diff options
Diffstat (limited to 'Master/texmf-dist/doc')
44 files changed, 0 insertions, 25499 deletions
diff --git a/Master/texmf-dist/doc/latex/bclogo/bcbombe.eps b/Master/texmf-dist/doc/latex/bclogo/bcbombe.eps deleted file mode 100644 index 4add04af43e..00000000000 --- a/Master/texmf-dist/doc/latex/bclogo/bcbombe.eps +++ /dev/null @@ -1,2392 +0,0 @@ -%!PS-Adobe-2.0 EPSF-2.0 -%%Creator: dvips(k) 5.96dev Copyright 2007 Radical Eye Software -%%Title: CompileEps.dvi -%%CreationDate: Sat Sep 19 14:18:30 2009 -%%BoundingBox: 71 690 90 721 -%%EndComments -%DVIPSWebPage: (www.radicaleye.com) -%DVIPSCommandLine: dvips -E -o -%+ C:\Users\Alain_2\Documents\LaTeX\Logos\bcbombe.eps CompileEps.dvi -%DVIPSParameters: dpi=600 -%DVIPSSource: TeX output 2009.09.19:1418 -%%BeginProcSet: tex.pro 0 0 -%! -/TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S -N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 -mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 -0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ -landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize -mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ -matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round -exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ -statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] -N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin -/FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array -/BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 -array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N -df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A -definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get -}B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} -B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr -1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S -/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy -setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask -restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn -/BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put -}if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ -bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A -mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ -SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ -userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X -1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 -index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N -/p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ -/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) -(LaserWriter 16/600)]{A length product length le{A length product exch 0 -exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse -end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask -grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} -imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round -exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto -fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p -delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} -B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ -p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S -rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end - -%%EndProcSet -%%BeginProcSet: pstricks.pro 0 0 -% $Id: pstricks.pro 34 2008-06-25 17:20:01Z herbert $ -% -%% PostScript prologue for pstricks.tex. -%% Version 1.05, 2008/06/25 -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -% -% -% Define the follwing gs-functions if not known, eg when using distiller -% -systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if -systemdict /.setblendmode known not {/.setblendmode { pop } def } if -systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if -% -/tx@Dict 200 dict def % the main PSTricks dictionary -tx@Dict begin -/ADict 25 dict def % The arrow dictionaray -/CM { matrix currentmatrix } bind def -/SLW /setlinewidth load def -/CLW /currentlinewidth load def -/CP /currentpoint load def -/ED { exch def } bind def -/L /lineto load def -/T /translate load def -/TMatrix { } def -/RAngle { 0 } def -/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments -/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known -/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) -/Div { dup 0 eq { pop } { div } ifelse } def % control the division -/tan { dup cos abs 1.e-10 lt - { pop 1.e10 } % return 1.e10 as infinit - { dup sin exch cos div } ifelse % default sin/cos -} def -/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees -/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root - pop pop 0 }{ sqrt exch atan} ifelse } def -/NET { neg exch neg exch T } def % change coordinate system to the negative one -/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter -/Pyth2 { % Pythagoras, xA yA xB yB - 3 -1 roll % xA xB yB yA - sub % xA xB yB-yA - 3 1 roll % yB-yA xA xB - sub % yB-yA xA-xB - Pyth } def -/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian -/Rand { rand 4294967295 div } def % a real random number -%----------------- hv added 20050516 --------------- -/PiDiv2 1.57079632680 def -/Pi 3.14159265359 def -/TwoPi 6.28318530718 def -/Euler 2.71828182846 def -%/e Euler bind def -/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees -/DegtoRad { Pi mul 180 div } bind def % viceversa -%----------------- hv end--------------------------- -/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def -/PathLength { - flattenpath /z 0 def - { /y1 ED /x1 ED /y2 y1 def /x2 x1 def } - { /y ED /x ED PathLength@ } - {} - { /y y2 def /x x2 def PathLength@ } - /pathforall load stopped { pop pop pop pop } if - z -} def -% -/STP { .996264 dup scale } def % BP/PT scaling -/STV { SDict begin normalscale end STP } def % -% -%%-------------- DG begin patch 15 ---------------%% -%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def -%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y -%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul -%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] -%0 } ifelse setdash stroke } def -/DashLine { - dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse - /b ED /x1 ED /y1 ED /x ED /y ED - /z y x add y1 add x1 add def - /Coef b a .5 sub 2 mul y mul sub z Div round - z mul a .5 sub 2 mul y mul add b exch Div def - /y y Coef mul def - /x x Coef mul def - /y1 y1 Coef mul def - /x1 x1 Coef mul def - x1 0 gt y1 0 gt or x 0 gt or y 0 gt and - { [ y x y1 x1 ] 1 a sub y mul } - { [ 1 0 ] 0 } ifelse - setdash stroke -} def -%%-------------- DG end patch 15 ---------------%% -/DotLine { - /b PathLength def - /a ED /z ED /y CLW def - /z y z add def - a 0 gt { - /b b a div def - }{ - a 0 eq { - /b b y sub def - }{ a -3 eq { - /b b y add def } if - } ifelse - } ifelse - [ 0 b b z Div round Div dup 0 le { pop 1 } if ] - a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse - setdash 1 setlinecap stroke -} def -% -/LineFill { % hv ------------ patch 7 ------------- - gsave - abs /hatchWidthInc ED - abs /hatchSepInc ED - abs CLW add /a ED - a 0 dtransform round exch round exch - 2 copy idtransform - exch Atan rotate - idtransform pop /a ED - .25 .25 itransform pathbbox - /y2 ED - a Div ceiling cvi /x2 ED /y1 ED - a Div cvi /x1 ED /y2 y2 y1 sub def - clip - newpath - 2 setlinecap - systemdict - /setstrokeadjust known { true setstrokeadjust } if - x2 x1 sub 1 add { - x1 a mul y1 moveto 0 y2 rlineto stroke - /x1 x1 1 add - hatchWidthInc 0 gt { CLW add } if - def - hatchSepInc 0 gt hatchWidthInc 0 gt or { - /a a hatchSepInc add def - CLW hatchWidthInc add SLW - } if - } repeat - grestore - pop pop } def -% -/PenroseFill {% on stack: scaling factor - dup dup scale - 1 exch div round /penroseFactor ED - a 0 dtransform round exch round exch - 2 copy idtransform - exch Atan rotate - idtransform pop /a ED - .25 .25 itransform pathbbox - /y2 ED - a Div ceiling cvi /x2 ED /y1 ED - a Div cvi /x1 ED /y2 y2 y1 sub def - clip - newpath - systemdict - /setstrokeadjust known { true setstrokeadjust } if - /I/S/L/W/G/+/Z/F/E/D[/def/exch/for{E D}/add{s E get mul} - { Z -36.2001 1 33 }{25 E S rlineto}{/q Z dup q G E q 1 + G}{Z 2 2}]{cvx def}forall - [0 72 1008 {dup sin E cos }F ]1 setlinejoin/s W{/a W{/b I 10{/i I 4{/m I moveto - i m +/j I 10{/l Z b m l + G a l G sub s m get div .2 + floor .3 + 25 - mul j l + S rmoveto}F i L j L stroke }F}F}F}F - grestore - pop pop -} def -% -%gsave abs CLW add /a ED a 0 dtransform round exch round exch -%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 -%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 -%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a -%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a -%% DG/SR modification end -%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict -%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 -%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) -%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } -%% def -%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore -%pop pop } def -%% DG/SR modification end -% -/BeginArrow { - ADict begin % hold it local, for end see EndArrow - /@mtrx CM def - gsave - 2 copy T - 2 index sub neg exch - 3 index sub exch Atan - rotate newpath -} def -% -/EndArrow { @mtrx setmatrix CP grestore end } def % end the ADict -% -/Arrow { - CLW mul add dup - 2 div /w ED - mul dup /h ED - mul /a ED - { 0 h T 1 -1 scale } if - w neg h moveto - 0 0 L w h L w neg a neg rlineto - gsave fill grestore -} def -% -/ArrowD { % the sides are drawn as curves (hv 20071211) - CLW mul add dup - 2 div /w ED - mul dup /h ED - mul /Inset ED - { 0 h T 1 -1 scale } if % changes the direction -% we use y=w/h^2 * x^2 as equation for the control points -% for the coordinates the arrow is seen from top to bottom -% the bottom (tip) is (0;0) - w neg h moveto % lower left of > - w 9 div 4 mul neg h 3 div 2 mul - w 9 div neg h 3 div - 0 0 curveto % tip of > - w 9 div h 3 div - w 9 div 4 mul h 3 div 2 mul - w h curveto % upper left of > - w neg Inset neg rlineto % move to x=0 and inset - gsave fill grestore -} def -% -/Tbar { - CLW mul add /z ED - z -2 div CLW 2 div moveto - z 0 rlineto stroke - 0 CLW moveto -} def -% -/Bracket { - CLW mul add dup CLW sub 2 div - /x ED mul CLW add /y ED /z CLW 2 div def - x neg y moveto - x neg CLW 2 div L x CLW 2 div L x y L stroke - 0 CLW moveto -} def -% -/RoundBracket { - CLW mul add dup 2 div - /x ED mul /y ED /mtrx CM def - 0 CLW 2 div T x y mul 0 ne { x y scale } if - 1 1 moveto - .85 .5 .35 0 0 0 curveto - -.35 0 -.85 .5 -1 1 curveto - mtrx setmatrix stroke 0 CLW moveto -} def -% -/SD { 0 360 arc fill } def -% -/EndDot { % DS is the dot size - { /z DS def } { /z 0 def } ifelse - /b ED 0 z DS SD b { 0 z DS CLW sub SD } if - 0 DS z add CLW 4 div sub moveto } def -% -/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { - /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto - load } if ] cvx newpath 3 1 roll T exec } def -% -%/NArray { -% aload length 2 div dup dup cvi eq not { exch pop } if /n exch -% cvi def -%} def -% -/NArray { % holds the coordinates and on top of stack the showpoints boolean - /showpoints ED - counttomark 2 div dup cvi /n ED - n eq not { exch pop } if - showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse -} def -% -/Line { - NArray n 0 eq not - { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def - n { Lineto } repeat - CP 4 2 roll ArrowB L pop pop - } if -} def -% -/Arcto { - /a [ 6 -2 roll ] cvx def - a r - /arcto load stopped { 5 } { 4 } ifelse { pop } repeat - a -} def -% -/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq - and { pop pop /n n 1 sub def } if } def -/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } - repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 - ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 - moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto - Lineto pop pop closepath } ifelse } def -/Diamond { - /mtrx CM def - T rotate - /h ED - /w ED - dup 0 eq { pop } { CLW mul neg - /d ED - /a w h Atan def - /h d a sin Div h add def - /w d a cos Div w add def } ifelse - mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div - /ArrowA { moveto } def - /ArrowB { } def - false Line - closepath mtrx setmatrix } def -% DG modification begin - Jan. 15, 1997 -%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { -%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 -%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 -%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx -%setmatrix } def -/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup -CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 -div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 -d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx -% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) -% setmatrix } def -setmatrix pop } def -% DG/SR modification end -% -/CCA { - /y ED /x ED - 2 copy y sub /dy1 ED - x sub /dx1 ED - /l1 dx1 dy1 Pyth def -} def -% -/CC { - /l0 l1 def - /x1 x dx sub def - /y1 y dy sub def - /dx0 dx1 def - /dy0 dy1 def - CCA - /dx dx0 l1 c exp mul dx1 l0 c exp mul add def - /dy dy0 l1 c exp mul dy1 l0 c exp mul add def - /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def - /x2 x l0 dx mul m mul sub def - /y2 y l0 dy mul m mul sub def - /dx l1 dx mul m mul neg def - /dy l1 dy mul m mul neg def -} def -% -/IC { - /c c 1 add def - c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse - /a a 2 mul 3 div 45 cos b exp div def - CCA - /dx 0 def - /dy 0 def -} def -% -/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def -/NC { CC x1 y1 x2 y2 x y curveto } def -/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def -/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def -/NAC { x2 y2 x y curveto CC x1 y1 } def -/EAC { x2 y2 x y ArrowB curveto pop pop } def -% -/OpenCurve { - NArray n 3 lt - { n { pop pop } repeat } - { BOC /n n 3 sub def n { NC } repeat EOC } ifelse -} def -% -/AltCurve { - { false NArray n 2 mul 2 roll - [ n 2 mul 3 sub 1 roll ] aload - /Points ED - n 2 mul -2 roll } - { false NArray } ifelse - n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse -} def -% -/ClosedCurve { - NArray n 3 lt - { n { pop pop } repeat } - { n 3 gt { CheckClosed } if - 6 copy n 2 mul 6 add 6 roll - IC CC x y moveto n { NC } repeat - closepath pop pop - } ifelse -} def -% -/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def -/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def -/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } -def -/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix -rotate matrix concatmatrix exch findfont exch makefont setfont } def -/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto -x1 y1 lineto closepath } def -/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 -y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div -exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse -/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto -x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } -ifelse } def -/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add -/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { -pop pop Rect } { OvalFrame } ifelse } def -% -/BezierNArray { - /f ED - counttomark 2 div dup cvi /n ED - n eq not { exch pop } if - n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat - f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse -} def -% -/OpenBezier { - BezierNArray - n 1 eq - { pop pop } - { ArrowA n 4 sub 3 idiv - { 6 2 roll 4 2 roll curveto } repeat - 6 2 roll 4 2 roll ArrowB curveto } ifelse -} def -% -/ClosedBezier { - BezierNArray - n 1 eq - { pop pop } - { moveto n 1 sub 3 idiv - { 6 2 roll 4 2 roll curveto } repeat - closepath } ifelse -} def -% -/BezierShowPoints { - gsave - Points aload length 2 div cvi /n ED - moveto - n 1 sub { lineto } repeat - CLW 2 div SLW [ 4 4 ] 0 setdash stroke - grestore -} def -% -/Parab { - /y0 ED /x0 ED /y1 ED /x1 ED - /dx x0 x1 sub 3 div def - /dy y0 y1 sub 3 div def - x0 dx sub y0 dy add x1 y1 ArrowA - x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB - curveto - /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def -} def -% -/Grid { - newpath - /a 4 string def - /b ED /c ED /n ED - cvi dup 1 lt { pop 1 } if - /s ED - s div dup 0 eq { pop 1 } if - /dy ED s div dup 0 eq { pop 1 } if - /dx ED dy div round dy mul - /y0 ED dx div round dx mul - /x0 ED dy div round cvi - /y2 ED dx div round cvi - /x2 ED dy div round cvi - /y1 ED dx div round cvi - /x1 ED - /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def - /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def - b 0 gt { - /z1 b 4 div CLW 2 div add def -% /Helvetica findfont b scalefont setfont - /b b .95 mul CLW 2 div add def } if - systemdict /setstrokeadjust known - { true setstrokeadjust /t { } def } - { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add - exch itransform } bind def } ifelse - gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse - /i x1 def - /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def - /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def - x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if - { i dx mul dup y0 moveto - b 0 gt - { gsave c i a cvs dup stringwidth pop - /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse - h 0 gt {b neg}{z1} ifelse - rmoveto show grestore } if - dup t f moveto - g t L stroke - /i i w add def - } repeat - grestore - gsave - n 0 gt - % DG/SR modification begin - Nov. 7, 1997 - Patch 1 - %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } - { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } - % DG/SR modification end - { 2 setlinecap } ifelse - /i y1 def - /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def - /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def - y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if - { newpath i dy mul dup x0 exch moveto - b 0 gt { gsave c i a cvs dup stringwidth pop - /z2 ED - w 0 gt {z1 z2 add neg} {z1} ifelse - h 0 gt {z1} {b neg} ifelse - rmoveto show grestore } if - dup f exch t moveto - g exch t L stroke - /i i h add def - } repeat - grestore -} def -% -/ArcArrow { - /d ED /b ED /a ED - gsave - newpath 0 -1000 moveto clip - newpath - 0 1 0 0 b - grestore - c mul - /e ED - pop pop pop r a e d PtoC y add exch x add - exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c - mul neg d -} def -% -/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def -% -/ArcAdjust { %%%% Vincent Guirardel -% given a target length (targetLength) and an initial angle (angle0) [in the stack], -% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). -% This computes an angle t such that (x0,y0) is at distance -% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). -% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 -% contrary to TvZ's code. -% To achieve, this, one iterates the following process: start with some angle t, -% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. -% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. -% -% Another difference with TvZ's code is that we need d (=add/sub) to be defined. -% the value of d = add/sub is used to know on which side we have to move. -% It is only used in the initialisation of the angle before the iteration. -% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% Input stack: 1: target length 2: initial angle -% variables used : rx, ry, d (=add/sub) -% - /targetLength ED /angle0 ED - /x0 rx angle0 cos mul def - /y0 ry angle0 sin mul def -% we are looking for an angle t such that (x0,y0) is at distance targetLength -% from the point M(t)=(rx*cos(t),ry*sin(t))) -%initialisation of angle (using 1st order approx = TvZ's code) - targetLength 57.2958 mul - angle0 sin rx mul dup mul - angle0 cos ry mul dup mul - add sqrt div -% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees -% (if the ellipse is very curved at the point where we draw the arrow, % -% the value can be much more than 360 degrees !) -% this should avoid going on the wrong side (more than 180 degrees) or go near -% a bad attractive point (at 180 degrees) - dup 90 ge { pop 90 } if - angle0 exch d % add or sub -% maximum number of times to iterate the iterative procedure: -% iterative procedure: takes an angle t on top of stack, computes a -% better angle (and put it on top of stack) - 30 { dup -% compute distance D between (x0,y0) and M(t) - dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt -% if D almost equals targetLength, we stop - dup targetLength sub abs 1e-5 le { pop exit } if -% stack now contains D t -% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: -% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) - exch dup cos rx mul x0 sub exch sin ry mul y0 sub -% stack contains: y(t)-y0, x(t)-x0, d - 2 index Div targetLength mul y0 add ry Div exch - 2 index Div targetLength mul x0 add rx Div -% stack contains x(t')/rx , y(t')/ry , d -% now compute t', and remove D from stack - atan exch pop - } repeat -% we don't look at what happened... in particular, if targetLength is greater -% than the diameter of the ellipse... -% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... -% after iteration, stack contains an angle t such that M(t) is the tail of the arrow -% to give back the result as a an angle relative to angle0 we could add the following line: -% angle0 sub 0 exch d -% -% begin bug fix 2006-01-11 -% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 -%(we don't want to make the ellipse turn more or less than it should)... -dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse -% end bug fix -} def -% -/EllipticArcArrow { - /d ED % is add or sub - /b ED % arrow procedure - /a1 ED % angle - gsave - newpath - 0 -1000 moveto - clip % Set clippath far from arrow. - newpath - 0 1 0 0 b % Draw arrow to determine length. - grestore -% Length of arrow is on top of stack. Next 3 numbers are junk. -% - a1 exch ArcAdjust % Angular position of base of arrow. - /a2 ED - pop pop pop - a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig - a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig - a1 cos rx mul xOrig add % - a1 sin ry mul yOrig add % -% Now arrow tip coor and base coor are on stack. - b pop pop pop pop % Draw arrow, and discard coordinates. - a2 CLW 8 div -% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) - 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse - ArcAdjust -% resets original value of d - 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. -} def -%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% -% -/Rot { CP CP translate 3 -1 roll neg rotate NET } def -% -/RotBegin { - tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if - /TMatrix [ TMatrix CM ] cvx def - /a ED - a Rot /RAngle [ RAngle dup a add ] cvx def -} def -% -/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def -% -/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def -/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def -/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def -/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s -abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b -div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { -h1 abs h sub dup s mul abs } ifelse } def -/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s -mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q -{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add -exch } def -/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible -/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def -} if } ifelse } def -/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def -/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit -neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def -/IfVisible true def } def -end -%-----------------------------------------------------------------------------% - -% END pstricks.pro - -%%EndProcSet -%%BeginProcSet: pst-algparser.pro 0 0 -% $Id: pst-algparser.pro 26 2008-06-14 11:50:02Z herbert $ -%% -%% PostScript prologue for PSTricks algorithm parser -%% Version 0.01, 2008/01/01 -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -%% -%%-----------------------------------------------------------------------------% -% -/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez -% -/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin -% -% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 -% E->T|E+T -% T->FS|T*FS -% FS -> F | +FS | -FS -% F->P|F^SF -% P->(E)|literal -% literal->number|var|var[E]|func(params) -% params->E|E,param -% number->TOBEFINISHED -% -%% E expression, T term, SF signed factor, F factor, P power -% -%% parser -% -%% str -% -%% C->E<condition_operators>E -%% STR index -> STR index+lenExpr -/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def -% -%% analyze Expression List (separator , or | ) -%% STR index -> STR index+lenExpr -%% /AnalyzeListOfE { -%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar -%% NextNonBlankChar dup 0 eq { pop exit } if -%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if -%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop -%% AnalyzeListOfEPostHook -%% } def -/AnalyzeListOfE { - /NotFirst false def - { NextNonBlankChar pop AnalyzeExpr - NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse - dup Strlen eq { exit } if NextNonBlankChar - dup 44 ne 1 index 124 ne and - { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } - if pop 1 add } loop - AnalyzeListOfEPostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% E->T|E+T -%% STR index -> STR index+lenExpr -/AnalyzeExpr { - AnalyzePreHook AnalyzeTerm IsEndingExpr - { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } - { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } - ifelse - AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% T->FS|T*FS -%% STR index -/AnalyzeTerm { - AnalyzePreHook AnalyzeSignedFactor IsEndingTerm - { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } - { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } - ifelse - AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% FS -> F | +FS | -FS -%% STR index -/AnalyzeSignedFactor { - AnalyzePreHook 2 copy get dup IsUnaryOp - { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } - { pop AnalyzeFactor } - ifelse AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% F->P|F^P -%% STR index -/AnalyzeFactor { - AnalyzePreHook AnalyzePower IsEndingFactor - { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } - { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } - ifelse AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% P->(E)|literal -%% STR index -/AnalyzePower { - %% depending of first char either a number, or a literal - 2 copy get dup 40 eq%%an open par - { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } - { AnalyzeLiteral } - ifelse -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index STR[index] -> STR index -%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def -/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% recognize + or - -%% chr -> T/F -/IsUnaryOp { dup 43 eq exch 45 eq or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a number can contain only : 0123456789. -%% chr -> T/F -/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index -> STR index number -%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? -%% STR index -> STR index' number -/ReadNumber { - exch dup 3 -1 roll dup 3 1 roll - %%read mantissa - { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop - dup 101 eq exch 69 eq or - %%% there is a "e" or "E" -> read exponant - { 1 add 2 copy get dup IsUnaryOp - { pop 1 add 2 copy get } if - { IsNumber not { exit } if 1 add 2 copy get } loop } - if - dup 4 1 roll - 3 -1 roll exch 1 index sub getinterval -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a number can contain only : 0123456789. -%% chr -> T/F -/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index -> STR index number -%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? -%% STR index -> STR index' number -/ReadCondOp { - NextNonBlankChar 1 index 4 1 roll - { IsCondOp not { exit } if 1 add 2 copy get } loop - 2 copy 5 -1 roll - exch 1 index sub getinterval 3 1 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a literal can contain only : 0123456789. -%% chr -> T/F -/IsLiteral {% - dup 48 ge exch dup 57 le 3 -1 roll and exch - dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch - dup 97 ge exch 122 le and or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? -%% STR index -> literal STR index' nextchr -/ReadLiteral { - exch dup 3 -1 roll dup 3 1 roll - %%read literal core - { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop - 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or a clpar -%% STR index -> STR index STR[index] T/F -/IsEndingExpr {% - 2 copy dup Strlen eq - %% if end of str is reached -> end ! - { pop pop 0 true } - %% ending chr -> clpar, comma, |, <, >, =, !, - {get dup dup 41 eq - exch dup 124 eq - exch dup 93 eq - exch dup 44 eq - exch dup 30 eq - exch dup 60 ge exch 62 le and or or or or or} - ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or a +- -%% STR index -> STR index STR[index] T/F -/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or */ -%% STR index -> STR index STR[index] T/F -/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or ^ -%% STR index -> STR index STR[index] T/F -/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index -> STR index STR[index] -/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def -/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def -%%%%%%%%%%%%%%%%%%%%%%%% -%% DEBUG -/BRK {false} def -/BRKtrue {/BRK true def} def -/BRKStop {BRK {BRKtoto} if } def -/BRKEvalStop {BRK exch if } def -/BRKBRK2true {BRK {BRK2true} if } def -/BRK2 {false} def -/BRK2true {/BRK2 true def} def -/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def -end -% -%-------------------------------------------------------------------------------% -% -/tx@AlgToPs 12 dict def tx@AlgToPs begin -% -%% algExpr -> PSVector -/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def -/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def -/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def -/Strlen 0 def -/EvalListOfExpr {} def% -/EvalNumber {% - ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx - exch 1 add array astore def NextNonBlankChar pop } def -/EvalAddSub {% - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll - 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def -} def -/EvalMulDiv {% - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll - 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def -} def -/EvalPower {% - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll - pop /exp cvx exch 1 add array astore def -} def -/EvalLiteral {% - ReadLiteral - dup 40 eq%%% there is an open par -> function call - { pop 2 index - dup (Sum) eq { EvalSum } - { dup (IfTE) eq { EvalCond } - { dup (Derive) eq { pop EvalDerive } - { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx - exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } - { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def - dup 91 eq%%% there is an open bracket -> vector element - { pop 1 add NextNonBlankChar pop AnalyzeExpr - /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } - { pop NextNonBlankChar pop } - ifelse} - ifelse -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% the derive function : Derive(n,f(x)) -%% firstparindex lastparindex -> -/EvalDerive { - %% manage the function descripiton - 1 add ReadNumber 3 1 roll NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - 1 add NextNonBlankChar pop - 3 -1 roll cvi - dup 0 eq - { pop AnalyzeExpr 3 -1 roll pop 1 add } - { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll - { (x) tx@Derive begin Derive end } repeat - ExpressionVector exch /ExpressionVector [] def - AlgToPs aload length - /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def - l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add - 1 index length /Strlen exch def } ifelse -} def -/EvalSum {% - pop 1 add NextNonBlankChar pop - %% read the variable name - ReadLiteral pop NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if - %% read the initial value - 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - %% read the increment value - 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - %% read the limit value - 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll - 5 -1 roll 4 add array astore def - %% keep ExpressionVector for later and create a new one for internal Sum computation - ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def - 1 add NextNonBlankChar pop AnalyzeExpr - %% add each term - /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def - /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add - array astore def 3 -1 roll pop 1 add -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Convert to radians if trigo function call -%% (name) -> -/TrigoFunc { - dup (cos) eq 1 index (sin) eq or exch (tan) eq or - { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add - array astore def - } if -} def -/EvalCond {% - pop 1 add AnalyzeCond NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if - ExpressionVector 3 1 roll /ExpressionVector [] def - 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def - NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if - 1 add AnalyzeExpr - NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if - ExpressionVector - /ExpressionVector 6 -1 roll aload length dup - 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def - 1 add 3 -1 roll pop -} def -%% CondOp STR index -/EvalCondOp {% - 3 -1 roll - dup (=) eq { /eq } {% - dup (<) eq { /lt } {% - dup (>) eq { /gt } {% - dup (>=) eq { /ge } {% - dup (<=) eq { /ge } {% - dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } - ifelse } ifelse } ifelse } ifelse } ifelse } ifelse - cvx exch pop - /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def -/EvalUnaryOp { - 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% H O O K S -/AnalyzePreHook {} bind def -/PreEvalHook {} bind def -/AnalyzeListOfEPostHook {} bind def -/AnalyzePostHook {} def -/RollOp { 3 1 roll } bind def -end %tx@CoreAnalyzerDict -% -%--------------------------------------------------------------------% -% -/tx@Derive 41 dict def tx@Derive begin -%%increase ^^ for each function added -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% algExpr variable -> PSVector -/Derive {% - 10240 string 3 1 roll 0 3 1 roll - /Variable exch def - tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end -} def -/Strlen 0 def -/InitParser { dup length /Strlen exch def 0 } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% algExpr variable index -> PSVector -/DeriveIndexed {% - 3 1 roll 10240 string 3 1 roll 0 3 1 roll - /Variable exch def - tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u,v)'=-(u',v') -/EvalListOfExpr {% - 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe - 2 copy 7 -1 roll dup length 4 1 roll putinterval add - 6 -2 roll pop pop - 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (-u)'=-(u') -/EvalUnaryOp { - 4 -2 roll 4 index (0) eq - { (0) StrConcat 7 -1 roll pop } - { 7 -1 roll 45 eq - { AddSub AddOpPar true } { false } ifelse - 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (number)'=0 -/EvalNumber { ReadNumber (0) 6 2 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u+v)'=u'+v' -/EvalAddSub {% - 7 index dup (0) eq - { pop true }%% du=0 nothing added - { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } - ifelse - 5 index dup (0) eq - { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 - { exch - { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added - { 5 -2 roll 7 index 43 eq%%something yet added - { AddAdd false } { AddSub AddOpPar true } ifelse } - ifelse 11 1 roll - 3 -1 roll StrConcat 10 -1 roll { AddClPar } if - 2 copy pop 0 6 2 roll GetIntervalNewStr } - ifelse - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u*v)' or (u/v)' -/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u*v)'=u'*v+u*v' -/EvalMul {% - 4 -2 roll 7 index dup (0) eq - { pop false }%%du=0 - { (1) eq%%du=1 - { false } - { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse - 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if - true }%%du!=0 - ifelse - 5 1 roll 5 index (0) eq - { 5 -1 roll not { (0) StrConcat } if }%%dv=0 - { 5 -1 roll { AddAdd } if - 4 index (1) eq - { 8 index StrConcat } - { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } - ifelse - }%%dv!=0 - ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u/v)'=(u'*v-u*v')/v^2 -/EvalDiv {% - 4 -2 roll - 4 index (0) eq%%dv=0 -> u'/v - { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } - { 7 index dup (0) eq - { pop }%%du=0 - { (1) eq%%du=1 - { false } - { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse - 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 - ifelse - AddSub - 4 index (1) eq - { 8 index StrConcat } - { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } - ifelse - %}%%dv!=0 - 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar - AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } - ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% str1 index str2 -> str1 index -/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def -/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) -/EvalPower {% - 4 -2 roll 7 index (0) eq - {%%if du=0 then (u^v)'=v'ln(u)u^v - 4 index (0) eq - { (0) StrConcat }%%if dv=0 then (u^v)'=0 - { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if - 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if - AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse - } - {%%du!=0 - 4 index (0) eq - {%%if dv=0 then (u^v)'=vu'u^(v-1) - 5 index dup IsStrNumber - { dup (0) eq - { StrConcat } - { dup dup (1) eq exch (1.0) eq or - { StrConcat } - { StrConcat - 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 - { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 - (*\() StrConcat 8 index StrConcat (\)) StrConcat - 5 index dup dup (2) eq exch (2.0) eq or - { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } - { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat - 5 index StrConcat (-1\)) StrConcat } ifelse - } - {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) - 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if - AddOpPar 5 index StrConcat (\)*\() StrConcat - 8 index StrConcat (\)^\() StrConcat - 5 index StrConcat (-1\)+\() StrConcat - 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if - 8 index StrConcat (\)^\() StrConcat - 5 index StrConcat (\)*ln\() StrConcat - 8 index StrConcat AddClPar - } ifelse - } ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% str -> true/false -/IsStrNumber {% - true exch - { dup 48 lt exch dup 57 gt 3 -1 roll or - exch dup 46 ne%%. - exch dup 43 ne%%+ - exch 45 ne%%- - and and and { pop false } if } forall -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% literal switch -> func call, vector, variables -/EvalLiteral {% - ReadLiteral dup 40 eq%%% there is an open par -> function call - { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } - { dup 91 eq%%% there is an open bracket -> vector element - { ERROR_vector_not_yet_implemented } - { pop EvalVariable } - ifelse } - ifelse -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% first last parpos Expr[first:parpos-1] -> -/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (f(u))'=u'f'(u) -/EvalFunc { - 4 2 roll 4 index (1) ne - { AddOpPar 4 index StrConcat (\)*) StrConcat } if - (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Func derivative -> Eval<func> -/EvalFunc_sin {% - PreCommonFunc - { (cos\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_cos {% - PreCommonFunc - { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_tan {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if - PostCommonFunc } def -/EvalFunc_asin {% - PreCommonFunc - { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_acos {% - PreCommonFunc - { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_atg {% - PreCommonFunc - { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_ln {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_exp {% - PreCommonFunc - { (exp\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_sqrt {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_Fact {% - PreCommonFunc { ERROR_no_variable_expression_in_Fact } if - PostCommonFunc } def -/EvalFunc_sh {% - PreCommonFunc - { (ch\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_ch {% - PreCommonFunc - { (sh\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_th {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if - PostCommonFunc } def -/EvalFunc_Argsh {% - PreCommonFunc - { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_Argch {% - PreCommonFunc - { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_Argth {% - PreCommonFunc - { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -/PreCommonFunc { - 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop - 4 2 roll 4 index (0) eq - { (0) StrConcat false } - { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse -} def -/PostCommonFunc { - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -/EvalFunc_Derive {% - 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs - 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add - 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar - 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval - exch 6 2 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% literal switch -> func call, vector, variables -/EvalFunc_Sum {% - 1 add NextNonBlankChar pop - %% read the variable name - ReadLiteral pop 3 -1 roll pop NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if - %% read the initial value - 1 add NextNonBlankChar pop ReadNumber pop - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - %% read the increment value - 1 add NextNonBlankChar pop ReadNumber pop - 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if - %% read the limit value - 1 add NextNonBlankChar pop ReadNumber pop - 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if - 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop - 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat - 4 index StrConcat AddClPar - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% literal switch -> func call, vector, variables -/EvalFunc_IfTE {% - 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond - NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if - 1 add NextNonBlankChar pop dup 5 1 roll - AnalyzeExpr NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if - 1 add NextNonBlankChar pop - AnalyzeExpr 1 add NextNonBlankChar pop - 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat - 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% advance in str until a comma is found (no error detection!) -%% str index -> str index' -/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Convert to radians if trigo function call -%% (name) -> -/TrigoFunc { - dup (cos) eq 1 index (sin) eq or exch (tan) eq or - { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add - array astore def - } if -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% No derivative for condition.... -/EvalCondOp { 3 -1 roll pop } bind def -/PutIntervalOneAdd {putinterval 1 add} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add open parenthesis in string at the given index -%% str index -> str index+1 -/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add close parenthesis in string at the given index -%% str index -> str index+1 -/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add 0 in string at the given index -%% str index -> str index+1 -/AddZero {2 copy (0) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add open parenthesis in string at the given index -%% str index -> str index+1 -/AddMul {2 copy (*) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add open parenthesis in string at the given index -%% str index -> str index+1 -/AddDiv {2 copy (/) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add a plus sign in string at the given index -%% str index -> str index+1 -/AddAdd {2 copy (+) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add a minus sign in string at the given index -%% str index -> str index+1 -/AddSub {2 copy (-) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add a pipe sign in string at the given index -%% str index -> str index+1 -/AddPipe {2 copy (|) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% H O O K S -/AnalyzePreHook { dup 5 1 roll } bind def -/PreEvalHook {} def -/AnalyzePostHook { 7 -1 roll pop } bind def -/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def -/RollOp { 5 1 roll } bind def -end%%%tx@CoreAnalyzerDict -/tx@AddMathFunc 12 dict def tx@AddMathFunc begin -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% NEW FUNC -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) -%% x -> theta -/asin {% - dup abs 1 gt { EQDFasinrangeerror } if - dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad -} def -%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) -%% x -> theta -/acos {% - dup abs 1 gt { EQDFacosrangeerror } if - dup dup mul 1 exch sub sqrt exch atan DegtoRad -} def -%% function arctangent in radians -%% x -> theta -/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def -%% HYPERBOLIC FUNCTIONS -/sh { dup Ex exch neg Ex sub 2 div } def -/ch { dup Ex exch neg Ex add 2 div } def -/th { dup sh exch ch div } def -/Argsh { dup dup mul 1 add sqrt add ln } def -/Argch { dup dup mul 1 sub sqrt add ln } def -/Argth { dup 1 add exch 1 exch sub div ln 2 div } def -%% modified exponential funtion for 0 -%% x n -> x^n -/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def -%% modified exponential funtion for 0 -%% x -> e^x -/Ex { Euler exch exp } bind def -%% -%% factorial function -%% n -> n! -/Fact { 1 exch 2 exch 1 exch { mul } for } bind def -/fact { Fact } bind def -end - -% END pstricks.pro - -%%EndProcSet -%%BeginProcSet: pst-dots.pro 0 0 -% $Id: pst-dots.pro 26 2008-06-14 11:50:02Z herbert $ -% -%% PostScript prologue for pstricks.tex. -%% Version 2.02, 2008/04/18 -%% -%% For distribution, see pstricks.tex. -%% -%% Timothy Van Zandt <tvz@Princeton.EDU> -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -%% -%% Modified by Etienne Riga - Dec. 16, 1999 -%% Modified by Etienne Riga - 2005/01/01 (er) -%% to add /Diamond, /SolidDiamond and /BoldDiamond -%% Modified by Herbert Voss (hv) - 2008/04/17 -% -10 dict dup begin % hold local - /FontType 3 def - /FontMatrix [.001 0 0 .001 0 0] def - /FontBBox [-571.5 -742.5 571.5 742.5] def -% /FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph - /Encoding 256 array def - 0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef - Encoding % replace with given dot names - dup (b) 0 get /Bullet put % get the numerical position of b in ASCII -% % and save /Bullet at this place in Encoding - dup (c) 0 get /Circle put - dup (C) 0 get /BoldCircle put % 67 - dup (u) 0 get /SolidTriangle put - dup (t) 0 get /Triangle put - dup (T) 0 get /BoldTriangle put - dup (r) 0 get /SolidSquare put - dup (s) 0 get /Square put - dup (S) 0 get /BoldSquare put - dup (q) 0 get /SolidPentagon put - dup (p) 0 get /Pentagon put - dup (P) 0 get /BoldPentagon put -%%% - dup (k) 0 get /Asterisk put - dup (K) 0 get /BoldAsterisk put - dup (J) 0 get /SolidAsterisk put - dup (h) 0 get /Hexagon put - dup (H) 0 get /BoldHexagon put - dup (G) 0 get /SolidHexagon put - dup (f) 0 get /Octogon put % 2008-04-18 hv - dup (F) 0 get /BoldOctogon put % 2008-04-18 hv - dup (g) 0 get /SolidOctogon put % 2008-04-18 hv - dup (a) 0 get /Add put - dup (A) 0 get /BoldAdd put % 65 - dup (x) 0 get /Mul put - dup (X) 0 get /BoldMul put - dup (m) 0 get /Oplus put - dup (M) 0 get /BOplus put - dup (e) 0 get /SolidOplus put - dup (n) 0 get /Otimes put - dup (N) 0 get /BOtimes put - dup (E) 0 get /SolidOtimes put - dup (i) 0 get /Bar put - dup (I) 0 get /BoldBar put - dup (l) 0 get /SolidDiamond put - dup (d) 0 get /Diamond put - (D) 0 get /BoldDiamond put -%%% -/CharProcs 47 dict def -CharProcs begin - /CirclePath {0 0 500 0 360 arc closepath} def - /Bullet {CirclePath fill} def - /Circle {CirclePath .9 .9 scale CirclePath eofill} def - /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def - /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def - /SolidTriangle {TrianglePath fill} def - /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def - /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def - /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def - /SolidSquare {SquarePath fill} def - /Square {SquarePath .89 .89 scale SquarePath eofill} def - /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def - /PentagonPath { - -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto - 0 574.7 lineto -546.6 177.6 lineto closepath - } def - /SolidPentagon {PentagonPath fill} def - /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def - /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def -%-------------- hv begin 2004/07/25 from: er 2003/03/24 - /HexagonPath { - 0 550 moveto -476 275 lineto -476 -275 lineto - 0 -550 lineto 476 -275 lineto 476 275 lineto closepath - } def - /SolidHexagon {HexagonPath fill} def - /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def - /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def -% 2008-04-18 hv - /OctogonPath { - 550 dup 22.5 tan mul dup neg dup add /xMove exch def - exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def - /SolidOctogon { OctogonPath fill } def - /Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def - /BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def -% - /AsteriskPath { - 20 0 moveto 10 250 180 500 0 500 curveto - -180 500 -10 250 -20 0 curveto closepath - } def - /Asterisk { - AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath - 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill - } def -% - /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def - /BoldAsteriskPath { - 50 30 cos 100 mul moveto Basterp - 60 rotate Basterp 60 rotate Basterp - 60 rotate Basterp 60 rotate Basterp - 60 rotate Basterp closepath - } def - /BoldAsterisk {BoldAsteriskPath fill} def - /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def - /CrossPath { - 40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto - -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto - 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath - } def - /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto - -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto - 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath - } def - /Add {CrossPath fill} def - /Mul {45 rotate CrossPath fill} def - /BoldAdd {BoldCrossPath fill} def - /BoldMul {45 rotate BoldCrossPath fill} def - /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def - /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def - /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def - /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def - /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def - /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def - /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def - /Bar {BarPath fill} def - /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def - /BoldBar {BoldBarPath fill} def - /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath} def - /SolidDiamond {DiamondPath fill} def - /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def - /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def -%%% - /.notdef { } def -end -% -/BuildGlyph { - exch - begin -% Metrics 1 index get exec 0 - 0 0 -% BBoxes 3 index get exec - -1000 -1000 1000 1000 -% -571.5 -742.5 571.5 742.5 - setcachedevice - CharProcs begin load exec end - end -} def -% -/BuildChar { - 1 index /Encoding get exch get - 1 index /BuildGlyph get exec -} bind def - -end -/PSTricksDotFont exch definefont pop - -%% end - -%%EndProcSet -%%BeginProcSet: pst-node.pro 0 0 -% $Id: pst-node.pro 26 2008-06-14 11:50:02Z herbert $ -%% -%% PostScript prologue for pst-node.tex. -%% Version 1.00, 2008/01/01. -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -% -/tx@NodeDict 400 dict def tx@NodeDict begin -tx@Dict begin % from main pstricks dict - /T /translate load def -end -/NewNode { % on stack: { x y } boolean N@name type InitXnode - gsave - /next ED % { x y } boolean N@name type - dict dup % { x y } boolean N@name dict dict - 3 1 roll def % { x y } boolean dict N@name dict def - exch { dup 3 1 roll def } if % { x y } dict boolean - begin % { x y } dict begin - tx@Dict begin - STV CP T exec % set scaling - end - /NodeMtrx CM def % save CM - next % InitXNode - end - grestore -} def -% -/InitPnode { - /Y ED /X ED - /NodePos { NodeSep Cos mul NodeSep Sin mul } def -} def -% -/InitCnode { - /r ED /Y ED /X ED - /NodePos { NodeSep r add dup Cos mul exch Sin mul } def -} def -% -/GetRnodePos { - Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse - Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse - dx Sin mul abs dy - Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse -} def -% -/InitRnode { - /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED - /NodePos { GetRnodePos } def -} def -% -/DiaNodePos { - w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup - Cos mul exch Sin mul -} def -% -/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h -mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul -} ifelse } def -/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d -ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d -sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan -sin def /NodePos { TriNodePos } def } def -/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos -hh mul Atan dup cos ww mul exch sin hh mul } def -/GetCenter { begin X Y NodeMtrx transform CM itransform end } def -% -/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist - Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } - { 0 Dist Sin mul } ifelse } ifelse Do -} def -/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform - exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx - dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop - XYPos } ifelse -} def -/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 -roll sin mul sub exch } ifelse } def -/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA -AddOffset yA add /yA1 ED xA add /xA1 ED } def -/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB -AddOffset yB add /yB1 ED xB add /xB1 ED } def -/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA -AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED -ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED -} ifelse } def -/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB -AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED -ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED -} ifelse } def -/InitNC { - /b ED /a ED % second and first node - /NodeSepTypeB ED /NodeSepTypeA ED - /NodeSepB ED /NodeSepA ED - /OffsetB ED /OffsetA ED - tx@NodeDict a known tx@NodeDict b known and dup { - /NodeA a load def - /NodeB b load def - NodeA GetCenter /yA ED /xA ED - NodeB GetCenter /yB ED /xB ED } if -} def -% -/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub -mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def -/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt -{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop -} repeat LPutLine cleartomark } def -/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED -/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 -mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx -sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul -add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add -y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul -mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def -/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def -} def -/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def -/NAngle yyB yyA sub xxB xxA sub Atan def } def -/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def -/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def -} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit -} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd -} def -/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def -} def -/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def -/NAngle yyB yyA sub xxB xxA sub Atan def } def -/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def -/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def -} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { -exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark -VPosEnd } def -/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 -roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx -def grestore exec /LPutVar /SaveLPutVar load def } def -/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def -GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { -LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { -LPutVar VPutLine } def LPutVar } def -/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop -end } def -/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub -Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan -/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 -yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { -LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } -ifelse } def -/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 -roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA -GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict -begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] -cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines -} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def -% -/NCAngles { - GetEdgeA GetEdgeB GetArmA GetArmB - /mtrx AngleA matrix rotate def - xA2 yA2 mtrx transform pop - xB2 yB2 mtrx transform exch pop - mtrx itransform - /y0 ED /x0 ED - mark ArmB 0 ne { xB1 yB1 } if - xB2 yB2 x0 y0 xA2 yA2 - ArmA 0 ne { xA1 yA1 } if - tx@Dict begin false Line end - /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def - /LPutPos { LPutLines } def - /HPutPos { HPutLines } def - /VPutPos { VPutLines } def } def -% -/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 -yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform -/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 -tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] -cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { -VPutLines } def } def -/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def -xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx -transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } -{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB -0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict -begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx -def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { -VPutLines } def } def -/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if -xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end -/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { -LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } -def -/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED -GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin -false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { -LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } -def -/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate -def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 -mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 -mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 -xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false -Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] -cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { -VPutLines } def } def -% DG/SR modification begin - May 9, 1997 - Patch 1 -%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r -%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add -%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 -%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED -/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r -r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add -exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 -mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED -% DG/SR modification end -} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add -AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r -Div def /y ED /x ED } def -/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB -180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos -mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def -/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy -add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos -{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar -tx@Dict begin false Polygon end } def -/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan -def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 -mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def -/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div -def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def -GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul -sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 -eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } -{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def -0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 -roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 -0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 -roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } -ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos -{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { -r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } -{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add -add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub -mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t -sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse -y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { -LPutPos } def } def -/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB -sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 -ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB -w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos -{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } -{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } -def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin -/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def - -/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg -exch X sub neg exch moveto setmatrix CP grestore } def - -/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 -def } ifelse LPutCoor } def -/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } -if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } -ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } -def -/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if -r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } -ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } -def -end -% END pst-node.pro - -%%EndProcSet -%%BeginProcSet: pstricks-add.pro 0 0 -%% $Id: pstricks-add.pro 49 2008-10-13 10:59:27Z herbert $ -% PostScript prologue for pstricks-add.tex. -% Version 0.21, 2008/10/15 -% For distribution, see pstricks.tex. -% -% HISTORY -> see file Changes -% -/tx@addDict 410 dict def tx@addDict begin -%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -/GTriangle { - gsave - /mtrx CM def - /colorA ED /colorB ED /colorC ED % save the colors - /yA ED /xA ED % save the origin - xA yA translate - rotate % \psk@gangle - /yB ED /xB ED /yC ED /xC ED % save other coordinates - /ds [ % save data in a array - 0 0 0 colorA aload pop % fd x y xr xg xb - 0 xB xA sub yB yA sub colorB aload pop - 0 xC xA sub yC yA sub colorC aload pop -% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD - ] def - newpath - << - /ShadingType 4 % single Gouraud - /ColorSpace [ /DeviceRGB ] - /DataSource ds - >> - shfill - closepath - mtrx - setmatrix grestore} def -% -/RGBtoCMYK { % on stack r g b -> C M Y K - 3 dict begin - /Blue ED /Green ED /Red ED - 1 Red sub % Cyan - 1 Green sub % Magenta - 1 Blue sub % Yellow - 0 % Black - end -} def -% -/CMYKtoGRAY { % on stack c m y k -> gray - exch 0.11 mul add - exch 0.59 mul add - exch 0.3 mul add - dup 1 gt { pop 1 } if - neg 1 add -} def -% -/RGBtoGRAY { % on stack r g b -> gray - 0.11 mul - exch 0.59 mul add - exch 0.3 mul add -} def -% -/HSBtoGRAY { - 6 dict begin - /b exch def - /s exch def 6 mul dup cvi dup - /i exch def sub - /f exch def - /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def - F i get { s mul neg 1 add b mul} forall - 0.11 mul - exch 0.59 mul add - exch 0.3 mul add - end -} def -% -%% convertisseur longueur d'onde ->R,G,B Manuel Luque -%% lambda max=780 nanometres -%% lambda min=380 nanometres -%% adaptation de : -%% http://www.physics.sfasu.edu/astro/color.html -%% www.efg2.com/lab -% -/Gamma 0.8 def -/calculateRGB { - lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if - lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if - lambda 380 ge {lambda 439 le { - /R {lambda 440 sub neg 440 380 sub div} def - /Red R factor mul Gamma exp def - /G 0 def - /Green G factor mul Gamma exp def - /B 1 def - /Blue B factor mul Gamma exp def} if - } if - lambda 440 ge { lambda 489 le { - /G {lambda 440 sub 490 440 sub div} def - /Green G factor mul Gamma exp def - /R 0 def /Red 0 def - /B 1 def - /Blue B factor mul Gamma exp def } if - } if - lambda 490 ge {lambda 509 le { - /B {lambda 510 sub neg 510 490 sub div} def - /Blue B factor mul Gamma exp def - /R 0 def /Red 0 def - /G 1 def - /Green G factor mul Gamma exp def } if - } if - lambda 510 ge {lambda 579 le { - /R {lambda 510 sub 580 510 sub div } def - /Red R factor mul Gamma exp def - /Blue 0 def - /G 1 def - /Green G factor mul Gamma exp def } if - } if - lambda 580 ge {lambda 644 le { - /G {lambda 645 sub neg 645 580 sub div } def - /Green G factor mul Gamma exp def - /Blue 0 def - /R 1 def - /Red R factor mul Gamma exp def } if - } if - lambda 645 ge { lambda 780 le { - /Red 1 factor mul Gamma exp def - /Blue 0 def - /Green 0 def } if - } if -} def -% -/factor { - lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if - lambda 420 ge {lambda 700 le { 1 } if } if - lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if -} def -% -/wavelengthToRGB { % the wavelength in nm must be on top of the stack - 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N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 -0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ -landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize -mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ -matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round -exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ -statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] -N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin -/FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array -/BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 -array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N -df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A -definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get -}B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} 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pstricks.tex. -%% Version 1.05, 2008/06/25 -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -% -% -% Define the follwing gs-functions if not known, eg when using distiller -% -systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if -systemdict /.setblendmode known not {/.setblendmode { pop } def } if -systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if -% -/tx@Dict 200 dict def % the main PSTricks dictionary -tx@Dict begin -/ADict 25 dict def % The arrow dictionaray -/CM { matrix currentmatrix } bind def -/SLW /setlinewidth load def -/CLW /currentlinewidth load def -/CP /currentpoint load def -/ED { exch def } bind def -/L /lineto load def -/T /translate load def -/TMatrix { } def -/RAngle { 0 } def -/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments -/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known -/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) -/Div { dup 0 eq { pop } { div } ifelse } def % control the division -/tan { dup cos abs 1.e-10 lt - { pop 1.e10 } % return 1.e10 as infinit - { dup sin exch cos div } ifelse % default sin/cos -} def -/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees -/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root - pop pop 0 }{ sqrt exch atan} ifelse } def -/NET { neg exch neg exch T } def % change coordinate system to the negative one -/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter -/Pyth2 { % Pythagoras, xA yA xB yB - 3 -1 roll % xA xB yB yA - sub % xA xB yB-yA - 3 1 roll % yB-yA xA xB - sub % yB-yA xA-xB - Pyth } def -/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian -/Rand { rand 4294967295 div } def % a real random number -%----------------- hv added 20050516 --------------- -/PiDiv2 1.57079632680 def -/Pi 3.14159265359 def -/TwoPi 6.28318530718 def -/Euler 2.71828182846 def -%/e Euler bind def -/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees -/DegtoRad { Pi mul 180 div } bind def % viceversa -%----------------- hv end--------------------------- -/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def -/PathLength { - flattenpath /z 0 def - { /y1 ED /x1 ED /y2 y1 def /x2 x1 def } - { /y ED /x ED PathLength@ } - {} - { /y y2 def /x x2 def PathLength@ } - /pathforall load stopped { pop pop pop pop } if - z -} def -% -/STP { .996264 dup scale } def % BP/PT scaling -/STV { SDict begin normalscale end STP } def % -% -%%-------------- DG begin patch 15 ---------------%% -%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def -%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y -%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul -%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] -%0 } ifelse setdash stroke } def -/DashLine { - dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse - /b ED /x1 ED /y1 ED /x ED /y ED - /z y x add y1 add x1 add def - /Coef b a .5 sub 2 mul y mul sub z Div round - z mul a .5 sub 2 mul y mul add b exch Div def - /y y Coef mul def - /x x Coef mul def - /y1 y1 Coef mul def - /x1 x1 Coef mul def - x1 0 gt y1 0 gt or x 0 gt or y 0 gt and - { [ y x y1 x1 ] 1 a sub y mul } - { [ 1 0 ] 0 } ifelse - setdash stroke -} def -%%-------------- DG end patch 15 ---------------%% -/DotLine { - /b PathLength def - /a ED /z ED /y CLW def - /z y z add def - a 0 gt { - /b b a div def - }{ - a 0 eq { - /b b y sub def - }{ a -3 eq { - /b b y add def } if - } ifelse - } ifelse - [ 0 b b z Div round Div dup 0 le { pop 1 } if ] - a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse - setdash 1 setlinecap stroke -} def -% -/LineFill { % hv ------------ patch 7 ------------- - gsave - abs /hatchWidthInc ED - abs /hatchSepInc ED - abs CLW add /a ED - a 0 dtransform round exch round exch - 2 copy idtransform - exch Atan rotate - idtransform pop /a ED - .25 .25 itransform pathbbox - /y2 ED - a Div ceiling cvi /x2 ED /y1 ED - a Div cvi /x1 ED /y2 y2 y1 sub def - clip - newpath - 2 setlinecap - systemdict - /setstrokeadjust known { true setstrokeadjust } if - x2 x1 sub 1 add { - x1 a mul y1 moveto 0 y2 rlineto stroke - /x1 x1 1 add - hatchWidthInc 0 gt { CLW add } if - def - hatchSepInc 0 gt hatchWidthInc 0 gt or { - /a a hatchSepInc add def - CLW hatchWidthInc add SLW - } if - } repeat - grestore - pop pop } def -% -/PenroseFill {% on stack: scaling factor - dup dup scale - 1 exch div round /penroseFactor ED - a 0 dtransform round exch round exch - 2 copy idtransform - exch Atan rotate - idtransform pop /a ED - .25 .25 itransform pathbbox - /y2 ED - a Div ceiling cvi /x2 ED /y1 ED - a Div cvi /x1 ED /y2 y2 y1 sub def - clip - newpath - systemdict - /setstrokeadjust known { true setstrokeadjust } if - /I/S/L/W/G/+/Z/F/E/D[/def/exch/for{E D}/add{s E get mul} - { Z -36.2001 1 33 }{25 E S rlineto}{/q Z dup q G E q 1 + G}{Z 2 2}]{cvx def}forall - [0 72 1008 {dup sin E cos }F ]1 setlinejoin/s W{/a W{/b I 10{/i I 4{/m I moveto - i m +/j I 10{/l Z b m l + G a l G sub s m get div .2 + floor .3 + 25 - mul j l + S rmoveto}F i L j L stroke }F}F}F}F - grestore - pop pop -} def -% -%gsave abs CLW add /a ED a 0 dtransform round exch round exch -%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 -%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 -%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a -%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a -%% DG/SR modification end -%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict -%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 -%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) -%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } -%% def -%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore -%pop pop } def -%% DG/SR modification end -% -/BeginArrow { - ADict begin % hold it local, for end see EndArrow - /@mtrx CM def - gsave - 2 copy T - 2 index sub neg exch - 3 index sub exch Atan - rotate newpath -} def -% -/EndArrow { @mtrx setmatrix CP grestore end } def % end the ADict -% -/Arrow { - CLW mul add dup - 2 div /w ED - mul dup /h ED - mul /a ED - { 0 h T 1 -1 scale } if - w neg h moveto - 0 0 L w h L w neg a neg rlineto - gsave fill grestore -} def -% -/ArrowD { % the sides are drawn as curves (hv 20071211) - CLW mul add dup - 2 div /w ED - mul dup /h ED - mul /Inset ED - { 0 h T 1 -1 scale } if % changes the direction -% we use y=w/h^2 * x^2 as equation for the control points -% for the coordinates the arrow is seen from top to bottom -% the bottom (tip) is (0;0) - w neg h moveto % lower left of > - w 9 div 4 mul neg h 3 div 2 mul - w 9 div neg h 3 div - 0 0 curveto % tip of > - w 9 div h 3 div - w 9 div 4 mul h 3 div 2 mul - w h curveto % upper left of > - w neg Inset neg rlineto % move to x=0 and inset - gsave fill grestore -} def -% -/Tbar { - CLW mul add /z ED - z -2 div CLW 2 div moveto - z 0 rlineto stroke - 0 CLW moveto -} def -% -/Bracket { - CLW mul add dup CLW sub 2 div - /x ED mul CLW add /y ED /z CLW 2 div def - x neg y moveto - x neg CLW 2 div L x CLW 2 div L x y L stroke - 0 CLW moveto -} def -% -/RoundBracket { - CLW mul add dup 2 div - /x ED mul /y ED /mtrx CM def - 0 CLW 2 div T x y mul 0 ne { x y scale } if - 1 1 moveto - .85 .5 .35 0 0 0 curveto - -.35 0 -.85 .5 -1 1 curveto - mtrx setmatrix stroke 0 CLW moveto -} def -% -/SD { 0 360 arc fill } def -% -/EndDot { % DS is the dot size - { /z DS def } { /z 0 def } ifelse - /b ED 0 z DS SD b { 0 z DS CLW sub SD } if - 0 DS z add CLW 4 div sub moveto } def -% -/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { - /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto - load } if ] cvx newpath 3 1 roll T exec } def -% -%/NArray { -% aload length 2 div dup dup cvi eq not { exch pop } if /n exch -% cvi def -%} def -% -/NArray { % holds the coordinates and on top of stack the showpoints boolean - /showpoints ED - counttomark 2 div dup cvi /n ED - n eq not { exch pop } if - showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse -} def -% -/Line { - NArray n 0 eq not - { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def - n { Lineto } repeat - CP 4 2 roll ArrowB L pop pop - } if -} def -% -/Arcto { - /a [ 6 -2 roll ] cvx def - a r - /arcto load stopped { 5 } { 4 } ifelse { pop } repeat - a -} def -% -/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq - and { pop pop /n n 1 sub def } if } def -/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } - repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 - ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 - moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto - Lineto pop pop closepath } ifelse } def -/Diamond { - /mtrx CM def - T rotate - /h ED - /w ED - dup 0 eq { pop } { CLW mul neg - /d ED - /a w h Atan def - /h d a sin Div h add def - /w d a cos Div w add def } ifelse - mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div - /ArrowA { moveto } def - /ArrowB { } def - false Line - closepath mtrx setmatrix } def -% DG modification begin - Jan. 15, 1997 -%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { -%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 -%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 -%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx -%setmatrix } def -/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup -CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 -div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 -d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx -% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) -% setmatrix } def -setmatrix pop } def -% DG/SR modification end -% -/CCA { - /y ED /x ED - 2 copy y sub /dy1 ED - x sub /dx1 ED - /l1 dx1 dy1 Pyth def -} def -% -/CC { - /l0 l1 def - /x1 x dx sub def - /y1 y dy sub def - /dx0 dx1 def - /dy0 dy1 def - CCA - /dx dx0 l1 c exp mul dx1 l0 c exp mul add def - /dy dy0 l1 c exp mul dy1 l0 c exp mul add def - /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def - /x2 x l0 dx mul m mul sub def - /y2 y l0 dy mul m mul sub def - /dx l1 dx mul m mul neg def - /dy l1 dy mul m mul neg def -} def -% -/IC { - /c c 1 add def - c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse - /a a 2 mul 3 div 45 cos b exp div def - CCA - /dx 0 def - /dy 0 def -} def -% -/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def -/NC { CC x1 y1 x2 y2 x y curveto } def -/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def -/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def -/NAC { x2 y2 x y curveto CC x1 y1 } def -/EAC { x2 y2 x y ArrowB curveto pop pop } def -% -/OpenCurve { - NArray n 3 lt - { n { pop pop } repeat } - { BOC /n n 3 sub def n { NC } repeat EOC } ifelse -} def -% -/AltCurve { - { false NArray n 2 mul 2 roll - [ n 2 mul 3 sub 1 roll ] aload - /Points ED - n 2 mul -2 roll } - { false NArray } ifelse - n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse -} def -% -/ClosedCurve { - NArray n 3 lt - { n { pop pop } repeat } - { n 3 gt { CheckClosed } if - 6 copy n 2 mul 6 add 6 roll - IC CC x y moveto n { NC } repeat - closepath pop pop - } ifelse -} def -% -/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def -/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def -/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } -def -/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix -rotate matrix concatmatrix exch findfont exch makefont setfont } def -/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto -x1 y1 lineto closepath } def -/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 -y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div -exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse -/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto -x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } -ifelse } def -/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add -/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { -pop pop Rect } { OvalFrame } ifelse } def -% -/BezierNArray { - /f ED - counttomark 2 div dup cvi /n ED - n eq not { exch pop } if - n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat - f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse -} def -% -/OpenBezier { - BezierNArray - n 1 eq - { pop pop } - { ArrowA n 4 sub 3 idiv - { 6 2 roll 4 2 roll curveto } repeat - 6 2 roll 4 2 roll ArrowB curveto } ifelse -} def -% -/ClosedBezier { - BezierNArray - n 1 eq - { pop pop } - { moveto n 1 sub 3 idiv - { 6 2 roll 4 2 roll curveto } repeat - closepath } ifelse -} def -% -/BezierShowPoints { - gsave - Points aload length 2 div cvi /n ED - moveto - n 1 sub { lineto } repeat - CLW 2 div SLW [ 4 4 ] 0 setdash stroke - grestore -} def -% -/Parab { - /y0 ED /x0 ED /y1 ED /x1 ED - /dx x0 x1 sub 3 div def - /dy y0 y1 sub 3 div def - x0 dx sub y0 dy add x1 y1 ArrowA - x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB - curveto - /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def -} def -% -/Grid { - newpath - /a 4 string def - /b ED /c ED /n ED - cvi dup 1 lt { pop 1 } if - /s ED - s div dup 0 eq { pop 1 } if - /dy ED s div dup 0 eq { pop 1 } if - /dx ED dy div round dy mul - /y0 ED dx div round dx mul - /x0 ED dy div round cvi - /y2 ED dx div round cvi - /x2 ED dy div round cvi - /y1 ED dx div round cvi - /x1 ED - /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def - /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def - b 0 gt { - /z1 b 4 div CLW 2 div add def -% /Helvetica findfont b scalefont setfont - /b b .95 mul CLW 2 div add def } if - systemdict /setstrokeadjust known - { true setstrokeadjust /t { } def } - { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add - exch itransform } bind def } ifelse - gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse - /i x1 def - /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def - /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def - x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if - { i dx mul dup y0 moveto - b 0 gt - { gsave c i a cvs dup stringwidth pop - /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse - h 0 gt {b neg}{z1} ifelse - rmoveto show grestore } if - dup t f moveto - g t L stroke - /i i w add def - } repeat - grestore - gsave - n 0 gt - % DG/SR modification begin - Nov. 7, 1997 - Patch 1 - %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } - { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } - % DG/SR modification end - { 2 setlinecap } ifelse - /i y1 def - /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def - /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def - y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if - { newpath i dy mul dup x0 exch moveto - b 0 gt { gsave c i a cvs dup stringwidth pop - /z2 ED - w 0 gt {z1 z2 add neg} {z1} ifelse - h 0 gt {z1} {b neg} ifelse - rmoveto show grestore } if - dup f exch t moveto - g exch t L stroke - /i i h add def - } repeat - grestore -} def -% -/ArcArrow { - /d ED /b ED /a ED - gsave - newpath 0 -1000 moveto clip - newpath - 0 1 0 0 b - grestore - c mul - /e ED - pop pop pop r a e d PtoC y add exch x add - exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c - mul neg d -} def -% -/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def -% -/ArcAdjust { %%%% Vincent Guirardel -% given a target length (targetLength) and an initial angle (angle0) [in the stack], -% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). -% This computes an angle t such that (x0,y0) is at distance -% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). -% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 -% contrary to TvZ's code. -% To achieve, this, one iterates the following process: start with some angle t, -% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. -% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. -% -% Another difference with TvZ's code is that we need d (=add/sub) to be defined. -% the value of d = add/sub is used to know on which side we have to move. -% It is only used in the initialisation of the angle before the iteration. -% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% Input stack: 1: target length 2: initial angle -% variables used : rx, ry, d (=add/sub) -% - /targetLength ED /angle0 ED - /x0 rx angle0 cos mul def - /y0 ry angle0 sin mul def -% we are looking for an angle t such that (x0,y0) is at distance targetLength -% from the point M(t)=(rx*cos(t),ry*sin(t))) -%initialisation of angle (using 1st order approx = TvZ's code) - targetLength 57.2958 mul - angle0 sin rx mul dup mul - angle0 cos ry mul dup mul - add sqrt div -% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees -% (if the ellipse is very curved at the point where we draw the arrow, % -% the value can be much more than 360 degrees !) -% this should avoid going on the wrong side (more than 180 degrees) or go near -% a bad attractive point (at 180 degrees) - dup 90 ge { pop 90 } if - angle0 exch d % add or sub -% maximum number of times to iterate the iterative procedure: -% iterative procedure: takes an angle t on top of stack, computes a -% better angle (and put it on top of stack) - 30 { dup -% compute distance D between (x0,y0) and M(t) - dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt -% if D almost equals targetLength, we stop - dup targetLength sub abs 1e-5 le { pop exit } if -% stack now contains D t -% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: -% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) - exch dup cos rx mul x0 sub exch sin ry mul y0 sub -% stack contains: y(t)-y0, x(t)-x0, d - 2 index Div targetLength mul y0 add ry Div exch - 2 index Div targetLength mul x0 add rx Div -% stack contains x(t')/rx , y(t')/ry , d -% now compute t', and remove D from stack - atan exch pop - } repeat -% we don't look at what happened... in particular, if targetLength is greater -% than the diameter of the ellipse... -% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... -% after iteration, stack contains an angle t such that M(t) is the tail of the arrow -% to give back the result as a an angle relative to angle0 we could add the following line: -% angle0 sub 0 exch d -% -% begin bug fix 2006-01-11 -% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 -%(we don't want to make the ellipse turn more or less than it should)... -dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse -% end bug fix -} def -% -/EllipticArcArrow { - /d ED % is add or sub - /b ED % arrow procedure - /a1 ED % angle - gsave - newpath - 0 -1000 moveto - clip % Set clippath far from arrow. - newpath - 0 1 0 0 b % Draw arrow to determine length. - grestore -% Length of arrow is on top of stack. Next 3 numbers are junk. -% - a1 exch ArcAdjust % Angular position of base of arrow. - /a2 ED - pop pop pop - a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig - a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig - a1 cos rx mul xOrig add % - a1 sin ry mul yOrig add % -% Now arrow tip coor and base coor are on stack. - b pop pop pop pop % Draw arrow, and discard coordinates. - a2 CLW 8 div -% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) - 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse - ArcAdjust -% resets original value of d - 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. -} def -%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% -% -/Rot { CP CP translate 3 -1 roll neg rotate NET } def -% -/RotBegin { - tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if - /TMatrix [ TMatrix CM ] cvx def - /a ED - a Rot /RAngle [ RAngle dup a add ] cvx def -} def -% -/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def -% -/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def -/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def -/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def -/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s -abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b -div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { -h1 abs h sub dup s mul abs } ifelse } def -/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s -mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q -{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add -exch } def -/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible -/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def -} if } ifelse } def -/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def -/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit -neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def -/IfVisible true def } def -end -%-----------------------------------------------------------------------------% - -% END pstricks.pro - -%%EndProcSet -%%BeginProcSet: pst-algparser.pro 0 0 -% $Id: pst-algparser.pro 26 2008-06-14 11:50:02Z herbert $ -%% -%% PostScript prologue for PSTricks algorithm parser -%% Version 0.01, 2008/01/01 -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -%% -%%-----------------------------------------------------------------------------% -% -/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez -% -/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin -% -% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 -% E->T|E+T -% T->FS|T*FS -% FS -> F | +FS | -FS -% F->P|F^SF -% P->(E)|literal -% literal->number|var|var[E]|func(params) -% params->E|E,param -% number->TOBEFINISHED -% -%% E expression, T term, SF signed factor, F factor, P power -% -%% parser -% -%% str -% -%% C->E<condition_operators>E -%% STR index -> STR index+lenExpr -/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def -% -%% analyze Expression List (separator , or | ) -%% STR index -> STR index+lenExpr -%% /AnalyzeListOfE { -%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar -%% NextNonBlankChar dup 0 eq { pop exit } if -%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if -%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop -%% AnalyzeListOfEPostHook -%% } def -/AnalyzeListOfE { - /NotFirst false def - { NextNonBlankChar pop AnalyzeExpr - NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse - dup Strlen eq { exit } if NextNonBlankChar - dup 44 ne 1 index 124 ne and - { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } - if pop 1 add } loop - AnalyzeListOfEPostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% E->T|E+T -%% STR index -> STR index+lenExpr -/AnalyzeExpr { - AnalyzePreHook AnalyzeTerm IsEndingExpr - { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } - { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } - ifelse - AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% T->FS|T*FS -%% STR index -/AnalyzeTerm { - AnalyzePreHook AnalyzeSignedFactor IsEndingTerm - { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } - { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } - ifelse - AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% FS -> F | +FS | -FS -%% STR index -/AnalyzeSignedFactor { - AnalyzePreHook 2 copy get dup IsUnaryOp - { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } - { pop AnalyzeFactor } - ifelse AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% F->P|F^P -%% STR index -/AnalyzeFactor { - AnalyzePreHook AnalyzePower IsEndingFactor - { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } - { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } - ifelse AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% P->(E)|literal -%% STR index -/AnalyzePower { - %% depending of first char either a number, or a literal - 2 copy get dup 40 eq%%an open par - { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } - { AnalyzeLiteral } - ifelse -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index STR[index] -> STR index -%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def -/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% recognize + or - -%% chr -> T/F -/IsUnaryOp { dup 43 eq exch 45 eq or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a number can contain only : 0123456789. -%% chr -> T/F -/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index -> STR index number -%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? -%% STR index -> STR index' number -/ReadNumber { - exch dup 3 -1 roll dup 3 1 roll - %%read mantissa - { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop - dup 101 eq exch 69 eq or - %%% there is a "e" or "E" -> read exponant - { 1 add 2 copy get dup IsUnaryOp - { pop 1 add 2 copy get } if - { IsNumber not { exit } if 1 add 2 copy get } loop } - if - dup 4 1 roll - 3 -1 roll exch 1 index sub getinterval -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a number can contain only : 0123456789. -%% chr -> T/F -/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index -> STR index number -%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? -%% STR index -> STR index' number -/ReadCondOp { - NextNonBlankChar 1 index 4 1 roll - { IsCondOp not { exit } if 1 add 2 copy get } loop - 2 copy 5 -1 roll - exch 1 index sub getinterval 3 1 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a literal can contain only : 0123456789. -%% chr -> T/F -/IsLiteral {% - dup 48 ge exch dup 57 le 3 -1 roll and exch - dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch - dup 97 ge exch 122 le and or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? -%% STR index -> literal STR index' nextchr -/ReadLiteral { - exch dup 3 -1 roll dup 3 1 roll - %%read literal core - { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop - 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or a clpar -%% STR index -> STR index STR[index] T/F -/IsEndingExpr {% - 2 copy dup Strlen eq - %% if end of str is reached -> end ! - { pop pop 0 true } - %% ending chr -> clpar, comma, |, <, >, =, !, - {get dup dup 41 eq - exch dup 124 eq - exch dup 93 eq - exch dup 44 eq - exch dup 30 eq - exch dup 60 ge exch 62 le and or or or or or} - ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or a +- -%% STR index -> STR index STR[index] T/F -/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or */ -%% STR index -> STR index STR[index] T/F -/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or ^ -%% STR index -> STR index STR[index] T/F -/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index -> STR index STR[index] -/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def -/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def -%%%%%%%%%%%%%%%%%%%%%%%% -%% DEBUG -/BRK {false} def -/BRKtrue {/BRK true def} def -/BRKStop {BRK {BRKtoto} if } def -/BRKEvalStop {BRK exch if } def -/BRKBRK2true {BRK {BRK2true} if } def -/BRK2 {false} def -/BRK2true {/BRK2 true def} def -/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def -end -% -%-------------------------------------------------------------------------------% -% -/tx@AlgToPs 12 dict def tx@AlgToPs begin -% -%% algExpr -> PSVector -/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def -/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def -/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def -/Strlen 0 def -/EvalListOfExpr {} def% -/EvalNumber {% - ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx - exch 1 add array astore def NextNonBlankChar pop } def -/EvalAddSub {% - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll - 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def -} def -/EvalMulDiv {% - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll - 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def -} def -/EvalPower {% - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll - pop /exp cvx exch 1 add array astore def -} def -/EvalLiteral {% - ReadLiteral - dup 40 eq%%% there is an open par -> function call - { pop 2 index - dup (Sum) eq { EvalSum } - { dup (IfTE) eq { EvalCond } - { dup (Derive) eq { pop EvalDerive } - { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx - exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } - { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def - dup 91 eq%%% there is an open bracket -> vector element - { pop 1 add NextNonBlankChar pop AnalyzeExpr - /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } - { pop NextNonBlankChar pop } - ifelse} - ifelse -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% the derive function : Derive(n,f(x)) -%% firstparindex lastparindex -> -/EvalDerive { - %% manage the function descripiton - 1 add ReadNumber 3 1 roll NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - 1 add NextNonBlankChar pop - 3 -1 roll cvi - dup 0 eq - { pop AnalyzeExpr 3 -1 roll pop 1 add } - { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll - { (x) tx@Derive begin Derive end } repeat - ExpressionVector exch /ExpressionVector [] def - AlgToPs aload length - /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def - l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add - 1 index length /Strlen exch def } ifelse -} def -/EvalSum {% - pop 1 add NextNonBlankChar pop - %% read the variable name - ReadLiteral pop NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if - %% read the initial value - 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - %% read the increment value - 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - %% read the limit value - 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll - 5 -1 roll 4 add array astore def - %% keep ExpressionVector for later and create a new one for internal Sum computation - ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def - 1 add NextNonBlankChar pop AnalyzeExpr - %% add each term - /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def - /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add - array astore def 3 -1 roll pop 1 add -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Convert to radians if trigo function call -%% (name) -> -/TrigoFunc { - dup (cos) eq 1 index (sin) eq or exch (tan) eq or - { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add - array astore def - } if -} def -/EvalCond {% - pop 1 add AnalyzeCond NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if - ExpressionVector 3 1 roll /ExpressionVector [] def - 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def - NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if - 1 add AnalyzeExpr - NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if - ExpressionVector - /ExpressionVector 6 -1 roll aload length dup - 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def - 1 add 3 -1 roll pop -} def -%% CondOp STR index -/EvalCondOp {% - 3 -1 roll - dup (=) eq { /eq } {% - dup (<) eq { /lt } {% - dup (>) eq { /gt } {% - dup (>=) eq { /ge } {% - dup (<=) eq { /ge } {% - dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } - ifelse } ifelse } ifelse } ifelse } ifelse } ifelse - cvx exch pop - /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def -/EvalUnaryOp { - 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% H O O K S -/AnalyzePreHook {} bind def -/PreEvalHook {} bind def -/AnalyzeListOfEPostHook {} bind def -/AnalyzePostHook {} def -/RollOp { 3 1 roll } bind def -end %tx@CoreAnalyzerDict -% -%--------------------------------------------------------------------% -% -/tx@Derive 41 dict def tx@Derive begin -%%increase ^^ for each function added -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% algExpr variable -> PSVector -/Derive {% - 10240 string 3 1 roll 0 3 1 roll - /Variable exch def - tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end -} def -/Strlen 0 def -/InitParser { dup length /Strlen exch def 0 } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% algExpr variable index -> PSVector -/DeriveIndexed {% - 3 1 roll 10240 string 3 1 roll 0 3 1 roll - /Variable exch def - tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u,v)'=-(u',v') -/EvalListOfExpr {% - 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe - 2 copy 7 -1 roll dup length 4 1 roll putinterval add - 6 -2 roll pop pop - 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (-u)'=-(u') -/EvalUnaryOp { - 4 -2 roll 4 index (0) eq - { (0) StrConcat 7 -1 roll pop } - { 7 -1 roll 45 eq - { AddSub AddOpPar true } { false } ifelse - 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (number)'=0 -/EvalNumber { ReadNumber (0) 6 2 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u+v)'=u'+v' -/EvalAddSub {% - 7 index dup (0) eq - { pop true }%% du=0 nothing added - { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } - ifelse - 5 index dup (0) eq - { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 - { exch - { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added - { 5 -2 roll 7 index 43 eq%%something yet added - { AddAdd false } { AddSub AddOpPar true } ifelse } - ifelse 11 1 roll - 3 -1 roll StrConcat 10 -1 roll { AddClPar } if - 2 copy pop 0 6 2 roll GetIntervalNewStr } - ifelse - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u*v)' or (u/v)' -/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u*v)'=u'*v+u*v' -/EvalMul {% - 4 -2 roll 7 index dup (0) eq - { pop false }%%du=0 - { (1) eq%%du=1 - { false } - { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse - 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if - true }%%du!=0 - ifelse - 5 1 roll 5 index (0) eq - { 5 -1 roll not { (0) StrConcat } if }%%dv=0 - { 5 -1 roll { AddAdd } if - 4 index (1) eq - { 8 index StrConcat } - { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } - ifelse - }%%dv!=0 - ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u/v)'=(u'*v-u*v')/v^2 -/EvalDiv {% - 4 -2 roll - 4 index (0) eq%%dv=0 -> u'/v - { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } - { 7 index dup (0) eq - { pop }%%du=0 - { (1) eq%%du=1 - { false } - { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse - 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 - ifelse - AddSub - 4 index (1) eq - { 8 index StrConcat } - { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } - ifelse - %}%%dv!=0 - 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar - AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } - ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% str1 index str2 -> str1 index -/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def -/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) -/EvalPower {% - 4 -2 roll 7 index (0) eq - {%%if du=0 then (u^v)'=v'ln(u)u^v - 4 index (0) eq - { (0) StrConcat }%%if dv=0 then (u^v)'=0 - { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if - 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if - AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse - } - {%%du!=0 - 4 index (0) eq - {%%if dv=0 then (u^v)'=vu'u^(v-1) - 5 index dup IsStrNumber - { dup (0) eq - { StrConcat } - { dup dup (1) eq exch (1.0) eq or - { StrConcat } - { StrConcat - 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 - { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 - (*\() StrConcat 8 index StrConcat (\)) StrConcat - 5 index dup dup (2) eq exch (2.0) eq or - { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } - { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat - 5 index StrConcat (-1\)) StrConcat } ifelse - } - {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) - 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if - AddOpPar 5 index StrConcat (\)*\() StrConcat - 8 index StrConcat (\)^\() StrConcat - 5 index StrConcat (-1\)+\() StrConcat - 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if - 8 index StrConcat (\)^\() StrConcat - 5 index StrConcat (\)*ln\() StrConcat - 8 index StrConcat AddClPar - } ifelse - } ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% str -> true/false -/IsStrNumber {% - true exch - { dup 48 lt exch dup 57 gt 3 -1 roll or - exch dup 46 ne%%. - exch dup 43 ne%%+ - exch 45 ne%%- - and and and { pop false } if } forall -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% literal switch -> func call, vector, variables -/EvalLiteral {% - ReadLiteral dup 40 eq%%% there is an open par -> function call - { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } - { dup 91 eq%%% there is an open bracket -> vector element - { ERROR_vector_not_yet_implemented } - { pop EvalVariable } - ifelse } - ifelse -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% first last parpos Expr[first:parpos-1] -> -/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (f(u))'=u'f'(u) -/EvalFunc { - 4 2 roll 4 index (1) ne - { AddOpPar 4 index StrConcat (\)*) StrConcat } if - (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Func derivative -> Eval<func> -/EvalFunc_sin {% - PreCommonFunc - { (cos\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_cos {% - PreCommonFunc - { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_tan {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if - PostCommonFunc } def -/EvalFunc_asin {% - PreCommonFunc - { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_acos {% - PreCommonFunc - { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_atg {% - PreCommonFunc - { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_ln {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_exp {% - PreCommonFunc - { (exp\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_sqrt {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_Fact {% - PreCommonFunc { ERROR_no_variable_expression_in_Fact } if - PostCommonFunc } def -/EvalFunc_sh {% - PreCommonFunc - { (ch\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_ch {% - PreCommonFunc - { (sh\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_th {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if - PostCommonFunc } def -/EvalFunc_Argsh {% - PreCommonFunc - { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_Argch {% - PreCommonFunc - { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_Argth {% - PreCommonFunc - { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -/PreCommonFunc { - 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop - 4 2 roll 4 index (0) eq - { (0) StrConcat false } - { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse -} def -/PostCommonFunc { - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -/EvalFunc_Derive {% - 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs - 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add - 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar - 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval - exch 6 2 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% literal switch -> func call, vector, variables -/EvalFunc_Sum {% - 1 add NextNonBlankChar pop - %% read the variable name - ReadLiteral pop 3 -1 roll pop NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if - %% read the initial value - 1 add NextNonBlankChar pop ReadNumber pop - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - %% read the increment value - 1 add NextNonBlankChar pop ReadNumber pop - 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if - %% read the limit value - 1 add NextNonBlankChar pop ReadNumber pop - 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if - 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop - 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat - 4 index StrConcat AddClPar - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% literal switch -> func call, vector, variables -/EvalFunc_IfTE {% - 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond - NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if - 1 add NextNonBlankChar pop dup 5 1 roll - AnalyzeExpr NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if - 1 add NextNonBlankChar pop - AnalyzeExpr 1 add NextNonBlankChar pop - 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat - 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% advance in str until a comma is found (no error detection!) -%% str index -> str index' -/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Convert to radians if trigo function call -%% (name) -> -/TrigoFunc { - dup (cos) eq 1 index (sin) eq or exch (tan) eq or - { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add - array astore def - } if -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% No derivative for condition.... -/EvalCondOp { 3 -1 roll pop } bind def -/PutIntervalOneAdd {putinterval 1 add} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add open parenthesis in string at the given index -%% str index -> str index+1 -/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add close parenthesis in string at the given index -%% str index -> str index+1 -/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add 0 in string at the given index -%% str index -> str index+1 -/AddZero {2 copy (0) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add open parenthesis in string at the given index -%% str index -> str index+1 -/AddMul {2 copy (*) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add open parenthesis in string at the given index -%% str index -> str index+1 -/AddDiv {2 copy (/) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add a plus sign in string at the given index -%% str index -> str index+1 -/AddAdd {2 copy (+) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add a minus sign in string at the given index -%% str index -> str index+1 -/AddSub {2 copy (-) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add a pipe sign in string at the given index -%% str index -> str index+1 -/AddPipe {2 copy (|) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% H O O K S -/AnalyzePreHook { dup 5 1 roll } bind def -/PreEvalHook {} def -/AnalyzePostHook { 7 -1 roll pop } bind def -/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def -/RollOp { 5 1 roll } bind def -end%%%tx@CoreAnalyzerDict -/tx@AddMathFunc 12 dict def tx@AddMathFunc begin -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% NEW FUNC -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) -%% x -> theta -/asin {% - dup abs 1 gt { EQDFasinrangeerror } if - dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad -} def -%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) -%% x -> theta -/acos {% - dup abs 1 gt { EQDFacosrangeerror } if - dup dup mul 1 exch sub sqrt exch atan DegtoRad -} def -%% function arctangent in radians -%% x -> theta -/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def -%% HYPERBOLIC FUNCTIONS -/sh { dup Ex exch neg Ex sub 2 div } def -/ch { dup Ex exch neg Ex add 2 div } def -/th { dup sh exch ch div } def -/Argsh { dup dup mul 1 add sqrt add ln } def -/Argch { dup dup mul 1 sub sqrt add ln } def -/Argth { dup 1 add exch 1 exch sub div ln 2 div } def -%% modified exponential funtion for 0 -%% x n -> x^n -/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def -%% modified exponential funtion for 0 -%% x -> e^x -/Ex { Euler exch exp } bind def -%% -%% factorial function -%% n -> n! -/Fact { 1 exch 2 exch 1 exch { mul } for } bind def -/fact { Fact } bind def -end - -% END pstricks.pro - -%%EndProcSet -%%BeginProcSet: pst-dots.pro 0 0 -% $Id: pst-dots.pro 26 2008-06-14 11:50:02Z herbert $ -% -%% PostScript prologue for pstricks.tex. -%% Version 2.02, 2008/04/18 -%% -%% For distribution, see pstricks.tex. -%% -%% Timothy Van Zandt <tvz@Princeton.EDU> -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -%% -%% Modified by Etienne Riga - Dec. 16, 1999 -%% Modified by Etienne Riga - 2005/01/01 (er) -%% to add /Diamond, /SolidDiamond and /BoldDiamond -%% Modified by Herbert Voss (hv) - 2008/04/17 -% -10 dict dup begin % hold local - /FontType 3 def - /FontMatrix [.001 0 0 .001 0 0] def - /FontBBox [-571.5 -742.5 571.5 742.5] def -% /FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph - /Encoding 256 array def - 0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef - Encoding % replace with given dot names - dup (b) 0 get /Bullet put % get the numerical position of b in ASCII -% % and save /Bullet at this place in Encoding - dup (c) 0 get /Circle put - dup (C) 0 get /BoldCircle put % 67 - dup (u) 0 get /SolidTriangle put - dup (t) 0 get /Triangle put - dup (T) 0 get /BoldTriangle put - dup (r) 0 get /SolidSquare put - dup (s) 0 get /Square put - dup (S) 0 get /BoldSquare put - dup (q) 0 get /SolidPentagon put - dup (p) 0 get /Pentagon put - dup (P) 0 get /BoldPentagon put -%%% - dup (k) 0 get /Asterisk put - dup (K) 0 get /BoldAsterisk put - dup (J) 0 get /SolidAsterisk put - dup (h) 0 get /Hexagon put - dup (H) 0 get /BoldHexagon put - dup (G) 0 get /SolidHexagon put - dup (f) 0 get /Octogon put % 2008-04-18 hv - dup (F) 0 get /BoldOctogon put % 2008-04-18 hv - dup (g) 0 get /SolidOctogon put % 2008-04-18 hv - dup (a) 0 get /Add put - dup (A) 0 get /BoldAdd put % 65 - dup (x) 0 get /Mul put - dup (X) 0 get /BoldMul put - dup (m) 0 get /Oplus put - dup (M) 0 get /BOplus put - dup (e) 0 get /SolidOplus put - dup (n) 0 get /Otimes put - dup (N) 0 get /BOtimes put - dup (E) 0 get /SolidOtimes put - dup (i) 0 get /Bar put - dup (I) 0 get /BoldBar put - dup (l) 0 get /SolidDiamond put - dup (d) 0 get /Diamond put - (D) 0 get /BoldDiamond put -%%% -/CharProcs 47 dict def -CharProcs begin - /CirclePath {0 0 500 0 360 arc closepath} def - /Bullet {CirclePath fill} def - /Circle {CirclePath .9 .9 scale CirclePath eofill} def - /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def - /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def - /SolidTriangle {TrianglePath fill} def - /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def - /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def - /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def - /SolidSquare {SquarePath fill} def - /Square {SquarePath .89 .89 scale SquarePath eofill} def - /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def - /PentagonPath { - -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto - 0 574.7 lineto -546.6 177.6 lineto closepath - } def - /SolidPentagon {PentagonPath fill} def - /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def - /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def -%-------------- hv begin 2004/07/25 from: er 2003/03/24 - /HexagonPath { - 0 550 moveto -476 275 lineto -476 -275 lineto - 0 -550 lineto 476 -275 lineto 476 275 lineto closepath - } def - /SolidHexagon {HexagonPath fill} def - /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def - /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def -% 2008-04-18 hv - /OctogonPath { - 550 dup 22.5 tan mul dup neg dup add /xMove exch def - exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def - /SolidOctogon { OctogonPath fill } def - /Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def - /BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def -% - /AsteriskPath { - 20 0 moveto 10 250 180 500 0 500 curveto - -180 500 -10 250 -20 0 curveto closepath - } def - /Asterisk { - AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath - 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill - } def -% - /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def - /BoldAsteriskPath { - 50 30 cos 100 mul moveto Basterp - 60 rotate Basterp 60 rotate Basterp - 60 rotate Basterp 60 rotate Basterp - 60 rotate Basterp closepath - } def - /BoldAsterisk {BoldAsteriskPath fill} def - /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def - /CrossPath { - 40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto - -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto - 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath - } def - /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto - -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto - 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath - } def - /Add {CrossPath fill} def - /Mul {45 rotate CrossPath fill} def - /BoldAdd {BoldCrossPath fill} def - /BoldMul {45 rotate BoldCrossPath fill} def - /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def - /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def - /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def - /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def - /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def - /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def - /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def - /Bar {BarPath fill} def - /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def - /BoldBar {BoldBarPath fill} def - /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath} def - /SolidDiamond {DiamondPath fill} def - /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def - /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def -%%% - /.notdef { } def -end -% -/BuildGlyph { - exch - begin -% Metrics 1 index get exec 0 - 0 0 -% BBoxes 3 index get exec - -1000 -1000 1000 1000 -% -571.5 -742.5 571.5 742.5 - setcachedevice - CharProcs begin load exec end - end -} def -% -/BuildChar { - 1 index /Encoding get exch get - 1 index /BuildGlyph get exec -} bind def - -end -/PSTricksDotFont exch definefont pop - -%% end - -%%EndProcSet -%%BeginProcSet: pst-node.pro 0 0 -% $Id: pst-node.pro 26 2008-06-14 11:50:02Z herbert $ -%% -%% PostScript prologue for pst-node.tex. -%% Version 1.00, 2008/01/01. -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -% -/tx@NodeDict 400 dict def tx@NodeDict begin -tx@Dict begin % from main pstricks dict - /T /translate load def -end -/NewNode { % on stack: { x y } boolean N@name type InitXnode - gsave - /next ED % { x y } boolean N@name type - dict dup % { x y } boolean N@name dict dict - 3 1 roll def % { x y } boolean dict N@name dict def - exch { dup 3 1 roll def } if % { x y } dict boolean - begin % { x y } dict begin - tx@Dict begin - STV CP T exec % set scaling - end - /NodeMtrx CM def % save CM - next % InitXNode - end - grestore -} def -% -/InitPnode { - /Y ED /X ED - /NodePos { NodeSep Cos mul NodeSep Sin mul } def -} def -% -/InitCnode { - /r ED /Y ED /X ED - /NodePos { NodeSep r add dup Cos mul exch Sin mul } def -} def -% -/GetRnodePos { - Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse - Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse - dx Sin mul abs dy - Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse -} def -% -/InitRnode { - /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED - /NodePos { GetRnodePos } def -} def -% -/DiaNodePos { - w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup - Cos mul exch Sin mul -} def -% -/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h -mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul -} ifelse } def -/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d -ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d -sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan -sin def /NodePos { TriNodePos } def } def -/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos -hh mul Atan dup cos ww mul exch sin hh mul } def -/GetCenter { begin X Y NodeMtrx transform CM itransform end } def -% -/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist - Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } - { 0 Dist Sin mul } ifelse } ifelse Do -} def -/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform - exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx - dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop - XYPos } ifelse -} def -/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 -roll sin mul sub exch } ifelse } def -/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA -AddOffset yA add /yA1 ED xA add /xA1 ED } def -/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB -AddOffset yB add /yB1 ED xB add /xB1 ED } def -/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA -AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED -ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED -} ifelse } def -/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB -AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED -ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED -} ifelse } def -/InitNC { - /b ED /a ED % second and first node - /NodeSepTypeB ED /NodeSepTypeA ED - /NodeSepB ED /NodeSepA ED - /OffsetB ED /OffsetA ED - tx@NodeDict a known tx@NodeDict b known and dup { - /NodeA a load def - /NodeB b load def - NodeA GetCenter /yA ED /xA ED - NodeB GetCenter /yB ED /xB ED } if -} def -% -/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub -mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def -/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt -{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop -} repeat LPutLine cleartomark } def -/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED -/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 -mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx -sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul -add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add -y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul -mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def -/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def -} def -/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def -/NAngle yyB yyA sub xxB xxA sub Atan def } def -/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def -/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def -} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit -} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd -} def -/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def -} def -/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def -/NAngle yyB yyA sub xxB xxA sub Atan def } def -/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def -/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def -} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { -exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark -VPosEnd } def -/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 -roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx -def grestore exec /LPutVar /SaveLPutVar load def } def -/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def -GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { -LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { -LPutVar VPutLine } def LPutVar } def -/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop -end } def -/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub -Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan -/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 -yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { -LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } -ifelse } def -/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 -roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA -GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict -begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] -cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines -} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def -% -/NCAngles { - GetEdgeA GetEdgeB GetArmA GetArmB - /mtrx AngleA matrix rotate def - xA2 yA2 mtrx transform pop - xB2 yB2 mtrx transform exch pop - mtrx itransform - /y0 ED /x0 ED - mark ArmB 0 ne { xB1 yB1 } if - xB2 yB2 x0 y0 xA2 yA2 - ArmA 0 ne { xA1 yA1 } if - tx@Dict begin false Line end - /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def - /LPutPos { LPutLines } def - /HPutPos { HPutLines } def - /VPutPos { VPutLines } def } def -% -/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 -yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform -/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 -tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] -cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { -VPutLines } def } def -/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def -xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx -transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } -{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB -0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict -begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx -def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { -VPutLines } def } def -/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if -xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end -/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { -LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } -def -/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED -GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin -false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { -LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } -def -/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate -def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 -mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 -mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 -xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false -Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] -cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { -VPutLines } def } def -% DG/SR modification begin - May 9, 1997 - Patch 1 -%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r -%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add -%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 -%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED -/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r -r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add -exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 -mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED -% DG/SR modification end -} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add -AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r -Div def /y ED /x ED } def -/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB -180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos -mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def -/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy -add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos -{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar -tx@Dict begin false Polygon end } def -/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan -def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 -mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def -/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div -def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def -GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul -sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 -eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } -{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def -0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 -roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 -0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 -roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } -ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos -{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { -r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } -{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add -add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub -mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t -sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse -y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { -LPutPos } def } def -/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB -sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 -ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB -w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos -{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } -{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } -def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin -/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def - -/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg -exch X sub neg exch moveto setmatrix CP grestore } def - -/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 -def } ifelse LPutCoor } def -/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } -if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } -ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } -def -/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if -r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } -ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } -def -end -% END pst-node.pro - -%%EndProcSet -%%BeginProcSet: pstricks-add.pro 0 0 -%% $Id: pstricks-add.pro 49 2008-10-13 10:59:27Z herbert $ -% PostScript prologue for pstricks-add.tex. -% Version 0.21, 2008/10/15 -% For distribution, see pstricks.tex. -% -% HISTORY -> see file Changes -% -/tx@addDict 410 dict def tx@addDict begin -%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -/GTriangle { - gsave - /mtrx CM def - /colorA ED /colorB ED /colorC ED % save the colors - /yA ED /xA ED % save the origin - xA yA translate - rotate % \psk@gangle - /yB ED /xB ED /yC ED /xC ED % save other coordinates - /ds [ % save data in a array - 0 0 0 colorA aload pop % fd x y xr xg xb - 0 xB xA sub yB yA sub colorB aload pop - 0 xC xA sub yC yA sub colorC aload pop -% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD - ] def - newpath - << - /ShadingType 4 % single Gouraud - /ColorSpace [ /DeviceRGB ] - /DataSource ds - >> - shfill - closepath - mtrx - setmatrix grestore} def -% -/RGBtoCMYK { % on stack r g b -> C M Y K - 3 dict begin - /Blue ED /Green ED /Red ED - 1 Red sub % Cyan - 1 Green sub % Magenta - 1 Blue sub % Yellow - 0 % Black - end -} def -% -/CMYKtoGRAY { % on stack c m y k -> gray - exch 0.11 mul add - exch 0.59 mul add - exch 0.3 mul add - dup 1 gt { pop 1 } if - neg 1 add -} def -% -/RGBtoGRAY { % on stack r g b -> gray - 0.11 mul - exch 0.59 mul add - exch 0.3 mul add -} def -% -/HSBtoGRAY { - 6 dict begin - /b exch def - /s exch def 6 mul dup cvi dup - /i exch def sub - /f exch def - /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def - F i get { s mul neg 1 add b mul} forall - 0.11 mul - exch 0.59 mul add - exch 0.3 mul add - end -} def -% -%% convertisseur longueur d'onde ->R,G,B Manuel Luque -%% lambda max=780 nanometres -%% lambda min=380 nanometres -%% adaptation de : -%% http://www.physics.sfasu.edu/astro/color.html -%% www.efg2.com/lab -% -/Gamma 0.8 def -/calculateRGB { - lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if - lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if - lambda 380 ge {lambda 439 le { - /R {lambda 440 sub neg 440 380 sub div} def - /Red R factor mul Gamma exp def - /G 0 def - /Green G factor mul Gamma exp def - /B 1 def - /Blue B factor mul Gamma exp def} if - } if - lambda 440 ge { lambda 489 le { - /G {lambda 440 sub 490 440 sub div} def - /Green G factor mul Gamma exp def - /R 0 def /Red 0 def - /B 1 def - /Blue B factor mul Gamma exp def } if - } if - lambda 490 ge {lambda 509 le { - /B {lambda 510 sub neg 510 490 sub div} def - /Blue B factor mul Gamma exp def - /R 0 def /Red 0 def - /G 1 def - /Green G factor mul Gamma exp def } if - } if - lambda 510 ge {lambda 579 le { - /R {lambda 510 sub 580 510 sub div } def - /Red R factor mul Gamma exp def - /Blue 0 def - /G 1 def - /Green G factor mul Gamma exp def } if - } if - lambda 580 ge {lambda 644 le { - /G {lambda 645 sub neg 645 580 sub div } def - /Green G factor mul Gamma exp def - /Blue 0 def - /R 1 def - /Red R factor mul Gamma exp def } if - } if - lambda 645 ge { lambda 780 le { - /Red 1 factor mul Gamma exp def - /Blue 0 def - /Green 0 def } if - } if -} def -% -/factor { - lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if - lambda 420 ge {lambda 700 le { 1 } if } if - lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if -} def -% -/wavelengthToRGB { % the wavelength in nm must be on top of the stack - cvi /lambda exch def % no floating point here - calculateRGB -} def % now the colors are saved in Red Green Blue -% -/wavelengthToCMYK { % the wavelength in nm must be on top of the stack - cvi /lambda exch def % no floating point here - gsave - calculateRGB Red Green Blue RGBtoCMYK - /Black ED /Yellow ED /Magenta ED /Cyan ED - grestore -} def % now the colors are saved in Cyan Magenta Yellow Black -% -/axfill { - 8 dict begin - /xw exch def /nl exch def - /C1 exch def /y1 exch def/x1 exch def - /C0 exch def /y0 exch def/x0 exch def - << /ShadingType 2 - /ColorSpace /DeviceRGB - /Coords [ x0 y0 x1 y1 ] - /EmulatorHints [ xw 2 div dup ] - /Function << - /FunctionType 2 - /Domain [0 1] - /C0 C0 - /C1 C1 - /N 1 - >> - >> shfill - end -} bind def -% -%%%%% ### bubblesort ### -%% syntax : array bubblesort --> array2 trie par ordre croissant -%% code de Bill Casselman -%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/ -/bubblesort { -4 dict begin - /a exch def - /n a length 1 sub def - n 0 gt { - % at this point only the n+1 items in the bottom of a remain to - % the sorted largest item in that blocks is to be moved up into - % position n - n { - 0 1 n 1 sub { - /i exch def - a i get a i 1 add get gt { - % if a[i] > a[i+1] swap a[i] and a[i+1] - a i 1 add - a i get - a i a i 1 add get - % set new a[i] = old a[i+1] - put - % set new a[i+1] = old a[i] - put - } if - } for - /n n 1 sub def - } repeat - } if - a -end -} def -% -end -% -% END pstricks-add.pro - - -%%EndProcSet -%%BeginProcSet: lm-ec.enc 0 0 -% This file belongs to the Latin Modern package. The work is released -% under the GUST Font License. See the MANIFEST-Latin-Modern.txt and -% README-Latin-Modern.txt files for the details. For the most recent version of -% this license see http://www.gust.org.pl/fonts/licenses/GUST-FONT-LICENSE.txt -% or http://tug.org/fonts/licenses/GUST-FONT-LICENSE.txt - -/enclmec[ -/grave -/acute -/circumflex -/tilde -/dieresis -/hungarumlaut -/ring -/caron -/breve -/macron -/dotaccent -/cedilla -/ogonek -/quotesinglbase -/guilsinglleft -/guilsinglright -/quotedblleft -/quotedblright -/quotedblbase -/guillemotleft -/guillemotright -/endash -/emdash -/cwm -/perthousandzero -/dotlessi -/dotlessj -/ff -/fi -/fl -/ffi -/ffl -/visiblespace -/exclam -/quotedbl -/numbersign -/dollar -/percent -/ampersand -/quoteright -/parenleft -/parenright -/asterisk -/plus -/comma -/hyphen -/period -/slash -/zero -/one -/two -/three -/four -/five -/six -/seven -/eight -/nine -/colon -/semicolon -/less -/equal -/greater -/question -/at -/A -/B -/C -/D -/E -/F -/G -/H -/I -/J -/K -/L -/M -/N -/O -/P -/Q -/R -/S -/T -/U -/V -/W -/X -/Y -/Z -/bracketleft -/backslash -/bracketright -/asciicircum -/underscore -/quoteleft -/a -/b -/c -/d -/e -/f -/g -/h -/i -/j -/k -/l -/m -/n -/o -/p -/q -/r -/s -/t -/u -/v -/w -/x -/y -/z -/braceleft -/bar -/braceright -/asciitilde -/hyphen.alt -/Abreve -/Aogonek -/Cacute -/Ccaron -/Dcaron -/Ecaron -/Eogonek -/Gbreve -/Lacute -/Lcaron -/Lslash -/Nacute -/Ncaron -/Eng -/Ohungarumlaut -/Racute -/Rcaron -/Sacute -/Scaron -/Scedilla -/Tcaron -/Tcedilla -/Uhungarumlaut -/Uring -/Ydieresis -/Zacute -/Zcaron -/Zdotaccent -/IJ -/Idotaccent -/dcroat -/section -/abreve -/aogonek -/cacute -/ccaron -/dcaron -/ecaron -/eogonek -/gbreve -/lacute -/lcaron -/lslash -/nacute -/ncaron -/eng -/ohungarumlaut -/racute -/rcaron -/sacute -/scaron -/scedilla -/tcaron -/tcedilla -/uhungarumlaut -/uring -/ydieresis -/zacute -/zcaron -/zdotaccent -/ij -/exclamdown -/questiondown -/sterling -/Agrave -/Aacute -/Acircumflex -/Atilde -/Adieresis -/Aring -/AE -/Ccedilla -/Egrave -/Eacute -/Ecircumflex -/Edieresis -/Igrave -/Iacute -/Icircumflex -/Idieresis -/Eth -/Ntilde -/Ograve -/Oacute -/Ocircumflex -/Otilde -/Odieresis -/OE -/Oslash -/Ugrave -/Uacute -/Ucircumflex -/Udieresis -/Yacute -/Thorn -/Germandbls -/agrave -/aacute -/acircumflex -/atilde -/adieresis -/aring -/ae -/ccedilla -/egrave -/eacute -/ecircumflex -/edieresis -/igrave -/iacute -/icircumflex -/idieresis -/eth -/ntilde -/ograve -/oacute -/ocircumflex -/otilde -/odieresis -/oe -/oslash -/ugrave -/uacute -/ucircumflex -/udieresis -/yacute -/thorn -/germandbls -] def - -%%EndProcSet -%%BeginProcSet: texps.pro 0 0 -%! 