); + Dist3d(A,B); + Dist3d(A3d,B3d); \end{verbatim} - \\ +\vspace{\baselineskip} \hypertarget{drawpoint3d}{} -\item[関数] Drawpoint3d(座標) -\item[機能] 空間点を描く -\item[説明] 引数で与えた空間座標の点を描く。この点は幾何点ではない。また，TeX にも出力されない。幾何点にするには \hyperlink{putpoint3d}{Putpoint3d()} と用いる。TeXに点を出力するには，\hyperlink{pointdata}{Pointdata()} または \hyperlink{drwpt}{Drawpoint()} を用いる。\\ +\item[関数] Drawpoint3d(座標) +\item[機能] 空間点を描く +\item[説明] 引数で与えた空間座標の点を描く。この点は幾何点ではない。また，TeX にも出力されない。幾何点にするには \hyperlink{putpoint3d}{Putpoint3d()} を用いる。TeXに点を出力するには，\hyperlink{pointdata3d}{Pointdata3d()} を用いる。 + 引数は，座標のリストにすることもできる。\\ - \\ +\vspace{\baselineskip} 【例】 \begin{verbatim} - Drawpoint3d([1,1,1]); - Drawpoint3d([[1,1,1],[0,1,0]]); + Drawpoint3d([1,1,1]); + Drawpoint3d([[1,1,1],[0,1,0]]); +\end{verbatim} +\vspace{\baselineskip} + +\hypertarget{execcmdc}{} +\item[関数] ExeccmdC(name,options1,options2) +\item[機能] 曲面を表示する。戻り値は，対象にしたプロットデータのリスト。 +\item[説明] データが作成された曲面を表示する。 + +options1 には"r","m", "Wait=n" と輪郭線の線種が指定できる。Wait の初期値は20 + + "r","m"に関しては，オプションなしまたは，”” のとき + + i) データファイルがなければ，新しく作る + + ii) データファイルが既にあればそれを読み込む + + "m" のとき，強制的にデータファイルを作り直す。 + + "r" のとき，すでにあるデータファイルを読み込む。 + +options2 には 軸の陰線について "nodisp" または線種が指定できる。 初期設定は "do"。 + +options2だけを指定したい場合は，options1 を空リスト [ ] にする。 + + +\vspace{\baselineskip} +【例】回転放物面と座標軸，線分を陰線処理したデータを作って表示する。線分の端点A,Bはあらかじめ作図しておく。 + + 初期設定では陰線は点線で表示される。（下図左） +\begin{verbatim} + Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]"); + Putpoint3d(["A",[0,-3,0],"B",[0,3,3]],"fix"); + Spaceline([A,B]); + fd=["z=4-(x^2+y^2)","x=R*cos(T)","y=R*sin(T)","R=[0,2]","T=[0,2*pi]","e"]; + Startsurf(); + Sfbdparadata("1",fd); + Crvsfparadata("1","AB3d","sfbd3d1",fd); + Crvsfparadata("2","ax3d","sfbd3d1",fd); + ExeccmdC("1"); +\end{verbatim} +options2を ["nodisp"] にすると，陰線は非表示になる。（下図右） +\begin{verbatim} + ExeccmdC("1",[],["nodisp"]); \end{verbatim} - \\ + \begin{center} \input{Fig/crvsfparadata2} \input{Fig/crvsfparadata1} \end{center} + +戻り値を使うと，陰線のスタイル（線種，色）を変えることができる。戻り値と同じものがコンソールに「readoutdata from template3D1.txt : 」として表示されるので，これを見て操作対象を決めればよい。たとえば，上の左図で，線分ABの陰線はリストの４番目の crvsfh3d1 なので， + +\begin{verbatim} + ret=ExeccmdC("1"); + Changestyle3d(ret_4,["da","Color=red"]); +\end{verbatim} + +とすると，赤の破線になる。 + +\hspace{20mm} \input{Fig/execcmdc1} + +この他，\hyperlink{sfbdparadata}{Sfbdparadata()},\hyperlink{wireparadata}{Wireparadata()} も参照のこと。 + +\vspace{\baselineskip} \hypertarget{embed}{} -\item[関数] Embed(name,PDリスト,式,変数リスト) -\item[機能] ２Ｄ図形の空間内平面へ埋め込む -\item[説明] 第２引数は２Ｄの図形のプロットデータのリスト，式と変数は平面を記述する式と変数。平面は原点$vo$と２つの基本ベクトル $\overrightarrow{vx}，\overrightarrow{vy}$を用いて，$vo+x \cdot \overrightarrow{vx}+y \cdot \overrightarrow{vy}$ の形で表すことができる。変数（基本ベクトルの係数）は$x,y$ でなく，$s,t$ でもよい。式，変数リストともに文字列にする。また，基本ベクトルは直交していなくてもよいし，長さが異なってもよいが，縦横同じスケールの直交座標系にするのがわかりやすいだろう。\\ - \\ +\item[関数] Embed(name,PDリスト,式,変数リスト) +\item[機能] 2Ｄ図形の空間内平面へ埋め込む +\item[説明] 第2引数は2Ｄの図形のプロットデータのリスト，式と変数は平面を記述する式と変数。平面は原点$vo$と2つの基本ベクトル $\overrightarrow{vx}，\overrightarrow{vy}$を用いて，$vo+x \cdot \overrightarrow{vx}+y \cdot \overrightarrow{vy}$ の形で表すことができる。変数（基本ベクトルの係数）は$x,y$ でなく，$s,t$ でもよい。式，変数リストともに文字列にする。また，基本ベクトルは直交していなくてもよいし，長さが異なってもよいが，縦横同じスケールの直交座標系にするのがわかりやすいだろう。 + +\vspace{\baselineskip} 【例】正三角形と外接円を空間内の平面に埋め込む \begin{verbatim} - Xyzax3data("","x=[-5,4]","y=[-10,4]","z=[-5,5]",["a","O"]); - Spaceline("1",[[3,0,0],[3,6,0],[3,6,6],[3,0,6],[3,0,0]]); - Defvar("vo=[3,3,3]"); - Defvar("vx=[0,1,0]"); - Defvar("vy=[0,0,1]"); - Putpoint3d(["A",[3,3,3]],"fix"); - Circledata("1",[[0,0],[2,0]],["nodisp"]); - Listplot("1",[[0,2],[-sqrt(3),-1],[sqrt(3),-1],[0,2]],["nodisp"]); - Embed("1",["cr1","sg1"],"vo+x*vx+y*vy","[x,y]"); - Ptsize(3); - Drawpoint(A); -\end{verbatim} - \input{Fig3d/embed01} - - ここで，Embed()で引き渡す vo,vx,vy については，Scilabでの変数定義が必要なので（KeTCindyでは行わない）Defvar() によって定義をしている。 + Xyzax3data("","x=[-5,4]","y=[-10,4]","z=[-5,5]",["a","O"]); + Spaceline("1",[[3,0,0],[3,6,0],[3,6,6],[3,0,6],[3,0,0]]); + Defvar("vo=[3,3,3]"); + Defvar("vx=[0,1,0]"); + Defvar("vy=[0,0,1]"); + Putpoint3d(["A",[3,3,3]],"fix"); + Circledata("1",[[0,0],[2,0]],["nodisp"]); + Listplot("1",[[0,2],[-sqrt(3),-1],[sqrt(3),-1],[0,2]],["nodisp"]); + Embed("1",["cr1","sg1"],"vo+x*vx+y*vy","[x,y]"); + Ptsize(3); + Drawpoint(A); +\end{verbatim} + \begin{center} \input{Fig/embed01} \end{center} + +ここで，Embed()で引き渡す vo,vx,vy については，Rでの変数定義が必要なので（\ketcindy では行わない）Defvar() によって定義をしている。 + 原点，基本ベクトルを，点を作図して次のようにすることもできる。この場合は Defvar() は不要。 + \begin{verbatim} - Putpoint3d(["A",[3,3,3],"B",[0,1,0],"C",[0,0,1]],"fix"); - Embed("1",["cr1","sg1"],"A3d+x*B3d+y*C3d","[x,y]"); + Putpoint3d(["A",[3,3,3],"B",[0,1,0],"C",[0,0,1]],"fix"); + Embed("1",["cr1","sg1"],"A3d+x*B3d+y*C3d","[x,y]"); \end{verbatim} - \includegraphics[bb=0 0 954 766 , width=6cm]{Fig3d/embed03.png}\\ +\begin{center} +\includegraphics[bb=0 0 477.02 383.02 , width=6cm]{Fig/embed03.pdf} +\end{center} この場合，点B,Cの座標がそのまま基本ベクトルとなっているが，原点Aに対して描画平面上にはB,Cがないので図がわかりにくい。図をわかりやすくするならば次のようにする。 \begin{verbatim} - Putpoint3d(["A",[3,3,3],"B",[3,4,3],"C",[3,3,4]],"fix"); - Embed("1",["cr1","sg1"],"A3d+x*(B3d-A3d)+y*(C3d-A3d)","[x,y]"); + Putpoint3d(["A",[3,3,3],"B",[3,4,3],"C",[3,3,4]],"fix"); + Embed("1",["cr1","sg1"],"A3d+x*(B3d-A3d)+y*(C3d-A3d)","[x,y]"); \end{verbatim} - また，平面を記述するのに，平面の原点と法線ベクトルを用いて Perpplane() を用いると，基本ベクトルが生成されるので、これを利用することができる。次のスクリプトでは，Skeletonparadata() を用いて陰線処理もしている。 + また，平面を記述するのに，平面の原点と法線ベクトルを用いて Perpplane() を用いると，基本ベクトルが生成されるので、これを利用することができる。次のスクリプトでは，Skeletonparadata() を用いて陰線処理もしている。 \begin{verbatim} - Xyzax3data("","x=[-5,5]","y=[-8,5]","z=[-5,5]"); - Putpoint3d(["O",[0,0,0],"P",[1,1,2]],"fix"); - Perpplane("E-F","P",P3d-O3d,"put"); - vec1=3*(E3d-P3d); - vec2=3*(F3d-P3d); - Putpoint3d(["A",P3d+vec1+vec2],"fix"); - Putpoint3d(["B",P3d+vec1-vec2],"fix"); - Putpoint3d(["C",P3d-vec1-vec2],"fix"); - Putpoint3d(["D",P3d-vec1+vec2],"fix"); - Spaceline([A,B,C,D,A]); - Circledata("1",[[0,0],[2,0]],["nodisp"]); - Listplot("1",[[0,2],[-sqrt(3),-1],[sqrt(3),-1],[0,2]],["nodisp"]); - Embed("1",["cr1","sg1"],"P3d+x*(E3d-P3d)+y*(F3d-P3d)","[x,y]"); - Ptsize(3); - Drawpoint(P); - Skeletonparadata("1"); + Xyzax3data("","x=[-5,5]","y=[-8,5]","z=[-5,5]"); + Putpoint3d(["O",[0,0,0],"P",[1,1,2]],"fix"); + Perpplane("E-F","P",P3d-O3d,"put"); + vec1=3*(E3d-P3d); + vec2=3*(F3d-P3d); + Putpoint3d(["A",P3d+vec1+vec2],"fix"); + Putpoint3d(["B",P3d+vec1-vec2],"fix"); + Putpoint3d(["C",P3d-vec1-vec2],"fix"); + Putpoint3d(["D",P3d-vec1+vec2],"fix"); + Spaceline("1",[A,B,C,D,A]); + Circledata("1",[[0,0],[2,0]],["nodisp"]); + Listplot("1",[[0,2],[-sqrt(3),-1],[sqrt(3),-1],[0,2]],["nodisp"]); + Embed("1",["cr1","sg1"],"P3d+x*(E3d-P3d)+y*(F3d-P3d)","[x,y]"); + Ptsize(3); + Drawpoint(P); + Skeletonparadata("1"); \end{verbatim} - \input{Fig3d/embed02} + \begin{center} \input{Fig/embed02} \end{center} -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} \hypertarget{intersectcrvsf}{} -\item[関数] Intersectcrvsf(name,PD，式) -\item[機能] 曲線と曲面の交点の座標を求める -\item[説明] PDは曲線のプロットデータ。式は曲面の式。\\ - \\ -【例】回転放物面と線分の交点の座標を表示する。曲面は表示されていなくてもよい。 -\begin{verbatim} -Putpoint3d(["A",[0,-3,0],"B",[0,3,2]],"fix"); -Spaceline([A,B]); -fd=["z=4-(x^2+y^2)","x=R*cos(T)","y=R*sin(T)","R=[0,2]","T=[0,2*pi]","e"]; -println("Intersect="+Intersectcrvsf("1","AB3d",fd)); +\item[関数] Intersectcrvsf(name,PD，式) +\item[機能] 曲線と曲面の交点の座標を求める +\item[説明] PDは曲線のプロットデータ。式は曲面の式。 + + 曲面は，Sfbdparadata()でデータを作成し，ExeccmdC()で表示しておく。交点の座標は，"intercrvsf"+name に代入される。コマンドの実行順序は次の例のようにする。 + +\vspace{\baselineskip} +【例】回転放物面と線分の交点の座標を表示する。 +\begin{verbatim} + Putpoint3d(["A",[0,-3,0],"B",[0,3,2]],"fix"); + Spaceline("1",[A,B]); + fd=[ + "z=4-(x^2+y^2)","x=R*cos(T)","y=R*sin(T)", + "R=[0,2]","T=[0,2*pi]","e" + ]; + Startsurf(); + Sfbdparadata("1",fd); + Intersectcrvsf("1","sl3d1",fd); + ExeccmdC("1",[""]); + println("Intersect="+intercrvsf1); + Drawpoint3d(intercrvsf1); \end{verbatim} 実行すると，コンソールに\\ - \verb|Intersect=[[0,-1.91,0.36,1.18],[0,1.57,1.52,1.76]] | -と表示される。\\ + \verb|Intersect=[[0,1.57,1.52],[0,-1.91,0.36]] | +と表示され，画面には緑で交点が表示される。。 + +\vspace{\baselineskip} \hypertarget{intersectsgpL}{} -\item[関数] IntersectsgpL(点名，線分，面，描画方法) -\item[機能] 空間の線分と平面の交点を作図する -\item[説明] 引数の線分は線分の端点を "A-B" の形もしくは座標のリスト形で与える。\\ - 引数の面は，面内の３点を "C-D-E" の形もしくは座標のリストで与える。\\ - 描画方法は，"put" または "draw" で，描画方法を指定しない場合は "draw" と同じ。"draw"では交点が緑の点で表示されるだけで，幾何点はできない。"put" では幾何点を作る。\\ - \\ +\item[関数] IntersectsgpL(点名，線分，面，描画方法) +\item[機能] 空間の線分と平面の交点を作図する +\item[説明] 引数の線分は線分の端点を "A-B" の形もしくは空間座標のリストで与える。 + + 引数の面は，面内の3点を "C-D-E" の形もしくは空間座標のリストで与える。 + + 描画方法は，"put" または "draw" で，描画方法を指定しない場合は "draw" と同じ。"draw"では交点が緑の点で表示されるだけで，幾何点はできない。"put" では幾何点を作る。 + +\vspace{\baselineskip} 【例】座標のリストで与える記述例\\ - \verb|IntersectsgpL("P",[p1,p2],[p3,p4,p5],"draw");| \\ - \\ -【例】立方体を平面で切った図を描く。\\ - いろいろな手順が考えられるが，ここでは次の手順で描く。\\ - (1) 立方体の頂点をとる。１辺の長さをHnとする。\\ - ここでは軸上の点はPutaxes3d()でとる。\\ -(2) 切断面を決める点E,F,Gを辺上の自由点としてPutonseg3d()でとる。\\ -(3) E,F,Gを通る平面と，辺AC,DYとの交点をとり，M,Nとする。\\ + \verb|IntersectsgpL("P",[p1,p2],[p3,p4,p5],"draw");| + +\vspace{\baselineskip} +【例】立方体を平面で切った図を描く。 + + いろいろな手順が考えられるが，ここでは次の手順で描く。 + + (1) 立方体の頂点をとる。１辺の長さをHnとする。 + + ここでは軸上の点はPutaxes3d()でとる。 + +(2) 切断面を決める点E,F,Gを辺上の自由点としてPutonseg3d()でとる。 + +(3) E,F,Gを通る平面と，辺AC,DYとの交点をとり，M,Nとする。 + (4) 全体を多面体として面データを作って描画する。 \begin{verbatim} - Hn=3; - Putaxes3d(Hn); - Putpoint3d("A",[Hn,Hn,0],"fix"); - Putpoint3d("B",[Hn,0,Hn],"fix"); - Putpoint3d("C",[Hn,Hn,Hn],"fix"); - Putpoint3d("D",[0,Hn,Hn],"fix"); - Putonseg3d("E",X,B); - Putonseg3d("F",Z,B); - Putonseg3d("G",Z,D); - IntersectsgpL("M","A-C","E-F-G","put"); - IntersectsgpL("N","D-Y","E-F-G","put"); - phd=Concatobj([[O,X,A,Y],[X,A,M,E],[A,Y,N,M],[Y,N,G,Z,O], - [O,Z,F,E,X],[Z,F,G],[E,M,N,G,F]]); - VertexEdgeFace("1",phd,["Edg=nogeo"]); - Nohiddenbyfaces("1","phf3d1"); -\end{verbatim} -Cinderellaの描画面はつぎのようになる。点E,F,Gをドラッグして，適当な位置の断面にできる。ただし，M,Nは辺上にあることが条件である。 -\\ - \\ -\includegraphics[bb=0 0 1426 654 , width=12cm]{Fig3d/IntersectsgpL0.png}\\ + Hn=3; + Putaxes3d(Hn); + Putpoint3d("A",[Hn,Hn,0],"fix"); + Putpoint3d("B",[Hn,0,Hn],"fix"); + Putpoint3d("C",[Hn,Hn,Hn],"fix"); + Putpoint3d("D",[0,Hn,Hn],"fix"); + Putonseg3d("E",X,B); + Putonseg3d("F",Z,B); + Putonseg3d("G",Z,D); + IntersectsgpL("M","A-C","E-F-G","put"); + IntersectsgpL("N","D-Y","E-F-G","put"); + phd=Concatobj([[O,X,A,Y],[X,A,M,E],[A,Y,N,M],[Y,N,G,Z,O], + [O,Z,F,E,X],[Z,F,G],[E,M,N,G,F]]); + VertexEdgeFace("1",phd,["Edg=nogeo"]); + Nohiddenbyfaces("1","phf3d1"); +\end{verbatim} +Cinderellaの描画面はつぎのようになる。点E,F,Gをドラッグして，適当な位置の断面にする。ただし，M,Nは辺上にあることが条件である。 + +\vspace{\baselineskip} +\includegraphics[bb=0 0 713.04 327.02 , width=12cm]{Fig/IntersectsgpL0.pdf} + できた図は下図左。これに，次のスクリプトを追加すれば，断面上方の立方体の各辺も点線で描かれる。（下図右） \begin{verbatim} - Spaceline([E,B,F],["do"]); - Spaceline([B,C,M],["do"]); - Spaceline([C,D,N],["do"]); - Spaceline([D,G],["do"]); + Spaceline("1",[E,B,F],["do"]); + Spaceline("2",[B,C,M],["do"]); + Spaceline("3",[C,D,N],["do"]); + Spaceline("4",[D,G],["do"]); \end{verbatim} -\input{Fig3d/IntersectsgpL1} \input{Fig3d/IntersectsgpL2} +\begin{center} \input{Fig/IntersectsgpL1} \input{Fig/IntersectsgpL2} \end{center} -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} \hypertarget{invparapt}{} -\item[関数] Invparapt(座標，PD) -\item[機能] 描画面上の座標に対応する曲線上の点の座標を返す -\item[説明] Cinderellaの描画面上の座標を与えて，それに対応する曲線上の３次元座標を返す。 +\item[関数] Invparapt(座標，PD) +\item[機能] 描画面上の座標に対応する曲線上の点の座標を返す +\item[説明] Cinderellaの描画面上の座標を与えて，それに対応する曲線上の3次元座標を返す。 \\ -空間内の曲線を作図すると，曲線の空間内のプロットデータとともに，描画面上に描くためのプロットデータも作られる。これを利用すると，描画面上の位置から曲線上の座標を求めることができる。\\ - \\ -【例】螺旋と線分を描いたとき，描画面上での交点（空間内の交点ではない）に対応する螺旋上の点の座標を求め部分曲線を描く。\\ +空間内の曲線を作図すると，曲線の空間内のプロットデータとともに，描画面上に描くためのプロットデータも作られる。これを利用すると，描画面上の位置から曲線上の座標を求めることができる。 + +\vspace{\baselineskip} +【例】螺旋と線分を描いたとき，描画面上での交点（空間内の交点ではない）に対応する螺旋上の点の座標を求め部分曲線を描く。 + \begin{verbatim} - Spaceline("1",[[-1,-1,-1],[1,2,3]]); - Spacecurve("1","[2*cos(t),2*sin(t),0.2*t]","t=[0,4*pi]",["do"]); - tmp=Intersectcrvs("sl2d1","sc2d1"); - p1=Invparapt(tmp_1,"sc3d1"); - p2=Invparapt(tmp_2,"sc3d1"); - Partcrv3d("1",p1,p2,"sc3d1"); + Spaceline("1",[[-1,-1,-1],[1,2,3]]); + Spacecurve("1","[2*cos(t),2*sin(t),0.2*t]","t=[0,4*pi]",["do"]); + tmp=Intersectcrvs("sl2d1","sc2d1"); + p1=Invparapt(tmp_1,"sc3d1"); + p2=Invparapt(tmp_2,"sc3d1"); + Partcrv3d("1",p1,p2,"sc3d1"); \end{verbatim} - \input{Fig3d/invparapt}\\ -ここで，sl2d1,sc2d1 は線分と螺旋の描画面上での（平面の）プロットデータである。Intersectcrvs() で平面上の交点の座標（複数あるのでリストが返る）を求め，Invparapt() で対応する螺旋上の点の座標を求めて部分曲線を描いている。実際に交わる点での部分曲線ではないことに注意。\\ - \\ + \begin{center} \input{Fig/invparapt} \end{center} + +ここで，sl2d1,sc2d1 は線分と螺旋の描画面上での（平面の）プロットデータである。Intersectcrvs() で平面上の交点の座標（複数あるのでリストが返る）を求め，Invparapt() で対応する螺旋上の点の座標を求めて部分曲線を描いている。実際に交わる点での部分曲線ではないことに注意。 +\vspace{\baselineskip} \hypertarget{mkbezierptcrv3d}{} -\item[関数] Mkbezierptcrv3d(点リスト) -\item[機能] 制御点を自動的にとる空間ベジェ曲線 -\item[説明] リストで与えた点に対し，制御点を自動的に生成してベジェ曲線を描く。\\ - 制御点は，２つの点に対して，その点を端点とする線分上に２つ作られる。これを適宜移動して任意の曲線にすることができる。\hyperlink{bezier3d}{空間ベジェ曲線 Bezier3d()} を参照のこと。\\ - \\ +\item[関数] Mkbezierptcrv3d(点リスト) +\item[機能] 制御点を自動的にとる空間ベジェ曲線 +\item[説明] リストで与えた点に対し，制御点を自動的に生成してベジェ曲線を描く。 + + 制御点は，2つの点に対して，その点を端点とする線分上に2つ作られる。これを適宜移動して任意の曲線にすることができる。\hyperlink{bezier3d}{空間ベジェ曲線 Bezier3d()} を参照のこと。 + +\vspace{\baselineskip} 【例】\verb|Mkbezierptcrv3d(["A","B","C","D"]);|\\ - 線分AB上に２点a1p,a2p，線分BC上に２点a2p,a2q，線分CD上に２点a3p,a3qができる。\\ + 線分AB上に2点a1p,a2p，線分BC上に2点a2p,a2q，線分CD上に2点a3p,a3qができる。 + -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} \hypertarget{nohiddenbyfaces}{} -\item[関数] Nohiddenbyfaces(name,PD1,PD2,option1,option2) -\item[機能] 面に対し曲線を陰線処理する -\item[説明] PD2で与えられた面に対し，曲線PD1の面に隠れている部分を陰線処理する。\\ -引数PD1を省略するとすべての曲線が対象となる。陰線処理された線は初期設定では点線で表される。この線種はoption2で変更できる。たとえば，["da"] とすると破線になる。option1は曲線全体のoptionであるので，option2 だけを指定する場合は，option1 として空リスト[ ] が必要である。\\ - \\ +\item[関数] Nohiddenbyfaces(name,PD1,PD2,option1,option2) +\item[機能] 面に対し曲線を陰線処理する +\item[説明] PD2で与えられた面に対し，曲線PD1の面に隠れている部分を陰線処理する。 + +引数PD1を省略するとすべての曲線が対象となる。陰線処理された線は初期設定では点線で表される。この線種はoption2で変更できる。たとえば，["da"] とすると破線になる。option1は曲線全体のoptionであるので，option2 だけを指定する場合は，option1 として空リスト[ ] が必要である。 +option2では，"Eps=" で，陰線処理時の許容限界を設定できる。陰線処理がうまくいかないときは，この値を \verb|Eps=10^(-4)| のように変えてみるとよい。初期設定は \verb|Eps=10^(-2)|。 + +\vspace{\baselineskip} 【例】座標平面上に正四面体を描き，各軸と正四面体の辺を陰線処理する。（下図左） \begin{verbatim} Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,4]"); Putpoint3d("A",2*[-1,-1/sqrt(3),0],"fix"); Putpoint3d("B",2*[1,-1/sqrt(3),0],"fix"); Putpoint3d("C",2*[0,sqrt(3)-1/sqrt(3),0],"fix"); -Putpoint3d("D",2*[0,0,sqrt(3)],"fix"); +Putpoint3d("D",2*[0,0,2*sqrt(6)/3],"fix"); phd=Concatobj([[A,B,C],[A,B,D],[A,C,D],[B,C,D]]); VertexEdgeFace("1",phd,["Edg=nogeo"]); Nohiddenbyfaces("1","phf3d1"); \end{verbatim} - \verb|VertexEdgeFace("1",phd,["Edg=nogeo"]);| によって，辺，頂点，面のプロットデータが作られる。\verb|phf3d1| は，面のプロットデータである。\\ - ここで，\verb|Nohiddenbyfaces("1","phe3d1","phf3d1",["dr,2"],["da"]); | とすると，座標軸は陰線処理されず，正四面体の辺（\verb|phe3d1|）だけが陰線処理されて破線で描かれる。四面体は太く描かれる。（下図右）\\ - \\ - \input{Fig3d/nohiddenbyfaces1} \input{Fig3d/nohiddenbyfaces2}\\ -同様に，\\ - \verb|Nohiddenbyfaces("1","ax3d","phf3d1",[],["da"]);|\\ -とすれば，座標軸だけが陰線処理されて破線で描かれる。\\ -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} + \verb|VertexEdgeFace("1",phd,["Edg=nogeo"]);| によって，辺，頂点，面のプロットデータが作られる。\verb|phf3d1| は，面のプロットデータである。 + +ここで，\verb|Nohiddenbyfaces("1","phe3d1","phf3d1",["dr,2"],["da"]); | とすると，座標軸は陰線処理されず，正四面体の辺（\verb|phe3d1|）だけが陰線処理されて破線で描かれる。四面体は太く描かれる。（下図右） + +\vspace{\baselineskip} + \begin{center} \input{Fig/nohiddenbyfaces1} \input{Fig/nohiddenbyfaces2} \end{center} +同様に， + + \verb|Nohiddenbyfaces("1","ax3d","phf3d1",[],["da"]);| + +とすれば，座標軸だけが陰線処理されて破線で描かれる。 +%\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\vspace{\baselineskip} \hypertarget{parapt}{} -\item[関数] Parapt(座標) -\item[機能] 点の投影面での座標 -\item[説明] 引数の空間座標に対応するCinderellaの描画面の座標を返す。\\ - \\ -【例】\verb|Parapt([2,1,5]);| により，点(2,1,5) が表示されている描画面の座標，たとえば [-0.52,3.27] が返される。\\ -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +\item[関数] Parapt(座標) +\item[機能] 点の投影面での座標 +\item[説明] 引数の空間座標に対応するCinderellaの描画面の座標を返す。 -\hypertarget{perpplane}{} -\item[関数] Perpplane(点名,点,ベクトル，option) -\item[機能] 点を通り線分に垂直な平面上に基準点を２つとる -\item[説明] 引数の点名は，作成する２点で "A-B" の形\\ - 第２引数は通る点の名称または座標\\ - 第３引数は法線ベクトル\\ - optionは "put" で，２つの幾何点を作図する。optionがない場合は幾何点は作らず，無名の点のみを表示する。put以外の文字列を書いたときは無効な命令とし，何も作成されない。\\ - 記述例を示すと\\ - \verb|Perpplane("A-B","P",[1,1,1],"put");|\\ - 点Pを通り，法線ベクトル(1,1,1)に垂直な平面上に点A,Bをとる。\\ - \verb|Perpplane("A-B","P",P3d-O3d);|\\ - 点Pを通り，線分OPに垂直な平面上に点A,Bをとる。\\ - これらにおいて，PAとPBは垂直で，PA=PB=1 となる。\\ - \\ -【例】ベクトル $\vec{p}=(1,1,1)$ に垂直で点$(1,1,1)$を通る平面を描く。 -\begin{verbatim} - Putaxes3d(2); - Putpoint3d(["P",[1,1,1]],"fix"); - Ptseg3data(); - Perpplane("E-F","P",P3d-O3d,"put"); - vec1=2*(E3d-P3d); - vec2=2*(F3d-P3d); - Putpoint3d(["A",P3d+vec1+vec2],"fix"); - Putpoint3d(["B",P3d+vec1-vec2],"fix"); - Putpoint3d(["C",P3d-vec1-vec2],"fix"); - Putpoint3d(["D",P3d-vec1+vec2],"fix"); - Spaceline([A,B,C,D,A]); - Letter([P,"w","P",A,"ne","A",B,"e","B",C,"ws","C",D,"nw","D",]); - Skeletonparadata("1"); -\end{verbatim} - \input{Fig3d/perpplane} -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} - \\ +\vspace{\baselineskip} +【例】\verb|Parapt([2,1,5]);| により，点(2,1,5) が表示されている描画面の座標，たとえば [-0.52,3.27] が返される。 +%\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\hypertarget{perppt}{} -\item[関数] Perppt(点名，点，点リスト,option) -\item[機能] 平面に下ろした垂線の足を求める -\item[説明] 第２引数の点から，第３引数の点リストで決まる平面に下した垂線の足を，第１引数の名前の点とする。\\ -オプションは次の通り。デフォルトは "draw"\\ - draw：点を打つ。幾何点は作らない\\ - put ：幾何点を作る\\ - none：計算だけ行い，点は作図しない。\\ - \\ -【例】原点から点ABCを通る平面に下した垂線の足Hの座標を求める。\\ - \verb|Perppt("H","O","A-B-C","none");| 表示はされない。\\ - \verb|Perppt("N","O","A-B-C");| Ｈの位置に緑色の点が表示される。\\ - \verb|Perppt("N","O","A-B-C","put");| 幾何点Hが作図される。\\ - いずれの場合も，Hの座標は変数H3d に代入される\\ - \\ -作図例 -\begin{verbatim} - Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,4]"); - Putpoint3d("O",[0,0,0],"fix"); - Putpoint3d("A",[3,0,0],"fix"); - Putpoint3d("B",[0,3,0],"fix"); - Putpoint3d("C",[0,0,3],"fix"); - Perppt("H","O","A-B-C","put"); - Spaceline([A,B,C,A]); - Spaceline([O,H]); - Letter([A,"nw","A",B,"ne","B",C,"ne","C",O,"nw","O",H,"ne","H"]); -\end{verbatim} - \\ - \input{Fig3d/perppt} - \\ +\vspace{\baselineskip} +\hypertarget{perpplane}{} +\item[関数] Perpplane(点名,点,ベクトル，option) +\item[機能] 点を通り線分に垂直な平面上に基準点を2つとる +\item[説明] 引数の点名は，作成する2点で "A-B" の形 -\hypertarget{partcrv3d}{} -\item[関数] Partcrv3d(name，始点，終点，PD) -\item[機能] 部分曲線のプロットデータを作成する -\item[説明] 曲線PDにおいて，始点から終点までのプロットデータを作成する。\\ -始点と終点は，プロットデータの番号もしくは曲線上にとった点の識別名で示す。\\ - -【例】螺旋を描き，CからDまでの部分を太くする。PutonCurve3d() で螺旋上に点C,Dをとり，ドラッグして適当な位置に移動する。 -\begin{verbatim} - Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,4]"); - Spacecurve("1","[2*cos(t),2*sin(t),0.2*t]","t=[0,4*pi]",["Num=100"]); - PutonCurve3d("C","sc3d1"); - PutonCurve3d("D","sc3d1"); - Partcrv3d("1",C,D,"sc3d1",["dr,3"]); - Letter([C,"n2","C",D,"n2","D"]); -\end{verbatim} - ここで，\verb|"sc3d1"| は，螺旋のプロットデータ，\verb|"part3d1"| は，部分曲線のプロットデータである。\\ - \input{Fig3d/partcrv3d1}\\ - \\ -【例】稲妻状の螺旋を点線で描き，その一部を実線にする。位置はプロットデータの番号で示す。小数にすると曲線を分割している線分の途中の位置になる。 -\begin{verbatim} -Spacecurve("1","[2*cos(t),2*sin(t),0.2*t]","t=[0,4*pi]",["Num=10","do"]); -Partcrv3d("1",3.3,8.5,"sc3d1"); -\end{verbatim} - \input{Fig3d/partcrv3d2}\\ +第2引数は通る点の名称または座標 + +第3引数は法線ベクトル + +optionは "put" で，2つの幾何点を作図する。optionがない場合は幾何点は作らず，無名の点のみを表示する。put以外の文字列を書いたときは無効な命令とし，何も作成されない。 + +記述例を示すと + + \verb|Perpplane("A-B","P",[1,1,1],"put");| + +点Pを通り，法線ベクトル(1,1,1)に垂直な平面上に点A,Bをとる。 -\hypertarget{phparadata}{} -\item[関数] Phparadata(name,name2,options) -\item[機能] 多面体を陰線処理して描く -\item[説明] 多面体を陰線処理して描く。多面体は面データ（頂点リストと面リスト）を与えて，VertexEdgeFace() でプロットデータを作る。このプロットデータに対し，隠れている面（辺）を非表示にして表示する。第1引数は通常のname，第2引数のname2は，VertexEdgeFace() で与えたnameと同じものとする。\\ - optionsは，全体の線種（"dr,2"など）と，陰線の線種を"Hidden=線種" で指定できる。デフォルトでは陰線は表示しない。\\ - \\ -【例】小林・鈴木・三谷による多面体データ polyhedrons obj から，s06の切頂二十面体（サッカーボール型）を描く。 -\begin{verbatim} - Setdirectory( Dirhead+"/data/polyhedrons_obj"); - phd=Readobj("s06.obj",["size=3"]); - Setdirectory(Dirwork); - VertexEdgeFace("s06",phd,["Edg=nogeo"]); - Phparadata("1","s06"); -\end{verbatim} - VertexEdgeFace() の name は通常の "1" でもよい。その場合は，\verb|Phparadata("1","1");| とするが，わかりにくいので上のようにした。\\ - 実行すると，Cinderellaの描画面は次のように頂点だけが描かれる。\\ - \\ - \includegraphics[bb=0 0 1452 730 , width=12cm]{Fig3d/phparadata01.png}\\ - \\ -「Texview」「Exekc」ボタンを押すと陰線処理したデータがFhead.txt に書き出され，これを用いてFhead.texが作成される。そのため，Exekcボタンを押してから処理が完了するまでにかなり時間がかかる。(下図左)\\ - なお，もう一度実行すると，こんどは，Fhead.txt ができているために，これを読み込んでCinderellaの画面でも陰線処理された図が描かれる。\\ - 全体の線種と，陰線の線種を\\ - \verb|Phparadata("1","s05",["dr,2","Hidden=do"]);|\\ -で指定したのが下図右である。\\ - - \input{Fig3d/phparadata02} \input{Fig3d/phparadata03}\\ - -【注意】\\ - polyhedrons obj のデータを使って，続けて異なる多面体を描きたい場合は注意が必要である。Readobj()だけを変更して別のデータを読めばよさそうであるが，VertexEdgeFace() のname も（したがって，Phparadata()の第2引数も）書き換えないと，前のデータが残っていてうまくいかない。たとえば，上のコードで切頂十二面体を描いた後，正八面体（r02）を描こうとするならば， -\begin{verbatim} - Setdirectory( Dirhead+"/data/polyhedrons_obj"); - phd=Readobj("r02.obj",["size=3"]); - Setdirectory(Dirwork); - VertexEdgeFace("2",phd,["Edg=nogeo"]); - Phparadata("1","2"); -\end{verbatim} - のようにする。\\ - -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} + \verb|Perpplane("A-B","P",P3d-O3d);| + + 点Pを通り，線分OPに垂直な平面上に点A,Bをとる。 + これらにおいて，PAとPBは垂直で，PA=PB=1 となる。 + +\vspace{\baselineskip} +【例】ベクトル $\vec{p}=(1,1,1)$ に垂直で点$(1,1,1)$を通る平面ABCDを描く。 -\hypertarget{projcoordpara}{} -\item[関数] Projcoordpara(座標) -\item[機能] 投影座標を求める -\item[説明] 空間座標を投影した座標を求める。\\ - 戻り値の第１，第２要素はCinderellaの描画面のx,y座標。第３要素はxy平面に垂直なzの座標で．投影面からの（符号付）距離を表す。\\ - \\ -【例】\verb|Projcoordpara([3,1,2]);|\\ - 戻り値は [-0.65,1.7,3.27] となる。\\ + 点A,B,C,Dは作図ツールで適当に取っておく。正確な位置はスクリプトで決める。 +\begin{layer}{120}{0} +\putnotese{80}{20}{ \input{Fig/perpplane}} +\end{layer} -\hypertarget{putaxes3d}{} -\item[関数] Putaxes3d([x,y,z]) -\item[機能] 軸上に幾何点を作る。 -\item[説明] 引数のリスト [x,y,z] に対し，点X(x,0,0) ,Y(0,y,0) , Z(0,0,z) および 原点Oを主画面上にとり，副画面上に対応する点Xz，Yz，Zz，Oz を作る。すでに同じ名称の点がある場合は，指定された位置に移動する。\\ - 引数は，実数にすることもでき，Putaxes3d(a) は，Putaxes3d([a,a,a]) と同じになる。\\ -【例】Putaxes3d(5); 原点と，$x(5,0,0),y(0,5,0),z(0,0,5)$ を作る。\\ - Putaxes3d([1,2,3]); 原点と，$x(1,0,0),y(0,2,0),z(0,0,3)$ を作る。\\ +\begin{verbatim} + Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,4]"); + Putpoint3d(["O",[0,0,0]],"fix"); + Putpoint3d(["P",[1,1,1]],"fix"); + Perpplane("E-F","P",P3d-O3d,"put"); + vec1=2*(E3d-P3d); + vec2=2*(F3d-P3d); + Putpoint3d(["A",P3d+vec1+vec2],"fix"); + Putpoint3d(["B",P3d+vec1-vec2],"fix"); + Putpoint3d(["C",P3d-vec1-vec2],"fix"); + Putpoint3d(["D",P3d-vec1+vec2],"fix"); + Spaceline("1",[A,B,C,D,A]); + Arrowdata([O,P],["dr,2"]); + Letter([P,"w","P",A,"ne","A",B,"e","B",C,"ws","C",D,"nw","D",]); + Skeletonparadata("1"); +\end{verbatim} -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} -\hypertarget{putonCurve3d}{} -\item[関数] PutonCurve3d(点名，PD) -\item[機能] 空間曲線上に点をとる -\item[説明] プロットデータPDの曲線上に，点名の点をとる。\\ - とった点は固定点ではなく，曲線上にインシデントとなる。したがって，ドラッグして曲線上を動かすことができる。例は \hyperlink{partcrv3d}{Partcrv3d()} を参照のこと。\\ - \\ +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\vspace{\baselineskip} -\hypertarget{putonseg3d}{} -\item[関数] Putonseg3d(点名，点１，点２) -\item[機能] 線分上に点を取る -\item[説明] 点１と点２の中点に，指定された名前の点を取る。点１と点２が線分として結ばれていなくてもよい。とった点は線分にインシデントとなる（線分が描かれていなくても）。点１と点２はリストにすることもできる。\\ - \\ -【例】AとBの中点に点Cをとる。つぎのいずれでもよい。\\ - \verb|Putonseg3d("C",A,B);|\\ - \verb|Putonseg3d("C",[A,B]);|\\ - \\ +\hypertarget{perppt}{} +\item[関数] Perppt(点名，点，点リスト,option) +\item[機能] 平面に下ろした垂線の足を求める +\item[説明] 第2引数の点から，第3引数の点リストで決まる平面に下した垂線の足を，第１引数の名前の点とする。 -\hypertarget{putpoint3d}{} -\item[関数] Putpoint3d(リスト,option) -\item[機能] 空間に幾何点を作図する -\item[説明] 点の名称と座標を与えて点を作図する。複数の点を一度に作図できる。\\ - optionは，"fix" または "free" (デフォルト)。\\ - "fix" をつけると，固定点（ドラッグで移動できない点）とする。同じ名称の点がすでに存在する場合は，指定した位置に移動して固定点とする。\\ - "free" をつけると，自由点（ドラッグで移動できる）とする。同じ名称の点がすでに存在する場合はなにもしない。\\ - \\ -【例】いくつか記述例を示す。\\ - \verb|Putpoint3d(["A",[2,1,3]]);|\\ - \verb|Putpoint3d(["A",[1,1,1],"C",[1,0,1]],"fix");|\\ - \verb|Putpoint3d(["A",[2,1,3]],"free");|\\ - \\ - なお，この関数は幾何点を作るものであり，TeXには出力されない。TeXに点を出力するには，\hyperlink{pointdata}{Pointdata()} または \hyperlink{drwpt}{Drawpoint()}を併用する。\\ - 空間における点の座標は，点名に"3d"を付加した名前の変数に代入される。たとえば，点Aの座標はA3dである。これにより，点の座標を取得できる。 - -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +オプションは次の通り。 初期設定は "draw" -\hypertarget{readobj}{} -\item[関数] Readobj(ファイル名) -\item[機能] objファイルを読み込む． -\item[説明] 小林・鈴木・三谷による多面体データ polyhedrons\_obj を読み込む。\\ -オプションは ["size=n"] で，n倍したデータにする。負の数にすると上下が反転される。\\ -データはKeTCindyのdataフォルダの中にある。したがって，次のようなスクリプトを書く。読み込むのは一度だけなので， Draw スロットではなくInitialization スロットに置けばよいが，コードの可読性を高めるには Draw スロットでもよい。 -\begin{verbatim} - Setdirectory( Dirhead+"/data/polyhedrons_obj"); - polydt=Readobj("r02.obj"); - Setdirectory(Dirwork); -\end{verbatim} -これで，r02.obj データが，変数 polydt に代入される。\\ -この多面体データは，頂点リストと面リストからなっているが，頂点リストは座標のリストなので，読み込んで表示するときには，点の名称を v1,v2,・・・ とする。\\ -読み込んだあとの使い方を含めて例を示す。\\ +draw：点を打つ。幾何点は作らない -【例】正八面体を描く -\begin{verbatim} - Setdirectory( Dirhead+"/data/polyhedrons_obj"); - polydt=Readobj("r02.obj",["size=2"]); - Setdirectory(Dirwork); - VertexEdgeFace("1",polydt,["Edg=nogeo"]); - Nohiddenbyfaces("1","phf3d1"); -\end{verbatim} - \input{Fig3d/readobj} +put ：幾何点を作る -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +none：計算だけ行い，点は作図しない。 -\hypertarget{reflectpoint3d}{} -\item[関数] Reflectpoint3d(座標,リスト) -\item[機能] 点の鏡映点を求める -\item[説明] 第2引数のタイプにより，点に関する鏡映，直線に関する鏡映，面に関する鏡映のそれぞれの点の座標を返す。\\ - \\ -【例】点A,B,C,Dを空間にとり，点Aの鏡映点の座標を求める。\\ - 点Bに関する鏡映点 \verb|Reflectpoint3d(A3d,[B3d]);|\\ - 直線BCに関する鏡映点 \verb|Reflectpoint3d(A3d,[B3d,C3d]);|\\ - 平面BCDに関する鏡映点 \verb|Reflectpoint3d(A3d,[B3d,C3d,D3d]);|\\ - -\hypertarget{rotate3pt}{} -\item[関数] Rotate3pt(座標,vec,角度,中心点) -\item[機能] 点を回転する -\item[説明] 第１引数の座標の点を回転する。vecは回転軸の方向ベクトル。中心点は方向ベクトルの始点。第４引数を省略した場合は原点とする。\\ - \\ -【例】点Aを(0,-1,0) に置いたときの記述例と結果（戻り値）\\ - \verb|Rotate3pt(A3d,[0,0,1],pi/2)|; 戻り値は [1,0,0]\\ - \verb|Rotate3pt(A3d,[0,0,1],pi/2,[1,1,1]);| 戻り値は[3,0,0]\\ - \\ +\vspace{\baselineskip} +【例】原点から点ABCを通る平面に下した垂線の足Hの座標を求める。 -\hypertarget{rotatedata3d}{} -\item[関数] Rotatedata3d(name,PDリスト,vec,角度,options) -\item[機能] プロットデータを回転 -\item[説明] プロットデータを，原点を始点とするベクトルvec 周りに回転する。複数のプロットデータをまとめて回転することができる。\\ -options として，中心点（vecの始点），線種を指定することができる。\\ - \\ -【例】コード例と結果を示す。 + \verb|Perppt("H","O","A-B-C","none");| 表示はされない。 + + \verb|Perppt("H","O","A-B-C");| Ｈの位置に緑色の点が表示される。 + + \verb|Perppt("H","O","A-B-C","put");| 幾何点Hが作図される。 + + いずれの場合も，Hの座標は変数H3d に代入される + +\vspace{\baselineskip} +作図例 \begin{verbatim} - Xyzax3data("","x=[-5,4]","y=[-5,5]","z=[-5,4]",["a","O"]); - Putpoint3d(["A",[0,-2,0],"B",[2,-2,0],"C",[1,-2,2],"D",[1,-2,3]],"fix"); - Spaceline("1",[A,B,C,A]); - Spaceline([C,D]); - Rotatedata3d("1",["sl3d1","CD3d"],[0,0,1],pi/2,["dr,2"]); - Letter([A,"s","A",B,"w","B",C,"ne","C",D,"ne","D"]); + Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,4]"); + Putpoint3d("O",[0,0,0],"fix"); + Putpoint3d("A",[3,0,0],"fix"); + Putpoint3d("B",[0,3,0],"fix"); + Putpoint3d("C",[0,0,3],"fix"); + Perppt("H","O","A-B-C","put"); + Spaceline("1",[A,B,C,A]); + Spaceline("2",[O,H]); + Letter([A,"nw","A",B,"ne","B",C,"ne","C",O,"nw","O",H,"ne","H"]); \end{verbatim} -これを\\ - \verb|Rotatedata3d("1",["sl3d1","CD3d"],[0,0,1],pi/2,[[1,0,0],"dr,2"]);|\\ -とした場合が右図である。\\ - \input{Fig3d/rotatedata3d01} \input{Fig3d/rotatedata3d02}\\ +\vspace{\baselineskip} +\begin{center} \input{Fig/perppt} \end{center} -\hypertarget{sf3data}{} -\item[関数] Sf3data(name,リスト,options) -\item[機能] 陰線処理なしの曲面をワイヤーフレームモデルで描く -\item[説明] リストは，関数式と定義域，境界指定をそれぞれ文字列にしたもののリスト。\\ -optionsは，解像度（各変数に対応する分割数）とメッシュの密度，境界指定。\\ -解像度は，"Num=[a,b]" で指定。初期値はa,bとも25\\ -メッシュ密度は，縦横で "Wire=[a,b]" で指定。初期値はa,bとも20\\ -境界指定は"ewsn"で行う。"ewsn" の意味は次のように考える。\\ - 変数が u,v のとき，u,v平面において，$a \leq u \leq b,c \leq v \leq d$ の矩形を考え，\\ - その東西南北(ewsn)の境界を示す。\\ - \input{Fig/ewsn}\\ - \\ -関数式のパターンはつぎの3通り。\\ - \\ -(1) $z=f(x,y)$\\ - 【例】：$z=x^2-y^2$を定義域$x=[-2,2],y=[-2,2]$ で描画する。\\ - \verb|Sf3data("1",["z=x^2-y^2","x=[-2,2]","y=[-2,2]"])|;\\ - \input{Fig3d/saddle1}\\ - 【例】：同じく，解像度をx,yとも10，メッシュの数を縦横とも10にする。\\ - 解像度，メッシュ密度とも下げるので粗い描画となる。\\ - \verb|Sf3data("1",["z=x^2-y^2","x=[-2,2]","y=[-2,2]"],|\\ - \verb|["Num=[10,10]","Wire=[10,10]"]);|\\ - \\ -(2) $z=f(x,y),x=g(R,T),y=h(R,T)$\\ - x,y の媒介変数 r,t は大文字にする。\\ - 【例】：次図左\\ - \verb|fd=["z=4-(x^2+y^2)","x=R*cos(T)","y=R*sin(T)","R=[0,2]","T=[0,2*pi]"];|\\ - \verb|Sf3data("1",fd);|\\ - 【例】：次図右\\ - \verb|fd=["z=sin(sqrt(abs(x^2+y^2)))","x=r*cos(t)","y=r*sin(t)",|\\ - \verb|"r=[0,3]","t=[0,2*pi]"];|\\ - \verb|Sf3data("1",fd);|\\ -\\ - \input{Fig3d/parabola} \input{Fig3d/sf3ddata3}\\ -\\ -(3) $x=f(u,v),y=g(u,v),z=h(u,v),$\\ - この場合，(2)と区別するために，"p" を先頭につけておく。\\ - 【例】球面\\ - \verb|fd=["p","x=2*sin(u)*cos(v)","y=2*sin(u)*sin(v)","z=2*cos(u)",|\\ - \verb|"u=[0,pi]","v=[0,2*pi]"];|\\ - \verb|Sf3data("1",fd);|\\ - - \input{Fig3d/sf3ddata4}\\ +\vspace{\baselineskip} +\hypertarget{partcrv3d}{} +\item[関数] Partcrv3d(name，始点，終点，PD) +\item[機能] 部分曲線のプロットデータを作成する +\item[説明] 曲線PDにおいて，始点から終点までのプロットデータを作成する。 -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +始点と終点は，プロットデータの番号もしくは曲線上にとった点の識別名で示す。 -\hypertarget{sfbdparadata}{} -\item[関数] Sfbdparadata(name,式,options1,options2) -\item[機能] 空間曲面の陰線処理 -\item[説明] 曲面について陰線処理を行う。 - 曲面の式はSf3data()の場合と同じ。ただし，(2) と(3)のパターンでは式の最後に境界の指定 ewns を明示する必要がある。(3)では境界の指定を" "(中は半角スペース)とする。省略すると不要な境界線が表示されることがある。境界指定については，Sf3data()の項を参照のこと。\\ -options1は，"Wait=n","r","m",線種。Wait の初期値は30。\\ - "r","m"に関しては，オプションなしまたは，”” のとき\\ - i) データファイルがなければ，新しく作る\\ - ii) データファイルが既にあればそれを読み込む\\ - "m" のとき，強制的にデータファイルを作り直す。\\ - "r" のとき，すでにあるデータファイルを読み込む。\\ -options2は，陰線に関するoptionで，"nodisp" または 線種。"nodisp" にすると陰線は消去されるため，輪郭線だけが描かれることになる（デフォルト）。options2 だけを指定する場合は，options1 を空リストにしてつける必要がある。\\ - - \textcolor{red}{【注意】} この処理はScilabで行うが，非常に時間がかかるため，この関数を実行した状態で画面上のスライダを動かしたりしないこと。何か操作を行う場合は，いったん行頭に//を書いてコメント化してから行う。\\ - -【例】サドル面\\ -陰線を消去して表示（デフォルト）（下図左） -\begin{verbatim} - fd=["x=x^2-y^2","x=[-2,2]","y=[-2,2]"]; - Sfbdparadata("1",fd); -\end{verbatim} -全体を実線で太めにして，陰線を点線で表示（下図右） +\vspace{\baselineskip} +【例】螺旋を描き一部分を太くする。PutonCurve3d() で螺旋上に点C,Dができるので，ドラッグして適当な位置に移動する。 \begin{verbatim} - fd=["x=x^2-y^2","x=[-2,2]","y=[-2,2]"]; - Sfbdparadata("1",fd,["dr,2"],["do"]); + Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,4]"); + Spacecurve("1","[2*cos(t),2*sin(t),0.2*t]","t=[0,4*pi]",["Num=100"]); + PutonCurve3d("C","sc3d1"); + PutonCurve3d("D","sc3d1"); + Partcrv3d("1",C,D,"sc3d1",["dr,3"]); + Letter([C,"n2","C",D,"n2","D"]); \end{verbatim} - \input{Fig3d/sfbdpara01} \input{Fig3d/sfbdpara02} + ここで，\verb|"sc3d1"| は，螺旋，\verb|"part3d1"| は，部分曲線のプロットデータである。 + +\begin{center} \input{Fig/partcrv3d1} \end{center} -【例】放物面\\ -デフォルト（下図左） -\begin{verbatim} - fd=["z=4-(x^2+y^2)","x=R*cos(T)","y=R*sin(T)","R=[0,2]","T=[0,2*pi]","e"]; - Sfbdparadata("1",fd); -\end{verbatim} -陰線を破線で表示（下図右） +\vspace{\baselineskip} +【例】稲妻状の螺旋を点線で描き，その一部を実線にする。位置はプロットデータの番号で示す。小数にすると曲線を分割している線分の途中の位置になる。 \begin{verbatim} - fd=["z=4-(x^2+y^2)","x=R*cos(T)","y=R*sin(T)","R=[0,2]","T=[0,2*pi]","e"]; - Sfbdparadata("1",fd,[],["da"]); +Spacecurve("1","[2*cos(t),2*sin(t),0.2*t]","t=[0,4*pi]",["Num=10","do"]); +Partcrv3d("1",3.3,8.5,"sc3d1"); \end{verbatim} - \input{Fig3d/sfbdpara03} \input{Fig3d/sfbdpara04 -} + \begin{center} \input{Fig/partcrv3d2} \end{center} -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +\hypertarget{phparadata}{} +\item[関数] Phparadata(name,name2,options) +\item[機能] 多面体を陰線処理して描く +\item[説明] 多面体を陰線処理して描く。多面体は面データ（頂点リストと面リスト）を与えて，VertexEdgeFace() でプロットデータを作る。このプロットデータに対し，隠れている面（辺）を非表示にして表示する。第1引数は通常のname，第2引数のname2は，VertexEdgeFace() で与えたnameと同じものとする。 -\hypertarget{skeletonparadata}{} -\item[関数] Skeletonparadata(name,PDリスト,PDリスト,option) -\item[機能] 陰線処理（スケルトン処理）をおこなう -\item[説明] 描画されている線と軸について陰線処理をおこなう。\\ -第２引数の線（プロットデータ）が，第３引数の線（プロットデータ）によって隠される部分を消去する。第２，第３引数を省略した場合は，すべての線について，互いの陰線処理をおこなう。optionで消去する部分の長さを指定できる。\\ - \\ -【例】螺旋と線分，座標軸の陰線処理\\ -次のように螺旋と線分，座標軸を描いておく。 + optionsは，全体の線種（"dr,2"など）と，陰線の線種を"Hidden=線種" で指定できる。 初期設定では陰線は表示しない。 + +\vspace{\baselineskip} +【例】小林・鈴木・三谷による多面体データ \verb|polyhedrons_obj| から，s06の切頂二十面体（サッカーボール型）を描く。 \verb|polyhedrons_obj| は KeTCindyシステムの data ディレクトリにあるので，Setdirectory() でカレントディレクトリを作業ディレクトリと切替ながら出力する。 \begin{verbatim} - Xyzax3data("","x=[-5,5]","y=[-5,4]","z=[-5,3]"); - Putpoint3d(["A",[0,-2,-2]],"fix"); - Putpoint3d(["B",[-1,1,3]],"fix"); - Spaceline([A,B]); - Spacecurve("1","[2*cos(t),2*sin(t),0.2*t]","t=[0,4*pi]",["Num=100"]); -\end{verbatim} -座標軸のプロットデータは ax3d，線分は AB3d，螺旋は sc3d1 である。これに対し，\\ - \verb|Skeletonparadata("1");|\\ - 描画されている線と軸について陰線処理をおこなう。（図左）\\ - \verb|Skeletonparadata("1",[2]);|\\ - 重なった部分の空きを2にする。（図中央）\\ - \verb|Skeletonparadata("1",["AB3d","ax3d"],["sc3d1"]);|\\ - 螺旋によって隠れる部分だけ消去する。（図右）\\ - -\input{Fig3d/skeletonparadata01} \input{Fig3d/skeletonparadata02} - \input{Fig3d/skeletonparadata03} - -このほか，\\ - \verb|Skeletonparadata("1",["AB3d","ax3d"],["sc3d1"],[2]);|\\ - \verb|Skeletonparadata("1",["AB3d"],["ax3d","sc3d1"]);|\\ -も可能である。 + Setdirectory( Dirhead+"/data/polyhedrons_obj"); + phd=Readobj("s06.obj",["size=3"]); + Setdirectory(Dirwork); + VertexEdgeFace("s06",phd,["Edg=nogeo"]); + Phparadata("1","s06"); +\end{verbatim} + VertexEdgeFace() の name は通常の "1" でもよい。その場合は，\verb|Phparadata("1","1");| とするが，わかりにくいので上のようにした。 + +実行すると，Cinderellaの描画面は次のように頂点だけが描かれる。 -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +\vspace{\baselineskip} +\begin{center} + \includegraphics[bb=0 0 726.04 365.02 , width=10cm]{Fig/phparadata01.pdf} +\end{center} + +\vspace{\baselineskip} +全体の線種と，陰線の線種を + +\verb|Phparadata("1","s06",["dr,2","Hidden=do"]);| -\hypertarget{skeletondatacindy}{} -\item[関数] Skeletondatacindy(name,PDリスト,PDリスト,option) -\item[機能] 陰線処理（スケルトン処理）をCindyscriptでおこなう -\item[説明] 描画されている線と軸について陰線処理をおこなう。\\ - Scilabを呼ばず，Cindyscriptだけで行うので，多面体などでインタラクティブに図を動かすことができる。ただし，曲線では処理が遅くなる。\\ +で指定したのが下図右である。 + \begin{center} \input{Fig/phparadata02} \input{Fig/phparadata03} \end{center} -\hypertarget{spacecurve}{} -\item[関数] Spacecurve(name,式,定義域,options) -\item[機能] 空間曲線を描く -\item[説明] 媒介変数で表された曲線を描く。optionは解像度 Num\\ - \\ -【例】螺旋を描く\\ - \verb|Spacecurve("1","[2*cos(t),2*sin(t),0.2*t]","t=[0,4*pi]",["Num=100"]);|\\ - \\ - \input{Fig3d/rasen}\\ +【注意】 -\hypertarget{spaceline}{} -\item[関数] Spaceline(リスト) -\item[機能] 折れ線を描く -\item[説明] 点の名称または座標のリストを与えて折れ線を描く。平面での Listplot() にあたる。\\ -【例】Spaceline("1",[[2,5,1],[4,2,3]]); 指定された２点を結んだ線分を描く。\\ - Spaceline([A,B,C,A]); 作図されている２点A,B,Cを結んだ三角形を描く。\\ - options は線種（dr,da,do）\\ - \\ - -\hypertarget{translatedata3d}{} -\item[関数] Translatedata3d(name,PD,平行移動量) -\item[機能] 空間プロットデータを平行移動 -\item[説明] PDで表される図形を，平行移動する。\\ - \\ -【例】曲線 sc3d1 をy軸方向に２だけ平行移動する。\\ - \verb|Translatedata3d("1",["sc3d1"],[0,2,0]);|\\ - 結果として，もとの曲線と平行移動した曲線の２つが描かれる。\\ - \\ -【例】多面体の平行移動\\ - VertexEdgeFace() で描いた多角形はこの関数では平行移動できないので，面データを直接操作して平行移動を行う。\\ - たとえば，小林・鈴木・三谷による多面体データ polyhedrons obj を用いて正八面体を描く場合，次のようにする。$y$軸方向に２だけ平行移動する場合である。\\ + polyhedrons obj のデータを使って，続けて異なる多面体を描きたい場合は注意が必要である。Readobj()だけを変更して別のデータを読めばよさそうであるが，VertexEdgeFace() のname も（したがって，Phparadata()の第2引数も）書き換えないと，前のデータが残っていてうまくいかない。たとえば，上のコードで切頂二十面体を描いた後，正八面体（r02）を描こうとするならば， \begin{verbatim} - Setdirectory( Dirhead+"/data/polyhedrons_obj"); - phd=Readobj("r02.obj",["size=2"]); - Setdirectory(Dirwork); - dn=length(phd_1); - repeat(dn,s,phd_1_s=phd_1_s+[0,2,0]); - VertexEdgeFace("1",phd,["Edg=nogeo"]); + Setdirectory( Dirhead+"/data/polyhedrons_obj"); + phd=Readobj("r02.obj",["size=3"]); + Setdirectory(Dirwork); + VertexEdgeFace("2",phd,["Edg=nogeo"]); + Phparadata("1","2"); \end{verbatim} - \input{Fig3d/translate01} + のようにする。 + -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\hypertarget{translatept3d}{} -\item[関数] Translatept3d(座標，平行移動量) -\item[機能] 空間点を平行移動 -\item[説明] 点を平行移動する。\\ - \\ -【例】点A(1,0,0) を(-1,1,1)だけ平行移動した点をBとする。点Aの空間座標は A3d で表される。 -\begin{verbatim} - Putpoint3d(["A",[1,0,0]],"fix"); - pt=Translatept3d(A3d,[-1,1,1]); - Putpoint3d(["B",pt],"fix"); -\end{verbatim} - \\ -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +\hypertarget{pointdata3d}{} +\item[関数] Pointdata3d(名前,点リスト,options) +\item[機能] 点の3Dデータと2Dデータを作成し，画面と\TeX に出力する。 +\item[説明] optionsは\hyperlink{pointdata}{Pointdata()}と同様。 +\vspace{\baselineskip} -\hypertarget{vertexedgeface}{} -\item[関数] VertexEdgeFace(name,面データ,options) -\item[機能] 多面体の面データを用いて多面体を描く -\item[説明] 面データは，頂点リストと，面リストからなる。面リストは，各面を構成する頂点を，外側から見て反時計回り（左回り）に並べたリストである。\\ -たとえば，四面体ABCDの面データは，[[A,B,C,D],[[1,2,3],[1,2,4],[1,3,4],[2,3,4]]] となる。\\ -４点A,B,C,Dをとっておき，このリストを引数に与えると，四面体の辺が描かれる。\\ -このとき，option がなければ，Cinderellaの幾何要素として辺が描かれるが，それだけではTeXには書き出されないので注意が必要である。(変数未定義のエラーになる) TeXに書き出すには，optionとして ["Edg=nogeo"] をつける。このときは各辺は幾何要素にならない。\\ -また，"Pt=free" optionをつけると，頂点は自由点となり，マウスドラッグで動かすことができる。\\ -生成されるプロットデータは，\\ -phv3d：頂点のリスト\\ -phe3d：辺のリスト\\ -phf3d：面リスト\\ -なお，それぞれ末尾にnameが付加される。\\ - \\ -【例】：正四面体を描く +【例】 \begin{verbatim} - Putpoint3d("A",2*[-1,-1/sqrt(3),0],"fix"); - Putpoint3d("B",2*[1,-1/sqrt(3),0],"fix"); - Putpoint3d("C",2*[0,sqrt(3)-1/sqrt(3),0],"fix"); - Putpoint3d("D",2*[0,0,sqrt(3)],"fix"); - phd=Concatobj([[A,B,C],[A,B,D],[A,C,D],[B,C,D]]); - VertexEdgeFace("1",phd,["Edg=nogeo"]); + Pointdata3d("1",[[1,1,1],[0,1,0]],["Size=2","Color=red"]); \end{verbatim} - \input{Fig3d/vertex01} +\vspace{\baselineskip} -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\hypertarget{wireparadata}{} -\item[関数] Wireparadata(name,PD,式,整数,整数,optons1,options2) -\item[機能] 曲面のワイヤフレームを陰線処理して描く -\item[説明] PDは，第３引数の式で描いたワイヤフレームモデルのプロットデータ名。第４，第５引数は分割線の数。\\ -options1 には "r","m","Wait=n" が指定できる。Wait の初期値は30。\\ - "r","m"に関しては，オプションなしまたは，”” のとき\\ - i) データファイルがなければ，新しく作る\\ - ii) データファイルが既にあればそれを読み込む\\ - "m" のとき，強制的にデータファイルを作り直す。\\ - "r" のとき，すでにあるデータファイルを読み込む。\\ -optons2 には陰線の表示方法について "nodisp" または線種 がある。デフォルトは"nodisp" 。何も指定しないときは，[""] （空文字）を書いておく。\\ -曲面の陰線処理を行うので，Sfbdparadata() とペアで使う。\\ - \\ - \textcolor{red}{【注意】} \\ - この処理はScilabで行うが，Sfbdparadata() とペアで使うために非常に時間がかかる。コンピュータの性能にもよるが２分以上かかこともある。したがって，この関数を実行した状態で画面上のスライダを動かしたりしないこと。何か操作を行う場合は，いったん行頭に//を書いてコメント化してから行う。球面やトーラスのタイプでは，Texview や Exekc ボタンの反応も鈍くなる。Exekc が動作しない（タイムアウト）場合は，kc.sh（Mac） / kc.bat（Windows）を直接起動すれば TeX の図ができる。\\ - \\ -【例】式のタイプ別に例を示す。\\ - \\ -サドル面：下図左 -\begin{verbatim} - fd=["z=x^2-y^2","x=[-2,2]","y=[-2,2]"]; - Sfbdparadata("1",fd); - Wireparadata("1","sfbd3d1",fd,4,5,[""]); -\end{verbatim} - \\ -回転放物面：下図中央 -\begin{verbatim} - fd=["z=4-(x^2+y^2)","x=r*cos(t)","y=r*sin(t)","r=[0,2]","t=[0,2*pi]","e"]; - Sfbdparadata("1",fd); - Wireparadata("1","sfbd3d1",fd,5,7,[""]); -\end{verbatim} - \\ -球面：下図右\\ - このタイプでは，媒介変数形式の識別のため，先頭に "p" をつけておくとよい。 -\begin{verbatim} - fd=["p","x=2*sin(u)*cos(v)","y=2*sin(u)*sin(v)","z=2*cos(u)","u=[0,pi]", - "v=[0,2*pi]","s"]; - Sfbdparadata("1",fd); - Wireparadata("1","sfbd3d1",fd,12,12,[""]); -\end{verbatim} - \\ -\input{Fig3d/wirepara1} \input{Fig3d/wirepara2} \input{Fig3d/wirepara3}\\ - \\ -【例】球面で座標軸を陰線処理して点線で表す。（次図左） -\begin{verbatim} - fd=["p","x=2*sin(u)*cos(v)","y=2*sin(u)*sin(v)","z=2*cos(u)","u=[0,pi]", - "v=[0,2*pi]","s"]; - Sfbdparadata("1",fd); - Wireparadata("1","sfbd3d1",fd,12,12,[""]); - Crvsfparadata("1","ax3d","sfbd3d1",fd,[],["do"]); -\end{verbatim} -【例】トーラスを描く（次図右） -\begin{verbatim} - fd=["p","x=(2+cos(u))*cos(v)","y=(2+cos(u))*sin(v)","z=sin(u)", - "u=[0,2*pi]","v=[0,2*pi]","s"]; - Sfbdparadata("1",fd); - Wireparadata("1","sfbd3d1",fd,12,12,[""]); -\end{verbatim} - \\ - \input{Fig3d/wirepara4} \input{Fig3d/wirepara5}\\ - -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} - \\ -\hypertarget{xyzax3data}{} -\item[関数] Xyzax3data(name，ｘの範囲，yの範囲，zの範囲,options) -\item[機能] 座標軸を描く -\item[説明] 描画面に座標軸を描く。nameは空文字列でよい。プロットデータ ax3d が作成される。option は次の2つ。\\ -矢じり："an"：nは数字で矢じりの大きさ。nはなくてもよい。\\ -原点O："Onesw"：neswは微小位置。数字も付けられる。neswをつけない場合の初期値はsw。\\ -【例】デフォルトの座標軸\\ - \verb|Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]");|\\ - 矢じりをつける\\ - \verb|Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]","a");|\\ - 矢じりを大きくする\\ - \verb|Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]",["a2"]);|\\ - 原点のOを表示する。\\ - \verb|Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]",["O"]);|\\ - 原点のOの位置を調整して右上に表示する。やじりもつける。\\ - \verb|Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]",["a","Oe2n2"]);|\\ - -【注意】Putaxes3d() で点を取ると原点に点Oが作成される。この点名Oと表示が重複するのが煩わしい場合は，作図後にこのoptionをつけてから出力するとよい。\\ +\hypertarget{projcoordpara}{} +\item[関数] Projcoordpara(座標) +\item[機能] 投影座標を求める +\item[説明] 空間座標を平面に投影した座標を求める。 +戻り値の第１，第2要素はCinderellaの描画面のx,y座標。第3要素はxy平面に垂直なzの座標で．投影面からの（符号付）距離を表す。 -\hypertarget{xyzcoord}{} -\item[関数] Xyzcoord(P.x,P.y,Pz.y) -\item[機能] 主副画面で決まる点の座標 -\item[説明] Cinderellaの描画面上の点が表す空間座標を求める\\ - 点Ｐについて，主画面の点Ｐに対応するのが副画面のPzである。点Pの２次元座標はP.x,P.yで，Pzのy座標はPz.yで表される。これを引数として与えると，点Ｐの空間座標が返される。\\ - \\ -【例】点Aをドラッグして動かしたとき，Aの座標を求める。\\ - \verb|println(Xyzcoord(A.x,A.y,Az.y));|\\ - により，コンソールに座標が表示される。\\ +\vspace{\baselineskip} +【例】\verb|Projcoordpara([3,1,2]);| -\end{description} -\newpage -% 逆引辞典 ================================== -\section{逆引辞典} + 戻り値は [-0.65,1.7,3.27] のようになる。（視点によって値は異なる） -幾何の作図は，補助線などはCinderellaの作図ツールかCindyscriptを用いて描き，TeXに出力する線をKeTCindyで描くと，効率のよい作図ができる。 -関数のグラフも，Cindyscriptで描くものと，TeXに出力するKeTCindyで描くものを使い分けるとよい。 +\vspace{\baselineskip} +\hypertarget{putaxes3d}{} +\item[関数] Putaxes3d([x,y,z]) +\item[機能] 軸上に幾何点を作る。 +\item[説明] 引数のリスト [x,y,z] に対し，点X(x,0,0) ,Y(0,y,0) , Z(0,0,z) および 原点Oを主画面上にとり，副画面上に対応する点Xz，Yz，Zz，Oz を作る。すでに同じ名称の点がある場合は，指定された位置に移動する。 -以下で，【Cinderella】は，Cinderellaの作図ツールを用いた描画，【Cindyscript】はCindyscriptの関数，【KeTCindy】および【KeTCindy3D】はKeTCindyの関数を示す。\\ +引数は，実数にすることもでき，Putaxes3d(a) は，Putaxes3d([a,a,a]) と同じになる。 + +\vspace{\baselineskip} +【例】Putaxes3d(5); 原点と，$x(5,0,0),y(0,5,0),z(0,0,5)$ を作る。 -\subsection{点の作図} -\subsubsection{点をとる} + Putaxes3d([1,2,3]); 原点と，$x(1,0,0),y(0,2,0),z(0,0,3)$ を作る。 -\begin{tabbing} -12\=34567890123456789\=\kill\\ +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\>【Cinderella】 \>「点を加える」ツール \includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/single-add.png} を用いる\\ - \>【KeTCindy】 \>Drwpt(点),Drawpoint(点),Pointdata(name,リスト),Putpoint(name,座標),\\ - \>【KeTCindy3D】\>Drawpoint3d(座標),Putpoint3d(リスト),\\ -\end{tabbing} +\vspace{\baselineskip} +\hypertarget{putonCurve3d}{} +\item[関数] PutonCurve3d(点名，PD) +\item[機能] 空間曲線上に点をとる +\item[説明] プロットデータPDの曲線上に，点名の点をとる。 -点をとる関数はいくつかある。Cinderellaの描画面上に単に点を表示するもの，幾何点を作るもの，TeXに出力するためのもの，と用途が異なる。 -Putpoint(),Putpoint3d()は座標を与えて幾何点を作るが，作図ツールの「点を加える」で作図しておいてスクリプトで座標を指定してもよい。 +とった点は固定点ではなく，曲線上にインシデントとなる。したがって，ドラッグして曲線上を動かすことができる。例は \hyperlink{partcrv3d}{Partcrv3d()} を参照のこと。 - \\ -【例】座標(1,1) に点Aをとる。\\ - （方法１） 磁石ツール \includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/snap.png} でスナップモードにしておき，作図ツールで点をとる。\\ - （方法２）KeTCindyの関数で \verb|Putpoint("A,[1,1])| とする。 +\vspace{\baselineskip} +\hypertarget{putonseg3d}{} +\item[関数] Putonseg3d(点名，点１，点2) +\item[機能] 線分上に点を取る +\item[説明] 点１と点2の中点に，指定された名前の点を取る。点１と点2が線分として結ばれていなくてもよい。とった点は線分にインシデントとなる（線分が描かれていなくても）。点１と点2はリストにすることもできる。\\ +\vspace{\baselineskip} +【例】AとBの中点に点Cをとる。つぎのいずれでもよい。 -（方法１）では，この点は自由点となる。固定点にするには，インスペクタで「ピンで留める」にする。また，点名はCinderellaが自動的につけるので，変更するには，点を選択しておき，インスペクタを開いて「要素の情報」で変更する。 + \verb|Putonseg3d("C",A,B);| -[1,1] のような格子点でない場合は，作図ツールで適当な位置に点をとったのち，Cindyscriptで \verb|A.xy=[2,sqrt(3)]| のようにして座標を指定する。 + \verb|Putonseg3d("C",[A,B]);| + +\vspace{\baselineskip} -（方法２）では，この点は固定点となる。自由点とするには \verb|Putpoint("A",[1,1],[A.x,A.y])| とする必要がある。 +\hypertarget{putpoint3d}{} +\item[関数] Putpoint3d(リスト,option) +\item[機能] 空間に幾何点を作図する +\item[説明] 点の名称と座標を与えて点を作図する。複数の点を一度に作図できる。 -これらの方法で点を取ったとき，画面上には点が表示されるがTeXの図には出力されない。TeXの図に出力するには，KeTCindyのDrwpt()または，Drawpoint()を用いる必要がある。\\ +optionは，"fix" または "free" ( 初期設定)。 + +"fix" をつけると，固定点（ドラッグで移動できない点）とする。同じ名称の点がすでに存在する場合は，指定した位置に移動して固定点とする。 - 以下は，それぞれの関数についての比較表である。「描画」は緑色の点で描画するが幾何点は作らない。\\ - \\ - \input{Fig/poiintable} -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +"free" をつけると，自由点（ドラッグで移動できる）とする。同じ名称の点がすでに存在する場合はなにもしない。 -\subsubsection{点の大きさを変える} +\vspace{\baselineskip} +【例】いくつか記述例を示す。 -\begin{tabbing} -12\=34567890123456\=\kill\\ + \verb|Putpoint3d(["A",[2,1,3]]);| + + \verb|Putpoint3d(["A",[1,1,1],"C",[1,0,1]],"fix");| + + \verb|Putpoint3d(["A",[2,1,3]],"free");| + +\vspace{\baselineskip} + なお，この関数は幾何点を作るものであり，TeXには出力されない。TeXに点を出力するには，\hyperlink{pointdata}{Pointdata()} または \hyperlink{drwpt}{Drawpoint()}を併用する。 + + 空間における点の座標は，点名に"3d"を付加した名前の変数に代入される。たとえば，点Aの座標はA3dである。これにより，点の座標を取得できる。 -\>【Cinderella】 \>インスペクタの「表示方法」を使う\\ -\>【Cindyscript】 \>A.size=n\\ - \>【KeTCindy】 \>Ptsize(n)，Setpt(n)\\ -\end{tabbing} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -インスペクタ，Cindyscriptによる点の大きさの設定は画面上には反映されるが，TeXには書き出されない。逆に，KeTCindyで設定した点の大きさは，Cinderellaの画面上には反映されない。そのことを考慮の上，適宜使い分ける必要がある。画面上の点の大きさと，TeXの図の点の大きさは連動しないので注意が必要である。 +\vspace{\baselineskip} +\hypertarget{readobj}{} +\item[関数] Readobj(ファイル名) +\item[機能] objファイルを読み込む． +\item[説明] 小林・鈴木・三谷による多面体データ \verb|polyhedrons_obj| を読み込む。 -KeTCindyの描画関数を使って点をとるときは，["size=n"]オプションをつけて大きさを設定することもできる。 +オプションは "size=n" で，n倍したデータにする。負の数にすると上下が反転される。 -KeTCindyでは，Drwpt() または Drawpoint() に０オプションをつけることで白抜きの点を描くことができる。ただし，この場合，これよりあとに書かれた線は白で抜いたあとに書かれてしまうので，記述の順番を考慮する必要がある。\\ -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +データはKeTCindyのdataフォルダの中にある。したがって，次のようなスクリプトを書く。読み込むのは一度だけなので， Draw スロットではなくInitialization スロットに置けばよいが，コードの可読性を高めるには Draw スロットでもよい。 +\begin{verbatim} + Setdirectory( Dirhead+"/data/polyhedrons_obj"); + polydt=Readobj("r02.obj"); + Setdirectory(Dirwork); +\end{verbatim} +これで，r02.obj データが，変数 polydt に代入される。 -\subsubsection{曲線上に点をとる} +この多面体データは，頂点リストと面リストからなっているが，頂点リストは座標のリストなので，読み込んで表示するときには，点の名称を v1,v2,・・・ とする。 -\begin{tabbing} -12\=34567890123456789\=\kill\\ +読み込んだあとの使い方を含めて例を示す。 -\>【Cinderella】 \>「点を加える」ツールを用いる\\ -\>【KeTCindy】 \>PutonCurve(name,PD,初期値)\\ -\>【KeTCindy3d】 \>PutonCurve3d(点名,PD)\\ -\end{tabbing} +\vspace{\baselineskip} +【例】正八面体を描く +\begin{layer}{150}{0} +\putnotese{55}{0}{ \input{Fig/readobj}} +\end{layer} -Cinderellaの作図ツールで描いた曲線上には，「点を加える」ツールで点をとることで，その点は曲線上だけを動かすことができるようになる（インシデント）。作図ツールで描いた曲線でなければこの方法では曲線上に点は取れない。 +\begin{verbatim} -Cindyscriptで描いた曲線の場合，たとえば，関数$f(x)$のグラフ上に点を置くには，A.y=[A.x,f(A.x)] のようにすればよい。（あらかじめ点を作図しておく） + Setdirectory( Dirhead+"/data/polyhedrons_obj"); + polydt=Readobj("r02.obj",["size=2"]); + Setdirectory(Dirwork); + VertexEdgeFace("1",polydt,["Edg=nogeo"]); + Nohiddenbyfaces("1","phf3d1"); +\end{verbatim} -KeTCindyのPutonCurve()を使うと，プロットデータを用いて曲線上に点をとることができる。また， -KeTCindyで直線，線分上に取りたい場合は，PutonLine( )，PutonSeg( )を用いることもできる。\\ -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} - -\subsubsection{交点をとる} -\begin{tabbing} -12\=34567890123456789\=\kill\\ +主なデータは次の通り。 -\>【Cinderella】 \>「２つの曲線の交点を求める」ツール \includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/intersection.png} を用いる\\ - \>【KeTCindy】 \>Intersectcrvs(PD,PD), Crosspoint(name,PD,PD,リスト),\\ - \> \> Putintersect(点名,PD,PD)\\ - \>【KeTCindy3D】 \>Intersectcrvsf(name,PD,式), IntersectsgpL(点名,線分,面,方法)\\ -\end{tabbing} +\vspace{\baselineskip} + \input{Fig/kobayashi} + +この他にn01〜n92まで整面凸多面体がある。 + +Webページは，http://mitani.cs.tsukuba.ac.jp/polyhedron/ -Cinderellaの作図機能で作図した幾何要素の交点はCinderellaの「２つの曲線の交点を求める」ツールを用いるのが簡便であるが，関数のグラフや方程式による曲線の場合は，Cinderellaの作図機能は使えないので，KeTCindyの関数を使うことになる。 -KeTCindyの関数は３通りあるが，intersectcrvs() は２曲線の交点のリストを取得する関数なので，既存の点を交点に持ってきたい場合は +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\hypertarget{reflectdata3d}{} +\item[関数] Reflectdata3d(name , PDlist , list , options) +\item[機能] PDの鏡映を作る +\item[説明] 第3引数のタイプにより，点に関する鏡映，直線に関する鏡映，面に関する鏡映を作る。 + +\vspace{\baselineskip} +【例】点A,B,C,D,Eを空間にとり，三角形ABCの鏡映を作る。 + \begin{verbatim} - tmp=Intersectcrvs(gr1, crAB); - P.xy=tmp_1; +Putpoint3d(["A",[0,-2,0],"B",[2,-2,0],"C",[1,-2,2],"D",[1,0,1], + "E",[1,0,0]],"fix"); +Spaceline("1",[A,B,C,A]); \end{verbatim} -のようにすればよい。 -Crosspoint()，Putintersect()では交点に新たな幾何点を作ることができる。 +で点をとり，三角形を描いておく。 -Intersectcrvsf() は曲線と曲面の交点， IntersectsgpL() は直線と平面の交点を求める。 +点Dに関する鏡映 -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} + \verb| Reflectdata3d("1",["sl3d1"],[D3d],["Color=blue","dr,2"]);| -\subsection{線の作図} -\subsubsection{線分を引く} +\hspace{20mm} \input{Fig/reflectdata3d01} -\begin{tabbing} -12\=34567890123456789\=\kill\\ +直線DEに関する鏡映 -\>【Cinderella】 \>「線分を加える」ツール \includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/segment.png} を用いる \\ -\>【Cindyscript】 \>draw([A,B]) \\ - \>【KeTCindy】 \>Listplot([A,B]) \\ - \>【KeTCindy3D】 \>Spaceline([A,B]) \\ -\end{tabbing} - Cinderellaの描画ツールを使うと，描かれた線分は幾何要素となり，インスペクタでその属性（色・太さなど）を変えることができる。また，点を線分上にインシデントさせることができる。Scilabに出力しない線分を描くときはこれで十分で，スクリプトも簡素になる。\\ - Cindyscript のdraw関数とKeTCindyのListplot関数では，線の色，太さ，線種を指定できる。また，点の識別名ではなく座標を引数にすることもできる。\\ - 推奨するのは，補助線などはCinderellaの描画ツールで描き，最終的に必要な線だけListplot()で出力する方法。\\ -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} + \verb| Reflectdata3d("1",["sl3d1"],[D3d,E3d],["Color=blue","dr,2"]);| +\hspace{20mm} \input{Fig/reflectdata3d02} -\subsubsection{折れ線を描く} +平面BDEに関する鏡映 -\begin{tabbing} -12\=34567890123456789\=\kill\\ +\verb| Reflectdata3d("1",["sl3d1"],[D3d,E3d,B3d],["Color=blue","dr,2"]);| -\>【Cindyscript】 \>connect(点のリスト)\\ -\>【KeTCindy】 \>Listplot(点のリスト)\\ -\>【KeTCindy3D】 \>Spaceline(点のリスト)\\ -\end{tabbing} +\hspace{20mm} \input{Fig/reflectdata3d03} + -Cinderellaの描画ツールで折れ線を描くのはインタラクティブではあるが本数が多くなると現実的ではない。ただ，描かれた線分は幾何要素となり，インスペクタでその属性（色・太さなど）を変えることができる。折れ線全体の属性を変えるには，すべての折れ線を同時に選択する。（Shift＋クリック） +\vspace{\baselineskip} +\hypertarget{reflectpoint3d}{} +\item[関数] Reflectpoint3d(座標,リスト) +\item[機能] 点の鏡映点を求める +\item[説明] 第2引数のタイプにより，点に関する鏡映，直線に関する鏡映，面に関する鏡映のそれぞれの点の座標を返す。 -Cindyscript のconnect() と KeTCindyの Listplot() ,Spaceline()では，引数に点のリストを与えれば折れ線が描ける。 +\vspace{\baselineskip} +【例】点A,B,C,Dを空間にとり，点Aの鏡映点の座標を求める。 -節点を明示した折れ線を描くには，Listplot()とDrawpoint()を組み合わせることが考えられるが，あらかじめ点のリストを作っておくのが簡便である。 -\begin{verbatim} - Ptsize(3); - pd=[[1,2],[3,4],[6,2]]; - Pointdata("1",pd); - Listplot("1",pd); -\end{verbatim} +点Bに関する鏡映点 \verb| Reflectpoint3d(A3d,[B3d]);| + +直線BCに関する鏡映点 \verb| Reflectpoint3d(A3d,[B3d,C3d]);| + +平面BCDに関する鏡映点 \verb| Reflectpoint3d(A3d,[B3d,C3d,D3d]);| + + +\vspace{\baselineskip} +\hypertarget{rotatedata3d}{} +\item[関数] Rotatedata3d(name,PDリスト,vec,角度,options) +\item[機能] プロットデータを回転 +\item[説明] プロットデータを，原点を始点とするベクトルvec 周りに回転する。複数のプロットデータをまとめて回転することができる。 -KeTCindy3Dの場合は空間座標で点をTeXに書き出すことができないので，次のように点を作って書き出す。 +options として，中心点（vecの始点），線種を指定することができる。 + +\vspace{\baselineskip} +【例】コード例と結果を示す。 \begin{verbatim} - Putpoint3d(["A",[2,0,0],"B",[2,0,2],"C",[2,2,2]],"fix"); - Spaceline([A,B,C]); - Ptsize(3); - Drawpoint([A,B,C]); + Xyzax3data("","x=[-5,4]","y=[-5,5]","z=[-5,4]",["a","O"]); + Putpoint3d(["A",[0,-2,0],"B",[2,-2,0],"C",[1,-2,2],"D",[1,-2,3]],"fix"); + Spaceline("1",[A,B,C,A]); + Spaceline("2",[C,D]); + Rotatedata3d("1",["sl3d1","CD3d"],[0,0,1],pi/2,["dr,2"]); + Letter([A,"s","A",B,"w","B",C,"ne","C",D,"ne","D"]); \end{verbatim} -節点が多い場合は，空間の点のリストと，投影した点のリストを作って描画する。 +これを + + \verb|Rotatedata3d("1",["sl3d1","CD3d"],[0,0,1],pi/2,[[1,0,0],"dr,2"]);| + +とした場合が右図である。 + + \input{Fig/rotatedata3d01} \hspace{5mm} \input{Fig/rotatedata3d02} + +%\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\vspace{\baselineskip} +\hypertarget{rotatepoint3d}{} +\item[関数] Rotatepoint3d(座標, vec , 角度, [点] ) +\item[機能] 点の位置を回転する +\item[説明] 点をvecの周りに回転する。角度は弧度法で与える。 + +第4引数に点を与えた場合，vecの始点が第4引数の位置になる。デフォルトは原点 + +点Aを，$(0,-1,0)$に置いたときの記述例と戻り値 + +\verb| Putpoint3d("A",[0,-1,0]);| \\ +\verb| Rotatepoint3d(A3d,[0,0,1],pi/2); | // 戻り値は [1,0,0]\\ +\verb| Rotatepoint3d(A3d,[0,0,1],pi/2,[1,1,0]); | // 戻り値は [3,0,0]\\ + +\vspace{\baselineskip} +\hypertarget{scaledata3d}{} +\item[関数] Scaledata3d(name , PDリスト , vec , [中心,options]) +\item[機能] PDを拡大/縮小する。 +\item[説明] 点は空間座標，vec は３次元ベクトルで倍率を表す。 + +中心とoptionsはリストで与える。 + +\vspace{\baselineskip} +【例】三角形と円を拡大/縮小する。 + \begin{verbatim} - pt=[[2,0,0],[2,0,2],[2,2,2],[0,2,2],[0,4,2],[0,4,4]]; - pt2d=apply(pt,[Projcoordpara(#)_1,Projcoordpara(#)_2]); - Spaceline("1",pt); - Ptsize(4); - Drawpoint(pt2d); + Putpoint3d(["A",[0,-2,0],"B",[2,-2,0],"C",[1,-2,2]],"fix"); + Spaceline("1",[A,B,C,A]); + Spacecurve("1","[cos(t)+1,sin(t)+1,1]","t=[0,2*pi]",["Num=100"]); + Scaledata3d("1",["sl3d1","sc3d1"],[2,2,2],[[0,0,0],"dr,2"]); \end{verbatim} - \input{Gfig/oresenex01}\\ -点の名前が必要であれば\\ - \verb|pname=apply(1..6,"P"+text(#));|\\ -のようにして，名前リストを作る。\\ -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +\hspace{20mm}\input{Fig/scaledata3d} +\vspace{\baselineskip} +\hypertarget{scalepoint3d}{} +\item[関数] Scalepoint3d(点,vec,中心) +\item[機能] 点の位置を拡大/縮小する。 +\item[説明] 点は空間座標，vec は３次元ベクトルで与える。 -\subsubsection{直線を引く} +\vspace{\baselineskip} +【例】コード例と結果を示す。 -\begin{tabbing} -12\=34567890123456789\=\kill\\ - \\ -\>【Cinderella】 \>「直線を加える」ツール \includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/multi-add-line.png} を用いる \\ -\>【Cindyscript】 \>draw(join([1,2],[2,-1]))\\ - \>【KeTCindy】 \>Lineplot([A,B]) \\ -\end{tabbing} - Cinderellaの描画ツールを使うと，描かれた線分は幾何要素となり，インスペクタでその属性（色・太さ・線種など）を変えることができる。また，点を直線上にインシデントさせることができる。Scilabに出力しない直線を描くときはこれで十分で，スクリプトも簡素になる。半直線にしたい場合は，線分を描いて一方の端点を描画領域（SW,NE）の外に出して見かけ上半直線にすればよい。 +\begin{verbatim} + Putpoint3d(["A",[2,-1,2]],"fix"); + pt=Scalepoint3d(A3d,[3,2,4],[1,1,1]); + Putpoint3d(["B",pt],"fix"); +\vspace{\baselineskip} +\end{verbatim} -Cindyscript のdraw関数とKeTCindyのLineplot関数では，線の色，太さ，線種を指定することができる。点の識別名ではなく座標を引数にすることもできる。 +点Bの位置は(4,-3,5)になる。 +\vspace{\baselineskip} +\hypertarget{sf3data}{} +\item[関数] Sf3data(name,リスト,options) +\item[機能] 陰線処理なしの曲面をワイヤーフレームモデルで描く +\item[説明] リストは，関数式と定義域，境界指定をそれぞれ文字列にしたもののリスト。 -TeXへの出力は，Lineplot()に "+" オプションをつけると半直線になる。 +optionsは，解像度（各変数に対応する分割数）とメッシュの密度，境界指定。 -KeTCindy3Dには直線を描く関数はないが，線分の外分点を適当にとって線分として描けば，ほとんど直線として扱うことができる。 -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +解像度は，"Num=[a,b]" で指定。初期値はa,bとも25 +メッシュ密度は，縦横で "Wire=[a,b]" で指定。初期値はa,bとも20 +境界指定は"ewsn"で行う。"ewsn" の意味は次のように考える。 -\subsubsection{点線や破線を描く} +変数が u,v のとき，u,v平面において，$a \leq u \leq b,c \leq v \leq d$ の矩形を考え， -\begin{tabbing} -12\=34567890123456789\=\kill\\ +その東西南北(ewsn)の境界を示す。 -\>【Cinderella】 \>インスペクタの「特別な表示方法」で線種を変える \\ -\>【Cindyscript】 \>修飾子 dashtype を使う \\ - \>【KeTCindy】 \>do ,da オプションをつける\\ - \>【KeTCindy3D】 \>do ,da オプションをつける\\ -\end{tabbing} - Cinderellaの描画ツールで引いた線分・直線の線種は，その要素を選んで「Ctrl+i」(Macは ⌘+i) で表示されるインスペクタを用いて，「特別な表示方法」で変えることができる。点線，破線だけでなく，一点鎖線もある。\\ - Cindyscriptの draw() で引いた線分・半直線は，修飾子を用いて， draw([A,B],dashtype-$>$2) のようにして描く。\\ - KeTCindyでは，オプションに，["do"] (点線：dotline) ["da"]（破線：dashline）をつける。 -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} + \begin{center} \input{Fig/ewsn} \end{center} +\vspace{\baselineskip} +関数式のパターンはつぎの3通り。 +\vspace{\baselineskip} +(1) $z=f(x,y)$ -\subsubsection{線の太さを変える} -\begin{tabbing} -12\=34567890123456\=\kill\\ + 【例】：$z=x^2-y^2$を定義域$x=[-2,2],y=[-2,2]$ で描画する。 + + \verb|Sf3data("1",["z=x^2-y^2","x=[-2,2]","y=[-2,2]"])|; + + \begin{center} \input{Fig/saddle1} \end{center} -\>【Cinderella】 \>インスペクタの「表示方法」を使う\\ -\>【Cindyscript】 \>size オプションをつける\\ - \>【KeTCindy】 \>Setpen(n) \\ -\end{tabbing} - インスペクタ，Cindyscriptによる点の大きさの設定は画面上には反映されるが，TeXには書き出されない。逆に，KeTCindyで設定した点の大きさは，Cinderellaの画面上には反映されない。そのことを考慮の上，適宜使い分ける必要がある。画面上の点の大きさと，TeXの図の点の大きさは連動しないので注意が必要である。\\ - KeTCindynの描画関数を使うときは，"size=n" オプションをつけて大きさを設定できるものもある。 -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} + 【例】：同じく，解像度をx,yとも10，メッシュの数を縦横とも10にする。 + + 解像度，メッシュ密度とも下げるので粗い描画となる。 + +\verb|Sf3data("1",["z=x^2-y^2","x=[-2,2]","y=[-2,2]"],| + +\verb|["Num=[10,10]","Wire=[10,10]"]);| + +\vspace{\baselineskip} +(2) $z=f(x,y),x=g(R,T),y=h(R,T)$ + x,y の媒介変数 r,t は大文字にする。 + +\vspace{\baselineskip} +【例】：次図左 + +\verb|fd=["z=4-(x^2+y^2)","x=R*cos(T)","y=R*sin(T)","R=[0,2]","T=[0,2*pi]"];| -\subsubsection{垂線を引く} + \verb|Sf3data("1",fd);| + +【例】：次図右\\ + \verb|fd=["z=sin(sqrt(abs(x^2+y^2)))","x=r*cos(t)","y=r*sin(t)",| -\begin{tabbing} -12\=34567890123456789\=\kill\\ +\verb|"r=[0,3]","t=[0,2*pi]"];| + +\verb|Sf3data("1",fd);| -\>【Cinderella】 \>「垂線を加える」ツール \includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/multi-add-perp.png} を用いる \\ -\>【Cindyscript】 \>perpendicular(A,a)\\ - \>【KeTCindy】 \>作図後，Listplot()で線分を引く\\ - \>【KeTCindy3D】 \>Perppt()で垂線の足を求めて線分を引く\\ + \begin{center} \input{Fig/parabola} \input{Fig/sf3ddata3} \end{center} -\end{tabbing} - Cinderellaの「垂線を描く」ツールを用いて作図するのが簡便だが，何か条件を与えて垂線を引くような場合はCindyscriptを使うことになる。ただし，点と直線（線分）が幾何要素になっていないと垂線は引けない。perpendicular(A,a) で，Aは点の識別子，aは直線（線分）の識別子。TeXには，適当な図が描けたところでLineplot()もしくはListplot()で出力すればよい。 +(3) $x=f(u,v),y=g(u,v),z=h(u,v),$ -対象が幾何要素でない場合は，Cindyscriptで方程式を求めて引くことになる。 + この場合，(2)と区別するために，"p" を先頭につけておく。 + + \vspace{\baselineskip} + 【例】球面 + + \verb|fd=["p","x=2*sin(u)*cos(v)","y=2*sin(u)*sin(v)","z=2*cos(u)",| + +\verb|"u=[0,pi]","v=[0,2*pi]"];| +\verb|Sf3data("1",fd);| -KeTCindy3D の Perppt() 関数は，ある点から平面に下した垂線の足を求める。Perppt() の項にある例を参照のこと。 -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +\begin{center} \input{Fig/sf3ddata4} \end{center} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\subsubsection{平行線を引く} +\hypertarget{sfbdparadata}{} +\item[関数] Sfbdparadata(name,式,options) +\item[機能] 空間曲面の陰線処理 +\item[説明] 曲面について陰線処理を行う。 + 曲面の式はSf3data()の場合と同じ。ただし，(2) と(3)のパターンでは式の最後に境界の指定 ewns を明示する必要がある。(3)では境界の指定を" "(中は半角スペース)とする。省略すると不要な境界線が表示されることがある。境界指定については，Sf3data()の項を参照のこと。 + +optionsは，"Wait=n","r","m",線種。Wait の初期値は30。 -\begin{tabbing} -12\=34567890123456\=\kill\\ + "r","m"に関しては，オプションなしまたは，”” のとき + + i) データファイルがなければ，新しく作る + + ii) データファイルが既にあればそれを読み込む + +"m" のとき，強制的にデータファイルを作り直す。 -\>【Cinderella】 \>「平行線を加える」ツール \includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/multi-add-parallel.png} を用いる \\ -\>【Cindyscript】 \>parallel(B,a)\\ - \>【KeTCindy】 \>作図後，Listplot()で線分を引く\\ -\end{tabbing} - Cinderellaの「平行線を描く」ツールを用いて作図するのが簡便だが，なにか条件を与えて平行線を引くような場合はCindyscriptを使うことになる。ただし，点と直線（線分）が幾何要素になっていないと平行線は引けない。parallel(B,a) で，Bは点の識別子，aは直線（線分）の識別子。 +"r" のとき，すでにあるデータファイルを読み込む。 -TeXには，適当な図が描けたところでLineplot()もしくはListplot() で出力すればよい。 +この処理は時間がかかるため，この関数を実行した状態で画面上のスライダを動かそうとすると反応が悪くなる。そこで，Isangle() を用いて，スライダの点を選択しているときはワイヤフレームモデルを描画するようにするとよい。 -対象が幾何要素でない場合は，Cindyscriptで方程式を求めて引くことになる。 -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +また，この関数はデータを作るだけなので，表示するには ExeccmdC() を用いる。 -\subsection{多角形を描く} +C言語の環境がない場合は，ExeccmdC() が使えないので，SfbdparadataR(name,式,optons1,optons2) を使う。options2には陰線の表示方法について "nodisp" または線種 を指定する。 初期設定は"nodisp" 。options2のみ指定するときは，options1に [""] （空文字）を書いておく。 -\subsubsection{頂点を与えて多角形を描く} +\vspace{\baselineskip} +【例】サドル面 -\begin{tabbing} -12\=34567890123456789\=\kill\\ +陰線を消去して表示（下図左） +\begin{verbatim} + fd=["x=x^2-y^2","x=[-2,2]","y=[-2,2]"]; + if(Isangle(), + Sf3data("1",fd); + , + Startsurf(); + Sfbdparadata("1",fd); + ExeccmdC("1",[],["nodisp"]); + ); +\end{verbatim} +全体を実線で太めにして，陰線を点線で表示（下図右）: \verb|ExeccmdC()| を変更する。 +\begin{verbatim} + ExeccmdC("1",["dr,2"],["do"]); +\end{verbatim} + \begin{center} \input{Fig/sfbdpara01} \input{Fig/sfbdpara02}\end{center} - \>【Cinderella】 \>多角形ツール \includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/polygon.png} を用いる \\ - \>【Cindyscript】 \>drawpoly(点リスト)\\ - \>【KeTCindy】 \>Listplot(点リスト)\\ - \>【KeTCindy3D】 \>Spaceline(点リスト)\\ -\end{tabbing} +【例】放物面 ： 式を変更する。 +\begin{verbatim} + fd=["z=4-(x^2+y^2)","x=R*cos(T)","y=R*sin(T)","R=[0,2]","T=[0,2*pi]","e"]; +\end{verbatim} + + 陰線を消去（下図左）：\verb|ExeccmdC("1",[],["nodisp"]);| + + 陰線を破線で表示（下図右）：\verb|ExeccmdC("1",[],["da"]);| + \begin{center} \input{Fig/sfbdpara03} \input{Fig/sfbdpara04} \end{center} - Cinderellaの描画ツールの多角形ツールは，既存の点を結んで多角形を作り色塗りをするもの。色塗りをしないのであれば，単に線分でつないでいく。 +なお，表示については，\hyperlink{execcmdc}{ExeccmdC()} を参照のこと。 - Cindyscriptのdrawpoly() ，およびKeTCindyのListplot(),Spaceline() での点リストは，既存の幾何点でなく座標でもよい。Listplot() ,Spaceline() の点リストが必ず閉じたリスト（[A,B,C,D,A]）でなければならないのに対し，Cindyscriptのdrawplory()では閉じている必要はない。drawpoly([A,B,C,D])でよい。 -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\hypertarget{skeletonparadata}{} +\item[関数] Skeletonparadata(name,PDリスト,PDリスト,option) +\item[機能] 陰線処理（スケルトン処理）をおこなう +\item[説明] 描画されている線と軸について陰線処理をおこなう。 -\subsubsection{１辺を与えて正多角形を描く} - \\ - 平面上で，与えられた線分ABを１辺とする正多角形を描く。 +第2引数の線（プロットデータ）が，第3引数の線（プロットデータ）によって隠される部分を消去する。第2，第3引数を省略した場合は，すべての線について，互いの陰線処理をおこなう。optionで消去する部分の長さを指定できる。 -線分ABは，Cinderellaの作図ツールなどで描かれているものとする。ただし，線分でなく，両端の点が与えられているだけでもよい。点A,Bが複素平面上にあるものとして，多角形の頂点の位置を計算すればよい。 +\vspace{\baselineskip} +【例】螺旋と線分，座標軸の陰線処理 -CindyscriptのDrawスロットに，次のスクリプトを書く。(n=5で正五角形を描く) +次のように螺旋と線分，座標軸を描いておく。 \begin{verbatim} - n=5; - pti=[complex(A),complex(B)]; - th=2*pi/n; - repeat(n-2,s, - z1=pti_s; - z2=pti_(s+1); - z=z2+(z2-z1)*(cos(th)+i*sin(th)); - pti=append(pti,z); - ); - pt=apply(pti,gauss(#)); - pt=append(pt,A.xy); - Listplot("1",pt); + Xyzax3data("","x=[-5,5]","y=[-5,4]","z=[-5,3]"); + Putpoint3d(["A",[0,-2,-2]],"fix"); + Putpoint3d(["B",[-1,1,3]],"fix"); + Spaceline([A,B]); + Spacecurve("1","[2*cos(t),2*sin(t),0.2*t]","t=[0,4*pi]",["Num=100"]); \end{verbatim} -ptiは，各頂点に対応する複素数のリスト，ptが各頂点の座標のリストである。 -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +座標軸のプロットデータは ax3d，線分は AB3d，螺旋は sc3d1 である。これに対し， +\hspace{10mm} \verb|Skeletonparadata("1");| -\subsubsection{接線を引く} - \\ -曲線上の点における接線を引く -\begin{tabbing} -12\=34567890123456789\=\kill\\ + 描画されている線と軸について陰線処理をおこなう。（図左） -\>【Cinderella】 \>幾何要素の２次曲線の場合，「点の極線を加える」ツール \includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/polar-of-point.png} を用いる\\ -\>【Cindyscript】 \>微分して接線の方程式を求めて直線を引く\\ - \>【KeTCindy】 \>同上 \\ -\end{tabbing} - Cinderellaの作図ツールで描いた２次曲線の場合は，曲線上の点において「点の極線を加える」ツールで接線が引ける。このツールは，初期状態では画面に出ていないので，モードメニューの「直線」から選ぶ。また，「設定」メニューの「上のツールバーをカスタマイズする」で，すべてのツールを表示すれば画面上に出る。 - - Cinderellaの作図ツールで描けない曲線の場合は方程式を求めて直線を引くことになる。微分をする関数は，Cindyscriptでは d(関数,変数)，KeTCindyではDerivative(関数, 変数,値) を用いる。\\ - -例：３次関数 $f(x)=x^3-4x$ 上の点$(1,-3)$における接線を引くCindyscriptとKeTCindyの組み合わせ\\ - f(x):=x\verb|^| 3-4*x;\\ - g(x0,x):=d(f(\#),x0)*(x-x0)+f(x0);\\ - p1=[1,-3];\\ - p2=[2,g(1,2)];\\ - plotdata("1","x\verb|^| 3-4*x","x");\\ - Lineplot("1",[p1,p2]);\\ - \\ - このスクリプトでは，g(x0,x)を点$(x_0,f(x_0))$における接線の方程式としている。\\ - また，接点をインタラクティブに決めるには，２点A,Bを作図しておき\\ - \\ - Deffun("f(x)",["regional(y)","y=x\verb|^|3-4*x","y"]);\\ - coef=Derivative("f(x)","x",A.x);\\ - A.y=f(A.x);\\ - B.y=coef*(B.x-A.x)+A.y;\\ - Plotdata("1","f(x)","x");\\ - Lineplot([A,B]);\\ - - として，接点Aをドラッグして位置決めをすることができる。\\ - \\ - ＜注＞\\ - Deffun("f(x)",["regional(y)","y=x\verb|^|3-4*x","y"]);\\ - は\\ - f(x):=x\verb|^| 3-4*x;\\ - でもよい。\\ -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} -\subsection{円の作図} -\subsubsection{円を描く} +\hspace{10mm} \verb|Skeletonparadata("1",[2]);| -\begin{tabbing} -12\=34567890123456789\=\kill\\ + 重なった部分の空きを2にする。（図中央） + +\hspace{10mm} \verb|Skeletonparadata("1",["AB3d","ax3d"],["sc3d1"]);| + +螺旋によって隠れる部分だけ消去する。（図右） -\>【Cinderella】 \>「円を加える」ツール \includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/multi-add-circle.png} を用いる\\ -\>【Cindyscript】 \>drawcircle([a,b],r)\\ - \>【KeTCindy】 \>Circledata([A,B])，Circledata(name,[[a,b],[c,d]])\\ -\end{tabbing} - Cinderellaの円を描くツールは３種類あるが，あとでTeXに書き出すならば「円を加える」ツールがよい。中心からドラッグすると円周上に点ができる。この２点を使ってCircledata([A,B]) で書き出すことができる。TeXに書き出す必要がない補助円などであれば，「半径付き円を加える」 \includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/circle-by-radius.png} が簡便。半径を一定にする（円周ドラッグで大きさが変わらないようにする）のであれば，「固定した半径の円を描く」ツールを用いる。Cinderellaの円を描くツールで描いた円は，インスペクタの「特別な表示方法」で線種を設定できる。 +\begin{center} \input{Fig/skeletonparadata01} \input{Fig/skeletonparadata02} + \input{Fig/skeletonparadata03} \end{center} -Cindyscript では，中心と半径を指定して円を描く。drawcircle([a,b],r) は [a,b] が中心の座標，r が半径（実数）。中心は，Cinderellaの作図ツールでとった点Aを中心とする場合は，drawcircle(A,r)。 +このほか， -KeTCindyのCircledata([A,B])は，中心Aで点Bを通る円を描く。A,Bを座標にする場合は，nameが必要。中心Aで半径rの円を描くのであれば，座標指定になるので，Circledata("1",[A,A+[3,0]]) または Circledata("1",[A.xy,A.xy+[3,0]]) とする。 -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +\hspace{10mm} \verb|Skeletonparadata("1",["AB3d","ax3d"],["sc3d1"],[2]);| -\subsection{領域を塗る} -\subsubsection{円の内部を塗る} -\begin{tabbing} -12\=34567890123456789\=\kill\\ +\hspace{10mm} \verb|Skeletonparadata("1",["AB3d"],["ax3d","sc3d1"]);| -\>【Cinderella】 \>「円を加える」ツールを用いたのち，インスペクタで設定\\ -\>【Cindyscript】 \>fillcircle(A,r) \\ - \>【KeTCindy】 \>Shade(PD)\\ -\end{tabbing} - 画面上で色を塗るだけならインスペクタの「表示方法」で色塗りをするのが簡便。透明度も設定できる。TeXの図版でも領域を塗るのであれば，Circledata()で円を描いた（プロットデータを作成）のち，Shade()で色を塗る。ここで色指定をすれば画面にも反映される。\\ -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +も可能である。 +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\vspace{\baselineskip} -\subsubsection{多角形の内部を塗る} +\hypertarget{spacecurve}{} +\item[関数] Spacecurve(name,式,定義域,options) +\item[機能] 空間曲線を描く +\item[説明] 媒介変数で表された曲線を描く。optionは解像度 Num -\begin{tabbing} -12\=34567890123456789\=\kill\\ +\vspace{\baselineskip} +【例】螺旋を描く -\>【Cinderella】 \>「多角形を加える」ツール \includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/polygon.png} を用いる \\ -\>【Cindyscript】 \>fillpoly(点リスト)\\ - \>【KeTCindy】 \>Shade(PD)\\ -\end{tabbing} - Cinderellaの描画ツールの多角形ツールは，既存の点を結んで多角形を作り色塗りをする。 +\verb|Spacecurve("1","[2*cos(t),2*sin(t),0.2*t]","t=[0,4*pi]",["Num=100"]);| + +\vspace{\baselineskip} + \begin{center} \input{Fig/rasen} \end{center} -Cindyscriptでの点リストは，既存の幾何点でなく座標でもよい。点リストは，始点と終点を結ぶので閉じている必要はない。([A,B,C,D]) +\hypertarget{spaceline}{} +\item[関数] Spaceline(name,list) +\item[機能] 折れ線を描く +\item[説明] 点の名称または座標のリストを与えて折れ線を描く。平面での Listplot() にあたる。 - TeXに書き出すのであれば Shade()を用いる。\\ -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +options は線種（dr,da,do） +\vspace{\baselineskip} +【例】いくつか示す。 -\subsubsection{曲線で囲まれた領域を塗る} -\begin{tabbing} -12\=34567890123456789\=\kill\\ +・Spaceline("1",[[2,5,1],[4,2,3]]); 指定された2点を結んだ線分を描く。 - \>【KeTCindy】 \>Shade(PD)\\ -\end{tabbing} - Shade()を用いて領域を塗る。Cinderellaの画面にも反映される。\\ -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +・Spaceline("2",[A,B,C,A]); 作図されている2点A,B,Cを結んだ三角形を描く。 -\subsubsection{領域を斜線で示す} +・節点を表示する場合は，Pointdata3d() で描画する。 -\begin{tabbing} -12\=34567890123456\=\kill\\ - \>【KeTCindy】 \>Hatchdata(name,方向,PD)\\ -\end{tabbing} - 領域を斜線で塗る。Cinderellaの画面にも反映される。Scilabとデータをやり取りしてハッチデータを作るので，バッチファイル（シェルファイル）が裏で実行される。