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author | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
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committer | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
commit | e0c6872cf40896c7be36b11dcc744620f10adf1d (patch) | |
tree | 60335e10d2f4354b0674ec22d7b53f0f8abee672 /graphics/ketcindy/ketcindyfolder/doc/source/ketmanual |
Initial commit
Diffstat (limited to 'graphics/ketcindy/ketcindyfolder/doc/source/ketmanual')
382 files changed, 54063 insertions, 0 deletions
diff --git a/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/Fig/3dscreen.pdf b/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/Fig/3dscreen.pdf Binary files differnew file mode 100644 index 0000000000..e6911f6fd8 --- /dev/null +++ b/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/Fig/3dscreen.pdf diff --git a/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/Fig/3dstart.pdf b/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/Fig/3dstart.pdf Binary files differnew file mode 100644 index 0000000000..8b400a0fd8 --- /dev/null +++ b/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/Fig/3dstart.pdf diff --git a/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/Fig/CindyhelpE.pdf b/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/Fig/CindyhelpE.pdf Binary files differnew file mode 100644 index 0000000000..e968c4153d --- /dev/null +++ b/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/Fig/CindyhelpE.pdf diff --git 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\ No newline at end of file diff --git a/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/Fig/checkbmain.tex b/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/Fig/checkbmain.tex new file mode 100644 index 0000000000..657cfb4760 --- /dev/null +++ b/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/Fig/checkbmain.tex @@ -0,0 +1,17 @@ +\documentclass{article} +\usepackage{ketpic,ketlayer} +\usepackage{amsmath,amssymb} +\usepackage{graphicx,color} + +\def\ketcindy{{K\kern-.20em% +\lower.5ex\hbox{E}\kern-.125em{TCindy}}} + +\setmargin{20}{20}{20}{20} + +\begin{document} +checkb +\vspace{5mm} + +\input{checkb.tex} + +\end{document} diff --git a/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/Fig/checkbs1.tex b/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/Fig/checkbs1.tex new file mode 100644 index 0000000000..adf01c568d --- /dev/null +++ b/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/Fig/checkbs1.tex @@ -0,0 +1,61 @@ +%%% checkb.tex 2015-1-13 17:48 +%%% checkb.sce 2015-1-13 13:55 +{\unitlength=1cm% +\begin{picture}% +( 8.99000, 3.00000)( -4.99000, -0.99000)% +\special{pn 8}% +% +\special{pa -1480 94}\special{pa -1458 -3}\special{pa -1433 -83}\special{pa -1405 -148}% +\special{pa -1373 -195}\special{pa -1339 -226}\special{pa -1301 -241}\special{pa -1260 -239}% +\special{pa -1216 -220}\special{pa -1169 -185}\special{pa -1118 -134}\special{pa -1067 -81}% +\special{pa -1018 -41}\special{pa -973 -15}\special{pa -930 -2}\special{pa -890 -2}% +\special{pa -853 -16}\special{pa -818 -43}\special{pa -787 -83}\special{pa -758 -137}% +\special{pa -732 -205}\special{pa -699 -268}\special{pa -651 -308}\special{pa -587 -326}% +\special{pa -507 -322}\special{pa -411 -295}\special{pa -300 -246}\special{pa -174 -175}% +\special{pa -32 -81}\special{pa 126 35}\special{pa 299 173}% +\special{fp}% +\special{pa -1466 81}\special{pa -1474 76}\special{pa -1484 75}\special{pa -1492 79}% +\special{pa -1498 86}\special{pa -1500 96}\special{pa -1497 105}\special{pa -1490 111}% +\special{pa -1482 114}\special{pa -1472 112}\special{pa -1465 107}\special{pa -1461 98}% +\special{pa -1462 89}\special{pa -1466 81}\special{sh 1}\special{fp}% +\special{pa -1364 -447}\special{pa -1372 -452}\special{pa -1382 -452}\special{pa -1390 -449}% +\special{pa -1396 -441}\special{pa -1398 -432}\special{pa -1395 -423}\special{pa -1388 -416}% +\special{pa -1379 -413}\special{pa -1370 -415}\special{pa -1362 -421}\special{pa -1359 -430}% +\special{pa -1359 -439}\special{pa -1364 -447}\special{sh 1}\special{fp}% +\special{pa -840 151}\special{pa -848 147}\special{pa -858 146}\special{pa -866 150}% +\special{pa -872 157}\special{pa -874 167}\special{pa -871 176}\special{pa -865 182}% +\special{pa -856 185}\special{pa -846 183}\special{pa -839 177}\special{pa -835 169}% +\special{pa -836 159}\special{pa -840 151}\special{sh 1}\special{fp}% +\special{pa -592 -589}\special{pa -600 -594}\special{pa -610 -594}\special{pa -618 -590}% +\special{pa -624 -583}\special{pa -626 -574}\special{pa -623 -565}\special{pa -616 -558}% +\special{pa -607 -555}\special{pa -598 -557}\special{pa -591 -563}\special{pa -587 -571}% +\special{pa -588 -581}\special{pa -592 -589}\special{sh 1}\special{fp}% +\special{pa 313 159}\special{pa 305 154}\special{pa 296 154}\special{pa 287 158}\special{pa 281 165}% +\special{pa 280 174}\special{pa 282 183}\special{pa 289 190}\special{pa 298 193}\special{pa 307 191}% +\special{pa 315 185}\special{pa 319 177}\special{pa 318 167}\special{pa 313 159}\special{sh 1}\special{fp}% +\settowidth{\Width}{A}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{A}\settodepth{\Depth}{A}\setlength{\Height}{-\Height}% +\put(-3.7600,-0.3900){\hspace*{\Width}\raisebox{\Height}{A}}% +% +% +\settowidth{\Width}{B}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{B}\settodepth{\Depth}{B}\setlength{\Height}{\Depth}% +\put(-3.5000,1.2500){\hspace*{\Width}\raisebox{\Height}{B}}% +% +% +\settowidth{\Width}{C}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{C}\settodepth{\Depth}{C}\setlength{\Height}{-\Height}% +\put(-2.1700,-0.5700){\hspace*{\Width}\raisebox{\Height}{C}}% +% +% +\settowidth{\Width}{D}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{D}\settodepth{\Depth}{D}\setlength{\Height}{\Depth}% +\put(-1.5400,1.6100){\hspace*{\Width}\raisebox{\Height}{D}}% +% +% +\settowidth{\Width}{E}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{E}\settodepth{\Depth}{E}\setlength{\Height}{-\Height}% +\put(0.7600,-0.5900){\hspace*{\Width}\raisebox{\Height}{E}}% +% +% +\end{picture}}%
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-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}% +\settoheight{\Height}{greenyellow}\settodepth{\Depth}{greenyellow}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(2.5000000,33.5000000){\hspace*{\Width}\raisebox{\Height}{greenyellow}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{[0.15,0,0.69,0]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0.15,0,0.69,0]}\settodepth{\Depth}{[0.15,0,0.69,0]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(7.5000000,33.5000000){\hspace*{\Width}\raisebox{\Height}{[0.15,0,0.69,0]}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{royalpurple}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{royalpurple}\settodepth{\Depth}{royalpurple}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(15.5000000,33.5000000){\hspace*{\Width}\raisebox{\Height}{royalpurple}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{[0.75,0.9,0,0]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0.75,0.9,0,0]}\settodepth{\Depth}{[0.75,0.9,0,0]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(20.5000000,33.5000000){\hspace*{\Width}\raisebox{\Height}{[0.75,0.9,0,0]}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{yellow}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{yellow}\settodepth{\Depth}{yellow}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(2.5000000,32.5000000){\hspace*{\Width}\raisebox{\Height}{yellow}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{[0,0,1,0]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0,0,1,0]}\settodepth{\Depth}{[0,0,1,0]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(7.5000000,32.5000000){\hspace*{\Width}\raisebox{\Height}{[0,0,1,0]}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{blueviolet}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{blueviolet}\settodepth{\Depth}{blueviolet}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(15.5000000,32.5000000){\hspace*{\Width}\raisebox{\Height}{blueviolet}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{[0.86,0.91,0,0.04]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0.86,0.91,0,0.04]}\settodepth{\Depth}{[0.86,0.91,0,0.04]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(20.5000000,32.5000000){\hspace*{\Width}\raisebox{\Height}{[0.86,0.91,0,0.04]}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{goldenrod}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{goldenrod}\settodepth{\Depth}{goldenrod}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(2.5000000,31.5000000){\hspace*{\Width}\raisebox{\Height}{goldenrod}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{[0,0.1,0.84,0]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0,0.1,0.84,0]}\settodepth{\Depth}{[0,0.1,0.84,0]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(7.5000000,31.5000000){\hspace*{\Width}\raisebox{\Height}{[0,0.1,0.84,0]}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{periwinkle}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{periwinkle}\settodepth{\Depth}{periwinkle}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(15.5000000,31.5000000){\hspace*{\Width}\raisebox{\Height}{periwinkle}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{[0.57,0.55,0,0]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0.57,0.55,0,0]}\settodepth{\Depth}{[0.57,0.55,0,0]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\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}% +\settowidth{\Width}{[0,0.32,0.52,0]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0,0.32,0.52,0]}\settodepth{\Depth}{[0,0.32,0.52,0]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(7.5000000,29.5000000){\hspace*{\Width}\raisebox{\Height}{[0,0.32,0.52,0]}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{cornflowerblue}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{cornflowerblue}\settodepth{\Depth}{cornflowerblue}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(15.5000000,29.5000000){\hspace*{\Width}\raisebox{\Height}{cornflowerblue}}% +% +}% +{% +\color[rgb]{0,0,0}% +\settowidth{\Width}{[0.65,0.13,0,0]}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{[0.65,0.13,0,0]}\settodepth{\Depth}{[0.65,0.13,0,0]}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\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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220}% +\special{pa -812 220}% +\special{fp}% +\special{pn 8}% +\special{pn 8}% +\special{pa -661 -12}\special{pa -520 -4}% +\special{fp}% +\special{pn 8}% +\special{pa -596 16}\special{pa -520 -4}\special{pa -593 -32}\special{pa -594 -8}% +\special{pa -596 16}\special{sh 1}\special{ip}% +\special{pn 8}% +\special{pa -596 16}\special{pa -520 -4}\special{pa -593 -32}\special{pa -594 -8}% +\special{pa -596 16}% +\special{fp}% +\special{pn 8}% +\special{pn 8}% +\special{pa -1311 -4}\special{pa -1437 -4}% +\special{fp}% +\special{pn 8}% +\special{pa -1362 -28}\special{pa -1437 -4}\special{pa -1362 20}\special{pa -1362 -4}% +\special{pa -1362 -28}\special{sh 1}\special{ip}% +\special{pn 8}% +\special{pa -1362 -28}\special{pa -1437 -4}\special{pa -1362 20}\special{pa -1362 -4}% +\special{pa -1362 -28}% +\special{fp}% +\special{pn 8}% +\special{pn 8}% +\special{pa -295 8}\special{pa -177 0}% +\special{fp}% +\special{pn 8}% +\special{pa -250 29}\special{pa -177 0}\special{pa -254 -19}\special{pa -252 5}\special{pa -250 29}% +\special{sh 1}\special{ip}% +\special{pn 8}% +\special{pa -250 29}\special{pa -177 0}\special{pa -254 -19}\special{pa -252 5}\special{pa -250 29}% +\special{fp}% +\special{pn 8}% +\special{pn 8}% +\special{pa 189 4}\special{pa 319 4}% +\special{fp}% +\special{pn 8}% +\special{pa 244 28}\special{pa 319 4}\special{pa 244 -20}\special{pa 244 4}\special{pa 244 28}% +\special{sh 1}\special{ip}% +\special{pn 8}% +\special{pa 244 28}\special{pa 319 4}\special{pa 244 -20}\special{pa 244 4}\special{pa 244 28}% +\special{fp}% +\special{pn 8}% +\special{pn 8}% +\special{pa -331 -402}\special{pa -213 -484}% +\special{fp}% +\special{pn 8}% +\special{pa -260 -421}\special{pa -213 -484}\special{pa -288 -461}\special{pa -274 -441}% +\special{pa -260 -421}\special{sh 1}\special{ip}% +\special{pn 8}% +\special{pa -260 -421}\special{pa -213 -484}\special{pa -288 -461}\special{pa -274 -441}% +\special{pa -260 -421}% +\special{fp}% +\special{pn 8}% +\special{pn 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\ No newline at end of file diff --git a/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/Fig/paramplot1.tex b/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/Fig/paramplot1.tex new file mode 100644 index 0000000000..075d6fd7dc --- /dev/null +++ b/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/Fig/paramplot1.tex @@ -0,0 +1,40 @@ +%%% test.tex 2014-10-18 20:24 +%%% test.sce 2014-10-18 20:24 +{\unitlength=5mm% +\begin{picture}% +( 7.50000, 3.50000)( -0.50000, -0.50000)% +\special{pn 8}% +% +\special{pa 0 0}\special{pa 0 -2}\special{pa 1 -6}\special{pa 2 -14}\special{pa 4 -25}% +\special{pa 8 -39}\special{pa 15 -55}\special{pa 23 -74}\special{pa 34 -95}\special{pa 47 -117}% +\special{pa 64 -141}\special{pa 83 -165}\special{pa 106 -191}\special{pa 132 -216}% +\special{pa 161 -241}\special{pa 194 -265}\special{pa 229 -288}\special{pa 268 -309}% +\special{pa 309 -329}\special{pa 352 -347}\special{pa 397 -362}\special{pa 445 -374}% +\special{pa 493 -384}\special{pa 543 -390}\special{pa 593 -393}\special{pa 644 -393}% +\special{pa 694 -390}\special{pa 744 -384}\special{pa 792 -374}\special{pa 839 -362}% +\special{pa 885 -347}\special{pa 928 -329}\special{pa 969 -309}\special{pa 1008 -288}% +\special{pa 1043 -265}\special{pa 1075 -241}\special{pa 1105 -216}\special{pa 1131 -191}% +\special{pa 1154 -165}\special{pa 1173 -141}\special{pa 1190 -117}\special{pa 1203 -95}% +\special{pa 1214 -74}\special{pa 1222 -55}\special{pa 1228 -39}\special{pa 1232 -25}% +\special{pa 1235 -14}\special{pa 1236 -6}\special{pa 1237 -2}\special{pa 1237 0}% +\special{fp}% +\special{pa -98 0}\special{pa 1378 0}% +\special{fp}% +\special{pa 0 98}\special{pa 0 -591}% +\special{fp}% +\settowidth{\Width}{$x$}\setlength{\Width}{0\Width}% +\settoheight{\Height}{$x$}\settodepth{\Depth}{$x$}\setlength{\Height}{-0.5\Height}\setlength{\Depth}{0.5\Depth}\addtolength{\Height}{\Depth}% +\put(7.0500,0.0000){\hspace*{\Width}\raisebox{\Height}{$x$}}% +% +% +\settowidth{\Width}{$y$}\setlength{\Width}{-0.5\Width}% +\settoheight{\Height}{$y$}\settodepth{\Depth}{$y$}\setlength{\Height}{\Depth}% +\put(0.0000,3.0500){\hspace*{\Width}\raisebox{\Height}{$y$}}% +% +% +\settowidth{\Width}{O}\setlength{\Width}{-1\Width}% +\settoheight{\Height}{O}\settodepth{\Depth}{O}\setlength{\Height}{-\Height}% +\put(-0.0500,-0.0500){\hspace*{\Width}\raisebox{\Height}{O}}% +% +% +\end{picture}}%
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\ No newline at end of file diff --git a/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/Fig/tablesample1E.tex b/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/Fig/tablesample1E.tex new file mode 100644 index 0000000000..0a78dad4db --- /dev/null +++ b/graphics/ketcindy/ketcindyfolder/doc/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}% 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\ No newline at end of file diff --git a/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/Fig/zoom-in.pdf b/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/Fig/zoom-in.pdf Binary files differnew file mode 100644 index 0000000000..12cf4f488d --- /dev/null +++ b/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/Fig/zoom-in.pdf diff --git a/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/Fig/zoom-out.pdf b/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/Fig/zoom-out.pdf Binary files differnew file mode 100644 index 0000000000..0417fb932c --- /dev/null +++ b/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/Fig/zoom-out.pdf diff --git a/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/KeTCindyGuideE.tex b/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/KeTCindyGuideE.tex new file mode 100644 index 0000000000..8ba5ed7707 --- /dev/null +++ b/graphics/ketcindy/ketcindyfolder/doc/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/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/KeTCindyGuideJ.tex b/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/KeTCindyGuideJ.tex new file mode 100644 index 0000000000..24f3457731 --- /dev/null +++ b/graphics/ketcindy/ketcindyfolder/doc/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/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/KeTCindyReferenceE.tex b/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/KeTCindyReferenceE.tex new file mode 100644 index 0000000000..1432b0ef18 --- /dev/null +++ b/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/KeTCindyReferenceE.tex @@ -0,0 +1,5901 @@ +\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} + +%----------Initglist,Setglist,Addglist---------------------------------- +\begin{cmd}{Initglist}{initglist} +\itemket{Usage}Initglist(), Setglist(), Addglist() +\itemket{Description}Add the list generated in \verb|"ketlib"| slot to that of \verb|"ketlib"| slot. +\itemket{Examples}\mbox{} + +\begin{verbatim} + Initglist(); // in ketlib slot + Implicitplot(''1'',fun,rng); + Setglist(); + + Ketinit(); // in figures slot + Addglist(); +\end{verbatim} +\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/addax2} +\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")\\ +8. Linestyle\\ +9. Color of axes\\ +10. Color of labels\\ + +\itemket{Examples}\mbox{} + +\verb|Setax(["a","","","","","","nw"]);|\\ +\verb|Setax(["","","","","","","","do","red"]);|\\ +\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|Pointdata("1",[[-pi,0]],["Inside=0"]);|\\ +\verb|Drwxy();|\\ +\verb|Plotdata("1","sin(x)","x",["dr","Num=300"]);|\\ +\verb|Pointdata("2",[[pi,0]],["Inside=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} +%------------Setarrow-------------------------------- +\begin{cmd}{Setarrow}{setarrow} +\itemket{Usage}Setarrow(size,angle,position,cut,segstyle) +\itemket{Description}Generic function to set the arrow. +\itemket{Details} Set the style of arrow. Same as options of \hyperlink{arrowdata}{Arrowdata()} .