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G a l G sub s m get div .2 + floor .3 + 25 - mul j l + S rmoveto}F i L j L stroke }F}F}F}F - grestore - pop pop -} def -% -%gsave abs CLW add /a ED a 0 dtransform round exch round exch -%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 -%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 -%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a -%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a -%% DG/SR modification end -%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict -%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 -%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) -%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } -%% def -%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore -%pop pop } def -%% DG/SR modification end -% -/BeginArrow { - ADict begin % hold it local, for end see EndArrow - /@mtrx CM def - gsave - 2 copy T - 2 index sub neg exch - 3 index sub exch Atan - rotate newpath -} def -% -/EndArrow { @mtrx setmatrix CP grestore end } def % end the ADict -% -/Arrow { - CLW mul add dup - 2 div /w ED - mul dup /h ED - mul /a ED - { 0 h T 1 -1 scale } if - w neg h moveto - 0 0 L w h L w neg a neg rlineto - gsave fill grestore -} def -% -/ArrowD { % the sides are drawn as curves (hv 20071211) - CLW mul add dup - 2 div /w ED - mul dup /h ED - mul /Inset ED - { 0 h T 1 -1 scale } if % changes the direction -% we use y=w/h^2 * x^2 as equation for the control points -% for the coordinates the arrow is seen from top to bottom -% the bottom (tip) is (0;0) - w neg h moveto % lower left of > - w 9 div 4 mul neg h 3 div 2 mul - w 9 div neg h 3 div - 0 0 curveto % tip of > - w 9 div h 3 div - w 9 div 4 mul h 3 div 2 mul - w h curveto % upper left of > - w neg Inset neg rlineto % move to x=0 and inset - gsave fill grestore -} def -% -/Tbar { - CLW mul add /z ED - z -2 div CLW 2 div moveto - z 0 rlineto stroke - 0 CLW moveto -} def -% -/Bracket { - CLW mul add dup CLW sub 2 div - /x ED mul CLW add /y ED /z CLW 2 div def - x neg y moveto - x neg CLW 2 div L x CLW 2 div L x y L stroke - 0 CLW moveto -} def -% -/RoundBracket { - CLW mul add dup 2 div - /x ED mul /y ED /mtrx CM def - 0 CLW 2 div T x y mul 0 ne { x y scale } if - 1 1 moveto - .85 .5 .35 0 0 0 curveto - -.35 0 -.85 .5 -1 1 curveto - mtrx setmatrix stroke 0 CLW moveto -} def -% -/SD { 0 360 arc fill } def -% -/EndDot { % DS is the dot size - { /z DS def } { /z 0 def } ifelse - /b ED 0 z DS SD b { 0 z DS CLW sub SD } if - 0 DS z add CLW 4 div sub moveto } def -% -/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { - /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto - load } if ] cvx newpath 3 1 roll T exec } def -% -%/NArray { -% aload length 2 div dup dup cvi eq not { exch pop } if /n exch -% cvi def -%} def -% -/NArray { % holds the coordinates and on top of stack the showpoints boolean - /showpoints ED - counttomark 2 div dup cvi /n ED - n eq not { exch pop } if - showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse -} def -% -/Line { - NArray n 0 eq not - { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def - n { Lineto } repeat - CP 4 2 roll ArrowB L pop pop - } if -} def -% -/Arcto { - /a [ 6 -2 roll ] cvx def - a r - /arcto load stopped { 5 } { 4 } ifelse { pop } repeat - a -} def -% -/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq - and { pop pop /n n 1 sub def } if } def -/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } - repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 - ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 - moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto - Lineto pop pop closepath } ifelse } def -/Diamond { - /mtrx CM def - T rotate - /h ED - /w ED - dup 0 eq { pop } { CLW mul neg - /d ED - /a w h Atan def - /h d a sin Div h add def - /w d a cos Div w add def } ifelse - mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div - /ArrowA { moveto } def - /ArrowB { } def - false Line - closepath mtrx setmatrix } def -% DG modification begin - Jan. 15, 1997 -%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { -%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 -%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 -%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx -%setmatrix } def -/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup -CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 -div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 -d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx -% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) -% setmatrix } def -setmatrix pop } def -% DG/SR modification end -% -/CCA { - /y ED /x ED - 2 copy y sub /dy1 ED - x sub /dx1 ED - /l1 dx1 dy1 Pyth def -} def -% -/CC { - /l0 l1 def - /x1 x dx sub def - /y1 y dy sub def - /dx0 dx1 def - /dy0 dy1 def - CCA - /dx dx0 l1 c exp mul dx1 l0 c exp mul add def - /dy dy0 l1 c exp mul dy1 l0 c exp mul add def - /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def - /x2 x l0 dx mul m mul sub def - /y2 y l0 dy mul m mul sub def - /dx l1 dx mul m mul neg def - /dy l1 dy mul m mul neg def -} def -% -/IC { - /c c 1 add def - c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse - /a a 2 mul 3 div 45 cos b exp div def - CCA - /dx 0 def - /dy 0 def -} def -% -/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def -/NC { CC x1 y1 x2 y2 x y curveto } def -/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def -/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def -/NAC { x2 y2 x y curveto CC x1 y1 } def -/EAC { x2 y2 x y ArrowB curveto pop pop } def -% -/OpenCurve { - NArray n 3 lt - { n { pop pop } repeat } - { BOC /n n 3 sub def n { NC } repeat EOC } ifelse -} def -% -/AltCurve { - { false NArray n 2 mul 2 roll - [ n 2 mul 3 sub 1 roll ] aload - /Points ED - n 2 mul -2 roll } - { false NArray } ifelse - n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse -} def -% -/ClosedCurve { - NArray n 3 lt - { n { pop pop } repeat } - { n 3 gt { CheckClosed } if - 6 copy n 2 mul 6 add 6 roll - IC CC x y moveto n { NC } repeat - closepath pop pop - } ifelse -} def -% -/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def -/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def -/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } -def -/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix -rotate matrix concatmatrix exch findfont exch makefont setfont } def -/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto -x1 y1 lineto closepath } def -/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 -y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div -exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse -/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto -x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } -ifelse } def -/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add -/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { -pop pop Rect } { OvalFrame } ifelse } def -% -/BezierNArray { - /f ED - counttomark 2 div dup cvi /n ED - n eq not { exch pop } if - n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat - f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse -} def -% -/OpenBezier { - BezierNArray - n 1 eq - { pop pop } - { ArrowA n 4 sub 3 idiv - { 6 2 roll 4 2 roll curveto } repeat - 6 2 roll 4 2 roll ArrowB curveto } ifelse -} def -% -/ClosedBezier { - BezierNArray - n 1 eq - { pop pop } - { moveto n 1 sub 3 idiv - { 6 2 roll 4 2 roll curveto } repeat - closepath } ifelse -} def -% -/BezierShowPoints { - gsave - Points aload length 2 div cvi /n ED - moveto - n 1 sub { lineto } repeat - CLW 2 div SLW [ 4 4 ] 0 setdash stroke - grestore -} def -% -/Parab { - /y0 ED /x0 ED /y1 ED /x1 ED - /dx x0 x1 sub 3 div def - /dy y0 y1 sub 3 div def - x0 dx sub y0 dy add x1 y1 ArrowA - x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB - curveto - /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def -} def -% -/Grid { - newpath - /a 4 string def - /b ED /c ED /n ED - cvi dup 1 lt { pop 1 } if - /s ED - s div dup 0 eq { pop 1 } if - /dy ED s div dup 0 eq { pop 1 } if - /dx ED dy div round dy mul - /y0 ED dx div round dx mul - /x0 ED dy div round cvi - /y2 ED dx div round cvi - /x2 ED dy div round cvi - /y1 ED dx div round cvi - /x1 ED - /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def - /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def - b 0 gt { - /z1 b 4 div CLW 2 div add def -% /Helvetica findfont b scalefont setfont - /b b .95 mul CLW 2 div add def } if - systemdict /setstrokeadjust known - { true setstrokeadjust /t { } def } - { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add - exch itransform } bind def } ifelse - gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse - /i x1 def - /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def - /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def - x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if - { i dx mul dup y0 moveto - b 0 gt - { gsave c i a cvs dup stringwidth pop - /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse - h 0 gt {b neg}{z1} ifelse - rmoveto show grestore } if - dup t f moveto - g t L stroke - /i i w add def - } repeat - grestore - gsave - n 0 gt - % DG/SR modification begin - Nov. 7, 1997 - Patch 1 - %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } - { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } - % DG/SR modification end - { 2 setlinecap } ifelse - /i y1 def - /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def - /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def - y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if - { newpath i dy mul dup x0 exch moveto - b 0 gt { gsave c i a cvs dup stringwidth pop - /z2 ED - w 0 gt {z1 z2 add neg} {z1} ifelse - h 0 gt {z1} {b neg} ifelse - rmoveto show grestore } if - dup f exch t moveto - g exch t L stroke - /i i h add def - } repeat - grestore -} def -% -/ArcArrow { - /d ED /b ED /a ED - gsave - newpath 0 -1000 moveto clip - newpath - 0 1 0 0 b - grestore - c mul - /e ED - pop pop pop r a e d PtoC y add exch x add - exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c - mul neg d -} def -% -/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def -% -/ArcAdjust { %%%% Vincent Guirardel -% given a target length (targetLength) and an initial angle (angle0) [in the stack], -% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). -% This computes an angle t such that (x0,y0) is at distance -% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). -% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 -% contrary to TvZ's code. -% To achieve, this, one iterates the following process: start with some angle t, -% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. -% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. -% -% Another difference with TvZ's code is that we need d (=add/sub) to be defined. -% the value of d = add/sub is used to know on which side we have to move. -% It is only used in the initialisation of the angle before the iteration. -% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% Input stack: 1: target length 2: initial angle -% variables used : rx, ry, d (=add/sub) -% - /targetLength ED /angle0 ED - /x0 rx angle0 cos mul def - /y0 ry angle0 sin mul def -% we are looking for an angle t such that (x0,y0) is at distance targetLength -% from the point M(t)=(rx*cos(t),ry*sin(t))) -%initialisation of angle (using 1st order approx = TvZ's code) - targetLength 57.2958 mul - angle0 sin rx mul dup mul - angle0 cos ry mul dup mul - add sqrt div -% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees -% (if the ellipse is very curved at the point where we draw the arrow, % -% the value can be much more than 360 degrees !) -% this should avoid going on the wrong side (more than 180 degrees) or go near -% a bad attractive point (at 180 degrees) - dup 90 ge { pop 90 } if - angle0 exch d % add or sub -% maximum number of times to iterate the iterative procedure: -% iterative procedure: takes an angle t on top of stack, computes a -% better angle (and put it on top of stack) - 30 { dup -% compute distance D between (x0,y0) and M(t) - dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt -% if D almost equals targetLength, we stop - dup targetLength sub abs 1e-5 le { pop exit } if -% stack now contains D t -% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: -% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) - exch dup cos rx mul x0 sub exch sin ry mul y0 sub -% stack contains: y(t)-y0, x(t)-x0, d - 2 index Div targetLength mul y0 add ry Div exch - 2 index Div targetLength mul x0 add rx Div -% stack contains x(t')/rx , y(t')/ry , d -% now compute t', and remove D from stack - atan exch pop - } repeat -% we don't look at what happened... in particular, if targetLength is greater -% than the diameter of the ellipse... -% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... -% after iteration, stack contains an angle t such that M(t) is the tail of the arrow -% to give back the result as a an angle relative to angle0 we could add the following line: -% angle0 sub 0 exch d -% -% begin bug fix 2006-01-11 -% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 -%(we don't want to make the ellipse turn more or less than it should)... -dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse -% end bug fix -} def -% -/EllipticArcArrow { - /d ED % is add or sub - /b ED % arrow procedure - /a1 ED % angle - gsave - newpath - 0 -1000 moveto - clip % Set clippath far from arrow. - newpath - 0 1 0 0 b % Draw arrow to determine length. - grestore -% Length of arrow is on top of stack. Next 3 numbers are junk. -% - a1 exch ArcAdjust % Angular position of base of arrow. - /a2 ED - pop pop pop - a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig - a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig - a1 cos rx mul xOrig add % - a1 sin ry mul yOrig add % -% Now arrow tip coor and base coor are on stack. - b pop pop pop pop % Draw arrow, and discard coordinates. - a2 CLW 8 div -% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) - 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse - ArcAdjust -% resets original value of d - 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. -} def -%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% -% -/Rot { CP CP translate 3 -1 roll neg rotate NET } def -% -/RotBegin { - tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if - /TMatrix [ TMatrix CM ] cvx def - /a ED - a Rot /RAngle [ RAngle dup a add ] cvx def -} def -% -/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def -% -/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def -/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def -/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def -/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s -abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b -div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { -h1 abs h sub dup s mul abs } ifelse } def -/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s -mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q -{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add -exch } def -/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible -/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def -} if } ifelse } def -/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def -/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit -neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def -/IfVisible true def } def -end -%-----------------------------------------------------------------------------% - -% END pstricks.pro - -%%EndProcSet -%%BeginProcSet: pst-algparser.pro 0 0 -% $Id: pst-algparser.pro 26 2008-06-14 11:50:02Z herbert $ -%% -%% PostScript prologue for PSTricks algorithm parser -%% Version 0.01, 2008/01/01 -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -%% -%%-----------------------------------------------------------------------------% -% -/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez -% -/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin -% -% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 -% E->T|E+T -% T->FS|T*FS -% FS -> F | +FS | -FS -% F->P|F^SF -% P->(E)|literal -% literal->number|var|var[E]|func(params) -% params->E|E,param -% number->TOBEFINISHED -% -%% E expression, T term, SF signed factor, F factor, P power -% -%% parser -% -%% str -% -%% C->E<condition_operators>E -%% STR index -> STR index+lenExpr -/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def -% -%% analyze Expression List (separator , or | ) -%% STR index -> STR index+lenExpr -%% /AnalyzeListOfE { -%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar -%% NextNonBlankChar dup 0 eq { pop exit } if -%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if -%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop -%% AnalyzeListOfEPostHook -%% } def -/AnalyzeListOfE { - /NotFirst false def - { NextNonBlankChar pop AnalyzeExpr - NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse - dup Strlen eq { exit } if NextNonBlankChar - dup 44 ne 1 index 124 ne and - { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } - if pop 1 add } loop - AnalyzeListOfEPostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% E->T|E+T -%% STR index -> STR index+lenExpr -/AnalyzeExpr { - AnalyzePreHook AnalyzeTerm IsEndingExpr - { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } - { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } - ifelse - AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% T->FS|T*FS -%% STR index -/AnalyzeTerm { - AnalyzePreHook AnalyzeSignedFactor IsEndingTerm - { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } - { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } - ifelse - AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% FS -> F | +FS | -FS -%% STR index -/AnalyzeSignedFactor { - AnalyzePreHook 2 copy get dup IsUnaryOp - { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } - { pop AnalyzeFactor } - ifelse AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% F->P|F^P -%% STR index -/AnalyzeFactor { - AnalyzePreHook AnalyzePower IsEndingFactor - { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } - { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } - ifelse AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% P->(E)|literal -%% STR index -/AnalyzePower { - %% depending of first char either a number, or a literal - 2 copy get dup 40 eq%%an open par - { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } - { AnalyzeLiteral } - ifelse -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index STR[index] -> STR index -%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def -/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% recognize + or - -%% chr -> T/F -/IsUnaryOp { dup 43 eq exch 45 eq or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a number can contain only : 0123456789. -%% chr -> T/F -/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index -> STR index number -%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? -%% STR index -> STR index' number -/ReadNumber { - exch dup 3 -1 roll dup 3 1 roll - %%read mantissa - { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop - dup 101 eq exch 69 eq or - %%% there is a "e" or "E" -> read exponant - { 1 add 2 copy get dup IsUnaryOp - { pop 1 add 2 copy get } if - { IsNumber not { exit } if 1 add 2 copy get } loop } - if - dup 4 1 roll - 3 -1 roll exch 1 index sub getinterval -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a number can contain only : 0123456789. -%% chr -> T/F -/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index -> STR index number -%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? -%% STR index -> STR index' number -/ReadCondOp { - NextNonBlankChar 1 index 4 1 roll - { IsCondOp not { exit } if 1 add 2 copy get } loop - 2 copy 5 -1 roll - exch 1 index sub getinterval 3 1 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a literal can contain only : 0123456789. -%% chr -> T/F -/IsLiteral {% - dup 48 ge exch dup 57 le 3 -1 roll and exch - dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch - dup 97 ge exch 122 le and or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? -%% STR index -> literal STR index' nextchr -/ReadLiteral { - exch dup 3 -1 roll dup 3 1 roll - %%read literal core - { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop - 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or a clpar -%% STR index -> STR index STR[index] T/F -/IsEndingExpr {% - 2 copy dup Strlen eq - %% if end of str is reached -> end ! - { pop pop 0 true } - %% ending chr -> clpar, comma, |, <, >, =, !, - {get dup dup 41 eq - exch dup 124 eq - exch dup 93 eq - exch dup 44 eq - exch dup 30 eq - exch dup 60 ge exch 62 le and or or or or or} - ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or a +- -%% STR index -> STR index STR[index] T/F -/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or */ -%% STR index -> STR index STR[index] T/F -/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or ^ -%% STR index -> STR index STR[index] T/F -/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index -> STR index STR[index] -/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def -/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def -%%%%%%%%%%%%%%%%%%%%%%%% -%% DEBUG -/BRK {false} def -/BRKtrue {/BRK true def} def -/BRKStop {BRK {BRKtoto} if } def -/BRKEvalStop {BRK exch if } def -/BRKBRK2true {BRK {BRK2true} if } def -/BRK2 {false} def -/BRK2true {/BRK2 true def} def -/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def -end -% -%-------------------------------------------------------------------------------% -% -/tx@AlgToPs 12 dict def tx@AlgToPs begin -% -%% algExpr -> PSVector -/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def -/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def -/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def -/Strlen 0 def -/EvalListOfExpr {} def% -/EvalNumber {% - ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx - exch 1 add array astore def NextNonBlankChar pop } def -/EvalAddSub {% - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll - 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def -} def -/EvalMulDiv {% - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll - 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def -} def -/EvalPower {% - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll - pop /exp cvx exch 1 add array astore def -} def -/EvalLiteral {% - ReadLiteral - dup 40 eq%%% there is an open par -> function call - { pop 2 index - dup (Sum) eq { EvalSum } - { dup (IfTE) eq { EvalCond } - { dup (Derive) eq { pop EvalDerive } - { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx - exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } - { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def - dup 91 eq%%% there is an open bracket -> vector element - { pop 1 add NextNonBlankChar pop AnalyzeExpr - /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } - { pop NextNonBlankChar pop } - ifelse} - ifelse -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% the derive function : Derive(n,f(x)) -%% firstparindex lastparindex -> -/EvalDerive { - %% manage the function descripiton - 1 add ReadNumber 3 1 roll NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - 1 add NextNonBlankChar pop - 3 -1 roll cvi - dup 0 eq - { pop AnalyzeExpr 3 -1 roll pop 1 add } - { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll - { (x) tx@Derive begin Derive end } repeat - ExpressionVector exch /ExpressionVector [] def - AlgToPs aload length - /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def - l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add - 1 index length /Strlen exch def } ifelse -} def -/EvalSum {% - pop 1 add NextNonBlankChar pop - %% read the variable name - ReadLiteral pop NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if - %% read the initial value - 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - %% read the increment value - 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - %% read the limit value - 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll - 5 -1 roll 4 add array astore def - %% keep ExpressionVector for later and create a new one for internal Sum computation - ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def - 1 add NextNonBlankChar pop AnalyzeExpr - %% add each term - /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def - /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add - array astore def 3 -1 roll pop 1 add -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Convert to radians if trigo function call -%% (name) -> -/TrigoFunc { - dup (cos) eq 1 index (sin) eq or exch (tan) eq or - { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add - array astore def - } if -} def -/EvalCond {% - pop 1 add AnalyzeCond NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if - ExpressionVector 3 1 roll /ExpressionVector [] def - 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def - NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if - 1 add AnalyzeExpr - NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if - ExpressionVector - /ExpressionVector 6 -1 roll aload length dup - 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def - 1 add 3 -1 roll pop -} def -%% CondOp STR index -/EvalCondOp {% - 3 -1 roll - dup (=) eq { /eq } {% - dup (<) eq { /lt } {% - dup (>) eq { /gt } {% - dup (>=) eq { /ge } {% - dup (<=) eq { /ge } {% - dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } - ifelse } ifelse } ifelse } ifelse } ifelse } ifelse - cvx exch pop - /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def -/EvalUnaryOp { - 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% H O O K S -/AnalyzePreHook {} bind def -/PreEvalHook {} bind def -/AnalyzeListOfEPostHook {} bind def -/AnalyzePostHook {} def -/RollOp { 3 1 roll } bind def -end %tx@CoreAnalyzerDict -% -%--------------------------------------------------------------------% -% -/tx@Derive 41 dict def tx@Derive begin -%%increase ^^ for each function added -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% algExpr variable -> PSVector -/Derive {% - 10240 string 3 1 roll 0 3 1 roll - /Variable exch def - tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end -} def -/Strlen 0 def -/InitParser { dup length /Strlen exch def 0 } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% algExpr variable index -> PSVector -/DeriveIndexed {% - 3 1 roll 10240 string 3 1 roll 0 3 1 roll - /Variable exch def - tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u,v)'=-(u',v') -/EvalListOfExpr {% - 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe - 2 copy 7 -1 roll dup length 4 1 roll putinterval add - 6 -2 roll pop pop - 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (-u)'=-(u') -/EvalUnaryOp { - 4 -2 roll 4 index (0) eq - { (0) StrConcat 7 -1 roll pop } - { 7 -1 roll 45 eq - { AddSub AddOpPar true } { false } ifelse - 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (number)'=0 -/EvalNumber { ReadNumber (0) 6 2 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u+v)'=u'+v' -/EvalAddSub {% - 7 index dup (0) eq - { pop true }%% du=0 nothing added - { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } - ifelse - 5 index dup (0) eq - { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 - { exch - { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added - { 5 -2 roll 7 index 43 eq%%something yet added - { AddAdd false } { AddSub AddOpPar true } ifelse } - ifelse 11 1 roll - 3 -1 roll StrConcat 10 -1 roll { AddClPar } if - 2 copy pop 0 6 2 roll GetIntervalNewStr } - ifelse - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u*v)' or (u/v)' -/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u*v)'=u'*v+u*v' -/EvalMul {% - 4 -2 roll 7 index dup (0) eq - { pop false }%%du=0 - { (1) eq%%du=1 - { false } - { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse - 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if - true }%%du!=0 - ifelse - 5 1 roll 5 index (0) eq - { 5 -1 roll not { (0) StrConcat } if }%%dv=0 - { 5 -1 roll { AddAdd } if - 4 index (1) eq - { 8 index StrConcat } - { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } - ifelse - }%%dv!=0 - ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u/v)'=(u'*v-u*v')/v^2 -/EvalDiv {% - 4 -2 roll - 4 index (0) eq%%dv=0 -> u'/v - { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } - { 7 index dup (0) eq - { pop }%%du=0 - { (1) eq%%du=1 - { false } - { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse - 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 - ifelse - AddSub - 4 index (1) eq - { 8 index StrConcat } - { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } - ifelse - %}%%dv!=0 - 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar - AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } - ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% str1 index str2 -> str1 index -/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def -/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) -/EvalPower {% - 4 -2 roll 7 index (0) eq - {%%if du=0 then (u^v)'=v'ln(u)u^v - 4 index (0) eq - { (0) StrConcat }%%if dv=0 then (u^v)'=0 - { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if - 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if - AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse - } - {%%du!=0 - 4 index (0) eq - {%%if dv=0 then (u^v)'=vu'u^(v-1) - 5 index dup IsStrNumber - { dup (0) eq - { StrConcat } - { dup dup (1) eq exch (1.0) eq or - { StrConcat } - { StrConcat - 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 - { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 - (*\() StrConcat 8 index StrConcat (\)) StrConcat - 5 index dup dup (2) eq exch (2.0) eq or - { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } - { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat - 5 index StrConcat (-1\)) StrConcat } ifelse - } - {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) - 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if - AddOpPar 5 index StrConcat (\)*\() StrConcat - 8 index StrConcat (\)^\() StrConcat - 5 index StrConcat (-1\)+\() StrConcat - 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if - 8 index StrConcat (\)^\() StrConcat - 5 index StrConcat (\)*ln\() StrConcat - 8 index StrConcat AddClPar - } ifelse - } ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% str -> true/false -/IsStrNumber {% - true exch - { dup 48 lt exch dup 57 gt 3 -1 roll or - exch dup 46 ne%%. - exch dup 43 ne%%+ - exch 45 ne%%- - and and and { pop false } if } forall -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% literal switch -> func call, vector, variables -/EvalLiteral {% - ReadLiteral dup 40 eq%%% there is an open par -> function call - { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } - { dup 91 eq%%% there is an open bracket -> vector element - { ERROR_vector_not_yet_implemented } - { pop EvalVariable } - ifelse } - ifelse -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% first last parpos Expr[first:parpos-1] -> -/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (f(u))'=u'f'(u) -/EvalFunc { - 4 2 roll 4 index (1) ne - { AddOpPar 4 index StrConcat (\)*) StrConcat } if - (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Func derivative -> Eval<func> -/EvalFunc_sin {% - PreCommonFunc - { (cos\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_cos {% - PreCommonFunc - { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_tan {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if - PostCommonFunc } def -/EvalFunc_asin {% - PreCommonFunc - { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_acos {% - PreCommonFunc - { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_atg {% - PreCommonFunc - { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_ln {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_exp {% - PreCommonFunc - { (exp\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_sqrt {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_Fact {% - PreCommonFunc { ERROR_no_variable_expression_in_Fact } if - PostCommonFunc } def -/EvalFunc_sh {% - PreCommonFunc - { (ch\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_ch {% - PreCommonFunc - { (sh\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_th {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if - PostCommonFunc } def -/EvalFunc_Argsh {% - PreCommonFunc - { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_Argch {% - PreCommonFunc - { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_Argth {% - PreCommonFunc - { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -/PreCommonFunc { - 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop - 4 2 roll 4 index (0) eq - { (0) StrConcat false } - { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse -} def -/PostCommonFunc { - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -/EvalFunc_Derive {% - 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs - 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add - 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar - 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval - exch 6 2 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% literal switch -> func call, vector, variables -/EvalFunc_Sum {% - 1 add NextNonBlankChar pop - %% read the variable name - ReadLiteral pop 3 -1 roll pop NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if - %% read the initial value - 1 add NextNonBlankChar pop ReadNumber pop - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - %% read the increment value - 1 add NextNonBlankChar pop ReadNumber pop - 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if - %% read the limit value - 1 add NextNonBlankChar pop ReadNumber pop - 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if - 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop - 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat - 4 index StrConcat AddClPar - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% literal switch -> func call, vector, variables -/EvalFunc_IfTE {% - 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond - NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if - 1 add NextNonBlankChar pop dup 5 1 roll - AnalyzeExpr NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if - 1 add NextNonBlankChar pop - AnalyzeExpr 1 add NextNonBlankChar pop - 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat - 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% advance in str until a comma is found (no error detection!) -%% str index -> str index' -/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Convert to radians if trigo function call -%% (name) -> -/TrigoFunc { - dup (cos) eq 1 index (sin) eq or exch (tan) eq or - { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add - array astore def - } if -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% No derivative for condition.... -/EvalCondOp { 3 -1 roll pop } bind def -/PutIntervalOneAdd {putinterval 1 add} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add open parenthesis in string at the given index -%% str index -> str index+1 -/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add close parenthesis in string at the given index -%% str index -> str index+1 -/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add 0 in string at the given index -%% str index -> str index+1 -/AddZero {2 copy (0) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add open parenthesis in string at the given index -%% str index -> str index+1 -/AddMul {2 copy (*) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add open parenthesis in string at the given index -%% str index -> str index+1 -/AddDiv {2 copy (/) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add a plus sign in string at the given index -%% str index -> str index+1 -/AddAdd {2 copy (+) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add a minus sign in string at the given index -%% str index -> str index+1 -/AddSub {2 copy (-) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add a pipe sign in string at the given index -%% str index -> str index+1 -/AddPipe {2 copy (|) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% H O O K S -/AnalyzePreHook { dup 5 1 roll } bind def -/PreEvalHook {} def -/AnalyzePostHook { 7 -1 roll pop } bind def -/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def -/RollOp { 5 1 roll } bind def -end%%%tx@CoreAnalyzerDict -/tx@AddMathFunc 12 dict def tx@AddMathFunc begin -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% NEW FUNC -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) -%% x -> theta -/asin {% - dup abs 1 gt { EQDFasinrangeerror } if - dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad -} def -%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) -%% x -> theta -/acos {% - dup abs 1 gt { EQDFacosrangeerror } if - dup dup mul 1 exch sub sqrt exch atan DegtoRad -} def -%% function arctangent in radians -%% x -> theta -/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def -%% HYPERBOLIC FUNCTIONS -/sh { dup Ex exch neg Ex sub 2 div } def -/ch { dup Ex exch neg Ex add 2 div } def -/th { dup sh exch ch div } def -/Argsh { dup dup mul 1 add sqrt add ln } def -/Argch { dup dup mul 1 sub sqrt add ln } def -/Argth { dup 1 add exch 1 exch sub div ln 2 div } def -%% modified exponential funtion for 0 -%% x n -> x^n -/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def -%% modified exponential funtion for 0 -%% x -> e^x -/Ex { Euler exch exp } bind def -%% -%% factorial function -%% n -> n! -/Fact { 1 exch 2 exch 1 exch { mul } for } bind def -/fact { Fact } bind def -end - -% END pstricks.pro - -%%EndProcSet -%%BeginProcSet: pst-dots.pro 0 0 -% $Id: pst-dots.pro 26 2008-06-14 11:50:02Z herbert $ -% -%% PostScript prologue for pstricks.tex. -%% Version 2.02, 2008/04/18 -%% -%% For distribution, see pstricks.tex. -%% -%% Timothy Van Zandt <tvz@Princeton.EDU> -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -%% -%% Modified by Etienne Riga - Dec. 16, 1999 -%% Modified by Etienne Riga - 2005/01/01 (er) -%% to add /Diamond, /SolidDiamond and /BoldDiamond -%% Modified by Herbert Voss (hv) - 2008/04/17 -% -10 dict dup begin % hold local - /FontType 3 def - /FontMatrix [.001 0 0 .001 0 0] def - /FontBBox [-571.5 -742.5 571.5 742.5] def -% /FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph - /Encoding 256 array def - 0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef - Encoding % replace with given dot names - dup (b) 0 get /Bullet put % get the numerical position of b in ASCII -% % and save /Bullet at this place in Encoding - dup (c) 0 get /Circle put - dup (C) 0 get /BoldCircle put % 67 - dup (u) 0 get /SolidTriangle put - dup (t) 0 get /Triangle put - dup (T) 0 get /BoldTriangle put - dup (r) 0 get /SolidSquare put - dup (s) 0 get /Square put - dup (S) 0 get /BoldSquare put - dup (q) 0 get /SolidPentagon put - dup (p) 0 get /Pentagon put - dup (P) 0 get /BoldPentagon put -%%% - dup (k) 0 get /Asterisk put - dup (K) 0 get /BoldAsterisk put - dup (J) 0 get /SolidAsterisk put - dup (h) 0 get /Hexagon put - dup (H) 0 get /BoldHexagon put - dup (G) 0 get /SolidHexagon put - dup (f) 0 get /Octogon put % 2008-04-18 hv - dup (F) 0 get /BoldOctogon put % 2008-04-18 hv - dup (g) 0 get /SolidOctogon put % 2008-04-18 hv - dup (a) 0 get /Add put - dup (A) 0 get /BoldAdd put % 65 - dup (x) 0 get /Mul put - dup (X) 0 get /BoldMul put - dup (m) 0 get /Oplus put - dup (M) 0 get /BOplus put - dup (e) 0 get /SolidOplus put - dup (n) 0 get /Otimes put - dup (N) 0 get /BOtimes put - dup (E) 0 get /SolidOtimes put - dup (i) 0 get /Bar put - dup (I) 0 get /BoldBar put - dup (l) 0 get /SolidDiamond put - dup (d) 0 get /Diamond put - (D) 0 get /BoldDiamond put -%%% -/CharProcs 47 dict def -CharProcs begin - /CirclePath {0 0 500 0 360 arc closepath} def - /Bullet {CirclePath fill} def - /Circle {CirclePath .9 .9 scale CirclePath eofill} def - /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def - /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def - /SolidTriangle {TrianglePath fill} def - /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def - /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def - /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def - /SolidSquare {SquarePath fill} def - /Square {SquarePath .89 .89 scale SquarePath eofill} def - /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def - /PentagonPath { - -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto - 0 574.7 lineto -546.6 177.6 lineto closepath - } def - /SolidPentagon {PentagonPath fill} def - /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def - /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def -%-------------- hv begin 2004/07/25 from: er 2003/03/24 - /HexagonPath { - 0 550 moveto -476 275 lineto -476 -275 lineto - 0 -550 lineto 476 -275 lineto 476 275 lineto closepath - } def - /SolidHexagon {HexagonPath fill} def - /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def - /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def -% 2008-04-18 hv - /OctogonPath { - 550 dup 22.5 tan mul dup neg dup add /xMove exch def - exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def - /SolidOctogon { OctogonPath fill } def - /Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def - /BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def -% - /AsteriskPath { - 20 0 moveto 10 250 180 500 0 500 curveto - -180 500 -10 250 -20 0 curveto closepath - } def - /Asterisk { - AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath - 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill - } def -% - /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def - /BoldAsteriskPath { - 50 30 cos 100 mul moveto Basterp - 60 rotate Basterp 60 rotate Basterp - 60 rotate Basterp 60 rotate Basterp - 60 rotate Basterp closepath - } def - /BoldAsterisk {BoldAsteriskPath fill} def - /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def - /CrossPath { - 40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto - -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto - 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath - } def - /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto - -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto - 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath - } def - /Add {CrossPath fill} def - /Mul {45 rotate CrossPath fill} def - /BoldAdd {BoldCrossPath fill} def - /BoldMul {45 rotate BoldCrossPath fill} def - /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def - /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def - /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def - /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def - /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def - /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def - /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def - /Bar {BarPath fill} def - /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def - /BoldBar {BoldBarPath fill} def - /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath} def - /SolidDiamond {DiamondPath fill} def - /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def - /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def -%%% - /.notdef { } def -end -% -/BuildGlyph { - exch - begin -% Metrics 1 index get exec 0 - 0 0 -% BBoxes 3 index get exec - -1000 -1000 1000 1000 -% -571.5 -742.5 571.5 742.5 - setcachedevice - CharProcs begin load exec end - end -} def -% -/BuildChar { - 1 index /Encoding get exch get - 1 index /BuildGlyph get exec -} bind def - -end -/PSTricksDotFont exch definefont pop - -%% end - -%%EndProcSet -%%BeginProcSet: pst-node.pro 0 0 -% $Id: pst-node.pro 26 2008-06-14 11:50:02Z herbert $ -%% -%% PostScript prologue for pst-node.tex. -%% Version 1.00, 2008/01/01. -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -% -/tx@NodeDict 400 dict def tx@NodeDict begin -tx@Dict begin % from main pstricks dict - /T /translate load def -end -/NewNode { % on stack: { x y } boolean N@name type InitXnode - gsave - /next ED % { x y } boolean N@name type - dict dup % { x y } boolean N@name dict dict - 3 1 roll def % { x y } boolean dict N@name dict def - exch { dup 3 1 roll def } if % { x y } dict boolean - begin % { x y } dict begin - tx@Dict begin - STV CP T exec % set scaling - end - /NodeMtrx CM def % save CM - next % InitXNode - end - grestore -} def -% -/InitPnode { - /Y ED /X ED - /NodePos { NodeSep Cos mul NodeSep Sin mul } def -} def -% -/InitCnode { - /r ED /Y ED /X ED - /NodePos { NodeSep r add dup Cos mul exch Sin mul } def -} def -% -/GetRnodePos { - Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse - Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse - dx Sin mul abs dy - Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse -} def -% -/InitRnode { - /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED - /NodePos { GetRnodePos } def -} def -% -/DiaNodePos { - w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup - Cos mul exch Sin mul -} def -% -/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h -mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul -} ifelse } def -/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d -ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d -sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan -sin def /NodePos { TriNodePos } def } def -/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos -hh mul Atan dup cos ww mul exch sin hh mul } def -/GetCenter { begin X Y NodeMtrx transform CM itransform end } def -% -/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist - Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } - { 0 Dist Sin mul } ifelse } ifelse Do -} def -/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform - exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx - dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop - XYPos } ifelse -} def -/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 -roll sin mul sub exch } ifelse } def -/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA -AddOffset yA add /yA1 ED xA add /xA1 ED } def -/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB -AddOffset yB add /yB1 ED xB add /xB1 ED } def -/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA -AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED -ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED -} ifelse } def -/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB -AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED -ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED -} ifelse } def -/InitNC { - /b ED /a ED % second and first node - /NodeSepTypeB ED /NodeSepTypeA ED - /NodeSepB ED /NodeSepA ED - /OffsetB ED /OffsetA ED - tx@NodeDict a known tx@NodeDict b known and dup { - /NodeA a load def - /NodeB b load def - NodeA GetCenter /yA ED /xA ED - NodeB GetCenter /yB ED /xB ED } if -} def -% -/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub -mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def -/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt -{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop -} repeat LPutLine cleartomark } def -/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED -/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 -mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx -sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul -add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add -y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul -mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def -/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def -} def -/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def -/NAngle yyB yyA sub xxB xxA sub Atan def } def -/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def -/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def -} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit -} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd -} def -/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def -} def -/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def -/NAngle yyB yyA sub xxB xxA sub Atan def } def -/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def -/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def -} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { -exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark -VPosEnd } def -/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 -roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx -def grestore exec /LPutVar /SaveLPutVar load def } def -/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def -GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { -LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { -LPutVar VPutLine } def LPutVar } def -/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop -end } def -/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub -Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan -/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 -yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { -LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } -ifelse } def -/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 -roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA -GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict -begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] -cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines -} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def -% -/NCAngles { - GetEdgeA GetEdgeB GetArmA GetArmB - /mtrx AngleA matrix rotate def - xA2 yA2 mtrx transform pop - xB2 yB2 mtrx transform exch pop - mtrx itransform - /y0 ED /x0 ED - mark ArmB 0 ne { xB1 yB1 } if - xB2 yB2 x0 y0 xA2 yA2 - ArmA 0 ne { xA1 yA1 } if - tx@Dict begin false Line end - /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def - /LPutPos { LPutLines } def - /HPutPos { HPutLines } def - /VPutPos { VPutLines } def } def -% -/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 -yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform -/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 -tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] -cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { -VPutLines } def } def -/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def -xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx -transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } -{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB -0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict -begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx -def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { -VPutLines } def } def -/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if -xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end -/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { -LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } -def -/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED -GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin -false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { -LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } -def -/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate -def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 -mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 -mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 -xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false -Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] -cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { -VPutLines } def } def -% DG/SR modification begin - May 9, 1997 - Patch 1 -%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r -%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add -%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 -%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED -/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r -r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add -exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 -mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED -% DG/SR modification end -} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add -AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r -Div def /y ED /x ED } def -/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB -180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos -mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def -/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy -add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos -{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar -tx@Dict begin false Polygon end } def -/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan -def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 -mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def -/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div -def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def -GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul -sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 -eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } -{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def -0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 -roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 -0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 -roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } -ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos -{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { -r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } -{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add -add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub -mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t -sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse -y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { -LPutPos } def } def -/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB -sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 -ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB -w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos -{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } -{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } -def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin -/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def - -/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg -exch X sub neg exch moveto setmatrix CP grestore } def - -/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 -def } ifelse LPutCoor } def -/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } -if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } -ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } -def -/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if -r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } -ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } -def -end -% END pst-node.pro - -%%EndProcSet -%%BeginProcSet: pstricks-add.pro 0 0 -%% $Id: pstricks-add.pro 49 2008-10-13 10:59:27Z herbert $ -% PostScript prologue for pstricks-add.tex. -% Version 0.21, 2008/10/15 -% For distribution, see pstricks.tex. -% -% HISTORY -> see file Changes -% -/tx@addDict 410 dict def tx@addDict begin -%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -/GTriangle { - gsave - /mtrx CM def - /colorA ED /colorB ED /colorC ED % save the colors - /yA ED /xA ED % save the origin - xA yA translate - rotate % \psk@gangle - /yB ED /xB ED /yC ED /xC ED % save other coordinates - /ds [ % save data in a array - 0 0 0 colorA aload pop % fd x y xr xg xb - 0 xB xA sub yB yA sub colorB aload pop - 0 xC xA sub yC yA sub colorC aload pop -% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD - ] def - newpath - << - /ShadingType 4 % single Gouraud - /ColorSpace [ /DeviceRGB ] - /DataSource ds - >> - shfill - closepath - mtrx - setmatrix grestore} def -% -/RGBtoCMYK { % on stack r g b -> C M Y K - 3 dict begin - /Blue ED /Green ED /Red ED - 1 Red sub % Cyan - 1 Green sub % Magenta - 1 Blue sub % Yellow - 0 % Black - end -} def -% -/CMYKtoGRAY { % on stack c m y k -> gray - exch 0.11 mul add - exch 0.59 mul add - exch 0.3 mul add - dup 1 gt { pop 1 } if - neg 1 add -} def -% -/RGBtoGRAY { % on stack r g b -> gray - 0.11 mul - exch 0.59 mul add - exch 0.3 mul add -} def -% -/HSBtoGRAY { - 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} if - lambda 490 ge {lambda 509 le { - /B {lambda 510 sub neg 510 490 sub div} def - /Blue B factor mul Gamma exp def - /R 0 def /Red 0 def - /G 1 def - /Green G factor mul Gamma exp def } if - } if - lambda 510 ge {lambda 579 le { - /R {lambda 510 sub 580 510 sub div } def - /Red R factor mul Gamma exp def - /Blue 0 def - /G 1 def - /Green G factor mul Gamma exp def } if - } if - lambda 580 ge {lambda 644 le { - /G {lambda 645 sub neg 645 580 sub div } def - /Green G factor mul Gamma exp def - /Blue 0 def - /R 1 def - /Red R factor mul Gamma exp def } if - } if - lambda 645 ge { lambda 780 le { - /Red 1 factor mul Gamma exp def - /Blue 0 def - /Green 0 def } if - } if -} def -% -/factor { - lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if - lambda 420 ge {lambda 700 le { 1 } if } if - lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if -} def -% -/wavelengthToRGB { % the wavelength in nm must be on top of the stack - 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-userdict /end-hook known{end-hook}if -%%EOF diff --git a/Master/texmf-dist/doc/latex/bclogo/bcdbelgique.pdf b/Master/texmf-dist/doc/latex/bclogo/bcdbelgique.pdf Binary files differdeleted file mode 100644 index 8ca0f29a389..00000000000 --- a/Master/texmf-dist/doc/latex/bclogo/bcdbelgique.pdf +++ /dev/null diff --git a/Master/texmf-dist/doc/latex/bclogo/bcdfrance.eps b/Master/texmf-dist/doc/latex/bclogo/bcdfrance.eps deleted file mode 100644 index fdadd41df69..00000000000 --- a/Master/texmf-dist/doc/latex/bclogo/bcdfrance.eps +++ /dev/null @@ -1,2414 +0,0 @@ -%!PS-Adobe-2.0 EPSF-2.0 -%%Creator: dvips(k) 5.96dev Copyright 2007 Radical Eye Software -%%Title: CompileEps.dvi -%%CreationDate: Sat Sep 19 14:16:28 2009 -%%BoundingBox: 71 693 90 721 -%%EndComments -%DVIPSWebPage: (www.radicaleye.com) -%DVIPSCommandLine: dvips -E -o -%+ C:\Users\Alain_2\Documents\LaTeX\Logos\bcdfrance.eps CompileEps.dvi -%DVIPSParameters: dpi=600 -%DVIPSSource: TeX output 2009.09.19:1416 -%%BeginProcSet: tex.pro 0 0 -%! -/TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S -N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 -mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 -0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ -landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize -mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ -matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round -exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ -statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] -N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin -/FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array -/BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 -array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N -df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A -definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get -}B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} -B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr -1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S -/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy -setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask -restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn -/BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put -}if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ -bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A -mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ -SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ -userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X -1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 -index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N -/p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ -/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) -(LaserWriter 16/600)]{A length product length le{A length product exch 0 -exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse -end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask -grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} -imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round -exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto -fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p -delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} -B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ -p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S -rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end - -%%EndProcSet -%%BeginProcSet: pstricks.pro 0 0 -% $Id: pstricks.pro 34 2008-06-25 17:20:01Z herbert $ -% -%% PostScript prologue for pstricks.tex. -%% Version 1.05, 2008/06/25 -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -% -% -% Define the follwing gs-functions if not known, eg when using distiller -% -systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if -systemdict /.setblendmode known not {/.setblendmode { pop } def } if -systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if -% -/tx@Dict 200 dict def % the main PSTricks dictionary -tx@Dict begin -/ADict 25 dict def % The arrow dictionaray -/CM { matrix currentmatrix } bind def -/SLW /setlinewidth load def -/CLW /currentlinewidth load def -/CP /currentpoint load def -/ED { exch def } bind def -/L /lineto load def -/T /translate load def -/TMatrix { } def -/RAngle { 0 } def -/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments -/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known -/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) -/Div { dup 0 eq { pop } { div } ifelse } def % control the division -/tan { dup cos abs 1.e-10 lt - { pop 1.e10 } % return 1.e10 as infinit - { dup sin exch cos div } ifelse % default sin/cos -} def -/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees -/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root - pop pop 0 }{ sqrt exch atan} ifelse } def -/NET { neg exch neg exch T } def % change coordinate system to the negative one -/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter -/Pyth2 { % Pythagoras, xA yA xB yB - 3 -1 roll % xA xB yB yA - sub % xA xB yB-yA - 3 1 roll % yB-yA xA xB - sub % yB-yA xA-xB - Pyth } def -/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian -/Rand { rand 4294967295 div } def % a real random number -%----------------- hv added 20050516 --------------- -/PiDiv2 1.57079632680 def -/Pi 3.14159265359 def -/TwoPi 6.28318530718 def -/Euler 2.71828182846 def -%/e Euler bind def -/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees -/DegtoRad { Pi mul 180 div } bind def % viceversa -%----------------- hv end--------------------------- -/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def -/PathLength { - flattenpath /z 0 def - { /y1 ED /x1 ED /y2 y1 def /x2 x1 def } - { /y ED /x ED PathLength@ } - {} - { /y y2 def /x x2 def PathLength@ } - /pathforall load stopped { pop pop pop pop } if - z -} def -% -/STP { .996264 dup scale } def % BP/PT scaling -/STV { SDict begin normalscale end STP } def % -% -%%-------------- DG begin patch 15 ---------------%% -%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def -%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y -%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul -%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] -%0 } ifelse setdash stroke } def -/DashLine { - dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse - /b ED /x1 ED /y1 ED /x ED /y ED - /z y x add y1 add x1 add def - /Coef b a .5 sub 2 mul y mul sub z Div round - z mul a .5 sub 2 mul y mul add b exch Div def - /y y Coef mul def - /x x Coef mul def - /y1 y1 Coef mul def - /x1 x1 Coef mul def - x1 0 gt y1 0 gt or x 0 gt or y 0 gt and - { [ y x y1 x1 ] 1 a sub y mul } - { [ 1 0 ] 0 } ifelse - setdash stroke -} def -%%-------------- DG end patch 15 ---------------%% -/DotLine { - /b PathLength def - /a ED /z ED /y CLW def - /z y z add def - a 0 gt { - /b b a div def - }{ - a 0 eq { - /b b y sub def - }{ a -3 eq { - /b b y add def } if - } ifelse - } ifelse - [ 0 b b z Div round Div dup 0 le { pop 1 } if ] - a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse - setdash 1 setlinecap stroke -} def -% -/LineFill { % hv ------------ patch 7 ------------- - gsave - abs /hatchWidthInc ED - abs /hatchSepInc ED - abs CLW add /a ED - a 0 dtransform round exch round exch - 2 copy idtransform - exch Atan rotate - idtransform pop /a ED - .25 .25 itransform pathbbox - /y2 ED - a Div ceiling cvi /x2 ED /y1 ED - a Div cvi /x1 ED /y2 y2 y1 sub def - clip - newpath - 2 setlinecap - systemdict - /setstrokeadjust known { true setstrokeadjust } if - x2 x1 sub 1 add { - x1 a mul y1 moveto 0 y2 rlineto stroke - /x1 x1 1 add - hatchWidthInc 0 gt { CLW add } if - def - hatchSepInc 0 gt hatchWidthInc 0 gt or { - /a a hatchSepInc add def - CLW hatchWidthInc add SLW - } if - } repeat - grestore - pop pop } def -% -/PenroseFill {% on stack: scaling factor - dup dup scale - 1 exch div round /penroseFactor ED - a 0 dtransform round exch round exch - 2 copy idtransform - exch Atan rotate - idtransform pop /a ED - .25 .25 itransform pathbbox - /y2 ED - a Div ceiling cvi /x2 ED /y1 ED - a Div cvi /x1 ED /y2 y2 y1 sub def - clip - newpath - systemdict - /setstrokeadjust known { true setstrokeadjust } if - /I/S/L/W/G/+/Z/F/E/D[/def/exch/for{E D}/add{s E get mul} - { Z -36.2001 1 33 }{25 E S rlineto}{/q Z dup q G E q 1 + G}{Z 2 2}]{cvx def}forall - [0 72 1008 {dup sin E cos }F ]1 setlinejoin/s W{/a W{/b I 10{/i I 4{/m I moveto - i m +/j I 10{/l Z b m l + G a l G sub s m get div .2 + floor .3 + 25 - mul j l + S rmoveto}F i L j L stroke }F}F}F}F - grestore - pop pop -} def -% -%gsave abs CLW add /a ED a 0 dtransform round exch round exch -%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 -%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 -%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a -%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a -%% DG/SR modification end -%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict -%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 -%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) -%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } -%% def -%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore -%pop pop } def -%% DG/SR modification end -% -/BeginArrow { - ADict begin % hold it local, for end see EndArrow - /@mtrx CM def - gsave - 2 copy T - 2 index sub neg exch - 3 index sub exch Atan - rotate newpath -} def -% -/EndArrow { @mtrx setmatrix CP grestore end } def % end the ADict -% -/Arrow { - CLW mul add dup - 2 div /w ED - mul dup /h ED - mul /a ED - { 0 h T 1 -1 scale } if - w neg h moveto - 0 0 L w h L w neg a neg rlineto - gsave fill grestore -} def -% -/ArrowD { % the sides are drawn as curves (hv 20071211) - CLW mul add dup - 2 div /w ED - mul dup /h ED - mul /Inset ED - { 0 h T 1 -1 scale } if % changes the direction -% we use y=w/h^2 * x^2 as equation for the control points -% for the coordinates the arrow is seen from top to bottom -% the bottom (tip) is (0;0) - w neg h moveto % lower left of > - w 9 div 4 mul neg h 3 div 2 mul - w 9 div neg h 3 div - 0 0 curveto % tip of > - w 9 div h 3 div - w 9 div 4 mul h 3 div 2 mul - w h curveto % upper left of > - w neg Inset neg rlineto % move to x=0 and inset - gsave fill grestore -} def -% -/Tbar { - CLW mul add /z ED - z -2 div CLW 2 div moveto - z 0 rlineto stroke - 0 CLW moveto -} def -% -/Bracket { - CLW mul add dup CLW sub 2 div - /x ED mul CLW add /y ED /z CLW 2 div def - x neg y moveto - x neg CLW 2 div L x CLW 2 div L x y L stroke - 0 CLW moveto -} def -% -/RoundBracket { - CLW mul add dup 2 div - /x ED mul /y ED /mtrx CM def - 0 CLW 2 div T x y mul 0 ne { x y scale } if - 1 1 moveto - .85 .5 .35 0 0 0 curveto - -.35 0 -.85 .5 -1 1 curveto - mtrx setmatrix stroke 0 CLW moveto -} def -% -/SD { 0 360 arc fill } def -% -/EndDot { % DS is the dot size - { /z DS def } { /z 0 def } ifelse - /b ED 0 z DS SD b { 0 z DS CLW sub SD } if - 0 DS z add CLW 4 div sub moveto } def -% -/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { - /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto - load } if ] cvx newpath 3 1 roll T exec } def -% -%/NArray { -% aload length 2 div dup dup cvi eq not { exch pop } if /n exch -% cvi def -%} def -% -/NArray { % holds the coordinates and on top of stack the showpoints boolean - /showpoints ED - counttomark 2 div dup cvi /n ED - n eq not { exch pop } if - showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse -} def -% -/Line { - NArray n 0 eq not - { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def - n { Lineto } repeat - CP 4 2 roll ArrowB L pop pop - } if -} def -% -/Arcto { - /a [ 6 -2 roll ] cvx def - a r - /arcto load stopped { 5 } { 4 } ifelse { pop } repeat - a -} def -% -/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq - and { pop pop /n n 1 sub def } if } def -/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } - repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 - ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 - moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto - Lineto pop pop closepath } ifelse } def -/Diamond { - /mtrx CM def - T rotate - /h ED - /w ED - dup 0 eq { pop } { CLW mul neg - /d ED - /a w h Atan def - /h d a sin Div h add def - /w d a cos Div w add def } ifelse - mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div - /ArrowA { moveto } def - /ArrowB { } def - false Line - closepath mtrx setmatrix } def -% DG modification begin - Jan. 15, 1997 -%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { -%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 -%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 -%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx -%setmatrix } def -/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup -CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 -div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 -d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx -% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) -% setmatrix } def -setmatrix pop } def -% DG/SR modification end -% -/CCA { - /y ED /x ED - 2 copy y sub /dy1 ED - x sub /dx1 ED - /l1 dx1 dy1 Pyth def -} def -% -/CC { - /l0 l1 def - /x1 x dx sub def - /y1 y dy sub def - /dx0 dx1 def - /dy0 dy1 def - CCA - /dx dx0 l1 c exp mul dx1 l0 c exp mul add def - /dy dy0 l1 c exp mul dy1 l0 c exp mul add def - /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def - /x2 x l0 dx mul m mul sub def - /y2 y l0 dy mul m mul sub def - /dx l1 dx mul m mul neg def - /dy l1 dy mul m mul neg def -} def -% -/IC { - /c c 1 add def - c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse - /a a 2 mul 3 div 45 cos b exp div def - CCA - /dx 0 def - /dy 0 def -} def -% -/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def -/NC { CC x1 y1 x2 y2 x y curveto } def -/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def -/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def -/NAC { x2 y2 x y curveto CC x1 y1 } def -/EAC { x2 y2 x y ArrowB curveto pop pop } def -% -/OpenCurve { - NArray n 3 lt - { n { pop pop } repeat } - { BOC /n n 3 sub def n { NC } repeat EOC } ifelse -} def -% -/AltCurve { - { false NArray n 2 mul 2 roll - [ n 2 mul 3 sub 1 roll ] aload - /Points ED - n 2 mul -2 roll } - { false NArray } ifelse - n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse -} def -% -/ClosedCurve { - NArray n 3 lt - { n { pop pop } repeat } - { n 3 gt { CheckClosed } if - 6 copy n 2 mul 6 add 6 roll - IC CC x y moveto n { NC } repeat - closepath pop pop - } ifelse -} def -% -/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def -/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def -/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } -def -/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix -rotate matrix concatmatrix exch findfont exch makefont setfont } def -/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto -x1 y1 lineto closepath } def -/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 -y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div -exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse -/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto -x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } -ifelse } def -/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add -/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { -pop pop Rect } { OvalFrame } ifelse } def -% -/BezierNArray { - /f ED - counttomark 2 div dup cvi /n ED - n eq not { exch pop } if - n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat - f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse -} def -% -/OpenBezier { - BezierNArray - n 1 eq - { pop pop } - { ArrowA n 4 sub 3 idiv - { 6 2 roll 4 2 roll curveto } repeat - 6 2 roll 4 2 roll ArrowB curveto } ifelse -} def -% -/ClosedBezier { - BezierNArray - n 1 eq - { pop pop } - { moveto n 1 sub 3 idiv - { 6 2 roll 4 2 roll curveto } repeat - closepath } ifelse -} def -% -/BezierShowPoints { - gsave - Points aload length 2 div cvi /n ED - moveto - n 1 sub { lineto } repeat - CLW 2 div SLW [ 4 4 ] 0 setdash stroke - grestore -} def -% -/Parab { - /y0 ED /x0 ED /y1 ED /x1 ED - /dx x0 x1 sub 3 div def - /dy y0 y1 sub 3 div def - x0 dx sub y0 dy add x1 y1 ArrowA - x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB - curveto - /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def -} def -% -/Grid { - newpath - /a 4 string def - /b ED /c ED /n ED - cvi dup 1 lt { pop 1 } if - /s ED - s div dup 0 eq { pop 1 } if - /dy ED s div dup 0 eq { pop 1 } if - /dx ED dy div round dy mul - /y0 ED dx div round dx mul - /x0 ED dy div round cvi - /y2 ED dx div round cvi - /x2 ED dy div round cvi - /y1 ED dx div round cvi - /x1 ED - /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def - /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def - b 0 gt { - /z1 b 4 div CLW 2 div add def -% /Helvetica findfont b scalefont setfont - /b b .95 mul CLW 2 div add def } if - systemdict /setstrokeadjust known - { true setstrokeadjust /t { } def } - { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add - exch itransform } bind def } ifelse - gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse - /i x1 def - /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def - /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def - x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if - { i dx mul dup y0 moveto - b 0 gt - { gsave c i a cvs dup stringwidth pop - /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse - h 0 gt {b neg}{z1} ifelse - rmoveto show grestore } if - dup t f moveto - g t L stroke - /i i w add def - } repeat - grestore - gsave - n 0 gt - % DG/SR modification begin - Nov. 7, 1997 - Patch 1 - %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } - { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } - % DG/SR modification end - { 2 setlinecap } ifelse - /i y1 def - /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def - /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def - y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if - { newpath i dy mul dup x0 exch moveto - b 0 gt { gsave c i a cvs dup stringwidth pop - /z2 ED - w 0 gt {z1 z2 add neg} {z1} ifelse - h 0 gt {z1} {b neg} ifelse - rmoveto show grestore } if - dup f exch t moveto - g exch t L stroke - /i i h add def - } repeat - grestore -} def -% -/ArcArrow { - /d ED /b ED /a ED - gsave - newpath 0 -1000 moveto clip - newpath - 0 1 0 0 b - grestore - c mul - /e ED - pop pop pop r a e d PtoC y add exch x add - exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c - mul neg d -} def -% -/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def -% -/ArcAdjust { %%%% Vincent Guirardel -% given a target length (targetLength) and an initial angle (angle0) [in the stack], -% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). -% This computes an angle t such that (x0,y0) is at distance -% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). -% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 -% contrary to TvZ's code. -% To achieve, this, one iterates the following process: start with some angle t, -% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. -% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. -% -% Another difference with TvZ's code is that we need d (=add/sub) to be defined. -% the value of d = add/sub is used to know on which side we have to move. -% It is only used in the initialisation of the angle before the iteration. -% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% Input stack: 1: target length 2: initial angle -% variables used : rx, ry, d (=add/sub) -% - /targetLength ED /angle0 ED - /x0 rx angle0 cos mul def - /y0 ry angle0 sin mul def -% we are looking for an angle t such that (x0,y0) is at distance targetLength -% from the point M(t)=(rx*cos(t),ry*sin(t))) -%initialisation of angle (using 1st order approx = TvZ's code) - targetLength 57.2958 mul - angle0 sin rx mul dup mul - angle0 cos ry mul dup mul - add sqrt div -% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees -% (if the ellipse is very curved at the point where we draw the arrow, % -% the value can be much more than 360 degrees !) -% this should avoid going on the wrong side (more than 180 degrees) or go near -% a bad attractive point (at 180 degrees) - dup 90 ge { pop 90 } if - angle0 exch d % add or sub -% maximum number of times to iterate the iterative procedure: -% iterative procedure: takes an angle t on top of stack, computes a -% better angle (and put it on top of stack) - 30 { dup -% compute distance D between (x0,y0) and M(t) - dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt -% if D almost equals targetLength, we stop - dup targetLength sub abs 1e-5 le { pop exit } if -% stack now contains D t -% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: -% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) - exch dup cos rx mul x0 sub exch sin ry mul y0 sub -% stack contains: y(t)-y0, x(t)-x0, d - 2 index Div targetLength mul y0 add ry Div exch - 2 index Div targetLength mul x0 add rx Div -% stack contains x(t')/rx , y(t')/ry , d -% now compute t', and remove D from stack - atan exch pop - } repeat -% we don't look at what happened... in particular, if targetLength is greater -% than the diameter of the ellipse... -% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... -% after iteration, stack contains an angle t such that M(t) is the tail of the arrow -% to give back the result as a an angle relative to angle0 we could add the following line: -% angle0 sub 0 exch d -% -% begin bug fix 2006-01-11 -% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 -%(we don't want to make the ellipse turn more or less than it should)... -dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse -% end bug fix -} def -% -/EllipticArcArrow { - /d ED % is add or sub - /b ED % arrow procedure - /a1 ED % angle - gsave - newpath - 0 -1000 moveto - clip % Set clippath far from arrow. - newpath - 0 1 0 0 b % Draw arrow to determine length. - grestore -% Length of arrow is on top of stack. Next 3 numbers are junk. -% - a1 exch ArcAdjust % Angular position of base of arrow. - /a2 ED - pop pop pop - a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig - a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig - a1 cos rx mul xOrig add % - a1 sin ry mul yOrig add % -% Now arrow tip coor and base coor are on stack. - b pop pop pop pop % Draw arrow, and discard coordinates. - a2 CLW 8 div -% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) - 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse - ArcAdjust -% resets original value of d - 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. -} def -%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% -% -/Rot { CP CP translate 3 -1 roll neg rotate NET } def -% -/RotBegin { - tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if - /TMatrix [ TMatrix CM ] cvx def - /a ED - a Rot /RAngle [ RAngle dup a add ] cvx def -} def -% -/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def -% -/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def -/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def -/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def -/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s -abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b -div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { -h1 abs h sub dup s mul abs } ifelse } def -/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s -mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q -{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add -exch } def -/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible -/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def -} if } ifelse } def -/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def -/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit -neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def -/IfVisible true def } def -end -%-----------------------------------------------------------------------------% - -% END pstricks.pro - -%%EndProcSet -%%BeginProcSet: pst-algparser.pro 0 0 -% $Id: pst-algparser.pro 26 2008-06-14 11:50:02Z herbert $ -%% -%% PostScript prologue for PSTricks algorithm parser -%% Version 0.01, 2008/01/01 -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -%% -%%-----------------------------------------------------------------------------% -% -/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez -% -/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin -% -% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 -% E->T|E+T -% T->FS|T*FS -% FS -> F | +FS | -FS -% F->P|F^SF -% P->(E)|literal -% literal->number|var|var[E]|func(params) -% params->E|E,param -% number->TOBEFINISHED -% -%% E expression, T term, SF signed factor, F factor, P power -% -%% parser -% -%% str -% -%% C->E<condition_operators>E -%% STR index -> STR index+lenExpr -/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def -% -%% analyze Expression List (separator , or | ) -%% STR index -> STR index+lenExpr -%% /AnalyzeListOfE { -%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar -%% NextNonBlankChar dup 0 eq { pop exit } if -%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if -%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop -%% AnalyzeListOfEPostHook -%% } def -/AnalyzeListOfE { - /NotFirst false def - { NextNonBlankChar pop AnalyzeExpr - NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse - dup Strlen eq { exit } if NextNonBlankChar - dup 44 ne 1 index 124 ne and - { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } - if pop 1 add } loop - AnalyzeListOfEPostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% E->T|E+T -%% STR index -> STR index+lenExpr -/AnalyzeExpr { - AnalyzePreHook AnalyzeTerm IsEndingExpr - { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } - { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } - ifelse - AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% T->FS|T*FS -%% STR index -/AnalyzeTerm { - AnalyzePreHook AnalyzeSignedFactor IsEndingTerm - { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } - { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } - ifelse - AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% FS -> F | +FS | -FS -%% STR index -/AnalyzeSignedFactor { - AnalyzePreHook 2 copy get dup IsUnaryOp - { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } - { pop AnalyzeFactor } - ifelse AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% F->P|F^P -%% STR index -/AnalyzeFactor { - AnalyzePreHook AnalyzePower IsEndingFactor - { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } - { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } - ifelse AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% P->(E)|literal -%% STR index -/AnalyzePower { - %% depending of first char either a number, or a literal - 2 copy get dup 40 eq%%an open par - { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } - { AnalyzeLiteral } - ifelse -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index STR[index] -> STR index -%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def -/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% recognize + or - -%% chr -> T/F -/IsUnaryOp { dup 43 eq exch 45 eq or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a number can contain only : 0123456789. -%% chr -> T/F -/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index -> STR index number -%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? -%% STR index -> STR index' number -/ReadNumber { - exch dup 3 -1 roll dup 3 1 roll - %%read mantissa - { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop - dup 101 eq exch 69 eq or - %%% there is a "e" or "E" -> read exponant - { 1 add 2 copy get dup IsUnaryOp - { pop 1 add 2 copy get } if - { IsNumber not { exit } if 1 add 2 copy get } loop } - if - dup 4 1 roll - 3 -1 roll exch 1 index sub getinterval -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a number can contain only : 0123456789. -%% chr -> T/F -/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index -> STR index number -%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? -%% STR index -> STR index' number -/ReadCondOp { - NextNonBlankChar 1 index 4 1 roll - { IsCondOp not { exit } if 1 add 2 copy get } loop - 2 copy 5 -1 roll - exch 1 index sub getinterval 3 1 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a literal can contain only : 0123456789. -%% chr -> T/F -/IsLiteral {% - dup 48 ge exch dup 57 le 3 -1 roll and exch - dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch - dup 97 ge exch 122 le and or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? -%% STR index -> literal STR index' nextchr -/ReadLiteral { - exch dup 3 -1 roll dup 3 1 roll - %%read literal core - { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop - 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or a clpar -%% STR index -> STR index STR[index] T/F -/IsEndingExpr {% - 2 copy dup Strlen eq - %% if end of str is reached -> end ! - { pop pop 0 true } - %% ending chr -> clpar, comma, |, <, >, =, !, - {get dup dup 41 eq - exch dup 124 eq - exch dup 93 eq - exch dup 44 eq - exch dup 30 eq - exch dup 60 ge exch 62 le and or or or or or} - ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or a +- -%% STR index -> STR index STR[index] T/F -/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or */ -%% STR index -> STR index STR[index] T/F -/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or ^ -%% STR index -> STR index STR[index] T/F -/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index -> STR index STR[index] -/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def -/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def -%%%%%%%%%%%%%%%%%%%%%%%% -%% DEBUG -/BRK {false} def -/BRKtrue {/BRK true def} def -/BRKStop {BRK {BRKtoto} if } def -/BRKEvalStop {BRK exch if } def -/BRKBRK2true {BRK {BRK2true} if } def -/BRK2 {false} def -/BRK2true {/BRK2 true def} def -/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def -end -% -%-------------------------------------------------------------------------------% -% -/tx@AlgToPs 12 dict def tx@AlgToPs begin -% -%% algExpr -> PSVector -/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def -/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def -/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def -/Strlen 0 def -/EvalListOfExpr {} def% -/EvalNumber {% - ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx - exch 1 add array astore def NextNonBlankChar pop } def -/EvalAddSub {% - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll - 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def -} def -/EvalMulDiv {% - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll - 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def -} def -/EvalPower {% - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll - pop /exp cvx exch 1 add array astore def -} def -/EvalLiteral {% - ReadLiteral - dup 40 eq%%% there is an open par -> function call - { pop 2 index - dup (Sum) eq { EvalSum } - { dup (IfTE) eq { EvalCond } - { dup (Derive) eq { pop EvalDerive } - { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx - exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } - { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def - dup 91 eq%%% there is an open bracket -> vector element - { pop 1 add NextNonBlankChar pop AnalyzeExpr - /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } - { pop NextNonBlankChar pop } - ifelse} - ifelse -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% the derive function : Derive(n,f(x)) -%% firstparindex lastparindex -> -/EvalDerive { - %% manage the function descripiton - 1 add ReadNumber 3 1 roll NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - 1 add NextNonBlankChar pop - 3 -1 roll cvi - dup 0 eq - { pop AnalyzeExpr 3 -1 roll pop 1 add } - { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll - { (x) tx@Derive begin Derive end } repeat - ExpressionVector exch /ExpressionVector [] def - AlgToPs aload length - /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def - l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add - 1 index length /Strlen exch def } ifelse -} def -/EvalSum {% - pop 1 add NextNonBlankChar pop - %% read the variable name - ReadLiteral pop NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if - %% read the initial value - 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - %% read the increment value - 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - %% read the limit value - 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll - 5 -1 roll 4 add array astore def - %% keep ExpressionVector for later and create a new one for internal Sum computation - ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def - 1 add NextNonBlankChar pop AnalyzeExpr - %% add each term - /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def - /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add - array astore def 3 -1 roll pop 1 add -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Convert to radians if trigo function call -%% (name) -> -/TrigoFunc { - dup (cos) eq 1 index (sin) eq or exch (tan) eq or - { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add - array astore def - } if -} def -/EvalCond {% - pop 1 add AnalyzeCond NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if - ExpressionVector 3 1 roll /ExpressionVector [] def - 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def - NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if - 1 add AnalyzeExpr - NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if - ExpressionVector - /ExpressionVector 6 -1 roll aload length dup - 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def - 1 add 3 -1 roll pop -} def -%% CondOp STR index -/EvalCondOp {% - 3 -1 roll - dup (=) eq { /eq } {% - dup (<) eq { /lt } {% - dup (>) eq { /gt } {% - dup (>=) eq { /ge } {% - dup (<=) eq { /ge } {% - dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } - ifelse } ifelse } ifelse } ifelse } ifelse } ifelse - cvx exch pop - /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def -/EvalUnaryOp { - 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% H O O K S -/AnalyzePreHook {} bind def -/PreEvalHook {} bind def -/AnalyzeListOfEPostHook {} bind def -/AnalyzePostHook {} def -/RollOp { 3 1 roll } bind def -end %tx@CoreAnalyzerDict -% -%--------------------------------------------------------------------% -% -/tx@Derive 41 dict def tx@Derive begin -%%increase ^^ for each function added -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% algExpr variable -> PSVector -/Derive {% - 10240 string 3 1 roll 0 3 1 roll - /Variable exch def - tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end -} def -/Strlen 0 def -/InitParser { dup length /Strlen exch def 0 } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% algExpr variable index -> PSVector -/DeriveIndexed {% - 3 1 roll 10240 string 3 1 roll 0 3 1 roll - /Variable exch def - tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u,v)'=-(u',v') -/EvalListOfExpr {% - 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe - 2 copy 7 -1 roll dup length 4 1 roll putinterval add - 6 -2 roll pop pop - 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (-u)'=-(u') -/EvalUnaryOp { - 4 -2 roll 4 index (0) eq - { (0) StrConcat 7 -1 roll pop } - { 7 -1 roll 45 eq - { AddSub AddOpPar true } { false } ifelse - 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (number)'=0 -/EvalNumber { ReadNumber (0) 6 2 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u+v)'=u'+v' -/EvalAddSub {% - 7 index dup (0) eq - { pop true }%% du=0 nothing added - { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } - ifelse - 5 index dup (0) eq - { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 - { exch - { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added - { 5 -2 roll 7 index 43 eq%%something yet added - { AddAdd false } { AddSub AddOpPar true } ifelse } - ifelse 11 1 roll - 3 -1 roll StrConcat 10 -1 roll { AddClPar } if - 2 copy pop 0 6 2 roll GetIntervalNewStr } - ifelse - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u*v)' or (u/v)' -/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u*v)'=u'*v+u*v' -/EvalMul {% - 4 -2 roll 7 index dup (0) eq - { pop false }%%du=0 - { (1) eq%%du=1 - { false } - { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse - 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if - true }%%du!