\\\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +\begin{layer}{150}{0} +\putnotese{80}{10}{ \input{Fig/oresenex01}} +\end{layer} +\begin{verbatim} + pt=[[2,0,0],[2,0,2],[2,2,2],[0,2,2],[0,4,2],[0,4,4]]; + Spaceline("1",pt); + Pointdata3d("1",pt,["Size=3"]); +\end{verbatim} +点の名前が必要であれば -\subsubsection{領域を細かい点で埋める} +\verb|pname=apply(1..6,"P"+text(#));| -\begin{tabbing} -12\=34567890123456\=\kill\\ +のようにして，名前リストを作ることができる。 - \>【KeTCindy】 \>Dotfilldata(name,方向,PD)\\ -\end{tabbing} - 曲線で囲まれた領域を斜線で塗るかわりに細かい点で埋める。 使い方はHatchdata() と同様。\\ -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +\vspace{\baselineskip} +\hypertarget{translatedata3d}{} +\item[関数] Translatedata3d(name,PD,平行移動量) +\item[機能] 空間プロットデータを平行移動 +\item[説明] PDで表される図形を，平行移動する。 +\vspace{\baselineskip} +【例】曲線 sc3d1 をy軸方向に2だけ平行移動する。 -\subsection{関数のグラフ・曲線} +\verb|Translatedata3d("1",["sc3d1"],[0,2,0]);| + +結果として，もとの曲線と平行移動した曲線の2つが描かれる。 -\subsubsection{関数のグラフを描く} -\begin{tabbing} -12\=34567890123456789\=\kill\\ +\vspace{\baselineskip} +【例】多面体の平行移動\\ +VertexEdgeFace() で描いた多角形はこの関数では平行移動できないので，面データを直接操作して平行移動を行う。 + +たとえば，小林・鈴木・三谷による多面体データ polyhedrons obj を用いて正八面体を描く場合，次のようにする。$y$軸方向に2だけ平行移動する場合である。 -\>【Cindyscript】 \>関数を定義して，plot()で表示する \\ - \>【KeTCindy】 \>（関数を定義して）Plotdata()で表示する \\ -\end{tabbing} +\begin{verbatim} + Setdirectory( Dirhead+"/data/polyhedrons_obj"); + phd=Readobj("r02.obj",["size=2"]); + Setdirectory(Dirwork); + dn=length(phd_1); + repeat(dn,s,phd_1_s=phd_1_s+[0,2,0]); + VertexEdgeFace("1",phd,["Edg=nogeo"]); +\end{verbatim} + \begin{center} \input{Fig/translate01} \end{center} - Cindyscriptでは，f(x):=式 の書式で関数を定義し，plot(fx)) でグラフを描くことができる。関数は，if関数による場合分けも可能。また，この関数概念は数学関数ではなく， プログラミングにおける関数なので，一連の操作を関数として定義して実行することもできる。\\ - KeTCindyでは，Deffun() で関数を定義して，Plotdata()でグラフを描く。Deffunでは，if文による条件分岐も可能だが，ifのネストはできない。\\ - 三角関数などの組み込み関数については，定義は不要で，そのまま plot() もしくは Plotdata()でグラフを描くことができる。ただし，CindyscriptにあってもKeTCindyにはない逆三角関数(arctanなど)はCindyscriptで画面には表示できるがTeXにはできない。\\ +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +\hypertarget{translatepoint3d}{} +\item[関数] Translatepoint3d(座標，平行移動量) +\item[機能] 空間点を平行移動 +\item[説明] 点を平行移動する。 -\subsubsection{媒介変数表示の曲線を描く} +\vspace{\baselineskip} +【例】点A(1,0,0) を(-1,1,1)だけ平行移動した点をBとする。点Aの空間座標は A3d で表される。 +\begin{verbatim} + Putpoint3d(["A",[1,0,0]],"fix"); + pt=Translatepoint3d(A3d,[-1,1,1]); + Putpoint3d(["B",pt],"fix"); +\end{verbatim} +\vspace{\baselineskip} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} -\begin{tabbing} -12\=34567890123456789\=\kill\\ +\hypertarget{vertexedgeface}{} +\item[関数] VertexEdgeFace(name,面データ,options) +\item[機能] 多面体の面データを用いて多面体を描く +\item[説明] 面データは，頂点リストと，面リストからなる。面リストは，各面を構成する頂点を，外側から見て反時計回り（左回り）に並べたリストである。 -\>【Cindyscript】 \>plot([f(t),g(t)])\\ - \>【KeTCindy】 \>Paramplot(name,式,定義域) \\ - \>【KeTCindy3D】 \>Spacecurve(name,式,定義域) \\ -\end{tabbing} - いずれもoptionで線種などの指定ができる。\\ - 平面における曲線で，Timer Tickスロットに書いてアニメーションを行う場合は，Cindyscriptの plot()の方を勧める。シンプルな分，実行速度において有利である。\\ -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +たとえば，四面体ABCDの面データは，[[A,B,C,D],[[1,2,3],[1,2,4],[1,3,4],[2,3,4]]] となる。 +4点A,B,C,Dをとっておき，このリストを引数に与えると，四面体の辺が描かれる。 -\subsubsection{２次曲線を描く} - 放物線，楕円，双曲線を描く。 -\begin{tabbing} -12\=34567890123456789\=\kill\\ +このとき，option がなければ，Cinderellaの幾何要素として辺が描かれるが，それだけではTeXには書き出されないので注意が必要である。(変数未定義のエラーになる) TeXに書き出すには，optionとして ["Edg=nogeo"] をつける。このときは各辺は幾何要素にならない。 -\>【Cinderella】 \>焦点などを作図してそれぞれの作図ツールを用いる\\ -\>【Cindyscript】 \>関数もしくは媒介変数で表してplot()で描く\\ - \>【KeTCindy】 \>Plotdata() もしくは Paramplot() ,Parabolaplot() などで描く\\ -\end{tabbing} - これらの曲線を描く方法は何通りかある。全体ではなく一部分を描く場合はCinderellaの作図ツールではできないのでplot()または Paramplot()で描く。 +また，"Pt=free" optionをつけると，頂点は自由点となり，マウスドラッグで動かすことができる。 - これらの曲線上に点をとり，接線を引いてインタラクティブに動かすような場合は，Cinderellaの作図ツールで描くとよい。点をインシデントにするのが容易であり，接線も簡単に引け，さらにその接線も幾何要素となるので都合がよい。 +生成されるプロットデータは， -KeTCindyでは，Plotdata() で媒介変数表示の式を与えるか，Parabolaplot(),Ellipsplot(),Hyperbolaplot() で焦点などを与えて描く。 +phv3d：頂点のリスト -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +phe3d：辺のリスト +phf3d：面リスト -\subsubsection{陰関数のグラフを描く} +なお，それぞれ末尾にnameが付加される。 -\begin{tabbing} -12\=34567890123456\=\kill\\ +\vspace{\baselineskip} +【例】：正四面体を描く +\begin{verbatim} + Putpoint3d("A",2*[-1,-1/sqrt(3),0],"fix"); + Putpoint3d("B",2*[1,-1/sqrt(3),0],"fix"); + Putpoint3d("C",2*[0,sqrt(3)-1/sqrt(3),0],"fix"); + Putpoint3d("D",2*[0,0,sqrt(3)],"fix"); + phd=Concatobj([[A,B,C],[A,B,D],[A,C,D],[B,C,D]]); + VertexEdgeFace("1",phd,["Edg=nogeo"]); +\end{verbatim} + \begin{center} \input{Fig/vertex01} \end{center} - \>【KeTCindy】 \>Implicitplot()\\ -\end{tabbing} - 陰関数で与えられた曲線を描く方法はCinderella，Cindyscriptにはない。 -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +%\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\hypertarget{wireparadata}{} +\item[関数] Wireparadata(name,PD,式,整数,整数,optons) +\item[機能] 曲面のワイヤフレームを陰線処理してプロットデータを作る。 +\item[説明] PDは，第3引数の式で描いたワイヤフレームモデルのプロットデータ名。第4，第5引数は分割線の数。 +options には "r","m","Wait=n" が指定できる。Wait の初期値は30。 -\subsubsection{プロットデータを自作して表示する} - \\ - 組み込み関数にない関数などを使ってプロットデータを自作して表示するには，Cindyscriptで作成したプロットデータをListplot() または AddGraph()に渡して描画する。それぞれの項の例を参照のこと。 + "r","m"に関しては，オプションなしまたは，”” のとき + + i) データファイルがなければ，新しく作る + + ii) データファイルが既にあればそれを読み込む + + "m" のとき，強制的にデータファイルを作り直す。 + + "r" のとき，すでにあるデータファイルを読み込む。 + +曲面の陰線処理を行うので，Sfbdparadata() とペアで使う。 -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +この処理は時間がかかるため，この関数を実行した状態で画面上のスライダを動かそうとすると反応が悪くなる。そこで，Isangle() を用いて，スライダの点を選択しているときはワイヤフレームモデルを描画するようにするとよい。 -\subsection{その他} +また，この関数はデータを作るだけなので，表示するには \hyperlink{execcmdc}{ExeccmdC()} を用いる。 -\subsubsection{幾何要素を非表示にする} -描いた点や線を非表示にする。 -\begin{tabbing} -12\=34567890123456\=\kill\\ +C言語の環境がない場合は，ExeccmdC() が使えないので，WireparadataR(name,PD,式,整数,整数,optons1,optons2) を使う。options2には陰線の表示方法について "nodisp" または線種 を指定する。 初期設定は"nodisp" 。options2のみ指定するときは，options1に [""] （空文字）を書いておく。 -\>【Cinderella】 \>インスペクタの「表示方法」で「表示する」のチェックを切る \\ -\>【Cindyscript】 \>幾何要素のvisibleプロパティをfalseにする \\ - \>【KeTCindy】 \>"notex" または "nodisp" オプションをつける \\ -\end{tabbing} - インスペクタの表示方法」で「表示する」のチェックを切った場合，「表示」に戻すには，「表示」メニューの「式による表示」を開いて，該当の幾何要素を選択し，インスペクタで「表示する」のチェックをつける。\\ - 幾何要素をCindyscriptで非表示/表示にするには，A.visible=false / true とする。幾何要素ではない関数のグラフなどはインスペクタでは非表示にできない。\\ - KeTCindy の "notex" オプションはTeXに出力しない。"nodisp"オプションでは，画面にも表示されない。プロットデータを作成するために使う。\\ -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +\vspace{\baselineskip} +【例】式のタイプ別に例を示す。 -\subsubsection{角に印をつける} -角に弧または平行四辺形の角の印をつける。 -\begin{tabbing} -12\=34567890123456\=\kill\\ +\vspace{\baselineskip} +サドル面 -\>【Cinderella】 \>「角に印をつける」ツール \includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/angle-mark.png} を用いる（弧の形状のみ）\\ -\>【Cindyscript】 \>なし\\ - \>【KeTCindy】 \>Anglemark() , Paramark() を用いる \\ -\end{tabbing} - TeXに出力しないのであれば，「角に印をつける」ツールを用いるのが簡便。ただし，平行四辺形の印はつけられない。\\ - 角に向きを示す矢印を付加する場合は，Anglemark()で描いておき，Arrowhead()で矢じりをつける。\\ -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +\begin{layer}{150}{0} +\putnotese{85}{5}{ \input{Fig/wirepara1}} +\end{layer} +\begin{verbatim} + fd=["z=x^2-y^2","x=[-2,2]","y=[-2,2]"]; + if(Isangle(), + Sf3data("1",fd); + , + Startsurf(); + Sfbdparadata("1",fd); + Wireparadata("1","sfbd3d1",fd,4,5); + ExeccmdC("1"); + ); +\end{verbatim} +回転放物面：次を変更 -\subsection{値の取得・変換} -\subsubsection{角度を測る} +\begin{layer}{150}{0} +\putnotese{85}{10}{ \input{Fig/wirepara2}} +\end{layer} +\begin{verbatim} + fd=["z=4-(x^2+y^2)","x=r*cos(t)","y=r*sin(t)","r=[0,2]","t=[0,2*pi]","e"]; + Wireparadata("1","sfbd3d1",fd,5,7); +\end{verbatim} +\vspace{25mm} -\begin{tabbing} -12\=34567890123456789\=\kill\\ +球面 -\>【Cinderella】 \>「角度を測る」ツール \includegraphics[bb=0 0 27 21 , width=0.6cm]{Cindytool/angle.png}を用いる。\\ -\>【Cindyscript】 \>arctan2(ベクトル)を用いる\\ -\end{tabbing} - Cinderellaの「角度を測る」ツールでは，画面上に角度が表示される。この値をスクリプトで利用するためには，その識別名を用いる。識別名は，表示メニューから「式による表示」で出る幾何要素の一覧表で判断する。識別名がα0であれば，変数α0に角の値が入っていると考えてよい。αは日本語入力モードで「あるふぁ」で入力する。たとえば，drawtext([1,1],α0) とすれば，(1,1) の位置に角度が表示される。このときの角は一般角であり，点をドラッグすると360°以上の角や負の角で表示される。また，表示は度数法で行われるが，処理によっては弧度法での表示となる。\\ - Cindyscriptで角度を取得するには，arctan2()を用いるのがよい。引数はベクトルで，x軸の正の方向とのなす角を −π 〜 π の範囲で弧度法で返す。角ABCの場合，th=arctan2(C.xy-B.xy)-arctan2(A.xy-B.xy) で取得できる。\\ -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +このタイプでは，媒介変数形式の識別のため，先頭に "p" をつけておく。 -\subsubsection{２点間の距離を測る} +\begin{layer}{150}{0} +\putnotese{80}{0}{ \input{Fig/wirepara3}} +\end{layer} +\begin{verbatim} + fd=["p","x=2*sin(u)*cos(v)", + "y=2*sin(u)*sin(v)", + "z=2*cos(u)","u=[0,pi]", + "v=[0,2*pi]","s"]; + Sfbdparadata("1",fd); + Wireparadata("1","sfbd3d1",fd,12,12); +\end{verbatim} -\begin{tabbing} -12\=34567890123456\=\kill\\ +\vspace{8mm} +%\begin{center} \input{Fig/wirepara1} \input{Fig/wirepara2} \input{Fig/wirepara3} \end{center} -\>【Cindyscript】 \>dist(A,B) または $|$A,B$|$ \\ - \>【KeTCindy3D】 \>dist3d(点，点)\\ -\end{tabbing} -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +\vspace{\baselineskip} +【例】球面で座標軸を陰線処理し，面の陰線は非表示で表す。 -\subsubsection{数値を文字に変換する} -関数の引数に文字列として与えるために数値を文字列に変換したい場合がある。このような場合は，text() 関数を用いる。引数は実数・複素数いずれでも可。\\ +\begin{layer}{150}{0} +\putnotese{70}{5}{ \input{Fig/wirepara4}} +\end{layer} -subsubsection{小数点の桁数を指定して表示} -\begin{tabbing} -12\=34567890123456\=\kill\\ +\begin{verbatim} + fd=["p","x=2*sin(u)*cos(v)", + "y=2*sin(u)*sin(v)", + "z=2*cos(u)", + "u=[0,pi]","v=[0,2*pi]","s"]; + if(Isangle(), + Sf3data("1",fd); + , + Startsurf(); + Sfbdparadata("1",fd); + Wireparadata("1","sfbd3d1",fd,12,12); + Crvsfparadata("1","ax3d","sfbd3d1",fd); + ret=ExeccmdC("1"); + forall(1..length(ret), + if(indexof(ret_#,"wireh")>0, + Changestyle3d([ret_#],["nodisp"]); + ); + ); + ); +\end{verbatim} +【例】トーラスを描く -\>【Cinderella】 \>なし \\ -\>【Cindyscript】 \>format()関数を用いる \\ - \>【KeTCindy】 \>Textformat() 関数を用いる\\ -\end{tabbing} - Cinderellaでは，小数点以下の桁数は第５位を四捨五入して表示するのがデフォルトである。小数点以下の桁数を指定するには，Cindyscriptでは format()関数，KeTCindydでは Textformat()関数を用いる。Textformat()関数は，リストで与えた数でも処理できる。\\ -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +式を次のように変え，軸は非表示にして，\verb|ExeccmdC("1",[],["nodisp"])| にする。 -\subsection{スライダを作る} -\subsubsection{線分スライダを作る} -変数の値をインタラクティブに決めるスライダを作る。 +\begin{verbatim} + fd=["p","x=(2+cos(u))*cos(v)","y=(2+cos(u))*sin(v)","z=sin(u)", + "u=[0,2*pi]","v=[0,2*pi]","s"]; +\end{verbatim} +\vspace{\baselineskip} + \begin{center} \input{Fig/wirepara5} \end{center} -まず，Cinderellaの作図ツールで，適当な線分（または直線）と，その上の点をとる。このとき，点が線分上にインシデントになるように，点を線分上にドラッグして線分がハイライトしたときにマウスボタンを離す。 +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\vspace{\baselineskip} +\hypertarget{xyzax3data}{} +\item[関数] Xyzax3data(name，ｘの範囲，yの範囲，zの範囲,options) +\item[機能] 座標軸を描く +\item[説明] 描画面に座標軸を描き，プロットデータ ax3d を作成する。nameは空文字列でよい。option は次の2つ。 -線分をAB，AB上の点をCとして，AとCの距離 $|$A,C$|$ を用いて変数の値を決めればよい。 +矢じり："an"：nは数字で矢じりの大きさ。nはなくてもよい。 - 例：x=$|$A,C$|$-5; +原点O："Onesw"：neswは微小位置。数字も付けられる。neswをつけない場合の初期値はsw。 -整数を取得したい場合は，天井関数ceil()または，床関数 floor()を用いて整数化する。 +【例】 初期設定の座標軸\\ +\verb|Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]");| + + 矢じりをつける + + \verb|Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]","a");| + + 矢じりを大きくする + + \verb|Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]",["a2"]);| + +原点のOを表示する。 - 例：n=ceil($|$A,C$|$) + \verb|Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]",["O"]);| + + 原点のOの位置を調整して右上に表示する。やじりもつける。 + + \verb|Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]",["a","Oe2n2"]);| + -点Cを端点までドラッグした後，さらに点Cをドラッグしようとすると端点も同時に動いてしまうことがある。そこで，端点を選択してインスペクタで「ピンで留める」にチェックを入れておくとよい。 -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +【注意】Putaxes3d() で点を取ると原点に点Oが作成される。この点名Oと表示が重複するのが煩わしい場合は，作図後にこのoptionをつけてから出力するとよい。 -\subsubsection{円形スライダを作る} -角の値をインタラクティブに決めるスライダを作る。 -まず，Cinderellaの作図ツールで，適当な円を描き，その上に点をとる。このとき，点が円周上にインシデントになるように，点を円周上にドラッグして円周がハイライトしたときにマウスボタンを離す。 +\vspace{\baselineskip} +\hypertarget{xyzcoord}{} +\item[関数] Xyzcoord(P.x,P.y,Pz.y) +\item[機能] 主副画面で決まる点の座標 +\item[説明] Cinderellaの描画面上の点が表す空間座標を求める -円の中心をA，円周上の点をBとしたとき，B.angleで角度を取得できる。ただし，戻り値は$0^\circ 〜 360^\circ$ + 点Ｐについて，主画面の点Ｐに対応するのが副画面のPzである。点Pの2次元座標はP.x,P.yで，Pzのy座標はPz.yで表される。これを引数として与えると，点Ｐの空間座標が返される。 + +\vspace{\baselineskip} +【例】点Aをドラッグして動かしたとき，Aの座標を求める。 +\verb|println(Xyzcoord(A.x,A.y,Az.y));| + +により，コンソールに座標が表示される。 -arctan2(B.xy-A.xy) で角を取得することもできる。この場合の戻り値は，$-180^\circ 〜 180^\circ$\\ -\begin{flushright} \hyperlink{functionlist3d}{$\Rightarrow$関数一覧}\end{flushright} +\end{description} +\newpage +% 付録 ================================== +\section{付録} +\subsection{用語解説} +Cinderellaで使っている用語に次のものがある。 +\begin{tabbing} +1234567890123\=456789890123456789012\=34567890123\=\kill +インシデント \>点が曲線（直線）上に乗っている状態を表す。\\ + \>曲線上に点をとるとインシデントになり，ドラッグしたとき曲線上だけを動く。\\ + \>インシデントの状態を変えるには，「点の取り付け/取り外し」ツールを使う。\\ +幾何要素 \>Cinderellaの作図ツールで作図した点や直線などの要素\\ +インスペクタ \>幾何要素の大きさや色などの属性を管理するウィンドウ。\\ +幾何点 \>幾何要素としての点。マウスドラッグで動かすことができる。\\ + \>CindyscriptやKeTCindyのスクリプトで取った点は幾何要素にならないことがある。\\ +自由点 \>マウスドラッグで任意に動かすことのできる点。\\ +固定点 \>マウスドラッグで移動することのできない点\\ + \>2曲線の交点などではない単独の点の場合，インスペクタで点を固定できる。\\ +スナップ \>マウスポイントが格子点の近くに来ると格子点上にぴったり移動する。\\ + \>Cinderellaの画面の下方ツールのうち，磁石アイコンによりこのモードになる。\\ + \end{tabbing} + +\hypertarget{geometrytool}{} +\subsection{Cinderellaの作図ツール} + \begin{tabbing} +1234567890123456789890123456789012\=34567890123\=\kill +\includegraphics[bb=0 0 6.48 5.04 , width=0.6cm]{Fig/move.pdf} 動かすモードにする \>：幾何要素を選択して動かす。これが標準状態\\ +\includegraphics[bb=0 0 6.48 5.04 , width=0.6cm]{Fig/single-add.pdf} 点を加える \>：クリックして点を作る\\ +\includegraphics[bb=0 0 6.48 5.04 , width=0.6cm]{Fig/multi-add-line.pdf} 直線を加える \>：2点間をドラッグする\\ +\includegraphics[bb=0 0 6.48 5.04 , width=0.6cm]{Fig/segment.pdf} 線分を加える \>：2点間をドラッグする\\ +\includegraphics[bb=0 0 6.48 5.04 , width=0.6cm]{Fig/middle.pdf} 中点を加える \>：2点間をドラッグする\\ +\includegraphics[bb=0 0 6.48 5.04 , width=0.6cm]{Fig/intersection.pdf} 交点を加える \>：2曲線を順にクリック\\ +\includegraphics[bb=0 0 6.48 5.04 , width=0.6cm]{Fig/multi-add-parallel.pdf} 平行線を加える \>：直線上から通る点へドラッグ\\ +\includegraphics[bb=0 0 6.48 5.04 , width=0.6cm]{Fig/multi-add-perp.pdf} 垂線を加える \>：直線上から通る点へドラッグ\\ +\includegraphics[bb=0 0 6.48 5.04 , width=0.6cm]{Fig/bisector.pdf} 角の二等分線を加える \>：2直線を順にクリック\\ +\includegraphics[bb=0 0 6.48 5.04 , width=0.6cm]{Fig/multi-add-circle.pdf} 円を加える \>：中心から半径分ドラッグ\\ +\includegraphics[bb=0 0 6.48 5.04 , width=0.6cm]{Fig/circle-by-radius.pdf} 半径つき円を加える \>：中心から半径分ドラッグ\\ +\includegraphics[bb=0 0 6.48 5.04 , width=0.6cm]{Fig/ellipse-by-foci.pdf} 焦点と通る点で決まる楕円 \>：焦点と通る点を順にクリック\\ +\includegraphics[bb=0 0 6.48 5.04 , width=0.6cm]{Fig/hyperbola-by-foci.pdf} 焦点と通る点で決まる双曲線 \>：焦点と通る点を順にクリック\\ +\includegraphics[bb=0 0 6.48 5.04 , width=0.6cm]{Fig/parabola-by-foci.pdf} 焦点と準線で決まる放物線 \>：焦点と準線を順にクリック\\ +\includegraphics[bb=0 0 6.48 5.04 , width=0.6cm]{Fig/polygon.pdf} 多角形を加える \>：多角形の頂点を順にクリック\\ +\includegraphics[bb=0 0 6.48 5.04 , width=0.6cm]{Fig/angle-mark.pdf} 角に印をつける \>：2直線を順にクリック\\ +\includegraphics[bb=0 0 6.48 5.04 , width=0.6cm]{Fig/angle.pdf} 角度を測る \>：2直線を順にクリック\\ +\includegraphics[bb=0 0 6.48 5.04 , width=0.6cm]{Fig/delete.pdf} 選択した要素を消去する \>：選択しておいてツールをクリック\\ +\includegraphics[bb=0 0 6.48 5.04 , width=0.6cm]{Fig/select-points.pdf} 点をまとめて選択する \>：点がすべて選択される\\ +\includegraphics[bb=0 0 6.48 5.04 , width=0.6cm]{Fig/select-lines.pdf} 線分をまとめて選択する \>：線分がすべて選択される\\ + \end{tabbing} + + \begin{tabbing} +1234567890123456789890123456789012\=34567890123\=\kill +画面ツール（下のツールバー）\\ +\includegraphics[bb=0 0 6.48 5.04 , width=0.6cm]{Fig/translate-view.pdf} 原点を移動する \>：画面上の任意の位置でドラッグする\\ +\includegraphics[bb=0 0 6.48 5.04 , width=0.6cm]{Fig/zoom-in.pdf} 矩形領域を画面サイズに拡大 \>：ドラッグしてできる矩形で領域を選択する\\ +\includegraphics[bb=0 0 6.48 5.04 , width=0.6cm]{Fig/zoom-out.pdf} 画面を矩形領域サイズに縮小 \>：どっらっぐしてで切る矩形で領域を選択する\\ +\includegraphics[bb=0 0 6.48 5.04 , width=0.6cm]{Fig/snap.pdf} 格子点にスナップする \>：軸と方眼を表示しスナップモードにする\\ +\includegraphics[bb=0 0 6.48 5.04 , width=0.6cm]{Fig/grid-more.pdf} \includegraphics[bb=0 0 6.48 5.04 , width=0.6cm]{Fig/grid-less.pdf} グリッドを粗く / 細かくする\\ + \end{tabbing} + +\hypertarget{colorcodelist}{} +\subsection{色名とカラーコード一覧} +\vspace{\baselineskip} +\scalebox{0.9}{\input{Fig/colortable}} -% 関数一覧 ================================== +\newpage +%--------------点の作図についての比較表-------------------------------------- +\hypertarget{mkpttable}{} +\subsection{点の作図についての比較表} +\vspace{\baselineskip} +\scalebox{0.9}{\input{Fig/mkpttable}} + +注) Intersectcrvsf は戻り値ではなく，プロットデータを使う。 + +\newpage +% 関数一覧 ================================== \hypertarget{functionlist}{} \section{関数一覧} +\hyperlink{index}{【目次】に戻る} + \begin{tabbing} 12345678901234567890123456789012345678\=\kill 【設定・定義】\\ -\hyperlink{addax}{Addax(0/1)} \>座標軸を描くかどうかを定める\\ -\hyperlink{addcolor}{Addcolor(com,color)} \>描画色を設定する\\ -\hyperlink{colorcode}{Colorcode(文字1，文字2,color)} \>カラーコードの変換\\ -\hyperlink{deffun}{Deffun(関数名 , 定義リスト )} \>関数を定義する\\ -\hyperlink{definecolor}{Definecolor(色名 , 定義リスト )} \>ユーザー定義色の設定\\ -\hyperlink{defvar}{Defvar(文字列)} \>変数を定義する\\ -\hyperlink{drwxy}{Drwxy()} \>座標軸を先に描く\\ -\hyperlink{fontsize}{Fontsize(記号)} \>フォントサイズを設定する\\ -\hyperlink{ketint}{Ketinit(options)} \>\ketcindy を初期化する\\ -\hyperlink{ptsie}{Ptsize(数)} \>表示する点の大きさを設定する\\ -\hyperlink{setax}{Setax(リスト)} \>座標軸の書式を設定する\\ -\hyperlink{setcolor}{Setcolor(color,options)} \>Windispgでの描画色を設定する\\ -\hyperlink{setmarklen}{Setmarklen(数)} \>軸の目盛の長さを設定する\\ -\hyperlink{setorigin}{Setorigin(座標)} \>表示する座標軸の原点の位置を設定する\\ -\hyperlink{setpen}{Setpen(数)} \>線の太さを設定する\\ -\hyperlink{setpt}{Setpt(数)} \>表示する点の大きさを設定する\\ -\hyperlink{setscaling}{Setscaling(数)} \>縦方向の倍率を設定する\\ -\hyperlink{setunitlen}{Setunitlen(数)} \>単位長を設定する\\ -\hyperlink{setwindow}{Setwindow()} \>描画領域を設定する\\ -\hyperlink{slider}{Slider()} \>スライダを作る\\ -\\ +\hyperlink{addax}{Addax(0/1)} \>座標軸を描くかどうかを定める\\ +\hyperlink{addpackage}{Addpackage(package)} \>プレビュー用のパッケージを追加\\ +\hyperlink{changework}{Changework(パス)} \>作業ディレクトリを変更する\\ +\hyperlink{deffun}{Deffun(関数名 , 定義list )} \>関数を定義する\\ +\hyperlink{definecolor}{Definecolor(色名 , 定義list )} \>ユーザー定義色の設定\\ +\hyperlink{defvar}{Defvar(文字列)} \>変数を定義する\\ +\hyperlink{drwxy}{Drwxy()} \>座標軸を先に描く\\ +\hyperlink{fontsize}{Fontsize(記号)} \>フォントサイズを設定する\\ +\hyperlink{ketinit}{Ketinit(options)} \>\ketcindy を初期化する\\ +\hyperlink{ptsize}{Ptsize(数)} \>表示する点の大きさを設定する\\ +\hyperlink{setax}{Setax(list)} \>座標軸の書式を設定する\\ +\hyperlink{setcolor}{Setcolor(color,options)} \>Windispgでの描画色を設定する\\ +\hyperlink{setfiles}{Setfiles(filename)} \>出力するファイル名を設定する\\ +\hyperlink{setparent}{Setparent(filename)} \>Parentで出力するファイル名を設定する\\ +\hyperlink{setmarklen}{Setmarklen(数)} \>軸の目盛の長さを設定する\\ +\hyperlink{setorigin}{Setorigin(座標)} \>表示する座標軸の原点の位置を設定する\\ +\hyperlink{setpen}{Setpen(数)} \>線の太さを設定する\\ +\hyperlink{setpt}{Setpt(数)} \>表示する点の大きさを設定する\\ +\hyperlink{setscaling}{Setscaling(数)} \>縦方向の倍率を設定する\\ +\hyperlink{setunitlen}{Setunitlen(数)} \>単位長を設定する\\ +\hyperlink{setwindow}{Setwindow()} \>描画領域を設定する\\ +\hyperlink{usegraphics}{Usegraphics()} \>グラフィクスパッケージを \verb|"pict2e"| に変更する\\ 【描画】\\ -\hyperlink{anglemark}{Anglemark(点リスト, options)} \>角の印を入れる\\ \hyperlink{addgraph}{AddGraph(name ,プロットデータ)} \>ユーザー定義のプロットデータを描画する\\ -\hyperlink{arrowdata}{Arrowdata(始点,終点,options)} \>2点間を結ぶ矢線を描く\\ -\hyperlink{arrowhead}{Arrowhead(点,方向,options)} \>点に矢じりだけを描く\\ -\hyperlink{bezier}{Bezier(name, リスト,リスト,options )} \>単独のベジェ曲線を描く\\ -\hyperlink{beziersmooth}{Beziersmooth(name , リスト,options )} \>なめらかなベジェ曲線を描く。その１\\ -\hyperlink{beziersym}{Beziersym(name , リスト,options )} \>なめらかなベジェ曲線を描く。その２\\ -\hyperlink{bowdata}{Bowdata(点リスト,options)} \>弓形を描く\\ -\hyperlink{bspline}{Bspline(name，リスト，options )} \>２次 Bスプライン曲線を描く\\ -\hyperlink{changestyle}{Changestyle(PD リスト, options)} \>描画オプションを変更する\\ -\hyperlink{circledata}{Circledata(name,点リスト,options)} \>円または多角形を描く\\ -\hyperlink{crosspoint}{Crosspoint(name,PD,PD,範囲リスト)} \>2曲線の交点を作る\\ -\hyperlink{cspline}{CRspline(name，リスト，options )} \>単独のCatmull-Rom スプライン曲線を描く\\ -\hyperlink{deqplot}{Deqplot(name,式,変数名,初期値,options])} \>微分方程式の解曲線を描く\\ -\hyperlink{dotfilldata}{Dotfilldata(name , 方向, PD , optionss)} \>領域に点を敷き詰める\\ -\hyperlink{drawsegmark}{Drawsegmark(name,リスト,options)} \>線分に印をつける\\ -\hyperlink{drawsegmark}{Segmark(name,リスト,options)} \>線分に印をつける\\ -\hyperlink{drwpt}{Drawpoint([点,options])} \>点を表示する\\ -\hyperlink{drwpt}{Drwpt([点,options])} \>点を表示する\\ -\hyperlink{ellipseplot}{Ellipseplot(name,list,str,options)} \>楕円を描く\\ -\hyperlink{enclosing}{Enclosing(name , [位置，方向，数式])} \>複数の曲線から閉曲線を描く\\ -\hyperlink{expr}{Expr(文字列)} \>\TeX 数式を書く\\ -\hyperlink{exprrot}{Exprrot(位置，向き，文字列)} \>傾いた\TeX 数式を書く\\ -\hyperlink{framedata}{Framedata(name , リスト)} \>矩形を描く\\ -\hyperlink{framedata}{Framedata2(name , リスト)} \>矩形を描く\\ -\hyperlink{hatchdata}{Hatchdata(name , 方向, PD , optionss)} \>領域に斜線を引く\\ -\hyperlink{htickmark}{Htickmark([横座標 , 方向 , 文字])} \>横軸に目盛りを描く\\ -\hyperlink{hyperbolaplot}{Hyperbolaplot(name,list,str,options)} \>双曲線を描く\\ -\hyperlink{implicitplot}{Implicitplot(name,str,,str,str,options)} \>陰関数のグラフを描く\\ -\hyperlink{joincrvs}{Joincrvs（name, PDリスト, options)} \>2つのプロットデータをつなげたデータを作る\\ -\hyperlink{letter}{Letter(「座標,位置,文字列]のリスト」)} \>文字列を表示する\\ -\hyperlink{letterrot}{Letterrot(「座標,方向,移動量,文字列])} \>文字列を回転して表示する\\ -\hyperlink{lineplot}{Lineplot(name,２点のリスト,options)} \>２点を結ぶ直線を描く\\ -\hyperlink{listplot}{Listplot(name,点のリスト,options)} \>点を線分で結ぶ\\ -\hyperlink{mkbeziercrv}{Mkbeziercrv(name,リスト,options)} \>作図した点を使ってベジエ曲線を描く\\ -\hyperlink{mkbezierptcrv}{Mkbezierptcrv(リスト，options ) } \>制御点を自動配置してベジエ曲線を描く\\ -\hyperlink{mkcircle}{Mkcircle()} \>幾何円のすべてのPD を作成する\\ -\hyperlink{mksegments}{Mksegments()} \> 幾何線分のすべてのPD を作成する\\ -\hyperlink{ovaldata}{Ovaldata(name, 点リスト,optionss)} \>角を丸くした矩形を描く\\ -\hyperlink{ospline}{Ospline(リスト，リスト，options )} \>大島のスプライン曲線を描く\\ -\hyperlink{parabolaplot}{Parabolaplot(name,list,str,options)} \>放物線を描く\\ -\hyperlink{parabolaplot}{Parabolaplot(name,点リスト,options)} \>楕円を描く\\ -\hyperlink{paramark}{Paramark(点リスト,options)} \>角の印を入れる\\ -\hyperlink{paramplot}{Paramplot(name,式,変数と定義域,options)} \>媒介変数で表された曲線を表示する\\ -\hyperlink{partcrv}{Partcrv(name,点1,点2,PD)} \>部分曲線を描く\\ -\hyperlink{plotdata}{Plotdata(name,式,変数と定義域,options)} \>関数のグラフを描く\\ -\hyperlink{pointdata}{Pointdata(name,点リスト,optionss)} \>点データを作る\\ -\hyperlink{polygonplot}{Polygonplot(name,点リスト,整数,options)} \>正多角形を描く\\ -\hyperlink{putintersect}{Putintersect(点名,PD1,PD2)} \>２曲線の交点を作る\\ -\hyperlink{putline}{PutonLine(点名,座標1,座標2)} \>直線上に点を作る\\ -\hyperlink{putoncurve}{PutonCurve(name,PD,初期値)} \>曲線上に点を作る\\ -\hyperlink{putpoint}{Putpoint(点名,座標1,座標2)} \>点を作る\\ -\hyperlink{putseg}{PutonSeg(点名,座標1,座標2)} \>線分上に点を作る\\ -\hyperlink{reflectdata}{Reflectdata(name,PD,点リスト,options)} \>プロットデータの鏡映を作成\\ -\hyperlink{reflectpoint}{Reflectpoint(点,対称点/対称軸)} \>点の鏡映を作成\\ -\hyperlink{rotatedata}{Rotatedate(name,PD,角度,中心,options)} \>プロットデータを回転する\\ -\hyperlink{rotatepoint}{Rotatepoint(点,角度,中心)} \>点の位置を回転する\\ -\hyperlink{rulerscale}{Rulerscale(点,リスト,リスト)} \>目盛を打つ\\ -\hyperlink{scaldedata}{Scaledata(name,PD,x,y,中心,options)} \>点を拡大・縮小する\\ -\hyperlink{scalepoint}{Scalepoint(点,比率ベクトル,中心)} \>点の位置を拡大・縮小する\\ -\hyperlink{shade}{Shade（PDリスト , 数)} \>閉曲線の内部にシェードをかける\\ -\hyperlink{translatedata}{Translatedata(name,PD,ベクトル,options)} \>プロットデータを平行移動する\\ -\hyperlink{translatepoint}{Translatepoint(点,ベクトル)} \>点を平行移動する\\ -\hyperlink{vtickmark}{Vtickmark([横座標 , 方向 , 文字])} \>縦軸に目盛りを描く\\ - - \\ -【微積分など】\\ -\hyperlink{derivative}{Derivative(関数式,変数,値)} \>関数の微分係数を求める\\ -\hyperlink{integrate}{Integrate(関数式,変数,範囲,options)} \>関数の定積分値を求める\\ -\hyperlink{inversefun}{Inversefun(関数式,範囲,値)} \>逆関数値を求める\\ - \\ +\hyperlink{anglemark}{Anglemark(点list, options)} \>角の印を入れる\\ +\hyperlink{arrowdata}{Arrowdata(name.[始点,終点],options)} \>2点間を結ぶ矢線を描く\\ +\hyperlink{arrowhead}{Arrowhead(点,方向,options)} \>点に矢じりだけを描く\\ +\hyperlink{bezier}{Bezier(name, list,list,options )} \>単独のベジェ曲線を描く\\ +\hyperlink{beziersmooth}{Beziersmooth(name , list,options )} \>なめらかなベジェ曲線を描く。その１\\ +\hyperlink{beziersym}{Beziersym(name , list,options )} \>なめらかなベジェ曲線を描く。その2\\ +\hyperlink{bowdata}{Bowdata(点list,options)} \>弓形を描く\\ +\hyperlink{bspline}{Bspline(name，list，options )} \>2次 Bスプライン曲線を描く\\ +\hyperlink{changestyle}{Changestyle(PD list, options)} \>描画オプションを変更する\\ +\hyperlink{circledata}{Circledata(name,点list,options)} \>円または正多角形を描く\\ +\hyperlink{crspline}{CRspline(name，list，options )} \>単独のCatmull-Rom スプライン曲線を描く\\ +\hyperlink{deqplot}{Deqplot(name,式,変数名,初期値,options])} \>微分方程式の解曲線を描く\\ +\hyperlink{dotfilldata}{Dotfilldata(name , 方向, PD , options)} \>領域に点を敷き詰める\\ +\hyperlink{drawsegmark}{Drawsegmark(name,list,options)} \>線分に印をつける\\ +\hyperlink{drwpt}{Drawpoint([点,options])} \>点を表示する\\ +\hyperlink{drwpt}{Drwpt([点,options])} \>点を表示する\\ +\hyperlink{ellipseplot}{Ellipseplot(name,list,str,options)} \>楕円を描く\\ +\hyperlink{enclosing}{Enclosing(name , [位置，方向，数式])} \>複数の曲線から閉曲線を描く\\ +\hyperlink{expr}{Expr(文字列)} \>\TeX 数式を書く\\ +\hyperlink{exprrot}{Exprrot(位置，向き，文字列)} \>傾いた\TeX 数式を書く\\ +\hyperlink{fourierseries}{Fourierseries(name,係数,周期,項数)} \>フーリエ級数を描く\\ +\hyperlink{framedata}{Framedata(name , list)} \>矩形を描く\\ +\hyperlink{hatchdata}{Hatchdata(name , 方向, PD , options)} \>領域に斜線を引く\\ +\hyperlink{htickmark}{Htickmark([横座標 , 方向 , 文字])} \>横軸に目盛りを描く\\ +\hyperlink{hyperbolaplot}{Hyperbolaplot(name,list,str,options)} \>双曲線を描く\\ +\hyperlink{implicitplot}{Implicitplot(name,str,,str,str,options)} \>陰関数のグラフを描く\\ +\hyperlink{invert}{Invert(PD)} \>プロットデータの点を逆順にする（reverseと同じ）\\ +\hyperlink{joincrvs}{Joincrvs（name, PDlist, options)} \>2つのプロットデータをつなげたデータを作る\\ +\hyperlink{letter}{Letter(「座標,位置,文字列]のlist」)} \>文字列を表示する\\ +\hyperlink{letterrot}{Letterrot(「座標,方向,移動量,文字列])} \>文字列を回転して表示する\\ +\hyperlink{lineplot}{Lineplot(name,2点のlist,options)} \>2点を結ぶ直線を描く\\ +\hyperlink{listplot}{Listplot(name,点のlist,options)} \>点を線分で結ぶ\\ +\hyperlink{mkbeziercrv}{Mkbeziercrv(name,list,options)} \>作図した点を使ってベジェ曲線を描く\\ +\hyperlink{mkbezierptcrv}{Mkbezierptcrv(list，options ) } \>制御点を自動配置してベジェ曲線を描く\\ +\hyperlink{mkcircles}{Mkcircles()} \>幾何円のすべてのPD を作成する\\ +\hyperlink{mksegments}{Mksegments()} \> 幾何線分のすべてのPD を作成する\\ +\hyperlink{ospline}{Ospline(list，list，options )} \>大島のスプライン曲線を描く\\ +\hyperlink{ovaldata}{Ovaldata(name, 点list,options)} \>角を丸くした矩形を描く\\ +\hyperlink{parabolaplot}{Parabolaplot(name,list,str,options)} \>放物線を描く\\ +\hyperlink{paramark}{Paramark(点list,options)} \>角の印を入れる\\ +\hyperlink{paramplot}{Paramplot(name,式,変数と定義域,options)} \>媒介変数で表された曲線を描く\\ +\hyperlink{polarplot}{Polarplot(name,式,変数と定義域,options)} \>極座標表示の曲線を描く\\\hyperlink{partcrv}{Partcrv(name,点1,点2,PD)} \>部分曲線を描く\\ +\hyperlink{periodfun}{Periodfun(定義式,周期,options)} \>周期関数のグラフを描く\\ +\hyperlink{plotdata}{Plotdata(name,式,変数と定義域,options)} \>関数のグラフを描く\\ +\hyperlink{pointdata}{Pointdata(name,点list,options)} \>点データを作る\\ +\hyperlink{polygonplot}{Polygonplot(name,点list,整数,options)} \>正多角形を描く\\ +\hyperlink{putintersect}{Putintersect(点名,PD1,PD2)} \>2曲線の交点を作る\\ +\hyperlink{putoncurve}{PutonCurve(name,PD,初期値)} \>曲線上に点を作る\\ +\hyperlink{putonline}{PutonLine(点名,座標1,座標2)} \>直線上に点を作る\\ +\hyperlink{putonseg}{PutonSeg(点名,座標1,座標2)} \>線分上に点を作る\\ +\hyperlink{putpoint}{Putpoint(点名,座標1,座標2)} \>点を作る\\ +\hyperlink{reflectdata}{Reflectdata(name,PD,点list,options)} \>プロットデータの鏡映を作成\\ +\hyperlink{reflectpoint}{Reflectpoint(点,対称点/対称軸)} \>点の鏡映を作成\\ +\hyperlink{rotatedata}{Rotatedata(name,PD,角度,中心,options)} \>プロットデータを回転する\\ +\hyperlink{rotatepoint}{Rotatepoint(点,角度,中心)} \>点の位置を回転する\\ +\hyperlink{rulerscale}{Rulerscale(点,list,list)} \>目盛を打つ\\ +\hyperlink{scaledata}{Scaledata(name,PD,x,y,中心,options)} \>点を拡大・縮小する\\ +\hyperlink{scalepoint}{Scalepoint(点,比率ベクトル,中心)} \>点の位置を拡大・縮小する\\ +\hyperlink{drawsegmark}{Segmark(name,list,options)} \>線分に印をつける\\ +\hyperlink{shade}{Shade（PDlist , 数)} \>閉曲線の内部にシェードをかける\\ +\hyperlink{tangentplot}{Tangentplot(name,PD, 位置)} \>曲線の接線を引く\\ +\hyperlink{translatedata}{Translatedata(name,PD,ベクトル,options)} \>プロットデータを平行移動する\\ +\hyperlink{translatepoint}{Translatepoint(点,ベクトル)} \>点を平行移動する\\ +\hyperlink{vtickmark}{Vtickmark([横座標 , 方向 , 文字])} \>縦軸に目盛りを描く\\ 【作表】\\ -\hyperlink{tabledata}{Tabledata("" , 縦横 ,除外 , options)} \>表の枠を作成する\\ -\hyperlink{tabledatalight}{Tabledatalight("" , 縦横 ,除外 , options)} \>幾何点を持たない表の枠を作成する\\ -\hyperlink{changetablestyle}{ChangeTablestyle(罫線リスト, options)} \>Table の罫線の描画オプションを変更する。\\ +\hyperlink{changetablestyle}{ChangeTablestyle(罫線list, options)} \>Table の罫線の描画オプションを変更する。\\ \hyperlink{findcell}{Findcell(列番号, 行番号)} \>セルの情報listを返す\\ \hyperlink{putcell}{Putcell (列番号, 行番号, 位置, 文字)} \>セルに文字列を入れる\\ -\hyperlink{putcol}{PutcoL (列番号, 位置，文字列リスト)} \>１列に順に文字を書き入れる\\ -\hyperlink{putcolexpr}{PutcoLexpr (列番号, 位置，文字列リスト)} \>１列に順に\TeX 書式の文字を書き入れる\\ -\hyperlink{putrow}{Putrow (行番号, 位置，文字列リスト)} \>１行に順に文字を書き入れる\\ -\hyperlink{putrowexpr}{Putrowexpr (行番号, 位置，文字列リスト)} \>１行に順に\TeX 書式の文字を書き入れる\\ -\hyperlink{settable}{Settable((左上) , 右下)} \>表データを書き出す\\ -\hyperlink{tgrid}{Tgird(セルラベル} \>セル（格子点）の座標を返す\\ +\hyperlink{putcol}{PutcoL (列番号, 位置，文字列list)} \>１列に順に文字を書き入れる\\ +\hyperlink{putcolexpr}{PutcoLexpr (列番号, 位置，文字列list)} \>１列に順に\TeX 書式の文字を書き入れる\\ +\hyperlink{putrow}{Putrow (行番号, 位置，文字列list)} \>１行に順に文字を書き入れる\\ +\hyperlink{putrowexpr}{Putrowexpr (行番号, 位置，文字列list)} \>１行に順に\TeX 書式の文字を書き入れる\\ +\hyperlink{tabledata}{Tabledata("" , 縦横 ,除外 , options)} \>表の枠を作成する\\ +\hyperlink{tabledatalight}{Tabledatalight("" , 縦横 ,除外 , options)} \>幾何点を持たない表の枠を作成する\\ +\hyperlink{tgrid}{Tgrid(セルラベル)} \>セル（格子点）の座標を返す\\ \hyperlink{tlistplot}{Tlistplot(セルラベル1,セルラベル2)} \>セルに斜線を引く\\ - \\ +\vspace{\baselineskip} 【値の取得と入出力】\\ -\hyperlink{crossprod}{Crossprod(リスト,リスト)} \>ベクトルの外積を計算する\\ -\hyperlink{dotprod}{Dotoprod(リスト,リスト)} \>ベクトルの内積を計算する\\ -\hyperlink{findarea}{Findarea(PD)} \>プロットデータで囲まれる部分の面積を求める\\ -\hyperlink{findlength}{Findlength(PD)} \>プロットデータで描く曲線の長さを求める\\ -\hyperlink{intersectcrvs}{Intersectcrvs(PD1,PD2,options)} \>プロットデータを交点のリストを返す\\ -\hyperlink{invert}{Invert(PD)} \>プロットデータの点を逆順にする（reverseと同じ）\\ -\hyperlink{meetcurve}{MeetCurve(PD,x,y)} \>曲線上の点を取得する\\ -\hyperlink{lcrd}{Lcrd()} \>幾何点，リスト点の論理座標を取得する\\ -\hyperlink{pcrd}{Pcrd()} \>幾何点，リスト点の物理（表示）座標を取得する\\ -\hyperlink{nearestpt}{Nearestpt(PD,PD)} \>２曲線間の最も近い点を取得する\\ -\hyperlink{nearestptcrv}{Nearestptcrv(点,PD)} \>点に一番近い曲線上の点を取得する\\ -\hyperlink{numptcrv}{Numptcrv(PD)} \>曲線PD の節点データの個数を取得する\\ -\hyperlink{paramoncurve}{ParamonCurve(PD,n,PtL)} \>PD上にある点P のデータを取得する\\ -\hyperlink{pointoncrv}{Pointoncrv(数,PD)} \>パラメータ値をもつプロットデータ上の点\\ -\hyperlink{ptcrv}{Ptcrv(n,PD)} \>曲線PD のn 番目の節点を取得する\\ -\hyperlink{ptstart}{Ptstart(PD)} \>プロットデータの始点を取得する\\ -\hyperlink{ptstart}{Ptend(PD)} \>プロットデータの終点を取得する\\ -\hyperlink{readoutdata}{ReadOutData(ファイル名)} \>外部データを読み込む\\ -\hyperlink{sprintf}{Sprintf(実数,長さ)} \>小数点以下の長さを固定した文字列に変換\\ -\hyperlink{writetosci}{WritetoSci(ファイル名,options)} \>すべてのソースを Scilab 用に書き出す\\ -\hyperlink{writetosci}{WritetoScibody(ファイル名)} \>ボディのソースを Scilab 用に書き出す\\ -\hyperlink{makeshell}{Makeshell(ファイル名)} \>Macのシェルスクリプトを書き出す\\ -\hyperlink{makeshell}{Makebat(ファイル名)} \>Windowsのバッチファイルを書き出す\\ -\hyperlink{textformat}{Textformat(数,桁数)} \>小数点以下の桁数を指定して数値を文字列化する\\ -\hyperlink{viewtex}{Viewtex()} \>\TeX のソースファイルを書き出す。引数なし\\ - \hyperlink{workprocess}{Workprocess()} \>作図の経過を取得する\\ - \\ +\hyperlink{crossprod}{Crossprod(list,list)} \>ベクトルの外積を計算する\\ +\hyperlink{derivative}{Derivative(関数式,変数,値)} \>関数の微分係数を求める\\ +\hyperlink{dotprod}{Dotprod(list,list)} \>ベクトルの内積を計算する\\ +\hyperlink{extractdata}{Extractdata(データ名,属性)} \>ReadOutDataで読み込んだデータに属性をつける。\\ +\hyperlink{findarea}{Findarea(PD)} \>プロットデータで囲まれる部分の面積を求める\\ +\hyperlink{findlength}{Findlength(PD)} \>プロットデータで描く曲線の長さを求める\\ +\hyperlink{integrate}{Integrate(関数式,変数,範囲,options)} \>関数の定積分値を求める\\ +\hyperlink{intersectcrvs}{Intersectcrvs(PD1,PD2)} \>プロットデータの交点の座標listを返す\\ +\hyperlink{intersectcrvspp}{IntersectcrvsPp(PD1,PD2)} \>プロットデータの交点のパラメータlistを返す\\ +\hyperlink{inversefun}{Inversefun(関数式,範囲,値)} \>逆関数値を求める\\ +%\hyperlink{makeshell}{Makeshell(ファイル名)} \>Macのシェルスクリプトを書き出す\\ +%\hyperlink{makeshell}{Makebat(ファイル名)} \>Windowsのバッチファイルを書き出す\\ +\hyperlink{nearestpt}{Nearestpt(PD,PD)} \>2曲線間の最も近い点を取得する\\ +\hyperlink{nearestptcrv}{Nearestptcrv(点,PD)} \>点に一番近い曲線上の点を取得する\\ +\hyperlink{numptcrv}{Numptcrv(PD)} \>曲線PD の節点データの個数を取得する\\ +\hyperlink{paramoncrv}{ParamonCurve(PD,n,PtL)} \>PD上にある点P のデータを取得する\\ +\hyperlink{pointoncrv}{Pointoncrv(数,PD)} \>パラメータ値をもつプロットデータ上の点\\ +\hyperlink{ptcrv}{Ptcrv(n,PD)} \>曲線PD のn 番目の節点を取得する\\ +\hyperlink{ptstart}{Ptstart(PD)} \>プロットデータの始点・終点を取得する\\ +\hyperlink{readoutdata}{ReadOutData(ファイル名)} \>外部データをPDとして読み込む\\ +\hyperlink{viewtex}{Viewtex()} \>\TeX のソースファイルを書き出す。引数なし\\ +\hyperlink{workprocess}{Workprocess()} \>作図の経過を取得する\\ +\hyperlink{writeoutdata}{WriteOutData()} \>PDデータを書き出す\\ +\vspace{\baselineskip} 【その他】\\ -\hyperlink{assign}{Assign(文字列)} \>文字列中のある文字を値で置き換える\\ -\hyperlink{bbdata}{BBdata(ファイル名)} \>画像のサイズを求める\\ -\hyperlink{changework}{Changework(パス)} \>作業ディレクトリを変更する\\ -\hyperlink{com0th}{Com0th(コマンド)} \>ScilabのOpenfileの前に置くコマンドを定義する\\ -\hyperlink{com1st}{Com1st(コマンド)} \>ScilabのOpenfileの前に置くコマンドを定義する\\ -\hyperlink{com2nd}{Com2nd(コマンド)} \>ScilabのOpenfileのあとに置くコマンドを定義する\\ -\hyperlink{com2ndpre}{Com2ndpre(コマンド)} \>ScilabのOpenfileのあとに置くコマンドを定義する\\ -\hyperlink{dashline}{Dashline(PD名)} \>プロットデータを破線で描く\\ -\hyperlink{dottedline}{Dottedline(PD名)} \>プロットデータを点線で描く\\ -\hyperlink{drwline}{Drwline(PD名)} \>プロットデータを実線で描く\\ +\hyperlink{assign}{Assign(文字列)} \>文字列中のある文字を値で置き換える\\ +\hyperlink{bbdata}{BBdata(ファイル名)} \>画像のサイズを求める\\ +%\hyperlink{com0th}{Com0th(コマンド)} \>RのOpenfileの前に置くコマンドを定義する\\ +%\hyperlink{com1st}{Com1st(コマンド)} \>RのOpenfileの前に置くコマンドを定義する\\ +%\hyperlink{com2nd}{Com2nd(コマンド)} \>RのOpenfileのあとに置くコマンドを定義する\\ +%\hyperlink{com2ndpre}{Com2ndpre(コマンド)} \>RのOpenfileのあとに置くコマンドを定義する\\ +\hyperlink{cindyname}{Cindyname()} \>作図しているファイル名を取得する。