\\ +\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 0 299.02 250.01 , 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=", "Inside=","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],["Inside=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{minipage}{80mm} +\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"]);| +\end{minipage}\hspace{5mm} +\begin{minipage}{30mm} + +\vspace{3mm} + +\input{Fig/putintersect} +\end{minipage} + +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} + +%-------------Setarrow------------------------------ +\begin{cmd}{Setarrow}{setarrow} +\itemket{Usage}Setarrow([arrowsize,angle,position,cut,linestyle]); +\itemket{Description}Generic function to set styles of arrows. +\itemket{Details}Defaults are arrowsize(1),angle(18),position(1),cut(1),linestyle("dr"). +\verb|-1| means to unchange the default. +\itemket{Examples}Setsarrow([-1,30,-1,0.2]); +\end{cmd} + +%------------Arrowdata-------------------------------- +\begin{cmd}{Arrowdata}{arrowdata} +\itemket{Usage}Arrowdata(name,[starting point, ending point] , options) +\itemket{Description}draw an arrow line between two points. + +Options : arrowhead size, arrowhead angle,position,cut position,line type,line color,trimming.\\ +All options do not always reflect on Euclidean view. +\itemket{Examples}\mbox{} + +\verb| Arrowdata("1",[A,B]);|\\ +\verb| Arrowdata("2",[[1,0],[2,3]],[2]);|\\ +\verb| Arrowdata("3",[[2,0],[3,3]],[3,45]);|\\ +\verb| Arrowdata("4",[[3,0],[4,3]],[3,1,0.5]);|\\ +\verb| Arrowdata("5",[[4,0],[5,3]],[3,1,1,0.5]);|\\ +\verb| Arrowdata("6",[[5,0],[6,3]],[3,1,1,1]);|\\ +\verb| Arrowdata("7",[[6,0],[7,3]],[3,"dr,2"]);|\\ +\verb| Arrowdata("8",[[7,0],[8,3]],[3,1,1,0.5,"Color=red"]);|\\ + +\begin{center} +\input{Fig/arrowdata} +\end{center} + +\begin{minipage}{80mm} +\verb| Circledata("1",[A,A.xy+[0.5,0]]);|\\ +\verb| Circledata("2",[B,B.xy+[0.7,0]]);|\\ +\verb| Arrowdata([A,B],["Cutend=[0.5,0.7]"]);|\\ +\verb| Letter([A,"c","A",B,"c","B"]);|\\ +\end{minipage} +\hspace{5mm} +\begin{minipage}{40mm} +\input{Fig/trimarrow} +\end{minipage} + +\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{} + +Let A=[1,1]. +\begin{enumerate}[(a)] +\item \verb|Arrowhead(A,[-1,1]);| +\item \verb|Arrowhead([1,1],[-1,1],[2,60]);| +\item \verb|Arrowhead(A,[-1,1],[2,30,"b"]);| +\item \verb|Arrowhead([1,1],[-1,1],[2,20,"lc"]);| +\end{enumerate} + +\hspace*{17mm}% +\Ltab{30mm}{(a)}\Ltab{30mm}{(b)}\Ltab{30mm}{(c)}\Ltab{30mm}{(d)}\\ +\hspace*{20mm}% +\Ltab{30mm}{\input{Fig/ForRef-Arrowhead-2}}% +\Ltab{30mm}{\input{Fig/ForRef-Arrowhead-3}} +\Ltab{30mm}{\input{Fig/ForRef-Arrowhead-4}} +\Ltab{30mm}{\input{Fig/ForRef-Arrowhead-5}} + +Let D be on the curve crBC. +\begin{enumerate}[(a)]% +\setcounter{enumi}{4}% +\item \verb|Arrowhead(D,"crBC");| +\item \verb|Arrowhead(D,"crBC",[2]);| +\item \verb|Arrowhead(D,"crBC",[2,30,"l"]);| +\item \verb|Arrowhead(D,"Invert(crBC)");| +\end{enumerate} + +\hspace*{17mm}% +\Ltab{30mm}{(e)}\Ltab{30mm}{f)}\Ltab{30mm}{(g)}\Ltab{30mm}{(h)}\\ +\hspace*{20mm}% +\Ltab{30mm}{\input{Fig/ForRef-Arrowhead-7}} +\Ltab{30mm}{\input{Fig/ForRef-Arrowhead-8}} +\Ltab{30mm}{\input{Fig/ForRef-Arrowhead-9}} +\Ltab{30mm}{\input{Fig/ForRef-Arrowhead-10}} + +\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{minipage}[t]{70mm} +2nd-order Bezier curve\\ +\verb|Bezier("1",[A,B],[C]);| +\end{minipage}% +\hspace{5mm}bz1% +\begin{minipage}[t]{60mm} +\mbox{}\vspace{-15mm}\\ +\input{Fig/checkbe1} +\end{minipage}% + +\begin{minipage}[t]{70mm} +3rd-order Bezier curve\\ +\verb|Bezier("c",[A,B],[C,D]);| +\end{minipage}% +\hspace{5mm}bzc% +\begin{minipage}[t]{60mm} +\mbox{}\vspace{-15mm}\\ +\input{Fig/checkbe2} +\end{minipage}% + +\begin{minipage}[t]{70mm} +Connecting two curves,\\ +\verb|Bezier("3",[A,B,C],[[D],[E,F]]);| +\end{minipage}% +\hspace{5mm}bz3% +\begin{minipage}[t]{60mm} +\mbox{}\vspace{-15mm}\\ +\input{Fig/checkbe3} +\end{minipage}% + +\begin{minipage}[t]{70mm} +If D,B,E are on the straight line,\\ the curve becomes smoothly.\\ +\verb|Bezier("S",[A,B,C],[[D],[E,F]]);| +\end{minipage}% +\hspace{5mm}bzS% +\begin{minipage}[t]{60mm} +\mbox{}\vspace{-15mm}\\ +\input{Fig/checkbe4} +\end{minipage}% + +\noindent +\verb|Bezier("name",[A,B,C,D],[E,F,G,H,K,L] );| + +\begin{center} +\input{Fig/checkbe7} +\end{center} + +\noindent +\verb|Bezier("1a",[A,B,C],[[D],[E,F]],["Num=3"]);| + +\begin{center} +\input{Fig/checkbe5} +\end{center} + +\noindent +\verb|Bezier("d5e",[A,B,C],[[D],[E,F]],["Num=200","da"]);| + +\begin{center} +\input{Fig/checkbe6} +\end{center} + +\noindent +\verb|Bezier("1",[A,B,C,D],[E,F,G,H,K,L],["Num=[2,3,4]"]);|\\ + +\begin{center} +\input{Fig/checkbe8} +\end{center} +\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 or the radius. +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]]);|(or \verb|[[0,0],2]|)\\ +\verb| Circledata("1",[A,A+[2,0]]);|(or \verb|[A,2]|)\\ + +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| Drwxy(); |\\ +\verb| repeat(7,s,start -> -2, |\\ +\verb| Pointdata(text(s+3),[s+1,s],["Inside=0","Size=3"]);|\\ +\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],options) +\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). +Option is size of font. For example, ["size=32"] +\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"| or \verb|"Let=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} + +draw $\circ$ at interior angles of a triangle.\\ + +\verb| Listplot([A,B,C,A]);|\\ +\verb| Letter([A,"n1","A",B,"w1","B",C,"e1","C"]);|\\ +\verb| Anglemark([C,B,A],["Expr=\circ","nodisp"]);|\\ + +\begin{center} +\input{Fig/anglemark2} + +\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} + +%--------Drawfigures ------------------------------------ +\begin{cmd}{Drawfigures}{drawfigures} + +\itemket{Usage}Drawfigures(or Drwfigs)(name,List of PDs,List of Options) +\itemket{Description}Manipulate a plural number of PDs together. +\itemket{Remark} List of Options should corrensponds to that of PDs. + +%\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.\\ + +\begin{verbatim} +opcr=["dr"]; +oppt=["Size=2","Color=red"]; +Circledata("1",[[0,1],[0,0]],opcr); +Pointdata("1",[0,0],oppt); +ad1=["cr1","pt1"]; +dt=2*pi/32; +opcr=["dr,0.3"]; +nn=32; +forall(1..nn, + t=dt*#; + Rotatedata(2,ad1,-t,[[0,1],"nodisp"]); + Translatedata(2,"rt2",[t,0],["nodisp"]); + Drawfigures(text(#),["tr2_1","tr2_2"],[opcr,oppt]); +); +\end{verbatim} + +\begin{center} + \input{Fig/drawfigures1} +\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|"No=pointlist"| not executed when any point is selected\\ +\hspace*{5mm}\verb|"File=y/m/n(default:n)"| whether to make data file or not\\ +\hspace*{5mm}\verb|"Check=pointlist"| data file updated if any point is changed + +\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/HatchZuKita8E.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} + +%------------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} + +%------------Readlines-------------------------------- +\begin{cmd}{Readlines}{readlines} + +\itemket{Usage}Readlines(path,filename,option) +\itemket{Description}read a text file line by line. The return value is a list of strings. +\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" ). +\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\\ +\hspace*{10mm}''Setwindow=y/n''\ if "n", command setwindow is not executed.\\ +\hspace*{10mm}''Move=point''\ The lower left changes to the point.\\ +\hspace*{10mm}''Geo=n/y''\ if ''y'', geometric points are created.\\ +\hspace*{10mm}integer\ decides to put names par each interval.\\ +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,["Geo=y"]);| + +\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} + +%--------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|Tabledata([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|Tabledata([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, Putcellexpr}{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|Tabledata(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|xL=apply(1..5,20);|\\ +\verb|xL=apply(1..3,15);|\\ +\verb|Tabledata(xL,yL,["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} +%-----------Asin--------------------------------- +\begin{cmd}{Asin}{asin} +\itemket{Usage}Asin(real) , Acos(real) +\itemket{Description} Return arcsine and arccosine. + +\end{cmd} + +%-----------Sqr--------------------------------- +\begin{cmd}{Sqr}{sqr} +\itemket{Usage}Sqr(real) +\itemket{Description} Return square root. + +\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);\vspace{-2mm} +\itemket{}Slider("pt",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} + +%----------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} +%----------Fracform---------------------------------- +\begin{cmd}{Fracform}{fracform} +\itemket{Usage}Fracform(number,list of denominators) +\itemket{Description}returns Tex-like form of the fraction +\itemket{Examples}\verb|Fracform(0.33,[2,3]); => fr(1,3)| + +\end{cmd} + +%----------Totexform---------------------------------- +\begin{cmd}{Totexform}{totexform} +\itemket{Usage}Totexform(Tex-like form) +\itemket{Description}returns TeX form +\itemket{Examples}\verb|Totexform(fr(1,3)); => frac{1}{3}| + +\end{cmd} + +%----------Totexform---------------------------------- +\begin{cmd}{Tocindyform}{tocindyform} +\itemket{Usage}Tocindyform(Tex-like form) +\itemket{Description}returns Cindy form +\itemket{Examples}\verb|Tocindyform(fr(1,3)); => (1)/(3)| +\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.\\ +Return value is list of breaks and frequency. + +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} + + +%------------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{minipage}[t]{65mm} +\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{minipage}\hspace{5mm}% +\begin{minipage}[t]{65mm} +\mbox{}\vspace{20mm} + +\input{Fig/mxtex03} +\end{minipage} +\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{} + +\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"]);| + +\begin{center} +\includegraphics[bb=0 0 287.01 228.01 , width=50mm]{Fig/meshlab03.pdf} +\end{center} + +\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 uses Maxima. + +\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"]); |\\ + +\begin{center} +\includegraphics[bb=0 0 287.01 189.01 , width=5cm]{Fig/meshlab06.pdf} +\end{center} + +\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"],["Frate=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{Screen} +The screen of KETCindy3D is structured as follows. + +There are two areas surrounded by a white rectangle on the drawing surface of Cinderella. The area on the left side where the NE and the SW are diagonal is referred to as the main screen, and the area on the right side is referred to as the sub screen. + +\vspace{\baselineskip} +\begin{center} + \includegraphics[bb=0 0 879.05 447.02 , width=8cm]{Fig/3dstart.pdf} +\end{center} +As in the case of a flat surface, the main screen shows the range output to TeX and it can be changed by dragging two points of NE and SW. The viewpoint can be moved with the slider below the main screen, and the axis rotates on the main screen. You can think of the sub screen as a viewpoint placed on the xy plane. + +When you draw points and line segments with Cinderella's drawing tool on the main screen, points corresponding to the secondary screen are drawn. You can change the x, y coordinates by dragging the point on the main screen, and drag the point on the sub screen to change the z coordinate. + +\vspace{\baselineskip} +\begin{center} + \includegraphics[bb=0.00 0.00 863.04 378.52 , width=10cm]{Fig/3dscreen.pdf} +\end{center} +KeTCindy3D performs hidden line processing on lines and surfaces. Hidden line processing speeds up processing in cooperation with C language. + +It is necessary to develop an environment that uses C language, but now it is standardized. If you can not use C language, you will use a function to compute with R, but in that case it will take quite a while. + +\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. Ketinit () is also placed in the Initialization Slot, unlike 2D. +\end{cmd} + +%------------ Setangle -------------------------------- +\begin{cmd}{Setangle}{setangle} +\itemket{Usage}Setanlge(TH,FI) +\itemket{Description}Specify rotation angle +\itemket{Details}Specify the TH and FI values of the slider that determines the rotation angle (position of the viewpoint).\\ +For example, if you set \verb| Setangle (70,40) |, then TH and FI are in that position. Since the slider is fixed, if you want to activate the slider again, comment it and re-execute it.\\ +If you want to decide only the initial state\\ +\verb| if (!Ptselected (), Setangle (70, 40))|;\\ +or\\ +\verb| if (!Isangle (), Setangle (70, 40));|\\ + The slider becomes effective. + +If any point on the slider is selected, the figure button is also valid. Click anywhere on the screen and return to the original if you deselect the point selection state. + +\end{cmd} + +%------------ Getangle -------------------------------- +\begin{cmd}{Getangle}{getangle} +\itemket{Usage}Getanlge() +\itemket{Description}Acquire rotation angle +\itemket{Details}Acquires the rotation angle (viewpoint position) TH and FI that can be set with the slider. This is the value displayed on the left side of the slider. The return value is the list [TH, FI], and the angle is expressed by the Degree measure. In addition, the internal variables are THETA and PHI, expressed in circular measure. +\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{}\\ +If option is given a list of exclusion points, that point is not a point of space. (The position does not change even if moving the viewpoint with the slider) + +\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} + +%-------------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} + +\newpage +%================== 3D Drawing =============== + +\subsection{Command for Drawing} +\subsubsection{Point and line} + +%--------------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} + +%--------------Pointdata3d------------------------------ +\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} +%---------------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 "free" or "fix"(default). +\itemket{Examples} \mbox{} + +\verb|Putpoint3d(["A",[2,1,3]]);|\\ +\verb|Putpoint3d(["A",[2,1,3]],"free");| \\ +\verb|Putpoint3d(["A",[1,1,1],"C",[1,0,1]]);|\\ + +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} + +%-----------------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} +%--------------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\\ +\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"]);| + +\begin{center} +\input{Fig/oresenex01} +\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} + +%-------------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} + +%---------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} +%-------------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. + +Options:\\ +\hspace*{5mm}\verb|real number| gap of line\\ +\hspace*{5mm}\verb|"No=pointlist"| not executed when any point is selected\\ +\hspace*{5mm}\verb|"File=y/m/n(default:n)"| whether to make data file or not\\ +\hspace*{5mm}\verb|"Check=pointlist"| data file updated if any point is changed + +\itemket{Examples} \mbox{} + +\verb| Xyzax3data("","x=[-5,5]","y=[-5,4]","z=[-5,3]");| //Data name is "ax3d".\\ +\verb| Putpoint3d(["A",[0,-2,-2]]);|\\ +\verb| Putpoint3d(["B",[-1,1,3]]);|\\ +\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} + +%================== 3D polyhedron =============== +\subsubsection{Polyhedron} + + The description of polyhedron drawing will be explained by taking the case of tetrahedron as an example. + +The tetrahedron is composed of four sides. Letting the vertices be A, B, C, D, the four faces are + +\hspace{20mm}$\triangle\mathrm{ABC}$, $\triangle\mathrm{ABD}$, $\triangle\mathrm{ACD}$, $\triangle\mathrm{BCD}$ + +\begin{center} \input{Fig/concatobj} \end{center} + +If numbers are given to the vertex list [A, B, C, D] in order from A, the vertex order of each face is [1, 2, 3], [1, 2, 4], [1, 3 , 4], [2, 3, 4]. + +[A, B, C, D], [[1, 2, 3], [1, 2, 4], [1, 3, 4], [2 , 3, 4]]] is called "surface data". VertexEdgeFace () draws a polyhedron using this surface data. + +There are two kinds of hidden line processing of polyhedron. The first method is to treat polyhedron as a line drawing, and to process only the hidden part, using Skeletonparadata (). + +The other is to use Phparadata () as a way to draw a part hidden in the surface with a dotted line or hide it, considering it as a surface. + +\vspace{\baselineskip} +%------------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 $\triangle\mathrm{ABC}$, $\triangle\mathrm{ABD}$, $\triangle\mathrm{ACD}$, $\triangle\mathrm{BCD}$.\\ + +\verb| Putpoint3d("A",2*[0,0,sqrt(3)]); |\\ +\verb| Putpoint3d("B",2*[1,-1/sqrt(3),0]);|\\ +\verb| Putpoint3d("C",2*[0,sqrt(3)-1/sqrt(3),0]);|\\ +\verb| Putpoint3d("D",2*[-1,-1/sqrt(3),0]);|\\ +\verb| phd=Concatobj([[A,B,C],[A,B,D],[A,C,D],[B,C,D]]);|\\ +\verb| VertexEdgeFace("1",phd);|\\ +\verb| Skeletonparadata("1");|\\ +\verb| Letter3d([A3d,"ne","A",B3d,"sw","B",C3d,"se","C",D3d,"e","D"]);|\\ + +\begin{center} \input{Fig/concatobj} \end{center} + +If you are drawing tetrahedrons without creating geometric points, you can do as follows. + +\verb| a=2*[-1,-1/sqrt(3),0];|\\ +\verb| b=2*[1,-1/sqrt(3),0];|\\ +\verb| c=2*[0,sqrt(3)-1/sqrt(3),0];|\\ +\verb| d=2*[0,0,sqrt(3)];|\\ +\verb| phd=Concatobj([[a,b,c],[a,b,d],[a,c,d],[b,c,d]]);|\\ + +In the case of a convex polygon such as a tetrahedron, we can use CindyScript 's convexhull 3 d () function as follows. You can save time and effort by simply providing a vertex list instead of a surface list. + +\verb| a=2*[0,0,sqrt(3)];|\\ +\verb| b=2*[1,-1/sqrt(3),0];|\\ +\verb| c=2*[0,sqrt(3)-1/sqrt(3),0];|\\ +\verb| d=2*[-1,-1/sqrt(3),0];|\\ +\verb| phd=convexhull3d([a,b,c,d]);|\\ + +\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]]].\\ + +The generated data is as follows. + +phv3d: list of vertices + +phe3d: list of edges + +phf3d: Surface list + +Each name is appended to the end. + +\itemket{Examples} \mbox{} + +\verb| Putpoint3d("A",2*[-1,-1/sqrt(3),0]); |\\ +\verb| Putpoint3d("B",2*[1,-1/sqrt(3),0]); |\\ +\verb| Putpoint3d("C",2*[0,sqrt(3)-1/sqrt(3),0]); |\\ +\verb| Putpoint3d("D",2*[0,0,sqrt(3)]); |\\ +\verb| phd=[[A,B,C,D],[[1,2,3],[1,2,4],[1,3,4],[2,3,4]]];|\\ +\verb| VertexEdgeFace("1",phd); |\\ + //Three data lists are made, phv3d1:vertex, phe3d1:edge and phf3d1:face. + \begin{center} \input{Fig/vertex01} \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}Make polyhedral plot data with VertexEdgeFace (). For this plot data, hidden surfaces (sides) are hidden-line processed and displayed. The second argument name2 is the same as the name given by VertexEdgeFace (). The hidden line type is specified by the option "Hidden = line type". Hidden lines are not displayed by default setting. +\itemket{Examples} \mbox{} + +To draw a tetrahedron, + +\begin{minipage}[t]{100mm} +\verb| Putpoint3d("A",2*[-1,-1/sqrt(3),0]);|\\ +\verb| Putpoint3d("B",2*[1,-1/sqrt(3),0]);|\\ +\verb| Putpoint3d("C",2*[0,sqrt(3)-1/sqrt(3),0]);|\\ +\verb| Putpoint3d("D",2*[0,0,sqrt(3)]);|\\ +\verb| phd=Concatobj([[A,B,C],[A,B,D],[A,C,D],[B,C,D]]);|\\ +\verb| VertexEdgeFace("1",phd);|\\ +\verb| Phparadata("1","1",["Hidden=do"]);|\\ +\end{minipage}\hspace{5mm}% +\begin{minipage}[t]{30mm} +\mbox{}\vspace{-15mm} + +\input{Fig/phparadata04} +\end{minipage} + + + +A tetrahedron is drawn by VertexEdgeFace (), but it is hidden by Phparadata (). Since it is correctly output if it is drawn with the figure button, it is good to execute Phparadata () after confirming it by displaying it on the screen before executing Phparadata (). + +\vspace{\baselineskip} +Draw a truncated icosahedron of s06 (soccer ball type) using polyhedron data \verb|polyhedrons_obj| by Kobayashi, Suzuki, Mitani. + +\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);|\\ +\verb|Phparadata("1","s06");| //default usage, left figure\\ + +The last two lines we can write the following.