\\ +\hyperlink{colorcode}{Colorcode(文字1，文字2,color)} \>カラーコードの変換\\ +\hyperlink{dqq}{Dqq(文字列)} \>文字列の前後に\verb|"|をつける。\\ +\hyperlink{factorial}{Factorial(n)} \>nの階乗を計算する。\\ +\hyperlink{norm}{Norm(ベクトル)} \>ベクトルの大きさを計算する。\\ \hyperlink{figpdf}{Figpdf(option)} \>出力枠サイズのPDFを作る\\ -\hyperlink{helplist}{Helplist()} \>ヘルプデータを作る\\ -\hyperlink{help}{Help(str)} \>コマンドヘルプを表示する\\ -\hyperlink{helpkey}{Helpkey(str)} \>キーワードで関数を検索する\\ -\hyperlink{help}{Ketcindylogo()} \>\ketcindy のロゴを書き出す\\ +\hyperlink{help}{Help(str)} \>コマンドヘルプを表示する\\ +\hyperlink{helpkey}{Helpkey(str)} \>キーワードで関数を検索する\\ \hyperlink{indexall}{Indexall(str1,str2)} \>文字列 str1 から str2 を検索しその位置をすべて返す\\ -\hyperlink{op}{Op(n,list)} \> リストまたは文字列から要素を抜き出す\\ +\hyperlink{op}{Op(n,list)} \> listまたは文字列から要素を抜き出す\\ +\hyperlink{isptselected}{Isptselected(点名)} \>点が選択されていればtrueを返す\\ +\hyperlink{isptselected}{Ptselected(点名)} \>点が選択されていればtrueを返す\\ +\hyperlink{slider}{Slider()} \>スライダを作る\\ +\hyperlink{sprintf}{Sprintf(実数,長さ)} \>小数点以下の長さを固定した文字列に変換\\ +\hyperlink{strsplit}{Strsplit(文字列,文字)} \>文字列を分解する。\\ \hyperlink{texcom}{Texcom(コード)} \>\TeX のコードを書き出す\\ -\hyperlink{windispg}{Windispg()} \>定義されたプロットデータを描画面に描く\\ - \\ +\hyperlink{textformat}{Textformat(数,桁数)} \>小数点以下の桁数を指定して数値を文字列化する\\ +\hyperlink{windispg}{Windispg()} \>定義されたプロットデータを描画面に描く\\ +\vspace{\baselineskip} 【Ｒとの連携】\\ \hyperlink{boxplot}{Boxplot(名前,データ,位置,高さ,option)} \>箱ひげ図を描く\\ -\hyperlink{calcbyr}{CalcbyR(変数名,コマンド列，option)} \>Rのコマンドを実行して結果を返す\\ +\hyperlink{rfun}{Rfun(変数名,コマンド,引数, option)} \>Rの1つコマンドを実行して結果を返す\\ +\hyperlink{calcbyr}{CalcbyR(変数名,コマンド列, option)} \>Rのコマンド列を実行して結果を返す\\ \hyperlink{histplot}{Histplot(name,data)} \>ヒストグラムを描く\\ \hyperlink{plotdatar}{PlotdataR(name,式,変数)} \>Rの関数のグラフを描く\\ \hyperlink{plotdiscr}{PlotdiscR(name,式,変数)} \>離散型のグラフを描く\\ \hyperlink{readcsv}{Readcsv(name,filename,option)} \>csvファイルを読む\\ -\hyperlink{scatterplot}{Scatterplot(name,filename,option)} \>２次元データを読み込み，散布図を描く\\ - \\ +\hyperlink{scatterplot}{Scatterplot(name,filename,option)} \>2次元データを読み込み，散布図を描く\\ +\vspace{\baselineskip} 【Maximaとの連携】\\ -\hyperlink{calcbyM}{CalcbyM(name,リスト,option)} \>Maximaのスクリプトを実行する\\ -\hyperlink{example}{Example("Mxfun",文字)} \>Mxfunの使用例を表示\\ -\hyperlink{mxbatch}{Mxbatch(リスト)} \>Maximaの外部スクリプト用コマンドを作る\\ -\hyperlink{mxfun}{Mxfun(name,式,リスト,option)} \>Maximaの関数を実行する\\ +\hyperlink{calcbyM}{CalcbyM(name,list,option)} \>Maximaのスクリプトを実行する\\ +%\hyperlink{example}{Example("Mxfun",文字)} \>Mxfunの使用例を表示\\ +\hyperlink{mxbatch}{Mxbatch(list)} \>Maximaの外部スクリプト用コマンドを作る\\ +\hyperlink{mxfun}{Mxfun(name,式,list,option)} \>Maximaの関数を実行する\\ \hyperlink{mxtex}{Mxtex(num,式)} \>式をTeX書式にする\\ - \\ +\vspace{\baselineskip} 【Risa/Asirとの連携】\\ -\hyperlink{calcbyA}{CalcbyA(name,リスト,option)} \>Risa/Asirのスクリプトを実行する\\ -\hyperlink{asirfun}{Asirfun(name,式,リスト,option)} \>Risa/Asirの関数を実行する\\ - \\ +\hyperlink{asirfun}{Asirfun(name,式,list,option)} \>Risa/Asirの関数を実行する\\ +\hyperlink{calcbyA}{CalcbyA(name,list,option)} \>Risa/Asirのスクリプトを実行する\\ +\vspace{\baselineskip} 【FriCASとの連携】\\ -\hyperlink{calcbyF}{CalcbyF(name,リスト,option)} \>FriCASのスクリプトを実行する\\ -\hyperlink{frfun}{Frfun(name,式,リスト,option)} \>FriCASの関数を実行する\\ - \\ +\hyperlink{calcbyF}{CalcbyF(name,list,option)} \>FriCASのスクリプトを実行する\\ +\hyperlink{frfun}{Frfun(name,式,list,option)} \>FriCASの関数を実行する\\ +\vspace{\baselineskip} 【MeshLabとの連携】\\ \hyperlink{mkobjcmd}{Mkobjcmd(name,式,option)} \>厚みを持たない曲面のコマンドを作成\\ \hyperlink{mkobjcrvcmd}{Mkobjcrvcmd(name,PD,option)} \>空間曲線のコマンドを作成\\ @@ -6038,65 +7562,67 @@ arctan2(B.xy-A.xy) で角を取得することもできる。この場合の戻 \hyperlink{mkobjsymbcmd}{Mkobjsymbcmd(PD, 実数,実数,vec,vec)} \>文字等のコマンドを作成\\ \hyperlink{mkobjthickcmd}{Mkobjthickcmd(name,式)} \>厚みを持つ曲面のコマンドを作成\\ \hyperlink{mkviewobj}{Mkviewobj(name,PD, options)} \>obj ファイルを作成\\ - \\ +\vspace{\baselineskip} 【表計算ソフトとの連携】\\ -\hyperlink{tab2list}{Tab2list(str，option)} \>str の内容をリストに変換する\\ -\hyperlink{dispmat}{Dispmat(list)} \>リストの内容を行列型にコンソールに表示する\\ +\hyperlink{dispmat}{Dispmat(list)} \>listの内容を行列型にコンソールに表示する\\ +\hyperlink{tab2list}{Tab2list(str，option)} \>str の内容をlistに変換する\\ \hyperlink{writecsv}{Writecsv(namelist,data,option)} \>dataの内容をcsvファイルに書き出す\\ - \\ -%\hypertarget{functionlist3d}{} - -【KeTCindy3D 設定・定義】\\ -\hyperlink{ketinit3d}{Ketinit3d()} \>KeTCindy3Dの使用宣言\\ -\hyperlink{start3d}{Start3d()} \>3Dの開始\\ - \\ -【KeTCindy3D 描画】\\ -\hyperlink{bezier3d}{Bezier3d(name, リスト, リスト)} \>空間ベジェ曲線を描く\\ -\hyperlink{changstyle3d}{Changstyle3d(リスト, リスト)} \>3dプロットデータの属性を変更\\ -\hyperlink{concatobj}{Concatob(リスト,option)} \>いくつかのobjデータを結合\\ -\hyperlink{crvsfparadata}{Crvsfparadata(name,PD,PD2,式,opt,opt)} \>曲線の曲面による陰線処理\\ -\hyperlink{datalist}{Datalist2d()} \>画面に描かれているすべてのプロットデータ\\ -\hyperlink{datalist}{Datalist3d()} \>画面に描かれているすべてのプロットデータ\\ -\hyperlink{dist3d}{Dist3d(点名,点名)} \>空間の２点の距離\\ -\hyperlink{drawpoint3d}{Drawpoint3d(座標)} \>空間点を描く\\ -\hyperlink{embed}{Embed(name,PD,式)} \>埋め込みデータ作成\\ -\hyperlink{intersectcrvsf}{Intersectcrvsf(name,PD,式)} \>曲線と曲面の交点を求める\\ -\hyperlink{intersectsgpL}{IntersectsgpL(点名,線分,面,描画方法)} \>空間の直線と平面の交点\\ -\hyperlink{invparapt}{Invparapt(座標,PD)} \>描画面座標に対応する曲線上の座標\\ -\hyperlink{mkbezierptcrv3d}{Mkbezierptcrv3d(点リスト)} \>制御点を自動的にとる空間ベジェ曲線\\ -\hyperlink{nohiddenbyfaces}{Nohiddenbyfaces(name,PD,PD,opt1,opt2)} \>多面体と空間曲線を陰線処理\\ -\hyperlink{parapt}{Parapt(座標)} \>点の投影面での座標\\ -\hyperlink{partcrv3d}{Partcrv3d(name,始点,終点,PD)} \>曲線PDの部分曲線を作る\\ -\hyperlink{perpplane}{Perpplane(点名, 点, ベクトル,option)} \>点を通り垂直な平面上の基準点\\ -\hyperlink{perppt}{Perppt(点名,点,点リスト,option)} \>平面に下ろした垂線の足\\ -\hyperlink{phparadata}{Phparadata(name,name2,options)} \>多面体を陰線処理して描く\\ -\hyperlink{projcoordpara}{Projcoordpara()} \>投影座標を求める\\ -\hyperlink{putaxes3d}{Putaxes3d([x,y,z])} \>軸上に幾何点をとる\\ -\hyperlink{putonCurve3d}{PutonCurve3d(点名,PD)} \>空間曲線上に点をとる\\ -\hyperlink{putonseg3d}{Putonseg3d(点名,点1,点2)} \>線分上に点をとる\\ -\hyperlink{putpoint3d}{Putpoint3d(リスト,option)} \>空間点をとる\\ -\hyperlink{readobj}{Readobj(ファイル名)} \>objファイルを読み込む\\ -\hyperlink{reflectpoint3d}{Reflectpoint3d(点,リスト)} \>点を鏡映\\ -\hyperlink{rotate3pt}{Rotate3pt( 点,vec,角度,点)} \>空間点を回転\\ -\hyperlink{rotatedata3d}{Rotatedatat3d(name,PD,vec,角度,点)} \>プロットデータを回転\\ -\hyperlink{sf3data}{Sf3data(name, リスト,options)} \>陰線処理なしの空間曲面を描く\\ -\hyperlink{sfbdparadata}{Sfbdparadata(name, 式,options)} \>曲面を陰線処理して描く\\ -\hyperlink{skeletondatacindy}{Skeletondatacindy(name,PD,PD,options)} \>スケルトン処理のデータ作成\\ -\hyperlink{skeletonparadata}{Skeletonparadata(name,PD,PD,options)} \>スケルトン処理のデータ作成\\ -\hyperlink{spacecurve}{Spacecurve(name, 式, 定義域,options)} \>空間曲線のデータ作成\\ -\hyperlink{spaceline}{Spaceline(リスト)} \>空間の折線データ作成\\ -\hyperlink{translatedata3d}{Translatedata3d(name,PD, 平行移動量)} \>空間プロットデータを平行移動\\ -\hyperlink{translatept3d}{Translatept3d(座標,平行移動量)} \>空間点を平行移動\\ -\hyperlink{vertexedgeface}{VertexEdgeFace(面データ,option)} \>頂点と面から辺を求め，辺を描く\\ -\hyperlink{wireparadata}{Wireparadata(name,PD,式,int,int,opt,opt)} \>曲面のワイヤフレームを陰線処理\\ -\hyperlink{xyzax3data}{Xyzax3data(name,文字,文字,文字,options)} \>座標軸の表示\\ -\hyperlink{xyzcoord}{Xyzcoord(P.x,P.y,Pz.y)} \>主副画面で決まる点の座標\\ - \\ -【KeTCindymv】\\ -\hyperlink{moviedata}{Moviedata(str1,str2,options)} \>動画データの作成\\ -\hyperlink{setpara}{Setpata(str)} \>パラパラ動画のタイトル指定\\ +\vspace{\baselineskip} +【アニメーション】\\ +%\hyperlink{moviedata}{Moviedata(str1,str2,options)} \>動画データの作成\\ +\hyperlink{setpara}{Setpata(str)} \>パラパラ動画のタイトル指定\\ +【スライド】\\ +\hyperlink{settitle}{Settitle(タイトルlist,options)} \>スライドのタイトル設定\\ +【KeTCindy3D 設定・定義】\\ +\hyperlink{ketinit3d}{Ketinit3d()} \>KeTCindy3Dの使用宣言\\ +\hyperlink{isangle}{Isangle} \>角度スライダが選択されているか\\ +\hyperlink{start3d}{Start3d()} \>3Dの開始\\ +\hyperlink{startsurf}{Startsurf} \>曲面描画の初期化\\ +\vspace{\baselineskip} +【KeTCindy3D 描画】\\ +\hyperlink{bezier3d}{Bezier3d(name, list, list)} \>空間ベジェ曲線を描く\\ +\hyperlink{changestyle3d}{Changestyle3d(list, list)} \>3dプロットデータの属性を変更\\ +\hyperlink{concatobj}{Concatobj(list,option)} \>いくつかのobjデータを結合\\ +\hyperlink{crvsfparadata}{Crvsfparadata(name,PD,PD2,式,opt,opt)} \>曲線の曲面による陰線処理\\ +\hyperlink{datalist}{Datalist2d()} \>画面に描かれているすべてのプロットデータ\\ +\hyperlink{datalist}{Datalist3d()} \>画面に描かれているすべてのプロットデータ\\ +\hyperlink{dist3d}{Dist3d(点名,点名)} \>空間の2点の距離\\ +\hyperlink{drawpoint3d}{Drawpoint3d(座標)} \>空間点を描く\\ +\hyperlink{embed}{Embed(name,PD,式)} \>埋め込みデータ作成\\ +\hyperlink{execcmdc}{ExeccmdC(name,options1,options2)} \>C言語で命令実行\\ +\hyperlink{intersectcrvsf}{Intersectcrvsf(name,PD,式)} \>曲線と曲面の交点を求める\\ +\hyperlink{intersectsgpL}{IntersectsgpL(点名,線分,面,描画方法)} \>空間の直線と平面の交点\\ +\hyperlink{invparapt}{Invparapt(座標,PD)} \>描画面座標に対応する曲線上の座標\\ +\hyperlink{mkbezierptcrv3d}{Mkbezierptcrv3d(点list)} \>制御点を自動的にとる空間ベジェ曲線\\ +\hyperlink{nohiddenbyfaces}{Nohiddenbyfaces(name,PD,PD,opt1,opt2)} \>多面体と空間曲線を陰線処理\\ +\hyperlink{parapt}{Parapt(座標)} \>点の投影面での座標\\ +\hyperlink{partcrv3d}{Partcrv3d(name,始点,終点,PD)} \>曲線PDの部分曲線を作る\\ +\hyperlink{perpplane}{Perpplane(点名, 点, ベクトル,option)} \>点を通り垂直な平面上の基準点\\ +\hyperlink{perppt}{Perppt(点名,点,点list,option)} \>平面に下ろした垂線の足\\ +\hyperlink{phparadata}{Phparadata(name,name2,options)} \>多面体を陰線処理して描く\\ +\hyperlink{pointdata3d}{Pointdata3d(名前,点list,options)} \>空間点のデータを作成する\\ +\hyperlink{putaxes3d}{Putaxes3d([x,y,z])} \>軸上に幾何点をとる\\ +\hyperlink{putonCurve3d}{PutonCurve3d(点名,PD)} \>空間曲線上に点をとる\\ +\hyperlink{putonseg3d}{Putonseg3d(点名,点1,点2)} \>線分上に点をとる\\ +\hyperlink{putpoint3d}{Putpoint3d(list,option)} \>空間点をとる\\ +\hyperlink{readobj}{Readobj(ファイル名)} \>objファイルを読み込む\\ +\hyperlink{reflectdata3d}{Reflectdata3d(点,PDlist,list,options)} \>PDを鏡映\\ +\hyperlink{reflectpoint3d}{Reflectpoint3d(点,list)} \>点を鏡映\\ +\hyperlink{rotatedata3d}{Rotatedata3d(name,PD,vec,角度,点)} \>プロットデータを回転\\ +\hyperlink{rotatepoint3d}{Rotatepoint(点 , vec , 角度 , 点)} \>点を回転\\ +\hyperlink{scaledata3d}{Scaledata3d(点, vec, 中心)} \>プロットデータを拡大/縮小\\ +\hyperlink{scalepoint3d}{Scalepoint3d(点, vec, 中心)} \>点の位置を拡大/縮小\\ +\hyperlink{sf3data}{Sf3data(name, list,options)} \>陰線処理なしの空間曲面を描く\\ +\hyperlink{sfbdparadata}{Sfbdparadata(name, 式,options)} \>曲面を陰線処理して描く\\ +\hyperlink{skeletonparadata}{Skeletonparadata(name,PD,PD,options)} \>スケルトン処理のデータ作成\\ +\hyperlink{spacecurve}{Spacecurve(name, 式, 定義域,options)} \>空間曲線のデータ作成\\ +\hyperlink{spaceline}{Spaceline(name,list)} \>空間の折線データ作成\\ +\hyperlink{translatedata3d}{Translatedata3d(name,PD, 平行移動量)} \>空間プロットデータを平行移動\\ +\hyperlink{translatepoint3d}{Translatepoint3d(座標,平行移動量)} \>空間点を平行移動\\ +\hyperlink{vertexedgeface}{VertexEdgeFace(面データ,option)} \>頂点と面から辺を求め，辺を描く\\ +\hyperlink{wireparadata}{Wireparadata(name,PD,式,int,int,opt,opt)} \>曲面のワイヤフレームを陰線処理\\ +\hyperlink{xyzax3data}{Xyzax3data(name,文字,文字,文字,options)} \>座標軸の表示\\ +\hyperlink{xyzcoord}{Xyzcoord(P.x,P.y,Pz.y)} \>主副画面で決まる点の座標 \end{tabbing} - -%3D第３節 \end{document} diff --git a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/KeTCindyguideE.tex b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/KeTCindyguideE.tex new file mode 100644 index 00000000000..8ba5ed7707b --- /dev/null +++ b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/KeTCindyguideE.tex @@ -0,0 +1,1100 @@ +\documentclass[papersize,a4paper,12pt]{article} +\usepackage{ketpic,ketlayer} +\usepackage{amsmath,amssymb} +% \usepackage{amsmath,newtxmath} +%\usepackage[dvipdfmx]{graphicx,color} +\usepackage{graphicx,color} +\usepackage{wrapfig} +%\usepackage[dvipdfmx,bookmarks=false,colorlinks=true,linkcolor=blue]{hyperref} +\usepackage[bookmarks=false,colorlinks=true,linkcolor=blue]{hyperref} +\setmargin{20}{20}{15}{25} +\usepackage{setspace} +\usepackage{comment} +\usepackage{bm,enumerate} +\usepackage{pict2e} + +%\newcommand{\cmd}[1]{ +%\begin{center}{\bf\large #1}\end{center} +%\hypertarget{#1}{} +%} + +\newenvironment{cmd}[2]{ +\hypertarget{#2}{} +\begin{center}{\bf\large #1}\end{center} +\begin{description} +}{ +\end{description} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$Command List}\end{flushright} +} + +% item command for this documentation +\newcommand{\itemket}[1]{ +\item[\Ltab{27mm}{#1}] +} + + +\begin{document} +\title{Guide to \ketcindy} +\author{\ketcindy\ Project Team} +\maketitle + +\begin{center} - ver.3.2 -\end{center} + +\hypertarget{index}{} +\tableofcontents + +\newpage + +\section{About \ketcindy} + +\subsection{Overview} + +\ketcindy\ is a library of Cindyscript +which is a programming language of Cinderella. +It converts the data computed +for generating dynamic graphics on Cinderella +into \TeX\ graphical codes. +Synchronized use of +interactive graphics capabilities of Cinderella +and well-structured programming capabilities of Cindyscript +enables ordinary \TeX\ users to efficiently embed +high-quality graphics into \TeX\ documents. +Moreover, the collaborative use of \ketcindy\ +and other software such as R, Maxima and C +has been enabled. + +\begin{center} +\input{Fig/concept} +\end{center} + +Firstly, dynamic figure is generated on Cinderella. +Secondly, \ketcindy\ generates +a source file of R and makes R execute it +for the generation of \TeX\ graphical codes. +Thirdly, those codes are formatted into +\TeX\ file which is input in the targetting \TeX\ document +via the command \verb|\input|. +Finally, usual compilation procedure of \TeX\ results in +the generation of final PDF output +including the corresponding figure. +A batch file \verb|kc.bat| for Windows +or a shell file \verb|kc.sh| for Mac or Linux +is generated via \ketcindy\ +in order to batch-process all the steps +from the second to the last. +Also by using these files, +collaboration of Cinderella and other software +as shown in the schematic diagram above +is processed. + +Summarizingly, specific steps to generate a \TeX\ figure +are listed as follows. + +\begin{enumerate}[(1)] +\item +Generate the needed geometric elements +on the Euclidean view of Cinderella +using its drawing tools. +These elements can be moved interactively. + +\hspace{30mm}\includegraphics[bb=0.00 0.00 408.02 347.02,width=6cm]{Fig/incenter01.pdf} + +\item +Input the \ketcindy\ codes into Cindyscript editor +to specify the graphical elements to be displayed +in \TeX\ final output. +Also \ketcindy\ codes are used +to generate supplementary graphical elements +and handle them. + +\hspace{10mm}\includegraphics[bb=0.00 0.00 811.04 257.01,width=12cm]{Fig/incenter02E.pdf} + +In this stage, the programming capabilities +inherently implemented to Cindyscript can be used simultaneously. +Execute the whole program by clicking the "Run" button. +For more details, see section 3. + +\item +Click the button named \verb|Figures| in Euclidean view +to automatically generate the following files +in the folder named "fig". +Here, "incenter" is the name specified +via the command \verb|Setfiles("incenter")| +in step (2). + +\begin{tabbing} +12\=1234567897890123456\=\kill + + \> \verb|kc|.sh or \verb|kc.bat| \> shell script file(Mac) or batch file(Windows) \\ + \> \verb|incenter.r| \> \\ + \> \verb|incenter.tex| \> \TeX\ file composed of graphical codes\\ + \> \verb|incentermain.aux| \> \\ + \> \verb|incentermain.log| \> \\ + \> \verb|incentermain.pdf| \> PDF file to display the resulting graphical image\\ + \> \verb|incentermain.tex| \> \TeX\ file temporarily used to generate +the file \verb|incentermain.pdf| +\end{tabbing} + +Subsequently, the file \verb|incentermain.pdf| +is automatically displayed as shown below. + +\hspace{30mm}\includegraphics[bb=0.00 0.00 348.02 284.51,width=6cm]{Fig/incenter03.pdf} + +We can manipulate this final output +by modifying the inputs in steps (1) and (2) +before processing the step (3) again. + +\vspace{\baselineskip} +\item +Using \ketpic\ package of \TeX , +\verb|incenter.tex| can be read +into the targetting \TeX\ document +via the command +\begin{center} +\verb|\input{incenter}| +\end{center} +Then the same figure is embedded in the targetting PDF output. + +\end{enumerate} + + +\newpage + +\subsection{Geometric Figures} + +Producing geometric figures in the plane is easy. Moreover, we can add hatchings in some areas, which is better than shading +for monochrome printing. +The following are the main parts of the script. + +\begin{verbatim} + Listplot([A,B,C,A]); + Circledata([D,E]); + Bowdata([B,A],[1,0.5,"Expr=c","da"]); + Bowdata([C,B],[1,0.5,"Expr=a","da"]); + Bowdata([A,C],[1,0.5,"Expr=b","da"]); + Hatchdata("2",["oi"],[["crDE"],["sgABCA"]],["dr,0.7",""]); + Pointdata("I",D,["size=4"]); + Letter([A,"sw","A",B,"ne","B",C,"se","C",D,"se","I"]); +\end{verbatim} + +\begin{center} +\includegraphics[bb=0.00 0.00 416.00 347.00,height=42mm]{Fig/hatch.pdf} +\hspace{2mm} +\input{Fig/s106bowhatch.tex} +\end{center} + + +\subsection{Graphs of Functions} +\ketcindy\ can produce graphs of functions with +\begin{verbatim} + Plotdata("1","x^2","x"); +\end{verbatim} +or parametrically with +\begin{verbatim} + Paramplot("1","[2*cos(t),sin(t)]", "t=[0,2*pi]"); +\end{verbatim} +\noindent Here we give an example of the solution curve of a differential equation. The script is: +%\verb| // data are assigned to the variable de1.|\\ +%\verb| // [0,XMAX] is the range of t.|\\ +\begin{verbatim} + Deqplot("1","y``=-L.x*y`-G.x*y","t=[0,XMAX]",0,[C.y,0]); + // the equation is y''=-ay'-by (a=L.x, b=G.x). + // C.y,0 are initial values of y and y' at t=0. + Expr(M,"e","\displaystyle\frac{d^2 x}{dt^2}+" + +"+L.x+"\frac{dx}{dt}+"+G.x+"x=0"); +\end{verbatim} + +Note that points C, G, L on segments AB, EF, HK are movable, and +are used to decide the coefficients and the initial value as you can see in the above scripts. +\vspace{3mm} + +\begin{center} +\includegraphics[bb=0.00 0.00 385.00 398.00,height=60mm]{Fig/diffeq1.pdf} +\hspace{5mm} +\input{Fig/s210diffeq1.tex} + +\end{center} + +%\putnotes{35}{53}{\input{fig/s305incanddec.tex}} +%\putnotes{35}{110}{Figure \thefigno\ \ Table}\addtocounter{figno}{1}% +%\putnotes{97}{65}{\input{fig/kumamonthin.tex}} +%\putnotes{97}{59}{% +%\includegraphics[bb=0.00 0.00 183.63 142.07]{fig/figkumamon.pdf}} +%\putnotene{100}{72}{\input{fig/kumamoto.tex}} +%\putnotes{97}{110}{Figure \thefigno\ \ B\'ezier Curve}\addtocounter{figno}{1}% + +\subsection{Drawing Tables} +Writing the code for tables to be inserted into the \TeX\ documents is sometimes troublesome. +However, it is not a hard job for \ketcindy\ (see the output in Figure. + +\begin{verbatim} + xLst=apply(1..7,15); + yLst=[10,10,10,10,80]; + rmvL=apply(1..6,"c"+text(#)+"r4r5"); + rmvL=concat(rmvL,["r2c1c2","r3c1c2"]); + Tabledata("",xLst,yLst,rmvL); + Tlistplot(["c1r1","c2r4"]); + Tlistplot(["c2r1","c1r4"]); + Putrowexpr(1,"c", + ["x","0","\cdots","e","\cdots","e\sqrt{e}","\cdots"]); + Putrowexpr(2,"c",["y`","","+","0","-","-","-"]); + Putrowexpr(3,"c",["y``","","-","-","-","0","+"]); + Putrowexpr(4,"c",["y","","","10/e","","15/e\sqrt{e}",""]); + Putcell("c0r4","c7r5","c","\input{fig/graph}"); +\end{verbatim} + +\vspace{2mm} + +\begin{center} +\input{Fig/s305incanddec.tex} +\end{center} + + +\newpage + +\subsection{Plotting data} +Here we call the data computed +to generate the graphs of functions and geometric elements +"Plotting data" which is abbreviated as PD. +The PD to draw segment is the list of coordinates +of its two endpoints. +For example, +when the coordinates of the points A and B +are (1, 1) and (3, 2) respectively, +PD of the segment AB named \verb|Listplot ([A,B])| +is stored in the form \verb|[[1,1],[3,2]]|. +Also the PD to draw a curve is the collection of +those for drawing small segments +which connect contiguous dividing points of the curve. +PD are automatically given names via \ketcindy\ +following the rules below. + +\begin{itemize} +\item +The beginning part of the PD's name +depends on the kind of the corresponding graphical element. +For instance, +\verb|sg| is associated to segments and +\verb|cr| is associated to circles. + +\item +When some extra name is specified +as the first argument in the definition of PD, +it is added to the beginning part given above. +For instance, the PD defined below +is given the name \verb|sg1|. +\begin{center} +\verb|Listplot("1",[[0,0],[1,2]]);| +\end{center} + +\item +When the extra name is not needed, +the names of the points are added +to the beginning part given above. +For instance, the PD defined below +is given the name \verb|sgABC|. +\begin{center} +\verb|Listplot([A,B,C]);| +\end{center} + +\end{itemize} + +\noindent +Once PD are generated, +their names are displayed on the console view of Cinderella. +For instance, when the PD named \verb|sgABCA| is generated, +the corresponding message is displayed as shown below. + +\begin{center} +\includegraphics[bb=0.00 0.00 298.02 115.01,width=6cm]{Fig/pdtoconsole.pdf} +\end{center} +Also the content of PD is displayed +via the function \verb|println()| of Cindyscript. +For instance, inputting the command +\verb|println(sgABCA)| makes the following list displayed. +\begin{center} +\verb| [[1,3],[-1,0],[3,0],[1,3]] | +\end{center} +This list is composed of the coordinates of the points A, B, and C. + +These names of PD are used +when the corresponding PD need to be transformed. +For instance, +PD to draw the parallel transport of the segment AB +is generated via the \ketcindy\ command +\begin{center} +\verb|Translatedata("1","sgAB",[2,3]);| +\end{center} + +PD can be generated also +by using the programming capability of Cindyscript +which can be subsequently used in \ketcindy . +For more details, +see the example of \verb|Listplot()| +in the command reference. +Inclusion of too much elements into a single PD +may cause some error. +To prevent such error, +PD should be divided into several PD +each of which is composed of 200 elements or so. + + +\newpage + +\section{Cindyscript} + +\subsection{Cindyscript editor} + +Choose "Cindyscript" in the "Scripting" menu +or push keybuttons Ctrl+9 (Windows) / Command+9 (Mac), +then Cindyscript editor opens as shown below. + +\begin{layer}{150}{0} +\putnotese{7}{15}{\includegraphics[bb=0.00 0.00 703.04 425.02,width=14cm]{Fig/slotE.pdf}} +\arrowlineseg[16]{30}{20}{10}{90} +\putnotese{25}{5}{Slots} +\arrowlineseg[16]{50}{20}{10}{100} +\putnotese{42}{5}{Page name} +\arrowlineseg[16]{90}{20}{10}{110} +\putnotese{80}{5}{Font size} +%\arrowlineseg[16]{107}{20}{15}{140} +%\putnotese{80}{5}{描画面を前面に} +\arrowlineseg[16]{135}{20}{10}{110} +\putnotese{125}{5}{Run} +\arrowlineseg[16]{142}{20}{10}{100} +\putnotese{135}{5}{Help} +\putnotese{100}{35}{Text field} +\putnotese{100}{80}{Console} +\end{layer} + +\vspace{105mm} + +Commands can be input into preferred "slot". +Specific timing for execution of commands +is assigned to each slot. +The slot for current work can be chosen +only by clicking the corresponding tab in the menu. +Users can add extra pages to each slot. +For instance, +when some initialization other than +those included in \verb|KETlib| is needed, +clicking the folder icon of "Initialization" makes a new page open +in which extra commands can be input. +The name of each page can be given +by directly inputting it into the "Page name" column. +The font size of the scripts can be tuned +by changing the number in the "Font size" column. +Frequently used slots are listed below. + +\begin{itemize} + +\item +Draw + +The commnds in this slot are executed +when some change, like movement of point, +occurs in the Euclidean view. +In \verb|templatebasic1.cdy|, +the protoype page named \verb|figure| +including the \ketcindy\ commnads +like \verb|Ketinit();| and \verb|Windispg();| +which are unconditionally necessary +has been prepared. +The \ketcindy\ commands for drawing +should be input into this slot. + +\item +Initialization + +The definitions of functions +and the initial values of variables +are input here. +The commands in this slot are exected +only once just after the "Run" button is clicked. +Thus, the initial data in this slot is changed +when some modifications are made in other slots. +In \verb|templatebasic1.cdy|, +the protoype page named \verb|KETlib| +including the default setting of \ketcindy\ +has been prepared. + +\item +Key Typed + +The commnds in this slot are executed +when some key is pushed. + +\end{itemize} + +Clicking "Run" button or pushing the keybuttons Shift+Enter +makes the whole program be executed. +The results derived from executing the function \verb|print()| +and error messages are displayed on the console view +which is put at the bottom part of Cindyscript editor. +Each error and its location +is displayed together with the message +"WARNING" or "syntax error". +The outputs displayed on the console +can be copied to other usual text editors. + +Click the "Help" button, +then reference manual of Cinderella opens +as shown below. \\ + +\includegraphics[bb=0.00 0.00 712.04 577.03,width=14cm]{Fig/CindyhelpE.pdf} + + +\subsection{Input} + +The attribute of each input into Cindyscript +is specified via the color of the corresponding letters +as listed below. + +\begin{itemize} +\item +The functions which are inherently implemented to Cinderella +are displayed via blue color. +\item +The functions which are defined by user, +including those of \ketcindy , +are displayed via purple color. +\item +The functions which are not yet defined +are displayed via red color. +\item +Strings are displayed via green color. +\end{itemize} +As in the console view, +copying and pasting to the other usual editing software +via pushing the keybuttons Ctrl+C and Ctrl+V +is accessible. +Cutting and pasting via Ctrl+X and Ctrl+V +is also possible. +Also as in the other editing software, +preferred strings can be specified +via dragging mouse +or pushing the keybutton Shift and moving the sursor. +Serching for words via pushing Ctrl+F +has not been enabled. + +The fundamental rule of describing scripts on Cindyscript editor +are listed below. +\begin{itemize} +\item +Upper- and lowercase letters are distinguished. +Using lowercase letters is preferable. +\item +As in \TeX , +several blanks are regarded as a single blank. +\item +A semicolon should be located at the end of each row. +Starting a new paragraph +does not result in the ending of commnds. +\end{itemize} +Particularly, in case of \ketcindy , +the input of commands are controlled +by the following rules. +\begin{itemize} +\item +The names of global variables +begin with uppercase letters. +\item +The names of local variables +begin with lowercase letters. +Local variables are declared at the beginning part +of the definitions of functions +along with the Cinderella command \verb|regional()|. +\item +The names of functions +begin with uppercase letters. +\end{itemize} + + +\subsection{Variables and constants} + +The declaration of the attribute of each variable +is not needed in Cindyscript +since it is automatically decided +according to the input. +Moreover, +the different kind of value +can be input without any declaration. \\ + +\noindent +{\bf Example} + +\verb| a=10;| + +\verb| b=2;| + +\verb| c=a+sqrt(b);| + +\verb| a="the square root of"| + +\verb| println("The sum of"+a+b+''and 10 is''+c);|\\ + +In this example, +the attribute of variable \verb|a| was firstly integer, +and then changed to string at the fourth row. + +The strings should be input with double quotation marks. +The mathematical operations +which involve several kind of variables +must be taken much care. +Exceptionally, +connecting string and number with \verb|+| +results in the generation of one single string. + +The variable \verb|pi| is reserved in Cindyscript +as the ratio of the circumference of a circle to its diameter. +Also the variable \verb|i| is reserved +as the imaginary unit. +When \verb|i| is used as variable once, +it is changed to the imaginary unit via the command +\begin{center} +\verb|i=complex(0,1);| +\end{center} + +There are also some reserved variables in \ketcindy . +Among them, the following ones can be changed by users. +\begin{tabbing} +12\=3456789012345\=678989012345678901234567890123\=\kill +\>\verb|Fhead| \>the beginning part of the file name +which can be set by \verb|Setfiles()|\\ +\>\verb|Texparent| \>the name of parent file +which can be set by \verb|Setparent()|\\ +\>\verb|Dirhead| \>the beginning part of the path\\ +\>\verb|Dirlib| \>the path to the library ketlib\\ +\>\verb|Dirbin| \>the path to ketbin\\ +\>\verb|Dirwork| \>the path to the working directory +which can be set by \verb|Changework()|\\ +\>\verb|Shellfile| \>the name of shell file +\end{tabbing} +Contrarily, the reserved variables listed below are the global variables +usend in the library of \ketcindy , whence cannot be changed +by users. + +\vspace{\baselineskip} +\noindent +ADDAXES, ArrowlineNumber, ArrowheadNumber, BezierNumber, COM0thlist, COM1stlist, COM2ndlist, Dq, FUNLIST, Fnamesc ，Fnamescibody，Fnameout，Fnametex, GDATALIST, GLIST, GCLIST, GOUTLIST, KCOLOR, KETPICCOUNT,KETPICLAYER, LETTERlist, LFmark, MilliIn, PenThick,PenThickInit, POUTLIST, SCALEX, SCALEY, SCIRELIST, SCIWRLIST, TenSize, TenSizeInit, ULEN, XMAX, XMIN, YaSize, YaThick, YMAX, YMIN, VLIST + +\vspace{\baselineskip} + +A list can be defined by putting its elements in a square bracket +with commas separating each other. +The attribute of each element does not matter. +The $n$-th element can be referred by using an underbar. +For instance, the commands + +\begin{verbatim} + list=[1,2,3,4,5]; + list_2="a"; +\end{verbatim} +make the second element be substituted by the letter \verb|"a"|. + + +\subsection{Frequently used commands} + +\noindent +{\bf Displaying the computed output} + +\noindent +The following commands +make the current value of the variable +on the console view. + +\begin{tabbing} +12345\=6789012345678989012345678901234567890\=123\=\kill +\>\verb|print(the name of variable);| \> without a line break\\ +\>\verb|println(the name of variable);| \> with a line break\\ +\end{tabbing} + +\noindent +{\bf Conditional branching} + +\noindent +The commnad \verb|if(A,B,C)| executes \verb|B| if \verb|A| is true +and \verb|C| otherwise. +The followings are frequently used. +Nested conditions can be interpreted. + +\begin{tabbing} +12345\=67890123456789890\=12345678901234567890123\=\kill +\>\verb|if(a>b,...);|\\ +\>\verb|if(a<b,...);|\\ +\>\verb|if(a>=b,...);| \> $a\geqq b$\\ +\>\verb|if(a<=b,...);| \> $a\leqq b$\\ +\>\verb|if(a=b,...);|\\ +\>\verb|if(a!=b,...);| \> $a\neq b$\\ +\end{tabbing} + +\noindent +{\bf Loop program} + +\noindent +The commnad \verb|for(n,operation)| executes the operation +$n$ times. If the counter should be specified, +modify the command as \verb|for(n,s,operation)|. +where the value of $s$ is successively changed. +Loop program with respect to some list instead of counter +is also possible via the command as \verb|forall(list,operation)|. +For example, the commands + +\begin{verbatim} + sglist=[[A,B],[C,D],[E,F]]; + forall(sglist,Listplot(#)); +\end{verbatim} +have the same output as +\begin{verbatim} + Listplot([A,B]); + Listplot([C,D]); + Listplot([E,F]); +\end{verbatim} + +\noindent +{\bf User's definition of functions} + +\noindent +The format of definition is \verb|function name(argument):=(operation)|. +For example, if we define the function \verb|sign(n)| by +\begin{verbatim} + sign(n):=( + if(n>0,print("positive"),print("0 or negative")); + ); +\end{verbatim} +it can be used as +\begin{verbatim} + n=3; + println(sign(n)); +\end{verbatim} + +\mbox{} + +\noindent +{\bf Reference to geometric elements} + +\noindent +The position of a point can be specified +with both its name and the list of its $x,y$-coordinates. +Thus, both of the following formats are allowed. +\begin{verbatim} + Listplot("1",[[1,1],[4,5]]); + Listplot("1",[A,B]); +\end{verbatim} +Also we can get the coordinate of a point explicitly +via the commands +like \verb|A.xy|, \verb|A.x|, and \verb|A.y|. + +\mbox{} + +\noindent +{\bf List processing} + +\noindent +The list of integers between $a$ and $b$ +is generated via the command \verb|a..b|. +For instance, the synchronized use with the command \verb|apply| +as below gives the shape of pentagram. +\begin{verbatim} + r=2; + pt=apply(0..5,r*[cos(pi/2+#*4*pi/5),sin(pi/2+#*4*pi/5)]); + repeat(5,s,Listplot(text(s),[pt_s,pt_(s+1)])); +\end{verbatim} +Here the Cindyscript command \verb|text| +is used to convert the number into string. + + + +% -------------- Calling other softwares -------------- + +\newpage + +\section{Collaboration with other softwares} + +\subsection{Overview} + +\ketcindy\ has functionalies to call other softwares such as Maxima, Risa/Asir, R and C. +Here, we introduce how to call Maxima.\vspace{1mm} + +The steps are as follows.\vspace{-2mm} + +\begin{enumerate} +\item Generate the shell file to call a CAS.\vspace{-2mm} +\item Execute the file.\vspace{-2mm} +\item Return the result as text.