\\ +\verb|VertexEdgeFace("1",phd);|\\ +\verb|Phparadata("1","1");| +\begin{center} + \includegraphics[bb=0 0 726.04 365.02 , 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} + +%--------------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]); +Putpoint3d("B",2*[1,-1/sqrt(3),0]); +Putpoint3d("C",2*[0,sqrt(3)-1/sqrt(3),0]); +Putpoint3d("D",2*[0,0,2*sqrt(6)/3]); +phd=Concatobj([[A,B,C],[A,B,D],[A,C,D],[B,C,D]]); +VertexEdgeFace("1",phd); +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} +%================== 3D Surface =============== +\subsubsection{Surface} + +There are wire frame models and surface models for drawing curved surfaces. The wire frame model represents a curved surface with stitches, and the surface model draws its contour as a stitch-free surface. + +In KeTCindy, each drawing is done using the following function. +\begin{tabbing} +1234567890123456789012345678901234567890\=\kill +Wire frame model without hidden wire \>Sf3data(name,form,options)\\ +Surface model\>Sfbdparadata(name,form,options)\\ +Hidden-line wireframe model \>Wireparadata(name,PD,form,n1,n2,options) +\end{tabbing} + +However, in order to do hidden line processing, surface data is necessary, so after drawing with Sfbdparadata (), draw hidden lines with ireparadata (). + +Also, in the drawing of the surface model, it takes time to process the hidden line, so it is assumed to use the C language. Therefore, ExeccmdC () which draws using C language is used together. + + \begin{center} \input{Fig/surfacemodelE} \end{center} + +The form of the argument is an equation and a list of character strings for the domain of the variable. There are three patterns of equations as follows. + +\vspace{\baselineskip} +(1) $z=f(x,y)$ + + \hspace{5mm} 【Example】formula : $z=x^2-y^2$ + + \hspace{15mm} range : $x=(-2,2) , y=(-2,2)$ + +(2) $z=f(x,y),x=g(r,t),y=h(r,t)$ + + \hspace{5mm} 【Example】formula : $z=4-(x^2+y^2) , x=r\cos t , y=r\sin t$ + +\hspace{15mm} range : $r=(0,2) , t=(0,2\pi)$ + +(3) $x=f(u,v),y=g(u,v),z=h(u,v),$ + +\hspace{5mm} 【Example】formula : $x=2\sin u \cos v , y=2\sin u \sin v , z=2\cos u $ + +\hspace{15mm} range : $u=(0,\pi) , v=(0,2\pi)$ + +\vspace{\baselineskip} + +Here, (2) and (3) are parametric types, each consisting of expressions of $ x, y, z $ and two domain of parametric variables. Since it is indistinguishable as it is, when giving it as an argument, "p" is added to the type of (3) as the identification character at the beginning. + +Regarding the domain of definition, there are cases where it is taken in the open section and in the closed section. The distinction is indicated by "ewsn" as boundary designation (both are closed segments). I think the meaning of "ewsn" as follows. + +\vspace{\baselineskip} +For variable $u,v$ , $a \leq u \leq b,c \leq v \leq d$ + + \begin{center} \input{Fig/ewsn} \end{center} + +This boundary designation is added at the end, but it can be omitted, and if omitted, it is the initial value "ewsn" (closed interval). + +To make both open segments, add "". However, do not perform hidden line processing +Sf3data () draws a line also on the boundary, so you can omit this specification. + +\vspace{\baselineskip} +\verb|fd=["p","x=r*cos(t)","y=r*sin(t)","z=2*(2-r)","r=[1,2]","t=[0,2*pi]","ew"]| + +\vspace{\baselineskip} +If this is "e", $ 1 <r \leq 2 $ is obtained, and the top face is not displayed. + +Also, if this is set to "w", $ 1 \leq r <2 $ and the bottom is not displayed. + +Furthermore, if you specify "ewn" or "ews" or abbreviate the initial value "ewsn", it will contain either the left or right value of $ t = (0, 2 \ pi) $, A border appears. + +\vspace{\baselineskip} +\hspace{12mm}"ew" \hspace{25mm}"e" \hspace{25mm}"w" \hspace{25mm}"ewn" + +\input{Fig/frustumew} \input{Fig/frustume} \input{Fig/frustumw} \input{Fig/frustumewn} + +%--------------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:[]. + +\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{} + + +Hidden lines are not shown or shown. + +\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,[],["nodisp"); // Change "nodisp" to "do"|\\ +\verb| ExeccmdC("1"]);|\\ +\verb| );| + +\begin{center} +\input{Fig/sfbdpara01}\hspace{10mm}% +\input{Fig/sfbdpara02} +\end{center} + + +Make the whole thick with a solid line and + + display the hidden line with a dotted line (Default). + +\verb| ExeccmdC("1",["dr,2"]);| + +\vspace{10mm} + +Paraboloid + +\verb| fd=["z=4-(x^2+y^2)","x=R*cos(T)","y=R*sin(T)","R=[0,2]","T=[0,2*pi]","e"];|\\ + +Delete hidden line ( left figure):\verb|ExeccmdC("1",[],["nodisp"]);| + +Hidden lines are indicated by broken lines ( right figure ):\verb|ExeccmdC("1",[],["da"]);| + + \begin{center} \input{Fig/sfbdpara03} \input{Fig/sfbdpara04} \end{center} + +When displaying two curved surfaces, name of Sfbdparadata () is set to "1" and "2", but it can be displayed together as \verb | ExeccmdC ("1") |. + +\verb| fd=[|\\ +\verb| "p",|\\ +\verb| "x=r*cos(t)","y=r*sin(t)","z=2*(2-r)",|\\ +\verb| "r=[1,2]","t=[0,2*pi]","ew"|\\ +\verb| ];|\\ +\verb| fd2=[|\\ +\verb| "p",|\\ +\verb| "x=r*cos(t)-3","y=r*sin(t)+3","z=2*(2-r)",|\\ +\verb| "r=[0,2]","t=[0,2*pi]","ew"|\\ +\verb| ];|\\ +\verb| if(!ptselected(),|\\ +\verb| Startsurf(); |\\ +\verb| Sfbdparadata("1",fd);|\\ +\verb| Sfbdparadata("2",fd2);|\\ +\verb| ExeccmdC("1");|\\ +\verb| );|\\ + +\begin{center} \input{Fig/sfbdpara05} \end{center} + +\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| if(Ptselected(),|\\ +\verb| Sf3data("1",fd);|\\ +\verb| ,|\\ +\verb| Startsurf();|\\ +\verb| Sfbdparadata("1",fd);|\\ +\verb| Wireparadata("1","sfbd3d1",fd,12,12,[],["nodisp"]);|\\ +\verb| ExeccmdC("1",[],["nodisp"]);|\\ +\verb| );|\\ + +\begin{center} \input{Fig/wirepara5} \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| if(Ptselected(),|\\ +\verb| Sf3data("1",fd);|\\ +\verb| ,|\\ +\verb| Startsurf();|\\ +\verb| Sfbdparadata("1",fd);|\\ +\verb| Wireparadata("1","sfbd3d1",fd,12,12);|\\ +\verb| ExeccmdC("1");|\\ +\verb| );|\\ + +\begin{center} +\input{Fig/wirepara3} +\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|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|);| + +\begin{center} +\input{Fig/wirepara4} +\end{center} + +\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{} + +left figure + +\verb| Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]"); |\\ +\verb| Putpoint3d(["A",[0,-3,0],"B",[0,3,3]]); |\\ +\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} + +\end{cmd} + +%================== 3D Using Plot data =============== +\subsection{Using Plot data} + +%--------------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]]); |\\ +\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]]); |\\ +\verb| Spaceline("1",[A,B]); |\\ +\verb| println("PD="+Datalist3d()); | + +\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} + +%------------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]]);|\\ +\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 "I" or "e" .\\ + +\hspace{10mm} put : Create geometric points + +\hspace{10mm} i : Draw a point if it is within a line segment + +\hspace{10mm} e : Draw a point if you meet on the plane + +\vspace{\baselineskip} +Following two programs return the same result.\\ +\verb| IntersectsgpL("P","A-B","C-D-E"); |\\ +\verb| IntersectsgpL("P",[A3d,B3d],[C3d,D3d,E3d]); | + +\vspace{\baselineskip} +Return value is [pt,flag1,flag2,val1,val2] + +pt : The coordinates of the intersection of the straight line and the plane. If the straight line and the plane are parallel and the intersection does not exist, the empty list []. + +flag1 : True if the intersection is within the line segment, false otherwise + +flag2 : True if intersection is in plane, false otherwise + +val1,val2 :Parameter values for line segments, parameter values for planes + +% \verb|IntersectsgpL("P",[p1,p2],[p3,p4,p5],"draw");| +\itemket{Examples} \mbox{} + +Presence or absence of intersection and return value. + +The return value of \verb | flag 1, flag 2 | when changing \verb | p2 | with the following script + +\verb| p1=[1,-1,0];|\\ +\verb| p2=[0,0,1/2];|\\ +\verb| p3=[0,1,0];|\\ +\verb| p4=[-1,0,0];|\\ +\verb| p5=[0,0,1];|\\ +\verb| Spaceline("1",[p1,p2]);|\\ +\verb| Spaceline("2",[p3,p4,p5,p3]);|\\ +\verb| ret=IntersectsgpL("P",[p1,p2],[p3,p4,p5],"put");|\\ +\verb| println("flag1="+ret_2+": flag2="+ret_3);| + +\verb| p2=[0,0,1/2]; p2=[-1,1,1];|\\ +\verb| flag1=false : flag2=true flag1=true : flag2=true |\\ + + +\hspace*{20mm} +\begin{minipage}{60mm} +\input{Fig/wire01} +\end{minipage}\hspace{10mm}% +\begin{minipage}{60mm} +\input{Fig/wire02} +\end{minipage} + +\verb| p2=[1,2,1]; p2=[1,0,1/2];|\\ +\verb| flag1=true : flag2=false flag1=false : flag2=false | + +\hspace*{20mm} +\begin{minipage}{60mm} +\input{Fig/wire03} +\end{minipage}\hspace{10mm}% +\begin{minipage}{60mm} +\input{Fig/wire04} +\end{minipage} + +{\bf Cutcube} + +\verb| Hn=3; |\\ +\verb| Putaxes3d(Hn); |\\ +\verb| Putpoint3d("A",[Hn,Hn,0]); |\\ +\verb| Putpoint3d("B",[Hn,0,Hn]); |\\ +\verb| Putpoint3d("C",[Hn,Hn,Hn]); |\\ +\verb| Putpoint3d("D",[0,Hn,Hn]); |\\ +\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); |\\ +\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} +%-------------Sfcutparadatacdy------------------------------- + +\begin{cmd}{Sfcutparadatacdy}{sfcutparadatacdy} +\itemket{Usage}Sfcutparadatacdy(name,string,list,options) +\itemket{Description}Obtain a line of intersection between a plane and a curved surface. +\itemket{Details}string is equation of plane, list is equation of a surface. +\itemket{Examples} \mbox{} +Cross section of cone. + +\verb|fd=[|\\ +\verb| "p",|\\ +\verb| "x=r*cos(t)","y=r*sin(t)","z=2*(2-r)",|\\ +\verb| "r=[0,2]","t=[0,2*pi]","e"|\\ +\verb|];|\\ +\verb|Startsurf(); |\\ +\verb|Sfbdparadata("1",fd);|\\ +\verb|Sfcutparadatacdy("1","y+2*z=3",fd);|\\ +\verb|ExeccmdC("1");| + +\begin{center} +\input{Fig/sfcut} +\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} + + +%---------------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]]); |\\ +\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]]); |\\ +\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]]);|\\ +\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]]);|\\ +\verb|pt=Scalepoint3d(A3d,[3,2,4],[1,1,1]); //pt=[4,-3,5]|\\ +\verb|Putpoint3d(["B",pt]);| + +\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); |\\ + +\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]]); |\\ +\verb|pt=Translatepoint3d(A3d,[-1,1,1]); |\\ +\verb|Putpoint3d(["B",pt]); | + +\end{cmd} +% Others ================================== +\subsection{Others} +%--------------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. + +\verb| Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,4]"); |\\ +\verb| Putpoint3d(["O",[0,0,0]]); |\\ +\verb| Putpoint3d(["P",[1,1,1]]); |\\ +\verb| Perpplane("E-F","P",P3d-O3d,"put"); |\\ +\verb| vec1=2*(E3d-P3d); |\\ +\verb| vec2=2*(F3d-P3d); |\\ +\verb| Putpoint3d(["A",P3d+vec1+vec2]); |\\ +\verb| Putpoint3d(["B",P3d+vec1-vec2]); |\\ +\verb| Putpoint3d(["C",P3d-vec1-vec2]); |\\ +\verb| Putpoint3d(["D",P3d-vec1+vec2]); |\\ +\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"); | + +\begin{center} +\input{Fig/perpplane} +\end{center} + +\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]); |\\ +\verb|Putpoint3d("A",[3,0,0]); |\\ +\verb|Putpoint3d("B",[0,3,0]); |\\ +\verb|Putpoint3d("C",[0,0,3]); |\\ +\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} +%---------------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} +%-------------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}\mbox{} + +Data of all \verb|Johnson solid| can be downloaded from\\ +\hspace*{20mm}\url{http://mitani.cs.tsukuba.ac.jp/polyhedron/}\\ +Store the folder into the work folder of \ketcindy\ for example, and execute\\ +\verb| Setdirectory(gethome+"/ketcindy/polyhedrons_obj");|\\ +\verb| polydt=Readobj("r02.obj",["size=2"]);|\\ +\verb| Setdirectory(Dirwork);|\\ +Then the data of \verb|r02.obj| are assigned to the variable \verb|polydt|. + +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|VertexEdgeFace("1",polydt);| //output data name is phf3d1\\ +\verb|Nohiddenbyfaces("1","phf3d1");| + +\begin{center} \input{Fig/readobj} \end{center} + +The main polyhedral data is as follows. + + \input{Fig/kobayashiE} + +\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} + +%--------------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} + +%--------------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} +%--------------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]]);|\\ +\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]]);|\\ +\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]]);|\\ +\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]]);|\\ +\verb|Perpplane("E-F","P",P3d-O3d,"put");|\\ +\verb|vec1=3*(E3d-P3d);|\\ +\verb|vec2=3*(F3d-P3d);|\\ +\verb|Putpoint3d(["A",P3d+vec1+vec2]);|\\ +\verb|Putpoint3d(["B",P3d+vec1-vec2]);|\\ +\verb|Putpoint3d(["C",P3d-vec1-vec2]);|\\ +\verb|Putpoint3d(["D",P3d-vec1+vec2]);|\\ +\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} + + +%-------------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} +%-------------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} + +%-----------Expr3d--------------------------------- +\begin{cmd}{Expr3D}{expr3d} +\itemket{Usage}Expr([position, direction, string],options) +\itemket{Description}Display the string. +\itemket{Details} The position is the space coordinate. Other than that it is the same as Expr(). +\end{cmd} + +%-----------Letter3d--------------------------------- +\begin{cmd}{Letter3D}{letter3d} +\itemket{Usage}Letter([position, direction, string],options) +\itemket{Description}Display the string. +\itemket{Details} The position is the space coordinate. Other than that it is the same as Letter(). +\itemket{Examples} \mbox{} + +\verb|Putpoint3d("A",2*[0,0,2*sqrt(6)/3]);|\\ +\verb|Putpoint3d("B",2*[1,-1/sqrt(3),0]);|\\ +\verb|Putpoint3d("C",2*[0,sqrt(3)-1/sqrt(3),0]);|\\ +\verb|Putpoint3d("D",2*[-1,-1/sqrt(3),0]);|\\ +\verb|Putpoint3d("M",(B3d+C3d)/2);|\\ +\verb|phd=Concatobj([[A,B,C],[A,B,D],[A,C,D],[B,C,D]]);|\\ +\verb|VertexEdgeFace("1",phd);|\\ +\verb|Spaceline("1",[A,M,D]);|\\ +\verb|Nohiddenbyfaces("1","phf3d1");|\\ +\verb|Letter3d([A3d,"ne","A",B3d,"w","B",C3d,"se","C",D3d,"e","D"]);|\\ +\verb|Letter3d(M3d,"sw","M",["Color=blue"]);|\\ + +\begin{center} +\input{Fig/letter3d} +\end{center} +\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{initglist}{Initglist} \> add the list in ketlib slot to that of figures slot.\\ +\hyperlink{ptsize}{Ptsize} \> set the size of points.\\ +\hyperlink{setarrow}{Setarrow} \> set the style of arrow.\\ +\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{drawfigures}{Drawfigures} \> manipulate a plural number of PDs together.\\ +\hyperlink{anglemark}{Anglemark} \> draw an angle mark.\\ +\hyperlink{setarrow}{Setarrowdata} \> set styles of arrows.\\ +\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{asin}{Asin} \> return arcsine and arccosine.\\ +\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{readcsv}{Readcsv} \> read a file in csv format.\\ +\hyperlink{readlines}{Readlines} \> read a text file line by line.\\ +\hyperlink{readoutdata}{ReadOutData} \> read external data.\\ +\hyperlink{sqr}{Sqr} \> return square root.\\ +\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{putcell}{Putcellexpr} \> put a math expression at the cell.\\ +\hyperlink{putcol}{Putcol} \> put strings to a column.\\ +\hyperlink{putcolexpr}{Putcolexpr} \> put math expressions to a column.\\ +\hyperlink{putrow}{Putrow} \> put strings to a row.\\ +\hyperlink{putrowexpr}{Putrowexpr} \> put math expressions to a row.\\ +\hyperlink{tabledata}{Tabledata} \> draw rules of a table.\\ +\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.\\ +\hyperlink{fracform}{Fracform} \>return TeX-like form of the fraction.\\ +\hyperlink{totexform}{Totexform} \> return TeX form.\\ +\hyperlink{tocindyform}{Tocindyform} \> return Cindy form.\\ + +{\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{expr3d}{Expr3d} \> display the string.\\ +\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{letter3d}{Letter3d} \> display the string.\\ +\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} \> create a basic vector on a vertical plane\\ +\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{sfcutparadatacdy}{Sfcutparadatacdy} \> Display intersection line of surface and surface.\\ +\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.\\ +\hyperlink{setangle}{Setangle} \>Set TH and FI\\ +\hyperlink{getangle}{Getangle}\>Get TH and FI\\ +\end{tabbing} + +\end{document}