\vspace{-2mm} +\item Use the result in \ketcindy .\vspace{-2mm} +\item Produce the PDF file.\vspace{-2mm} +\end{enumerate} + +And the flowchart is as follows: +\begin{center} +{\scalebox{0.9}{\input{Fig/calling.tex}}} + +\end{center} + +When interfacing with Maxima, commands \texttt{Mxfun}, \texttt{CalcbyM} and \texttt{Mxtex} are all we need to complete the task. \texttt{Mxfun} and \texttt{CalcbyM} are for calling single command and multi commands of Maxima respectively. \texttt{Mxtex} is used for code conversion to \LaTeX. The output of Maxima is returned to \ketcindy\ as a string or a list of strings for further processing. + +The options of these commands are:\\ +\hspace*{10mm}\Ltab{25mm}{{\tt "m/r"}}To decide whether the result file will be made again or not. \\ +\hspace*{10mm}\Ltab{25mm}{}If these options are not given, \ketcindy\ decides automatically.\\ +\hspace*{10mm}\Ltab{25mm}{{\tt "Disp=y/n"}}To decide whether the result will be displayed in the console or not. \\ +\hspace*{10mm}\Ltab{25mm}{}It is only availabe for \texttt{Mxfun} and \texttt{Mxtex}. +The default is "y". + + +\subsection{Commands related to Maxima} + +\subsubsection*{Mxfun} + +The arguments are name of variable in \ketcindy, name of a function of Maxima, and a list of arguments of the function.\\ +\hspace*{10mm}\verb|Mxfun("1","diff",["sin(x)","x"]);| // The return is "cos(x)", assgined to mx1.\\ +The above is equivallent to\\ +\hspace*{10mm}\verb|Mxfun("1","diff(sin(x),x)",[]);| + + +\subsubsection*{Mxtex} + +The arguments are name of variable in \ketcindy, an expression in Maxima format.\\ +\hspace*{10mm}\verb|Mxtex("1",mx1);| // The return is \verb|"\cos x"|, assgined to tx1.\\ +\hspace*{10mm}\verb|Expr([0,1],"e",tx1]);| + +\begin{center} +\input{Fig/maxima1.tex} +\end{center} + +\subsubsection*{CalcbyM} + +The arguments are name of variable in \ketcindy, a list of commands and the arguments of Maxima.\\ +\hspace*{10mm}\verb|fn="sin(x)^4";|\\ +\hspace*{10mm}\verb|cmdL=[|\\ +\hspace*{10mm}\verb| "df:diff",[fn,"x"],|\\ +\hspace*{10mm}\verb| "df:ratsimp",["df"],|\\ +\hspace*{10mm}\verb| "F:integrate",[fn,"x"],|\\ +\hspace*{10mm}\verb| "F","ratsimp",["F"],|\\ +\hspace*{10mm}\verb| "df::F",[]|\\ +\hspace*{10mm}\verb|];|\\ +\hspace*{10mm}\verb|CalcbyM("ans",cmdL);|\vspace{2mm}\\ +The returned value is a list of df and F as strings, though these are not displayed in the console. They can be used, for example,\vspace{2mm}\\ +\hspace*{10mm}\verb|Plotdata("1",fn,"x",["Num=200","do"]);|\\ +\hspace*{10mm}\verb|Plotdata("2",ans_1,"x",["Num=200","dr"]);|\\ +\hspace*{10mm}\verb|Plotdata("3",ans_2,"x",["Num=200","da"]);|\\ +\hspace*{10mm}\verb|Mxtex("1",fn);|\\ +\hspace*{10mm}\verb|Mxtex("1",ans_1);|\\ +\hspace*{10mm}\verb|Mxtex("2",ans_2);|\\ +\hspace*{10mm}\verb|Expr([A,"e",tx1,B,"e",tx2,C,"w",tx3]);| + +\vspace{2mm} + +\begin{center} +\input{Fig/s10diffint.tex} +\end{center} + +\noindent +{\bf Remark} See KeTCindyreferenceE.pdf for more information. + +\subsection{Commands related to R} + +\verb|Rfun| and \verb|CalcbyR| are simillar to \verb|Mxfun| and \verb|CalcbyM|.\\ + See \verb|KeTCindyreferenceE.pdf| or \verb|samples/s08R| for more information. + +% -------------- 3d figures -------------- + +\newpage + +\section{Three Dimentional figures of \ketcindy} + +\subsection{Summary and Geometric Elements} + +In KeTCindy's 3D-mode, there are two rectangular areas surrounded by a white frame on the Euclidean view. + +The main area on the left side of the screen is simillar to that of two dimentional figures. Figures in this area will be drawn to the \TeX\ document. The view direction can be moved with sliders under the main area. \verb|TH| and \verb|FI| mean angles $\theta$ and $\varphi$ respectively, which are polar cocordinates of the view direction. + +Figures from the view direction $(0,\ \varphi)$ are displayed in the sub area on the right side. + + \hspace{40mm} mainarea \hspace{40mm} subarea +\begin{center} +\includegraphics[bb=0.00 0.00 863.04 378.52,width=12cm]{Fig/3dscreen.pdf} +\end{center} + +With internal command \verb|Ptseg3data| which is called in \verb|Start3d|, +a point put to the main area with the drawing tool of Cinderella is regarded as a 3D point by \ketcindy, and a correspoinding point is put in the sub area. +Though the initial coordinate of $z$ is 0, we can change it moving the point in the sub area. + +For example, if we put point \verb|A| on the main area, point \verb|Az| will be put in the sub area and the 3D coordinates calculated from \verb|A| and \verb|Az| are assigned to varible \verb|A3d|.\vspace{-1mm} + +\begin{description} +\item[\bf Remark]Note that point \verb|Az| will not be deleted automatically even if point \verb|A| is deleted. We should delete it manually. +\end{description} + +Geometric segment in the main area generates the corresponding geometric segment in the sub area as well. + +\subsection{Lines and Curves} + +\ketcindy\ commands \verb|Spaceline| and \verb|Spacecurve| are used do draw lines and curves in the space. Additionally, \verb|Xyzax3data| is used to draw axis. + +\begin{description} +\item[Examples]\mbox{}\\ +\verb|Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]");|\\ +\verb|Spacecurve("1","3*[cos(t),sin(t),0.1*t]","t=[0,4*pi]",["Num=200"]);|\\ +\verb|pt1=[3,0,0]; pt2=[3,0,3*0.1*4*pi];|\\ +\verb|Spaceline("1",[pt1,pt2]);|\\ +\verb|Skeletonparadata("1");| + +\item[Remark]The last command skeleton elimination is for skeleton elimination. +Compare two figures below. The right one is with skeleton elimination. + +\end{description} + +\begin{center} +\input{Fig/spacelinecurve1.tex}\hspace{10mm}\input{Fig/spacelinecurve2.tex} +\end{center} + +\subsection{Two Dimensional Figures} + +Data of two dimensional figures such as polyhedra or planes are given in obj format. + +\begin{description} +\item[Examples]\mbox{}\\ +\verb|Start3d();|\\ +\verb|vertex=[[2,2,-2],[2,-2,-2],[-2,-2,-2],[-2,2,-2]];|\\ +\verb|Reflect3d1(``1'',vertex,[[0,0,0],[1,0,0],[0,1,0]];|\\ +\verb|vertex=concat(vertex,ref3d1);|\\ +\verb|edge=[[1,2,6,5],[1,5,8,4],[1,4,3,2],[2,3,7,6],[3,4,8,7],[5,6,7,8]];|\\ +\verb|cube=[vertex,edge];|\\ +\verb|plane=[[[-3,1,-3],[3,-1,-3],[-4,5,3],[2,3,3]],[[1,2,4,3]]];|\\ +\verb|tmp=Concatobj([cubic,plane]);|\\ +\verb|VertexEdgeFace("1",tmp,["Vtx=nogeo","Edg=nogeo"]);|\\ +\verb|Nohiddenbyfaces("1","phf3d1");| // for the figure on the left + +\item[Remark]\mbox{}\\ +Command \verb|Concatobj| combines data in obj format.\\ +Command \verb|VertexEdgeFace| assigns vertices to {\tt phv}, edges to {\tt phe} and faces to {\tt phf}.\\ +Command \verb|Nohiddenbyfaces| is for hiddenline elimination.\\ +Use \verb|Skeletonparadata("1")| if the figure on the right is desirable. +\end{description} + +\vspace{-10mm} + +\begin{center} +\input{Fig/polygonplane1.tex}\hspace{10mm}\input{Fig/polygonplane2.tex} +\end{center} + +\noindent +{\bf Remark} See \verb|KeTCindyreferenceE.pdf| or \verb|samples/s05spacefigure| for more information. + +\subsection{Surfaces} + +Two variable function is defined as a list of one of the followings. + +\begin{enumerate}[\hspace*{5mm}\bf 1.] +\item \verb|["z=f(x,y)","x=[a,b]","y=[c,d]"]| +\item \verb|["z=f(x,y)","x=x(u,v)","y(u,v)","u=[a,b]","v=[c,d]"]| +\item \verb|["p","x=x(u,v)","y=y(u,v)","z=z(u,v)","u=[a,b]","v=[c,d]"]| +\end{enumerate} + +Optionally, you can add what boundaries should be drawn. +The default is "wesn". Here, for example, "w" means the boundary defined by $[a,t]\ (c\leqq t\leqq d)$. + +\ketcindy\ calls C to speed up the calculation of hidden lines elimination. + +\begin{description} +\item[Example]\mbox{}\\ +\verb|Start3d();|\\ +\verb|Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]");|\\ +\verb|fd=["z=x^2-y^2","x=[-2,2]","y=[-2,2]","senw"];|\\ +\verb|Startsurf();|\\ +\verb|Sfbdparadata("1",fd);|\\ +\verb|Crvsfparadata("1","ax3d","sfbd3d1",fd);|\\ +\verb|ExeccmdC("1");| +\verb|Windispg();| + +\begin{center} +\input{Fig/saddle1E.tex}\hspace{10mm}\input{Fig/saddle2E.tex} +\end{center} + +\item[Remark]Wires can be added if necessary with command \verb|Wireparadata| as seen in the upper right side figure. +The line-style also can be changed. + +See \verb|KeTCindyreferenceE.pdf| or \verb|samples/s09surfaceC| for more information. +\end{description} + +\subsection{Generating Files in Obj Format} + +\ketcindy\ can generate files of 3D figures in obj format. Moreover, \ketcindy\ also can call Meshlab which is a 3D viewer. + +\begin{description} +\item[Examples]\mbox{}\\ +\verb|Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]");|\\ +\verb|fd=["p","x=4*sin(V)*cos(U)","y=4*sin(V)*sin(U)","z=4*cos(V)",|\\ +\verb| "U=[pi/2,4*pi/2]","V=[0,pi]","we"];|\\ +\verb|Mkobjcmd("1",fd,[40,40,"-"]);|\\ +\verb|Mkobjcrvcmd("2","ax3d",[0.05,"xy"]);|\\ +\verb|Mkobjsymbcmd("x",0.2,0,[0,1,0],[5.2,0,0]);|\\ +\verb|Mkobjsymbcmd("y",0.2,0,[1,0,0],[0,5.2,0]);|\\ +\verb|Mkobjsymbcmd("z",0.2,0,[0,1,0],[0,0,5.2]);|\\ +\verb|SetObj();| +\item[Remark]See \verb|KeTCindyreferenceE.pdf| or \verb|samples/s13meshlab| for more information. +\end{description} + +% -------------- Making slide -------------- + +\newpage + +\section{Making Slides} + +\subsection{Outline} + +\ketcindy\ has functions to make slides for presentation with the help of \verb|layer| environment which is defined in \verb|ketlayer.sty|. +See \verb|KeTpicStyleE.pdf| for details about \verb|layer|. + +You need both a cindy file and a text file with the same header. For simple preparation, copy \verb|template2slide.cdy| to your work folder, rename the name, for example \verb|makeslide.cdy|, double click the file and press the button \verb|title| in the screen, then \verb|makeslide.txt| will be generated. + +The following chart shows the relation between them. + +\begin{center} +\input{Fig/makeslideE} +\end{center} + +If necessary, edit \verb|Settitle| in CindyScript editor, and press the gear mark. Open the text file, and write commands of \ketcindy\ Slide and \TeX\ as follows. + +\begin{verbatim} + title::slide0// + main::Introduction// + \slidepage[m]// + new::Programming Language// + %repeat=6,para// + \slidepage// + itemize// + item::Python// + %thin[2,-]::item::Ruby// + %thin[3,-]::item::Java// + %thin[4,-]::item::JavaScript// + %thin[5,-]::item::CindyScript// + %thin[6,-]::item::C// + end// +\end{verbatim} + +\begin{description} +\item[Remark]``//'' should be added to the end of all lines. Use ``||||'' when you want to write \verb|//|. +\end{description} + +%\begin{center} +%\includegraphics[bb=0.00 0.00 743.00 632.00,height=60mm]{fig/slidescreen.pdf}\hspace{5mm} +%\includegraphics[bb=0.00 0.00 802.00 633.00,height=60mm]{fig/slidescript.pdf} +%\end{center} + +Press the button \verb|Slide| in Cindy Screen, then \ketcindy\ will make \TeX\ file \verb|makeslide.tex|, +typeset it and displays the pdf file as follows. If there occurs an error, check the text file or the \TeX\ file. + +\begin{center} +\fbox{\includegraphics[bb=0.00 0.00 542.00 385.00,height=35mm]{Fig/slidepdf1.pdf}}\hspace{5mm}% +\fbox{\includegraphics[bb=0.00 0.00 541.00 380.00,height=35mm]{Fig/slidepdf2.pdf}}\hspace{5mm}% +\fbox{\includegraphics[bb=0.00 0.00 543.00 382.00,height=35mm]{Fig/slidepdf3.pdf}}\hspace{5mm}% +\end{center} + +\subsection{Commands of \ketcindy\ slide} + +You can use the following commands.\\ +\verb| title::slide0 (::wallpaper)//|\\ +\verb| Rem) Put only once at the first line.|\\ +\verb| main::(main title)//|\\ +\verb| new::(page title)//|\\ +\verb| enumerate//|\\ +\verb| =\begin{enumerate}|\\ +\verb| Rem) Add the option such as [(1)] using :: .|\\ +\verb| itemize//|\\ +\verb| =\begin{itemize}|\\ +\verb| layer::{xsize}{ysize}//|\\ +\verb| =\begin{layer}{xsize}{ysize}|\\ +\verb| Rem) "layer" is an environment defined in ketlayer.sty.|\\ +\verb| item::sentence//|\\ +\verb| =\item sentence|\\ +\verb| putnote::dir{xpos}{ypos}::filename(,scale)//|\\ +\verb| =putnotedir{xpos}{ypos}{\input{fig/filename}}||\\ +\verb| Rem) "putnote" is a command defined in ketlayer.sty|\\ +\verb| end//|\\ +\verb| =\end{itemize,enumerate,layer}|\\ +\verb| ...//|\\ +\verb| To insert a blank line.| + +\noindent +You can also use the following \TeX\ mcores added by \ketcindy.\\ +\verb| \slidepage,\slidepage[m]//|\\ +\verb| To display the number each page.|\\ +\verb| \slidepage[m] is used for the \verb|main| page.|\\ +\verb| \setthin{thickness}|\\ +\verb| To change the thickness of thin letters temporarily.|\\ +\verb| \inputsound, \inputmovie|\\ +\verb| To insert mp3/mp4 files.| + + +\begin{description} +\item[Remark]Any other \TeX\ macroes are available. Put \verb|%%| instead of \verb|%| to comment out . +\end{description} + + +\subsection{Display of Page step by step} + +\begin{enumerate}[1)] +\item Put just after new,\\ +\verb| %repeat=number of steps//| +\item Put at the head of each line as\\ +\verb| %[2,-]::sentences|\\ +\verb| display at all steps from 2|\\ +\verb| %[-,2]::sentences|\\ +\verb| display at all steps until 2|\\ +\verb| %[1..3,5]::sentences|\\ +\verb| display at steps of 1,2,3 and 5| +\item Use \verb|%thin| to display with thin letters.\\ +\verb| %thin::[2,-]::sentence| +\item The dencity can be changed with Setslidebody or \verb|\setthin|. +\end{enumerate} + +\subsection{Making Flip Animation} + +\begin{enumerate}[1)] +\item Define function \verb|Mf(s)|, the state at s. +\item Put command \verb|Setpara| in the script editor as\\ +\verb| Setpara(subfolder,funcitonstr(mf(s)),range,options);|\\ +\verb| options=["m/r", "Div=25"];| +\item Describe in the text file as\\ +\verb| %repeat=, para=subfolder:{0}:s{60}{10}:input(:scale)//| +\item Press buttons \verb|ParaF| and \verb|Flip|, then \verb|subfolder| will be generated. +\item Press button \verb|Slide|. +\end{enumerate} + +\subsection{Making Animation} + +\begin{enumerate}[1)] +\item Add the following in the script editor\\ +\verb| Addpackage(["[dvipdfmx]{animate}"]);| +\item Add in the second option of Setpara,\\ +\verb| "Frate=num of frame in the second,"Scale=scale,"OpA=option of animation" | +\item Press buttons \verb|ParaF| and \verb|Anime|, then \verb|subfolder| will be generated. +\item Use \verb|\input|, not layer, to display. +\end{enumerate} + +\subsection{Commands to Insert a mp3/mp4 file} + +To insert a mp3 or mp4 file, change the first line to\\ +\verb| title::slide0|\\ +\verb| ::\usepackage{ketmedia}|\\ +\verb| ::\usepackage[dvipdfmx]{media9}//|\vspace{2mm} + +\noindent +Use \verb|\inputsound| or \verb|\inputsoundclick| for mp3 files.\\ +\verb| \inputsountclik[90]{folder/}{mp3file} %starts when the button clicked|\\ +The arguments are horizontal position(default is 90) of buttons, the folder, the file name. +\vspace{2mm} + +\noindent +Use \verb|\inputmovie| for mp4 files.\\ +\verb| \inputsountclik[90]{1}{0.4}{folder/}{mp4file} %starts when the button clicked| +The 2nd and 3rd arguments are width and height as the coefficiients of \verb|\linewidth| + +\subsection{Changing Style} + +The default styles such as size and color of letters can be changed. +See \verb|KeTCindyReferenceE,pdf| or \verb|samples/s07slides|. + +\end{document}
\ No newline at end of file diff --git a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/KeTCindyguideJ.tex b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/KeTCindyguideJ.tex new file mode 100644 index 00000000000..24f34577315 --- /dev/null +++ b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/KeTCindyguideJ.tex @@ -0,0 +1,583 @@ +\documentclass[papersize,a4paper,12pt,uplatex]{jsarticle} +\usepackage{ketpic,ketlayer} +\usepackage{amsmath} +% \usepackage{amsmath,newtxmath} +\usepackage[dvipdfmx]{graphicx,color} +\usepackage{wrapfig} +\usepackage[dvipdfmx,bookmarks=false,colorlinks=true,linkcolor=blue]{hyperref} +\setmargin{20}{20}{15}{25} +\usepackage{setspace} +\usepackage{comment} +\setcounter{tocdepth}{3} + +\begin{document} +\title{\ketcindy の概要} +\author{\ketcindy\ Project Team} +\maketitle + +\begin{center} - 第3.2版 -\end{center} +\hypertarget{index}{} +\tableofcontents + +\newpage + +\section{\ketcindy について} +\subsection{システムの構成} +\ketcindy は，Cinderella の作図機能を利用して，作図データの\LaTeX ファイルを作成するためのスクリプトライブラリである。\ketcindy はCinderellaのプログラミング言語Cindyscriptで記述されており，ユーザーはCinderella によるインタラクティブな作図機能と，CindyScript によるプログラミングを用いて，\LaTeX 文書の挿入図を効率よく作成することができる。また，各種数式処理ソフトと連携して計算を行うことができる。 + +\begin{center} +\scalebox{0.9}{ \input{Fig/concept}} +\end{center} + +Cinderellaで作図した図のデータは，\ketcindy により，いったんRのファイルに書き出される。これをRで処理して\TeX ファイルを作成する。できた\TeX ファイルを，本文中に inputコマンド で挿入すれば図が表示される。（\ketcindy の初期の版ではこのデータ処理にScilabを用いていた。） + +CinderellaとRやその他のソフトウェアとの連携には，バッチファイル（Macではシェルファイル）を用いている。(概念図の両方向矢印) バッチファイルは kc.bat，シェルファイルは kc.sh で，\ketcindy が目的に応じてこれらのファイルを書き出して実行するようになっている。 + +したがって，KeTCindyでの図ファイルの作成手順は次のようになる。 + +(1) 必要に応じてCinderellaの作図ツールで，点や線を作図しておく。 + +(2) Cindyscript エディタでプログラムを書く。 + +(3) 出力する。 + +\newpage +%--------- ketcindy による作図手順---------------- +\subsection{\ketcindy による作図手順} + +\ketcindy で作図し，TeXのファイルを作図する手順をチュートリアル形式で示す。 + +\subsubsection{平面幾何} + +\ketcindy のシステムに同梱されている，template1basic.cdy をひな形として用いる。適当な場所に複製を作り，名前を変えておこう。ここでは，単に template.cdy とする。 + +template.cdy をダブルクリックして開き，図が表示されたら，Ctrl+9 ( Windows ) / ⌘+9 ( Mac ) でスクリプトエディタを開く。２つの画面はマルチウィンドウにしておくのがよい。 + +\vspace{\baselineskip} +\begin{center}\includegraphics[bb=0.00 0.00 500.03 306.52,width=10cm]{Fig/start01.pdf}\end{center} + +この三角形で Cinderellaの作図機能を用いて内心を求め，内接円を描く。 + +まず，スクリプトエディタの \verb|Listplot([A,B,C,A]);| の行頭にスラッシュを２本書き入れ，Shift+Enter で実行する。こうすると，この行はコメント行となり実行されない行になる。その結果，三角形が消えて点だけ残る。 + +画面上部の作図ツールから「線分を加える」\includegraphics[bb=0.00 0.00 6.48 5.04,width=8mm]{Fig/segment.pdf} をクリックして選択し，点Aから点Bへドラッグすると線分が描かれる。同様にして，BC, CAを引く。 + +\begin{center}\includegraphics[bb=0.00 0.00 414.02 329.02,height=3.5cm]{Fig/start02.pdf} \end{center} + +次に，角の二等分線を引く。「角の二等分線を加える」ツール \includegraphics[bb=0.00 0.00 6.48 5.04,width=8mm]{Fig/bisector.pdf} を選択し，辺BA，BCを順にクリックすると角ABCの二等分線が引かれる。 このとき，次図左のように，該当する角を表すガイドが出る。 + +\hspace{20mm}\includegraphics[bb=0.00 0.00 402.02 325.02,height=3cm]{Fig/start03.pdf} \hspace{5mm}\includegraphics[bb=0.00 0.00 413.02 320.02,height=3cm]{Fig/start04.pdf} + +同様にして，角Aの二等分線を引き，「交点を求める」ツール\includegraphics[bb=0.00 0.00 6.48 5.04,width=8mm]{Fig/intersection.pdf}をクリックして，２本の二等分線を順にクリックすると交点が求められる。（角Aの二等分線を引いた直後はこれが選択状態にあるので，角Bの二等分線をクリックすればよい） + +\begin{center}\includegraphics[bb=0.00 0.00 397.02 319.02,height=3cm]{Fig/start05.pdf}\end{center} + +内接円の半径を決めるために，辺ACに垂直で点Dを通る直線を描く。「垂線を加える」ツール \includegraphics[bb=0.00 0.00 6.48 5.04,width=8mm]{Fig/multi-add-perp.pdf} を選択し，辺AC上でマウスボタンを押し，そのまま点Dへドラッグすると垂線が引ける。 + +\hspace{20mm}\includegraphics[bb=0.00 0.00 403.02 319.02,height=3cm]{Fig/start06.pdf} \hspace{5mm}\includegraphics[bb=0.00 0.00 394.02 315.02,height=3cm]{Fig/start07.pdf} + +最後に，垂線と辺ACの交点を求める。 + +\begin{center}\includegraphics[bb=0.00 0.00 409.02 312.02,height=3cm]{Fig/start08.pdf}\end{center} + +図が描かれたら，「要素を動かす」ツール \includegraphics[bb=0.00 0.00 6.48 5.04,width=8mm]{Fig/move.pdf} を選択して，始めの状態（動かすモード）に戻しておく。 + +これで内心の作図と半径の作図ができた。内心円は描かなくてよい。 + +スクリプトエディタに戻り，先ほど書いた // を消して \verb|Listplot([A,B,C,A]);| を有効にし，次のスクリプトを追加し，Shift+Enterで実行すると，内接円が描かれる。なお，２行目を \verb|Setfiles("innercircle")| として，ファイル名も設定しておく。 + +\begin{verbatim} + Circledata([D,E]); + Pointdata("1",[D],["size=3"]); + Letter([A,"sw","A",B,"ne","B",C,"se","C",D,"ne2","I"]); +\end{verbatim} + +\begin{center}\includegraphics[bb=0.00 0.00 396.02 322.02,height=4cm]{Fig/start09.pdf} \end{center} + + +画面左上の「Figure」ボタンをクリックすると，プレビュー用のPDFができて表示される（下図左）。 +描画面で点Bをドラッグして三角形の形を変えれば，それに応じて出力する図も変えることができる（下図右）。 + +\begin{center} \includegraphics[bb=0.00 0.00 396.02 331.02,height=4cm]{Fig/start10.pdf} \includegraphics[bb=0.00 0.00 348.02 284.51,height=4cm]{Fig/incenter03.pdf} \end{center} + +\vspace{\baselineskip} +\ketcindy がTikZなどの作図支援ツールと異なるのは，Cinderellaの作図機能を用いてインタラクティブに図の調整ができる点である。簡単な図であれば，座標の計算は不要で，Cinderellaの作図画面を見ながら\ketcindy の作図関数でプログラムを書くだけでよい。 + +なお，Cinderellaの作図機能については，付録の \hyperlink{geometrytool}{作図ツール} を参照されたい。 + +%---------------- 関数のグラフ-------------------------- +\subsubsection{関数のグラフ} + +例として，$y=\sin x$ と $y=x$ のグラフを描く。 + +template.cdy をダブルクリックして開き，Ctrl+9 ( Windows ) / ⌘+9 ( Mac ) でスクリプトエディタを開く。 + +座標軸を描くので，\verb|Addax(0);| を \verb|Addax(1);| に変え，\verb|Listplot([A,B,C,A]);| は使わないので削除し，かわりに次のスクリプトを書く。 + +\begin{layer}{150}{0} +\putnotese{80}{5}{\includegraphics[bb=0.00 0.00 552.03 409.02,height=30mm]{Fig/xsinx01.pdf} } +\end{layer} +\begin{verbatim} + Plotdata("1","y=sin(x)","x"); + Plotdata("2","y=x","x"); +\end{verbatim} + +これだけで右のようにグラフが描かれる。 + +\vspace{15mm} +%\begin{center}\includegraphics[bb=0.00 0.00 552.03 409.02,height=30mm]{Fig/xsinx01.pdf} \end{center} + +描画範囲は点NEとSWをドラッグして適当に決めよう。また，点A,B,Cが残ったままだが，これを関数名を表示する場所として利用するために適当な位置にドラッグして移動する。 + +\begin{center}\includegraphics[bb=0.00 0.00 556.03 238.01,height=30mm]{Fig/xsinx02.pdf} \end{center} + +関数名と$x$軸上の交点を表示するために，関数 \verb|Expr()| を使って次のように書く。 +\begin{verbatim} + Expr([A,"e","y=\sin x",B,"e","y=x",[-pi,0],"s2","-\pi",[pi,0],"s2","\pi", + [2*pi,0],"s2","2\pi"]); +\end{verbatim} + +注）改行せず１行に書いてよい。 + +\begin{center}\includegraphics[bb=0.00 0.00 546.03 236.01,height=30mm]{Fig/xsinx03.pdf} \end{center} + +\verb|Figure| ボタンをクリックすると，次の図が描かれる。 + +\vspace{\baselineskip} +\begin{center}\input{Fig/xsinx} \end{center} + + +%---------------- 空間図形 -------------------------- +\subsubsection{空間図形} + +\ketcindy のシステムに同梱されている samples フォルダから，s05spacefigure フォルダを開き，s0501basic.cdy をひな形として使う。適当な場所に複製を作り，名前を変えておくとよい。ここでは，3Dbasic.cdy として進める。 + +3Dbasic.cdy を開くと次のような画面になる。 + +\vspace{\baselineskip} +\begin{center} + \includegraphics[bb=0 0 879.05 447.02 , width=8cm]{Fig/3dstart.pdf} +\end{center} + +下のスライダで点TH,Fl をドラッグすると，空間での視点の位置が変わる。（座標軸が回転する） + +ここでは，正四面体と，高さを求めるのによく使われる補助線を描いてみよう。スクリプトエディタを開き，次の3行を消す。 + +\begin{verbatim} + Ch=[1]; + if(contains(Ch,1), + Skeletonparadata("1",[1.5]); + ); +\end{verbatim} + +かわりに次のスクリプトを書いて Shift+Enter で実行する。 + +\begin{layer}{150}{0} +\putnotese{90}{0}{ \input{Fig/tetrahedron}} +\end{layer} +\begin{verbatim} + Putpoint3d("A",2*[-1,-1/sqrt(3),0],"fix"); + Putpoint3d("B",2*[1,-1/sqrt(3),0],"fix"); + Putpoint3d("C",2*[0,sqrt(3)-1/sqrt(3),0],"fix"); + Putpoint3d("D",2*[0,0,sqrt(3)],"fix"); + Putpoint3d("M",(B3d+C3d)/2,"fix"); + phd=Concatobj([[A,B,C],[A,B,D],[A,C,D],[B,C,D]]); + Spaceline("1",[D,M,A]); + VertexEdgeFace("1",phd,["Edg=nogeo"]); + Nohiddenbyfaces("1","phf3d1"); +\end{verbatim} + + +%---------------- 作表 -------------------------- +\subsubsection{作表} + +\TeX\ で表を作るのはかなり面倒だが，\ketcindy\ を使えば比較的簡単に作表ができる。次の図は関数の増減・凹凸表である。以下は紹介にとどめる。関数リファレンスに例を掲載しているので参照されたい。 + +\begin{center} \input{Fig/zogen3} \end{center} + +% ====== 他のソフトとの連携 =============== + +\subsubsection{他のソフトとの連携} + +\ketcindy\ はCindyscriptで記述されているが，Cindyscriptはプログラミング言語であり，数式処理ソフトではない。そこで，R や Maxima などと連携することにより，機能を拡張することができるようになっている。統計計算はＲ，数式処理を用いた計算はMaximaを利用すると便利である。 + +【例】Rを用いて箱ひげ図を描く + + \begin{center}\scalebox{0.8}{ \input{Fig/boxplot} } \end{center} + + +【例】Maxima を用いて $ \sin x $の7次のテイラー展開を行う。 + + \begin{center}\scalebox{0.8}{ \input{Fig/taylor}} \end{center} + +% ====== プロットデータ =============== +\newpage +\section{プロットデータ} +プロットデータ(Plot Data) とは，関数のグラフや幾何要素を描くデータのことである。\ketcindy\ では PD と略すことがある。 + +たとえば，線分は端点の座標2つからなるリストで表現できる。曲線は，描画範囲を分割して線分の集まりとして描画しており，このときのプロットデータはそれらの線分の端点のリストである。 + +プロットデータの名称は\ketcindy が次の規則により命名する。 + +\vspace{\baselineskip} +・名称の頭部は，プロットデータを作成する関数ごとに決まっている。 + +・第１引数に name が与えられる場合，name を頭部に付加する。 + +\hspace{10mm} 【例】\verb|Listplot("1",[[0,0],[1,2]]);| のとき，sg1 + +・第１引数の name を省略できる場合，引数で用いられた点の名前を頭部に付加する。 + +\hspace{10mm} 【例】\verb|Listplot([A,B,C]);| のとき，sgABC + + +\vspace{\baselineskip} +プロットデータを生成したときは，Cindyscriptエディタのコンソールにその名称を表示する。たとえば，\verb|Listplot([A,B,C,A])| で三角形ABCを描くと，コンソールに + +\hspace{10mm} \verb|generate Listplot sgABCA| + +と表示される。プロットデータを操作する関数では，この名称を用いる。 + +\begin{center}\includegraphics[bb=0.00 0.00 298.02 115.01,width=6cm]{Fig/pdtoconsole.pdf} \end{center} + +プロットデータの内容は，Cindyscriptの println() 関数を用いてコンソールに表示することができる。たとえば上記の場合， + +\hspace{10mm} \verb|println(sgABCA)| + +とすると， + +\hspace{10mm} \verb| [[1,3],[-1,0],[3,0],[1,3]] | + +と表示される。A,B,C,A のそれぞれの座標からなるリストである。 + +プロットデータは，Cindyscriptによるプログラムで作成してそれを\ketcindy で利用することもできる。( \hyperlink{listplot}{Listplot()の例} を参照）ただし，要素の数が大きいとエラーとなるので，１つのプロットデータの要素は200程度とするのがよい。これより多い場合は分割する。 + +\newpage +%======= Cindyscript =========== + +\section{Cindyscript} +\subsection{Cindyscriptエディタ} +CindyscriptはCinderellaのプログラミング言語で，Cinderella上のスクリプトエディタで記述する。スクリプトエディタは，「スクリプト」メニューの「Cindyscript」を選択するか，Ctrl+9 (Windows) / ⌘＋9 (Mac) で開く。\\ +\vspace{110mm} +\begin{layer}{150}{0} +\putnotese{5.5}{15}{\includegraphics[bb=0.00 0.00 687.84 451.68,width=12.5cm]{Fig/slot.pdf}} +\arrowlineseg[16]{20}{20}{10}{90} +\putnotese{15}{5}{スロット} +\arrowlineseg[16]{40}{20}{10}{100} +\putnotese{32}{5}{ページ名} +\arrowlineseg[16]{80}{20}{15}{140} +\putnotese{50}{5}{フォントサイズ} +\arrowlineseg[16]{107}{20}{15}{140} +\putnotese{80}{5}{描画面を前面に} +\arrowlineseg[16]{120}{20}{10}{110} +\putnotese{110}{5}{実行} +\arrowlineseg[16]{125}{20}{10}{90} +\putnotese{120}{5}{ヘルプ} +\putnotese{90}{35}{メインウィンドウ} +\putnotese{90}{65}{コンソール} +\end{layer} + +\noindent +{\bf スロット} + +スロットはそれぞれの実行タイミングでスクリプトを実行するものであり，他のプログラミング言語にはない特徴である。（スロットが隠れているときは境界線をドラッグする） + +よく使うスロットは次の通り。 + +\begin{tabbing} +123456789012345678\=\kill +Draw \>描画面になにか変化が起きる（点を動かすなど）と実行される。\\ + \>通常はここにスクリプトを書く。ひな形の templatebasic1.cdy では，\\ + \>Ketinit() などが記述された figures ページが用意されている。\\ +Initialization \>スクリプトを実行すると、始めに1度 だけ実行される。\\ + \>したがって，関数定義や変数の初期設定などを書く。\\ + \>ひな形の templatebasic1.cdy ではここに KETlib というページがあり，\\ + \>\ketcindy の初期設定に関する記述がある。\\ +Key Typed \>キーボードが押されたとき実行される。\\ + \> KeTCindyでは，ボタンによらずキーボードで出力を行うための\\ + \>スクリプトが書かれている。 +\end{tabbing} + +１つのスロットに複数のページを作ることができる。たとえば，KETlib以外に初期設定のスクリプトを書く場合は，Initialzation スロットのフォルダアイコンをクリックすることで新しいページができる。 + +KeTCindyの描画コマンドは Draw スロットに書く。 + +\vspace{\baselineskip}\noindent +{\bf ページ名} + +各スロットでは，ページを分けて記述することができる。各ページの名前はスクリプトエディタの上の欄に書くことができる。 + +%\vspace{\baselineskip} +\noindent +{\bf フォントサイズ} + +編集エリアのフォントサイズを変更する。 + +%\vspace{\baselineskip} +\noindent +{\bf 実行ボタン} + +プログラムを実行する。プログラムの実行は Shift+Enter でもできる。 + +%\vspace{\baselineskip} +\noindent +{\bf ヘルプボタン} + +ブラウザを開いてマニュアルを表示する。 + +%\vspace{\baselineskip} +\noindent +{\bf コンソール} + +print() 関数の結果やエラーメッセージが表示する。エラーメッセージは，「WARNING:」または「syntax error」に続いてその内容と該当する行番号が示される。これを読んでスクリプトの書き間違いをチェックする。 + +\subsection{スクリプトの記述} +編集エリアにプログラムを書くと，文字が色分けされて表示される。組み込み関数は青，ユーザー定義関数は紫，定義されていない関数は赤，文字列は緑で表示される。KeTCindyの関数はユーザー定義関数なので紫色で表示される。 + +\begin{layer}{150}{0} +\putnotese{35}{5}{\includegraphics[bb=0.00 0.00 350.02 184.01,width=7cm]{Fig/coloring.pdf} } +\putnotee{5}{27}{組み込み関数} +\arrowlineseg[20]{35}{27}{10}{180} +\putnotee{77}{9}{ユーザー定義関数} +\arrowlineseg[10]{67}{9}{8}{0} +\putnotee{110}{17}{文字列} +\arrowlineseg[15]{80}{17}{28}{0} +\end{layer} +\vspace{45mm} + +編集エリアでは，Ctrl+C と Ctrl+V によるコピーアンドペースト，Ctrl+X と Ctrl+V によるカットアンドぺーストができる。他のテキストエディタなどとの間でのコピーも同様にできる。 + +文字列の選択はマウスドラッグまたは Shift+カーソルキーでおこなえる。 + +Ctrl+F による検索はできない。 + +スクリプトを記述するときの基本的なルールは次の通り。 + +\vspace{\baselineskip} +・基本的に小文字で書く。大文字と小文字は区別される。 + +\hspace{5mm}\ketcindy では，Cindyscriptに組み込みの変数名・関数名と区別しやすいように， + +\hspace{5mm}次の規則により名前を付けている。 + +\hspace{5mm}・グローバルな変数はすべて大文字か，大文字で始まるものとする。 + +\hspace{5mm}・局所変数は小文字で，関数定義の冒頭で regional() により局所変数として宣言する。 + +\hspace{5mm}・関数名は大文字で始まる。 + +・複数の半角スペースは無視され，一つの半角スペースと見なされる。 + +・行末にはセミコロンを書く。改行だけでは命令文の終わりにならない。 + +\subsection{変数と定数} +\vspace{\baselineskip}\noindent +{\bf 変数} + +Cindyscriptでは，変数の型の宣言は不要。使用されたときに何が代入されたかで自動的に型が決まり，さらに，宣言し直さなくても異なる型の値を代入することができる。 + +\vspace{\baselineskip} + +【例】 +\begin{verbatim} + a=10; + b=2; + c=a+sqrt(b); + a="の平方根"; + println("10に "+b+a+" を加えると"+c); +\end{verbatim} + +この例では，始めにaは整数型であるが，4行目で文字列に変わる。 + +文字列はダブルクウォートでくくる。異なる型の演算には注意を要するが，例外的に，5行目のように，文字列と数を＋演算子で結ぶと，数は文字列化されて結合される。 + +\vspace{\baselineskip}\noindent +{\bf 予約定数} + +Cindyscriptでは，円周率 (pi) と虚数単位(i) が定数として予約されている。i は，変数として使用することもでき，そのような場合，虚数単位に戻すには \verb|i=complex(0,1)| を実行する。 + +\vspace{\baselineskip}\noindent +{\bf KeTCindyの予約変数} + + \ketcindy が内部的に使用する予約変数がある。そのうち次のものはユーザーが値を変更または設定することができる。 +\begin{tabbing} +1234\=567890123\=45678989012345678901234567890123\=\kill + \>Fhead \>書き出されるファイル名の頭部。Setfiles() によって設定できる。\\ + \>Texparent \>親プロセスのファイル名。Setparent()によって設定できる。\\ + \>Dirhead \>パスの頭部\\ + \>Dirlib \>ライブラリ ketlib のパス\\ + \>Dirbin \>ketbin のパス\\ + \>Dirwork \>作業ディレクトリのパス。Changework()によって設定できる。\\ + \>Shellfile \>シェルファイル名 +\end{tabbing} + +以下の予約変数は，ライブラリが使用するグローバル変数であるので，ユーザーはこれらの変数に値を代入してはいけない。なお，変数は大文字小文字を区別するので，すべて小文字で書く分には支障はない。ユーザーが作るプログラムでは，すべて小文字か，先頭だけが大文字の変数を使うことを勧める。 + +\vspace{\baselineskip} +ADDAXES, ArrowlineNumber, ArrowheadNumber, BezierNumber, COM0thlist, COM1stlist, COM2ndlist, Dq, FUNLIST, Fnamesc ，Fnamescibody，Fnameout，Fnametex, GDATALIST, GLIST, GCLIST, GOUTLIST, KCOLOR, KETPICCOUNT,KETPICLAYER, LETTERlist, LFmark, MilliIn, PenThick,PenThickInit, POUTLIST, SCALEX, SCALEY, SCIRELIST, SCIWRLIST, TenSize, TenSizeInit, ULEN, XMAX, XMIN, YaSize, YaThick, YMAX, YMIN, VLIST + + +\vspace{\baselineskip}\noindent +{\bf リスト} + +リストとは，数や文字などを集めたもので，それぞれのものを「要素」といい，\verb|[ ]|の中にコンマで区切って記述する。要素は型を問わない。\ketcindy\ では，曲線を描くプロットデータが座標のリストであり，リスト処理をうまく使えば \ketcindy\ で効率的に作図ができる。 + +リストのn番目の要素にアクセスするのに，アンダーバー\_ を使う。 + +\begin{verbatim} + list=[1,2,3,4,5]; + println(list_2); +\end{verbatim} +とすると，list の中の2番目の要素 2 が表示される。 +\begin{verbatim} + list=[1,2,3,4,5]; + list_2="a"; +\end{verbatim} +とすると，list の中の2番目の要素が文字 a に変わる。 + +たとえば，曲線の交点を求める \hyperlink{intersectcrvs}{Intersectcrvs()} の戻り値から交点の座標を求めるにはアンダーバーを使う。使用例は，Intersectcrvs() の例を参照されたい。 + +\subsection{よく使うCindyscriptのコマンド} +\vspace{\baselineskip}\noindent +{\bf 値の表示} + +print(値) ：コンソールに値を表示する。改行しない。 + +println(値) ：コンソールに値を表示する。改行する。 + +\vspace{\baselineskip} +【例】関数Intersectcrvs() の戻り値を表示する。 +\begin{verbatim} + tmp=intersectcrvs("sgAB","crCD"); + println(tmp); +\end{verbatim} + +\vspace{\baselineskip}\noindent +{\bf 条件判断} + +if(A,B,C) ： もしAが真なら（成り立てば）Bを，偽ならCを実行する。 + +Aの条件判断には次のものがよく使われる。 + \begin{tabbing} +1234\=56789012345678989012\=3456789012\=34567890123\=\kill + \> \verb|a|が\verb|b|より大きい \> \verb|if(a>b|,$\cdots$\\ + \> \verb|a|が\verb|b|より小さい \> \verb|if(a<b|,$\cdots$\\ + \> \verb|a|が\verb|b|以上 \> \verb|if(a>=b|,$\cdots$ （\verb|>|と=の順序に注意）\\ + \> \verb|a|が\verb|b|以下 \> \verb|if(a<=b|,$\cdots$ （\verb|<|と=の順序に注意）\\ + \> \verb|a|と\verb|b|が等しい \> \verb|if(a==b|,$\cdots$ （等号を2つ）\\ + \> \verb|a|と\verb|b|が異なる \> \verb|if(a!=b|,$\cdots$\\ +\end{tabbing} + +if 文はネストして使うことができる。 + +\vspace{\baselineskip} + 【例】n が正，負，ゼロのいずれかを判断して，コンソールに表示する。 +\begin{verbatim} + if(n>0,print("正"),if(n==0,print("０"),print("負"))); +\end{verbatim} + +\vspace{\baselineskip}\noindent +{\bf 繰り返し} + +repeat(n,操作) ：操作をn回繰り返す。 + +repeat(n,s,操作) ：操作をn回繰り返す。カウンタとしてsを使う。（文字は他でも可） + +\vspace{\baselineskip} + 【例】Aを4個並べて描画面に表示する。 +\begin{verbatim} + repeat(4,s,drawtext([s,0],4)); +\end{verbatim} + ここで，sの値は4回繰り返すうちに，1,2,3,4と変化する。 + +\vspace{\baselineskip}\noindent +{\bf リストによる繰り返し} + + forall(list,処理） ：リストの要素すべてに渡るように繰り返す。 + +\vspace{\baselineskip} + 【例】点のペアをリストとし，線分を描く。 +\begin{verbatim} + sglist=[[A,B],[C,D],[E,F]]; + forall(sglist,Listplot(#)); +\end{verbatim} + これは， +\begin{verbatim} + Listplot([A,B]); + Listplot([C,D]); + Listplot([E,F]); +\end{verbatim} +とするのと同じ。ここで，\verb|#|は実行変数と呼ばれ，リストのそれぞれの要素を表す。 + +\vspace{\baselineskip}\noindent +{\bf ユーザー定義関数} + +ユーザー定義関数は次の書式で定義する。 + +\hspace{10mm}関数名(引数):=(処理) + +\vspace{\baselineskip} +【例】 引数の値の正負を表示する関数 sign(n) を定義する。 +\begin{verbatim} + sign(n):=( + if(n>0,print("正"),print("０または負")); + ); +\end{verbatim} +定義した関数は +\begin{verbatim} + n=3; + println(sign(n)); +\end{verbatim} +のようにして使う。 + +KeTCindyでは，アニメーションPDFを作成するときに，フレームを定義するのに使う。 + +\vspace{\baselineskip}\noindent +{\bf 幾何要素へのアクセス} + +Cinderellaでは，点の座標は同次座標で表されており，点の名称でそのまま座標を取得できることが多い。そのため，たとえば Listplot() 関数では，点を指定するのに，座標 \verb|[a,b]| の代わりに点名を使うことができる。 + +\vspace{\baselineskip} +Listplot() の書式１ \verb|Listplot("1",[[1,1],[4,5]])| + +Listplot() の書式2 \verb|Listplot("1",[A,B])| + +\vspace{\baselineskip} + +しかし，明確に直交座標で取得したい場合は \verb|A.xy|（x,y 座標） \verb|A.x|（x 座標 ） \verb|A.y|（y 座標） として取得する。 + +\vspace{\baselineskip}\noindent +{\bf リスト処理} + +Cindyscriptのリスト処理のうち，よく使うものを挙げる。 + +aからbまでの整数のリストは \verb|a..b| （ドット2つ）で生成できる。このリストの各要素を番号代わりに使って，\verb|apply(list,expr)| を用いると座標のリストを作ることができる。\verb|apply(list,expr)| は，\verb|list| の各要素に，処理 \verb|expr| を施したリストを作る関数である。 + +\vspace{\baselineskip} +【例】星形五角形を描く +\begin{verbatim} + r=2; + pt=apply(0..5,r*[cos(pi/2+#*4*pi/5),sin(pi/2+#*4*pi/5)]); + repeat(5,s,Listplot(text(s),[pt_s,pt_(s+1)])); +\end{verbatim} + +ここで，\verb|text(s)| は，数を文字列に変換するCindyscriptの組み込み関数。 + +\vspace{\baselineskip}\noindent +{\bf よくあるエラーメッセージ} +\begin{tabbing} +1234\=5678901234567890123456789\=\kill + \>Index out of range \>リストの要素の個数外の値を指定した。\\ + \>String Index out of range \>文字列のインデックスが範囲外。\\ + \>Potential type mismatch \>変数の型が合わない。文字と実数をかけ算したときなど。\\ + \>unexpected ) \>括弧の種類が前後で合っていない。\\ + \>close without open \>閉じ括弧に対応する開き括弧がない。\\ + \>open without close \>開き括弧に対応する閉じ括弧がない。\\ + \>Unknown function \>関数が定義されていない。 +\end{tabbing} + + +\vspace{\baselineskip} +その他，Cindyscriptについては，スクリプトエディタからヘルプを参照されたい。 + +\end{document}
\ No newline at end of file diff --git a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/KeTPicStyleE.tex b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/KeTPicStyleE.tex new file mode 100644 index 00000000000..5ca2f21268a --- /dev/null +++ b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/KeTPicStyleE.tex @@ -0,0 +1,552 @@ +\documentclass[papersize,a4paper,12pt]{article} +\usepackage{ketpic,ketlayer} +\usepackage{amsmath} +% \usepackage{amsmath,newtxmath} +%\usepackage[dvipdfmx]{graphicx,color} +\usepackage{graphicx,color} +\usepackage{wrapfig} +%\usepackage[dvipdfmx,bookmarks=false,colorlinks=true,linkcolor=blue]{hyperref} +\usepackage[bookmarks=false,colorlinks=true,linkcolor=blue]{hyperref} +\setmargin{20}{20}{15}{25} +\usepackage{setspace} +\usepackage{comment} +\usepackage{bm,enumerate} + +\newcommand{\bs}{$\backslash$} + +\newcommand{\br}[1]{\{#1\}} + +\newenvironment{cmd}[2]{ +\hypertarget{#2}{} +\begin{center}{\bf\large #1}\end{center} +\begin{description} +}{ +\end{description} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$Command List}\end{flushright} +} + +% item command for this documentation +\newcommand{\itemket}[1]{ +\item[\Ltab{27mm}{#1}] +} + + +\begin{document} +\title{Macros of ketpic.sty and ketlayer.sty} +\author{\ketcindy\ Project Team} +\maketitle + +\begin{center} - ver.1.1 -\end{center} + +%\hypertarget{index}{} +%\tableofcontents + +%\newpage + +\section{Outlines} + +\begin{itemize} +\item ketpic.sty, ketpic2e.sty(it is necessary in pict2e) are used for ketpic. +\item ketlayer.sty, ketlayer2e.sty(it is necessary in pict2e) are used for ketlayer. +\item \bs\verb|Width|, \bs\verb|Height|,\ \bs\verb|Depth| are defined. +\item Temporary counters \verb|ketpictctra|,\ $\cdots$,\ \verb|ketpicctrj| are defined. +\item Package \verb|graphicx|, \verb|color| are required. + +\end{itemize} + + +%========= Envilonment ===================== +\section{Envilonment} + +%------------layer-------------------------------- +\begin{cmd}{layer}{layer} +\itemket{Usage}\verb|\begin{layer}[Ho]{W}{H}|\ $\cdots$\ \verb|\end{layer}| +\itemket{Description}This enviroment draws grids and adds a note or a figure. + +\item[Details]\mbox{}\\ +\Ltab{10mm}{W}Width of grids. The unit is \verb|mm|. + +\Ltab{10mm}{H}Height of grids. The unit is \verb|mm|.\\ +\hspace*{20mm}If \verb|H=0|, grids don't appear.\\ +\hspace*{20mm}If \verb|H<0|, grids appear on the upside. + + +\itemket{Example} \mbox{}\\ +\verb|\begin{layer}{120}{30}|\\ +\verb|\putnotec{20}{10}{abc}|\\ +\verb|\putnotes{60}{0}{\input{Fig/FigE.tex}}|\\ +\verb|\end{layer}| + +\vspace{5mm} + +\begin{layer}{120}{30} +\putnotec{20}{10}{abc} +\putnotes{60}{0}{\input{Fig/FigE.tex}}\end{layer} +%% "FigE.tex" is copy of "addax2.tex" + +\vspace{35mm} + +\item[Remark]Set \verb|H=0| if placement of all components is proper. + +\end{cmd} + + +%========= Macros ===================== +\section{Macros} +%=-=-=-=-= Macros of ketpic =-=-=-=-= +\subsection{Macros of ketpic} +Macros of ketpic are used just like regular commands of \TeX. + +%------------ ketpic ------------ +\begin{cmd}{\bs ketpic}{ketpic} +\itemket{Usage}\verb|\ketpic| +\itemket{Description}This macro displays the logo of {\ketpic}. +\itemket{Examples} \verb|\ketpic| +\end{cmd} + +%------------ ketcindy ------------ +\begin{cmd}{\bs ketcindy}{ketcindy} +\itemket{Usage}\verb|\ketcindy| +\itemket{Description}This macro displays the logo of {\ketcindy}. +\itemket{Examples} \verb|\ketcindy| +\end{cmd} + +%------------ tab ------------ +\begin{cmd}{\bs Ltab, \bs Rtab, \bs Ctab}{tab} +\itemket{Usage}\verb|\Ltab{W}{S}|, \verb|\Rtab{W}{S}|, \verb|\Ctab{W}{S}| +\itemket{Description}This is tab macro. +\itemket{}\verb|\Ltab{W}{S}| secures the width of W and writes S by left justifying it. +\itemket{}\verb|\Rtab{W}{S}| secures the width of W and writes S by right justifying it. +\itemket{}\verb|\Ctab{W}{S}| secures the width of W and writes S at the center. +\end{cmd} + +%------------ ketcalc ------------ +\begin{cmd}{\bs ketcalcwidth, \bs ketcalcheight, \bs ketcalcdepth}{ketcalc} +\itemket{Usage}\verb|\ketcalcwidth[0]{C}|, \verb|\ketcalcheight[0]{C}|, \verb|\ketcalcdepth[0]{C}| +\itemket{Description}These functions return the size of C using current unit to the counter \verb|ketpicctr1|. +If option is 1, it displays the value. +\itemket{}\verb|\ketcalcwidth[0]{C}| returns the width of C. +\itemket{}\verb|\ketcalcheight[0]{C}| returns the height of C. +\itemket{}\verb|\ketcalcdepth[0]{C}| returns the depth of C. +\itemket{Examples} \verb|\ketcalcwidth[0]{abc}, \theketpicctra, \ketcalcwidth[1]{abc}| \par +It displays ``\ketcalcwidth[0]{abc}, \theketpicctra, \ketcalcwidth[1]{abc}''. +\end{cmd} + +%------------ ketcalcwh ------------ +\begin{cmd}{\bs ketcalcwh}{ketcalcwh} +\itemket{Usage}\verb|\ketcalcwh{C}| +\itemket{Description}This function displays the width and height of C using \verb|mm| in the form \{width\}\{height\}. +\itemket{Examples} \verb|\ketcalcwh{abc}|\par +It displays ``\ketcalcwh{abc}''. +\end{cmd} + +%------------ dangerbendmark ------------ +\begin{cmd}{\bs dangerbendmark}{dangerbendmark} +\itemket{Usage}\verb|\dangerbendmark[size]| +\itemket{Description}This function displays the symbol ``Dangerous turning point'' of Bulbaki. +\itemket{Examples} \verb|\dangerbendmark[1.2]| --->\ \ \dangerbendmark[1.2] +\end{cmd} + +%------------ cautionmark ------------ +\begin{cmd}{\bs cautionmark}{cautionmark} +\itemket{Usage}\verb|\cautionmark[size]| +\itemket{Description}This function displays the caution mark. +\itemket{Examples} \verb|\caoutionmark[1.2]| --->\ \ \cautionmark[1.2] +\end{cmd} + +%------------ circlemark ------------ +\begin{cmd}{\bs circlemark}{circlemark} +\itemket{Usage}\verb|\circlemark[thickness]{size}| +\itemket{Description}This function displays the circle. +If size=1, the diameter of the circle is 4mm. +\itemket{Examples} \verb|\circlemark[8]{1.2}| --->\ \ \circlemark[8]{1.2} +\end{cmd} + +%------------ circleshade ------------ +\begin{cmd}{\bs circleshade}{circleshade} +\itemket{Usage}\verb|\circleshade[thickness]{size}{density}| +\itemket{Description}This function displays the solid circle. +\itemket{Examples} \verb|\circleshade[8]{1.2}{0.3}| --->\ \ \circleshade[8]{1.2}{0.3} +\end{cmd} + +%------------ arrow of increase or decrease ------------ +\begin{cmd}{\bs NEarrow, \bs NELarrow, ...}{arrow of i or d} +\itemket{Usage}\verb|\NEarrow[size]|, \verb|\NELarrow[size}|, \verb|\NERarrow[size]|, +\itemket{Description}These functions display the arrow of increase or decrease. +\itemket{Examples} \mbox{} + +\vspace{-3mm}\hspace{16mm} +\begin{tabular}{|rl|rl|rl|rl|} +\hline + \verb|\NEarrow| & \NEarrow & \verb|\SEarrow| & \SEarrow & \verb|\NWarrow| & \NWarrow & \verb|\SWarrow| & \SWarrow \\ +\hline +\verb|\NELarrow| & \NELarrow & \verb|\SELarrow| & \SELarrow & \verb|\NWLarrow| & \NWLarrow & \verb|\SWLarrow| & \SWLarrow \\ +\hline +\verb|\NERarrow| & \NERarrow & \verb|\SERarrow| & \SERarrow & \verb|\NWRarrow| & \NWRarrow & \verb|\SWRarrow| & \SWRarrow \\ +\hline +\end{tabular} +\end{cmd} + +%=-=-=-=-= Macros of ketlayer =-=-=-=-= +\subsection{Macros of ketlayer} +Macros of ketlayer are used in layer environment. + +Some macros take the form of connected main part and direction (``c'', ``e'', ``w'', ``s'', ``n''). +In the following we write them as ``main part + dir''. +Direction can be combine like as options of {\ketcindy} commands. +% (``ne'', ``nw'', ``se'', ``sw'') + +For example, if main part is ``\verb|putnote|'', ``\verb|putnote+dir|'' are \par +``\verb|putnotec|'', ``\verb|putnotee|'', ``\verb|putnotew|'', ``\verb|putnotes|'', ``\verb|putnoten|'', ``\verb|putnotene|'', ``\verb|putnotenw|'', ``\verb|putnotese|'', ``\verb|putnotesw|''. + +%-------------putnote+dir------------------------------- +\begin{cmd}{\bs putnote+dir}{putnote} +\itemket{Usage}\verb|\putnote+dir{x}{y}{Char}| +\itemket{Description}These functions put Char in the direction of dir of coordinates (x, y). +\itemket{}\verb|putnotec{x}{y}{Char}| puts Char with (x,y) as the center. +\itemket{}\verb|putnotee{x}{y}{Char}| puts Char on the right of (x,y). +\itemket{}\verb|putnotew{x}{y}{Char}| puts Char on the left of (x,y). +\itemket{}\verb|putnotes{x}{y}{Char}| puts Char under (x,y). +\itemket{}\verb|putnoten{x}{y}{Char}| puts Char above (x,y). +\itemket{Example}\mbox{}\\ +\verb|\putnotese{20}{10}{\fbox{$\dfrac{1}{2}$}}|\\ +\verb|\putnotec{40}{10}{\fbox{$\dfrac{1}{3}$}}|\\ + +\begin{layer}{60}{30} +\putnotese{20}{10}{\fbox{$\dfrac{1}{2}$}} +\putnotec{40}{10}{\fbox{$\dfrac{1}{3}$}} +\end{layer} +\vspace{30mm} +\end{cmd} + +%-------------boxframe+dir------------------------------- +\begin{cmd}{\bs boxframe+dir}{boxframe} +\itemket{Usage}\verb|\boxframe+dir[thickness]{x}{y}{W}{H}{Strings}| +\itemket{Description}These functions draw a rectangle with width W and height H in the direction of dir of coordinates (x, y), and put the strings inside. +\end{cmd} + +%-------------dashboxframe+dir------------------------------- +\begin{cmd}{\bs dashboxframe+dir}{dashboxframe} +\itemket{Usage}\verb|\dashboxframe+dir[thickness]{x}{y}{W}{H}{Strings}| +\itemket{Description}These functions draw a dashed rectangle with width W and height H in the direction of dir of coordinates (x, y), and put the strings inside. +\end{cmd} + +%-------------jaggyboxframe+dir------------------------------- +\begin{cmd}{\bs jaggyboxframe+dir}{jaggyboxframe} +\itemket{Usage}\verb|\jaggyboxframe+dir[thickness]{x}{y}{W}{H}{Strings}| +\itemket{Description}These functions draw a jaggy rectangle with width W and height H in the direction of dir of coordinates (x, y), and put the strings inside. +\end{cmd} + +%-------------diaboxframe+dir------------------------------- +\begin{cmd}{\bs diaboxframe+dir}{diaboxframe} +\itemket{Usage}\verb|\diaboxframe+dir[thickness]{x}{y}{W}{H}{Strings}| +\itemket{Description}These functions draw a rectangle with width W, height H, connecting diamond shapes, in the direction of dir of coordinates (x, y), and put the strings inside. +\end{cmd} + +%-------------eraser+dir------------------------------- +\begin{cmd}{\bs eraser+dir}{eraser} +\itemket{Usage}\verb|\eraser+dir[F]{x}{y}{W}{H}| +\itemket{Description}These functions erase the interior of rectangle with width W and height H in the direction of dir of coordinates (x, y). +If F=0, it don't draw border lines. By default, F=1. +\end{cmd} + +%-------------shadebox+dir------------------------------- +\begin{cmd}{\bs shadebox+dir}{shadebox} +\itemket{Usage}\verb|\shadebox+dir[F]{x}{y}{W}{H}{C1}{C2}| +\itemket{Description}These functions draw a rectangle with width W and height H in the direction of dir of coordinates (x, y), paint inside with color C1, and draw a border with color C2. +If F=0, they don't draw border lines. By default, F=0. + +\end{cmd} + +%-------------example 1------------------------------- +\vspace{5mm} + +\begin{layer}{160}{0} + \boxframese{000}{0}{30}{16}{boxframe} + \dashboxframese{035}{0}{30}{16}{dashboxframe} +\jaggyboxframese{070}{0}{30}{16}{jaggyboxframe} + \diaboxframese{105}{0}{30}{16}{diaboxframe} + \shadeboxse[0]{140}{0}{30}{16}{yellow}{black} +\end{layer} + +\vspace{15mm} +\newpage + +%-------------popframe------------------------------- +\begin{cmd}{\bs popframe}{popframe} +\itemket{Usage}\verb|\popframe[thickness]{x}{y}{Dummy}{Cs}{Dummy}{Cp}{Cf}{Strings}| +\itemket{Description}This function draws a rectangle on the lower right (se) of the coordinates \text{(x, y)}, put strings inside and add a shadow of the color Cs. +\itemket{Details}Cp is background color. Cf is border color.\par +\Ltab{18.5mm}{}{\tt Note.\ }Dummy(color name) are currently ignored.\par +\Ltab{18.5mm}{}The size of the rectangle is determined automatically from strings.\par +\Ltab{18.5mm}{}The line thickness is 8 by default.\par +\Ltab{18.5mm}{}Strings must be width$\leq$ 200 mm, height$\leq$ 100 mm. +\end{cmd} + +%-------------colorframe------------------------------- +\begin{cmd}{\bs colorframe}{colorframe} +\itemket{Usage}\verb|\colorframe[thickness]{x}{y}{Cp}{Cs}{Cf}{Strings}| +\itemket{Description}This function draws a rectangle on the lower right (se) of the coordinates \text{(x, y)}, put strings inside. +\itemket{Details}Cp is background color. Cf is border color.\par +\Ltab{18.5mm}{}{\tt Note.\ }Dummy(color name) is ignored.\par +\Ltab{18.5mm}{}The size of the rectangle is determined automatically from strings.\par +\Ltab{18.5mm}{}The line thickness is 8 by default.\par +\Ltab{18.5mm}{}Strings must be width$\leq$ 200 mm, height$\leq$ 100 mm. +\end{cmd} + +%-------------example 2------------------------------- +\vspace{15mm} +\noindent{\bf Examples.}\par +\verb|\definecolor{shade}{cmyk}{0,0,0,0.4}| $\gets$ color name ``shade'' defined.\par +\verb|\popframe[16]{40}{5}{white}{shade}{white}{cyan}{red}{\Large\tt POP frame}| \par +\verb|\colorframe[16]{90}{5}{yellow}{white}{blue}{\Large\tt COLOR frame}| \\ + +\begin{layer}{160}{0} +\definecolor{shade}{cmyk}{0,0,0,0.4} +% \popframe[16]{40}{5}{Ds}{shade}{Dp}{yellow}{green}{\Large\tt POP frame} + \popframe[16]{40}{5}{Ds}{shade}{Dp}{cyan}{red}{\Large\tt POP frame} +\colorframe[16]{90}{5}{yellow}{green}{blue}{\Large\tt COLOR frame} +\end{layer} + +\vspace{25mm} + +%-------------cirscoremark------------------------------- +\begin{cmd}{\bs cirscoremark}{cirscoremark} +\itemket{Usage}\verb|\cirscoremark[thickness]{size}| +\itemket{Description}This function draws a handwritten double circle. +\end{cmd} + +%-------------scirscoremark------------------------------- +\begin{cmd}{\bs scirscoremark}{scirscoremark} +\itemket{Usage}\verb|\scirscoremark[thickness]{size}| +\itemket{Description}This function draws a handwritten single circle. +\end{cmd} + +%-------------triscoremark------------------------------- +\begin{cmd}{\bs triscoremark}{triscoremark} +\itemket{Usage}\verb|\triscoremark[thickness]{size}| +\itemket{Description}This function draws a handwritten triangle. +\end{cmd} + +%-------------crosscoremark------------------------------- +\begin{cmd}{\bs crosscoremark}{crosscoremark} +\itemket{Usage}\verb|\crosscoremark[thickness]{size}| +\itemket{Description}This function draws a handwritten cross mark. +\end{cmd} + +\begin{layer}{170}{0} +\putnotec{30}{25}{\cirscoremark{0.8}} +\putnotec{60}{25}{\scirscoremark{0.8}} +\putnotec{90}{25}{\triscoremark{0.8}} +\putnotec{120}{25}{\crosscoremark{0.8}} +\end{layer} + +\vspace{45mm} + +%-------------lineseg------------------------------- +\begin{cmd}{\bs lineseg}{lineseg} +\itemket{Usage}\verb|\lineseg[thickness]{x}{y}{L}{|{$\theta$}\verb|}| +\itemket{Description}This function draws a line segment of length L from the coordinates (x, y) in the direction of $\theta^\circ$ degrees. +\itemket{Details}Unit of length L is mm.\par +\Ltab{18.5mm}{}The line thickness is 12 by default. Unit is milli inch\par +\Ltab{18.5mm}{}x, y, $\theta$ may be decimal. +\itemket{Example}\verb|\lineseg[16]{135}{25}{30}{25}| + +\begin{layer}{160}{0} +\lineseg[16]{60}{20}{30}{25} +%\arrowlineseg[16]{130}{50}{10}{45} +\end{layer} + +\vspace{25mm} +\end{cmd} +%-------------dashlineseg------------------------------- +\begin{cmd}{\bs dashlineseg}{dashlineseg} +\itemket{Usage}\verb|\dashlineseg[thickness]{x}{y}{L}{|{$\theta$}\verb|}| +\itemket{Description}This function draws a dash line segment of length L from the coordinates \text{(x, y)} in the direction of $\theta^\circ$ degrees. +\itemket{Details}Unit of length L is mm.\par +\Ltab{18.5mm}{}The line thickness is 12 by default. Unit is milli inch\par +\Ltab{18.5mm}{}x, y, $\theta$ may be decimal. + +\end{cmd} +%-------------arrowlineseg------------------------------- +\begin{cmd}{\bs arrowlineseg}{arrowlineseg} +\itemket{Usage}\verb|\arrowlineseg[thickness]{x}{y}{L}{|{$\theta$}\verb|}| +\itemket{Description}This function draws a arrow line segment of length L from the coordinates \text{(x, y)} in the direction of $\theta^\circ$ degrees. +\itemket{Details}The arrowhead is drawn at the starting point.\par +\Ltab{18.5mm}{}The line thickness is 12 by default. Unit is milli inch.\par +\Ltab{18.5mm}{}x, y, $\theta$ may be decimal. +\itemket{Example}\verb|\arrowlineseg[16]{60}{20}{10}{45}| + +\begin{layer}{160}{0} +%\lineseg[16]{60}{20}{30}{25} +\arrowlineseg[16]{60}{15}{10}{45} +\end{layer} + +\vspace{20mm} +\end{cmd} + +%-------------arrowhead------------------------------- +\begin{cmd}{\bs arrowhead}{arrowhead} +\itemket{Usage}\verb|\arrowhead[size]{x}{y}{|{$\theta$}\verb|}| +\itemket{Description}This function draws a arrowhead on the coordinates (x, y) in the direction of $\theta^\circ$ degrees. +\itemket{Details}The line thickness is 12 by default. Unit is milli inch.\par +\Ltab{18.5mm}{}x, y, $\theta$ may be decimal. +\end{cmd} + +%-------------hjaggyline------------------------------- +\begin{cmd}{\bs hjaggyline}{hjaggyline} +\itemket{Usage}\verb|\hjaggyline[thickness]{x}{y}{W}| +\itemket{Description}This function draws a jagged line of length W from the coordinates (x, y) to the right. +\end{cmd} + +%-------------hjaggylineb------------------------------- +\begin{cmd}{\bs hjaggylineb}{hjaggylineb} +\itemket{Usage}\verb|\hjaggylineb[thickness]{x}{y}{W}| +\itemket{Description}This function draws a jagged line of length W from the coordinates (x, y) to the right. +\itemket{Details}This function draws a reverse jagged line against ``hjaggyline''.\par +\end{cmd} + +%-------------vjaggyline------------------------------- +\begin{cmd}{\bs vjaggyline}{vjaggyline} +\itemket{Usage}\verb|\vjaggyline[thickness]{x}{y}{W}| +\itemket{Description}This function draws a jagged line of length W from the coordinates (x, y) to the right. +\end{cmd} + +%-------------vjaggylineb------------------------------- +\begin{cmd}{\bs vjaggylineb}{vjaggylineb} +\itemket{Usage}\verb|\vjaggylineb[thickness]{x}{y}{W}| +\itemket{Description}This function draws a jagged line of length W from the coordinates (x, y) to the right. +\itemket{Details}This function draws a reverse jagged line against ``vjaggyline''.\par +\end{cmd} + +%-------------example 3------------------------------- +\noindent{\bf Examples.}\par +\Ltab{18.5mm}{}\verb|\hjaggyline{40}{10}{15}| \par +\Ltab{18.5mm}{}\verb|\hjaggylineb{40}{20}{15}| \par +\Ltab{18.5mm}{}\verb|\vjaggyline{70}{10}{15}| \par +\Ltab{18.5mm}{}\verb|\vjaggylineb{90}{10}{15}| \par + +\begin{layer}{160}{0} + \hjaggyline{40}{10}{15} +\hjaggylineb{40}{20}{15} + \vjaggyline{70}{10}{15} +\vjaggylineb{90}{10}{15} +\end{layer} + +\vspace{35mm} + +%-------------circleline------------------------------- +\begin{cmd}{\bs circleline}{circleline} +\itemket{Usage}\verb|\circleline{x}{y}{size}| +\itemket{Description}This function draws a circle with (x, y) as the center. +\end{cmd} + +%-------------ballonr------------------------------- +\begin{cmd}{\bs ballonr}{ballonr} +\itemket{Usage}\verb|\ballonr[thickness]{x}{y}{size}{Char}| +\itemket{Description}This function draws a balloon in the upper right side from (x, y) and, puts Char inside. +\end{cmd} + +%-------------ballonl------------------------------- +\begin{cmd}{\bs ballonl}{ballonl} +\itemket{Usage}\verb|\ballonl[thickness]{x}{y}{size}{Char}| +\itemket{Description}This function draws a balloon in the upper left side from (x, y) and, puts Char inside. +\end{cmd} + +%-------------lefthand------------------------------- +\begin{cmd}{\bs lefthand}{lefthand} +\itemket{Usage}\verb|\lefthand[thickness]{x}{y}| +\itemket{Description}This function draws a fingertip on (x, y). +\end{cmd} + +%-------------righthand------------------------------- +\begin{cmd}{\bs righthand}{righthand} +\itemket{Usage}\verb|\righthand[thickness]{x}{y}| +\itemket{Description}This function draws a fingertip on (x, y). +\end{cmd} + +%-------------leftdownhand------------------------------- +\begin{cmd}{\bs leftdownhand}{leftdownhand} +\itemket{Usage}\verb|\leftdownhand[thickness]{x}{y}| +\itemket{Description}This function draws a fingertip on (x, y). +\end{cmd} + +%-------------rightdownhand------------------------------- +\begin{cmd}{\bs rightdwonhand}{rightdownhand} +\itemket{Usage}\verb|\rightdownhand[thickness]{x}{y}| +\itemket{Description}This function draws a fingertip on (x, y). +\end{cmd} + +%-------------example 3------------------------------- +\noindent{\bf Examples.}\par + +\begin{layer}{170}{0} + \ballonr{30}{35}{1}{Example1} + \ballonl{90}{30}{1}{Example2} + \lefthand{120}{25} + \righthand{140}{25} + \leftdownhand{120}{15} +\rightdownhand{140}{15} +\end{layer} + +\newpage + +%-==Command List ======================== +\hypertarget{functionlist}{} +\section{Command List} +%\hyperlink{index}{To index} + +\begin{tabbing} +12345678901234567890\=\kill + +{\bf Macros of ketpic} \> \\ +\hyperlink{ketpic}{\bs ketpic} \> logo of \ketpic\\ +\hyperlink{ketcindy}{\bs ketcindy} \> logo of \ketcindy\\ +\hyperlink{tab}{\bs Ltab} \> left tab\\ +\hyperlink{tab}{\bs Rtab} \> right tab\\ +\hyperlink{tab}{\bs Ctab} \> center tab\\ +\hyperlink{ketcalc}{\bs ketcalcwidth} \> returns the width of strings\\ +\hyperlink{ketcalc}{\bs ketcalcheight} \> returns the height of strings\\ +\hyperlink{ketcalc}{\bs ketcalcdepth} \> returns the depth of strings\\ +\hyperlink{ketcalcwh}{\bs ketcalcwh} \> returns the width and height of strings\\ +\hyperlink{dangerbendmark}{\bs dangerbendmark} \> symbol ``Dangerous turning point'' of Bulbaki\\ +\hyperlink{cautionmark}{\bs cautionmark} \> caution mark\\ +\hyperlink{circlemark}{\bs circlemark} \> circle\\ +\hyperlink{circleshade}{\bs circleshade} \> solid circle\\ +\hyperlink{arrow of i or d}{\bs NEarrow, ...} \> arrow of increase or decrease\\ + +{\bf Macros of ketlayer} \> \\ +\hyperlink{putnote}{\bs putnote+dir} \> puts Char\\ +\hyperlink{boxframe}{\bs boxframe+dir} \> draws a rectangle and puts strings\\ +\hyperlink{dashboxframe}{\bs dashboxframe+dir} \> draws a dashed rectangle and puts strings\\ +\hyperlink{jaggyboxframe}{\bs jaggyboxframe+dir} \> draws a jaggy rectangle and puts strings\\ +\hyperlink{diaboxframe}{\bs diaboxframe+dir} \> draws a diamond chaining rectangle and puts strings\\ +\hyperlink{eraser}{\bs eraser+dir} \> erases the interior of a rectangle\\ +\hyperlink{shadebox}{\bs shadebox+dir} \> draws a shaded rectangle and puts strings\\ +\hyperlink{popframe}{\bs popframe} \> draws a rectangle and shade with the specified color and puts strings\\ +\hyperlink{colorframe}{\bs colorframe} \> draws a rectangle with the specified color and puts strings\\ +\hyperlink{cirscoremark}{\bs cirscoremark} \> draws a handwritten double circle\\ +\hyperlink{scirscoremark}{\bs scirscoremark} \> draws a handwritten single circle\\ +\hyperlink{triscoremark}{\bs triscoremark} \> draws a handwritten triangle\\ +\hyperlink{crosscoremark}{\bs crosscoremark} \> draws a handwritten cross mark\\ +\hyperlink{lineseg}{\bs lineseg} \> draws a line segment specified angle\\ +\hyperlink{dashlineseg}{\bs dashlineseg} \> draws a dashed line segment specified angle\\ +\hyperlink{arrowlineseg}{\bs arrowlineseg} \> draws a arrow line segment specified angle\\ +\hyperlink{arrowhead}{\bs arrowhead} \> draws a arrowhead specified angle\\ +\hyperlink{hjaggyline}{\bs hjaggyline} \> draws a horizontal jaggy line segment\\ +\hyperlink{hjaggylineb}{\bs hjaggylineb} \> draws a horizontal jaggy line segment against \bs hjaggyline\\ +\hyperlink{vjaggyline}{\bs vjaggyline} \> draws a vertical jaggy line segment\\ +\hyperlink{vjaggylineb}{\bs vjaggylineb} \> draws a vertical jaggy line segment against \bs vjaggyline\\ +\hyperlink{circleline}{\bs circleline} \> draws a circle\\ +\hyperlink{ballonl}{\bs ballonl} \> draws a ballon and puts strings inside\\ +\hyperlink{ballonr}{\bs ballonr} \> draws a ballon and puts strings inside\\ +%\hyperlink{lefthand}{\bs lefthand} \> draws a leftward fingertip\\ +%\hyperlink{righthand}{\bs righthand} \> draws rightward fingertip\\ +\hyperlink{lefthand}{\bs lefthand} \> draws fingertip\\ +\hyperlink{righthand}{\bs righthand} \> draws fingertip\\ +\hyperlink{leftdownhand}{\bs leftdownhand} \> draws fingertip\\ +\hyperlink{rightdownhand}{\bs rightdownhand} \> draws fingertip\\ + +\end{tabbing} + +\end{document}
\ No newline at end of file diff --git a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/KeTpicStyleJ.tex b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/KeTpicStyleJ.tex new file mode 100644 index 00000000000..1649dd10b64 --- /dev/null +++ b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/KeTpicStyleJ.tex @@ -0,0 +1,572 @@ +\documentclass[a4j,12pt,dvipdfmx]{ujarticle} +%\documentclass[papersize,a4paper,12pt]{article} +\usepackage{ketpic,ketlayer} +\usepackage{amsmath,amssymb} +\usepackage{graphicx,color} +\usepackage{wrapfig} +%\usepackage[dvipdfmx,bookmarks=false,colorlinks=true,linkcolor=blue]{hyperref} +\usepackage[bookmarks=false,colorlinks=true,linkcolor=blue]{hyperref} +\setmargin{20}{20}{15}{25} +\usepackage{setspace} +\usepackage{comment} +\usepackage{bm,enumerate} + +\newcommand{\tab}[2][50mm]{% % \tabの定義でzwを㎜に変換した。 +\noindent +\hspace*{6.7mm}\Ltab{#1 }{{\tt #2}}% % 使用法を考えて書体\tt（タイプライタ体）を指定した。 +} + +\newcommand{\bs}{$\backslash$} + +\newcommand{\br}[1]{\{#1\}} + +\newenvironment{cmd}[2]{% "Command List" を"コマンド一覧"にした。 +\hypertarget{#2}{} +\begin{center}{\bf\large #1}\end{center} +\begin{description} +}{ +\end{description} +%\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$Command List}\end{flushright} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$コマンド一覧}\end{flushright} +} + +% item command for this documentation +\newcommand{\itemket}[1]{ +\item[\Ltab{27mm}{#1}] +} + +% item command for this documentation % 日本語マニュアル用の寸法 +\newcommand{\itemketj}[1]{ +\item[\Ltab{15mm}{#1}] +} + +\newcommand{\Chuu}[1][6.7mm]{% \chuu の15zwより狭い\Chuuは，6.7mm +\Ltab{#1}{}※ % +} + + +\西暦 + +\begin{document} +\title{{\bf\huge ketpic.sty と ketlayer.sty}} +\author{\ketcindy\ Project Team} +\maketitle + +\begin{center} - ver.1.1 -\end{center} + +%\hypertarget{index}{} +%\tableofcontents +%\newpage + +\section{概要} + +\begin{itemize} +\item パッケージの指定\\ +\quad\verb|\usepackage{ketpic, ketlayer}|\\ +\quad\verb|\usepackage{ketpic2e, ketlayer2e}| (pict2eを用いるとき) +\item \verb|\usepackage{graphicx,color}| が必要. +\item 距離変数 \bs\verb|Width|, \bs\verb|Height|,\ \bs\verb|Depth| を定義してある. +\item 10個の一時カウンタ \verb|ketpictctra|,\ $\cdots$,\ \verb|ketpicctrj| を定義してある. + +\end{itemize} + +\section{プリアンブル用マクロ(ketpic)} +\vspace{\baselineskip} +\begin{cmd}{\bs setmargin}{setmargin} +\itemketj{使用法}\verb|\setmargin{left}{right}{top}{bottom}| +\itemketj{説明}余白設定（単位はmm） +\itemketj{例}\verb|\setmargin{20}{20}{15}{25}| +\end{cmd} + +\section{本文用マクロ} +%========= Envilonment ===================== +%\setcounter{subsection}{-1} + +\subsection{方向指定} + +ketpic,ketlayer,\ketcindy では，方向を指定するのに，東西南北の頭文字 e,w,s,n を用いることがよくある．なお，中心は c． + +\hspace{60mm} n + +\hspace{50.5mm} w\hspace{5mm} c\hspace{5mm} e + +\hspace{60mm} s + + +さらに，これを組み合わせて en または en は北東すなわち右上 などとなる． + +本マニュアルでは，これらの方向を "\verb|dir|'' として表し，c,e,w,s,n が使えることを示す． + +たとえば，"\verb|putnote+dir|'' は，"\verb|putnotec|'', "\verb|putnotee|'' などとして，方向私邸を合わせて使うことを意味する． + + +%=-=-=-=-= Macros of ketpic =-=-=-=-= +\subsection{ketpicのマクロ} +ketpic のマクロは，通常の\TeX\ コマンドと同様に使用する. + +%------------ ketpic ------------ +\vspace{\baselineskip} +\begin{cmd}{\bs ketpic}{ketpic} +\itemketj{使用法}\verb|\ketpic| +\itemketj{説明}ロゴ {\ketpic} を出力. +\end{cmd} + +%------------ ketcindy ------------ +\begin{cmd}{\bs ketcindy}{ketcindy} +\itemketj{使用法}\verb|\ketcindy| +\itemketj{説明}ロゴ {\ketcindy} を出力. +\end{cmd} + +%------------ tab ------------ +\begin{cmd}{\bs Ltab, \bs Rtab, \bs Ctab}{tab} +\itemketj{使用法}\verb|\Ltab{W}{S}|, \verb|\Rtab{W}{S}|, \verb|\Ctab{W}{S}| +\itemketj{説明} +\Ltab{50mm}{{\tt \bs Ltab\br{W}\br{S}}}{}幅Wを確保してSを左寄せで書く.\\ +\tab{{\tt \bs Rtab\br{W}\br{S}}}{}幅Wを確保してSを右寄せで書く.\\ +\tab{{\tt \bs Ctab\br{W}\br{S}}}{}幅Wを確保してSを中央寄せで書く. +\itemketj{例} +\Ltab{30mm}{text}text2 + +\Rtab{30mm}{text}text2 + +\Ctab{30mm}{text}text2 + +\end{cmd} + +%------------ ketcalc ------------ +\begin{cmd}{\bs ketcalcwidth, \bs ketcalcheight, \bs ketcalcdepth}{ketcalc} +\itemketj{使用法}\verb|\ketcalcwidth[0]{C}|, \verb|\ketcalcheight[0]{C}|, \verb|\ketcalcdepth[0]{C}| +\itemketj{説明}文字列Cのサイズを単位長で計ってカウンタ\verb|ketpicctr1|に返す.オプションが1のときは, 値を表示する.\\ +\tab{\bs ketcalcwidth[0]\br{C}} 文字列Cの幅を計る.\\ +\tab{\bs ketcalcheight[0]\br{C}} 文字列Cの高さを計る.\\ +\tab{\bs ketcalcdepth[0]\br{C}} 文字列Cの深さを計る. +\itemketj{例} \verb|\ketcalcwidth[0]{abc}, \theketpicctra, \ketcalcwidth[1]{abc}| とすれば，\par +``\ketcalcwidth[0]{abc}, \theketpicctra, \ketcalcwidth[1]{abc}'' を出力する. +\end{cmd} + +%------------ ketcalcwh ------------ +\begin{cmd}{\bs ketcalcwh}{ketcalcwh} +\itemketj{使用法}\verb|\ketcalcwh{C}| +\itemketj{説明}文字列 C の幅と高さを\{width\}\{height\}の形式で返す. 単位長は\verb|mm| とする. +\itemketj{例} \verb|\ketcalcwh{abc}|とすれば，"\ketcalcwh{abc}'' を出力する. +\end{cmd} + +%------------ dangerbendmark ------------ +\begin{cmd}{\bs dangerbendmark}{dangerbendmark} +\itemketj{使用法}\verb|\dangerbendmark[size]| +\itemketj{説明}「ブルバキの危険な曲がり角」" {\dangerbendmark[1.2]} '' を出力する. +\end{cmd} + +%------------ cautionmark ------------ +\begin{cmd}{\bs cautionmark}{cautionmark} +\itemketj{使用法}\verb|\cautionmark[size]| +\itemketj{説明}注意書きのマーク`` {\cautionmark[1.2]}'' を出力する. +\end{cmd} + +%------------ circlemark ------------ +\begin{cmd}{\bs circlemark}{circlemark} +\itemketj{使用法}\verb|\circlemark[thickness]{size}| +\itemketj{説明}円を出力する. size=1のとき, 円の直径は4mm. +\end{cmd} + +%------------ circleshade ------------ +\begin{cmd}{\bs circleshade}{circleshade} +\itemketj{使用法}\verb|\circleshade[thickness]{size}{density}| +\itemketj{説明}中塗りの円を出力する. 中塗りの濃さをdensity で指定する. +\itemketj{例} \verb|\circleshade[8]{1.2}{0.3}| で \circleshade[8]{1.2}{0.3} が出力される. +\end{cmd} + +%------------ arrow of increase or decrease ------------ +\begin{cmd}{\bs dir+arrow/Larrow/Rarrow}{arrow of i or d} +\itemketj{使用法}\verb|\arrow[size]|の頭部に，方向を大文字で付加する． + +\hspace{8mm}{\bs Larrow}, {\bs Rarrow} は凹凸用の湾曲した矢印． +\itemketj{説明}増減矢印を出力する．sizeは倍率． +\itemketj{例} \mbox{} + +\vspace{-3mm}\hspace{16mm} +\begin{tabular}{|rl|rl|rl|rl|} +\hline + \verb|\NEarrow| & \NEarrow & \verb|\SEarrow| & \SEarrow & \verb|\NWarrow| & \NWarrow & \verb|\SWarrow| & \SWarrow \\ +\hline +\verb|\NELarrow| & \NELarrow & \verb|\SELarrow| & \SELarrow & \verb|\NWLarrow| & \NWLarrow & \verb|\SWLarrow| & \SWLarrow \\ +\hline +\verb|\NERarrow| & \NERarrow & \verb|\SERarrow| & \SERarrow & \verb|\NWRarrow| & \NWRarrow & \verb|\SWRarrow| & \SWRarrow \\ +\hline +\end{tabular} +\end{cmd} + +%=-=-=-=-= Macros of ketlayer =-=-=-=-= +\subsection{ketlayerのマクロ} +ketlayer のマクロは，layer環境の中で使用する.\\ + +%%==========layer環境========== +%\subsection*{layer環境} + +%------------layer-------------------------------- +\begin{cmd}{layer環境について}{layer} +\itemketj{使用法}\verb|\begin{layer}[Ho]{W}{H}|\ $\cdots$\ \verb|\end{layer}| +\itemketj{説明}メモや図表を配置するためのpicture環境を定義して，方眼を描く.\\ +\Chuu W：方眼の幅，H：方眼の高さ，Ho：方眼の水平移動\\ +\Chuu 長さの単位はいずれもmmである.（水平移動のデフォルトは0）\\ +\Chuu \verb|H=0|のとき, 方眼を描かない. \verb|H<0|のとき, 上側に方眼を描く. + +\itemketj{例} \mbox{}\\ +\verb|\begin{layer}{120}{30}|\\ +\verb|\putnotec{20}{10}{abc}|\\ +\verb|\putnotes{60}{0}{\input{Fig/FigE.tex}}|\\ +\verb|\end{layer}| + +\vspace{5mm} + +\begin{layer}{120}{30} +\putnotec{20}{10}{abc} +\putnotes{60}{0}{\input{Fig/FigE.tex}}\end{layer} +%% "FigE.tex" is copy of "addax2.tex" + +\vspace{35mm} + +\item[注意]対象物の配置が決まれば，\verb|\begin{layer}{120}{0}|とすることで方眼が消えて思い通りの配置が得られる. +\end{cmd} + +%-------------putnote+dir------------------------------- +\begin{cmd}{\bs putnote+dir}{putnote} +\itemketj{使用法}\verb|\putnote+dir{x}{y}{Char}| +\itemketj{説明}{\bs putnote}に続く\verb|dir| 指定により，次のように配置する．\\ +\tab{\bs putnotec\br{x}\br{y}\br{Char}} (x, y) を中心にCharを配置する.\\ +\tab{\bs putnotee\br{x}\br{y}\br{Char}} (x, y) の右にCharを配置する.\\ +\tab{その他，s,n,neなども同様} +\itemketj{例}\verb|\putnotese{20}{10}{\fbox{$\dfrac{1}{2}$}}|\\ +\hspace{7mm}\verb|\putnotec{40}{10}{\fbox{$\dfrac{1}{3}$}}|\\ + +\begin{layer}{60}{30} +\putnotese{20}{10}{\fbox{$\dfrac{1}{2}$}} +\putnotec{40}{10}{\fbox{$\dfrac{1}{3}$}} +\end{layer} +\vspace{30mm} +\end{cmd} + +%-------------boxframe+dir------------------------------- +\begin{cmd}{\bs boxframe+dir}{boxframe} +\itemketj{使用法}\verb|\boxframe+dir[thickness]{x}{y}{W}{H}{Strings}| +\itemketj{説明}(x, y) の dir 方向に，幅W, 高さH の矩形を描き，中に文字を入れる. \\ +\Chuu 線の太さ(thickness)のデフォルトは8とする. +\itemketj{例}{\bs shadebox+dir} にまとめて例示． + +\end{cmd} + +%-------------dashboxframe+dir------------------------------- +\begin{cmd}{\bs dashboxframe+dir}{dashboxframe} +\itemketj{使用法}\verb|\dashboxframe+dir[thickness]{x}{y}{W}{H}{Strings}| +\itemketj{説明}(x, y) の dir 方向に，破線の矩形を描き，中に文字を入れる． +\itemketj{例}{\bs shadebox+dir} にまとめて例示． +\end{cmd} + +%-------------jaggyboxframe+dir------------------------------- +\begin{cmd}{\bs jaggyboxframe+dir}{jaggyboxframe} +\itemketj{使用法}\verb|\jaggyboxframe+dir[thickness]{x}{y}{W}{H}{Strings}| +\itemketj{説明}(x, y) の dir 方向に，ギザの矩形を描き，中に文字を入れる． +\itemketj{例}{\bs shadebox+dir} にまとめて例示． +\end{cmd} + +%-------------diaboxframe+dir------------------------------- +\begin{cmd}{\bs diaboxframe+dir}{diaboxframe} +\itemketj{使用法}\verb|\diaboxframe+dir[thickness]{x}{y}{W}{H}{Strings}| +\itemketj{説明}(x, y) の dir 方向に，ダイヤ型を連ねた矩形を描き，中に文字を入れる． + \itemketj{例}{\bs shadebox+dir} にまとめて例示． +\end{cmd} + +%-------------eraser+dir------------------------------- +\begin{cmd}{\bs eraser+dir}{eraser} +\itemketj{使用法}\verb|\eraser+dir[F]{x}{y}{W}{H}| +\itemketj{説明}(x, y) の dir 方向の長方形の内部を消す.