\ No newline at end of file diff --git a/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/KeTCindyReferenceJ.tex b/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/KeTCindyReferenceJ.tex new file mode 100644 index 0000000000..aa8c5bd234 --- /dev/null +++ b/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/KeTCindyReferenceJ.tex @@ -0,0 +1,8423 @@ +\documentclass[papersize,a4paper,12pt,uplatex]{jsarticle} +\usepackage{ketpic,ketlayer} +\usepackage{amsmath} +% \usepackage{amsmath,newtxmath} +\usepackage[dvipdfmx]{graphicx,color} +\usepackage{wrapfig} +\usepackage{jsverb} +\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 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} + +%設定・定義 ================================== + +\subsection{設定・定義} + +\subsubsection{環境設定} + +\begin{description} + +\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。 + +\vspace{\baselineskip} +\hypertarget{Initglist}{} +\item[関数]Initglist(), Setglist(), Addglist() +\item[機能]ketlibスロットで作られる描画データを描画リストに追加する。 +\item[説明]Implicitplot,Hatchdataなど実行時間のかかるコマンドをfiguresスロットにおくと,その都度実行されてしまう。それを避けるためketlibスロットにおいたときに用いる。 + +\begin{verbatim} + Initglist(); // ketlibスロットで + Implicitplot(''1'',fun,rng); + Setglist(); + + Ketinit(); // figuresスロットで + Addglist(); +\end{verbatim} + +\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} + 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。 +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} +Listplot([B,A,C]); +Letter([A,"ne","A",B,"se","B",C,"se","C"]); +\end{verbatim} + +\vspace{\baselineskip} +\hspace{10mm} \input{Fig/addax1}\input{Fig/addax2} + + +\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\\ + 矢印の大きさの倍率を指定するときは,"a0.5"のようにする。\\ + また,矢印のスタイルは Setarrowで指定する。 + +2. 横軸名 初期設定は \verb|"x"| + +3. 横軸名の位置 初期設定は \verb|"e"| + +4. 縦軸名 初期設定は \verb|"y"| + +5. 縦軸名の位置 初期設定は \verb|"n"| + +6. 原点名 初期設定は \verb|"O"|(文字として書かれる) + +7. 原点名の位置 初期設定は \verb|"sw"| + +8. 線種 + +9. 線の色 + +10. ラベルの色 + +それぞれダブルクォートでくくる。色は,色名が使える。"red" など。 + +10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】軸を赤の点線にする。 + +\hspace{10mm}\verb|Setax(["","","","","","","","do","red"]);| + +【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="] + +\begin{layer}{150}{0} +\putnotese{75}{10}{\scalebox{0.8} {\input{Fig/drwxy}}} +\end{layer} + +【例】点$(-\pi,\ 0)$と$(\pi,\ 0)$を白抜きの点で表示する。 +\begin{verbatim} +Setax([7,"se"]); +Setpt(5); +Pointdata("1",[[-pi,0]],["Inside=0"]); +Drwxy(); +Plotdata("1","sin(x)","x",["dr","Num=200"]); +Pointdata("2",[[pi,0]],["Inside=0"]); +\end{verbatim} + +このスクリプトでは,\verb| Pointdata("1",[[-pi,0]],["Inside=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,再び \verb| ["Inside=0"]);|にして実行するので,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{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} +Definecolor("darkmaz",[0.8,0,0.8]); +Setcolor("darkmaz"); +\end{verbatim} + + +\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。 + + +\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} +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。 + + +\vspace{\baselineskip} +\hspace{20mm} \includegraphics[width=3.5cm,bb=0 0 161 134]{Fig/setcolor.pdf} + +\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\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。 + +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。 + +\vspace{\baselineskip} +【例】 +$f(x)=\dfrac{1}{x^2+1}$ を定義し,グラフを描く。 + +\begin{verbatim} +Deffun("f(x)",["regional(y)","y=1/(x^2+1)","y"]); +Plotdata("1","f(x)","x"); +\end{verbatim} + +\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{verbatim} +Deffun("f(x)",["regional(y)","if(x>=0,y=1,y=-1)","y"]); +Plotdata("1","f(x)","x",["Dis=1","Num=100"]; +\end{verbatim} + +\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} +Pointdata("1",[A,B,C,D,E,F,G],["Size=2"]); +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{layer}{150}{0} +\putnotese{60}{5}{\input{Fig/pointsize}} +\end{layer} + +\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} + + +\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\hypertarget{setarrow}{} +\item[関数]Setarrow(size,angle,position,cut,segstyle) +\item[機能]矢線の形状の設定をする。 +\item[説明]引数は,順に,矢じりの大きさ, 開き角, 矢じり位置, 切り込み位置, 線種と表示色 + +それぞれの意味と値は,\hyperlink{arrowdata}{Arrowdata()} を参照のこと。 + +\vspace{\baselineskip} +\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] \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。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。 + +\hspace{10mm}\verb|Setorigin([3,2]);| + +原点を点Aの位置にして座標軸を描く。 + +\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]); +Pointdata("1",[1,1],["Size=3"]); +Letter([[1,1],"s2","P"]); +\end{verbatim} +左が実行時のCinderellaの画面,右が\TeX の結果。\\ + +\hspace{10mm} \includegraphics[bb=0 0 299.02 250.01, width=4cm]{Fig/setorigin.pdf} +\hspace{5mm}\input{Fig/setorigin} + +\vspace{\baselineskip} +\hypertarget{setpen}{} +\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。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}{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} +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} + +\vspace{\baselineskip} +\hypertarget{setunitlen}{} +\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(xの範囲, yの範囲) +\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。 + +\vspace{\baselineskip} +【例】\verb|Setwindow([-5,5],[-1,3]);| + +\vspace{\baselineskip} +\hspace{10mm}\includegraphics[bb=0.00 0.00 415.02 199.01,width=6cm]{Fig/setwindow.pdf} + +\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\end{description} + +%\newpage +%=========== 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。 + +基本的な書式は次の通り。 + +\hspace{20mm} 関数名(name , 点リストなど , options); + +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。なお,name に演算記号は使えないので,番号として負の数は使えない。 + +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。 + +\begin{tabbing} +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} + +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} + +\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=","Inside"。 + +Inside オプションは,点の内部についての指定。ただし,Cinderellaの描画面には反映されない。 + +0 : 白抜き + +0から1まで : 濃度 + +-1 : 塗らない + +カラーコードまたは色名 : その色で塗る + +\vspace{\baselineskip} +【例】 + +(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],["Inside=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"]);| + +\begin{layer}{150}{0} +\putnotese{90}{5}{ \input{Fig/pointdata}} +\end{layer} + +(7) 節点を明示した木を描く +\begin{verbatim} +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} + +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} + +%\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。 + +%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 + +%\begin{layer}{150}{0} +%\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} + + +%\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。 + +\begin{layer}{150}{0} +\putnotese{80}{5}{\input{Fig/putintersect}} +\end{layer} + +\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} + +\vspace{\baselineskip} + 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} \scalebox{0.9}{\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を端点とす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。指定した点がすでに存在する場合は動かさない。 + +\vspace{\baselineskip} +【例】 + +線分AB上に点Cをとる。 + + \verb|Putonseg("C",A,B);| + +点(-1,0),(2,2)を通る線分上に点Cをとる。 + + \verb|Putonseg("C",[[-1,0],[2,2]]);| + +\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{70}{10}{\scalebox{0.9}{\input{Fig/reflectpoint}}} +\end{layer} + +\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{75}{5}{ \scalebox{0.8}{\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} $だけ回転した点 + +\begin{verbatim} +C.xy=Rotatepoint(A,2*pi/3,B); +D.xy=Rotatepoint((5,2),pi/3,B); +E.xy=Rotatepoint([3,0],-pi/4,A); +\end{verbatim} +注)図の点線は位置関係を示すためのもの。 + +点名や座標は,実際にはLetter()関数で記述する。 + +\vspace{\baselineskip} +\hypertarget{scalepoint}{} +\item[関数]Scalepoint(点,比率ベクトル,中心) +\item[機能]点の位置の拡大・縮小を行う +\item[説明]点を,指定された中心を原点とする座標系で,比率ベクトルの分だけ拡大・縮小した位置の座標を返す。 + +\vspace{\baselineskip} +【例】点A〜Fは作図ツールで適当な位置にとっておく。 + +点Dを,点Aを原点を中心に横に3倍,縦に2倍した位置に置く。 + +点Eを,点Aを点Bを中心に横に3倍,縦に2倍した位置に置く。 + +点Fを,点Aを原点を中心にベクトル$\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} $だけ平行移動した点にする。 +\begin{verbatim} +C.xy=Translatepoint(A,[2,3]); +D.xy=Translatepoint(A,B.xy); +\end{verbatim} + +\hspace{20mm} \scalebox{0.9}{\input{Fig/translatepoint}} + +\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\hypertarget{arrowdata}{} +\item[関数]Arrowdata(name,[始点 , 終点] , options) +\item[機能]2点間を結ぶ矢線を描く。 +\item[説明]name は,座標を数値で与えるときに必要。幾何要素の識別名で与えるときはなくてもよい。 + +optionsは矢じりの形状などの指定。 + +\hspace{10mm} [ 矢じりの大きさ, 開き角, 矢じり位置,切り込み位置, 線種, 線の表示色,トリミング] + +のリストで与える。矢じりの大きさから切り込み位置までは数で,後方のオプションを指定するときは,前方も書く。 + +開き角は60分法で与える。ただし,° はつけない。5未満の時は18°の倍数指定とする。 + +矢じり位置は,線分の長さを1とした始点からの距離。 + +切り込み位置は,0のとき三角形の矢じり,1のとき線のみの矢じりとなる。 + +ただし,Cinderellaの画面上には全ては反映されない。たとえば,太さ指定をしても画面上では太さは同じ。 + +トリミング :"Cutend=m" または "Cutend=[m,n]" で,右辺が数のときは両端をmだけカットする。リストのときは始点をm,終点をnだけカットする。mが負のときは延長する。 + +これらの設定は,\hyperlink{setarrow}{Setarrow()} で初期設定を変更することができる。 + +\vspace{\baselineskip} +【例】オプションの設定とその結果を示す。 + +\begin{verbatim} +Arrowdata("1",[A,B]); +Arrowdata("2",[[1,0],[2,3]],[2]); +Arrowdata("3",[[2,0],[3,3]],[3,45]); +Arrowdata("4",[[3,0],[4,3]],[3,1,0.5]); +Arrowdata("5",[[4,0],[5,3]],[3,1,1,0.5]); +Arrowdata("6",[[5,0],[6,3]],[3,1,1,1]); +Arrowdata("7",[[6,0],[7,3]],[3,"dr,2"]); +Arrowdata("8",[[7,0],[8,3]],[3,1,1,0.5,"Color=red"]); +\end{verbatim} +\hspace{20mm}\input{Fig/arrowdata} + +【例】2つの円を矢線で結ぶ。 + +\begin{layer}{150}{0} +\putnotese{75}{0}{\input{Fig/trimarrow}} +\end{layer} +\hspace{20mm} + +\begin{verbatim} + Circledata("1",[A,A.xy+[0.5,0]]); + Circledata("2",[B,B.xy+[0.7,0]]); + Arrowdata([A,B],["Cutend=[0.5,0.7]"]); + Letter([A,"c","A",B,"c","B"]); +\end{verbatim} +Cinderellaの作図ツールで2点ABをとっておく。 + +円A,Bの半径が同じ(たとえば0.5)であれば,\verb|Arrowdata([A,B],["Cutend=0.5"]);| でよい。 + +\vspace{\baselineskip} +\hypertarget{setarrow}{} +\item[関数]Setarrow([arrowsize,angle,position,cut,linestyle]) +\item[機能]Arrowdata,Arrowheadで描く矢印のスタイルを設定する。 +\item[説明]arrowsize,angle,position,cut,linestyleは,順に大きさ(1),開き角(18),位置(1),切り込み(0),矢線スタイル("dr")である。(カッコ内はデフォルト値) + + +%\begin{flushright}\hyperlink{functionlist}{$\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。 + +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{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} + +\vspace{70mm} + +\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。 + +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。mが負のときは延長する。 + +\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} \scalebox{0.9}{\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{75}{0}{\input{Fig/listplot1}} +\end{layer} +\hspace{20mm} + +\begin{verbatim} +Addax(0); +Listplot([A,B,C,A]); +\end{verbatim} + +点の位置は座標で指定してもよい。 + +その場合は name が必要。 + +\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{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。 + +円A,Bの半径が同じであれば,\verb|Listplot([A,B],["Cutend=0.5"]);| でよい。 + +\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{\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{0.8}{ \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=5.5cm]{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{60}{-10}{\scalebox{0.9}{ \input{Fig/checkbe1}}} +\end{layer} + +2次ベジェ曲線 + +\verb|Bezier("1",[A,B],[C]);| + +\vspace{20mm} + +\begin{layer}{150}{0} +\putnotese{60}{-10}{\scalebox{0.9}{\input{Fig/checkbe2}}} +\end{layer} + +3次ベジェ曲線 + +\verb|Bezier("2",[A,B],[C,D]);| + +\vspace{20mm} + +\begin{layer}{150}{0} +\putnotese{60}{-10}{\scalebox{0.9}{ \input{Fig/checkbe3}}} +\end{layer} + +%ベジェ曲線をつなげる + +%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。 + +\verb|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。 +\newpage + +\verb|Bezier("4",[A,B,C,D],[E,F,G,H,K,L] ); | + +\begin{layer}{150}{0} +\putnotese{20}{2}{\input{Fig/checkbe7}} +\end{layer} + +\vspace{35mm} + +オプションの例 + +\verb|Bezier("5",[A,B,C],[[D],[E,F]],["Num=3"]);| + +\hspace{20mm}\input{Fig/checkbe5} + +\verb|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。 + +\verb|Bezier("1",[A,B,C,D],[E,F,G,H,K,L],["Num=[2,3,4]"]);| + +\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。 + +\vspace{\baselineskip} +【例】 + +\verb|Beziersmooth("1",[A,B,C,D]);| + +\begin{layer}{150}{0} +\putnotese{70}{35}{bz1} +\putnotese{40}{5}{ \input{Fig/checksm1}} +\end{layer} + +\vspace{40mm} +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}{30}{bz1} +\putnotese{40}{05}{ \input{Fig/checksm2}} +\end{layer} + +\vspace{35mm} + +\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。 + +\vspace{\baselineskip} +【例】 + +\begin{layer}{150}{0} +\putnotese{70}{27}{bz1} +\putnotese{40}{00}{ \input{Fig/checksy1}} +%\putnotese{0}{0}{Beziersym("1",[A,B,C,D]);} +%\putnotese{0}{15}{C2p と C3p は表示されない} +\end{layer} + +\verb|Beziersym("1",[A,B,C,D]);| + +C2p と C3p は表示されない + +\vspace{25mm} + +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} + +\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +%\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]]]]);| + + \scalebox{0.95}{\input{Fig/checkmc1}} + +\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 + +\verb|"Deg=..."| 次数指定ができる。(初期設定は3次) + +\verb|"Num=..."| 各区間の区間数(分点数$-1$)を指定できる。(初期設定は10) + +\vspace{\baselineskip} + +【例】 + +\begin{layer}{150}{0} +\putnotese{70}{25}{bzA} +\putnotese{40}{-5}{ \input{Fig/checkb8}} +\end{layer} + +\verb|Mkbezierptcrv([A,B,C]);| + +\vspace{23mm} + +その後,節点や制御点を動かして,\par +描きたいものにする。 + +\begin{layer}{150}{0} +\putnotese{70}{25}{bzA} +\putnotese{55}{-15}{ \input{Fig/checkb11}} +\end{layer} + +\vspace{35mm} + +\begin{layer}{150}{0} +\putnotese{70}{28}{bzA} +\putnotese{50}{-3}{\input{Fig/checkb9}} +\end{layer} + +\verb|Mkbezierptcrv([A,B,C],["Deg=2"]);| + +\verb|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 + + \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。 + +\begin{center} \input{Fig/checkbs1}\end{center} + +【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。 + +\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[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,次が使える。 + +\verb|size ->n|:画面上での線の太さを指定する。 + +\vspace{\baselineskip} +【例】\verb|CRspline("1",[A,B,C,D]);| + +\hspace{20mm} \input{Fig/checkCR} + +%\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\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(か半径),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} +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]]);|\\ + \hspace{50mm}(\verb|[[0,0],2]|でもよい)\\ + \>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]]);|\\ + \hspace{50mm}(\verb|[A,2]|でもよい)\\ + \>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} +\vspace{\baselineskip} + +%\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。 + +\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\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。 +\newpage + +\vspace{\baselineskip} +\begin{layer}{150}{0} +\putnotese{75}{5}{ \includegraphics[bb=0 0 272.01 240.01, width=4cm]{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} \scalebox{0.9}{\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{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} + +\begin{center} \scalebox{0.9}{\input{Fig/ellipseplot2}} \end{center} + + +\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} \scalebox{0.9}{\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】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");| + +\vspace{\baselineskip} +\hspace{20mm} \scalebox{0.8}{\input{Fig/plotdata1}} + + \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} +Plotdata("1","tan(x)","x",["Num=200","Dis=50"]); +\end{verbatim} +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) + +\vspace{\baselineskip} +\hspace{20mm} \input{Fig/plotdatatan1}\hspace{20mm} \input{Fig/plotdatatan2} + +\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} +Plotdata("1","floor(x)","x",["Num=100","Dis=0.9"]); +Drwxy(); +repeat(7,s,start -> -2, +Pointdata(text(s+3),[s+1,s],["Inside=0","Size=3"]); +); +\end{verbatim} + +\hspace{45mm}\input{Fig/plotdata5} + +なお,ここで,Pointdata() のname を \verb|text(s+3)| としているのは,s が $-2$ から始まるので,負の数が使えない name を $1$ から始まるようにするためである。 + +\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{layer}{150}{0} +\putnotese{95}{3}{\scalebox{0.8}{{\input{Fig/assign}}}} +\end{layer} +\begin{verbatim} +repeat(50,t, + cb=t/5-5; + Plotdata(text(t),Assign("b*x-b^2","b",cb),"x"); +); +\end{verbatim} + +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}\scalebox{0.9}{\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。 + +\vspace{\baselineskip} +【例】$y''=-y$で,初期値が$x=0$のとき$y=1,y'=0$ の解曲線 + +\verb|Deqplot("1","y''=-y","x",0, [1,0]); | + +注) 微分記号のプライムは,シングルクォートまたはバッククォート。 + +\vspace{\baselineskip} +\hspace{20mm}\input{Fig/deqplot1} + +\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} + +\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 +\begin{verbatim} +Deqplot("3","[x,y]'=[x*(1-y),0.3*y*(x-1)]","t=[0,20]", +[1,0.5],["Num=200"]); +\end{verbatim} + +\vspace{\baselineskip} +\hspace{20mm}\input{Fig/deqplot3} + +\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 + +\vspace{\baselineskip} +【例】サイクロイド曲線を描く。 + +\hspace{10mm} \verb|Paramplot("1","[t-sin(t),1-cos(t)]","t=[0,2*pi]");| + +\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} +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} +\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{10mm}\verb|Polarplot("1","2*(1+cos(t))","t=[0,2*pi]",["Num=200"]);| + +\vspace{\baselineskip} +\begin{center}\scalebox{0.7}{\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 + +\begin{verbatim} +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} + +\hspace{20mm}\input{Fig/periodfun.tex} + +\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} + +\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} + Fourierseries("1",["1/2","0","(1-(-1)^n)/(pi*n)"],2,6,["Num=200"]); +\end{verbatim} + +\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} + +\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],option) +\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。 + +optionは フォントサイズで,["size=32"] のように指定する。 + +\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} +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} +\vspace{\baselineskip} +\begin{center} \input{Fig/expr}\end{center} + +【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 , 方向,文字列,option) +\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 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。 + +optionは フォントサイズで,["size=32"] のように指定する。 + +\begin{verbatim} +Exprrot([3,2],[2,-1],"t0n1","\sqrt{3}"); +Exprrot(C,B-A,"\frac{2}{3}"); +\end{verbatim} + +\vspace{\baselineskip} +\hspace{10mm}\includegraphics[bb=0.00 0.00 181.01 131.01,width=4cm]{Fig/exprrot.pdf} \hspace{10mm} \input{Fig/exprrot} + +\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\vspace{\baselineskip} +\hypertarget{letter}{}\item[関数]Letter([位置, 方向, 文字列],option) +\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。 + +場所は上下左右を東西南北で表し, n/s/w/e/c の方向で表す。cは中央。 + +%\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。 + +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$'$(シングルクォート)を用いる。 + +optionは フォントサイズで,["size=32"] のように指定する。 + +文字列が一つのときは, + +Letter(位置, 方向, 文字列,option) + +にできる。 + +\vspace{\baselineskip} +【例】 + +座標 (2,1) の南東にPを表示 + +\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 $"]);| + +\vspace{\baselineskip} +\hypertarget{letterrot}{}\item[関数]Letterrot(座標, 方向ベクトル,移動量, 文字列,option) +\item[機能]文字列を回転して表示する +\item[説明]座標で示された位置に,方向ベクトルで指定された向きに回転して文字を書き込む。 + +第3引数は微小移動量で,略すこともできる。 + +optionは フォントサイズで,["size=32"] のように指定する。 + +\begin{verbatim} +Letterrot(C,B-A,"t2n5","AB"); +\end{verbatim} + +移動量を略して + +\hspace{10mm}\verb|Letterrot(C,B-A,"AB");| + +とすることもできる。この場合は,微小な移動はされない。 + +\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +%\newpage +\end{description} +% ====== マーキング ============== +\subsubsection{マーキング} +\begin{description} + +\hypertarget{anglemark}{} +\item[関数]Anglemark(name,点リスト , options) +\item[機能]点リストで示された角に弧の形状の角の印をつける。 +\item[説明]Listplot() などと同様,点リストが点名の場合はnameは省略できる。弧を描かず文字だけを入れる場合は options に "nodisp" を指定する。 + +optionsは次の通り。 + +数値角の印の大きさ。 初期設定は1 + +線種"dr, n", "da,m,n" , "do,m,n" + +"Expr=文字" または "Letter=文字" : 文字を入れる + +"Expr=位置 , 文字": 位置を指定して文字を入れる。位置は頂点からの距離。 + +\vspace{\baselineskip} +【例】三角形の内角に印をいれ,文字を書き込む。(下図左) +\begin{verbatim} +Listplot([A,B,C,A]); +Letter([A,"n1","A",B,"w1","B",C,"e1","C"]); +Anglemark([B,A,C]); +Anglemark([C,B,A],["Expr=\theta"]); +Anglemark([A,C,B],[2,"dr,3","Expr=2,\alpha"]); +\end{verbatim} + +【例】三角形の内角に弧を描かず,$\circ$ だけ書き込む。(下図右) +\begin{verbatim} +Listplot([A,B,C,A]); +Letter([A,"n1","A",B,"w1","B",C,"e1","C"]); +Anglemark([C,B,A],["Expr=\circ","nodisp"]); +\end{verbatim} + + +\input{Fig/anglemark}\hspace{5mm}\input{Fig/anglemark2} + +※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。 + +\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。 + +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} +\begin{layer}{150}{0} +\putnotese{85}{0}{ \scalebox{0.8}{\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 tn + + 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}{0}{ \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} \scalebox{0.7}{\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} +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} + +【例】四角形ABCDを描き線分に印をつける。 + +\begin{layer}{150}{0} +\putnotese{90}{0}{ \input{Fig/segmark}} +\end{layer} +\hspace{50mm} +\begin{verbatim} +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} + +%\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:\verb|Htickmark([1,"1",2,"n1","2",3,"se","3",4,"4"]);| + +\vspace{\baselineskip} +\begin{center} +\input{Fig/htickmark01} +\end{center} + +%\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。 + +\begin{center} \scalebox{0.8}{\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{\baselineskip} +【例】点$(0,\ 1),\ (0,\ 2)$の西側に$1,\ 2$を表示する。 + +\hspace{10mm}\verb|Vtickmark([1,"1",2,"2"]);| + +\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} +\vspace{\baselineskip} +\begin{center} \scalebox{0.9}{\input{Fig/ruler1}} \end{center} +\vspace{\baselineskip} +%\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +【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}\scalebox{0.9}{ \input{Fig/ruler}} \end{center} +%\vspace{\baselineskip} +\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\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} + +\hypertarget{drawfigures}{} +\item[関数]Drawfigures(or Drwfigs)(name ,データリスト,オプションリスト) +\item[機能]複数のプロットデータのスタイル(オプション)をリストで与えて描画する +\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) + +%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} +opcr=["dr"]; +oppt=["Size=2","Color=red"]; +Circledata("1",[[0,1],[0,0]],opcr); +Pointdata("1",[0,0],oppt); +ad1=["cr1","pt1"]; +dt=2*pi/32; +opcr=["dr,0.3"]; +nn=32; +forall(1..nn, + t=dt*#; + Rotatedata(2,ad1,-t,[[0,1],"nodisp"]); + Translatedata(2,"rt2",[t,0],["nodisp"]); + Drawfigures(text(#),["tr2_1","tr2_2"],[opcr,oppt]); +); +\end{verbatim} + +\vspace{\baselineskip} +\hspace{20mm} \input{Fig/drawfigures1} + +最初に,まとめて平行移動や回転をするデータをリスト化しておく。また,各データのオプションをリストとして与えていることに注意。こうすることで,サイズや色などのスタイルを元のスタイルに合わせることができる。 + +%\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) +% +%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} +%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} +% +%\vspace{\baselineskip} +%\hspace{20mm} \input{Fig/addgraph} +% +%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。 + +\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\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。 + +\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。 + +\hspace{10mm} \verb|Changestyle(["sgAB","crAB"],["da","notex"]);| + + +\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" + +\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{80}{5}{ \input{Fig/joincrvs}} +\end{layer} + +\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。 + +optionsは線種"dr, n", "da,m,n" , "do,m,n" + +\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");| + +\begin{center} \input{Fig/partcrv1} \end{center} + +【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{\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{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} + +\vspace{\baselineskip} +\vspace{\baselineskip} +\vspace{\baselineskip} + +%\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\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。 + +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。 + +\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} + +\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 + +反時計回りで\verb|Enclosing("1",["ln1","ln2","Invert(gr1)"]);| + +時計回りで\verb|Enclosing("1",["gr1","Invert(ln2)","Invert(ln1)"]);| + +\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\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|"No=点リスト"| 点リストの点が選ばれているときは実行しない\\ + \verb|"File=y/m/n (n)"| データファイルを作るか\\ + \verb|"Check=点リスト"| 点リストの点が変更されていたら,ファイルを作り直す + +\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】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} +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} +\vspace{\baselineskip} +\hspace{5mm} \input{Fig/hatch1} \hspace{5mm} \input{Fig/hatch2} + +【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} + +【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} + + +【例】3次曲線と接線で囲まれた領域 + +点Aを原点付近に作図しておく。 +\begin{verbatim} +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} +\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} + 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} + +\hspace{40mm}\input{Fig/HatchZuKita9.tex} + +\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\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。 + +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。 + +\vspace{\baselineskip} +【例】円グラフ + +Partcrv() と Enclosing() で閉曲線を作って点を敷き詰める。 + + +%\begin{center}\scalebox{0.9}{\input{Fig/dotfill}} \end{center} +\begin{layer}{150}{0} +\putnotese{85}{-3}{\scalebox{0.9}{ \input{Fig/dotfill}}} +\end{layer} + +\begin{verbatim} +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,次のものがある。 + +・Enclosingを使うかどうか:''Enc=y/n''(初期値は y) + +・Enclosingのときの開始点,描画色 + +・描画領域のトリミング:Trim=y/n (初期値は n ) + +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} +\begin{center} \input{Fig/shade} \end{center} + +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","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} + + +\vspace{\baselineskip} +【例】2つの放物線で囲まれた部分を赤で塗る。 +\begin{verbatim} +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} + +ここで,\verb|alpha->0.4| は画面上の色濃度指定。 + +\vspace{\baselineskip} +\begin{center}\scalebox{0.9}{\input{Fig/shade01}} \end{center} + +\vspace{\baselineskip} +【例】描画領域(NE,SWの矩形領域)からはみ出した部分は表示しないようにする。 + +\begin{verbatim} +Plotdata("1","x^2","x"); +Partcrv("1",[-1,1],[3,9],"gr1"); +Listplot("1",[[3,9],[-1,1]]); +Joincrvs("1",["sg1","part1"]); +Shade(["join1"],["Color=[0,0,0.2,0]","Trim=y"]); +\end{verbatim} + +SW,NE を動かしてみると,白枠内だけが色塗りされる。 + +\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。 + +\begin{verbatim} +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} +\begin{center}\input{Fig/greenring} \end{center} + +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} + +\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。 + +\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。 + +点Cに関して対称な円を実線 + +点(-1,2)に関して対称な円を太い実線 + +直線DEに関して対称な円を破線 + +\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。 + +\begin{spacing}{1.5} +【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} + 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} +\vspace{\baselineskip} +\begin{center}\scalebox{0.9}{ \input{Fig/rotatedata} }\end{center} + +\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\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 + +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。 + + 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{\mathrm{OD}} $だけ拡大し,破線で描く。 +\begin{verbatim} +Circledata([A,B]); +Scaledata("1","crAB",3,2,[[0,0]]); +Scaledata("2","crAB",3,2,[C,"dr,2"]); +Scaledata("3","crAB",[D.x,D.y],[[0,0],"da"]); +\end{verbatim} + +\vspace{0mm} + \begin{center} \input{Fig/scaledata} \end{center} + +%\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\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{\mathrm{OC}} $だけ平行移動し,実線で太く描く。 + +ベクトル$\overrightarrow{\mathrm{OD}} $だけ平行移動し,破線で描く。 + +\begin{verbatim} +Circledata([A,B]); +Translatedata("1","crAB",[2,3]); +Translatedata("2","crAB",C,["dr,2"]); +Translatedata("3","crAB",D,["da"]); +\end{verbatim} + +\vspace{0mm} +\begin{center} \input{Fig/translatedata} \end{center} + +%\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +%\vspace{\baselineskip} +\hypertarget{intersectcrvs}{} +\item[関数]Intersectcrvs(プロットデータ1, プロットデータ2) +\item[機能]2曲線の交点リストを取得する。 +\item[説明]オプションとして,共有点があるかどうかを判断するための限界値があるが,通常は使わない。 + +\vspace{\baselineskip} +【例】円と曲線の交点をP,Qとする。 + +\begin{layer}{150}{0} +\putnotese{80}{0}{ \input{Fig/Intersectcrvs1}} +\end{layer} + +\begin{verbatim} +Plotdata("1", "sin(x)", "x", ["Num=100"]); +Circledata([A, B]); +tmp=Intersectcrvs("gr1","crAB"); +P.xy=tmp_1; +Q.xy=tmp_2; + \end{verbatim} + +この関数は,交点のデータのリストを返すので,tmp=[ [ -0.37, -0.36 ], [ 2.13, 0.85 ] ] のように値が返ってくる。交点の順序は PD1, PD2 の順序と曲線の向きによって決まる。曲線の向きは,$y=f(x)$のグラフではx座標が増加する向きで,パラメーター表示曲線ではパラメータの増加する向き。また,PD1 上から探し始めて PD2 との交点を拾っていく。 + +交点がひとつの場合も tmp=[ [ 2.45, 0.63 ] ] と2重のリストに入っているので,点として取出すには \verb|P.xy=tmp_1; |とする。 + +\vspace{\baselineskip} +注)交点の算出は,数式処理によるのではなく,プロットデータからの数値探索のアルゴリズムによっている。 + +\vspace{\baselineskip} +\hypertarget{intersectcrvspp}{} +\item[関数]IntersectcrvsPp(プロットデータ1, プロットデータ2) +\item[機能]2曲線の交点のパラメータリストを取得する。 +\item[説明]2曲線の交点の座標とパラメータのリストを返す。 + +Intersectcrvs() との違いは,パラメータがあるかどうかである。 + +\vspace{\baselineskip} +【例】放物線と直線の交点のパラメータを求める。 + +2点A(-1,1),B(2.4) を作図しておく。 +\begin{verbatim} +Plotdata("1","x^2","x"); +Lineplot([A,B]); +p1=Intersectcrvs("gr1","lnAB"); +p2=IntersectcrvsPp("gr1","lnAB"); +println("p1="+p1); +println("p2="+p2); +\end{verbatim} +とすると,コンソールには +\begin{verbatim} +p1=[[-1,1],[2,4]] +p2=[[[-1,1],17.68,1],[[2,4],42.66,1]] +\end{verbatim} +と表示される。 +%\begin{flushright}\hyperlink{functionlist}{$\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}{-10}{ \input{Fig/nearestpt}} +\end{layer} + +\begin{verbatim} +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"]); +Pointdata("1",[A,B],["Size=2"]); +Letter([A,"n2w","A",B,"s2e","B",(A+B)/2,"e",text(plist_5)]); +\end{verbatim} + +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}{\scalebox{1.0}{\input{Fig/Nearestpt1}}} +\end{layer} + +\begin{verbatim} +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} + +\vspace{\baselineskip} +\vspace{\baselineskip} +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。 + +\begin{verbatim} +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} +\includegraphics[bb=0.00 0.00 305.02 133.01,width=8cm]{Fig/numptcrv.pdf} +\end{center} + +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{verbatim} + 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{\baselineskip} +\begin{center} + \input{Fig/paramoncrv} +\end{center} + +\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} + +によって,点Aを中点に置くことができる。 + +\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。 + +\begin{layer}{150}{0} +\putnotese{70}{05}{ \input{Fig/ptcrv}} +\end{layer} +\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} + +%\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\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。 + +\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} +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} +\vspace{\baselineskip} +\begin{center} \input{Fig/ptstart} \end{center} + +\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。 + +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。 + +\hypertarget{readcsv}{} +\item[関数]Readcsv(path,filename,option) +\item[機能]csvファイルを読む。 +\item[説明]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。 + +\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。 + +\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\hypertarget{readlines}{} +\item[関数]Readlines(path,filename,option) +\item[機能]テキストファイルを1行ずつ読む。 +\item[説明]テキストファイルを1行ずつ読みこむ。戻り値は読み込んだ文字列のリスト。 + +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" + +\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。 + +\begin{verbatim} + Plotdata("1", "x^2","x"); + Circledata("1",[[0,0],[1,0]]); + WriteOutData("figdata.txt",["gr1",gr1,"cr1",cr1]); +\end{verbatim} + +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{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} + +\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} +ReadOutData("figdata.txt"); +Extractdata("gr1",["da"]); +\end{verbatim} + +\end{description} +\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +%\newpage +% ======== 計算 ======================= +\subsection{計算} + +\begin{description} + +\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} +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} +%\vspace{\baselineskip} +\begin{center} \input{Fig/derivative} \end{center} +%\vspace{\baselineskip} + + +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) + +\begin{verbatim} + 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} + +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} +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} + +\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} +plotdata("1","x^3-2*x^2+2","x"); +println(Integrate("gr1",[0,3])); +\end{verbatim} + +数値積分ではなく,数式処理として定積分の値を求める場合は,Maxima を利用する。\hyperlink{calcbyM}{CalcbyM} +を参照。 + +\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} + +%\newpage +%==========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{asin}{} +\item[関数]Asin(実数),Acos(実数) +\item[機能]逆三角関数の値を求める。 +\item[説明]CindyScriptの組み込み関数に,arcsin(x),arccos(x) があるが,xの絶対値が1より大きい場合は虚数を返す。このことがRではエラーになるので,計算誤差により1よりわずかに大きくなる場合のために用意した関数。 + +\vspace{\baselineskip} +\hypertarget{sqr}{} +\item[関数]Sqr(実数) +\item[機能]平方根を求める。 +\item[説明]CindyScriptの組み込み関数に,sqrt(x) があるが,xが負の場合は虚数を返す。これに対し,xが負の場合は0を返すようにした関数。計算誤差により1よりわずかに大きくなる場合のために用意した。 + +\vspace{\baselineskip} +\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。 + +"w=40mm" でwidth=40mm が,"h=40mm"で height=40mm が付加される。 + +\vspace{\baselineskip} +【例】 + +\vspace{\baselineskip} +\includegraphics[bb=0.00 0.00 562.03 124.01,width=10cm]{Fig/bbdata.pdf} + +\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\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(横データ,縦データ, 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。 + +除外線がない場合は空リストを指定する。(必須) + +optionsのうち,Tabledataに特有なものは\\ +\hspace*{3zw}ラベルのスキップ幅,''Setwindow=n'',''Geo=n'',''Move=[0,0]''\\ +である。 + +"Setwindow=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。 + +縦横データは,次のように,間隔の幅で与える。ただし,幅はCinderellaの描画面の0.1を単位とする。 + +\begin{verbatim} +Yoko=[20,20,20,20]; +Tate=[10,10,10,10,10]; +Tabledata(Yoko,Tate,[]); + \end{verbatim} + + + +"Geo=y"とすると,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} \\ + + +"Geo=y"の場合は,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。 + +ラベルのスキップ値は,いくつおきにラベルをつけるかの設定である。0とするとラベルが表示されない。ただし,ラベルはCinderellaの画面上だけの問題。 + +\vspace{\baselineskip}"Move=点の座標"とすると,指定された点が左下になるように平行移動される。 + + +\vspace{\baselineskip} +【例】4つの罫線を非表示にする +\begin{verbatim} +Rmv=["r1c0c1","c3r0r1","c3r3r5","r4c2c4"]; +Yoko=[20,20,20,20]; +Tate=[10,10,10,10,10]; +Tabledata(Yoko,Tate,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> + +"Geo=y"の場合,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。 + +\vspace{\baselineskip} +"Geo=n"(デフォルト)の場合,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。 + +\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。 + +\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} +複数の表を描くこともできる。 + +\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\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。 + +\vspace{\baselineskip} +【例】\verb|Tabledata(Tate,Yoko,[]);| + +\verb|println(Findcell(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。 + +\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} +yoko=[20,20,20,20,20]; +tate=[20,20]; +Tabledata(yoko,tate,["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} + +※数式の場合は,{\bf Putcellexpr} を用いる。 + +\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 + +\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。 + + +\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 + +文字を入れる例を示す。 +\begin{verbatim} +Tate=[20,20,20,20,20]; +Yoko=[15,15,15]; +Tabledata(Tate,Yoko,["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} + +※ r0,c0,・・は画面に表示される番号。 + +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。 + +\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} +Tate=[40,40,40]; +Yoko=[20,20,20]; +Tabledata(Tate,Yoko,[],["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$}"); +Letter(Ptstart(tr2),"w1","\small O"); +Expr(Ptend(tr1),"nw-2","y=x-\sqrt{x}"); +\end{verbatim} +\begin{center} \input{Fig/tablesample2} \end{center} + +\vspace{\baselineskip} +【例】凹凸を含めた増減表 +\begin{verbatim} +Tate=apply(1..8,20); +Yoko=[apply(1..4,10); +Tabledata(Tate,Yoko,[]); +Putrowexpr(1,c,["x","\cdots","-1","\cdots","0","\cdots","1","\cdots"]); +Putrowexpr(2,c,["y`","+","+","+","0","-","-","-"]); +Putrowexpr(3,c,["y``","+","0","-","-","-","0","+"]); +Putrowexpr(4,c,["y","\nelarrow","\frac{1}{\sqrt{e}}","\nerarrow", +"1","\serarrow","\frac{1}{\sqrt{e}}","\selarrow"]); +\end{verbatim} +\begin{center} \input{Fig/zogen3} \end{center} +%\vspace{\baselineskip} +ここで,凹凸を示す矢印は,ketpic.sty で定義されているものである。 + +nelarrow,nerarrow,selarrow,serarrow,NELarrow,NERarrow,SELarrow,SERrarrow がある。先頭の ne,se で北東・南東(右上・右下)次の r,l は回転の向き(r:right:反時計回り,l:left:時計回り)の矢印(arrow)と覚えるとよい。直線系の矢印は NEarrow,SEarrrow。 少しずつ違うので試されたい。 + +なお,これらの矢印はCindyTeXにはないので,Cinderellaの描画面には表示されない。 + +%\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\vspace{\baselineskip} +\hypertarget{tgrid}{} +\item[関数]Tgrid(セルラベル) +\item[機能]表のセルの座標を返す +\item[説明]指定されたセルの左上の座標を返す。実際には,セルラベルは罫線を示しているので,指定した罫線の交点(格子点)ということもできる。 + +\vspace{\baselineskip} +\hypertarget{tlistplot}{} +\item[関数]Tlistplot(セルラベル1,セルラベル2) +\item[機能]指定された2つの格子点を線分で結ぶ +\item[説明]セルに斜線を引くのに用いる。 + +\vspace{\baselineskip} +【例】\verb|Tlistplot(["c0r1","c1r2"]);| + +\vspace{\baselineskip} +\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\end{description} + +%=================================================== +\subsection{その他} + +\begin{description} + +%\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{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。 + +\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} + +\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} + +%\vspace{\baselineskip} +\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + + +% ===========commentedto com2th() ========== +\begin{comment} + +\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。 + + +\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} +col=Colorcode("rgb","cmyk",[1,0,0]); +println(col); +\end{verbatim} + +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。 + +\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。 + +\begin{verbatim} +col=Colorcode("rgb","hsv",[1,0,0]); +println(col); +\end{verbatim} + +\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} +str="abc"; +str2=Dqq(str); +println([str,str2]); +\end{verbatim} + +\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。 + +\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。 + +\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} +Setparent("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。 + +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。 + +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。 + +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。 + +\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。 + +\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\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。 + +\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} + +\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。 + +\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} + +\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} 点A以外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。単に"C"としたときは端点をとらない。 +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{2mm} +\hspace{15mm} +\includegraphics[bb=0.00 0.00 445.02 193.01,height=35mm]{Fig/slider.pdf} + +\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" ] \\ + +\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\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 + +\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,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。 + +%\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\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。 + +\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。 + +\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} + +\vspace{\baselineskip} +\hypertarget{fracform}{} +\item[関数]Fracform(数 , 分母のリストまたは最大値) +\item[機能]分母リストの1つを分母とする近似分数と誤差を返す。 +\item[説明]戻り値は,簡易TeX-like書式の文字列と誤差。 + +\vspace{\baselineskip} +【例】\verb|Fracform(0.33,[2,3]); => fr(1,3)| + +\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\vspace{\baselineskip} +\hypertarget{totexform}{} +\item[関数]Totexform(簡易TeX-like書式) +\item[機能]TeX書式の文字列を返す。 + +\vspace{\baselineskip} +【例】\verb|Totexform(fr(1,3)); => frac{1}{3}| + +\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\vspace{\baselineskip} +\hypertarget{tocindyform}{} +\item[関数]Tocindyform(簡易TeX-like書式) +\item[機能]Cindy書式の文字列を返す。 + +\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============================= +\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。 + +\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,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); +\end{verbatim} +\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); +\end{verbatim} + +\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); +Framedata("1",[A,B],["corner"]); +Rulerscale(A,["r",0,6,1],["f",1,"\mbox{dt1}",3,"\mbox{dt2}"]); +\end{verbatim} +%\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} + +\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。 + +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。 +戻り値は,階級境界値と,対応する度数のリスト。 + +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。 + +\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]”); +\end{verbatim} + +\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。 + +\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} +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} +\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} +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} + +\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} +%\vspace{\baselineskip} +\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\vspace{\baselineskip} +\hypertarget{scatterplot}{} +\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} + +\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +\vspace{\baselineskip} +%\newpage + +%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に渡すコマンドを記述したファイル + +拡張子 txt:Maximaが出力したデータファイル + +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を記述したスクリプト。 + +コマンドと引数リストの繰り返しからなるスクリプトをリストとして作り,一度に実行する。 + +戻り値はない(未定義値)。実行結果は,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nameに代入される。 + +\vspace{\baselineskip} +【例】$\sin x$ とその導関数を表示する。 +\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,結果の f とdf のリストが変数 fdf に代入され,コンソールに,\verb|[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 + +\verb|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。 + +\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); +\end{verbatim} +コンソールには +\begin{verbatim} +(%e^a-%e^-a)*(x-a))/2+(%e^a+%e^-a)/2 +\end{verbatim} +が表示される。\\ +この,CalcbyM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}{10}{ \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。 + +\vspace{\baselineskip} +【例】定積分の値を求める。 + +\vspace{\baselineskip} +$\displaystyle \int _{-1} ^2 (-x^3+3x+2)dx$ の値を求める。結果は val で受け取り,Mxtex() に渡して,TeX書式にして表示する。 + +\begin{verbatim} +cmdL=[ + "val:integrate",["-x^3+3*x+2,x,-1,2"], + "val",[] +]; +CalcbyM("val",cmdL); +Mxtex("1",val); +Expr([[2,2],"e","S="+tx1]); +\end{verbatim} + + +\vspace{\baselineskip} +\hypertarget{mxbatch}{} +\item[関数]Mxbatch(ファイル名) +\item[機能]Maximaのライブラリを使うバッチファイルを作成 +\item[説明]ketcindy/ketlib/maximaL にあるライブラリを用いるコマンドでバッチファイルを作成する。 + +ketcindy/ketlib/maximaL には,fourier\_sec.max , matoperation.max , poincare.mac の3つのファイルがあり,関数を定義したライブラリが入っている。それぞれ次のような内容である。各ファイルをテキストエディタで開いて参照されたい。 + +fourier\_sec.max :フーリエ級数の計算を行う。 + +matoperation.max : 行列の計算を行う。 + +poincare : ハミルトニアンシステムに関する計算を行う。 + + +\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{10mm}\input{Fig/mxbatch} + +%\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\vspace{15mm} +\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 mx+name 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 3628800 と表示される。この値は変数 mx1 に代入されているので, + +\verb| Letter([[0,1],"e",mx1]);| + +とすればCinderellaの描画面上に表示される。mx1ではなく,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!",[]); +Letter([[0,1],"e",fact10]); +\end{verbatim} + +\vspace{\baselineskip} +【例】文字列の連結 + +文字列を引数とする場合,例えば,Maximaの文字列を連結するコマンドconcatでは, + +\verb| concat("a","b")| + +とするが,中にダブルクォートが入っているため,全体を文字列にすることができない。 + +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} +<参考> CindyScript の unicode(code) 関数を用いてダブルクォートを表し,次のようにすることもできる。 + +\begin{verbatim} +dq=unicode("22"); +comm="concat("+dq+"a"+dq+","+dq+"b"+dq+")"; +Mxfun("1",comm,[]); +\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 + +\verb| 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。 + +\vspace{\baselineskip} +{\bf <参考>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); +\end{verbatim} +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,\verb|Plotdata("1",mx1,"x")| でグラフが描ける。 + +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} +【例】$\sin x$ の テイラー展開による近似のグラフを表示する。 +\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} +なお,Mxtex() を用いれば,Mxfun()の結果の mx1をTeX書式にして表示できる。 + +\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} +【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。 + +同様の例を CalcbyM() で例示しているので参照されたい。 + +%\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。 + +\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。 +\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。 + +\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。 + +%\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, + +Cindyscriptの文字列の関数 replace を用いて, + +\hspace{10mm} \verb|dform=replace(form,"frac","dfrac");| + +としてもよい。 + +%\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{60}{05}{ \input{Fig/mxtex03}} +\end{layer} + +\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} + +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} +\newpage + + +%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。 + + +\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。 + + +\end{description} +\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +%\newpage +%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。 + + +\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。 + + +\end{description} +\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +%\newpage + +%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();| +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) + +\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"]); +); +\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 0 679.53 263.51 , 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, 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 +\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"]); +); +\end{verbatim} + +\verb|Mkobjcrvcmd("1","sc3d1",[0.1,8,"yz"]);| としたのが下図右。 + + \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。 + +\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。 + +\vspace{\baselineskip} +【例】三角形のプレートを描く + +\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"]); +\end{verbatim} + +\begin{center} \includegraphics[bb=0 0 287.01 228.01 , width=4cm]{Fig/meshlab03.pdf} \end{center} +%\begin{layer}{150}{0} +%\putnotese{80}{15}{ \includegraphics[bb=0 0 287.01 228.01 , width=3cm]{Fig/meshlab03.pdf} } +%\end{layer} + +\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。 + +\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。 + +\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] +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。 + +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。 + +\vspace{\baselineskip} +【例】回転放物線 + +\begin{layer}{150}{20} +\putnotes{58}{37}{ \includegraphics[bb=0 0 287.01 189.01 , width=5cm]{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"]); +\end{verbatim} + +%\begin{center}\includegraphics[bb=0 0 574 378 , width=4cm]{Fig/meshlab06.pdf}\end{center} + +\vspace{37mm} +\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。 +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。\\ +\end{tabbing} + + +\end{description} +\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +%\newpage +%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。 + +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。 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1412.3 → 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。 + +\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。 + + +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} + +\newpage + + +%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。これをひな形として使うのがよい。すでにあるスライダなどが邪魔であれば,消去ボタンで消去するか,template2allbuttons.cdy をひな形として用いる。 + +\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} +1234\=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(); \>アニメーションのフレームデータを作る\\ +\>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PDFを作るには,フレームを定義する関数を記述し,「ParaF」ボタンでフレームデータを作り,「Anime」または「Flip」ボタンでPDFを作成する。 +%たとえば,Fhead が "hoge" の場合,TeX の文書には\\ +% \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。 + +%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}| + +Anime ボタンを押すと,\verb|\usepackage[dvipdfmx]{animate}| でパッケージを読み込み,animateinline 環境のアニメーションを作る。 + +Flip ボタンを押すと,animateinline 環境ではなく,フレームに分割したPDFが生成される。 + +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 プレビューではアニメーションができない。 + +\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は定義した動画関数名,rangeは範囲 + +「Anime」ボタンを押すと,animate+fname.pdf が作られる。再生はコントローラか,画面クリックで行う。 + +「Flip」ボタンを押すと,flipanime+filename.pdf が作られる。再生(コマ送り)は,Acrobat Reader のページ送りボタンで行う。 + +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。指定しない場合は fname と同じ。\\ +Scale=n\> 図の大きさの拡大率 \\ +opA=[option]\> animateinline 環境のためのオプション \\ +\>初期設定は\verb|[loop,controls,buttonsize=3mm]|。\\ +\> loop:繰り返し再生する。\\ +\> controls:コントローラを表示する\\ +\> buttonsize:コントローラのサイズ\\ +\> palindrome:反転して繰り返し再生する\\ +\> step:コマ送りモードにする。コントローラもコマ送り仕様。\\ +\>\verb|"OpA=[controls,buttonsize=5mm]" |のように記述する。\\ +\> +をつけると初期設定のものに追加することができる。\\ +\>たとえば \verb|"OpA=+step"| で\\ +\>\verb|"OpA=[loop,controls,buttonsize=3mm,step]"| となる。\\ +\>\verb|"OpA=[]"| とすると,オプションなしとなり,\\ +\>画面をクリックすると繰り返しなしで再生される。\\ +記述例\\ +\verb|Setpara("cycloid","mf(t)","t=[0,60]",["Div=60"],|\\ +\verb| ["Frate=30","Title="サイクロイド","Scale=1.5","OpA=[controls]"]);|\\ +\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(フレーム)を定義する関数は,時刻を $t$ として, $t$ における図を定義すると考える。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。関数名は,たとえば mf(movie frame) とする。 + +\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。アニメーションを作る上では \verb|mf(C.x)| やスライダはなくてもよい。 + +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 「ParaF」「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"],["Frate=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{KeT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,Windows,MacではAdobe Reader で開く必要がある。Linux(Ubuntu)では Evince でプレゼンテーションができる。 + +\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]);| + +とする。 + +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} +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。 + +また,2行に分けずに + +\hspace{10mm} \verb|%repeat=,para=... |と続けて書いてもよい。 + + +\vspace{\baselineskip} +{\bf 【レイヤー】} + +ketlayerの\verb|\begin{layer}・・\end{layer}| として書き出す。本来の記述より簡素になっている。 + +\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|putnote::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|putnote::se{30}{10}::figure,0.8//| + + + 例)includegraphics で figure.pdf を表示する。 + +\hspace{10mm} \verb|putnote::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|\putnotee{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} + +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。 + +\vspace{\baselineskip} +{\bf 【余白などの編集】} + +スライドの上側余白として,初期状態で \verb|\vspace*{18mm}| が設定される。次のページにはみ出してしまうような場合は,出力された tex ファイルで調整すればよい。 + +その他,適宜編集して,kc.command(bat/sh) を実行すれば,細かい部分を修正したPDFを作成することができる。 + +\subsection{関数} +makeslide.cdy で使う,\ketcindy の関数。 + +\begin{description} + +\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} + +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。 + +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。 + +【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。 + +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" + +options は ["cl=bool,lc=col,fc=col","Pos=[x,y]","Size=n"] + +\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} + + +\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} + + +\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。 + +\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) + +\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。 + +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} + +\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\newpage +%================== 3D概要 =============== +\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) + +%================== 3D設定 =============== +\newpage +\subsection{設定} + +\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。スライダTHで角THETAを,スライダFIで角PHIを内部変数として定義する。 + +引数に0を入れて \verb|Ketinit3d(0)| とすると,副画面を表示しない。 + +\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。 + +%----------------Setangle -------------------------------------------- +\vspace{\baselineskip} +\hypertarget{setangle}{} +\item[関数]Setangle(TH,FI) +\item[機能]回転角の指定 +\item[説明]スライダで設定できる回転角(視点の位置)TH と FI を度数法で指定する。 +たとえば,\verb|Setangle(70,40)| とすると,TH,FIがその位置になる。スライダは固定されるので,再度スライダを有効にしたい場合は,コメント化して再実行する。 + +初期状態だけを決めたい場合は + +\verb| if(!Ptselected(),Setangle(70,40)); | + +または + +\verb| if(!Isangle(),Setangle(70,40)); | + +とすると,スライダは有効となり,スライダのいずれかの点を選択した状態であれば Figure ボタンも有効である。画面上のなにもないところをクリックして,点の選択状態を解除するともとに戻る。 + +回転角の取得については,\hyperlink{getangle}{回転角の取得}を参照のこと。 + +%----------------Start3d -------------------------------------------- +\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。(スライダで視点を移動しても位置は変わらない) + + %----------------Startsurf -------------------------------------------- +\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。 + +%-------------------Xyzaxdata3d----------------------------------------------- +\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。 + +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】 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。 + + \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。 + +\end{description} +%================== 3D描画 =============== + +%\newpage +\subsection{描画} + +%================== 3D点・線 =============== +\subsubsection{点・線} + +\begin{description} + %----------------Drawpoint3d -------------------------------------------- +%\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()} 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]]); +%\end{verbatim} + +%\vspace{\baselineskip} + + %----------------Pointdata3d -------------------------------------------- +\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} + +【例】 +\begin{verbatim} +Pointdata3d("1",[[1,1,1],[0,1,0]],["Size=2","Color=red"]); +\end{verbatim} +\vspace{\baselineskip} + + %---------------- Putpoint3d---------------------------------------------- +\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"( 初期設定) または "free"。リスト ["free"] にしてもよい。 + +"fix" では,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" では,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。 + +\vspace{\baselineskip} +【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");| + +\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()} 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。 + + %----------------Putaxes3d--------------------------------------------- +\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。 + +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。 + +Putaxes3d([1,2,3]);原点と,$x(1,0,0),y(0,2,0),z(0,0,3)$ を作る。 + + %----------------Putoncurve3d--------------------------------------------- +\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。 + +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。 + %---------------- Putonseg3d---------------------------------------------- +\vspace{\baselineskip} +\hypertarget{putonseg3d}{} +\item[関数]Putonseg3d(点名,点1,点2) +\item[機能]線分上に点を作る +\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。指定した点がすでに存在する場合は動かさない。 + +点1,点2は幾何点の名称または座標で指定する。 + +\vspace{\baselineskip} +【例】A(1,-1,0)とB(0,2,2) 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]);| + +\verb|Putonseg3d("C",[[1,-1,0],[0,2,2]]);| + +\vspace{\baselineskip} + +%------------------ Spaceline----------------------------------------------- +\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。 + +options は線種(dr,da,do) + +\vspace{\baselineskip} +【例】いくつか示す。 + +・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("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。 + +・節点を表示する場合は,Pointdata3d() で描画する。 + +\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 + +\verb|pname=apply(1..6,"P"+text(#));| + +のようにして,名前リストを作ることができる。 + +%\vspace{\baselineskip} +%\begin{layer}{150}{0} +%\putnotese{80}{10}{ \input{Fig/oresenex01}} +%\end{layer} + \begin{center} \input{Fig/oresenex01} \end{center} + +%------------------ Spacecurve----------------------------------------------- +\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 + +\vspace{\baselineskip} +【例】螺旋を描く + +\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} + + + %---------------- Bezier3d----------------------------------------------- +\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。 + +\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} + +%------------------ Mkbezierptcrv3d----------------------------------------------- +\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。 + +\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。 + +\vspace{\baselineskip} + +%------------------ Skeletonparadata----------------------------------------------- +\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。\\ +他のオプション\\ + \verb|"No=点リスト"| 点リストの点が選ばれているときは実行しない\\ + \verb|"File=y/m/n (n)"| データファイルを作るか\\ + \verb|"Check=点リスト"| 点リストの点が変更されていたら,ファイルを作り直す + + +\vspace{\baselineskip} +【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。 +\begin{verbatim} +Xyzax3data("","x=[-5,5]","y=[-5,4]","z=[-5,3]"); +Putpoint3d(["A",[0,-2,-2]]); +Putpoint3d(["B",[-1,1,3]]); +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, + +\hspace{10mm} \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) + +\hspace{10mm} \verb|Skeletonparadata("1",[2]);| + + 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) + +\begin{center} \input{Fig/skeletonparadata01} \input{Fig/skeletonparadata02} + \input{Fig/skeletonparadata03} \end{center} + +このほか,次も可能。 + +\hspace{10mm} \verb|Skeletonparadata("1",["AB3d","ax3d"],["sc3d1"],[2]);| + +\hspace{10mm} \verb|Skeletonparadata("1",["AB3d"],["ax3d","sc3d1"]);| + + +\end{description} + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +%\newpage +%================== 3D多面体 =============== +\subsubsection{多面体} + +多面体の描画について,四面体の場合を例にして説明する。 + +\begin{layer}{130}{0} +\putnotesw{130}{0}{\input{Fig/concatobj}} +\end{layer} + +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 + +\hspace{10mm} △ABC,△ABD,△ACD,△BCD + +である。 + +% \begin{center} \input{Fig/concatobj} \end{center} + +頂点のリスト[A,B,C,D] に対し,Aから順に番号を + +つけると,各面の頂点の順番は + +\hspace{20mm}[1,2,3],[1,2,4],[1,3,4],[2,3,4] + +と表現できる。 + +頂点のリストと,この面リストを組にして [[A,B,C,D],[[1,2,3],[1,2,4],[1,3,4],[2,3,4]]] としたものを「面データ」という。この面データを使って,多面体を描画するのが VertexEdgeFace() である。 + +多面体の陰線処理は2通りある。ひとつは,多面体を線画と考えて,隠れる部分だけを処理する方法で,Skeletonparadata() を用いる。\hyperlink{concatobj}{Concatobj()} の例を参照のこと。 + +もうひとつは,面と考えて,面に隠れる部分を点線で描いたり,非表示にしたりする方法で,Phparadata() を用いる。 \hyperlink{phparadata}{Phparadata()}の例を参照のこと。 + +\begin{description} + + %-----------------Concatobj ----------------------------------------------- +\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。 + +たとえば,\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。 + +\vspace{\baselineskip} +【例】4点A,B,C,Dを幾何点として作り,これを頂点とする四面体を描く。 + +\begin{verbatim} +Putpoint3d("A",2*[0,0,sqrt(3)]); +Putpoint3d("B",2*[1,-1/sqrt(3),0]); +Putpoint3d("C",2*[0,sqrt(3)-1/sqrt(3),0]); +Putpoint3d("D",2*[-1,-1/sqrt(3),0]); +phd=Concatobj([[A,B,C],[A,B,D],[A,C,D],[B,C,D]]); +VertexEdgeFace("1",phd); +Skeletonparadata("1"); +Letter3d([A3d,"ne","A",B3d,"sw","B",C3d,"se","C",D3d,"e","D"]); +\end{verbatim} + +\begin{center} \input{Fig/concatobj} \end{center} + +<参考1> + +幾何点を作らないで四面体を描くのであれば, + +\begin{verbatim} +a=2*[-1,-1/sqrt(3),0]; +b=2*[1,-1/sqrt(3),0]; +c=2*[0,sqrt(3)-1/sqrt(3),0]; +d=2*[0,0,sqrt(3)]; +phd=Concatobj([[a,b,c],[a,b,d],[a,c,d],[b,c,d]]); +\end{verbatim} + +としてもよい。 + +\vspace{\baselineskip} +<参考2> +四面体のような凸型多角形の場合は,CindyScriptの convexhull3d() 関数を用いて次のようにすることができる。面リストではなく頂点リストを与えるだけなので手間を省くことができる。 + +\begin{verbatim} +a=2*[0,0,sqrt(3)]; +b=2*[1,-1/sqrt(3),0]; +c=2*[0,sqrt(3)-1/sqrt(3),0]; +d=2*[-1,-1/sqrt(3),0]; +phd=convexhull3d([a,b,c,d]); +\end{verbatim} + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +%-------------------VertexEdgeFace ----------------------------------------------- +\hypertarget{vertexedgeface}{} +\item[関数]VertexEdgeFace(name,面データ,options) +\item[機能]面データを用いて多面体を描く +\item[説明]面データは,たとえば四面体ABCDの場合は,[[A,B,C,D],[[1,2,3],[1,2,4],[1,3,4],[2,3,4]]] である。 + +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,四面体が描かれる。 + +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。 + +\vspace{\baselineskip} +【例】4点A,B,C,Dを取り,正四面体ABCDを描く +\begin{verbatim} +Putpoint3d("A",2*[-1,-1/sqrt(3),0]); +Putpoint3d("B",2*[1,-1/sqrt(3),0]); +Putpoint3d("C",2*[0,sqrt(3)-1/sqrt(3),0]); +Putpoint3d("D",2*[0,0,sqrt(3)]); +phd=[[A,B,C,D],[[1,2,3],[1,2,4],[1,3,4],[2,3,4]]]; +VertexEdgeFace("1",phd); +\end{verbatim} + \begin{center} \input{Fig/vertex01} \end{center} +面リストは,Congatobj() を使って作ることができる。陰線処理して描く場合も含め,\hyperlink{concatobj}{Concatobj()} の例を参照のこと。 + +\vspace{\baselineskip} + %------------------Phparadata ----------------------------------------------- +\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]多面体のプロットデータをVertexEdgeFace() で作る。このプロットデータに対し,隠れている面(辺)を陰線処理して表示する。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。 初期設定では陰線は表示しない。 + +\vspace{\baselineskip} +\begin{layer}{150}{0} +\putnotese{80}{-5}{ \input{Fig/phparadata04}} +\end{layer} + +【例】四面体を描く。 +\begin{verbatim} +Putpoint3d("A",2*[-1,-1/sqrt(3),0]); +Putpoint3d("B",2*[1,-1/sqrt(3),0]); +Putpoint3d("C",2*[0,sqrt(3)-1/sqrt(3),0]); +Putpoint3d("D",2*[0,0,sqrt(3)]); +phd=Concatobj([[A,B,C],[A,B,D],[A,C,D],[B,C,D]]); +VertexEdgeFace("1",phd); +Phparadata("1","1",["Hidden=do"]); +\end{verbatim} + +なお,VertexEdgeFace() で四面体が描かれるが,Phparadata() により非表示になる。 +Figureボタンで描き出せば正しく出力されるので,Phparadata() を実行する前に画面上に表示して確認してからPhparadata() を実行するとよい。 + +\vspace{\baselineskip} +【例】切頂二十面体を描く。 + +小林・鈴木・三谷による多面体データ\verb|polyhedrons_obj|を用いて,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} +Setdirectory( Dirhead+"/data/polyhedrons_obj"); +phd=Readobj("s06.obj",["size=3"]); +Setdirectory(Dirwork); +VertexEdgeFace("s06",phd); +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。 + +\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"]);| + +で指定したのが下図右である。 + + \begin{center}\scalebox{0.8} {\input{Fig/phparadata02}} \hspace{5mm}\scalebox{0.8}{\input{Fig/phparadata03}} \end{center} + +【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,前のデータが残っていてうまくいかない。VertexEdgeFace() のname を(したがって,Phparadata()の第2引数も)書き換えるか,作業フォルダ(fig) の中身を削除してから実行する。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=3"]); +Setdirectory(Dirwork); +VertexEdgeFace("2",phd); +Phparadata("1","2"); +\end{verbatim} +のようにする。 + + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +%------------------- Nohiddenbyfaces ----------------------------------------------- +\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。["nodsip"] とすると,陰線は表示されない。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]); +Putpoint3d("B",2*[1,-1/sqrt(3),0]); +Putpoint3d("C",2*[0,sqrt(3)-1/sqrt(3),0]); +Putpoint3d("D",2*[0,0,2*sqrt(6)/3]); +phd=Concatobj([[A,B,C],[A,B,D],[A,C,D],[B,C,D]]); +VertexEdgeFace("1",phd); +Nohiddenbyfaces("1","phf3d1"); +\end{verbatim} + +\verb|VertexEdgeFace("1",phd);| 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} + + +\end{description} + +%================== 3D曲面 =============== +\subsubsection{曲面} + +曲面の描画には,ワイヤーフレームモデルとサーフェスモデルがある。ワイヤーフレームモデルは,曲面を編目で表すものであり,サーフェスモデルは編目のない面として,その輪郭線を描くものである。 + + \begin{center} \input{Fig/surfacemodel} \end{center} + +%\hspace{20mm}ワイヤーフレームモデル \hspace{10mm}サーフェスモデル + +KeTCindyでは,それぞれ次の関数を用いて描画する。 +\begin{tabbing} +12345678901234567890123456789012345678\=\kill +陰線処理をしないワイヤーフレームモデル \>Sf3data(name,form,options)\\ +サーフェスモデル \>Sfbdparadata(name,form,options)\\ +サーフェスモデルにワイヤーを描く \>Wireparadata(name,PD,form,n1,n2,options) +\end{tabbing} +ワイヤーフレームモデルで陰線処理をするためには,面のデータが必要なので,Sfbdparadata() で描画した後,Wireparadata()で描画する。 + +また,サーフェスモデルの描画では,陰線処理に時間がかかるため,C言語の使用を前提としている。したがって,C言語を用いて描画を行う ExeccmdC() を併用する。 + +引数の form は,方程式 と,変数の定義域を文字列のリストにしたものである。方程式のパターンは次の3通りがある。 + +(1) $z=f(x,y)$ + + \hspace{5mm} 【例】式:$z=x^2-y^2$ + + \hspace{15mm} 定義域:$x=(-2,2) , y=(-2,2)$ + +(2) $z=f(x,y),x=g(r,t),y=h(r,t)$ + + \hspace{5mm} 【例】式:$z=4-(x^2+y^2) , x=r\cos t , y=r\sin t$ + +\hspace{15mm} 定義域:$r=(0,2) , t=(0,2\pi)$ + +(3) $x=f(u,v),y=g(u,v),z=h(u,v),$ + + \hspace{5mm} 【例】式:$x=2\sin u \cos v , y=2\sin u \sin v, z=2\cos u $ + +\hspace{15mm} 定義域:$u=(0,\pi) , v=(0,2\pi)$ + +ここで,(2)と(3)は媒介変数型で,$x,y,z$ それぞれの式と,媒介変数2つの定義域からなっている。そのままでは区別がつかないので,引数として与えるときは,(3) の型には,識別文字として "p" を先頭に付加する。 + +また,定義域については,開区間でとる場合と閉区間でとる場合がある。その区別を境界指定として"ewsn"で表す(ともに閉区間)。"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,境界値を東西南北(ewsn)で示す。それぞれの文字が書かれたときは境界値を含む。 + + \begin{center} \input{Fig/ewsn} \end{center} + +この境界指定を最後に付加するが,省略することもでき,省略した場合は初期値の "ewsn" (閉区間)とする。ともに開区間とする場合は,"" とする。ただし,陰線処理をしない Sf3data() では,境界にも線を引くので,この指定は無効となる。 + +具体的な例を示そう。 + +次は,円錐の form である。(formは form data を短縮した fd がよく使われる) + +\vspace{\baselineskip} +\verb|fd=["p","x=r*cos(t)","y=r*sin(t)","z=2*(2-r)","r=[1,2]","t=[0,2*pi]","ew"]| + +\vspace{\baselineskip} +"ew" は $1 \leq r \leq 2$ であることを示す。したがって,円錐台の上面と底面が表示される。 + +これを "e" とすると $1 <r \leq 2$ となり,上面が表示されない。 + +また,これを "w" とすると $1 \leq r < 2$ となり,底面が表示されない。 + +さらに,"ewn" あるいは "ews" としたり,指定を略して初期値の "ewsn" とすると,$t=(0,2\pi)$ の左右いずれかの値が含まれることになり,不要な境界線が現れる。 + +\vspace{\baselineskip} +\hspace{12mm}"ew" \hspace{25mm}"e" \hspace{25mm}"w" \hspace{25mm}"ewn" + +\input{Fig/frustumew} \input{Fig/frustume} \input{Fig/frustumw} \input{Fig/frustumewn} + +球面を描く場合はこの点で留意することがある。球面をサーフェスモデルで描くと単に円にしか見えないので,多くの場合はサーフェスモデルで描いた球面に Wireparadata() で陰線処理したワイヤーを入れることになるだろう。その場合,Wireparadata() では境界線には線を引かないので,境界指定を "s" として,境界線を引く必要がある。境界指定を "" とすると,経線が1本足りなくなるので注意されたい。具体例は,Wireparadata() に例示してある。 + +\begin{description} + +%------------------ Sf3data ----------------------------------------------- +\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]optionsは,メッシュの密度と解像度(各変数に対応する分割数)。 + +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。 + +解像度は,"Num=[a,b]" で指定。初期値はa,bとも25。 + +\begin{layer}{150}{0} +\putnotese{88}{10}{ \input{Fig/saddle1}} +\end{layer} + +\vspace{\baselineskip} +【例】 $z=f(x,y)$ 型 + + $z=x^2-y^2$を定義域$x=[-2,2],y=[-2,2]$ で描画する。 + +\verb| fd=["z=x^2-y^2","x=[-2,2]","y=[-2,2]"];|\\ +\verb| Sf3data("1",fd)|; + +メッシュの数を縦横とも10,解像度をx,yとも10にすると + + メッシュ密度,解像度とも下げるので粗い描画となる。 + +\verb|Sf3data("1",fd,["Num=[10,10]","Wire=[10,10]"]);| + +\vspace{\baselineskip} +【例】$z=f(x,y),x=g(r,t),y=h(r,t)$型 + +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);| + +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);| + +\begin{center} \input{Fig/parabola} \input{Fig/sf3ddata3} \end{center} + +(3) $x=f(u,v),y=g(u,v),z=h(u,v),$ 型 + +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);| + +\begin{center} \input{Fig/sf3ddata4} \end{center} + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +%------------------ Sfbdparadata ----------------------------------------------- +\hypertarget{sfbdparadata}{} +\item[関数]Sfbdparadata(name,式,options) +\item[機能]サーフェスモデルの輪郭線を描く +\item[説明]この関数はデータを作るだけなので,表示するには ExeccmdC() を併用する。 + +optionsは,"Wait=n","r","m",および線種。Wait の初期値は30。 + + "r","m"に関しては, + +\hspace{5mm} オプションなしまたは,”” のとき + +\hspace{10mm}i) データファイルがなければ,新しく作る + +\hspace{10mm}ii) データファイルが既にあればそれを読み込む + +\hspace{5mm}"m"のとき,強制的にデータファイルを作り直す。 + +\hspace{5mm}"r" のとき,すでにあるデータファイルを読み込む。 + +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やその他の点を動かそうとすると反応が悪くなる。そこで,Isangle() または Isptselected() 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。 + +なお,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。 + +作図例は 次の ExeccmdC を参照のこと。 + +%------------------- ExeccmdC ----------------------------------------------- +\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。 + +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】サドル面 + +\begin{layer}{150}{0} +\putnotese{85}{0}{ \input{Fig/sfbdpara01}} +\putnotese{85}{45}{ \input{Fig/sfbdpara02}} +\end{layer} + +陰線を消去して表示 +\begin{verbatim} +fd=["z=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,陰線は初期設定の + +点線で表示。 + +\verb|ExeccmdC()| を変更する。 + +\verb|ExeccmdC("1",["dr,2"]);| + +\vspace{10mm} +【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} + +【例】曲面を2つ表示するときは,Sfbdparadata() の name は "1" と "2" にするが,まとめて \verb|ExeccmdC("1")| で表示できる。 + +\begin{verbatim} +fd=[ + "p", + "x=r*cos(t)","y=r*sin(t)","z=2*(2-r)", + "r=[1,2]","t=[0,2*pi]","ew" +]; +fd2=[ + "p", + "x=r*cos(t)-3","y=r*sin(t)+3","z=2*(2-r)", + "r=[0,2]","t=[0,2*pi]","ew" +]; +if(!ptselected(), + Startsurf(); + Sfbdparadata("1",fd); + Sfbdparadata("2",fd2); + ExeccmdC("1"); +); +\end{verbatim} + +\begin{center} +\input{Fig/sfbdpara05} +\end{center} + +\vspace{\baselineskip} +【例】トーラスを描く:軸は非表示にしておく。 + +\begin{layer}{150}{0} +\putnotese{70}{-10}{ \input{Fig/wirepara5}} +\end{layer} + +\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"]; + if(Ptselected(), + Sf3data("1",fd); +, + Startsurf(); + Sfbdparadata("1",fd); + Wireparadata("1","sfbd3d1",fd,12,12,[],["nodisp"]); + ExeccmdC("1",[],["nodisp"]); + ); +\end{verbatim} +%\vspace{\baselineskip} + + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +%-------------------Wireparadata----------------------------------------------- +\hypertarget{wireparadata}{} +\item[関数]Wireparadata(name,PD,式,整数,整数,optons) +\item[機能]Sfbdparadataで作成した曲面について,陰線処理したワイヤーを描く +\item[説明]PDは,第3引数の式を用いてSfbdparadata()で描いたサーフェス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。 + +Sfbdparadata() とペアで使い,そのあとに ExeccmdC で描画する。 + +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。 + +\begin{layer}{150}{0} +\putnotese{85}{5}{ \input{Fig/wirepara1}} +\end{layer} + +%\vspace{\baselineskip} +【例】 + +サドル面 + +\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 + +\begin{layer}{150}{0} +\putnotese{85}{-5}{ \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{10mm} + +球面 + +\begin{layer}{150}{0} +\putnotese{80}{15}{ \input{Fig/wirepara3}} +\end{layer} +\begin{verbatim} + fd=["p","x=sin(u)*cos(v)","y=sin(u)*sin(v)","z=cos(u)", + "u=[0,pi]","v=[0,2*pi]","s"]; + if(Ptselected(), + Sf3data("1",fd); + , + Startsurf(); + Sfbdparadata("1",fd); + Wireparadata("1","sfbd3d1",fd,12,12); + ExeccmdC("1"); + ); +\end{verbatim} + +\vspace{8mm} + + +%------------------- Crvsfparadata ----------------------------------------------- + +\hypertarget{crvsfparadata}{} +\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と曲面PD2について,PD1はPD2による陰線処理を行う。 + +Crvsfparadata() のあとに ExeccmdC() でまとめて描画する。 + +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。 + +【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。 + +ExeccmdC()の 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]]); +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} +ExeccmdC()の 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}\scalebox{0.9}{ \input{Fig/crvsfparadata2}}\hspace{5mm} \scalebox{0.9}{\input{Fig/crvsfparadata1}} \end{center} + +戻り値を使うと,Changestyle3d() を使って陰線のスタイル(線種,色)を変えることができる。戻り値の内容は,コンソールに「readoutdata from template3D1.txt : 」として表示されるので,これをテキストエディタで開き,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,赤の破線にすることができる。 + +【例】球面で座標軸を陰線処理し,球面の陰線は非表示で表す。 + +\begin{layer}{150}{0} +\putnotese{70}{-5}{ \input{Fig/wirepara4}} +\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]",""]; +if(Isangle(), +Sf3data("1",fd); +, +Startsurf(); +Sfbdparadata("1",fd); +Wireparadata("1","sfbd3d1",fd,12,12,[],["nodisp]); +Crvsfparadata("1","ax3d","sfbd3d1",fd); +ExeccmdC("1"); +); +\end{verbatim} + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\end{description} +%\newpage +%================== 3Dプロットデータの操作 =============== +\subsection{プロットデータの操作} + +\begin{description} +%------------------- Datalist2d ----------------------------------------------- +\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]]); +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。 +%------------------- Datalist3d ----------------------------------------------- +\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 + +\vspace{\baselineskip} +【例】 +\begin{verbatim} +Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,5]"); +Putpoint3d(["A",[0,-3,0],"B",[0,3,3]]); +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。 + +\vspace{\baselineskip} + +%------------------- Changestyle3d ----------------------------------------------- +\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} + +%------------------- Intersectcrvsf ----------------------------------------------- +\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。 + +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。 + +\begin{layer}{150}{0} +\putnotese{80}{40}{ \includegraphics[bb=0 0 149.51 121.51 , height=4cm]{Fig/Intersectcurvsf.pdf}} +\end{layer} + +\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]]); +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); +Pointdata3d("1",intercrvsf1); +\end{verbatim} +実行すると,コンソールに + +\verb| Intersect=[[0,1.57,1.52],[0,-1.91,0.36]] | + +のように表示され,画面には交点が表示される。 + + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +%------------------- IntersectsgpL ----------------------------------------------- +\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(直線)と平面の交点を求める。 +\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。 + +戻り値は,[pt,flag1,flag2,val1,val2] + +pt:直線と平面の交点の座標。直線と平面が平行で交点が存在しない場合は空リスト[] + +flag1 : 交点が線分内にあれば true ,なければ false + +flag2 : 交点が面内にあれば true,なければ false + +val1,val2 : 線分についてのパラメータ値,平面についてのパラメータ値 + +描画方法は,"put" または "i" , "e" 。 + +\hspace{10mm} put : 幾何点を作る + +\hspace{10mm} i : 線分内にあれば点を描く + +\hspace{10mm} e :平面で交われば点を描く + +\vspace{\baselineskip} +【例】交点の有無と戻り値 + +次のスクリプトで\verb|p2| を変えたときの戻り値の \verb|flag1, flag2| + +\begin{verbatim} +p1=[1,-1,0]; +p2=[0,0,1/2]; +p3=[0,1,0]; +p4=[-1,0,0]; +p5=[0,0,1]; +Spaceline("1",[p1,p2]); +Spaceline("2",[p3,p4,p5,p3]); +ret=IntersectsgpL("P",[p1,p2],[p3,p4,p5],"put"); +println("flag1="+ret_2+": flag2="+ret_3); +\end{verbatim} + +\begin{layer}{150}{0} +\putnotese{10}{15}{ \input{Fig/wire01}} +\putnotese{60}{15}{ \input{Fig/wire02}} +\end{layer} + + \begin{verbatim} +p2=[0,0,1/2]; p2=[-1,1,1]; +flag1=false : flag2=trueflag1=true : flag2=true +\end{verbatim} + +\newpage%\vspace{55mm} +\begin{layer}{150}{0} +\putnotese{10}{15}{ \input{Fig/wire03}} +\putnotese{60}{15}{ \input{Fig/wire04}} +\end{layer} + + \begin{verbatim} + p2=[1,2,1]; p2=[1,0,1/2]; + flag1=true : flag2=false flag1=false : flag2=false +\end{verbatim} + +\vspace{30mm} +【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とし,軸上の点を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]); +Putpoint3d("B",[Hn,0,Hn]); +Putpoint3d("C",[Hn,Hn,Hn]); +Putpoint3d("D",[0,Hn,Hn]); +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); +Nohiddenbyfaces("1","phf3d1"); +\end{verbatim} +スクリプトを実行後,点E,F,Gをドラッグして適当な位置の断面にする。 + +\begin{center}\includegraphics[bb=0 0 713.04 327.02 , width=10cm]{Fig/IntersectsgpL0.pdf}\end{center} + +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("1",[E,B,F],["do"]); +Spaceline("2",[B,C,M],["do"]); +Spaceline("3",[C,D,N],["do"]); +Spaceline("4",[D,G],["do"]); +\end{verbatim} +\begin{center} \input{Fig/IntersectsgpL1}\input{Fig/IntersectsgpL2} \end{center} + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +%------------------- Sfcutparadatacdy ----------------------------------------------- +\vspace{\baselineskip} +\hypertarget{sfcutparadatacdy}{} +\item[関数]Sfcutparadatacdy(name,面,曲面,options) +\item[機能]平面と曲面の交線を求める。 +\item[説明]面の方程式はx,y,zの方程式,曲面は媒介変数表示で与える。 + +\vspace{\baselineskip} +【例】円錐を平面$y+2z=3$で切った断面を表示する。 + +\begin{layer}{150}{0} +\putnotese{70}{0}{\input{Fig/sfcut}} +\end{layer} +\begin{verbatim} +fd=[ + "p", + "x=r*cos(t)","y=r*sin(t)","z=2*(2-r)", + "r=[0,2]","t=[0,2*pi]","e" +]; +Startsurf(); +Sfbdparadata("1",fd); +Sfcutparadatacdy("1","y+2*z=3",fd); +ExeccmdC("1"); +\end{verbatim} +%\begin{center} \input{Fig/sfcut} \end{center} + + + %------------------Partcrv3d ----------------------------------------------- +\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。 + +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。 + +\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} +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,\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} + +\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} +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} +\begin{center} \input{Fig/partcrv3d2} \end{center} + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +%------------------Reflectdata3d----------------------------------------------- +\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。戻り値は鏡映したプロットデータのリスト。 + +\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} +Putpoint3d(["A",[0,-2,0],"B",[2,-2,0],"C",[1,-2,2],"D",[1,0,1],"E",[1,0,0]]); +Spaceline("1",[A,B,C,A]); +\end{verbatim} + +で点をとり,三角形を描いておく。 + +点Dに関する鏡映 + + \verb|Reflectdata3d("1",["sl3d1"],[D3d],["Color=blue","dr,2"]);| + +\hspace{20mm} \input{Fig/reflectdata3d01} + +直線DEに関する鏡映 + + \verb|Reflectdata3d("1",["sl3d1"],[D3d,E3d],["Color=blue","dr,2"]);| + +\hspace{20mm} \input{Fig/reflectdata3d02} + +平面BDEに関する鏡映 + +\verb|Reflectdata3d("1",["sl3d1"],[D3d,E3d,B3d],["Color=blue","dr,2"]);| + +\hspace{20mm} \input{Fig/reflectdata3d03} + + + %------------------Reflectpoint3d----------------------------------------------- +\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。 + +\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。 + +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]);| + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + + %------------------Rotatedata3d ----------------------------------------------- +\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。戻り値は回転したプロットデータのリスト。 + +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} +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]]); +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"]); +\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{Fig/rotatedata3d01} \hspace{5mm} \input{Fig/rotatedata3d02} + +%\begin{flushright}\hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + %------------------Rotatepoint3d ----------------------------------------------- +\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]\\ + + %------------------Scaledata3d ----------------------------------------------- +\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} +Putpoint3d(["A",[0,-2,0],"B",[2,-2,0],"C",[1,-2,2]]); +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} + +\hspace{20mm}\input{Fig/scaledata3d} +%------------------Scalepoint3d----------------------------------------------- +\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。 + +\vspace{\baselineskip} +【例】コード例と結果を示す。 + +\begin{verbatim} +Putpoint3d(["A",[2,-1,2]]); +pt=Scalepoint3d(A3d,[3,2,4],[1,1,1]); +Putpoint3d(["B",pt]); +\vspace{\baselineskip} +\end{verbatim} + +点Bの位置は(4,-3,5)になる。 + +%\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +%------------------ Translatedata3d ----------------------------------------------- +\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。戻り値は平行移動したプロットデータのリスト。 + +\vspace{\baselineskip} +【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。 + +\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。 + +\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); +\end{verbatim} +\begin{center} \input{Fig/translate01} \end{center} + +%------------------Translatepoint3d( ----------------------------------------------- +\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。 + +\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]]); +pt=Translatepoint3d(A3d,[-1,1,1]); +Putpoint3d(["B",pt]); +\end{verbatim} +%\vspace{\baselineskip} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + + \end{description} +\newpage +%その他================================== +\subsection{その他} + +\begin{description} + + +%------------------- Perpplane----------------------------------------------- +\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 + +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。 + +\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。 + +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}{150}{0} +\putnotese{80}{8}{ \input{Fig/perpplane}} +\end{layer} + +\begin{verbatim} +Xyzax3data("","x=[-5,5]","y=[-5,5]","z=[-5,4]"); +Putpoint3d(["O",[0,0,0]]); +Putpoint3d(["P",[1,1,1]]); +Perpplane("E-F","P",P3d-O3d,"put"); +vec1=2*(E3d-P3d); +vec2=2*(F3d-P3d); +Putpoint3d(["A",P3d+vec1+vec2]); +Putpoint3d(["B",P3d+vec1-vec2]); +Putpoint3d(["C",P3d-vec1-vec2]); +Putpoint3d(["D",P3d-vec1+vec2]); +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} + + %-----------------Perppt( ----------------------------------------------- +\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。 初期設定は "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。 + +\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。 + + \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=[-5,5]","y=[-5,5]","z=[-5,4]"); +Putpoint3d("O",[0,0,0]); +Putpoint3d("A",[3,0,0]); +Putpoint3d("B",[0,3,0]); +Putpoint3d("C",[0,0,3]); +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} + +%\vspace{\baselineskip} +\begin{center}\scalebox{0.9}{ \input{Fig/perppt}} \end{center} + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} +%\vspace{\baselineskip} + + %------------------Projcoordpara ----------------------------------------------- +\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。 + +\vspace{\baselineskip} +【例】\verb|Projcoordpara([3,1,2]);| + + 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) + + + %------------------Readobj----------------------------------------------- +\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・三谷による整面凸多面体のデータは\\ +\hspace*{20mm}\url{http://mitani.cs.tsukuba.ac.jp/polyhedron/}\\ +からダウンロードできる。\verb|polyhedrons_obj|を,例えば,ユーザホームのketcindy作業フォルダに入れておく。 +\begin{verbatim} +Setdirectory(gethome()+"/ketcindy/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。 + +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。 + +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。 + +\begin{layer}{150}{0} +\putnotese{80}{0}{ \input{Fig/readobj}} +\end{layer} + + +\vspace{\baselineskip} +【例】\verb|polydt|を用いて正八面体を描く + + +\begin{verbatim} + +VertexEdgeFace("1",polydt); +Nohiddenbyfaces("1","phf3d1"); +\end{verbatim} + +主なデータは次の通り。 + +\vspace{\baselineskip} + \input{Fig/kobayashi} + +この他にn01〜n92まで整面凸多面体がある。 + +%\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + + +%-------------------Xyzcoord----------------------------------------------- +\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 + +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。 + +%-------------------Isangle ----------------------------------------------- +\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} + +%------------------- Dist3d ----------------------------------------------- +\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 +\begin{verbatim} +Dist3d("A","B"); +Dist3d(A,B); +Dist3d(A3d,B3d); +\end{verbatim} + +%------------------- Embed ----------------------------------------------- +\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。 + +\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]"); +Pointdata("1",[A],["Size=3"]); +\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]]); +Embed("1",["cr1","sg1"],"A3d+x*B3d+y*C3d","[x,y]"); +\end{verbatim} +\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]]); +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。 +\begin{verbatim} +Xyzax3data("","x=[-5,5]","y=[-8,5]","z=[-5,5]"); +Putpoint3d(["O",[0,0,0],"P",[1,1,2]]); +Perpplane("E-F","P",P3d-O3d,"put"); +vec1=3*(E3d-P3d); +vec2=3*(F3d-P3d); +Putpoint3d(["A",P3d+vec1+vec2]); +Putpoint3d(["B",P3d+vec1-vec2]); +Putpoint3d(["C",P3d-vec1-vec2]); +Putpoint3d(["D",P3d-vec1+vec2]); +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]"); +Pointdata("1",[P],["Size=3"]); +Skeletonparadata("1"); +\end{verbatim} + \begin{center} \input{Fig/embed02} \end{center} + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +%------------------- Parapt ----------------------------------------------- +\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。 + +\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} +\vspace{\baselineskip} +%------------------- Invparapt ----------------------------------------------- +\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。 + +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"); +\end{verbatim} + \begin{center}\scalebox{0.8}{ \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。 +%------------------- Expr3d ----------------------------------------------- +\vspace{\baselineskip} +\hypertarget{expr3d}{} +\item[関数]Expr3d([位置, 方向, 文字列],option) +\item[機能]文字列を表示する +\item[説明]Expr() と同じ書式。「位置(座標)」だけ,空間座標にする。 + +%------------------- Letter3d ----------------------------------------------- +\vspace{\baselineskip} +\hypertarget{letter3d}{} +\item[関数]Letter3d([位置, 方向, 文字列],option) +\item[機能]文字列を表示する +\item[説明]Letter() と同じ書式。「位置(座標)」だけ,空間座標にする。 + +\vspace{\baselineskip} +【例】三角錐ABCDを描いて,BCの中点に点Mを取ってA,Dと結ぶ。 + +\begin{layer}{150}{0} +\putnotese{90}{0}{ \input{Fig/letter3d}} +\end{layer} +\begin{verbatim} +Putpoint3d("A",2*[0,0,2*sqrt(6)/3]); +Putpoint3d("B",2*[1,-1/sqrt(3),0]); +Putpoint3d("C",2*[0,sqrt(3)-1/sqrt(3),0]); +Putpoint3d("D",2*[-1,-1/sqrt(3),0]); +Putpoint3d("M",(B3d+C3d)/2); +phd=Concatobj([[A,B,C],[A,B,D],[A,C,D],[B,C,D]]); +VertexEdgeFace("1",phd); +Spaceline("1",[A,M,D]); +Nohiddenbyfaces("1","phf3d1"); +Letter3d([A3d,"ne","A",B3d,"w","B",C3d,"se","C",D3d,"e","D"]); +Letter3d(M3d,"sw","M",["Color=blue"]); +\end{verbatim} +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + + +%----------------Getangle -------------------------------------------- +\vspace{\baselineskip} +\hypertarget{getangle}{} +\item[関数]Getangle() +\item[機能]回転角の取得 +\item[説明]スライダで設定できる回転角(視点の位置)TH と FI を取得する。これは,スライダの左側に表示されている値である。戻り値は,リスト [TH,FI] で,角は度数法で表される。なお,内部変数は,THETAとPHIで,弧度法で表されている。 + +回転角の設定については,\hyperlink{setangle}{回転角の設定}を参照のこと。 + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$関数一覧}\end{flushright} + +\end{description} + +\newpage +%KeTJS================================== +\hypertarget{ketjs}{} +\section{KeTJS} + +\subsection{CindyJSとKeTJS} + +CindyJS は,Cinderellaの作品をHTMLにしてWeb上で動かせるようにしたものである。Cinderellaのファイルメニューには,「CindyJSに書き出す」があり,これにより,HTML ファイルができる。できたHTMLファイルをそのままダブルクリックすると,JavaScript で記述されたプログラムが走る。 + +現在のところはCinderellaと完全互換ではなく,Web上ではMouseスロットなどが使えなかったり,線種が指定できなかったりする。それでも,自作のボタンは有効なので,これでWeb上のアプリケーションを作ることができる。 + +KeTJSでは,CindyScriptにはないKeTCindyの関数(コマンド)を使って,作図アプリケーションを作ることができる。CindyJSの拡張版ともいえる。 + +ただし,CindyJSがCinderellaと完全互換でないように,KeTJSもKeTCindyと完全互換ではない。たとえば,いまのところ空間図形は描けない。それでも,KeTCindyのシステムが入っていない環境でもWebブラウザで教材が使えることのメリットは大きいだろう。なお,HTMLなので,TeXのファイルへの書き出し機能はない。 + +KeTJSでHTMLを作成するには,いったんCinderellaのファイルメニューから「CindyJSに書き出す」を選んでHTMLを作成した後,「KeTJS」ボタンをクリックする。「CindyJSに書き出す」で書き出されたHTMLは,実行のための環境設定しか書かれていない。これに,作図プログラムを追加するのが「KeTJS」「KeTJSoff」ボタンである。この2つのボタンの違いについては,次節「動作環境」を参照のこと。 + +また,ひな形として,template2slide.cdy または samplesフォルダの s16 に入っているものを使うとよい。「KeTJS」「KeTJSoff」ボタンが設定してある。 + +\subsection{KeTJSの動作環境} + +Cinderellaのファイルメニューから「CindyJSに書き出す」を選ぶと,CSSとランタイムへのリンク,およびJavaScriptのコードが書かれたHTMLファイルが書き出される。CSSとランタイムへのリンクは + +\begin{verbatim} +<link rel="stylesheet" href="https://cindyjs.org/dist/v0.8/CindyJS.css"> +<script type="text/javascript" src="https://cindyjs.org/dist/v0.8/Cindy.js"> +</script> +\end{verbatim} + +となっている。つまり,Web上からランタイム Cindy.js をオンラインでダウンロードしてJavaScriptを動かすことになる。そのため,ファイルをブラウザで開いたときに少し時間がかかる。また,インターネットに接続できないと実行できない。 + +このCSSとランタイムは,自分のコンピュータに置くことができ,KeTCindyでは,KeTCindyのライブラリとともに,ketcindyjsというフォルダ内に入っている。 + +また,JavaScriptのコードの方は,これだけではKeTCindyのコマンドでの作図はできない。 + +そこで,KeTJS ボタンをクリックすると,リンク先はそのままで,JavaScriptのコードを追加して,ファイル名に json を追加したHTMLファイルを作る。 + +また,KeTJSoff ボタン(オフラインで使う)をクリックすると,ランタイムをダウンロードして,Cinderellaのファイルと同じフォルダに ketcindyjs フォルダを作る。リンク先は次のようにketcindyjsに変え,JavaScriptのコードを追加して,ファイル名に jsoffL を追加したHTMLファイルを作る。 + +\begin{verbatim} +<link rel="stylesheet" href="ketcindyjs/CindyJS.css"> +<script type="text/javascript" src="ketcindyjs/Cindy.js"></script> +\end{verbatim} + +このとき,関数 \verb|Setketcindyjs() | で,オプションを \verb|"Local=n"| とすると,ランタイムとして,kettex の中にある ketcindyjs を使う。このときはファイル名に jsoff を追加する。 + +このときのリンク先は,Windowsの場合は + +\begin{verbatim} +<link rel="stylesheet" href="file:///C:/kettex/texlive/texmf-dist/ +scripts/ketcindy/ketcindyjs/CindyJS.css"> +<script type="text/javascript" src="file:///C:/kettex/texlive/ +texmf-dist/scripts/ketcindy/ketcindyjs/Cindy.js"></script> +\end{verbatim} + +Macの場合は + +\begin{verbatim} +<link rel="stylesheet" href="file:////Applications/kettex/texlive/ +texmf-dist/scripts/ketcindy/ketcindyjs/CindyJS.css"> +<script type="text/javascript" src="file:////Applications/kettex/ +texlive/texmf-dist/scripts/ketcindy/ketcindyjs/Cindy.js"></script> +\end{verbatim} + +である。 + +注)MacOS 10.14 Mojave の場合,Applicationsへのパスが通らないことがある。(2019年2月16日現在)その場合は,\verb|Setketcindyjs() | のオプションを \verb|"Local=n"| としない。 + +\vspace{\baselineskip} +{\bf ファイル名について} + +Cinderellaのファイルメニューから「CindyJSに書き出す」ときのファイル名は,初期設定では作図中のファイル名と同じ。このファイル名は書き出すときに指定できる。 + +「KeTJS」ボタンで書き出すときのファイル名は,\verb|Setfiles()| でファイル名が指定されていなければ,作図中のファイル名と同じ。これが「CindyJSに書き出す」で書き出したときのファイル名で同じでないと,KeTJSのHTMLは作成されない。したがって,次のいずれかでファイル名を決める。 + +(1) ファイル名は作図中のCinderellaのファイル名と同じにする。\\ + このときは,\verb|Setfiles()| を使わない。 + +(2) 作図中のCinderellaのファイル名と別の名前にする。\\ + このときは,\verb|Setfiles("filename")| を使い,CindyJSに書き出すときに\\ + \verb|"filename"| で書き出す。 + +%======KeTJSの設定============================ + +\subsection{KeTJSの設定} + +\begin{description} + +\hypertarget{setketcindyjs}{} +\item[関数]Setketcindyjs(options) +\item[機能] KeTJSの設定 +\item[説明] オプションを設定しない場合( Setketcindyjs() )は,初期値が使われる。 + +オプションは次の通り。 + +\begin{tabbing} +012345678\=3433778901234567\=890090666612345\=\kill +Local \> y/n \>動作環境の設定。 \>初期値は y\\ +Scale \> 実数 \> 拡大・縮小 \>初期値は 1\\ +Nolabel \> 点のリスト \> ラベルを表示しない点を指定する。"No"だけでも可。\\ +Color \> 色名またはコード\> 背景色の指定。初期値はCinderellaの画面の色。\\ +\end{tabbing} +【例】すべて設定するとき,次のように記述する。 + +\verb| Setketcindyjs(["Local=n","Scale=1.5","No=[A,B]","Color=[0.2,0,0,0]"]) | + +\vspace{\baselineskip} +注1)Cinderellaの画面に背景の方眼が描かれているとき,「CindyJSに書き出す」で,この方眼も表示される。方眼を消したい場合は,画面下の「グリッドを描く」ツールで非表示にしておく。 + +注2)「CindyJSに書き出す」で書き出すときの範囲は,ウィンドウ全体である。NE,SWの範囲ではない。2点NE,SWは\verb| Setketcindyjs(["No=[NE,SW]" | で非表示になるが,NE,SEの範囲を広くとっておき,ウィンドウサイズをこれより小さくすれば \verb|"No=[NE,SW]"| オプションを使わなくても表示されずにすむ。 + +注3)HTMLなので,画面に説明文などを表示したい場合は,HTMLファイルを開き,下の方の \verb|<body>| と \verb|</body>| の間,\verb|<div id="CSCanvas"></div>| の前後に書けば表示される。改行などは,HTMLのタグを用いる。 + +\vspace{\baselineskip} +\hypertarget{setketcindy}{} +\item[コメント化] no ketjs +\item[機能] KeTJSへの書き出しの有無を指定 +\item[説明] コマンドの末尾に \verb|//| に続いて書くと,その行はKeTJSに出力しない。 +ブロック単位で非出力にするには,ブロックを \verb|//no ketjs on|,\verb|//no ketjs off| ではさむ。 + +【例】次のスクリプトは,いずれも画面上では四角形ABCDと対角線AD,BCを描いている。 + +\begin{verbatim} +Listplot("1",[A,B,C,D,A]); +Listplot("2",[A,C]); +Listplot("3",[B,D]);// no ketjs +\end{verbatim} + +この場合,HTMLでは対角線BDは描かれない。 + +\begin{verbatim} +Listplot("1",[A,B,C,D,A]); +// no ketjs on +Listplot("2",[A,C]); +Listplot("3",[B,D]); +// no ketjs off +\end{verbatim} + +この場合,対角線は2本とも描かれない。 + +\begin{flushright} \hyperlink{functionlist}{$\Rightarrow$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}} + +\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{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{initglist}{Initglist} \> ketlib スロットの描画データを追加する\\ +\hyperlink{ptsize}{Ptsize(数)} \>表示する点の大きさを設定する\\ +\hyperlink{setarrow}{Setarrow(size,angle,pos,cut,style}\>矢線の形状を設定する\\ +\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{drawfigures}{Drawfigures(name ,figlist,optionlist)} \>複数のデータのスタイルをリストで与えて描画する\\ +%\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{anglemark}{Anglemark(点list, options)}\>角の印を入れる\\ +\hyperlink{setarrow}{Setarrow(options)}\>矢線をスタイルを設定する\\ +\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([座標,位置,文字列],options)}\>\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],options)}\>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{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{putcell}{Putcellexpr (列番号, 行番号, 位置, 文字)} \>セルに数式を入れる\\\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{asin}{Asin(real),Acos(real) }\>逆三角関数の値を返す\\ +\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{readcsv}{Readcsv(name,filename,option)}\>csvファイルを読む\\ +\hyperlink{readlines}{Readlines(name,filename,option)}\>テキストファイルを1行ずつ読む\\ +\hyperlink{sqr}{Sqr(real)}\>平方根を返す\\ +\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{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{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)} \> 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{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\\ +\hyperlink{fracform}{Fracform(数,分母リスト)}\>簡易TeX-like書式の文字列を返す\\ +\hyperlink{totexform}{Totexform(TeX-like書式)}\>TeX書式の文字列を返す\\ +\hyperlink{tocindyform}{Tocindyform(TeX-like書式}\>Cindy書式の文字列を返す\\ +\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{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{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,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{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,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\\ +\hyperlink{mkobjnrm}{Mkobjnrm(name,式)} \>法線ベクトルのデータを作成\\ +\hyperlink{mkobjplatecmd}{Mkobjplatecmd(name,面データ,options)} \>面を描く\\ +\hyperlink{mkobjpolycmd}{Mkobjpolycmd(name,PD,options)} \>多面体を描く\\ +\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{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\\ +\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{setangle}{Setangle} \>回転角の設定\\ +\hyperlink{getangle}{Getangle}\>回転角の取得\\ +\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{expr3d}{Expr3D([座標,位置,文字列],options)}\>文字列を表示する\\ +\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{letter3d}{Letter3D([座標,位置,文字列],options)}\>文字列を表示する\\ +\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{sfcutparadatacdy}{Sfcutparadatacdy(name,面,曲面,options)} \>平面と曲面の交線を求める。\\ +\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\\ +【KeTJS】\\ +\hyperlink{setketcindyjs}{Setketcindyjs(options)}\>KeTJSの設定\\ + +\end{tabbing} + +\end{document}
\ No newline at end of file diff --git a/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/KeTPicStyleE.tex b/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/KeTPicStyleE.tex new file mode 100644 index 0000000000..5ca2f21268 --- /dev/null +++ b/graphics/ketcindy/ketcindyfolder/doc/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/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/KeTPicStyleJ.tex b/graphics/ketcindy/ketcindyfolder/doc/source/ketmanual/KeTPicStyleJ.tex new file mode 100644 index 0000000000..1649dd10b6 --- /dev/null +++ b/graphics/ketcindy/ketcindyfolder/doc/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}
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