\\ +\Chuu F=0 とすると枠を描かない(デフォルトは F=1). +\end{cmd} + +%-------------shadebox+dir------------------------------- +\begin{cmd}{\bs shadebox+dir}{shadebox} +\itemketj{使用法}\verb|\shadebox+dir[F]{x}{y}{W}{H}{C1}{C2}| +\itemketj{説明}(x, y) の dir 方向に，矩形を描き，内部を色C1で塗る.\\ +\Chuu F=1 なら枠線を色C2で描く (デフォルトは F=0 : 枠線を描かない). + +\vspace{\baselineskip} +以下に，\verb|boxframe|系のコマンドを例示する．\\ +\verb| \begin{layer}{160}{0}|\\ +\verb| \boxframese{000}{0}{30}{16}{boxframe}|\\ +\verb| \dashboxframese{035}{0}{30}{16}{dashboxframe}|\\ +\verb| \jaggyboxframese{070}{0}{30}{16}{jaggyboxframe}|\\ +\verb| \diaboxframese{105}{0}{30}{16}{diaboxframe}|\\ +\verb| \shadeboxse[0]{140}{0}{30}{16}{yellow}{black}|\\ +\verb| \end{layer}| + +\vspace{\baselineskip} +\begin{layer}{160}{0} +\boxframese{000}{0}{30}{16}{boxframe} +\dashboxframese{035}{0}{30}{16}{dashboxframe} +\jaggyboxframese{070}{0}{30}{16}{jaggyboxframe} +\diaboxframese{105}{0}{30}{16}{diaboxframe} +\shadeboxse[0]{140}{0}{30}{16}{yellow}{black} +\end{layer} + +\vspace{15mm} +\end{cmd} +%-------------popframe------------------------------- +\begin{cmd}{\bs popframe}{popframe} +\itemketj{使用法}\verb|\popframe[thickness]{x}{y}{ダミー色}{色s}{ダミー色}{色p}{色f}{文字列}| +\itemketj{説明}(x, y) の 右下(se方向)に，文字入りの矩形を描き，色sの陰を付ける. \\ +\Chuu 色p：背景色，色f：枠の色. +(ダミー色には適当な色を入れる)\\ +%% Ds, Dp は空白でもよい。 +\Chuu 矩形の大きさは文字列から自動計算する.\\ +\Chuu 線の太さ(thickness)のデフォルトは8とする.\\ +\Chuu 文字列は，幅$\leqq$ 200mm, 高さ$\leqq$ 100mm とすること. +\itemketj{例}{\bs colorframe} にまとめて例示． +\end{cmd} + +\vspace*{-5mm} +%-------------colorframe------------------------------- +\begin{cmd}{\bs colorframe}{colorframe} +\itemketj{使用法}\verb|\colorframe[thickness]{x}{y}{色p}{ダミー色}{色f}{文字列}| +\itemketj{説明}(x, y) の 右下(se方向)に，文字入りの矩形を描く. \\ +\Chuu 色p：背景色，色f：枠の色．(ダミー色には適当な色を入れる)\\ +\Chuu 矩形の大きさは文字列から自動計算する.\\ +\Chuu 線の太さ(thickness)のデフォルトは8とする.\\ +\Chuu 文字列は，幅$\leqq$ 200mm, 高さ$\leqq$ 100mm とすること.\\ + +\itemketj{例}色 "shade'' を定義しておく． + +%\verb|\definecolor{shade}{cmyk}{0,0,0,0.4}| $\gets$ 色``shade'' を定義.\par +\verb|\popframe[16]{40}{5}{white}{shade}{white}{cyan}{red}{\Large\tt POP frame}| \par +\verb|\colorframe[16]{90}{5}{yellow}{white}{blue}{\Large\tt COLOR frame}| \\ + +\begin{layer}{160}{0} +\definecolor{shade}{cmyk}{0,0,0,0.4}% CMYK方式 +% \popframe[16]{40}{5}{Ds}{shade}{Dp}{yellow}{green}{\Large\tt POP frame} + \popframe[16]{40}{5}{white}{shade}{white}{cyan}{red}{\Large\tt POP frame} +\colorframe[16]{90}{5}{yellow}{white}{blue}{\Large\tt COLOR frame} +%\colorframe[16]{90}{5}{yellow}{}{blue}{\Large\tt COLOR frame} +\end{layer} + +\vspace{25mm} +\end{cmd} + +%-------------cirscoremark------------------------------- +\begin{cmd}{\bs cirscoremark}{cirscoremark} +\itemketj{使用法}\verb|\cirscoremark[thickness]{size}| +\itemketj{説明}手書きの2重丸を出力する. +\itemketj{例}{\bs crosscoremark} のあとにまとめて例示． +\end{cmd} + +%-------------scirscoremark------------------------------- +\begin{cmd}{\bs scirscoremark}{scirscoremark} +\itemketj{使用法}\verb|\scirscoremark[thickness]{size}| +\itemketj{説明}手書きの単丸を出力する. +\itemketj{例}{\bs crosscoremark} のあとにまとめて例示． +\end{cmd} + +%-------------triscoremark------------------------------- +\begin{cmd}{\bs triscoremark}{triscoremark} +\itemketj{使用法}\verb|\triscoremark[thickness]{size}| +\itemketj{説明}手書きの三角を出力する. +\itemketj{例}{\bs crosscoremark} のあとにまとめて例示． +\end{cmd} + +%-------------crosscoremark------------------------------- +\begin{cmd}{\bs crosscoremark}{crosscoremark} +\itemketj{使用法}\verb|\crosscoremark[thickness]{size}| +\itemketj{説明}手書きのバツを出力する. + +\begin{layer}{170}{0} +\putnotec{30}{15}{\cirscoremark{0.8}} +\putnotec{60}{15}{\scirscoremark{0.8}} +\putnotec{90}{15}{\triscoremark{0.8}} +\putnotec{120}{15}{\crosscoremark{0.8}} +\end{layer} + +\vspace{35mm} +\end{cmd} +%-------------lineseg, dashlineseg------------------------------- +\begin{cmd}{\bs lineseg, \bs dashlineseg}{lineseg} +\itemketj{使用法}\verb|\lineseg[thickness]{x}{y}{L}{|{$\theta$}\verb|}|\\ +\tab{\bs dashlineseg[thickness]\br{x}\br{y}\br{L}\br{$\theta$}} +\itemketj{説明}{\tt \bs lineseg}は，点 (x, y) から長さ L の線分を $\theta^\circ$ 方向に描く(単位はmm). \\ +\tab{\bs dashlineseg は破線を描く.}\\ +\Chuu 線の太さ (thickness)のデフォルトは 12 (単位は milli inch).\\ +\Chuu x, y, $\theta$ は小数でもよい. +\itemketj{例}\verb|\lineseg[16]{135}{25}{30}{25}| + +\begin{layer}{160}{0} +\lineseg[16]{60}{20}{30}{25} +%\arrowlineseg[16]{130}{50}{10}{45} +\end{layer} + +\vspace{20mm} +\end{cmd} +%%-------------dashlineseg------------------------------- +%\begin{cmd}{\bs dashlineseg}{dashlineseg} +%\itemketj{使用法}\verb|\dashlineseg[thickness]{x}{y}{L}{|{$\theta$}\verb|}| +%\itemketj{説明}点 (x, y) から長さ L の破線を $\theta^\circ$ 方向に描く(単位はmm). \\ +%%\itemket{Details}Unit of length L is mm.\par +%%\Ltab{18.5mm}{}The line thickness is 12 by default. Unit is milli inch\par +%%\Ltab{18.5mm}{}x, y, $\theta$ may be decimal. +%% +%\end{cmd} +%-------------arrowlineseg------------------------------- +\begin{cmd}{\bs arrowlineseg, \bs arrowhead}{arrowhead} +\itemketj{使用法}\verb|\arrowlineseg[thickness]{x}{y}{L}{|{$\theta$}\verb|}|\\ +\tab{\bs arrowhead[size]\br{x}\br{y}\br{$\theta$}} +\itemketj{説明}{\tt \bs arrowlineseg}は，点 (x, y) から長さ L の矢印を $\theta^\circ$ 方向に描く(単位はmm).\\ +\Chuu 鏃は始点(x, y)に描く. \\ +\Chuu 線の太さ (thickness)のデフォルトは 12 (単位は milli inch).\\ +\tab{\bs arrowhead は鏃だけを描く.}\\ +\Chuu x, y, $\theta$ は小数でもよい. +\itemketj{例}\verb|\arrowlineseg[16]{60}{20}{10}{45}| + +\vspace*{-5mm} +\begin{layer}{160}{0} +%\lineseg[16]{60}{20}{30}{25} +\arrowlineseg[16]{60}{20}{10}{45} +\end{layer} + +\vspace{20mm} +\end{cmd} + +%%-------------arrowhead------------------------------- +%\begin{cmd}{\bs arrowhead}{arrowhead} +%\itemketj{使用法}\verb|\arrowhead[size]{x}{y}{|{$\theta$}\verb|}| +%\itemketj{説明}This function draws a arrowhead on the coordinates (x, y) in the direction of $\theta^\circ$ degrees. +%\itemket{Details}The line thickness is 12 by default. Unit is milli inch.\par +%\Ltab{18.5mm}{}x, y, $\theta$ may be decimal. +%\end{cmd} + +%-------------hjaggyline------------------------------- +\begin{cmd}{\bs hjaggyline, \bs hjaggylineb}{hjaggyline} +\itemketj{使用法}\verb|\hjaggyline[thickness]{x}{y}{W}|\\ +\tab{\bs hjaggylineb[thickness]\br{x}\br{y}\br{W}} +\itemketj{説明}{\tt \bs hjaggyline}は，(x, y) から右に幅Wのギザ線を描く. +b を付加すると，線の出方が逆になる. +\end{cmd} + +%%-------------hjaggylineb------------------------------- +%\begin{cmd}{\bs hjaggylineb}{hjaggylineb} +%\itemketj{使用法}\verb|\hjaggylineb[thickness]{x}{y}{W}| +%\itemketj{説明}This function draws a jagged line of length W from the coordinates (x, y) to the right. +%\itemket{Details}This function draws a reverse jagged line against ``hjaggyline''.\par +%\end{cmd} + +%-------------hjaggyline------------------------------- +\begin{cmd}{\bs vjaggyline, \bs vjaggylineb}{vjaggyline} +\itemketj{使用法}\verb|\vjaggyline[thickness]{x}{y}{W}|\\ +\tab{\bs vjaggylineb[thickness]\br{x}\br{y}\br{W}} +\itemketj{説明}{\tt \bs vjaggyline}は，(x, y) から下に幅Wのギザ線を描く. +b を付加すると，線の出方が逆になる. +\itemketj{例}次のようになる． + +\begin{layer}{160}{0} +\hjaggyline{70}{10}{10} +\hjaggylineb{70}{20}{10} +\vjaggyline{100}{10}{10} +\vjaggylineb{120}{10}{10} +\end{layer} + +\verb|\hjaggyline{70}{10}{10}| \\ +\verb|\hjaggylineb{70}{20}{10}| \\ +\verb|\vjaggyline{100}{10}{10}| \\ +\verb|\vjaggylineb{120}{10}{10}| \\ + +\end{cmd} +%-------------circleline------------------------------- +\begin{cmd}{\bs circleline}{circleline} +\itemketj{使用法}\verb|\circleline{x}{y}{size}| +\itemketj{説明}(x, y) を中心に円を描く. +\end{cmd} + +%-------------ballonr------------------------------- +\begin{cmd}{\bs ballonr, \bs ballonl}{ballon} +\itemketj{使用法}\verb|\ballonr[thickness]{x}{y}{size}{Char}|\\ +\tab{\bs ballonl[thickness]\br{x}\br{y}\br{size}\br{Char}} +\itemketj{説明}{\tt \bs ballonr}は (x, y) から右上に吹き出しと Char を描く.\\ +\tab[0mm]{}{{\tt \bs ballonl}は (x, y) から左上に吹き出しと Char を描く.} +\end{cmd} + +%-------------lefthand------------------------------- +\begin{cmd}{\bs lefthand, ...}{lefthand} +\itemketj{使用法}\verb|\lefthand[thickness]{x}{y}|\\ +\tab{\bs righthand[thickness]\br{x}\br{y}}\\ +\tab{\bs leftdownhand[thickness]\br{x}\br{y}}\\ +\tab{\bs rightdownhand[thickness]\br{x}\br{y}} +\itemketj{説明}(x, y) に，それぞれの向きで指先を描く. +\itemketj{例} {\bs ballon }などの例 + +\begin{layer}{170}{0} + \ballonr{30}{35}{1}{Example1} + \ballonl{90}{30}{1}{Example2} + \lefthand{120}{25} + \righthand{140}{25} + \leftdownhand{120}{15} +\rightdownhand{140}{15} +\end{layer} +\vspace{30mm} +\end{cmd} + +\newpage + +%-==Command List ======================== +\hypertarget{functionlist}{} +\section{コマンド一覧} +%\hyperlink{index}{To index} + +\begin{tabbing} +12345678901234567890\=\kill + +{\bf ketpicのマクロ} \> \\ +\hyperlink{arrow of i or d}{\bs arrow, ...} \> 増減矢印\\ +\hyperlink{cautionmark}{\bs cautionmark} \> 注意書きのマーク\\ +\hyperlink{circlemark}{\bs circlemark} \> 円（サイズ指定）\\ +\hyperlink{circleshade}{\bs circleshade} \> 中塗りの円（サイズ指定）\\ +\hyperlink{tab}{\bs Ctab} \> 中央寄せタブ\\ +\hyperlink{tab}{\bs Ltab} \> 左寄せタブ\\ +\hyperlink{tab}{\bs Rtab} \> 右寄せタブ\\ +\hyperlink{dangerbendmark}{\bs dangerbendmark} \> ブルバキの「危険な曲がり角」\\ +\hyperlink{ketcalc}{\bs ketcalcdepth} \> 文字列の深さを計る\\ +\hyperlink{ketcalc}{\bs ketcalcheight} \> 文字列の高さを計る\\ +\hyperlink{ketcalc}{\bs ketcalcwidth} \> 文字列の幅を計る\\ +\hyperlink{ketcalcwh}{\bs ketcalcwh} \> 文字列の幅と高さを計る\\ +\hyperlink{ketcindy}{\bs ketcindy} \> ロゴ \ketcindy\ を出力\\ +\hyperlink{ketpic}{\bs ketpic} \> ロゴ \ketpic\ を出力\\ + +{\bf ketlayerのマクロ} \> \\ +\hyperlink{arrowhead}{\bs arrowhead} \> 角度を指定して鏃だけ描く\\ +\hyperlink{arrowhead}{\bs arrowlineseg} \> 角度を指定した矢印\\ +\hyperlink{ballon}{\bs ballonl, \bs ballonr} \> 吹き出しと文字列\\ +\hyperlink{boxframe}{\bs boxframe+dir} \> 文字入りの矩形\\ +\hyperlink{circleline}{\bs circleline} \> レイヤー環境での円\\ +\hyperlink{cirscoremark}{\bs cirscoremark} \> 手書きの2重丸\\ +\hyperlink{colorframe}{\bs colorframe} \> 文字列に合わせたサイズの矩形（色指定）\\ +\hyperlink{crosscoremark}{\bs crosscoremark} \> 手書きのバツ\\ +\hyperlink{dashboxframe}{\bs dashboxframe+dir} \> 文字入りの矩形（破線）\\ +\hyperlink{diaboxframe}{\bs diaboxframe+dir} \> 文字入りの矩形（ダイヤ型を連ねた）\\ +\hyperlink{eraser}{\bs eraser+dir} \> 長方形の内部を消す\\ +\hyperlink{hjaggyline}{\bs hjaggyline(b)} \> 水平なギザ線分\\ +\hyperlink{jaggyboxframe}{\bs jaggyboxframe+dir} \> 文字入りの矩形（ギザ線）\\ +\hyperlink{lefthand}{\bs lefthand, ...} \> 指先（4つ）\\ +\hyperlink{lineseg}{\bs lineseg, \bs dashlineseg} \> 角度を指定した線分と破線\\ +\hyperlink{popframe}{\bs popframe} \> 文字列に合わせたサイズの矩形（色指定，影付き）\\ +\hyperlink{putnote}{\bs putnote+dir} \> 文字・図・表の配置\\ +\hyperlink{scirscoremark}{\bs scirscoremark} \> 手書きの単丸\\ +\hyperlink{shadebox}{\bs shadebox+dir} \> 文字入りの矩形（中塗り）\\ +\hyperlink{triscoremark}{\bs triscoremark} \> 手書きの三角\\ +\hyperlink{vjaggyline}{\bs vjaggyline(b)} \> 垂直なギザ線分\\ +%\hyperlink{ballonr}{\bs ballonr} \> draws a ballon and puts strings inside\\ +%\hyperlink{dashlineseg}{\bs dashlineseg} \> draws a dashed line segment specified angle\\ +%\hyperlink{hjaggylineb}{\bs hjaggylineb} \> draws a horizontal jaggy line segment against \bs hjaggyline\\ +%\hyperlink{leftdownhand}{\bs leftdownhand} \> draws fingertip\\ +%\hyperlink{lineseg}{\bs dashlineseg} \> draws a dashed line segment specified angle\\ +%\hyperlink{rightdownhand}{\bs rightdownhand} \> draws fingertip\\ +%\hyperlink{righthand}{\bs righthand} \> draws fingertip\\ +%\hyperlink{vjaggylineb}{\bs vjaggylineb} \> draws a vertical jaggy line segment against \bs vjaggyline\\ + + +\end{tabbing} + +\end{document}
\ No newline at end of file diff --git a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/referenceR4_2_2_ltd.tex b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/referenceR4_2_2_ltd.tex deleted file mode 100644 index f77574b88f4..00000000000 --- a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/referenceR4_2_2_ltd.tex +++ /dev/null @@ -1,1422 +0,0 @@ -\documentclass[a4j]{jarticle} - -\usepackage{ketpic,ketlayer} -\usepackage{amsmath,amssymb} -\usepackage{enumerate} -%\usepackage{emathE} - -\newcommand{\tab}[2][12zw]{% -\noindent -\hspace*{2zw}\Ltab{#1 }{#2}% -} - -\newcommand{\chuu}[1][15zw]{% -\Ltab{#1}{}※ % -} - -\newcommand{\rei}[1][18zw]{% -\Rtab{#1}{例)\ }}% - -\newcommand{\reicr}[1][18zw]{% -\Rtab{#1}{ }}% - -\newcommand{\prompt}[1][+]{% -$>$ \verb#1} - -\newcommand{\dq}[1]{ -{\unitlength$<$- 0.0012in% -\begin{picture}% -(26.30,94.50)(2.40,0.00)% -\special{pn 8}% -\special{pa 3 -113}\special{pa 6 -78}\special{pa 12 -78}\special{pa 15 -113}\special{pa 3 -113}% -\special{sh 1}\special{ip}% -\special{pa 22 -113}\special{pa 25 -78}\special{pa 31 -78}\special{pa 34 -113}\special{pa 22 -113}% -\special{sh 1}\special{ip}% -\end{picture}}% -\,#1\,% -{\unitlength$<$- 0.0012in% -\begin{picture}% -(26.30,94.50)(2.40,0.00)% -\special{pn 8}% -\special{pa 3 -113}\special{pa 6 -78}\special{pa 12 -78}\special{pa 15 -113}\special{pa 3 -113}% -\special{sh 1}\special{ip}% -\special{pa 22 -113}\special{pa 25 -78}\special{pa 31 -78}\special{pa 34 -113}\special{pa 22 -113}% -\special{sh 1}\special{ip}% -\end{picture}}% -} - -\newcommand{\bq}{ -\hspace*{-2pt}% -{\unitlength=1pt% -\begin{picture}% -(1.80,7.00)(-0.90,0.00)% -\special{pn 8}% -% -\special{pn 12}% -\special{pa -11 -94}\special{pa 11 -72}% -\special{fp}% -\special{pn 8}% -\end{picture}}% -} - -\newenvironment{mini}[1]% -{\begin{minipage}[t]{#1}}% -{\end{minipage}% -} - - -%\enumSep{\narrowenumsep} - -\setmargin{15}{15}{15}{20} - -\begin{document} - -\begin{flushright} -2013年10月6日 -\end{flushright} - -\begin{center} -{\bf \huge \ketpic\ v4.2.2 ltd コマンド一覧}\vspace{3mm}\\ -{\bf \huge for R} -\end{center} - -\hfill -\begin{minipage}{4cm} -\Ltab{1.5cm}{PD}プロットデータ\\ -\end{minipage} - -%\vspace*{-2zw} - -\section{R についての注意} - -\begin{enumerate}[1.] - -\item KETpicの読込みには次を実行する．\\ -\hspace*{2zw}load("C:/work/ketpic.Rdata") （C:/work/は作業フォルダ名）\\\hspace*{-12zw}\chuu ディレクトリの変更は setwd("c:/work") - -\item 文字列は "（ダブル）で囲む\\ -\chuu 文字列の中に文字列を入れるときは ' と " を入れ子に使う． - -\item 関数などを引数とするときは，文字列とする．\\ -\hspace*{2zw}例）G$<$- Plotdata( "x\verb|^|2", "x=c(0,1)") -%\hspace*{2zw}注）プログラミングでは文字列を実行するコマンド evstr, execstr が重要である． -%\item -%数リスト，文字列，行列が混ざったデータ（基本データ）のリストはできない． -%Mixは混合リストを扱う． -%\hspace*{3zw}基本データ$\longrightarrow$混合列$\longrightarrow$混合リスト% -%$\longrightarrow$混合リスト$\longrightarrow\cdots$ - -\item \verb|\|（バックスラッシュ）を出力するには２つ並べてかく． - - -\item 注釈は \verb|#| - -%\item 実行の中断は abort - - -%\item 数値微分は derivative, 数値積分は integrate（またはintg） - -%\chuu Derivative, Integrate 参照 - -\item 数と文字列の変換\\ -\hspace*{2zw}as.character(数)\\ -\hspace*{2zw}as.numeric(文字列)\\ -\hspace*{2zw}eval(parse(text=文字列)))\\ -\hspace*{2zw}sprintf(書式,\ 数) 書式付き文字列 - -\item 異なる型のデータからリストを作るにはlistを用いる．\\ -\hspace*{2zw}作成 L\verb|<-| list(... , ... );\\ -\hspace*{2zw}取り出し A\verb|<-| L[[i]]\\ -\hspace*{2zw}部分リスト L[V]\ (V はベクトル)\\ -\hspace*{2zw}置き換え L[[i]]\verb|<-| ...\\ -%\hspace*{2zw}消去 L[[i]]<- NULL\\ -\hspace*{2zw}長さ length(L)\\ -\hspace*{2zw}追加 L\verb|<-| c(L1, L2)\\ -\hspace*{2zw}結合 c(L1,L2,...)\\ -\hspace*{2zw}空リスト list()\\ -\hspace*{2zw}タイプを見る is.list(L)（論理値）または mode(L) - -\end{enumerate} - -\section{Rのための追加コマンド} - -\tab{Member(D, L)}DがLの要素であればtrue，そうでなければfalseを返す．\\ -\chuu Lはベクトルまたは list - -\tab{Flattenlist(L)}Lを平準化して単層のリストを作る - -%\tab{Mix(D1, D2, $\cdots$)}FD列，MS，MLから（１段上の）MSまたはMLを作成 - -%\tab{Mixadd(L, D)}L（MSまたはML)にDを要素として加える - -\tab{Mixdisp({\it list})}listの要素を画面に簡易表示 - -%\tab{Mixjoin(L1, L2, ...)}要素を合併したlistを作る\\ -%\rei L1$<$- list(G1,G2,3); L2$<$- list(G3, "a")\\ -%\reicr L$<$- Mixjoin(L1,L2, c(3,6))\\ -%\reicr \hspace{2cm}LはG1, G2, 3, G3, "a", c(3, 6)のlist\\ -%\chuu \verb|c() , list()| は無視される - -%\tab{MixL(D1,D2, $\cdots$)}MS, MLから（１段上の）MLを作成 - -%\tab{Mixlength(L)}L（MSまたはML)の要素の個数 - -%\tab{Mixop(N, Data)}DataのN番目の要素（DataはMS, ML) - -%\tab{MixS(D1,D2, $\cdots$)}基本データ列からMSを作成 - -%\tab{Mixsub（範囲，L)}Lの範囲（リスト）の要素からなる部分MSまたはML\\ -%\rei S$<$- Mixsub( 2; 5, L); - -%\tab{Mixtype(Data)}Dataが基本データなら１，MSなら２，MLなら３を返す - -\tab{Op(N,\ Data)}DataのN番目の要素（Dataは文字列，ベクトル，list） - -\tab{Assign(式, 変数名, 値, ・・・)}\\ -\tab{}変数名（文字列）に値を割り当てた文字列を返す\\ -\chuu 値は，数，文字列，数行列，Scilablist\\ -\rei A$<$- 0.4; B$<$- c(2,1)\\ -\reicr Fn$<$- Assign("A*x\^{}2+B(1)*y\^{}2","A", A, "B", B) - -\tab{Assignset(変数名, 値, ・・・)}% -割り当て変数テーブルをセットする\\ -\rei Assignset("A", 0.4, "B", c(2,1), "C", list(...), "D", "string") - -%\tab{Assign(式)}式文字列の変数に割り当て変数リストを割り当てた文字列を返す\\ -%\rei Assign("A", 0.4, "B", c(2,1))\\ -%\reicr Fn$<$- Assign("A*x\^{}2+B(1)*y\^{}2") - -\tab{Assignset("?"+変数名)}変数名の値を返す\\ -\rei Assignset("?A") - -\tab{Assignset()}割り当て変数テーブルを初期化\\ -%\rei Assign("A", 0.4, "B", c(2,1))\\ -%\reicr Assign() - -\tab{Assignadd(変数名, 値, ・・・)}\\ -\tab{}割り当て変数テーブルに追加する\\ -\rei Assignadd("C", 0.4, "D", c(2,1)) - -\tab{Assignrep(変数名, 値, ・・・)}\\ -\tab{}割り当て変数テーブルを置き換える\\ -\rei Assignrep("C", 0.8) - -\tab{Prime(文字列)}文字列の最後に " をつける\\ -\rei Prime("A")\\ -\rei Prime() （" だけを出力）\\ -\chuu Assign("A\bq ") としてもよい． - - -%\tab{Strop(N,\ 文字列)}文字列のN番目の文字 - -%\tab{Subs(代入式,\ 有理式)}有理式に代入式で与えられる数値を代入した値を返す\\ -%\rei X$<$- poly(0,"X")\\ -%\reicr F$<$- X\verb|^|2+3\verb|*|X+3\\ -%\reicr V$<$- Subs("X$<$- 5",\ F) - -\tab{XMIN, XMAX, YMIN, YMAX}\\ -\tab{}ウィンドウ範囲 -（デフォルト$-5\leqq x\leqq 5,\ -5\leqq y\leqq 5$） - -\tab{Ptne(),Ptnw(),Ptsw(),Ptse()}\\ -\tab{}フレーム枠の各点 - -\tab{ThisVersion}Ketpicのバージョン - -\tab{Fracform(x\{, 分母の最大値\})}\\ -\tab{}xに近い分数（文字列）を返す\\ -\chuu 分母の最大値のデフォルトは100000\\\ -\rei Fracform(c(2.36)) - -\tab{Dotprod(v1,v2)}内積 - -\tab{Crossprod(v1,v2)}外積 - -\tab{Derivative(関数文字列，変数名，\{値ベクトル\}}\\ -\tab{}関数の微分係数を求める．\\ -\rei Derivative("x\verb|^|2+y", c("x","y"),c(2, 3))\\ -%\rei Assign("A", 3)\\ -%\reicr Derivative(Assign("x\verb|^|2+A*y"), "c(x,y)", c(2, 3), 2)\\ -%\chuu 変数の番号を指定しないときは，列ベクトルで返す． - -\tab{Integrate(関数文字列，変数文字列，積分区間（数リスト）)}\\ -\tab{}関数の定積分を求める．\\ -\rei Integrate("sin(x)","x",c(0,pi))\\ -\chuu 区間（リスト）は積分を分けて計算するときに指定\\ -%\reicr Fn(x)","if x>0,Y$<$- 1,else,Y$<$- -1,end")|\\ -\reicr \verb|Integrate("Fn(x)","x",c(-2,0,3))|\\ - -%\tab{Thetadegree()}平行投影で$\theta$（度） - -%\tab{Phidegree()}平行投影で$\varphi$（度） - -%\vspace{-2zw} - -\section{設定コマンド} - -\subsection{基本} - -\tab{Setwindow(c(xmin, xmax), c(ymin, ymax))}\\ -\tab{}ウィンドウ範囲を設定\\ -\rei Setwindow(c(-pi, pi),\ $c(-1.5,1.5)$\,)\\ -\chuu XMIN , XMAX , YMIN , YMAX で値を得られる． - -\tab{Setscaling({\it ratio})}\\ -\tab{}縦の横に対する比を{\it ratio}に設定（デフォルトは 1）\\ -\rei Setscaling(2)\\ -\chuu ウィンドウも連動 - -\tab{Setax(線種, 横軸名, 位置, 縦軸名, 位置, 原点名, 位置)}\\ -\tab{}座標軸を設定（引数 7 個）\\ -\rei Setax("a", "t", "s", "u", "w", "O", "nw")\\ -\chuu 線種は d : line , a : arrow\\ -\chuu arrowのとき "a0.5" のように，矢印の大きさを指定できる．\\ -\chuu ""とすると，現在の設定を変更しない．\\ -\chuu 以降が "" のとき省略できる．また途中からも指定できる\\ -\rei Setax("a"\,)\\ -\rei Setax(6, "O", "se"\,) （6番目から指定）\\ -\chuu 位置は"n", "s", "e", "w", "ne", "nw", "se", "sw"\\ -\chuu "s2w3"のように微小移動量を付加してよい．\\ -\chuu 空引数のとき，現在の設定値を表示 - -\tab{Setorigin(\,点\,)}座標軸の原点を指定（デフォルトは$(0,\ 0)$）\\ -\chuu 空引数のとき，現在の設定値を表示 - -\tab{Setpen( 倍率 )}線の太さを指定（標準からの倍率で）\\ -\rei Setpen(1.5)\\ -\chuu 空引数のとき，現在の設定値を表示 - -\tab{Setpt( 倍率 )}Drwptの点の大きさを指定（標準からの倍率で）\\ -\chuu 空引数のとき，現在の設定値を表示 - -\tab{Setmarklen( 倍率 )}目盛りの大きさを指定（標準からの倍率で）\\ -\chuu 目盛りの大きさは微小移動量の単位としても用いられる．\\ -\chuu 空引数のとき，現在の設定値を表示 - -\tab{Setunitlen("単位長")}単位長を指定する\\ -\chuu Beginpicture("")とすると指定された単位長が使われる.\\ -\chuu 空引数のとき，現在の設定値を表示 -%\tab(13zw){resetunitlen()}コード書き出しを終える - -\tab{Setarrow(鏃の大きさ \{, 開き角 \{, 鏃位置 \{, 太さ\}\}\} \{, 形と位置\})}\\ -\tab{}矢印の形状を指定する\\ -\rei Setarrow(0.5, 1, 1, 0.7, "tf"\,)\\ -\chuu デフォルト 大きさ１ ，角度 18°，位置は終点\\ -\chuu 5以下の開き角を指定したときは，18°からの倍率とする\\ -\chuu 形状\ "l" ：ライン "f" ：塗り（デフォルト）\\ -\chuu 位置微調整\ "c"：中央 "b"：下 "t"：トップ(〃）\\ -\chuu 空引数のとき，現在の設定値を表示 - -\tab{Ketinit(\,)}定数をデフォルトに初期化 - -\subsection{空間（平行投影）} - -\tab{Setangle(\,$\theta, \varphi$\,)}角度（°）を指定\\ -\chuu デフォルト値は $\theta$<$- 60,\ \varphi$<$- 30$\\ -\chuu 空引数のとき，現在の設定値を表示 - -\tab{Initangle(\,)}デフォルト値に戻す - -\subsection{空間（一点投影）} - -\tab{Setpers(\,注視点，視点\,)}一点投影のFocusPoint,\ EyePoint を指定\\ -\chuu デフォルト値は FocusPoint$<$- c(0,0,0),\ EyePoint$<$- c(5,5,5) - -\tab{Setpers()}現在のFocusPoint,\ EyePoint を表示\\ -\chuu 空引数のとき，現在の設定値を表示 - -\tab{SetstereoL(\,$R,\ \theta,\ \varphi,\ \varDelta$\,)}% -原点を注視点として，空間極座標により定まる左目の位置を\\ -\tab{}視点にセット（$\varDelta$は目の間隔） - -\tab{SetstereoR(\,$R,\ \theta,\ \varphi,\ \varDelta$\,)}% -原点を注視点として，空間極座標により定まる右目の位置を\\ -\tab{}視点にセット（$\varDelta$は目の間隔） - -\section{プロットデータの作成} - -\subsection{平面図形} - -\tab{Plotdata(関数,範囲,オプション)}\\ -\tab{}関数のグラフのPDを作成\\ -\rei G1$<$- Plotdata(\,"sin(x)",\ "x= c($-2$*pi,\ 2*pi)")\\ -\chuu 範囲を "x" とすると，XMINからXMAXにとる．\\ -\chuu x 以外の変数を使うときは関数に使われていないかを注意．\\ -\chuu オプション\\ -\hspace*{16zw}\tab[6zw]{"N=$\cdots$"}点の個数\\ -\hspace*{16zw}\tab[6zw]{"E=c($\cdots$)"}除外点のリスト\\ -\hspace*{16zw}\tab[6zw]{"E=関数"}関数の０点は除外\\ -\hspace*{16zw}\tab[6zw]{"D=$\cdots$"}連続限界値（これ以上離れたら結ばない）\\ -\chuu デフォルトはN=50, D=Inf \\ -%\chuu 関数は function で与えてもよい．\\ -\rei G1$<$- Plotdata("1/x", "x","N=200", "E=c(0)", "D=1")\\ -\rei G2$<$- Plotdata("1/((x-1)*(x+2))", "x", "E=(x-1)*(x+2)")\\ - -\tab{Listplot(点のベクトルまたは列またはlist)}\\ -\tab{}折れ線のPDを作成. ただし、点は線分で結ぶ. \\ -\rei G2$<$- Listplot(c(c(3,2),c(5,4)))\\ -\rei G2$<$- Listplot(c(3,2),c(5,4)) - -\tab{Lineplot(点A, 点B\{ , 長さ，半直線\})}\\ -\tab{}線分ABを延長した線分のPDを作成 \\ -\rei G3$<$- Lineplot(c(3,2),c(5,4))\\ -\rei G4$<$- Lineplot(A, B, "+")\\ -\reicr 半直線AB（B側に延長）\\ -\chuu 長さのデフォルトは片側100 - -\tab{Paramplot(パラメトリック関数,範囲,オプション)}\\ -\tab{}パラメトリック関数のグラフのPDを作成\\ -\chuu t 以外の変数を使うときは関数に使われていないかを注意\\ -%\chuu 関数は function で与えてもよい．\\ -\rei G3$<$- Paramplot(\,"c(cos(t),\ sin(t))",\ "t=c(0, 2*\%pi)")\\ -%\rei G4$<$- Paramplot(Fnx, Fny, "t=c(0, 1)") - -\tab{Rotatedata(PDまたは点,角度\{,中心\})}\\ -\tab{}平面のPDを回転したPDを作成 \\ -\rei G4$<$- Rotatedata(G1,pi/4) - -\tab{Translatedata(PD,\ x方向 y方向)}\\ -\tab{}PDを平行移動したPDを作成 \\ -\rei G5$<$- Translatedata(\,G1,\ 3,\ $-1$\,) - -\tab{Scaledata(PD, x方向, y方向\{,中心\})}\\ -\tab{}PDを拡大(縮小)したPDを作成 \\ -\rei G6$<$- Scaledata(\,G1,\ 2,\ 1/3\,) - -\tab{Reflectdata(PD,点)}点対称移動したPDを作成\\ -\tab{Reflectdata(PD, c(\,点1,点2\,))}\\ -\tab{}線対称移動したPDを作成\\ -\rei G7$<$- Reflectdata(\,G1,\ c(0,0)\,)\\ -\rei G8$<$- Reflectdata(\,G1,\ c(\,c(0,0),\ c(0,1)\,)\,) - -\tab{Pointdata(PD,\ $\cdots$)}PDの節点のlistを作成\\ -\rei G9=Pointdata(G1)\\ -\chuu Drwpt(G9)などで，点のプロットができる． - -\tab[21zw]{Circledata(中心,\ 半径\ \{,\ オプション\}\})}円のPDを作成\\ -\rei G10$<$- Circledata(\,c(3,1),\ 2\,) \\ -\chuu オプション\\ -\hspace*{16zw}\tab[5zw]{"R=..."}$\theta$の範囲\\ -\hspace*{16zw}\tab[5zw]{"N=..."}点の個数\\ -\rei G10a$<$- Circledata(\,c(3,1),\ 2,\ "R=c(0,\ pi/2)"\,)\\ -\rei G10b$<$- Circledata(\,c(3,1),\ 2,\ "N=100"\,) - -\tab{\,Framedata(P,\ dx\{,\ dy\})\,}% -点Pを中心に$\pm$dx,\ $\pm$dyの矩形（dyを省略するとdy$<$- dx）\\ -\rei G3$<$- Framedata(c(3,\ 1),\ 0.5\,) - -\tab[12zw]{\,Framedata(${\rm c}(x_1,\ x_2),\ {\rm c}(y_1,\ y_2)$)\,\\}% -\tab{}$x_1 \leqq x \leqq x_2,\ y_1 \leqq y \leqq y_2$の矩形のPDを作成（右上から反時計）\\ -\chuu 引数が空のとき，Setwindowで指定した枠\\ -\rei G1$<$- Framedata(${\rm c}(-2,\ 3)$,\ ${\rm c}(1,\ 4)$\,) \\ -\rei G2$<$- Framedata() - -\tab{Hatchdata( パターン文字(list)\{, 開始点\}, (閉)曲線の列\{,kaku\{,haba\}\,\}\,)}\\ -\tab{}パターンと一致する領域を斜線塗りするPDを作成\\ -\rei G1$<$- Hatchdata(list("io"),\ list(g1,g2),\ list(g3)\,)\\ -\mbox{}\hfill（i : 内部，o: 外部）\\ -\chuu 開始点が指定されたとき\\ -\hfill（仮想的に）その点を通る斜線から描き始める\\ -%\chuu パターンがリストのとき，どれかと一致する領域を斜線塗り\\ -\chuu% -\begin{mini}{23zw} -kakuは斜線の傾き(def=45)，habaは間隔（def=1） -\end{mini}\vspace{1mm}\\ -\rei G2$<$- Hatchdata(\,list("ii"),\ O,\ list(G1),\ $-45$,\ 1.5\,)\\ -\chuu 曲線リスト内のPDは隣接の順に指定\\ -\chuu 閉じていないとき\\ -\hspace*{18zw}(1)方向 "s","n","w","e" を指定する\\ -\hspace*{18zw}(2)窓枠とちょうど2点で交わる場合、領域の点を指定\\ -\hspace*{18zw}(3)指定しなければ端点を直線で結ぶ.\\ -\rei G3$<$- Hatchdata(list("ii),\ list(g1,"s"),\ list(g2,\ c(3,0))\,) - -\tab{Hatchdata( 領域の点）\{, 開始点\}, (閉)曲線listの列\{,kaku\{,haba\}\,\}\,)}\\ -\tab{}点（のどれか）が含まれる領域を斜線塗り\\ -\rei F4$<$- Hatchdata(list(A,B,C),\ \ list(G1),\ list(G2,G3)\,)\\ -\hspace*{4zw}\chuu % -\begin{mini}{23zw} -包含パターンが点A, B, Cのどれかと一致する領域を斜線塗り（領域は隣接するものとする） -\end{mini}\vspace{2mm} - -%\tab{enclosing( P, PDリスト )}PD列からPを囲む閉曲線となる部分曲線のPD列を作成\\ -%\rei G1$<$- enclosing(\,c(1,0),\ c(g1,\ g2,\ invert(g3))\,)\\ -%\chuu PD列は隣接順に指定する（向きが一致するようにする） - -%\tab{enclosing( n, PDリスト )}% -%PD列からできる閉曲線のうちn番目のPD列を作成\\ -%\rei G2$<$- enclosing(\,1,\ c(g1,\,g2,\,invert(g3))\,)\\ -%\chuu 0を指定すると，全ての閉曲線のリストを返す． - -\tab{Enclosing( PDリスト\{, 始点の近くの点\} )}\\ -\tab{}PD列の直近の交点を結んで閉曲線を作成\\ -\rei G2$<$- Enclosing(list(G1,\,invert(G2),\,G3),\,c(2,1)\,)\\ -\tab[14zw]{}G1と (最後の)G3の交点のうち，c(2,1)に近い点から始める\\ -\chuu 交点が１個の場合は，点を省略してよい． - -\tab{Dotfilldata( パターン文字列（リスト）\{, 開 始点\}, -(閉)曲線PDリストの列\{,濃さ\})}\\ -\tab{}パターンと一致する領域を点描するPDを作成\\ -\rei Fd$<$- Dotfilldata("ii",list(G1),list(G2),0.7)\\ -\chuu 濃さ$d$は $0< d \leqq 1$（デフォルトは$0.5$）\\ -\chuu 書き出しは，Drwptを用いる． - -\tab{Arrowdata}矢印のPDを作成（Arrowline参照）\\ -\chuu やじりは塗りつぶさず，線データのみ - -\tab{Arrowheaddata}やじりだけのPDを作成（Arrowhead参照） - -\tab[20zw]{Bowdata(\,$\mbox{点A},\ \mbox{点B}$\{,\ 曲がり\{,\ 切り\}\,\}\,)}\\ -\tab{}弓形のPDを作成\\ -\chuu 曲がり：弧の曲がり（デフォルトは1）\\ -\chuu 切り：中央に入れる切りの長さ（デフォルトは0）\\ -\chuu 点AからBに反時計まわりに弧をかく\\ -\rei G$<$- Bowdata(\,c(2,\ 1),\ c(3,\ 4),\ 0.8,\ 0.5\,) - -%\tab{Bowmiddle(\,$\mbox{点A},\ \mbox{点B}$\{,\ 曲がり\})}\\ -%\tab{}弓形の中点と角のlistを返す - -\tab{Bowmiddle(\,弧データ\ )}弓形の中点を返す - -\tab{Splinedata(点データ\{, オプション\}\})}\\ -\tab{}spline曲線のPDを作成\\ -%\chuu ファイルは，space, comma, tab 区切りのtextファイル\\ -%\chuu 開始位置：ファイルの読込み開始行と列．defaultはc(2,\ 1)\\ -\chuu 点データはリストまたはPD\\ -\chuu オプション：\\ -\hspace*{18zw}"N$<$- 点の個数" （デフォルトは50）\\ -\hspace*{18zw}"C" （閉曲線でスムーズにつなぐ）\\ -%\rei Fs$<$- Splinedata("c:/data.txt",\ c(2,4),\ "N$<$- 100")\\ -\rei Fs$<$- Splinedata(PL, "N$<$- 200", "C")（PLは点データ） - -%\tab{Skeleton2data(\,平面曲線list1，平面曲線list2\{,大きさ% -%\{,\ 遠近の閾値\}\}\,)}\\ -%\tab{}list2で隠されるlist1のスケルトンデータを作成 - -\tab{Anglemark(A, B, C \{, サイズ \})}\\ -\tab{}$\angle \mathrm{ABC}$の間の角度記号を作成\\ -\chuu BAからBCへ反時計回りに描く\\ -\chuu サイズのデフォルトは0.5 - -\tab{Paramark(A, B, C \{, サイズ\})}\\ -\tab{}$\angle \mathrm{ABC}$の間の角度記号（平行四辺形）を作成 - -%\tab{Sumfun(\{ 定数項, \}一般項, 添字のリスト，変数の範囲，\{ 点の個数 \})}\\ -%\tab{} $\displaystyle c+\sum_{k= a}^{b}f(x,\ k)$のPDを作成（{\bf Scilabに追加}）\\ -%\chuu 定数項が0のときは省略できる．\\ -%\chuu 点の個数は "N$<$- 個数" で指定（デフォルトは終わりまで）\\ -%\rei G1$<$- Sumfun(1, "x\verb|^|n/factorial(n)", "n$<$- 1:5", "x$<$- c($-2,\ 2)$") - -%\tab{Implicitplot(関数，x範囲，y範囲\{, 分割数\})}\\ -%\tab{Implicitplot(Zvalue, Xvalue, Yvalue) }\\ -%\tab{}陰関数のPDを作成\\ -%\chuu 分割数のデフォルトは c(50, 50)\\ -%\rei \verb|G1$<$- Implicitplot("x^2+y^2-1","x$<$- c(-1,1)","y$<$- c(-1,1)")| - -%\tab{Deqplot(方程式，x範囲，x0，y0\{, 分割数\})}\\ -%\tab{}微分方程式の解曲線のPDを作成\\ -%\chuu $y"$は y\bq と書く．\\ -%\chuu xの範囲を省略すると，描画範囲全体\\ -%\rei \verb|G1$<$- Deqplot("y|\bq \verb|$<$- y*(1-y)","x",0,0.2,"N$<$- 100")|\\ -%\rei \verb|G2$<$- Deqplot"("y|\bq\bq \verb|$<$- -0.4*y`-3*y","x$<$- c(0,5)",0,c(0,2))| -%\rei \verb|G3$<$- Deqplot("c(x,y)|\bq \verb|$<$- c(x*(1-y),0.3*y*(x-1))",...|\\ -%\reicr \verb| "t$<$- c(0,20)",0,c(1,0.5),"N$<$- 200")| - -% - -\subsection{空間図形} - -\tab{Spaceline(\,空間点のベクトルまたはlist\,)}\\ -\tab{}空間点を結ぶ線分のPD3dを作成\\ -\rei G1$<$- Spaceline(\,c(c(3,\ 2,\ 1),\ c(5,\ 6,\ 6))\,) - -\tab{Spacecurve(\,関数,範囲,オプション\,)}\\ -\tab{}空間曲線のPD3dを作成\\ -\rei G2$<$- Spacecurve( "c(cos(t),\ sin(t),\ t)",\ "t$<$- c(0, 2*\%pi)" ) - -\tab{Rotate3data(PD3, v1, v2\ \{, 中心\})}\\ -\tab{}PD3をv1がv2に重なるように回転したPD3dを作成\\ -\rei G2$<$- Rotate3data(\,G1, c(1, 0, 0), c(1, 2, 3)\,)\\ -\chuu PD3はlistでもよい（この場合はlistを返す） - -\tab{Rotate3datac(PD3, 回転軸, 角度\ \{, 中心\})}\\ -\tab{}PD3を回転軸のまわりに回転したPD3dを作成\\ -\rei G2$<$- Rotate3datac(\,G1, c(0, 0, 1), \%pi/4\,)\\ -\chuu PD3はlistでもよい（この場合はlistを返す） - -\tab{Translata3data(PD3, 移動ベクトルv)}\\ -\tab{}PD3をvだけ移動したPD3dを作成\\ -\rei G2$<$- Translate3datac(\,G1, c(3, 2, 1)\,)\\ -\rei G2$<$- Translate3datac(\,G1, 3, 2, 1\,)\\ -\chuu PD3はlistでもよい（この場合はlistを返す） - -\tab{Xyzax3data(\,$x$範囲, $y$範囲, $z$範囲\,)}\\ -\tab{}座標軸のPD3dのlistを作成 - -\tab{Projpara(\,PD3列またはlist\,)}\\ -\tab{}空間曲線の平行投影による射影PD( 2d )を作成 - -\tab{Projpers(\,PD3列またはlist\,)}\\ -\tab{}空間曲線の一点投影による射影PD( 2d )を作成 - -\tab{Skeletonparadata(\,空間曲線list1，空間曲線list2\{,大きさ% -\{,\ 遠近の閾値\}\}\,)}\\ -\tab{}\begin{mini}{30zw} -平行投影でlist1からlist2により隠される部分を除いた残りの平面PD列 -（スケルトンデータ）を作成\vspace*{2mm} -\end{mini} - -\tab{Skeletonpara3data(\,空間曲線list1，空間曲線list2\{,大きさ% -\{,\ 遠近の閾値\}\}\,)}\\ -\tab{}\begin{mini}{30zw} -平行投影でlist1からlist2により隠される部分を除いた残りの空間PD列 -（スケルトンデータ）を作成\vspace*{2mm} -\end{mini} - -\tab{Skeletonpersdata(\,空間曲線list1，空間曲線list2\{,大きさ% -\{,\ 遠近の閾値\}\}\,)}\\ -\tab{}一点投影でlist2によるlist1のスケルトンデータ(2D)を作成 - -\tab{Skeletonpers3data(\,空間曲線list1，空間曲線list2\{,大きさ% -\{,\ 遠近の閾値\}\}\,)}\\ -\tab{}一点投影でlist2によるlist1のスケルトンデータ(3D)を作成 - -\tab{Embed(\,平面曲線（リスト），埋め込み関数\,)}\\ -\tab{}埋め込み関数により空間曲線を作成\\ -\rei \verb|deff("Out$<$- Fun(x,y)","Out$<$- c(x,y,0)")|\\ -\reicr \verb|G1$<$- Listplot(c(0,0),c(3,2))|\\ -\reicr \verb|G1_3d$<$- Embed(G1,Fun)| - -% -\subsection{多面体の描画} - -\tab{Phcutdata(頂点リストVL, 面添字リストFL, 平面データPlaneD)}\\ -\tab{}多面体を平面で切ったときの多面体と切断面の3dリストを作成\\ -\chuu PlaneD（平面）の形式\\% -\hspace*{18zw}\begin{mini}{20zw} -"a*x+b*y+c*z-d",\ "a*x+b*y+c*z$<$- d"\\ -\hspace*{2zw}（x,\ y,\ zをクリアしておく）\\ -または "c(a, b, c, d)"\\ -\hspace*{4zw} "list(a, b, c, P)"（点Pを通る） -\end{mini}\vspace{2mm}\\ -\chuu 切断面はリストの最後の要素\\ -\rei VL$<$- list(c(0, 0, 0), c(1, 0, 0), c(0, 1, 0), c(0, 0, 1))\\ -\reicr FL$<$- list(c(1, 2, 3), c(1, 2, 4), c(1, 3, 4), c(2, 3, 4))\\ -\reicr PL$<$- Phcutdata(VL, FL, "c(1, 1, 1, 3)")\\ -\reicr Windisp(PL) - -\tab{Phcutoffdata(VL, FL, PlaneD, 符号)}\\ -\tab{}PlaneDで切断された部分多面体の3dデータリストを作成\\ -\chuu 符号は \verb|"+"| または \verb|"-"|\\ -\rei PL$<$- Phpcutoffdata(VL, FL, "x+y+(z-1/2)", "+")\\ -\chuu PhVertexL(), PhFaceL()で頂点，面リストを取り出せる． - -\tab{Phparadata(VL, FL)}陰線処理をした多面体のPD3d（平行投影）を作成\\ -\tab{Phpersdata(VL, FL)}陰線処理をした多面体のPD3d（一点投影）を作成\\ -\chuu PhHiddenData()で陰線のPDを取り出せる． - -\tab{Phsparadata(面datalist)}複数の多面体のPD3d（平行投影）を作成（陰線処理）\\ -\tab{Phspersdata(面datalists)}複数多面体のPD3d（一点投影）を作成（陰線処理）\\ -\chuu 面datalistはlist(VL, FL)，または，そのlist\\ -\chuu 面を点で直接指定するときには VL$<$- list()とする．\\ -\rei Fd$<$- list(list(),list(c(3,2,1),c(0,0,0),c(c(1,2,4)))\\ -\chuu PhHiddenData()で陰線のPDを取り出せる． - -\tab{Phsrawparadata(面datalist), Phsrawpersdata(面datalist)}\\ -\tab{}複数の多面体のPD3dを作成（陰線処理をしない） - -\tab{Facesdata(面datalist \{ ,追加曲線PDlist \}, 射影のタイプ)}\\ -\tab{}面の辺（と追加曲線）を面により陰線処理\\ -\chuu 射影のタイプは "para"，"pers"，"rawpara’，"rawpers" - -\tab{Faceremovaldata(面datalist，曲線PDlist, 射影のタイプ)}\\ -\tab{}曲線を面により陰線処理 - -\section{データの書き出し} - -\subsection{基本コマンド} - -\tab{Windisp( PD列またはlist )}\\ -\tab{}画面を開き，PD列を表示（確認のため）\\ -\rei Windisp(\,G1,\ G2\,)\\ -\rei Windisp(list(G1,G2)) - -\tab{WindispT( PD列またはlist \{, オプション\} )}\\ -\tab{}画面を開き，PD列を表示（確認のため）図を重ねて表示する．事前にWindispT()\\ -\rei WindispT(\,G1,\ G2\,color="red",width=1,new=TRUE\,)\\ -\rei WindispT(list(col="blue",border="white",G1),new=TRUE) \\ -\hspace*{18zw}(閉曲線G1を塗る)\\ -\rei WindispT(list(col="blue",border="white",density=200,G1,G2),new=TRUE)\\ -\hspace*{18zw} (閉曲線G1,G2を塗る.densityは内側を線分で塗りつぶす場合のパラメータ) - -\tab{Openfile('ファイル名'\,\{ソースファイル名\}) }\\ -\tab{}書き出し用ファイルを開く（デフォルトは画面）\\ -\rei setwd("C:/TeXF") \\ -\reicr Openfile(\, "fig.tex"\,)\\ -\reicr Openfile(\,'fig.tex',\,'fig.r'\,)\\ -\chuu ソースが同一フォルダにあるときは，第２引数は不要 - -\tab{Beginpicture("単位長"\,)}picture 環境を始める．\\ -\rei Beginpicture("1cm"\,)\\ -\rei Beginpicture("2*10/12cm"\,) - -\tab{Endpicture(\,1\,)}picture 環境を終える（座標軸をかく）\\ -\tab{Endpicture(\,0\,)}picture 環境を終える（座標軸をかかない） - -\tab{Closefile(\,)\,}書き出し用ファイルを閉じる（デフォルト＝画面に戻す） - -\subsection{プロットデータ} - -\tab{Drwline(\,PD列またはlist\{, 太さ\}\,)}\\ -\tab{}PD列またはを実線で書き出す\\ -\rei Drwline(\,G1,\ G2\,)\\ -\rei Drwline(\,G3,\ 0.5\.) - -\tab{Dashline(\,PD列またはlist\{, len \{, gap\}\,\}\,)}\\ -\tab{}PD列またはlistを破線で書き出す（実線部から始まる）\\ -\rei Dashline(\,G1,\ G2\,)\\ -\rei Dashline(\,G1,\ 1.5\,)\hfill（実線部，ギャップとも 1.5倍）\\ -\rei Dashline(\,G1,\ G2,\ 1.5,\ 0.5\,)\\ -\hfill（実線部 1.5倍，ギャップ 0.5倍） - -\tab{Invdashline(\,PD列またはlist\{, len\{, gap\}\,\}\ )}\\ -\tab{}破線を書き出す（ギャップから始まる） - -\tab{Dottedline(\,PD列またはlist\{, len \{, size\}\,\}\,)}\\ -\tab{}点線を書き出す\\ -\rei Dottedline(\,G1,\ G2\,)\\ -\rei Dottedline(\,G1,\ 1.5\,) （間隔 1.5倍）\\ -\rei Dottedline(\,G1,\ G2,\ 1,\ 0.5\,)（点の大きさ 0.5倍） - -\tab{Arrowline(\,A, B \{, 鏃の大きさ \{, 開き角 \{, 鏃位置 \{, 太さ\}\,\}\,\} \{, \\ -\hspace*{20zw}形と位置 -,\ "Cut=切り込み率"\}\,\}\,)}\\ - -\tab{}点AからBに向けて矢印をかくコードを書き出す\\ -\rei Arrowline(\,A,\ B\,)\\ -\rei Arrowline(\,A,\ B,\ 2,\ 10,"l"\,)\\ -\rei Arrowline(\,A,\ B,\ 1,\ 18,\ 0.5,\ 2,"lc"\,)\\ -\hspace*{6zw}\chuu ABの中点の位置に鏃をかく - - -\tab{Arrowhead(\,位置,\ 方向\{,\ 大きさ\{,\ 角度\},\ 形状と位置,\ "Cut=切り込み率"\}\,)} - -\tab{}鏃だけを書き出す\\ -\rei Arrowhead(\,c(0,\ 0),\ c(2,\ 1),\ "cl"\,) - -\tab{Arrowhead(\,P,\ PD\{,\ 大きさ\{,\ 角度\},\ 形状と位置\}\,)}\\ -\tab{}PD上の点Pに矢印を描く\\ -\rei Arrowhead(\,c(1,\ 1),\ Plotdata("x\^{}2","x"\,))\\ -\chuu 鏃はライン - -\tab{Drwpt(点の列 \{, 塗り\})}点を書き出す（大きさは Setptで指定，塗りのデフォルトは1）\\ -\rei Drwpt(\,c(2,\ 3),\ c(5,\ 7)\,) - -\tab{Drwxy(\,)}座標軸を書き出す - -\tab{Htickmark( 座標, 方向, 数式 , $\cdots$ )}\\ -\tab{}横軸上に目盛りをつける（方向のデフォルトは"s"\,） - -\tab{Vtickmark( 座標, 方向, 数式 , $\cdots$ )}\\ -\tab{}縦軸上に目盛りをつける（方向のデフォルトは"w"\,）\\ -\rei Htickmark(\,$-1$,"$-1$",\ 1,"1",\ pi,"$\backslash$pi"\,)\\ -\rei Vtickmark(\ $-1$,"e","$-1$",\ 1,"ne","1"\,)\\ -\rei Htickmark(c(2,1),\ "a"\,)\\ -\chuu 数式を省略すると目盛りだけをつける - -\tab{Htickmark("m..n..r..")}横軸全体に目盛りをつける - -\tab{Vtickmark("m..n..r.."\,)}縦軸全体に目盛りをつける\\ -\chuu m（目盛りの間隔），n（文字を何目盛り毎に），r（数の倍率）\\ -\rei Htickmark("mn")（目盛りと数を１間隔でつける）\\ -\rei Vtickmark("m1n2r1.5")（1.5倍した数を１つとびに） - -\tab[13zw]{Shade(\,PD列またはlist\{, 濃さ\}\,)\mbox{}}\\ -\tab{}閉曲線の内部を塗りつぶし 濃さ: 0 〜 1（デフォルトは１） - -\subsection{文字の書き入れ} - -\tab{Letter(\ 点, 方向, 文字列 ，・・・)}\\ -\tab{}点の位置の「方向」に文字列をかく（複数可）\\ -\rei Letter(\,c(4,\ 3),"n","文字")\\ -\chuu 位置は"n", "s", "e", "w", "ne", "nw", "se", "sw", "c"\\ -\chuu "n1" nの方向にさらに1目盛長だけ離す．\\ -\chuu "s-1w2" s方向に-1目盛長，w方向に2目盛長だけ離す． - -\tab{Expr(\ 点, 方向, 数式，・・・)}点の位置の「方向」に数式をかく（\$\$は不要）\\ -\rei Expr(c(4, 3),"s","y=f(x)") - -\tab{Letterrot(\ 点, 方向\ \{, 接線方向\ \{, 法線方向\}\}, 文字列)}\\ -\tab{Exprrot(\ 点, 方向\ \{, 接線方向\ \{, 法線方向\}\}, 文字列)}\\ -\tab{}「点」の位置に「方向」を右横方向にするように文字を傾けて書く\\ -\chuu 「接線方向」，「法線方向」はそれぞれの微少移動量\\ -\chuu graphicxパッケージが必要 - -\tab{Texletter(\ 点(list形式), 方向, 文字列 ，・・・)}\\ -\tab{}点の位置の「方向」に文字列をかく（複数可）\\ -\rei Texletter(\,list(4,,\ "\#1"),"n","文字")\\ -\chuu 位置は"n", "s", "e", "w", "ne", "nw", "se", "sw", "c"\\ -\chuu 点の位置はリスト形式で，\TeX の文字列を渡すことができる． - -\tab{Openphr(\,ユーザーコマンド名\,)，Closephr(\,)}\\ -\tab{}$\backslash$defのコマンド定義\\ -\rei Openphr("$\backslash$p"\,)\\ -\reicr Texcom("$\backslash$begin\{array\}\{cc\}"\,)\\ -\reicr Texcom("5 \& 3$\backslash\backslash$"\,)\\ -\reicr Texcom("8 \& 7"\,)\\ -\reicr Texcom("$\backslash$end\{array\}\$"\,)\\ -\reicr Closephr(\,) - -\tab{Openpar(\,ユーザーコマンド名，幅 \{ 縦方向 \}\,), Closepar(\,)}\\ -\tab{}minipage環境を含む$\backslash$def コマンド定義\\ -\rei Openpar("$\backslash$s","5cm", "t"\,)\\ -\reicr Texcom("$\backslash$input\{rei\}"\,)\\ -\reicr Closepar(\,)\\ -\reicr Letter(\,c(2,\ 3),"se","$\backslash$s"\,)\\ -\chuu 縦方向のデフォルトは c - -\tab{Fontsize("記号"\,)}文字サイズの変更コマンドを書き出す\\ -\tab[13zw]{}"n", "s", "f",% - "ss", "t", \\ -\tab[13zw]{}"la", "La", % -"LA", "h", "H"（""\,のとき"n"\,）\\ -\rei Fontsize("s") - -\tab{Texcom("コマンド"\,)}\TeX コマンドのコードを書き出す\\ -\rei Texcom("$\backslash$newcounter\{tmpct\}")\\ -\chuu "newline" のとき，空白行を挿入 - -\tab{Bowname(弓形，数式 )}弓形PDの中央に式を書き入れる\\ -\rei Gb$<$- Bowdata( A, B, 1, 0.5)\\ -\reicr Bowname(Gb, "d") - -\tab{Bownamerot( 弓形，数式\{，向き\} )}\\ -\tab{}弓形PDの中央に式を傾けて書き入れる\\ -\chuu graphicxパッケージが必要\\ -\chuu 向きに $-1$を指定すると向きが反対になる - -\tab{Xyzaxparaname(\,軸データ \{, 各軸のラベル名 \}\{，離れ\}\,)}\\ -\tab{}平行投影で，各軸のラベルを書き入れる\\ -\rei Gax$<$- Xyzax3data( "x$<$- c(0,1)", "y$<$- c(0,1)", "z$<$- c(0,2)" )\\% ($x,y,z$を書く）\\ -\reicr Xyzaxparaname(Gax)\\% ($x,y,z$を書く）\\ -\chuu "\yen sin x" など文字列で指定することもできる - -\tab{Xyzaxpersname(\,軸データ \{, 各軸のラベル名 \}\{，離れ\}\,)}\\ -\tab{}一点投影で，各軸のラベルを書き入れる\\ -\rei Xyzaxpersname(Gax, "", "", "w") - -%\vspace*{-0.5zw} - -%\vspace*{-2zw} - -\section{プロットデータの操作} - -\subsection{平面} - -\tab{Joingraphics(PD1,PD2,・・・\{ , "L" \})}\\ -\tab{}複数のPDを１つのPDに合併 \\ -\reicr G11$<$- Joingraphics(\,F9,\ G10\,)\\ -\chuu "L"を指定したときは，結果をリストで返す - -\tab{Dividegraphics(PD)}PDを要素に分けたlistを作成\\ -\rei FL$<$- Dividegraphics(G1)\\ -\rei G1$<$- Op(1, FL) - -\tab{Joincrvs(\,PD列\,)}複数の曲線をつなげたPDを作成（2D, 3D共通）\\ -\rei G3$<$- Joincrvs(\,G1,\ Invert(G2)\,)\\ -\chuu 曲線は隣接する順番で指定する - -\tab{Invert( PD )}PDの点列を逆順にしたPDを作成（2D, 3D共通） - -%\tab{connectseg(PD)}細切れの線分を結ぶPDリストを作成\\ -%\hspace*{-4zw}\rei connectseg(implicitplot(x\textasciicircum 2+y\textasciicircum 2$<$- 1,x$<$- -2..2,y$<$- -2..2)) - -\tab{Partcrv(\,s1,\ s2, PD\,)}曲線PD上のパラメータ値s1, s2を両端とするPDを作成\\ -\chuu s1 $>$ s2 の場合\\ -\hspace*{180pt}s2から終点，始点からs1までのPDのリストを出力\\ -\hspace*{180pt}PDが閉曲線のときは上の２つのPDをつなげる． - -\tab{Partcrv(\,A, B, PD\,)}曲線PD上の点A, Bの間の部分曲線のPDを作成\\ -\chuu -\begin{mini}{23zw}% -A, Bの順序が逆転しているとき，Bから終点，始点からAまでのPDのリスト（閉のとき接続）を出力 -\end{mini}\vspace{2mm}\\ -\rei G1$<$- Plotdata(\,"x\textasciicircum 2",\ "x=c(XMIN, XMAX)"\,)\\ -\reicr G2$<$- Partcrv(\,c(0,0),\ c(1,1),\ G1)\\ -\reicr G3$<$- Partcrv(\,c(1,1),\ c(0,0),\ G1) - - -\tab{Intersectcrvs(PD1, PD2)}２曲線PD1, PD2の交点リストを作成\\ -\rei G1$<$- Paramplot("c(cos(t),\ sin(t))",\ "t=c(0, 2*\%pi)")\\ -\reicr G2$<$- Plotdata("x+1/2",\ "x")\\ -\reicr PL$<$- Intersectcrvs(\,G1,G2\,) - -\tab{IntersectcrvsPp(PD1, PD2)}\\ -\tab{}２曲線PD1, PD2の交点とパラメータのリストを作成 - -\tab{Intersectlines(L1, L2)}２直線の交点を返す\\ -\rei L1$<$- Lineplot(A, B)\\ -\reicr L2$<$- Lineplot(C, D)\\ -\reicr P$<$- Intersectcrvs(\,L1,L2\,) - -\tab{Nearestpt(\ P, PD\ )}点Ｐに最も近い曲線PD上の点とパラメータ値のリストを返す\\ -\rei Pp$<$- Nearestpt(\,c(0,\ 1),\ G1\,)\\ -\reicr A$<$- Op(1,Pp) - -\tab{Nearestpt(\,PD1,\ PD2\,)}% -PD1の節点のうち、PD2に最も近い点データのリストを返す\\ -\rei Pp$<$- Nearestpt(\,G1,\ G2)\\ -\reicr A$<$- Op(1,Pp) - -\tab{Ptstart(\,PD\,), Ptend(\,PD)\,}曲線PDの始点（終点）を返す - - -%\tab{Ptlistcrv(\,PD)\,}曲線PDの節点データリストを返す - -\tab{Numptcrv(\,PD)\,}曲線PDの節点データの個数を返す - -\tab{Ptcrv(\,n,\,PD)\,}曲線PDのn番目の節点を返す - -\tab{Pointoncrv(\,s,\ PD\,)}PD上の点でパラメータ値sをもつ点を返す\\ -\rei Pointoncrv(5.3,\ G1)\\ -\reicr （5番目の線分上で0.3の位置にある点） - -\tab[13zw]{Paramoncrv(P \{,\ n \},\ PD)}% -PD（のn番目の線分）上にある点Pのパラメータを返す\\ -\rei Paramoncrv( c(3,\ 2), G1)\\ -\rei Paramoncrv(c(2,\ 4), 5, G1) - -%\tab[13zw]{Droppoint(PD \{, 限界値\})} 限界値以下の隣接点を落として点を少なくする．\\ -%\chuu 限界値のデフォルト値は0.02 - -%\tab{Powersum(\,係数リスト（list）, 変数値x \{, 中心c\} \,)}\\ -%\tab{}$\displaystyle \sum_{k= 0}^n a_n (x-c)^k$の値を返す．（Plotdataで使用）\\ -%\chuu 係数リストは list( 添字リスト，係数リスト)の形\\ -%\rei Tmp1$<$- 0:20\\ -%\reicr Tmp2$<$- ones(length(Tmp1))./factorial(Tmp1)\\ -%\reicr CL$<$- list(Tmp1, Tmp2)\\ -%\reicr G1$<$- Plotdata( "Powersum( CL, x)", "x") - -%\tab{FouriercoeffL(関数F, 周期T, 項数N )}\\ -%\tab{}FのN項までのフーリエ係数リスト(list）を求める．\\ -%\chuu list( 定数項, 余弦係数（行）, 正弦係数（行）, 周期 ) の形\\ -%\chuu Fouriersumで用いる． - -%\tab{Fouriersum( フーリエ係数リスト, 変数値)}\\ -%\tab{}フーリエ級数の値を返す．（Plotdataで使用）\\ -%\rei deff( "Out$<$- Fun(x)", "Out$<$- abs(x)")\\ -%\reicr CL$<$- FouriercoeffL(Fun, 2, 30)\\ -%\reicr G2$<$- Plotdata("Fouriersum(CL, x)", "x", "N$<$- 300" ) - -\subsection{空間} - -\tab{Partcrv3(\,S1,\ S2, PD\,)}曲線PD上のパラメータ値S1,S2を両端とするPDを作成 - -\tab{Rotate3pt(点, V1, V2\{, C\})}\\ -\tab{}回転移動した点を返す（Rotate3data参照） - -\tab{Rotate3ptc(点, 軸, 角度\{, C\})}\\ -\tab{}回転移動した点を返す（Rotate3data参照） - - -\tab{Parapt(\,点\,)\ ,\ \ Perspt(\,点\,)}\\ -\tab{}空間の点を投影した点を返す - -\tab{Zparapt(\,点\,)\ ,\ \ Zperspt(\,点\,)}\\ -\tab{}投影した平面を$X,\ Y$としたときの$Z$座標 - -\tab{Invparapt(\,P,\ PD3d\,)\ ,\ \ Invperspt(\,P,\ PD3d\,)}\\ -\tab{}PD3dを投影したPD上の点Pに対応するPD3d上の点\\ -\chuu Pd3dが線分のときは，延長線上の点でもよい． - -\tab{Invperspt(\,s,\ PD2d,\ PD3d\,)\ ,\ \ Invperspt(\,s,\ PD2d,\ PD3d\,)}\\ -\tab{}PD2d上のパラメータ値sの点に対応するPD3d上の点 - -\tab{Cancoordpers(\,投影座標\,)}平行投影で「投影座標」で表される点の標準座標 - -\tab{Cancoordpers(\,投影座標\,)}一点投影で「投影座標」で表される点の標準座標 - -\tab{Viewfrom(Vec, 曲線3D \{, 非表示オプション\})}\\ -\tab{}一時的にVec方向からみた射影データを返す\\ -\rei Out1$<$- Viewfrom(c(0,0,1), G1) （表示してデータを作成）\\ -\rei Out1$<$- Viewfrom(c(0,0,1), G1, 0) （データのみを作成） - - -%\section{曲面の描画} - -%% -%\subsection{関数データリストの定義} - -%\begin{enumerate}[\hspace*{1zw}(1)] -%\item -%$z$<$- f(x,\ y)\ \ (a \leqq x \leqq b,\ c \leqq y \leqq d)$のとき\vspace{1mm}\\ -%\hspace*{4zw}list(\,関数,\ xの範囲,\ yの範囲\,)\\ -%\hspace*{-6zw}\reicr \verb|Fd$<$- list("z$<$- x^2+y","x$<$- c(-1,2)","y$<$- c(-2,1)")|\\ -%\hspace*{-4zw}\chuu 変数名 x, y が関数名にある文字と重ならないようにする． - -%\item -%$z$<$- f(x,\ y)\ ,x$<$- x(u,\ v),\ ,y$<$- y(u,\ v)\ \ (a \leqq u \leqq b,\ c \leqq v \leqq d)$のとき\vspace{1mm}\\ -%\hspace*{4zw}list(\,関数z,\ 関数x,\ 関数y,\ uの範囲,\ vの範囲\{,\ 境界の指定\}\,)\\ -%\hspace*{-6zw}\rei \verb|Fd$<$- list("z$<$- sin(2*sqrt(abs(x^2+y^2))","x$<$- R*cos(T)",|\\ -%\hspace*{-6zw}\reicr \verb| "y$<$- R*sin(T)","R$<$- c(0,4)","T$<$- c(0,2*%pi)","e")|\\ -%\hspace*{-4zw}\chuu "e"は$r$<$- 1,\ 0\leqq t\leqq 2\pi$で定まる閉曲線を表す．\\ -%\hspace*{-4zw}\chuu sqrtの中はabsをつける（計算誤差のため）． - -%\item -%$x$<$- x(u,\ v),\ y$<$- y(u,\ v),\ z$<$- z(u,\ v)\ (a \leqq u \leqq b,\ c \leqq v \leqq d)$のとき\\ -%\hspace*{4zw}list(\,"p",\ 関数x\ 関数y,\ 関数z,\ Uの範囲,\ Vの範囲\{,\ 境界の指定\}\,)\\ -%\hspace*{-6zw}\rei \verb|Fd$<$- list("p","x$<$- sin(U)*cos(V)","y$<$- sin(U)*sin(V)",|\\ -%\hspace*{-6zw}\reicr \verb| "z$<$- cos(U)","U$<$- c(0,%pi)","V$<$- c(0,2*%pi),"")| - -%\end{enumerate} - -%\subsection{曲面のワイヤーフレーム図} - -%\tab{Sf3data(FD,\ \{,曲線の点の個数(リスト)\{,横方向の分割数,縦方向の分割数\}\})}\\ -%\tab{}曲面データリストFDの３次元ワイヤフレームデータを生成\\ -%\chuu デフォルトは 点の個数＝c(50,\ 50)，分割数$<$- 25\\ -%\chuu 点の個数を数nで指定したときは２方向ともnになる\\ -%\rei Out$<$- Sf3data(Fd) - -%\tab{Sfparadata(〃)}FDのワイヤフレームデータを平行投影した２次元データ - -%\tab{Sfpersdata(〃)}FDのワイヤフレームデータを平行投影した２次元データ - -%\subsection{輪郭線データの作成} - -%\tab{Sfbdparadata(関数データ\{,各方向の分割数,限界値1,限界値2\})}\\ -%\tab{Sfbdpersdata(関数データ\{,各方向の分割数,限界値1,限界値2\})} - -%\noindent -%\hspace*{3zw}\Ltab{10zw}{各方向の分割数}曲線，陰関数のグリッド数\\ -%\hspace*{3zw}\Ltab{14zw}{}デフォルトは50\\ -%\hspace*{3zw}\Ltab{10zw}{}リストか単独の数で与える\\ -%\hspace*{3zw}\Ltab{10zw}{限界値1}同一点と見なす限界（デフォルトは0.05）\\ -%\hspace*{3zw}\Ltab{10zw}{限界値2}交点の余裕幅（デフォルトは0.2） - -% -%\rei \verb|Out1$<$- Sfbdparadata(Fd,c(50,50))|\\ -%\reicr \verb| Windisp(Projpara(Out1))| - -%\noindent -%\chuu 曲面上の３次元データとして得られる．\\ -%\chuu BorderHiddenData()で -%陰線の３次元データが得られる．\\ -%\chuu CuspData()で輪郭線の３次元データが -%得られる．\\ -%\chuu CuspPt()でcusp点の２次元データが -%得られる．\\ -%\chuu BorderPt()で輪郭線の交点の２次元データが -%得られる． - -%\subsection{ワイヤーデータの作成} - -%\tab{Wireparadata(輪郭のリスト,関数データ,横の線数,縦の線数\{.分割数, 限界値1.限界値2\})} - -%\tab{Wirepersdata(輪郭,関数データ \{ ,横の線数,縦の線数\{.分割数, 限界値1.限界値2\}\})} - -%\noindent -%\hspace*{3zw}\Ltab{10zw}{輪郭}Sfbdpersdata( Sfbdparadata ) で作成したデータ\\ -%\hspace*{3zw}\Ltab{10zw}{線}個数か値のリストで与える\\ -%\hspace*{3zw}\Ltab{10zw}{限界値1}デフォルトは0.05\\ -%\hspace*{3zw}\Ltab{10zw}{限界値2}デフォルトは0.2 - -% -%\rei \verb|Out2$<$- Wireparadata(Out1,Fd1,5,5)|\\ -%\reicr \verb| Windisp(Projpara(Out1,Out2))|\\ -%\chuu WireHiddenData()で -%陰線の３次元データが得られる．\\ -%\chuu WirePt()で輪郭線との交点の２次元データが -%得られる． - -%\subsection{曲面と曲線} - -%\subsubsection{パラメータ平面上の曲線} - -%\tab{Crvonsfparadata(平面上の曲線2Dデータ,輪郭,関数データ \{,オプション\})} - -%\tab{Crvonsfpersdata(平面上の曲線2Dデータ,輪郭,関数データ \{,オプション\})} - -%\rei \verb|Fg$<$- Parametricplot("c(T, 0)","T$<$- c(0,2*\%pi)")|\\ -%\reicr \verb| Out4$<$- Crvonsfpersdata(Fg,Out1,Fd)|\\ -%\chuu CrvonsfHiddenData()で陰線の３次元データが得られる． - -% -%\subsubsection{曲面上の曲線} - -%\tab{Crv3onsfparadata(曲面上の曲線3Dデータ,輪郭,関数データ\{,オプション\})} - -%\tab{Crv3onsfpersdata(曲面上の曲線3Dデータ,輪郭,関数データ \{,オプション\})} - -%\rei \verb|Out5$<$- Crv3onsfparadata(Fg,Out1,Fd)|\\ -%\chuu Crv3onsfHiddenData()で陰線の３次元データが得られる． - -%\subsubsection{曲面外の曲線} - -%\tab{Crvsfparadata(曲線3D,輪郭,関数データ\{,オプション\})} - -%\tab{Crvsfpersdata(曲線3D,輪郭,関数データ \{,オプション\})} - -%\rei \verb|G2$<$- Xyzax3data("x$<$- c(-5,5)","y$<$- c(-5,5)",...|\\ -%\reicr \verb| "z$<$- c(-5,5)")|\\ -%\reicr \verb| Out2$<$- Crvsfparadata(G2,Out1,Fd)|\\ -%\chuu CrvsfHiddenData()で陰線の３次元データが得られる．\\ -%\chuu 曲線と曲面が交わらないときは，引数の最後に $-1$をつける． - -%\subsubsection{その他のコマンド} - -%\tab{Intersectcrvsf(曲線3D, 関数データ\{,分割数\{,限界値\}\})}\\ -%\tab{}曲線と曲面との交点（MD）を求める． - -%\subsection{曲面の切断} - -%%\tab{polarcoordx()}極座標$r,\ t$の$x$座標を与える関数を返す - -%%\tab{polarcoordx()}極座標$r,\ t$の$x$座標を与える関数を返す - -%\tab{Sfcutdata(曲面データ, 切断面データ \{, 分割数\} )}\\ -%\tab{}曲面を切ったときの切り口の3dデータを作成\\ -%\chuu 切断面は，$x,\ y,\ z$などの方程式で与える．\\ -%\hspace*{15zw}（平面の場合は，Phcutdataのように与えてもよい）\\ -%\rei \verb|Fd$<$- c("p","R*cos(T)","R*sin(T)","2*(1-R)",|\\ -%\reicr \verb| "R$<$- c(0,1)","T$<$- c(0,2*%pi)","se")|\\ -%\reicr \verb|Out$<$- Sfcutdata(Fd,"x^2+(z-1/2)^2$<$- 1/4")| - -%\tab{Sfcutoffparadata(関数データ, 切断面, 符号 \{ , 分割数\} )} - -%\tab{Sfcutoffrawparadata(関数データ, 切断面, 符号 \{ , 分割数\} )} - -%\tab{Sfcutoffpersdata(関数データ, 切断面, 符号 \{ , 分割数\} )} - -%\tab{Sfcutoffrawpersdata(関数データ, 切断面, 符号 \{ , 分割数\} )} - -%\tab{}切断面で切った曲面をリッジライン法で返す - -% -%\rei \verb|Fd$<$- list("z$<$- 2*(1-sqrt(abs(x^2+y^2)))","x$<$- R*cos(T)",|\\ -%\reicr \verb| "y$<$- R*sin(T)","R$<$- c(0,1)","T$<$- c(0,2*%pi)","e")|\\ -%\reicr \verb| Out$<$- Sfcutoffparadata(Fd,"z$<$- 1+2*x","-")| - - -\section{その他} - -%\tab{bksl("コマンド}\,)}コマンドに$\backslash$をつけた文字列を作る\\ -%\rei str$<$- bksl("sin x}\,) - -\tab{Readtextdata(ファイル名，\{開始位置\{,オプション\}\})}\\ -\tab{}% -\begin{mini}{30zw} -ファイルからコンマ，スペース，タブ区切りのテキストを読込み， -データ行列を返す\vspace{2mm} -\end{mini}\\ -\chuu オプション：\\ -\hspace*{18zw}"R=読み込み行数" （デフォルトはすべて）\\ -\hspace*{18zw}"C=読み込み列数"（デフォルトはすべて） \\ -\hspace*{18zw}"Cna=論理値" １行を列名にするか（デフォルトTRUE） \\ -\hspace*{18zw}"Rna=論理値" １列を行名にするか（デフォルトFALSE） \\ -\rei DL$<$- Readtextdata("dt.csv",\ c(2,\ 1),\ "R=1000",\ "C=2") - -\tab{Writetextdata(データフレーム，ファイル名)}\\ -\tab{}データフレームを .csvファイルに書き出す\\ -\chuu 列名は１行目におき，NAはblankにする\\ -\rei Writetextdata(Df, "ex.csv") - -\tab{Tonumeric(\,文字列からなるデータ行列 \{, 開始位置 \{ , 終了位置\}\}\.)}\\ -\tab{}行列の成分を数値に変換（変換できる行と列からなる部分行列）\\ -\rei Dn$<$- Tonumeric(DL) - -%\tab{Newlength(\,)}% -%\begin{mini}{30zw} -%距離変数 \verb+ \Width, \Height, \Depth +を定義する\TeX コマンドを画面に表示 -%\end{mini} -%\\ -%\rei \prompt newlength()+\\ -%\hspace*{6zw}\reicr \verb+\newlength{\Width}+\\% -%\hspace*{6zw}\reicr \verb+\newlength{\Height}+\\% -%\hspace*{6zw}\reicr \verb+\newlength{\Depth}+% - -%\tab{Mawarikomi("幅"\,)}% -%\begin{mini}{28zw} -%emathのmawarikomi環境のコードを生成表示 -%\end{mini}\\ -%\rei Mawarikomi("5cm"\,) - -\subsection{作表} - -\tab{Tabledata(\{大きさ,\}\ 縦線相対幅,\ 横線相対高さ\,)}\\% -\tab{}表のデータlistを返す\\ -\tab{}\hspace{-2zw}戻り値：PD，縦線添字，横線添字，枠縦PD，枠横PD，外枠PD\\ -\hspace*{10zw}大きさは次のベクトル\\ -\hspace*{12zw}横，縦（,\ 左margin,\ 右margin（,\ 上margin,\ 下margin))\\ -\chuu 横（縦）を -1 としたときは，縦（横）線のデータから\\ -\hspace*{16.3zw}自動的に計算される（デフォルト）\\ -\hspace*{10zw}縦線相対位置は左の罫線からの幅list（縦方向の始点，終点）\\ -\hspace*{10zw}横線相対位置は上の罫線からの幅list（横方向の始点，終点）\\ -\chuu 描画領域は自動的に設定される - -\rei Tmp1$<$- list(20, 30,list(30,0,10), list(0,15,20), 40)\\ -\reicr Tmp2$<$- list(15)\\ -\reicr Out$<$- Tabledata(c(150,20),Tmp1,Tmp)\\ -\reicr Tb$<$- Tabledata(Tmp1,Tmp2) - -\tab{Dividetable(表データ)}枠，縦罫線，横罫線を成分とするリストを返す\\ -\rei G$<$- Dividetable(Tb)（G[[1]],G[[2]],G[[3]]が枠，縦，横） - -\tab{Partframe(表データ,\ 開始位置，終了位置)}\\ -\tab{}枠の一部のPD\\ -\chuu 位置はそれぞれ，c(列番号,\ 行番号)\\ -\chuu 開始位置から終了位置までの反時計回りのPD\\ -\rei G$<$- Parframe(Tb,\ c(4,1),c(1,2)) - -\tab{Findcell(表データ,\ 列番号,\ 行番号\,)}\\% -\tab{}セルの情報list（中心，横幅／２，縦幅／２）を返す\\ -\chuu 番号は左上の位置\\ -\rei Out$<$- Findcell(Out,2,1)\\ -\chuu 番号がベクトルのときは，その範囲のセル\\ -\rei Out$<$- Findcell(Out,c(2,4),1)\\ -\chuu 番号がベクトルのときは，その範囲のセル\\ -\rei Out$<$- Findcell(Out,c(2,4),1)\\ -\tab{Findcell(表データ,\ 左セル，\{ 右セル\} )}\\ -\rei Out$<$- Findcell(Out,"A2") - -\tab{Diagcelldata(表データ，列番号，行番号)}\\ -\tab{}セルの対角線PDのリストを返す - -\tab{Putcell(表データ,\ 列番号,\ 行番号,\ 位置,\ 文字データ)}\\% -\tab{}セルに文字列を入れるコードを出力\\ -\chuu 位置は"c", "r", "l", "u", "d", "b" \\ -\chuu u : up , d : down, b : baseline （微小移動量を付加できる）\\ -\rei Putcell(Out,2,1,"c","221")\\ -\rei Putcell(Out,"B3","l","\$ab\$") - -\tab{Putrow(表データ,\ 行番号,\ 文字データの列)}\\% -\tab{}１行に順に文字を書き入れる\\ -\rei Putrow(TbL, 2, "a", "b", "c" )\\ -\chuu デフォルト位置は "c" それ以外のときはlist内で指定\\ -\chuu 複数列にわたるときは，列数を list 内で指定\\ -\rei Putrow(TbL, 2, list("r","a"), list(2, "b"), "c")\\ -\hspace*{20zw}（rの位置にa，2列とってbをおく） - -\tab{Putrowexpr(表データ,\ 行番号,\ 文字位置,\ 文字データの列)}\\% -\tab{}１行に順に数式を書き入れる - -\tab{PutcoL(表データ,\ 列番号（名前）（,\ 文字データの列)}\\% -\tab{}１列に順に文字を書き入れる\\ -\rei PutcoL(TbL, "C", "a", "b", "c" ) - -\tab{PutcoLexpr(表データ,\ 列番号(名前),\ 文字位置，文字データの列}\\% -\tab{}１列に順に数式を書き入れる - -\tab{Putrowstr(表データ,\ 行番号，文字位置，文字列}\\% -\tab{}１行に文字列の文字を１つずつ書き入れる\\ -\rei Putrowstr(TbL, 1, "c", "xyz" ) - -\tab{PutcoL(表データ,\ 列番号（名前），文字位置，文字列}\\% -\tab{}１列に文字列の文字を１つずつ書き入れる - -\subsection{\TeX のコマンド書き出し（メタコマンド）} - -\tab{Texcom("コマンド"\,)}\TeX コマンドのコードを書き出す\\ -\rei Texcom("$\backslash\backslash$begin\{minipage\}\{3cm\}")\\ -\chuu "newline" のとき，空白行を挿入 - - -\tab{Openphr(\,ユーザーコマンド名\,)，Closephr(\,)}\\ -\tab{}$\backslash$defのコマンド定義を始める\\ -\rei Openphr("$\backslash\backslash$p"\,)\\ -\reicr Texcom("$\backslash\backslash$begin\{array\}\{cc\}"\,)\\ -\reicr Texcom("5 \& 3$\backslash\backslash\backslash\backslash$"\,)\\ -\reicr Texcom("8 \& 7"\,)\\ -\reicr Texcom("$\backslash$end\{array\}\$"\,)\\ -\reicr Closephr(\,) - -\tab{Openpar(\,ユーザーコマンド名，幅\ \{,\ 位置 \}\,), Closepar(\,)}\\ -\tab{}minipage環境を含む$\backslash$def コマンド定義を始める\\ -\chuu 位置のデフォルトは "c"\\ -\rei Openpar("$\backslash\backslash$s","5cm"\,)\\ -\reicr Texcom("$\backslash\backslash$input\{rei\}"\,)\\ -\reicr Closepar(\,)\\ -\reicr Letter(\,c([2,3),"se","$\backslash\backslash$s"\,) - -\tab{Texletter(\ 点(list形式), 方向, 文字列 ，・・・)}\\ -\tab{}点の位置の「方向」に文字列をかく（複数可）\\ -\rei Texletter(\,list(4,"\#1"),"n","文字")\\ -\chuu 位置は"n", s", "e", "w", "ne", "nw", "se", "sw", "c"\\ -\chuu 点の位置はリスト形式で，\TeX の形式で渡すことができる． - -\tab{Texnewctr(番号または番号のベクトル)}\\ -\tab{}\ketpic で使うカウンタ(ketpicctra,...)を定義 - -\tab{Texctr(番号またはカウンタ名)}\\ -\tab{}番号のカウンタ名またはカウンタ名を返す - -\tab{Texthectr(番号)} \verb|\|the+カウンタ名の文字列を返す - -\tab{Texvalctr(番号)} \verb|\|value\{カウンタ名\}の文字列を返す - -\tab{Texsetctr(番号，文字列)}カウンタに値をセットする\TeX コマンド列を出力\\ -\rei Texsetctr(2, "1*2/3");\\ -\rei Texsetctr(2, "(-\verb|#|1)+2"); - -\tab{Texletter(位置（list），方向，文字列)}\\ -\tab{}位置listで表される点に文字列をかく\TeX コマンド列を出力\\ -\rei Texletter(list(10,paste("-",Texvctr(2),sep="")),"ne","\verb|\|content");\\ -\rei Texletter(list(0, "\verb|#|1"), "c", "A"); - -\tab{Texnewcmd(コマンド名，引数の個数，オプション値)}\\ -\tab{}\verb|\|newcommand を始める\TeX コマンドを出力 - -\tab{Texrenewcmd(コマンド名，引数の個数，オプション値)}\\ -\tab{}\verb|\|renewcommand を始める\TeX コマンドを出力 - -\tab{Texend()}\TeX のコマンド定義を終わる\TeX コマンドを出力 - -\tab{Texfor(カウンタ番号，初期値，終了値)}\\ -\tab{}\TeX のループ構造を始める．\\ -\chuu 初期値，終了値は文字列で与える．\\ -\rei Texfor(1,"1","\verb|#|1"); - -\tab{Texendfor(カウンタ番号)}\TeX のループ構造を終える．\\ -\rei Texendfor(1); - -\tab{Texforinit()}\TeX のループ構造を初期化 - -\tab{Texif(数値条件\ \{ ,1 \})}\TeX のif構造を始める．（ifnumまたは ifdim）\\ -\chuu 条件は文字列で与える．\\ -\chuu 1を追加したときは ifdim\\ -\rei Texif("Texctr(1)\verb|<#|2"); - -\tab{Texelse()}\TeX のelseブロック． - -\tab{Texendif()}\TeX のif構造を終える． -%\tab{Setmark()}マークシート用マークのコードを出力 - -%\tab{Putdashmark(表データ,\ 列番号,\ 行番号,文字列or番号)}\\ -%\rei Putdashmark(Out,2,1,0:9); - -%\tab{Putcirmark(表データ,\ 列番号,\ 行番号)} - -%\tab{Putrecmark(表データ,\ 列番号,\ 行番号} - -\subsection{カラー設定} - -\tab{Setcolor(色 \{, 濃さ\})}色を設定\\ -\chuu colorパッケージ必要\\ -\hspace*{2zw} 色は，次の文字列または [c,m,y,k]のベクトル\\ -\hspace*{2.5zw}"greenyellow"[0.15,0,0.69,0], -"yellow"[0,0,1,0], -"goldenrod"[0,0.1,0.84,0], -"dandelion"[0,0.29,0.84,0]\\ -\hspace*{2.5zw}"apricot"[0,0.32,0.52,0], -"peach"[0,0.5,0.7,0], -"melon"[0,0.46,0.5,0], -"yelloworange"[0,0.42,1,0]\\ -\hspace*{2.5zw}""orange"[0,0.61,0.87,0], -"burntorange"[0,0.51,1,0], -"bittersweet"[0,0.75,1,0.24],\\ -\hspace*{2.5zw}"redorange"[0,0.77,0.87,0]\\ -\hspace*{2.5zw}"mahogany"[0,0.85,0.87,0.35], -"maroon"[0,0.87,0.68,0.32], -"brickred"[0,0.89,0.94,0.28], -"red"[0,1,1,0]\\ -\hspace*{2.5zw}"orangered"[0,1,0.5,0], -"rubinered"[0,1,0.13,0], -"wildstrawberry"[0,0.96,0.39,0],\\ -\hspace*{2.5zw}"salmon"[0,0.53,0.38,0]\\ -\hspace*{2.5zw}"carnationpink"[0,0.63,0,0], -"magenta"[0,1,0,0], -"violetred"[0,0.81,0,0], -"rhodamine"[0,0.82,0,0]\\ -\hspace*{2.5zw}"mulberry"[0.34,0.9,0,0.02], -"redviolet"[0.07,0.9,0,0.34], -"fuchsia"[0.47,0.91,0,0.08],\\ -\hspace*{2.5zw}"lavender"[0,0.48,0,0]\\ -\hspace*{2.5zw}"thistle"[0.12,0.59,0,0], -"orchid"[0.32,0.64,0,0], -"darkorchid"[0.4,0.8,0.2,0], -"purple"[0.45,0.86,0,0]\\ -\hspace*{2.5zw}"plum"[0.5,1,0,0], -"violet"[0.79,0.88,0,0], -"royalpurple"[0.75,0.9,0,0], -"blueviolet"[0.86,0.91,0,0.04]\\ -\hspace*{2.5zw}"periwinkle"[0.57,0.55,0,0], -"cadetblue"[0.62,0.57,0.23,0], -"cornflowerblue"[0.65,0.13,0,0],\\ -\hspace*{2.5zw}"midnightblue"[0.98,0.13,0,0.43]\\ -\hspace*{2.5zw}"navyblue"[0.94,0.54,0,0], -"royalblue"[1,0.5,0,0], -"blue"[1,1,0,0], -"cerulean"[0.94,0.11,0,0]\\ -\hspace*{2.5zw}"cyan"[1,0,0,0], -"processblue"[0.96,0,0,0], -"skyblue"[0.62,0,0.12,0], -"turquoise"[0.85,0,0.2,0]\\ -\hspace*{2.5zw}"tealblue"[0.86,0,0.34,0.02], -"aquamarine"[0.82,0,0.3,0], -"bluegreen"[0.85,0,0.33,0],\\ -\hspace*{2.5zw}"emerald"[1,0,0.5,0]\\ -\hspace*{2.5zw}"junglegreen"[0.99,0,0.52,0], -"seagreen"[0.69,0,0.5,0], -"green"[1,0,1,0], -"forestgreen"[0.91,0,0.88,0.12]\\ -\hspace*{2.5zw}"pinegreen"[0.92,0,0.59,0.25], -"limegreen"[0.5,0,1,0], -"yellowgreen"[0.44,0,0.74,0],\\ -\hspace*{2.5zw}"springgreen"[0.26,0,0.76,0]\\ -\hspace*{2.5zw}"olivegreen"[0.64,0,0.95,0.4], -"rawsienna"[0,0.72,1,0.45], -"sepia"[0,0.83,1,0.7], -"brown"[0,0.81,1,0.6]\\ -\hspace*{2.5zw}"tan"[0.14,0.42,0.56,0], -"gray"[0,0,0,0.5], -"black"[0,0,0,1], -"white"[0,0,0,0] - -\end{document} - -\newpage - -\section{内部コマンド} - -\tab{CalcHeight} - -\tab{CalcWidth} - -\tab{Dataindex} - -\tab{Gaiseki} - -\tab{InWindow} - -\tab{Kouten} - -\tab{KoutenList} - -\tab{Koutenseg} - -\tab{Kyoukai} - -\tab{MakeBowdata} - -\tab{MakeCurves} - -\tab{Makehasen} - -\tab{Makeshasen} - -\tab{MeetWindow} - -\tab{Mixmake} - -\tab{Naigai} - -\tab{Naiseki} - -\tab{Vecnagasa(A, B)}$<$- norm(B-A) - -\tab{Makevaltable} - -\tab{Connectseg} - - - -\end{document} diff --git a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/refketlayer20161211J.tex b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/refketlayer20161211J.tex deleted file mode 100644 index 630e19f2a9f..00000000000 --- a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/refketlayer20161211J.tex +++ /dev/null @@ -1,273 +0,0 @@ -\documentclass[a4j]{jarticle} - -\usepackage{ketpic,ketlayer} - -\usepack - -\input{refstyle} - -\setmargin{20}{20}{15}{25} - -\begin{document} - -\begin{flushright} -2016.12.11 -\end{flushright} - - -\begin{center} -{\bf \huge \ketpic\ style ---ketlayer---}\vspace{3mm}\\ -\end{center} - -\section{スタイル名} -\tab{ketlayer.sty,\ ketlayer2e.sty(pict2e必要)} - -\section{概要} -追記（コメント，メモ，挿絵）用の環境，マクロを定義．\\ -\hspace*{5zw}ketpic.sty も読んでおく．\\ -\hspace*{5zw}graphicx,\ color も必要 - -\section{環境} - -\tab{\bs begin\br{layer}[方眼の水平移動]\br{W}\br{H}---\bs end\br{layer}}\\ -\tab{}メモを書くためのpicture環境を定義して，方眼を描く．\\ -\chuu 方眼の水平移動のデフォルトは 0\\ -\chuu $\mathrm{H}=0$のときは，方眼を描かない．\\ -\chuu $\mathrm{H}<0$のときは，上側に方眼を描く．\\ -\rei \bs begin\br{layer}\br{170}\br{30} - -\vspace{0.5\baselineskip} - -\begin{layerv}{0}{30} - -\end{layerv} - -\vspace{7\baselineskip} - -%\tab{\bs begin\br{layerv}[方眼の水平移動]\br{縦方向の移動}\br{H}---\bs end\br{layerv}}\\ -%\tab{}縦方向の移動をし，水平方向は紙幅から自動計算．縦方向は下が＋\\ -%\chuu 該当部分の下におき，$-$で指定するのが普通 - -\tab{\bs begin\br{layerg}[1 or 0]\br{C}---\bs end\br{layerg}} - -\tab{}C（図など）の下におき，Cの縦幅だけ方眼をおく\\ -\chuu オプション引数(def=1)：１のとき方眼を描き，０のとき描かない - -\section{シンボル} - - -\begin{layer}{170}{0} - -\putnotec{30}{35}{\cirscoremark{0.8}} - -\putnotec{60}{35}{\scirscoremark{0.8}} - -\putnotec{90}{35}{\triscoremark{0.8}} - -\putnotec{120}{35}{\crosscoremark{0.8}} - -\end{layer} - - -%\tab[6cm]{\bs circlemark[thickness]\br{size}}円\\ -%\chuu サイズは直径10mmからの倍率で与える．\\ -%\chuu thicknessのデフォルトは 8 ( milli inch） - -%\tab[6cm]{\bs remarkmark[thickness]\br{size}}注意マーク - -\tab[6cm]{\bs cirscoremark[thickness]\br{size}}手がきの2重丸 - -\tab[6cm]{\bs scirscoremark[thickness]\br{size}}手がきの単丸 - -\tab[6cm]{\bs triscoremark[thickness]\br{size}}手がきの三角 - -\tab[6cm]{\bs crosscoremark[thickness]\br{size}}手がきのバツ - -\vspace{6\baselineskip} - -\section{マクロ一覧} - -\begin{layer}{160}{0} - -\putnotee{120}{20}{\fbox{$\dfrac{1}{2}$}} - -\end{layer} - -\tab[14zw]{\bs putnotec\br{x}\br{y}\br{Char}}(x,\ y)を中心にCharを書く - -\tab[14zw]{\bs putnotee\br{x}\br{y}\br{Char}}(x,\ y)の右にCharを書く - -\tab[14zw]{\bs putnotew\br{x}\br{y}\br{Char}}(x,\ y)の左にCharを書く - -\tab[14zw]{\bs putnotes\br{x}\br{y}\br{Char}}(x,\ y)の下にCharを書く - -\tab[14zw]{\bs putnoten\br{x}\br{y}\br{Char}}(x,\ y)の上にCharを書く - -\tab{\bs putnotene\br{x}\br{y}\br{Char}\ ,\ -\bs putnotenw\br{x}\br{y}\br{Char}} - -\tab{\bs putnotese\br{x}\br{y}\br{Char}\ ,\ -\bs putnotesw\br{x}\br{y}\br{Char}} - -\noindent -\rei putnotee\br{20}\br{5}\br{\bs fbox\br{\$\bs dfrac\br{1}\br{2}\$}} - -\mbox{} - -\begin{layer}{160}{0} - -\lineseg[16]{135}{25}{30}{25} - -\arrowlineseg[16]{130}{50}{10}{45} - -\end{layer} - -\tab{\bs lineseg[thickness]\br{$x$}\br{$y$}\br{$L$}\br{$\theta$}}\\ -\tab{}点$(x, \ y)$から長さ$L$の線分を$\theta^{\circ}$ -方向に描く（単位はmm）\\ -\rei \bs lineseg[16]\br{130}\br{20}\br{30}\br{25}\\ -\chuu thicknessの単位は milli inch（デフォルト=12）\\ -\chuu $x,\ y,\ \theta$ は小数でもよい． - -\tab{\bs dashlineseg[thickness]\br{$x$}\br{$y$}\br{$L$}\br{$\theta$}}\\ -\tab{}点$(x, \ y)$から長さ$L$の破線を$\theta^{\circ}$ -方向に描く（単位はmm） - -\tab{\bs arrowlineseg[thickness]\br{$x$}\br{$y$}\br{$L$}\br{$\theta$}}\\ -\tab{}矢印を描く（鏃は始点に描く）\\ -\rei \bs arrowlineseg[16]\br{30}\br{20}\br{10}\br{45} - -\tab[13zw]{\bs arrowhead[size]\br{$x$}\br{$y$}\br{$\theta$}}鏃だけを描く - -\mbox{} - -%\tab{\bs boxline[線幅]\br{x}\br{y}\br{W}\br{H}}\\ -%\tab{}(x,\ y)の右上(ne)に幅W，高さHの矩形を描く．\\ -%\chuu 線幅のデフォルトは8 (milli inch）\\ -%\chuu n,\ s など8方向＋c を付加すれば，それぞれの方向に描く\\ -%\rei \bs boxlinen\br{30}\br{20}\br{50}\br{5} - -\tab{\bs boxframe+dir[thickness]\br{x}\br{y}\br{W}\br{H}\br{文字}}\\ -\tab{}(x,\ y)のdir方向に幅W，高さHの矩形を描き，中に文字を入れる\\ -\chuu dir=n,\ s,\ e,\ w,\ ne,\ nw,\ se,\ sw,\ c \\ -\rei \bs boxframen\br{30}\br{20}\br{50}\br{5}\br{} - -%\tab{\bs dashboxline[線幅]\br{x}\br{y}\br{W}\br{H}}\\ -%\tab{}(x,\ y)の右上(ne)に幅W，高さHの点線の矩形を描く．\\ -%\chuu 線幅のデフォルトは8 (milli inch）\\ -%\chuu 8方向＋c については，\bs boxlineと同じ - -\tab{\bs dashboxframe+dir[thickness]\br{x}\br{y}\br{W}\br{H}\br{文字}}\\ -\tab{}(x,\ y)のdir方向にギザの矩形を描き，中に文字を入れる\\ -\chuu dir=n,\ s,\ e,\ w,\ ne,\ nw,\ se,\ sw,\ c - -\tab{\bs jaggyboxframe+dir[thickness]\br{x}\br{y}\br{W}\br{H}\br{文字}}\\ -\tab{}(x,\ y)のdir方向にギザ四角形を描き，中に文字を入れる\\ -\chuu dir=n,\ s,\ e,\ w,\ ne,\ nw,\ se,\ sw,\ c - -\tab{\bs dialboxframe+dir[thickness]\br{x}\br{y}\br{W}\br{H}\br{文字}}\\ -\tab{}(x,\ y)のdir方向にダイヤ型からなる矩形を描き，中に文字を入れる\\ -\chuu dir=n,\ s,\ e,\ w,\ ne,\ nw,\ se,\ sw,\ c - -\tab{\bs eraser+dir[枠]\br{$x$}\br{$y$}\br{W}\br{H}}\\ -\tab{}$(x,\ y)$のdir方向の長方形の内部を消す\\ -\chuu 枠=0 とすると枠線を描かない（デフォルトは 1）\\ -\chuu dir=n,\ s,\ e,\ w,\ ne,\ nw,\ se,\ sw,\ c - -\tab{\bs shadebox+dir[枠描画]\br{$x$}\br{$y$}\br{W}\br{H}\br{D}\br{色}}\\ -\tab{}$(x,\ y)$のdir方向に幅W，高さHの矩形の内部を濃さDで塗る\\ -\chuu 枠描画のデフォルトは 0（枠線を描かない）\\ -\chuu dir=n,\ s,\ e,\ w,\ ne,\ nw,\ se,\ sw,\ c - -\vspace{\baselineskip} - -\begin{layer}{160}{0} - -\boxframese[24]{10}{0}{30}{16}{boxframe} -\dashboxframese{50}{0}{30}{16}{dashboxframe} -\jaggyboxframese{90}{0}{30}{16}{jaggyboxframe} -\diaboxframese{130}{0}{30}{16}{diaboxframe} -\shadeboxse{10}{0}{30}{16}{0.5}{green} - -\end{layer} - -\newpage - -\tab{\bs popframe[thickness]\br{x}\br{y}\br{Ds}\br{色s}\br{Dp}\br{色p}\br{色f}\br{文字}}\\ -\tab{}(x,\ y)の右下(se)に文字入り矩形を描き，濃さDsの陰をつける\\ -\chuu 色p : 背景色，色f : 枠の色\\ -\chuu 矩形の大きさは文字から自動計算する\\ -\chuu 線の太さ(thickness)のデフォルトは8\\ -\chuu 文字列の幅$\leqq 200mm$，高さ$\leqq 100mm$\\ -\rei \bs popframe\br{0}\br{5}\br{0.5}\br{black}\br{1}\br{yellow}\br{yellow}\br{タイトル} - -\tab{\bs colorframe[thickness]\br{x}\br{y}\br{Dp}\br{色p}\br{色f}\br{文字}}\\ -\tab{}(x,\ y)の右下(se)に文字入り矩形を描き，背景を色pで塗る\\ -\chuu 矩形の大きさは文字から自動計算する\\ -\chuu 線の太さ(thickness)のデフォルトは8\\ -\chuu 文字列の幅$\leqq 200$mm，高さ$\leqq 100$mm\\ -\rei \bs colorframe\br{100}\br{5}\br{0.3}\br{green}\br{blue}\br{文字列} - -\begin{layer}{160}{0} -\popframe{60}{5}{0.3}{black}{1}{yellow}{yellow}{\Large タイトル} -\colorframe{100}{5}{0.3}{green}{blue}{\Large\bf 強調文字} -\end{layer} - -\vspace{15mm} - -\begin{layer}{160}{0} - -\hjaggyline{130}{10}{25} - -\vjaggyline{140}{20}{15} - -\end{layer} - -%\vspace{6\baselineskip} - -\tab{\bs hjaggyline[thickness]\br{x}\br{y}\br{W}}\\ -\tab{}(x,\ y)から左に幅Wのギザ線を描く．\\ -\chuu bを付加すると，線の出方が逆になる． - -\tab{\bs vjaggyline[thickness]\br{x}\br{y}\br{W}}\\ -\tab{}(x,\ y)から下に幅Wのギザ線を描く．\\ -\chuu bを付加すると，線の出方が逆になる． - -\tab{\bs circleline[thickness]\br{x}\br{y}\br{size}}\\ -\tab{}(x,\ y)を中心に -円を描く - -\tab{\bs ballonr[thickness]\br{x}\br{y}\br{size}\br{Char}}\\ -\tab{}(x,\ y)から右上に吹き出しとCharを描く - -\tab{\bs ballonl[thickness]\br{x}\br{y}\br{size}\br{Char}}\\ -\tab{}(x,\ y)から左上に吹き出しとCharを描く - - -\tab[14zw]{\bs lefthand[thickness]\br{x}\br{y}}(x,\ y)に指先を描く - -\tab[14zw]{\bs righthand[thickness]\br{x}\br{y}}(x,\ y)に指先を描く - -\tab[16zw]{\bs leftdownhand[thickness]\br{x}\br{y}}(x,\ y)に指先を描く - -\tab[16zw]{\bs rightdownhand[thickness]\br{x}\br{y}}(x,\ y)に指先を描く - -\begin{layer}{180}{0} - -\ballonr{30}{40}{1}{Example1} - -\ballonl{90}{40}{1}{Example2} - -\lefthand{120}{30} - -\righthand{140}{30} - -\leftdownhand{120}{25} - -\rightdownhand{140}{25} - -\end{layer} - - - -\end{document} diff --git a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/refketpic161211J.tex b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/refketpic161211J.tex deleted file mode 100644 index c7755b1340b..00000000000 --- a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/refketpic161211J.tex +++ /dev/null @@ -1,90 +0,0 @@ -\documentclass[a4j]{jarticle} -%あいう - -\usepackage{ketpic,ketlayer} -\usepack - -\input{/tools/reference/refstyle} - -\setmargin{20}{20}{15}{25} - -\begin{document} - -\begin{flushright} -2016.12.11 -\end{flushright} - - -\begin{center} -{\bf \huge \ketpic\ --ketpic--}\vspace{3mm}\\ -\end{center} - -\section{スタイル名} -\tab{ketpic.sty,\ ketpic2e.sty(pict2e必要)} - -\section{概要} - -\bs Width,\ \bs Height,\ \bs Depthを定義する． - -また，10個の一時カウンタ ketpicctra,\ $\cdots$,\ ketpicctrj を定義する． - -\section{マクロ一覧} - -\subsection{プリアンブル用} - -%\tab{\bs usepack}amsmath, amssymb,graphicx,colorを読み込む - -\tab{\bs setmargin\br{left}\br{right}\br{top}\br{bottom}}\\ -\tab{}マージン設定（単位はmm）\\ -\rei \bs setmargin\br{20}\br{20}\br{15}\br{25} - -\subsection{本文用} - -\tab{\bs ketpic}ロゴ \ketpic - -\tab{\bs Ltab\br{W}\br{S}}Wの幅を確保して左寄せでSを書く\\ -\rei \bs Ltab\br{5cm}\br{abc}xyz - -\tab{\bs Rtab\br{W}\br{S}}Wの幅を確保して右寄せでSを書く - -\tab{\bs Ctab\br{W}\br{S}}Wの幅を確保して中央寄せでSを書く - -%\tab{\bs vbackward\br{C}}文字Cの高さ分だけ上に戻る\\ -%\rei \bs vbackward\br{\bs includegraphics\br{ex.eps}} - -%\tab{\bs vforward\br{C}}文字Cの高さ分だけ下に進む - -\tab{\bs ketcalcwidth[0]\br{C}}文字Cの幅を単位長で計ってカウンタ１に返す\\ -\chuu オプションが１のときは，値を表示 - -\tab{\bs ketcalcheight[0]\br{C}}文字Cの高さを単位長で計ってをカウンタ１に返す\\ -\chuu オプションが１のときは，値を表示 - -\tab{\bs ketcalcdepth[0]\br{C}}文字Cの深さを単位長で計ってカウンタ１に返す\\ -\chuu オプションが１のときは，値を表示 - -\tab{\bs ketcalcwh\br{C}}文字Cの横幅と縦幅をmm単位で返す\\ -\chuu \{横幅\}\{縦幅\}の形式で - -\subsection{シンボル} - -\begin{layer}[120]{120}{0} -\putnotee{5}{5}{\dangerbendmark} -\putnotee{10}{10}{\cautionmark} -\putnotee{15}{15}{\circlemark{1}} -\putnotee{20}{25}{\circleshade{1}{0.5}} -\putnotee{5}{30}{\NEarrow,\ \NELarrow,\ \NERarrow} -\end{layer} - -\tab[6cm]{\bs dangerbendmark[size]}ブルバキの「危険な曲がり角」 - -\tab[6cm]{\bs cautionmark[size]}注意書きのマーク - -\tab[6cm]{\bs circlemark[thickness]\br{size}} 円\\ -\chuu サイズ１= 4mm（直径） - -\tab[6cm]{\bs circleshade[thickness]\br{size}\br{density}}中塗りの円 - -\tab[6cm]{\bs NEarrow[倍率],\bs NELarrow[倍率]など} 増減矢印 - -\end{document} diff --git a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/refketslide161211.tex b/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/refketslide161211.tex deleted file mode 100644 index 31990d96dab..00000000000 --- a/Master/texmf-dist/doc/support/ketcindy/source/ketmanual/refketslide161211.tex +++ /dev/null @@ -1,72 +0,0 @@ -\documentclass[a4j]{jarticle} - -\usepackage{/tools/ketpic,/tools/ketlayer} -\usepack - -\input{/tools/reference/refstyle} - -\setmargin{20}{20}{15}{25} - -\begin{document} - -\begin{flushright} -2016.12.11 -\end{flushright} - - -\begin{center} -{\bf \huge \ketpic スタイル\ --ketslide--}\vspace{3mm}\\ -\end{center} - -\section{スタイル名} -\tab{ketslide.sty} - -\section{概要} - -プレゼン用スライドを作成する．\\ -\hspace*{2zw}\bs documentclass[landscape,10pt]\{jarticle または article\}\\ -\hspace*{2zw}スライドの大きさは 約130 $\times$ 85 (mm) - - -\section{マクロ一覧} - -\subsection{プリアンブル用} - -\tab{\bs ketmarginJ}jarticleのときのマージン設定 - -\tab{\bs ketmarginE}articleのときのマージン設定 - -\tab{\bs ketslideinit}パラメータ指定マクロへのdefault値設定 - -\noindent -\hspace*{2zw}\tab{\bs ketcletter}タイトルの文字色（black\\ -\hspace*{2zw}\tab{\bs ketcbox}ボックス内の色（white\\ -\hspace*{2zw}\tab{\bs ketdbox}ボックス内の色の濃さ（1）\\ -\hspace*{2zw}\tab{\bs ketcframe}枠の色（black）\\ -\hspace*{2zw}\tab{\bs ketcshadow}陰の色（black）\\ -\hspace*{2zw}\tab{\bs ketdshadow}陰の色の濃さ（0.5）\\ -\hspace*{2zw}\tab{\bs slidetitlex}タイトルの横位置（6）\\ -%\hspace*{2zw}\tab{\bs slidetitley}タイトルの縦位置（7）\\ -\hspace*{2zw}\tab{\bs slidetitlesize}タイトルの文字サイズ（2）\\ -\hspace*{2zw}\tab{\bs mketcletter}メインタイトルの文字色（black）\\ -\hspace*{2zw}\tab{\bs mketcbox}メインタイトルのボックス内の色（white）\\ -\hspace*{2zw}\tab{\bs mketdbox}メインタイトルのボックス内の色の濃さ（1）\\ -\hspace*{2zw}\tab{\bs mketcframe}メインタイトルの枠の色（white）\\ -\hspace*{2zw}\tab{\bs mslidetitlex}メインタイトルの横位置（62）\\ -%\hspace*{2zw}\tab{\bs mslidetitley}メインタイトルの立て位置（35）\\ -\hspace*{2zw}\tab{\bs mslidetitlesize}メインタイトルの文字サイズ（3）\\ -\hspace{6zw}注） これらのパラメータは本文中で \bs def を使って変更できる． - - -\subsection{本文用} - -\tab[15zw]{\bs newslide[縦位置]\{タイトル\}}新しいスライドを始める．（縦位置のdefault=6） - -\tab[15zw]{\bs sameslide}[縦位置]同じページとして，追加する． - -\tab[15zw]{\bs mainslide[縦位置]\{タイトル\}}新しいメインスライドを始める．（縦位置のdefault=35） - -\tab[15zw]{\bs mainsameslide[縦位置]}同じページとして，追加する． - - -\end{document}
\ No newline at end of file |