=0 - ifelse - 5 1 roll 5 index (0) eq - { 5 -1 roll not { (0) StrConcat } if }%%dv=0 - { 5 -1 roll { AddAdd } if - 4 index (1) eq - { 8 index StrConcat } - { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } - ifelse - }%%dv!=0 - ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u/v)'=(u'*v-u*v')/v^2 -/EvalDiv {% - 4 -2 roll - 4 index (0) eq%%dv=0 -> u'/v - { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } - { 7 index dup (0) eq - { pop }%%du=0 - { (1) eq%%du=1 - { false } - { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse - 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 - ifelse - AddSub - 4 index (1) eq - { 8 index StrConcat } - { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } - ifelse - %}%%dv!=0 - 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar - AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } - ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% str1 index str2 -> str1 index -/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def -/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) -/EvalPower {% - 4 -2 roll 7 index (0) eq - {%%if du=0 then (u^v)'=v'ln(u)u^v - 4 index (0) eq - { (0) StrConcat }%%if dv=0 then (u^v)'=0 - { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if - 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if - AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse - } - {%%du!=0 - 4 index (0) eq - {%%if dv=0 then (u^v)'=vu'u^(v-1) - 5 index dup IsStrNumber - { dup (0) eq - { StrConcat } - { dup dup (1) eq exch (1.0) eq or - { StrConcat } - { StrConcat - 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 - { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 - (*\() StrConcat 8 index StrConcat (\)) StrConcat - 5 index dup dup (2) eq exch (2.0) eq or - { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } - { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat - 5 index StrConcat (-1\)) StrConcat } ifelse - } - {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) - 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if - AddOpPar 5 index StrConcat (\)*\() StrConcat - 8 index StrConcat (\)^\() StrConcat - 5 index StrConcat (-1\)+\() StrConcat - 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if - 8 index StrConcat (\)^\() StrConcat - 5 index StrConcat (\)*ln\() StrConcat - 8 index StrConcat AddClPar - } ifelse - } ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% str -> true/false -/IsStrNumber {% - true exch - { dup 48 lt exch dup 57 gt 3 -1 roll or - exch dup 46 ne%%. - exch dup 43 ne%%+ - exch 45 ne%%- - and and and { pop false } if } forall -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% literal switch -> func call, vector, variables -/EvalLiteral {% - ReadLiteral dup 40 eq%%% there is an open par -> function call - { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } - { dup 91 eq%%% there is an open bracket -> vector element - { ERROR_vector_not_yet_implemented } - { pop EvalVariable } - ifelse } - ifelse -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% first last parpos Expr[first:parpos-1] -> -/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (f(u))'=u'f'(u) -/EvalFunc { - 4 2 roll 4 index (1) ne - { AddOpPar 4 index StrConcat (\)*) StrConcat } if - (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Func derivative -> Eval<func> -/EvalFunc_sin {% - PreCommonFunc - { (cos\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_cos {% - PreCommonFunc - { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_tan {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if - PostCommonFunc } def -/EvalFunc_asin {% - PreCommonFunc - { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_acos {% - PreCommonFunc - { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_atg {% - PreCommonFunc - { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_ln {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_exp {% - PreCommonFunc - { (exp\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_sqrt {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_Fact {% - PreCommonFunc { ERROR_no_variable_expression_in_Fact } if - PostCommonFunc } def -/EvalFunc_sh {% - PreCommonFunc - { (ch\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_ch {% - PreCommonFunc - { (sh\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_th {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if - PostCommonFunc } def -/EvalFunc_Argsh {% - PreCommonFunc - { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_Argch {% - PreCommonFunc - { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_Argth {% - PreCommonFunc - { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -/PreCommonFunc { - 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop - 4 2 roll 4 index (0) eq - { (0) StrConcat false } - { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse -} def -/PostCommonFunc { - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -/EvalFunc_Derive {% - 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs - 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add - 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar - 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval - exch 6 2 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% literal switch -> func call, vector, variables -/EvalFunc_Sum {% - 1 add NextNonBlankChar pop - %% read the variable name - ReadLiteral pop 3 -1 roll pop NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if - %% read the initial value - 1 add NextNonBlankChar pop ReadNumber pop - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - %% read the increment value - 1 add NextNonBlankChar pop ReadNumber pop - 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if - %% read the limit value - 1 add NextNonBlankChar pop ReadNumber pop - 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if - 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop - 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat - 4 index StrConcat AddClPar - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% literal switch -> func call, vector, variables -/EvalFunc_IfTE {% - 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond - NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if - 1 add NextNonBlankChar pop dup 5 1 roll - AnalyzeExpr NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if - 1 add NextNonBlankChar pop - AnalyzeExpr 1 add NextNonBlankChar pop - 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat - 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% advance in str until a comma is found (no error detection!) -%% str index -> str index' -/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Convert to radians if trigo function call -%% (name) -> -/TrigoFunc { - dup (cos) eq 1 index (sin) eq or exch (tan) eq or - { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add - array astore def - } if -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% No derivative for condition.... -/EvalCondOp { 3 -1 roll pop } bind def -/PutIntervalOneAdd {putinterval 1 add} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add open parenthesis in string at the given index -%% str index -> str index+1 -/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add close parenthesis in string at the given index -%% str index -> str index+1 -/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add 0 in string at the given index -%% str index -> str index+1 -/AddZero {2 copy (0) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add open parenthesis in string at the given index -%% str index -> str index+1 -/AddMul {2 copy (*) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add open parenthesis in string at the given index -%% str index -> str index+1 -/AddDiv {2 copy (/) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add a plus sign in string at the given index -%% str index -> str index+1 -/AddAdd {2 copy (+) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add a minus sign in string at the given index -%% str index -> str index+1 -/AddSub {2 copy (-) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add a pipe sign in string at the given index -%% str index -> str index+1 -/AddPipe {2 copy (|) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% H O O K S -/AnalyzePreHook { dup 5 1 roll } bind def -/PreEvalHook {} def -/AnalyzePostHook { 7 -1 roll pop } bind def -/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def -/RollOp { 5 1 roll } bind def -end%%%tx@CoreAnalyzerDict -/tx@AddMathFunc 12 dict def tx@AddMathFunc begin -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% NEW FUNC -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) -%% x -> theta -/asin {% - dup abs 1 gt { EQDFasinrangeerror } if - dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad -} def -%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) -%% x -> theta -/acos {% - dup abs 1 gt { EQDFacosrangeerror } if - dup dup mul 1 exch sub sqrt exch atan DegtoRad -} def -%% function arctangent in radians -%% x -> theta -/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def -%% HYPERBOLIC FUNCTIONS -/sh { dup Ex exch neg Ex sub 2 div } def -/ch { dup Ex exch neg Ex add 2 div } def -/th { dup sh exch ch div } def -/Argsh { dup dup mul 1 add sqrt add ln } def -/Argch { dup dup mul 1 sub sqrt add ln } def -/Argth { dup 1 add exch 1 exch sub div ln 2 div } def -%% modified exponential funtion for 0 -%% x n -> x^n -/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def -%% modified exponential funtion for 0 -%% x -> e^x -/Ex { Euler exch exp } bind def -%% -%% factorial function -%% n -> n! -/Fact { 1 exch 2 exch 1 exch { mul } for } bind def -/fact { Fact } bind def -end - -% END pstricks.pro - -%%EndProcSet -%%BeginProcSet: pst-dots.pro 0 0 -% $Id: pst-dots.pro 26 2008-06-14 11:50:02Z herbert $ -% -%% PostScript prologue for pstricks.tex. -%% Version 2.02, 2008/04/18 -%% -%% For distribution, see pstricks.tex. -%% -%% Timothy Van Zandt <tvz@Princeton.EDU> -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -%% -%% Modified by Etienne Riga - Dec. 16, 1999 -%% Modified by Etienne Riga - 2005/01/01 (er) -%% to add /Diamond, /SolidDiamond and /BoldDiamond -%% Modified by Herbert Voss (hv) - 2008/04/17 -% -10 dict dup begin % hold local - /FontType 3 def - /FontMatrix [.001 0 0 .001 0 0] def - /FontBBox [-571.5 -742.5 571.5 742.5] def -% /FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph - /Encoding 256 array def - 0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef - Encoding % replace with given dot names - dup (b) 0 get /Bullet put % get the numerical position of b in ASCII -% % and save /Bullet at this place in Encoding - dup (c) 0 get /Circle put - dup (C) 0 get /BoldCircle put % 67 - dup (u) 0 get /SolidTriangle put - dup (t) 0 get /Triangle put - dup (T) 0 get /BoldTriangle put - dup (r) 0 get /SolidSquare put - dup (s) 0 get /Square put - dup (S) 0 get /BoldSquare put - dup (q) 0 get /SolidPentagon put - dup (p) 0 get /Pentagon put - dup (P) 0 get /BoldPentagon put -%%% - dup (k) 0 get /Asterisk put - dup (K) 0 get /BoldAsterisk put - dup (J) 0 get /SolidAsterisk put - dup (h) 0 get /Hexagon put - dup (H) 0 get /BoldHexagon put - dup (G) 0 get /SolidHexagon put - dup (f) 0 get /Octogon put % 2008-04-18 hv - dup (F) 0 get /BoldOctogon put % 2008-04-18 hv - dup (g) 0 get /SolidOctogon put % 2008-04-18 hv - dup (a) 0 get /Add put - dup (A) 0 get /BoldAdd put % 65 - dup (x) 0 get /Mul put - dup (X) 0 get /BoldMul put - dup (m) 0 get /Oplus put - dup (M) 0 get /BOplus put - dup (e) 0 get /SolidOplus put - dup (n) 0 get /Otimes put - dup (N) 0 get /BOtimes put - dup (E) 0 get /SolidOtimes put - dup (i) 0 get /Bar put - dup (I) 0 get /BoldBar put - dup (l) 0 get /SolidDiamond put - dup (d) 0 get /Diamond put - (D) 0 get /BoldDiamond put -%%% -/CharProcs 47 dict def -CharProcs begin - /CirclePath {0 0 500 0 360 arc closepath} def - /Bullet {CirclePath fill} def - /Circle {CirclePath .9 .9 scale CirclePath eofill} def - /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def - /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def - /SolidTriangle {TrianglePath fill} def - /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def - /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def - /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def - /SolidSquare {SquarePath fill} def - /Square {SquarePath .89 .89 scale SquarePath eofill} def - /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def - /PentagonPath { - -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto - 0 574.7 lineto -546.6 177.6 lineto closepath - } def - /SolidPentagon {PentagonPath fill} def - /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def - /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def -%-------------- hv begin 2004/07/25 from: er 2003/03/24 - /HexagonPath { - 0 550 moveto -476 275 lineto -476 -275 lineto - 0 -550 lineto 476 -275 lineto 476 275 lineto closepath - } def - /SolidHexagon {HexagonPath fill} def - /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def - /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def -% 2008-04-18 hv - /OctogonPath { - 550 dup 22.5 tan mul dup neg dup add /xMove exch def - exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def - /SolidOctogon { OctogonPath fill } def - /Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def - /BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def -% - /AsteriskPath { - 20 0 moveto 10 250 180 500 0 500 curveto - -180 500 -10 250 -20 0 curveto closepath - } def - /Asterisk { - AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath - 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill - } def -% - /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def - /BoldAsteriskPath { - 50 30 cos 100 mul moveto Basterp - 60 rotate Basterp 60 rotate Basterp - 60 rotate Basterp 60 rotate Basterp - 60 rotate Basterp closepath - } def - /BoldAsterisk {BoldAsteriskPath fill} def - /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def - /CrossPath { - 40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto - -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto - 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath - } def - /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto - -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto - 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath - } def - /Add {CrossPath fill} def - /Mul {45 rotate CrossPath fill} def - /BoldAdd {BoldCrossPath fill} def - /BoldMul {45 rotate BoldCrossPath fill} def - /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def - /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def - /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def - /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def - /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def - /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def - /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def - /Bar {BarPath fill} def - /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def - /BoldBar {BoldBarPath fill} def - /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath} def - /SolidDiamond {DiamondPath fill} def - /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def - /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def -%%% - /.notdef { } def -end -% -/BuildGlyph { - exch - begin -% Metrics 1 index get exec 0 - 0 0 -% BBoxes 3 index get exec - -1000 -1000 1000 1000 -% -571.5 -742.5 571.5 742.5 - setcachedevice - CharProcs begin load exec end - end -} def -% -/BuildChar { - 1 index /Encoding get exch get - 1 index /BuildGlyph get exec -} bind def - -end -/PSTricksDotFont exch definefont pop - -%% end - -%%EndProcSet -%%BeginProcSet: pst-node.pro 0 0 -% $Id: pst-node.pro 26 2008-06-14 11:50:02Z herbert $ -%% -%% PostScript prologue for pst-node.tex. -%% Version 1.00, 2008/01/01. -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -% -/tx@NodeDict 400 dict def tx@NodeDict begin -tx@Dict begin % from main pstricks dict - /T /translate load def -end -/NewNode { % on stack: { x y } boolean N@name type InitXnode - gsave - /next ED % { x y } boolean N@name type - dict dup % { x y } boolean N@name dict dict - 3 1 roll def % { x y } boolean dict N@name dict def - exch { dup 3 1 roll def } if % { x y } dict boolean - begin % { x y } dict begin - tx@Dict begin - STV CP T exec % set scaling - end - /NodeMtrx CM def % save CM - next % InitXNode - end - grestore -} def -% -/InitPnode { - /Y ED /X ED - /NodePos { NodeSep Cos mul NodeSep Sin mul } def -} def -% -/InitCnode { - /r ED /Y ED /X ED - /NodePos { NodeSep r add dup Cos mul exch Sin mul } def -} def -% -/GetRnodePos { - Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse - Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse - dx Sin mul abs dy - Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse -} def -% -/InitRnode { - /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED - /NodePos { GetRnodePos } def -} def -% -/DiaNodePos { - w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup - Cos mul exch Sin mul -} def -% -/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h -mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul -} ifelse } def -/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d -ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d -sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan -sin def /NodePos { TriNodePos } def } def -/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos -hh mul Atan dup cos ww mul exch sin hh mul } def -/GetCenter { begin X Y NodeMtrx transform CM itransform end } def -% -/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist - Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } - { 0 Dist Sin mul } ifelse } ifelse Do -} def -/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform - exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx - dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop - XYPos } ifelse -} def -/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 -roll sin mul sub exch } ifelse } def -/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA -AddOffset yA add /yA1 ED xA add /xA1 ED } def -/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB -AddOffset yB add /yB1 ED xB add /xB1 ED } def -/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA -AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED -ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED -} ifelse } def -/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB -AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED -ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED -} ifelse } def -/InitNC { - /b ED /a ED % second and first node - /NodeSepTypeB ED /NodeSepTypeA ED - /NodeSepB ED /NodeSepA ED - /OffsetB ED /OffsetA ED - tx@NodeDict a known tx@NodeDict b known and dup { - /NodeA a load def - /NodeB b load def - NodeA GetCenter /yA ED /xA ED - NodeB GetCenter /yB ED /xB ED } if -} def -% -/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub -mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def -/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt -{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop -} repeat LPutLine cleartomark } def -/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED -/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 -mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx -sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul -add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add -y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul -mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def -/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def -} def -/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def -/NAngle yyB yyA sub xxB xxA sub Atan def } def -/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def -/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def -} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit -} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd -} def -/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def -} def -/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def -/NAngle yyB yyA sub xxB xxA sub Atan def } def -/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def -/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def -} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { -exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark -VPosEnd } def -/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 -roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx -def grestore exec /LPutVar /SaveLPutVar load def } def -/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def -GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { -LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { -LPutVar VPutLine } def LPutVar } def -/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop -end } def -/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub -Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan -/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 -yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { -LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } -ifelse } def -/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 -roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA -GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict -begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] -cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines -} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def -% -/NCAngles { - GetEdgeA GetEdgeB GetArmA GetArmB - /mtrx AngleA matrix rotate def - xA2 yA2 mtrx transform pop - xB2 yB2 mtrx transform exch pop - mtrx itransform - /y0 ED /x0 ED - mark ArmB 0 ne { xB1 yB1 } if - xB2 yB2 x0 y0 xA2 yA2 - ArmA 0 ne { xA1 yA1 } if - tx@Dict begin false Line end - /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def - /LPutPos { LPutLines } def - /HPutPos { HPutLines } def - /VPutPos { VPutLines } def } def -% -/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 -yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform -/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 -tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] -cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { -VPutLines } def } def -/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def -xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx -transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } -{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB -0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict -begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx -def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { -VPutLines } def } def -/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if -xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end -/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { -LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } -def -/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED -GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin -false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { -LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } -def -/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate -def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 -mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 -mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 -xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false -Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] -cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { -VPutLines } def } def -% DG/SR modification begin - May 9, 1997 - Patch 1 -%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r -%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add -%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 -%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED -/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r -r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add -exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 -mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED -% DG/SR modification end -} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add -AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r -Div def /y ED /x ED } def -/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB -180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos -mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def -/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy -add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos -{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar -tx@Dict begin false Polygon end } def -/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan -def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 -mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def -/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div -def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def -GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul -sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 -eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } -{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def -0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 -roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 -0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 -roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } -ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos -{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { -r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } -{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add -add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub -mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t -sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse -y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { -LPutPos } def } def -/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB -sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 -ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB -w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos -{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } -{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } -def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin -/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def - -/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg -exch X sub neg exch moveto setmatrix CP grestore } def - -/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 -def } ifelse LPutCoor } def -/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } -if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } -ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } -def -/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if -r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } -ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } -def -end -% END pst-node.pro - -%%EndProcSet -%%BeginProcSet: pstricks-add.pro 0 0 -%% $Id: pstricks-add.pro 49 2008-10-13 10:59:27Z herbert $ -% PostScript prologue for pstricks-add.tex. -% Version 0.21, 2008/10/15 -% For distribution, see pstricks.tex. -% -% HISTORY -> see file Changes -% -/tx@addDict 410 dict def tx@addDict begin -%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -/GTriangle { - gsave - /mtrx CM def - /colorA ED /colorB ED /colorC ED % save the colors - /yA ED /xA ED % save the origin - xA yA translate - rotate % \psk@gangle - /yB ED /xB ED /yC ED /xC ED % save other coordinates - /ds [ % save data in a array - 0 0 0 colorA aload pop % fd x y xr xg xb - 0 xB xA sub yB yA sub colorB aload pop - 0 xC xA sub yC yA sub colorC aload pop -% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD - ] def - newpath - << - /ShadingType 4 % single Gouraud - /ColorSpace [ /DeviceRGB ] - /DataSource ds - >> - shfill - closepath - mtrx - setmatrix grestore} def -% -/RGBtoCMYK { % on stack r g b -> C M Y K - 3 dict begin - /Blue ED /Green ED /Red ED - 1 Red sub % Cyan - 1 Green sub % Magenta - 1 Blue sub % Yellow - 0 % Black - end -} def -% -/CMYKtoGRAY { % on stack c m y k -> gray - exch 0.11 mul add - exch 0.59 mul add - exch 0.3 mul add - dup 1 gt { pop 1 } if - neg 1 add -} def -% -/RGBtoGRAY { % on stack r g b -> gray - 0.11 mul - exch 0.59 mul add - exch 0.3 mul add -} def -% -/HSBtoGRAY { - 6 dict begin - /b exch def - /s exch def 6 mul dup cvi dup - /i exch def sub - /f exch def - /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def - F i get { s mul neg 1 add b mul} forall - 0.11 mul - exch 0.59 mul add - exch 0.3 mul add - end -} def -% -%% convertisseur longueur d'onde ->R,G,B Manuel Luque -%% lambda max=780 nanometres -%% lambda min=380 nanometres -%% adaptation de : -%% http://www.physics.sfasu.edu/astro/color.html -%% www.efg2.com/lab -% -/Gamma 0.8 def -/calculateRGB { - lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if - lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if - lambda 380 ge {lambda 439 le { - /R {lambda 440 sub neg 440 380 sub div} def - /Red R factor mul Gamma exp def - /G 0 def - /Green G factor mul Gamma exp def - /B 1 def - /Blue B factor mul Gamma exp def} if - } if - lambda 440 ge { lambda 489 le { - /G {lambda 440 sub 490 440 sub div} def - /Green G factor mul Gamma exp def - /R 0 def /Red 0 def - /B 1 def - /Blue B factor mul Gamma exp def } if - } if - lambda 490 ge {lambda 509 le { - /B {lambda 510 sub neg 510 490 sub div} def - /Blue B factor mul Gamma exp def - /R 0 def /Red 0 def - /G 1 def - /Green G factor mul Gamma exp def } if - } if - lambda 510 ge {lambda 579 le { - /R {lambda 510 sub 580 510 sub div } def - /Red R factor mul Gamma exp def - /Blue 0 def - /G 1 def - /Green G factor mul Gamma exp def } if - } if - lambda 580 ge {lambda 644 le { - /G {lambda 645 sub neg 645 580 sub div } def - /Green G factor mul Gamma exp def - /Blue 0 def - /R 1 def - /Red R factor mul Gamma exp def } if - } if - lambda 645 ge { lambda 780 le { - /Red 1 factor mul Gamma exp def - /Blue 0 def - /Green 0 def } if - } if -} def -% -/factor { - lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if - lambda 420 ge {lambda 700 le { 1 } if } if - lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if -} def -% -/wavelengthToRGB { % the wavelength in nm must be on top of the stack - cvi /lambda exch def % no floating point here - calculateRGB -} def % now the colors are saved in Red Green Blue -% -/wavelengthToCMYK { % the wavelength in nm must be on top of the stack - cvi /lambda exch def % no floating point here - gsave - calculateRGB Red Green Blue RGBtoCMYK - /Black ED /Yellow ED /Magenta ED /Cyan ED - grestore -} def % now the colors are saved in Cyan Magenta Yellow Black -% -/axfill { - 8 dict begin - /xw exch def /nl exch def - /C1 exch def /y1 exch def/x1 exch def - /C0 exch def /y0 exch def/x0 exch def - << /ShadingType 2 - /ColorSpace /DeviceRGB - /Coords [ x0 y0 x1 y1 ] - /EmulatorHints [ xw 2 div dup ] - /Function << - /FunctionType 2 - /Domain [0 1] - /C0 C0 - /C1 C1 - /N 1 - >> - >> shfill - end -} bind def -% -%%%%% ### bubblesort ### -%% syntax : array bubblesort --> array2 trie par ordre croissant -%% code de Bill Casselman -%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/ -/bubblesort { -4 dict begin - /a exch def - /n a length 1 sub def - 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-userdict /end-hook known{end-hook}if -%%EOF diff --git a/Master/texmf-dist/doc/latex/bclogo/bcdfrance.pdf b/Master/texmf-dist/doc/latex/bclogo/bcdfrance.pdf Binary files differdeleted file mode 100644 index 9e8bb487b30..00000000000 --- a/Master/texmf-dist/doc/latex/bclogo/bcdfrance.pdf +++ /dev/null diff --git a/Master/texmf-dist/doc/latex/bclogo/bcditalie.eps b/Master/texmf-dist/doc/latex/bclogo/bcditalie.eps deleted file mode 100644 index 4980aa8b078..00000000000 --- a/Master/texmf-dist/doc/latex/bclogo/bcditalie.eps +++ /dev/null @@ -1,2414 +0,0 @@ -%!PS-Adobe-2.0 EPSF-2.0 -%%Creator: dvips(k) 5.96dev Copyright 2007 Radical Eye Software -%%Title: CompileEps.dvi -%%CreationDate: Sat Sep 19 14:15:29 2009 -%%BoundingBox: 71 693 90 721 -%%EndComments -%DVIPSWebPage: (www.radicaleye.com) -%DVIPSCommandLine: dvips -E -o -%+ C:\Users\Alain_2\Documents\LaTeX\Logos\bcditalie.eps CompileEps.dvi -%DVIPSParameters: dpi=600 -%DVIPSSource: TeX output 2009.09.19:1415 -%%BeginProcSet: tex.pro 0 0 -%! -/TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S -N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 -mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 -0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ -landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize -mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ -matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round -exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ -statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] -N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin -/FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array -/BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 -array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N -df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A -definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get -}B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} -B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr -1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S -/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy -setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask -restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn -/BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put -}if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ -bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A -mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ -SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ -userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X -1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 -index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N -/p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ -/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) -(LaserWriter 16/600)]{A length product length le{A length product exch 0 -exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse -end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask -grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} -imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round -exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto -fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p -delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} -B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ -p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S -rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end - -%%EndProcSet -%%BeginProcSet: pstricks.pro 0 0 -% $Id: pstricks.pro 34 2008-06-25 17:20:01Z herbert $ -% -%% PostScript prologue for pstricks.tex. -%% Version 1.05, 2008/06/25 -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -% -% -% Define the follwing gs-functions if not known, eg when using distiller -% -systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if -systemdict /.setblendmode known not {/.setblendmode { pop } def } if -systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if -% -/tx@Dict 200 dict def % the main PSTricks dictionary -tx@Dict begin -/ADict 25 dict def % The arrow dictionaray -/CM { matrix currentmatrix } bind def -/SLW /setlinewidth load def -/CLW /currentlinewidth load def -/CP /currentpoint load def -/ED { exch def } bind def -/L /lineto load def -/T /translate load def -/TMatrix { } def -/RAngle { 0 } def -/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments -/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known -/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) -/Div { dup 0 eq { pop } { div } ifelse } def % control the division -/tan { dup cos abs 1.e-10 lt - { pop 1.e10 } % return 1.e10 as infinit - { dup sin exch cos div } ifelse % default sin/cos -} def -/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees -/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root - pop pop 0 }{ sqrt exch atan} ifelse } def -/NET { neg exch neg exch T } def % change coordinate system to the negative one -/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter -/Pyth2 { % Pythagoras, xA yA xB yB - 3 -1 roll % xA xB yB yA - sub % xA xB yB-yA - 3 1 roll % yB-yA xA xB - sub % yB-yA xA-xB - Pyth } def -/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian -/Rand { rand 4294967295 div } def % a real random number -%----------------- hv added 20050516 --------------- -/PiDiv2 1.57079632680 def -/Pi 3.14159265359 def -/TwoPi 6.28318530718 def -/Euler 2.71828182846 def -%/e Euler bind def -/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees -/DegtoRad { Pi mul 180 div } bind def % viceversa -%----------------- hv end--------------------------- -/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def -/PathLength { - 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Dec. 12, 1997 - Patch 2 -%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a -%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a -%% DG/SR modification end -%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict -%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 -%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) -%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } -%% def -%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore -%pop pop } def -%% DG/SR modification end -% -/BeginArrow { - ADict begin % hold it local, for end see EndArrow - /@mtrx CM def - gsave - 2 copy T - 2 index sub neg exch - 3 index sub exch Atan - rotate newpath -} def -% -/EndArrow { @mtrx setmatrix CP grestore end } def % end the ADict -% -/Arrow { - CLW mul add dup - 2 div /w ED - mul dup /h ED - mul /a ED - { 0 h T 1 -1 scale } if - w neg h moveto - 0 0 L w h L w neg a neg rlineto - gsave fill grestore -} def -% -/ArrowD { % the sides are drawn as curves (hv 20071211) - CLW mul add dup - 2 div /w ED - mul dup /h ED - mul /Inset ED - { 0 h T 1 -1 scale } if % changes the direction -% we use y=w/h^2 * x^2 as equation for the control points -% for the coordinates the arrow is seen from top to bottom -% the bottom (tip) is (0;0) - w neg h moveto % lower left of > - w 9 div 4 mul neg h 3 div 2 mul - w 9 div neg h 3 div - 0 0 curveto % tip of > - w 9 div h 3 div - w 9 div 4 mul h 3 div 2 mul - w h curveto % upper left of > - w neg Inset neg rlineto % move to x=0 and inset - gsave fill grestore -} def -% -/Tbar { - CLW mul add /z ED - z -2 div CLW 2 div moveto - z 0 rlineto stroke - 0 CLW moveto -} def -% -/Bracket { - CLW mul add dup CLW sub 2 div - /x ED mul CLW add /y ED /z CLW 2 div def - x neg y moveto - x neg CLW 2 div L x CLW 2 div L x y L stroke - 0 CLW moveto -} def -% -/RoundBracket { - CLW mul add dup 2 div - /x ED mul /y ED /mtrx CM def - 0 CLW 2 div T x y mul 0 ne { x y scale } if - 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a r - /arcto load stopped { 5 } { 4 } ifelse { pop } repeat - a -} def -% -/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq - and { pop pop /n n 1 sub def } if } def -/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } - repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 - ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 - moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto - Lineto pop pop closepath } ifelse } def -/Diamond { - /mtrx CM def - T rotate - /h ED - /w ED - dup 0 eq { pop } { CLW mul neg - /d ED - /a w h Atan def - /h d a sin Div h add def - /w d a cos Div w add def } ifelse - mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div - /ArrowA { moveto } def - /ArrowB { } def - false Line - closepath mtrx setmatrix } def -% DG modification begin - Jan. 15, 1997 -%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { -%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 -%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 -%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx -%setmatrix } def -/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup -CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 -div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 -d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx -% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) -% setmatrix } def -setmatrix pop } def -% DG/SR modification end -% -/CCA { - /y ED /x ED - 2 copy y sub /dy1 ED - x sub /dx1 ED - /l1 dx1 dy1 Pyth def -} def -% -/CC { - /l0 l1 def - /x1 x dx sub def - /y1 y dy sub def - /dx0 dx1 def - /dy0 dy1 def - CCA - /dx dx0 l1 c exp mul dx1 l0 c exp mul add def - /dy dy0 l1 c exp mul dy1 l0 c exp mul add def - /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def - /x2 x l0 dx mul m mul sub def - /y2 y l0 dy mul m mul sub def - /dx l1 dx mul m mul neg def - /dy l1 dy mul m mul neg def -} def -% -/IC { - /c c 1 add def - c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse - /a a 2 mul 3 div 45 cos b exp div def - CCA - /dx 0 def - /dy 0 def -} def -% -/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def -/NC { CC x1 y1 x2 y2 x y curveto } def -/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def -/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def -/NAC { x2 y2 x y curveto CC x1 y1 } def -/EAC { x2 y2 x y ArrowB curveto pop pop } def -% -/OpenCurve { - NArray n 3 lt - { n { pop pop } repeat } - { BOC /n n 3 sub def n { NC } repeat EOC } ifelse -} def -% -/AltCurve { - { false NArray n 2 mul 2 roll - [ n 2 mul 3 sub 1 roll ] aload - /Points ED - n 2 mul -2 roll } - { false NArray } ifelse - n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse -} def -% -/ClosedCurve { - NArray n 3 lt - { n { pop pop } repeat } - { n 3 gt { CheckClosed } if - 6 copy n 2 mul 6 add 6 roll - IC CC x y moveto n { NC } repeat - closepath pop pop - } ifelse -} def -% -/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def -/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def -/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } -def -/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix -rotate matrix concatmatrix exch findfont exch makefont setfont } def -/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto -x1 y1 lineto closepath } def -/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 -y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div -exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse -/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto -x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } -ifelse } def -/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add -/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { -pop pop Rect } { OvalFrame } ifelse } def -% -/BezierNArray { - /f ED - counttomark 2 div dup cvi /n ED - n eq not { exch pop } if - n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat - f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse -} def -% -/OpenBezier { - BezierNArray - n 1 eq - { pop pop } - { ArrowA n 4 sub 3 idiv - { 6 2 roll 4 2 roll curveto } repeat - 6 2 roll 4 2 roll ArrowB curveto } ifelse -} def -% -/ClosedBezier { - BezierNArray - n 1 eq - { pop pop } - { moveto n 1 sub 3 idiv - { 6 2 roll 4 2 roll curveto } repeat - closepath } ifelse -} def -% -/BezierShowPoints { - gsave - Points aload length 2 div cvi /n ED - moveto - n 1 sub { lineto } repeat - CLW 2 div SLW [ 4 4 ] 0 setdash stroke - grestore -} def -% -/Parab { - /y0 ED /x0 ED /y1 ED /x1 ED - /dx x0 x1 sub 3 div def - /dy y0 y1 sub 3 div def - x0 dx sub y0 dy add x1 y1 ArrowA - x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB - curveto - /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def -} def -% -/Grid { - newpath - /a 4 string def - /b ED /c ED /n ED - cvi dup 1 lt { pop 1 } if - /s ED - s div dup 0 eq { pop 1 } if - /dy ED s div dup 0 eq { pop 1 } if - /dx ED dy div round dy mul - /y0 ED dx div round dx mul - /x0 ED dy div round cvi - /y2 ED dx div round cvi - /x2 ED dy div round cvi - /y1 ED dx div round cvi - /x1 ED - /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def - /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def - b 0 gt { - /z1 b 4 div CLW 2 div add def -% /Helvetica findfont b scalefont setfont - /b b .95 mul CLW 2 div add def } if - systemdict /setstrokeadjust known - { true setstrokeadjust /t { } def } - { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add - exch itransform } bind def } ifelse - gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse - /i x1 def - /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def - /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def - x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if - { i dx mul dup y0 moveto - b 0 gt - { gsave c i a cvs dup stringwidth pop - /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse - h 0 gt {b neg}{z1} ifelse - rmoveto show grestore } if - dup t f moveto - g t L stroke - /i i w add def - } repeat - grestore - gsave - n 0 gt - % DG/SR modification begin - Nov. 7, 1997 - Patch 1 - %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } - { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } - % DG/SR modification end - { 2 setlinecap } ifelse - /i y1 def - /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def - /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def - y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if - { newpath i dy mul dup x0 exch moveto - b 0 gt { gsave c i a cvs dup stringwidth pop - /z2 ED - w 0 gt {z1 z2 add neg} {z1} ifelse - h 0 gt {z1} {b neg} ifelse - rmoveto show grestore } if - dup f exch t moveto - g exch t L stroke - /i i h add def - } repeat - grestore -} def -% -/ArcArrow { - /d ED /b ED /a ED - gsave - newpath 0 -1000 moveto clip - newpath - 0 1 0 0 b - grestore - c mul - /e ED - pop pop pop r a e d PtoC y add exch x add - exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c - mul neg d -} def -% -/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def -% -/ArcAdjust { %%%% Vincent Guirardel -% given a target length (targetLength) and an initial angle (angle0) [in the stack], -% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). -% This computes an angle t such that (x0,y0) is at distance -% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). -% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 -% contrary to TvZ's code. -% To achieve, this, one iterates the following process: start with some angle t, -% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. -% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. -% -% Another difference with TvZ's code is that we need d (=add/sub) to be defined. -% the value of d = add/sub is used to know on which side we have to move. -% It is only used in the initialisation of the angle before the iteration. -% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% Input stack: 1: target length 2: initial angle -% variables used : rx, ry, d (=add/sub) -% - /targetLength ED /angle0 ED - /x0 rx angle0 cos mul def - /y0 ry angle0 sin mul def -% we are looking for an angle t such that (x0,y0) is at distance targetLength -% from the point M(t)=(rx*cos(t),ry*sin(t))) -%initialisation of angle (using 1st order approx = TvZ's code) - targetLength 57.2958 mul - angle0 sin rx mul dup mul - angle0 cos ry mul dup mul - add sqrt div -% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees -% (if the ellipse is very curved at the point where we draw the arrow, % -% the value can be much more than 360 degrees !) -% this should avoid going on the wrong side (more than 180 degrees) or go near -% a bad attractive point (at 180 degrees) - dup 90 ge { pop 90 } if - angle0 exch d % add or sub -% maximum number of times to iterate the iterative procedure: -% iterative procedure: takes an angle t on top of stack, computes a -% better angle (and put it on top of stack) - 30 { dup -% compute distance D between (x0,y0) and M(t) - dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt -% if D almost equals targetLength, we stop - dup targetLength sub abs 1e-5 le { pop exit } if -% stack now contains D t -% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: -% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) - exch dup cos rx mul x0 sub exch sin ry mul y0 sub -% stack contains: y(t)-y0, x(t)-x0, d - 2 index Div targetLength mul y0 add ry Div exch - 2 index Div targetLength mul x0 add rx Div -% stack contains x(t')/rx , y(t')/ry , d -% now compute t', and remove D from stack - atan exch pop - } repeat -% we don't look at what happened... in particular, if targetLength is greater -% than the diameter of the ellipse... -% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... -% after iteration, stack contains an angle t such that M(t) is the tail of the arrow -% to give back the result as a an angle relative to angle0 we could add the following line: -% angle0 sub 0 exch d -% -% begin bug fix 2006-01-11 -% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 -%(we don't want to make the ellipse turn more or less than it should)... -dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse -% end bug fix -} def -% -/EllipticArcArrow { - /d ED % is add or sub - /b ED % arrow procedure - /a1 ED % angle - gsave - newpath - 0 -1000 moveto - clip % Set clippath far from arrow. - newpath - 0 1 0 0 b % Draw arrow to determine length. - grestore -% Length of arrow is on top of stack. Next 3 numbers are junk. -% - a1 exch ArcAdjust % Angular position of base of arrow. - /a2 ED - pop pop pop - a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig - a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig - a1 cos rx mul xOrig add % - a1 sin ry mul yOrig add % -% Now arrow tip coor and base coor are on stack. - b pop pop pop pop % Draw arrow, and discard coordinates. - a2 CLW 8 div -% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) - 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse - ArcAdjust -% resets original value of d - 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. -} def -%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% -% -/Rot { CP CP translate 3 -1 roll neg rotate NET } def -% -/RotBegin { - tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if - /TMatrix [ TMatrix CM ] cvx def - /a ED - a Rot /RAngle [ RAngle dup a add ] cvx def -} def -% -/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def -% -/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def -/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def -/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def -/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s -abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b -div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { -h1 abs h sub dup s mul abs } ifelse } def -/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s -mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q -{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add -exch } def -/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible -/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def -} if } ifelse } def -/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def -/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit -neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def -/IfVisible true def } def -end -%-----------------------------------------------------------------------------% - -% END pstricks.pro - -%%EndProcSet -%%BeginProcSet: pst-algparser.pro 0 0 -% $Id: pst-algparser.pro 26 2008-06-14 11:50:02Z herbert $ -%% -%% PostScript prologue for PSTricks algorithm parser -%% Version 0.01, 2008/01/01 -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -%% -%%-----------------------------------------------------------------------------% -% -/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez -% -/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin -% -% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 -% E->T|E+T -% T->FS|T*FS -% FS -> F | +FS | -FS -% F->P|F^SF -% P->(E)|literal -% literal->number|var|var[E]|func(params) -% params->E|E,param -% number->TOBEFINISHED -% -%% E expression, T term, SF signed factor, F factor, P power -% -%% parser -% -%% str -% -%% C->E<condition_operators>E -%% STR index -> STR index+lenExpr -/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def -% -%% analyze Expression List (separator , or | ) -%% STR index -> STR index+lenExpr -%% /AnalyzeListOfE { -%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar -%% NextNonBlankChar dup 0 eq { pop exit } if -%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if -%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop -%% AnalyzeListOfEPostHook -%% } def -/AnalyzeListOfE { - /NotFirst false def - { NextNonBlankChar pop AnalyzeExpr - NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse - dup Strlen eq { exit } if NextNonBlankChar - dup 44 ne 1 index 124 ne and - { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } - if pop 1 add } loop - AnalyzeListOfEPostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% E->T|E+T -%% STR index -> STR index+lenExpr -/AnalyzeExpr { - AnalyzePreHook AnalyzeTerm IsEndingExpr - { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } - { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } - ifelse - AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% T->FS|T*FS -%% STR index -/AnalyzeTerm { - AnalyzePreHook AnalyzeSignedFactor IsEndingTerm - { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } - { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } - ifelse - AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% FS -> F | +FS | -FS -%% STR index -/AnalyzeSignedFactor { - AnalyzePreHook 2 copy get dup IsUnaryOp - { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } - { pop AnalyzeFactor } - ifelse AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% F->P|F^P -%% STR index -/AnalyzeFactor { - AnalyzePreHook AnalyzePower IsEndingFactor - { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } - { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } - ifelse AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% P->(E)|literal -%% STR index -/AnalyzePower { - %% depending of first char either a number, or a literal - 2 copy get dup 40 eq%%an open par - { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } - { AnalyzeLiteral } - ifelse -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index STR[index] -> STR index -%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def -/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% recognize + or - -%% chr -> T/F -/IsUnaryOp { dup 43 eq exch 45 eq or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a number can contain only : 0123456789. -%% chr -> T/F -/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index -> STR index number -%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? -%% STR index -> STR index' number -/ReadNumber { - exch dup 3 -1 roll dup 3 1 roll - %%read mantissa - { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop - dup 101 eq exch 69 eq or - %%% there is a "e" or "E" -> read exponant - { 1 add 2 copy get dup IsUnaryOp - { pop 1 add 2 copy get } if - { IsNumber not { exit } if 1 add 2 copy get } loop } - if - dup 4 1 roll - 3 -1 roll exch 1 index sub getinterval -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a number can contain only : 0123456789. -%% chr -> T/F -/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index -> STR index number -%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? -%% STR index -> STR index' number -/ReadCondOp { - NextNonBlankChar 1 index 4 1 roll - { IsCondOp not { exit } if 1 add 2 copy get } loop - 2 copy 5 -1 roll - exch 1 index sub getinterval 3 1 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a literal can contain only : 0123456789. -%% chr -> T/F -/IsLiteral {% - dup 48 ge exch dup 57 le 3 -1 roll and exch - dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch - dup 97 ge exch 122 le and or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? -%% STR index -> literal STR index' nextchr -/ReadLiteral { - exch dup 3 -1 roll dup 3 1 roll - %%read literal core - { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop - 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or a clpar -%% STR index -> STR index STR[index] T/F -/IsEndingExpr {% - 2 copy dup Strlen eq - %% if end of str is reached -> end ! - { pop pop 0 true } - %% ending chr -> clpar, comma, |, <, >, =, !, - {get dup dup 41 eq - exch dup 124 eq - exch dup 93 eq - exch dup 44 eq - exch dup 30 eq - exch dup 60 ge exch 62 le and or or or or or} - ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or a +- -%% STR index -> STR index STR[index] T/F -/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or */ -%% STR index -> STR index STR[index] T/F -/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or ^ -%% STR index -> STR index STR[index] T/F -/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index -> STR index STR[index] -/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def -/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def -%%%%%%%%%%%%%%%%%%%%%%%% -%% DEBUG -/BRK {false} def -/BRKtrue {/BRK true def} def -/BRKStop {BRK {BRKtoto} if } def -/BRKEvalStop {BRK exch if } def -/BRKBRK2true {BRK {BRK2true} if } def -/BRK2 {false} def -/BRK2true {/BRK2 true def} def -/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def -end -% -%-------------------------------------------------------------------------------% -% -/tx@AlgToPs 12 dict def tx@AlgToPs begin -% -%% algExpr -> PSVector -/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def -/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def -/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def -/Strlen 0 def -/EvalListOfExpr {} def% -/EvalNumber {% - ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx - exch 1 add array astore def NextNonBlankChar pop } def -/EvalAddSub {% - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll - 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def -} def -/EvalMulDiv {% - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll - 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def -} def -/EvalPower {% - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll - pop /exp cvx exch 1 add array astore def -} def -/EvalLiteral {% - ReadLiteral - dup 40 eq%%% there is an open par -> function call - { pop 2 index - dup (Sum) eq { EvalSum } - { dup (IfTE) eq { EvalCond } - { dup (Derive) eq { pop EvalDerive } - { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx - exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } - { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def - dup 91 eq%%% there is an open bracket -> vector element - { pop 1 add NextNonBlankChar pop AnalyzeExpr - /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } - { pop NextNonBlankChar pop } - ifelse} - ifelse -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% the derive function : Derive(n,f(x)) -%% firstparindex lastparindex -> -/EvalDerive { - %% manage the function descripiton - 1 add ReadNumber 3 1 roll NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - 1 add NextNonBlankChar pop - 3 -1 roll cvi - dup 0 eq - { pop AnalyzeExpr 3 -1 roll pop 1 add } - { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll - { (x) tx@Derive begin Derive end } repeat - ExpressionVector exch /ExpressionVector [] def - AlgToPs aload length - /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def - l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add - 1 index length /Strlen exch def } ifelse -} def -/EvalSum {% - pop 1 add NextNonBlankChar pop - %% read the variable name - ReadLiteral pop NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if - %% read the initial value - 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - %% read the increment value - 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - %% read the limit value - 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll - 5 -1 roll 4 add array astore def - %% keep ExpressionVector for later and create a new one for internal Sum computation - ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def - 1 add NextNonBlankChar pop AnalyzeExpr - %% add each term - /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def - /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add - array astore def 3 -1 roll pop 1 add -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Convert to radians if trigo function call -%% (name) -> -/TrigoFunc { - dup (cos) eq 1 index (sin) eq or exch (tan) eq or - { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add - array astore def - } if -} def -/EvalCond {% - pop 1 add AnalyzeCond NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if - ExpressionVector 3 1 roll /ExpressionVector [] def - 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def - NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if - 1 add AnalyzeExpr - NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if - ExpressionVector - /ExpressionVector 6 -1 roll aload length dup - 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def - 1 add 3 -1 roll pop -} def -%% CondOp STR index -/EvalCondOp {% - 3 -1 roll - dup (=) eq { /eq } {% - dup (<) eq { /lt } {% - dup (>) eq { /gt } {% - dup (>=) eq { /ge } {% - dup (<=) eq { /ge } {% - dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } - ifelse } ifelse } ifelse } ifelse } ifelse } ifelse - cvx exch pop - /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def -/EvalUnaryOp { - 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% H O O K S -/AnalyzePreHook {} bind def -/PreEvalHook {} bind def -/AnalyzeListOfEPostHook {} bind def -/AnalyzePostHook {} def -/RollOp { 3 1 roll } bind def -end %tx@CoreAnalyzerDict -% -%--------------------------------------------------------------------% -% -/tx@Derive 41 dict def tx@Derive begin -%%increase ^^ for each function added -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% algExpr variable -> PSVector -/Derive {% - 10240 string 3 1 roll 0 3 1 roll - /Variable exch def - tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end -} def -/Strlen 0 def -/InitParser { dup length /Strlen exch def 0 } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% algExpr variable index -> PSVector -/DeriveIndexed {% - 3 1 roll 10240 string 3 1 roll 0 3 1 roll - /Variable exch def - tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u,v)'=-(u',v') -/EvalListOfExpr {% - 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe - 2 copy 7 -1 roll dup length 4 1 roll putinterval add - 6 -2 roll pop pop - 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (-u)'=-(u') -/EvalUnaryOp { - 4 -2 roll 4 index (0) eq - { (0) StrConcat 7 -1 roll pop } - { 7 -1 roll 45 eq - { AddSub AddOpPar true } { false } ifelse - 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (number)'=0 -/EvalNumber { ReadNumber (0) 6 2 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u+v)'=u'+v' -/EvalAddSub {% - 7 index dup (0) eq - { pop true }%% du=0 nothing added - { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } - ifelse - 5 index dup (0) eq - { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 - { exch - { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added - { 5 -2 roll 7 index 43 eq%%something yet added - { AddAdd false } { AddSub AddOpPar true } ifelse } - ifelse 11 1 roll - 3 -1 roll StrConcat 10 -1 roll { AddClPar } if - 2 copy pop 0 6 2 roll GetIntervalNewStr } - ifelse - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u*v)' or (u/v)' -/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u*v)'=u'*v+u*v' -/EvalMul {% - 4 -2 roll 7 index dup (0) eq - { pop false }%%du=0 - { (1) eq%%du=1 - { false } - { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse - 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if - true }%%du!=0 - ifelse - 5 1 roll 5 index (0) eq - { 5 -1 roll not { (0) StrConcat } if }%%dv=0 - { 5 -1 roll { AddAdd } if - 4 index (1) eq - { 8 index StrConcat } - { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } - ifelse - }%%dv!=0 - ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u/v)'=(u'*v-u*v')/v^2 -/EvalDiv {% - 4 -2 roll - 4 index (0) eq%%dv=0 -> u'/v - { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } - { 7 index dup (0) eq - { pop }%%du=0 - { (1) eq%%du=1 - { false } - { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse - 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 - ifelse - AddSub - 4 index (1) eq - { 8 index StrConcat } - { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } - ifelse - %}%%dv!=0 - 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar - AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } - ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% str1 index str2 -> str1 index -/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def -/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) -/EvalPower {% - 4 -2 roll 7 index (0) eq - {%%if du=0 then (u^v)'=v'ln(u)u^v - 4 index (0) eq - { (0) StrConcat }%%if dv=0 then (u^v)'=0 - { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if - 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if - AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse - } - {%%du!=0 - 4 index (0) eq - {%%if dv=0 then (u^v)'=vu'u^(v-1) - 5 index dup IsStrNumber - { dup (0) eq - { StrConcat } - { dup dup (1) eq exch (1.0) eq or - { StrConcat } - { StrConcat - 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 - { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 - (*\() StrConcat 8 index StrConcat (\)) StrConcat - 5 index dup dup (2) eq exch (2.0) eq or - { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } - { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat - 5 index StrConcat (-1\)) StrConcat } ifelse - } - {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) - 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if - AddOpPar 5 index StrConcat (\)*\() StrConcat - 8 index StrConcat (\)^\() StrConcat - 5 index StrConcat (-1\)+\() StrConcat - 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if - 8 index StrConcat (\)^\() StrConcat - 5 index StrConcat (\)*ln\() StrConcat - 8 index StrConcat AddClPar - } ifelse - } ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% str -> true/false -/IsStrNumber {% - true exch - { dup 48 lt exch dup 57 gt 3 -1 roll or - exch dup 46 ne%%. - exch dup 43 ne%%+ - exch 45 ne%%- - and and and { pop false } if } forall -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% literal switch -> func call, vector, variables -/EvalLiteral {% - ReadLiteral dup 40 eq%%% there is an open par -> function call - { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } - { dup 91 eq%%% there is an open bracket -> vector element - { ERROR_vector_not_yet_implemented } - { pop EvalVariable } - ifelse } - ifelse -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% first last parpos Expr[first:parpos-1] -> -/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (f(u))'=u'f'(u) -/EvalFunc { - 4 2 roll 4 index (1) ne - { AddOpPar 4 index StrConcat (\)*) StrConcat } if - (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Func derivative -> Eval<func> -/EvalFunc_sin {% - PreCommonFunc - { (cos\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_cos {% - PreCommonFunc - { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_tan {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if - PostCommonFunc } def -/EvalFunc_asin {% - PreCommonFunc - { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_acos {% - PreCommonFunc - { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_atg {% - PreCommonFunc - { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_ln {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_exp {% - PreCommonFunc - { (exp\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_sqrt {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_Fact {% - PreCommonFunc { ERROR_no_variable_expression_in_Fact } if - PostCommonFunc } def -/EvalFunc_sh {% - PreCommonFunc - { (ch\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_ch {% - PreCommonFunc - { (sh\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_th {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if - PostCommonFunc } def -/EvalFunc_Argsh {% - PreCommonFunc - { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_Argch {% - PreCommonFunc - { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_Argth {% - PreCommonFunc - { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -/PreCommonFunc { - 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop - 4 2 roll 4 index (0) eq - { (0) StrConcat false } - { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse -} def -/PostCommonFunc { - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -/EvalFunc_Derive {% - 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs - 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add - 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar - 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval - exch 6 2 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% literal switch -> func call, vector, variables -/EvalFunc_Sum {% - 1 add NextNonBlankChar pop - %% read the variable name - ReadLiteral pop 3 -1 roll pop NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if - %% read the initial value - 1 add NextNonBlankChar pop ReadNumber pop - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - %% read the increment value - 1 add NextNonBlankChar pop ReadNumber pop - 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if - %% read the limit value - 1 add NextNonBlankChar pop ReadNumber pop - 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if - 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop - 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat - 4 index StrConcat AddClPar - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% literal switch -> func call, vector, variables -/EvalFunc_IfTE {% - 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond - NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if - 1 add NextNonBlankChar pop dup 5 1 roll - AnalyzeExpr NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if - 1 add NextNonBlankChar pop - AnalyzeExpr 1 add NextNonBlankChar pop - 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat - 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% advance in str until a comma is found (no error detection!) -%% str index -> str index' -/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Convert to radians if trigo function call -%% (name) -> -/TrigoFunc { - dup (cos) eq 1 index (sin) eq or exch (tan) eq or - { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add - array astore def - } if -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% No derivative for condition.... -/EvalCondOp { 3 -1 roll pop } bind def -/PutIntervalOneAdd {putinterval 1 add} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add open parenthesis in string at the given index -%% str index -> str index+1 -/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add close parenthesis in string at the given index -%% str index -> str index+1 -/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add 0 in string at the given index -%% str index -> str index+1 -/AddZero {2 copy (0) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add open parenthesis in string at the given index -%% str index -> str index+1 -/AddMul {2 copy (*) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add open parenthesis in string at the given index -%% str index -> str index+1 -/AddDiv {2 copy (/) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add a plus sign in string at the given index -%% str index -> str index+1 -/AddAdd {2 copy (+) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add a minus sign in string at the given index -%% str index -> str index+1 -/AddSub {2 copy (-) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add a pipe sign in string at the given index -%% str index -> str index+1 -/AddPipe {2 copy (|) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% H O O K S -/AnalyzePreHook { dup 5 1 roll } bind def -/PreEvalHook {} def -/AnalyzePostHook { 7 -1 roll pop } bind def -/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def -/RollOp { 5 1 roll } bind def -end%%%tx@CoreAnalyzerDict -/tx@AddMathFunc 12 dict def tx@AddMathFunc begin -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% NEW FUNC -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) -%% x -> theta -/asin {% - dup abs 1 gt { EQDFasinrangeerror } if - dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad -} def -%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) -%% x -> theta -/acos {% - dup abs 1 gt { EQDFacosrangeerror } if - dup dup mul 1 exch sub sqrt exch atan DegtoRad -} def -%% function arctangent in radians -%% x -> theta -/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def -%% HYPERBOLIC FUNCTIONS -/sh { dup Ex exch neg Ex sub 2 div } def -/ch { dup Ex exch neg Ex add 2 div } def -/th { dup sh exch ch div } def -/Argsh { dup dup mul 1 add sqrt add ln } def -/Argch { dup dup mul 1 sub sqrt add ln } def -/Argth { dup 1 add exch 1 exch sub div ln 2 div } def -%% modified exponential funtion for 0 -%% x n -> x^n -/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def -%% modified exponential funtion for 0 -%% x -> e^x -/Ex { Euler exch exp } bind def -%% -%% factorial function -%% n -> n! -/Fact { 1 exch 2 exch 1 exch { mul } for } bind def -/fact { Fact } bind def -end - -% END pstricks.pro - -%%EndProcSet -%%BeginProcSet: pst-dots.pro 0 0 -% $Id: pst-dots.pro 26 2008-06-14 11:50:02Z herbert $ -% -%% PostScript prologue for pstricks.tex. -%% Version 2.02, 2008/04/18 -%% -%% For distribution, see pstricks.tex. -%% -%% Timothy Van Zandt <tvz@Princeton.EDU> -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -%% -%% Modified by Etienne Riga - Dec. 16, 1999 -%% Modified by Etienne Riga - 2005/01/01 (er) -%% to add /Diamond, /SolidDiamond and /BoldDiamond -%% Modified by Herbert Voss (hv) - 2008/04/17 -% -10 dict dup begin % hold local - /FontType 3 def - /FontMatrix [.001 0 0 .001 0 0] def - /FontBBox [-571.5 -742.5 571.5 742.5] def -% /FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph - /Encoding 256 array def - 0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef - Encoding % replace with given dot names - dup (b) 0 get /Bullet put % get the numerical position of b in ASCII -% % and save /Bullet at this place in Encoding - dup (c) 0 get /Circle put - dup (C) 0 get /BoldCircle put % 67 - dup (u) 0 get /SolidTriangle put - dup (t) 0 get /Triangle put - dup (T) 0 get /BoldTriangle put - dup (r) 0 get /SolidSquare put - dup (s) 0 get /Square put - dup (S) 0 get /BoldSquare put - dup (q) 0 get /SolidPentagon put - dup (p) 0 get /Pentagon put - dup (P) 0 get /BoldPentagon put -%%% - dup (k) 0 get /Asterisk put - dup (K) 0 get /BoldAsterisk put - dup (J) 0 get /SolidAsterisk put - dup (h) 0 get /Hexagon put - dup (H) 0 get /BoldHexagon put - dup (G) 0 get /SolidHexagon put - dup (f) 0 get /Octogon put % 2008-04-18 hv - dup (F) 0 get /BoldOctogon put % 2008-04-18 hv - dup (g) 0 get /SolidOctogon put % 2008-04-18 hv - dup (a) 0 get /Add put - dup (A) 0 get /BoldAdd put % 65 - dup (x) 0 get /Mul put - dup (X) 0 get /BoldMul put - dup (m) 0 get /Oplus put - dup (M) 0 get /BOplus put - dup (e) 0 get /SolidOplus put - dup (n) 0 get /Otimes put - dup (N) 0 get /BOtimes put - dup (E) 0 get /SolidOtimes put - dup (i) 0 get /Bar put - dup (I) 0 get /BoldBar put - dup (l) 0 get /SolidDiamond put - dup (d) 0 get /Diamond put - (D) 0 get /BoldDiamond put -%%% -/CharProcs 47 dict def -CharProcs begin - /CirclePath {0 0 500 0 360 arc closepath} def - /Bullet {CirclePath fill} def - /Circle {CirclePath .9 .9 scale CirclePath eofill} def - /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def - /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def - /SolidTriangle {TrianglePath fill} def - /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def - /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def - /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def - /SolidSquare {SquarePath fill} def - /Square {SquarePath .89 .89 scale SquarePath eofill} def - /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def - /PentagonPath { - -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto - 0 574.7 lineto -546.6 177.6 lineto closepath - } def - /SolidPentagon {PentagonPath fill} def - /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def - /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def -%-------------- hv begin 2004/07/25 from: er 2003/03/24 - /HexagonPath { - 0 550 moveto -476 275 lineto -476 -275 lineto - 0 -550 lineto 476 -275 lineto 476 275 lineto closepath - } def - /SolidHexagon {HexagonPath fill} def - /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def - /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def -% 2008-04-18 hv - /OctogonPath { - 550 dup 22.5 tan mul dup neg dup add /xMove exch def - exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def - /SolidOctogon { OctogonPath fill } def - /Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def - /BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def -% - /AsteriskPath { - 20 0 moveto 10 250 180 500 0 500 curveto - -180 500 -10 250 -20 0 curveto closepath - } def - /Asterisk { - AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath - 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill - } def -% - /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def - /BoldAsteriskPath { - 50 30 cos 100 mul moveto Basterp - 60 rotate Basterp 60 rotate Basterp - 60 rotate Basterp 60 rotate Basterp - 60 rotate Basterp closepath - } def - /BoldAsterisk {BoldAsteriskPath fill} def - /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def - /CrossPath { - 40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto - -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto - 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath - } def - /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto - -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto - 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath - } def - /Add {CrossPath fill} def - /Mul {45 rotate CrossPath fill} def - /BoldAdd {BoldCrossPath fill} def - /BoldMul {45 rotate BoldCrossPath fill} def - /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def - /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def - /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def - /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def - /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def - /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def - /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def - /Bar {BarPath fill} def - /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def - /BoldBar {BoldBarPath fill} def - /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath} def - /SolidDiamond {DiamondPath fill} def - /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def - /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def -%%% - /.notdef { } def -end -% -/BuildGlyph { - exch - begin -% Metrics 1 index get exec 0 - 0 0 -% BBoxes 3 index get exec - -1000 -1000 1000 1000 -% -571.5 -742.5 571.5 742.5 - setcachedevice - CharProcs begin load exec end - end -} def -% -/BuildChar { - 1 index /Encoding get exch get - 1 index /BuildGlyph get exec -} bind def - -end -/PSTricksDotFont exch definefont pop - -%% end - -%%EndProcSet -%%BeginProcSet: pst-node.pro 0 0 -% $Id: pst-node.pro 26 2008-06-14 11:50:02Z herbert $ -%% -%% PostScript prologue for pst-node.tex. -%% Version 1.00, 2008/01/01. -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -% -/tx@NodeDict 400 dict def tx@NodeDict begin -tx@Dict begin % from main pstricks dict - /T /translate load def -end -/NewNode { % on stack: { x y } boolean N@name type InitXnode - gsave - /next ED % { x y } boolean N@name type - dict dup % { x y } boolean N@name dict dict - 3 1 roll def % { x y } boolean dict N@name dict def - exch { dup 3 1 roll def } if % { x y } dict boolean - begin % { x y } dict begin - tx@Dict begin - STV CP T exec % set scaling - end - /NodeMtrx CM def % save CM - next % InitXNode - end - grestore -} def -% -/InitPnode { - /Y ED /X ED - /NodePos { NodeSep Cos mul NodeSep Sin mul } def -} def -% -/InitCnode { - /r ED /Y ED /X ED - /NodePos { NodeSep r add dup Cos mul exch Sin mul } def -} def -% -/GetRnodePos { - Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse - Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse - dx Sin mul abs dy - Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse -} def -% -/InitRnode { - /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED - /NodePos { GetRnodePos } def -} def -% -/DiaNodePos { - w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup - Cos mul exch Sin mul -} def -% -/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h -mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul -} ifelse } def -/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d -ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d -sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan -sin def /NodePos { TriNodePos } def } def -/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos -hh mul Atan dup cos ww mul exch sin hh mul } def -/GetCenter { begin X Y NodeMtrx transform CM itransform end } def -% -/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist - Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } - { 0 Dist Sin mul } ifelse } ifelse Do -} def -/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform - exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx - dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop - XYPos } ifelse -} def -/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 -roll sin mul sub exch } ifelse } def -/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA -AddOffset yA add /yA1 ED xA add /xA1 ED } def -/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB -AddOffset yB add /yB1 ED xB add /xB1 ED } def -/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA -AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED -ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED -} ifelse } def -/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB -AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED -ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED -} ifelse } def -/InitNC { - /b ED /a ED % second and first node - /NodeSepTypeB ED /NodeSepTypeA ED - /NodeSepB ED /NodeSepA ED - /OffsetB ED /OffsetA ED - tx@NodeDict a known tx@NodeDict b known and dup { - /NodeA a load def - /NodeB b load def - NodeA GetCenter /yA ED /xA ED - NodeB GetCenter /yB ED /xB ED } if -} def -% -/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub -mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def -/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt -{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop -} repeat LPutLine cleartomark } def -/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED -/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 -mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx -sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul -add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add -y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul -mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def -/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def -} def -/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def -/NAngle yyB yyA sub xxB xxA sub Atan def } def -/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def -/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def -} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit -} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd -} def -/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def -} def -/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def -/NAngle yyB yyA sub xxB xxA sub Atan def } def -/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def -/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def -} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { -exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark -VPosEnd } def -/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 -roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx -def grestore exec /LPutVar /SaveLPutVar load def } def -/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def -GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { -LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { -LPutVar VPutLine } def LPutVar } def -/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop -end } def -/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub -Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan -/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 -yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { -LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } -ifelse } def -/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 -roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA -GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict -begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] -cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines -} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def -% -/NCAngles { - GetEdgeA GetEdgeB GetArmA GetArmB - /mtrx AngleA matrix rotate def - xA2 yA2 mtrx transform pop - xB2 yB2 mtrx transform exch pop - mtrx itransform - /y0 ED /x0 ED - mark ArmB 0 ne { xB1 yB1 } if - xB2 yB2 x0 y0 xA2 yA2 - ArmA 0 ne { xA1 yA1 } if - tx@Dict begin false Line end - /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def - /LPutPos { LPutLines } def - /HPutPos { HPutLines } def - /VPutPos { VPutLines } def } def -% -/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 -yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform -/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 -tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] -cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { -VPutLines } def } def -/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def -xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx -transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } -{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB -0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict -begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx -def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { -VPutLines } def } def -/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if -xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end -/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { -LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } -def -/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED -GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin -false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { -LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } -def -/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate -def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 -mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 -mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 -xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false -Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] -cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { -VPutLines } def } def -% DG/SR modification begin - May 9, 1997 - Patch 1 -%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r -%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add -%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 -%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED -/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r -r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add -exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 -mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED -% DG/SR modification end -} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add -AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r -Div def /y ED /x ED } def -/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB -180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos -mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def -/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy -add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos -{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar -tx@Dict begin false Polygon end } def -/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan -def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 -mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def -/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div -def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def -GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul -sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 -eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } -{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def -0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 -roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 -0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 -roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } -ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos -{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { -r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } -{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add -add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub -mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t -sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse -y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { -LPutPos } def } def -/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB -sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 -ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB -w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos -{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } -{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } -def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin -/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def - -/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg -exch X sub neg exch moveto setmatrix CP grestore } def - -/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 -def } ifelse LPutCoor } def -/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } -if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } -ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } -def -/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if -r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } -ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } -def -end -% END pst-node.pro - -%%EndProcSet -%%BeginProcSet: pstricks-add.pro 0 0 -%% $Id: pstricks-add.pro 49 2008-10-13 10:59:27Z herbert $ -% PostScript prologue for pstricks-add.tex. -% Version 0.21, 2008/10/15 -% For distribution, see pstricks.tex. -% -% HISTORY -> see file Changes -% -/tx@addDict 410 dict def tx@addDict begin -%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -/GTriangle { - gsave - /mtrx CM def - /colorA ED /colorB ED /colorC ED % save the colors - /yA ED /xA ED % save the origin - xA yA translate - rotate % \psk@gangle - /yB ED /xB ED /yC ED /xC ED % save other coordinates - /ds [ % save data in a array - 0 0 0 colorA aload pop % fd x y xr xg xb - 0 xB xA sub yB yA sub colorB aload pop - 0 xC xA sub yC yA sub colorC aload pop -% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD - ] def - newpath - << - /ShadingType 4 % single Gouraud - /ColorSpace [ /DeviceRGB ] - /DataSource ds - >> - shfill - closepath - mtrx - setmatrix grestore} def -% -/RGBtoCMYK { % on stack r g b -> C M Y K - 3 dict begin - /Blue ED /Green ED /Red ED - 1 Red sub % Cyan - 1 Green sub % Magenta - 1 Blue sub % Yellow - 0 % Black - end -} def -% -/CMYKtoGRAY { % on stack c m y k -> gray - exch 0.11 mul add - exch 0.59 mul add - exch 0.3 mul add - dup 1 gt { pop 1 } if - neg 1 add -} def -% -/RGBtoGRAY { % on stack r g b -> gray - 0.11 mul - exch 0.59 mul add - exch 0.3 mul add -} def -% -/HSBtoGRAY { - 6 dict begin - /b exch def - /s exch def 6 mul dup cvi dup - /i exch def sub - /f exch def - /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def - F i get { s mul neg 1 add b mul} forall - 0.11 mul - exch 0.59 mul add - exch 0.3 mul add - end -} def -% -%% convertisseur longueur d'onde ->R,G,B Manuel Luque -%% lambda max=780 nanometres -%% lambda min=380 nanometres -%% adaptation de : -%% http://www.physics.sfasu.edu/astro/color.html -%% www.efg2.com/lab -% -/Gamma 0.8 def -/calculateRGB { - lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if - lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if - lambda 380 ge {lambda 439 le { - /R {lambda 440 sub neg 440 380 sub div} def - /Red R factor mul Gamma exp def - /G 0 def - /Green G factor mul Gamma exp def - /B 1 def - /Blue B factor mul Gamma exp def} if - } if - lambda 440 ge { lambda 489 le { - /G {lambda 440 sub 490 440 sub div} def - /Green G factor mul Gamma exp def - /R 0 def /Red 0 def - /B 1 def - /Blue B factor mul Gamma exp def } if - } if - lambda 490 ge {lambda 509 le { - /B {lambda 510 sub neg 510 490 sub div} def - /Blue B factor mul Gamma exp def - /R 0 def /Red 0 def - /G 1 def - /Green G factor mul Gamma exp def } if - } if - lambda 510 ge {lambda 579 le { - /R {lambda 510 sub 580 510 sub div } def - /Red R factor mul Gamma exp def - /Blue 0 def - /G 1 def - /Green G factor mul Gamma exp def } if - } if - lambda 580 ge {lambda 644 le { - /G {lambda 645 sub neg 645 580 sub div } def - /Green G factor mul Gamma exp def - /Blue 0 def - /R 1 def - /Red R factor mul Gamma exp def } if - } if - lambda 645 ge { lambda 780 le { - /Red 1 factor mul Gamma exp def - /Blue 0 def - /Green 0 def } if - } if -} def -% -/factor { - lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if - lambda 420 ge {lambda 700 le { 1 } if } if - lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if -} def -% -/wavelengthToRGB { % the wavelength in nm must be on top of the stack - cvi /lambda exch def % no floating point here - calculateRGB -} def % now the colors are saved in Red Green Blue -% -/wavelengthToCMYK { % the wavelength in nm must be on top of the stack - cvi /lambda exch def % no floating point here - gsave - calculateRGB Red Green Blue RGBtoCMYK - /Black ED /Yellow ED /Magenta ED /Cyan ED - grestore -} def % now the colors are saved in Cyan Magenta Yellow Black -% -/axfill { - 8 dict begin - /xw exch def /nl exch def - /C1 exch def /y1 exch def/x1 exch def - /C0 exch def /y0 exch def/x0 exch def - << /ShadingType 2 - /ColorSpace /DeviceRGB - /Coords [ x0 y0 x1 y1 ] - /EmulatorHints [ xw 2 div dup ] - /Function << - /FunctionType 2 - /Domain [0 1] - /C0 C0 - /C1 C1 - /N 1 - >> - >> shfill - end -} bind def -% -%%%%% ### bubblesort ### -%% syntax : array bubblesort --> array2 trie par ordre croissant -%% code de Bill Casselman -%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/ -/bubblesort { -4 dict begin - /a exch def - /n a length 1 sub def - 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-%%EndProcSet -%%BeginProcSet: pstricks.pro 0 0 -% $Id: pstricks.pro 34 2008-06-25 17:20:01Z herbert $ -% -%% PostScript prologue for pstricks.tex. -%% Version 1.05, 2008/06/25 -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -% -% -% Define the follwing gs-functions if not known, eg when using distiller -% -systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if -systemdict /.setblendmode known not {/.setblendmode { pop } def } if -systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if -% -/tx@Dict 200 dict def % the main PSTricks dictionary -tx@Dict begin -/ADict 25 dict def % The arrow dictionaray -/CM { matrix currentmatrix } bind def -/SLW /setlinewidth load def -/CLW /currentlinewidth load def -/CP /currentpoint load def -/ED { exch def } bind def -/L /lineto load def -/T /translate load def -/TMatrix { } def -/RAngle { 0 } def -/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments -/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known -/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) -/Div { dup 0 eq { pop } { div } ifelse } def % control the division -/tan { dup cos abs 1.e-10 lt - { pop 1.e10 } % return 1.e10 as infinit - { dup sin exch cos div } ifelse % default sin/cos -} def -/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees -/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root - pop pop 0 }{ sqrt exch atan} ifelse } def -/NET { neg exch neg exch T } def % change coordinate system to the negative one -/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter -/Pyth2 { % Pythagoras, xA yA xB yB - 3 -1 roll % xA xB yB yA - sub % xA xB yB-yA - 3 1 roll % yB-yA xA xB - sub % yB-yA xA-xB - Pyth } def -/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian -/Rand { rand 4294967295 div } def % a real random number -%----------------- hv added 20050516 --------------- -/PiDiv2 1.57079632680 def -/Pi 3.14159265359 def -/TwoPi 6.28318530718 def -/Euler 2.71828182846 def -%/e Euler bind def -/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees -/DegtoRad { Pi mul 180 div } bind def % viceversa -%----------------- hv end--------------------------- -/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def -/PathLength { - flattenpath /z 0 def - { /y1 ED /x1 ED /y2 y1 def /x2 x1 def } - { /y ED /x ED PathLength@ } - {} - { /y y2 def /x x2 def PathLength@ } - /pathforall load stopped { pop pop pop pop } if - z -} def -% -/STP { .996264 dup scale } def % BP/PT scaling -/STV { SDict begin normalscale end STP } def % -% -%%-------------- DG begin patch 15 ---------------%% -%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def -%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y -%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul -%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] -%0 } ifelse setdash stroke } def -/DashLine { - dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse - /b ED /x1 ED /y1 ED /x ED /y ED - /z y x add y1 add x1 add def - /Coef b a .5 sub 2 mul y mul sub z Div round - z mul a .5 sub 2 mul y mul add b exch Div def - /y y Coef mul def - /x x Coef mul def - /y1 y1 Coef mul def - /x1 x1 Coef mul def - x1 0 gt y1 0 gt or x 0 gt or y 0 gt and - { [ y x y1 x1 ] 1 a sub y mul } - { [ 1 0 ] 0 } ifelse - setdash stroke -} def -%%-------------- DG end patch 15 ---------------%% -/DotLine { - /b PathLength def - /a ED /z ED /y CLW def - /z y z add def - a 0 gt { - /b b a div def - }{ - a 0 eq { - /b b y sub def - }{ a -3 eq { - /b b y add def } if - } ifelse - } ifelse - [ 0 b b z Div round Div dup 0 le { pop 1 } if ] - a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse - setdash 1 setlinecap stroke -} def -% -/LineFill { % hv ------------ patch 7 ------------- - gsave - abs /hatchWidthInc ED - abs /hatchSepInc ED - abs CLW add /a ED - a 0 dtransform round exch round exch - 2 copy idtransform - exch Atan rotate - idtransform pop /a ED - .25 .25 itransform pathbbox - /y2 ED - a Div ceiling cvi /x2 ED /y1 ED - a Div cvi /x1 ED /y2 y2 y1 sub def - clip - newpath - 2 setlinecap - systemdict - /setstrokeadjust known { true setstrokeadjust } if - x2 x1 sub 1 add { - x1 a mul y1 moveto 0 y2 rlineto stroke - /x1 x1 1 add - hatchWidthInc 0 gt { CLW add } if - def - hatchSepInc 0 gt hatchWidthInc 0 gt or { - /a a hatchSepInc add def - CLW hatchWidthInc add SLW - } if - } repeat - grestore - pop pop } def -% -/PenroseFill {% on stack: scaling factor - dup dup scale - 1 exch div round /penroseFactor ED - a 0 dtransform round exch round exch - 2 copy idtransform - exch Atan rotate - idtransform pop /a ED - .25 .25 itransform pathbbox - /y2 ED - a Div ceiling cvi /x2 ED /y1 ED - a Div cvi /x1 ED /y2 y2 y1 sub def - clip - newpath - systemdict - /setstrokeadjust known { true setstrokeadjust } if - /I/S/L/W/G/+/Z/F/E/D[/def/exch/for{E D}/add{s E get mul} - { Z -36.2001 1 33 }{25 E S rlineto}{/q Z dup q G E q 1 + G}{Z 2 2}]{cvx def}forall - [0 72 1008 {dup sin E cos }F ]1 setlinejoin/s W{/a W{/b I 10{/i I 4{/m I moveto - i m +/j I 10{/l Z b m l + G a l G sub s m get div .2 + floor .3 + 25 - mul j l + S rmoveto}F i L j L stroke }F}F}F}F - grestore - pop pop -} def -% -%gsave abs CLW add /a ED a 0 dtransform round exch round exch -%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 -%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 -%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a -%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a -%% DG/SR modification end -%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict -%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 -%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) -%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } -%% def -%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore -%pop pop } def -%% DG/SR modification end -% -/BeginArrow { - ADict begin % hold it local, for end see EndArrow - /@mtrx CM def - gsave - 2 copy T - 2 index sub neg exch - 3 index sub exch Atan - rotate newpath -} def -% -/EndArrow { @mtrx setmatrix CP grestore end } def % end the ADict -% -/Arrow { - CLW mul add dup - 2 div /w ED - mul dup /h ED - mul /a ED - { 0 h T 1 -1 scale } if - w neg h moveto - 0 0 L w h L w neg a neg rlineto - gsave fill grestore -} def -% -/ArrowD { % the sides are drawn as curves (hv 20071211) - CLW mul add dup - 2 div /w ED - mul dup /h ED - mul /Inset ED - { 0 h T 1 -1 scale } if % changes the direction -% we use y=w/h^2 * x^2 as equation for the control points -% for the coordinates the arrow is seen from top to bottom -% the bottom (tip) is (0;0) - w neg h moveto % lower left of > - w 9 div 4 mul neg h 3 div 2 mul - w 9 div neg h 3 div - 0 0 curveto % tip of > - w 9 div h 3 div - w 9 div 4 mul h 3 div 2 mul - w h curveto % upper left of > - w neg Inset neg rlineto % move to x=0 and inset - gsave fill grestore -} def -% -/Tbar { - CLW mul add /z ED - z -2 div CLW 2 div moveto - z 0 rlineto stroke - 0 CLW moveto -} def -% -/Bracket { - CLW mul add dup CLW sub 2 div - /x ED mul CLW add /y ED /z CLW 2 div def - x neg y moveto - x neg CLW 2 div L x CLW 2 div L x y L stroke - 0 CLW moveto -} def -% -/RoundBracket { - CLW mul add dup 2 div - /x ED mul /y ED /mtrx CM def - 0 CLW 2 div T x y mul 0 ne { x y scale } if - 1 1 moveto - .85 .5 .35 0 0 0 curveto - -.35 0 -.85 .5 -1 1 curveto - mtrx setmatrix stroke 0 CLW moveto -} def -% -/SD { 0 360 arc fill } def -% -/EndDot { % DS is the dot size - { /z DS def } { /z 0 def } ifelse - /b ED 0 z DS SD b { 0 z DS CLW sub SD } if - 0 DS z add CLW 4 div sub moveto } def -% -/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { - /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto - load } if ] cvx newpath 3 1 roll T exec } def -% -%/NArray { -% aload length 2 div dup dup cvi eq not { exch pop } if /n exch -% cvi def -%} def -% -/NArray { % holds the coordinates and on top of stack the showpoints boolean - /showpoints ED - counttomark 2 div dup cvi /n ED - n eq not { exch pop } if - showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse -} def -% -/Line { - NArray n 0 eq not - { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def - n { Lineto } repeat - CP 4 2 roll ArrowB L pop pop - } if -} def -% -/Arcto { - /a [ 6 -2 roll ] cvx def - a r - /arcto load stopped { 5 } { 4 } ifelse { pop } repeat - a -} def -% -/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq - and { pop pop /n n 1 sub def } if } def -/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } - repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 - ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 - moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto - Lineto pop pop closepath } ifelse } def -/Diamond { - /mtrx CM def - T rotate - /h ED - /w ED - dup 0 eq { pop } { CLW mul neg - /d ED - /a w h Atan def - /h d a sin Div h add def - /w d a cos Div w add def } ifelse - mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div - /ArrowA { moveto } def - /ArrowB { } def - false Line - closepath mtrx setmatrix } def -% DG modification begin - Jan. 15, 1997 -%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { -%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 -%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 -%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx -%setmatrix } def -/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup -CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 -div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 -d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx -% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) -% setmatrix } def -setmatrix pop } def -% DG/SR modification end -% -/CCA { - /y ED /x ED - 2 copy y sub /dy1 ED - x sub /dx1 ED - /l1 dx1 dy1 Pyth def -} def -% -/CC { - /l0 l1 def - /x1 x dx sub def - /y1 y dy sub def - /dx0 dx1 def - /dy0 dy1 def - CCA - /dx dx0 l1 c exp mul dx1 l0 c exp mul add def - /dy dy0 l1 c exp mul dy1 l0 c exp mul add def - /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def - /x2 x l0 dx mul m mul sub def - /y2 y l0 dy mul m mul sub def - /dx l1 dx mul m mul neg def - /dy l1 dy mul m mul neg def -} def -% -/IC { - /c c 1 add def - c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse - /a a 2 mul 3 div 45 cos b exp div def - CCA - /dx 0 def - /dy 0 def -} def -% -/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def -/NC { CC x1 y1 x2 y2 x y curveto } def -/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def -/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def -/NAC { x2 y2 x y curveto CC x1 y1 } def -/EAC { x2 y2 x y ArrowB curveto pop pop } def -% -/OpenCurve { - NArray n 3 lt - { n { pop pop } repeat } - { BOC /n n 3 sub def n { NC } repeat EOC } ifelse -} def -% -/AltCurve { - { false NArray n 2 mul 2 roll - [ n 2 mul 3 sub 1 roll ] aload - /Points ED - n 2 mul -2 roll } - { false NArray } ifelse - n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse -} def -% -/ClosedCurve { - NArray n 3 lt - { n { pop pop } repeat } - { n 3 gt { CheckClosed } if - 6 copy n 2 mul 6 add 6 roll - IC CC x y moveto n { NC } repeat - closepath pop pop - } ifelse -} def -% -/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def -/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def -/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } -def -/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix -rotate matrix concatmatrix exch findfont exch makefont setfont } def -/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto -x1 y1 lineto closepath } def -/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 -y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div -exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse -/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto -x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } -ifelse } def -/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add -/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { -pop pop Rect } { OvalFrame } ifelse } def -% -/BezierNArray { - /f ED - counttomark 2 div dup cvi /n ED - n eq not { exch pop } if - n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat - f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse -} def -% -/OpenBezier { - BezierNArray - n 1 eq - { pop pop } - { ArrowA n 4 sub 3 idiv - { 6 2 roll 4 2 roll curveto } repeat - 6 2 roll 4 2 roll ArrowB curveto } ifelse -} def -% -/ClosedBezier { - BezierNArray - n 1 eq - { pop pop } - { moveto n 1 sub 3 idiv - { 6 2 roll 4 2 roll curveto } repeat - closepath } ifelse -} def -% -/BezierShowPoints { - gsave - Points aload length 2 div cvi /n ED - moveto - n 1 sub { lineto } repeat - CLW 2 div SLW [ 4 4 ] 0 setdash stroke - grestore -} def -% -/Parab { - /y0 ED /x0 ED /y1 ED /x1 ED - /dx x0 x1 sub 3 div def - /dy y0 y1 sub 3 div def - x0 dx sub y0 dy add x1 y1 ArrowA - x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB - curveto - /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def -} def -% -/Grid { - newpath - /a 4 string def - /b ED /c ED /n ED - cvi dup 1 lt { pop 1 } if - /s ED - s div dup 0 eq { pop 1 } if - /dy ED s div dup 0 eq { pop 1 } if - /dx ED dy div round dy mul - /y0 ED dx div round dx mul - /x0 ED dy div round cvi - /y2 ED dx div round cvi - /x2 ED dy div round cvi - /y1 ED dx div round cvi - /x1 ED - /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def - /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def - b 0 gt { - /z1 b 4 div CLW 2 div add def -% /Helvetica findfont b scalefont setfont - /b b .95 mul CLW 2 div add def } if - systemdict /setstrokeadjust known - { true setstrokeadjust /t { } def } - { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add - exch itransform } bind def } ifelse - gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse - /i x1 def - /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def - /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def - x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if - { i dx mul dup y0 moveto - b 0 gt - { gsave c i a cvs dup stringwidth pop - /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse - h 0 gt {b neg}{z1} ifelse - rmoveto show grestore } if - dup t f moveto - g t L stroke - /i i w add def - } repeat - grestore - gsave - n 0 gt - % DG/SR modification begin - Nov. 7, 1997 - Patch 1 - %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } - { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } - % DG/SR modification end - { 2 setlinecap } ifelse - /i y1 def - /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def - /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def - y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if - { newpath i dy mul dup x0 exch moveto - b 0 gt { gsave c i a cvs dup stringwidth pop - /z2 ED - w 0 gt {z1 z2 add neg} {z1} ifelse - h 0 gt {z1} {b neg} ifelse - rmoveto show grestore } if - dup f exch t moveto - g exch t L stroke - /i i h add def - } repeat - grestore -} def -% -/ArcArrow { - /d ED /b ED /a ED - gsave - newpath 0 -1000 moveto clip - newpath - 0 1 0 0 b - grestore - c mul - /e ED - pop pop pop r a e d PtoC y add exch x add - exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c - mul neg d -} def -% -/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def -% -/ArcAdjust { %%%% Vincent Guirardel -% given a target length (targetLength) and an initial angle (angle0) [in the stack], -% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). -% This computes an angle t such that (x0,y0) is at distance -% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). -% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 -% contrary to TvZ's code. -% To achieve, this, one iterates the following process: start with some angle t, -% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. -% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. -% -% Another difference with TvZ's code is that we need d (=add/sub) to be defined. -% the value of d = add/sub is used to know on which side we have to move. -% It is only used in the initialisation of the angle before the iteration. -% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% Input stack: 1: target length 2: initial angle -% variables used : rx, ry, d (=add/sub) -% - /targetLength ED /angle0 ED - /x0 rx angle0 cos mul def - /y0 ry angle0 sin mul def -% we are looking for an angle t such that (x0,y0) is at distance targetLength -% from the point M(t)=(rx*cos(t),ry*sin(t))) -%initialisation of angle (using 1st order approx = TvZ's code) - targetLength 57.2958 mul - angle0 sin rx mul dup mul - angle0 cos ry mul dup mul - add sqrt div -% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees -% (if the ellipse is very curved at the point where we draw the arrow, % -% the value can be much more than 360 degrees !) -% this should avoid going on the wrong side (more than 180 degrees) or go near -% a bad attractive point (at 180 degrees) - dup 90 ge { pop 90 } if - angle0 exch d % add or sub -% maximum number of times to iterate the iterative procedure: -% iterative procedure: takes an angle t on top of stack, computes a -% better angle (and put it on top of stack) - 30 { dup -% compute distance D between (x0,y0) and M(t) - dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt -% if D almost equals targetLength, we stop - dup targetLength sub abs 1e-5 le { pop exit } if -% stack now contains D t -% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: -% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) - exch dup cos rx mul x0 sub exch sin ry mul y0 sub -% stack contains: y(t)-y0, x(t)-x0, d - 2 index Div targetLength mul y0 add ry Div exch - 2 index Div targetLength mul x0 add rx Div -% stack contains x(t')/rx , y(t')/ry , d -% now compute t', and remove D from stack - atan exch pop - } repeat -% we don't look at what happened... in particular, if targetLength is greater -% than the diameter of the ellipse... -% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... -% after iteration, stack contains an angle t such that M(t) is the tail of the arrow -% to give back the result as a an angle relative to angle0 we could add the following line: -% angle0 sub 0 exch d -% -% begin bug fix 2006-01-11 -% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 -%(we don't want to make the ellipse turn more or less than it should)... -dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse -% end bug fix -} def -% -/EllipticArcArrow { - /d ED % is add or sub - /b ED % arrow procedure - /a1 ED % angle - gsave - newpath - 0 -1000 moveto - clip % Set clippath far from arrow. - newpath - 0 1 0 0 b % Draw arrow to determine length. - grestore -% Length of arrow is on top of stack. Next 3 numbers are junk. -% - a1 exch ArcAdjust % Angular position of base of arrow. - /a2 ED - pop pop pop - a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig - a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig - a1 cos rx mul xOrig add % - a1 sin ry mul yOrig add % -% Now arrow tip coor and base coor are on stack. - b pop pop pop pop % Draw arrow, and discard coordinates. - a2 CLW 8 div -% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) - 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse - ArcAdjust -% resets original value of d - 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. -} def -%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% -% -/Rot { CP CP translate 3 -1 roll neg rotate NET } def -% -/RotBegin { - tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if - /TMatrix [ TMatrix CM ] cvx def - /a ED - a Rot /RAngle [ RAngle dup a add ] cvx def -} def -% -/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def -% -/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def -/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def -/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def -/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s -abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b -div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { -h1 abs h sub dup s mul abs } ifelse } def -/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s -mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q -{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add -exch } def -/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible -/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def -} if } ifelse } def -/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def -/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit -neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def -/IfVisible true def } def -end -%-----------------------------------------------------------------------------% - -% END pstricks.pro - -%%EndProcSet -%%BeginProcSet: pst-algparser.pro 0 0 -% $Id: pst-algparser.pro 26 2008-06-14 11:50:02Z herbert $ -%% -%% PostScript prologue for PSTricks algorithm parser -%% Version 0.01, 2008/01/01 -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -%% -%%-----------------------------------------------------------------------------% -% -/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez -% -/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin -% -% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 -% E->T|E+T -% T->FS|T*FS -% FS -> F | +FS | -FS -% F->P|F^SF -% P->(E)|literal -% literal->number|var|var[E]|func(params) -% params->E|E,param -% number->TOBEFINISHED -% -%% E expression, T term, SF signed factor, F factor, P power -% -%% parser -% -%% str -% -%% C->E<condition_operators>E -%% STR index -> STR index+lenExpr -/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def -% -%% analyze Expression List (separator , or | ) -%% STR index -> STR index+lenExpr -%% /AnalyzeListOfE { -%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar -%% NextNonBlankChar dup 0 eq { pop exit } if -%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if -%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop -%% AnalyzeListOfEPostHook -%% } def -/AnalyzeListOfE { - /NotFirst false def - { NextNonBlankChar pop AnalyzeExpr - NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse - dup Strlen eq { exit } if NextNonBlankChar - dup 44 ne 1 index 124 ne and - { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } - if pop 1 add } loop - AnalyzeListOfEPostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% E->T|E+T -%% STR index -> STR index+lenExpr -/AnalyzeExpr { - AnalyzePreHook AnalyzeTerm IsEndingExpr - { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } - { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } - ifelse - AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% T->FS|T*FS -%% STR index -/AnalyzeTerm { - AnalyzePreHook AnalyzeSignedFactor IsEndingTerm - { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } - { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } - ifelse - AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% FS -> F | +FS | -FS -%% STR index -/AnalyzeSignedFactor { - AnalyzePreHook 2 copy get dup IsUnaryOp - { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } - { pop AnalyzeFactor } - ifelse AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% F->P|F^P -%% STR index -/AnalyzeFactor { - AnalyzePreHook AnalyzePower IsEndingFactor - { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } - { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } - ifelse AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% P->(E)|literal -%% STR index -/AnalyzePower { - %% depending of first char either a number, or a literal - 2 copy get dup 40 eq%%an open par - { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } - { AnalyzeLiteral } - ifelse -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index STR[index] -> STR index -%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def -/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% recognize + or - -%% chr -> T/F -/IsUnaryOp { dup 43 eq exch 45 eq or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a number can contain only : 0123456789. -%% chr -> T/F -/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index -> STR index number -%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? -%% STR index -> STR index' number -/ReadNumber { - exch dup 3 -1 roll dup 3 1 roll - %%read mantissa - { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop - dup 101 eq exch 69 eq or - %%% there is a "e" or "E" -> read exponant - { 1 add 2 copy get dup IsUnaryOp - { pop 1 add 2 copy get } if - { IsNumber not { exit } if 1 add 2 copy get } loop } - if - dup 4 1 roll - 3 -1 roll exch 1 index sub getinterval -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a number can contain only : 0123456789. -%% chr -> T/F -/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index -> STR index number -%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? -%% STR index -> STR index' number -/ReadCondOp { - NextNonBlankChar 1 index 4 1 roll - { IsCondOp not { exit } if 1 add 2 copy get } loop - 2 copy 5 -1 roll - exch 1 index sub getinterval 3 1 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a literal can contain only : 0123456789. -%% chr -> T/F -/IsLiteral {% - dup 48 ge exch dup 57 le 3 -1 roll and exch - dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch - dup 97 ge exch 122 le and or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? -%% STR index -> literal STR index' nextchr -/ReadLiteral { - exch dup 3 -1 roll dup 3 1 roll - %%read literal core - { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop - 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or a clpar -%% STR index -> STR index STR[index] T/F -/IsEndingExpr {% - 2 copy dup Strlen eq - %% if end of str is reached -> end ! - { pop pop 0 true } - %% ending chr -> clpar, comma, |, <, >, =, !, - {get dup dup 41 eq - exch dup 124 eq - exch dup 93 eq - exch dup 44 eq - exch dup 30 eq - exch dup 60 ge exch 62 le and or or or or or} - ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or a +- -%% STR index -> STR index STR[index] T/F -/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or */ -%% STR index -> STR index STR[index] T/F -/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or ^ -%% STR index -> STR index STR[index] T/F -/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index -> STR index STR[index] -/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def -/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def -%%%%%%%%%%%%%%%%%%%%%%%% -%% DEBUG -/BRK {false} def -/BRKtrue {/BRK true def} def -/BRKStop {BRK {BRKtoto} if } def -/BRKEvalStop {BRK exch if } def -/BRKBRK2true {BRK {BRK2true} if } def -/BRK2 {false} def -/BRK2true {/BRK2 true def} def -/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def -end -% -%-------------------------------------------------------------------------------% -% -/tx@AlgToPs 12 dict def tx@AlgToPs begin -% -%% algExpr -> PSVector -/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def -/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def -/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def -/Strlen 0 def -/EvalListOfExpr {} def% -/EvalNumber {% - ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx - exch 1 add array astore def NextNonBlankChar pop } def -/EvalAddSub {% - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll - 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def -} def -/EvalMulDiv {% - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll - 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def -} def -/EvalPower {% - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll - pop /exp cvx exch 1 add array astore def -} def -/EvalLiteral {% - ReadLiteral - dup 40 eq%%% there is an open par -> function call - { pop 2 index - dup (Sum) eq { EvalSum } - { dup (IfTE) eq { EvalCond } - { dup (Derive) eq { pop EvalDerive } - { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx - exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } - { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def - dup 91 eq%%% there is an open bracket -> vector element - { pop 1 add NextNonBlankChar pop AnalyzeExpr - /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } - { pop NextNonBlankChar pop } - ifelse} - ifelse -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% the derive function : Derive(n,f(x)) -%% firstparindex lastparindex -> -/EvalDerive { - %% manage the function descripiton - 1 add ReadNumber 3 1 roll NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - 1 add NextNonBlankChar pop - 3 -1 roll cvi - dup 0 eq - { pop AnalyzeExpr 3 -1 roll pop 1 add } - { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll - { (x) tx@Derive begin Derive end } repeat - ExpressionVector exch /ExpressionVector [] def - AlgToPs aload length - /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def - l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add - 1 index length /Strlen exch def } ifelse -} def -/EvalSum {% - pop 1 add NextNonBlankChar pop - %% read the variable name - ReadLiteral pop NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if - %% read the initial value - 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - %% read the increment value - 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - %% read the limit value - 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll - 5 -1 roll 4 add array astore def - %% keep ExpressionVector for later and create a new one for internal Sum computation - ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def - 1 add NextNonBlankChar pop AnalyzeExpr - %% add each term - /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def - /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add - array astore def 3 -1 roll pop 1 add -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Convert to radians if trigo function call -%% (name) -> -/TrigoFunc { - dup (cos) eq 1 index (sin) eq or exch (tan) eq or - { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add - array astore def - } if -} def -/EvalCond {% - pop 1 add AnalyzeCond NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if - ExpressionVector 3 1 roll /ExpressionVector [] def - 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def - NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if - 1 add AnalyzeExpr - NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if - ExpressionVector - /ExpressionVector 6 -1 roll aload length dup - 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def - 1 add 3 -1 roll pop -} def -%% CondOp STR index -/EvalCondOp {% - 3 -1 roll - dup (=) eq { /eq } {% - dup (<) eq { /lt } {% - dup (>) eq { /gt } {% - dup (>=) eq { /ge } {% - dup (<=) eq { /ge } {% - dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } - ifelse } ifelse } ifelse } ifelse } ifelse } ifelse - cvx exch pop - /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def -/EvalUnaryOp { - 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% H O O K S -/AnalyzePreHook {} bind def -/PreEvalHook {} bind def -/AnalyzeListOfEPostHook {} bind def -/AnalyzePostHook {} def -/RollOp { 3 1 roll } bind def -end %tx@CoreAnalyzerDict -% -%--------------------------------------------------------------------% -% -/tx@Derive 41 dict def tx@Derive begin -%%increase ^^ for each function added -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% algExpr variable -> PSVector -/Derive {% - 10240 string 3 1 roll 0 3 1 roll - /Variable exch def - tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end -} def -/Strlen 0 def -/InitParser { dup length /Strlen exch def 0 } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% algExpr variable index -> PSVector -/DeriveIndexed {% - 3 1 roll 10240 string 3 1 roll 0 3 1 roll - /Variable exch def - tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u,v)'=-(u',v') -/EvalListOfExpr {% - 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe - 2 copy 7 -1 roll dup length 4 1 roll putinterval add - 6 -2 roll pop pop - 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (-u)'=-(u') -/EvalUnaryOp { - 4 -2 roll 4 index (0) eq - { (0) StrConcat 7 -1 roll pop } - { 7 -1 roll 45 eq - { AddSub AddOpPar true } { false } ifelse - 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (number)'=0 -/EvalNumber { ReadNumber (0) 6 2 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u+v)'=u'+v' -/EvalAddSub {% - 7 index dup (0) eq - { pop true }%% du=0 nothing added - { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } - ifelse - 5 index dup (0) eq - { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 - { exch - { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added - { 5 -2 roll 7 index 43 eq%%something yet added - { AddAdd false } { AddSub AddOpPar true } ifelse } - ifelse 11 1 roll - 3 -1 roll StrConcat 10 -1 roll { AddClPar } if - 2 copy pop 0 6 2 roll GetIntervalNewStr } - ifelse - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u*v)' or (u/v)' -/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u*v)'=u'*v+u*v' -/EvalMul {% - 4 -2 roll 7 index dup (0) eq - { pop false }%%du=0 - { (1) eq%%du=1 - { false } - { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse - 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if - true }%%du!=0 - ifelse - 5 1 roll 5 index (0) eq - { 5 -1 roll not { (0) StrConcat } if }%%dv=0 - { 5 -1 roll { AddAdd } if - 4 index (1) eq - { 8 index StrConcat } - { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } - ifelse - }%%dv!=0 - ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u/v)'=(u'*v-u*v')/v^2 -/EvalDiv {% - 4 -2 roll - 4 index (0) eq%%dv=0 -> u'/v - { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } - { 7 index dup (0) eq - { pop }%%du=0 - { (1) eq%%du=1 - { false } - { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse - 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 - ifelse - AddSub - 4 index (1) eq - { 8 index StrConcat } - { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } - ifelse - %}%%dv!=0 - 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar - AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } - ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% str1 index str2 -> str1 index -/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def -/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) -/EvalPower {% - 4 -2 roll 7 index (0) eq - {%%if du=0 then (u^v)'=v'ln(u)u^v - 4 index (0) eq - { (0) StrConcat }%%if dv=0 then (u^v)'=0 - { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if - 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if - AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse - } - {%%du!=0 - 4 index (0) eq - {%%if dv=0 then (u^v)'=vu'u^(v-1) - 5 index dup IsStrNumber - { dup (0) eq - { StrConcat } - { dup dup (1) eq exch (1.0) eq or - { StrConcat } - { StrConcat - 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 - { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 - (*\() StrConcat 8 index StrConcat (\)) StrConcat - 5 index dup dup (2) eq exch (2.0) eq or - { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } - { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat - 5 index StrConcat (-1\)) StrConcat } ifelse - } - {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) - 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if - AddOpPar 5 index StrConcat (\)*\() StrConcat - 8 index StrConcat (\)^\() StrConcat - 5 index StrConcat (-1\)+\() StrConcat - 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if - 8 index StrConcat (\)^\() StrConcat - 5 index StrConcat (\)*ln\() StrConcat - 8 index StrConcat AddClPar - } ifelse - } ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% str -> true/false -/IsStrNumber {% - true exch - { dup 48 lt exch dup 57 gt 3 -1 roll or - exch dup 46 ne%%. - exch dup 43 ne%%+ - exch 45 ne%%- - and and and { pop false } if } forall -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% literal switch -> func call, vector, variables -/EvalLiteral {% - ReadLiteral dup 40 eq%%% there is an open par -> function call - { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } - { dup 91 eq%%% there is an open bracket -> vector element - { ERROR_vector_not_yet_implemented } - { pop EvalVariable } - ifelse } - ifelse -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% first last parpos Expr[first:parpos-1] -> -/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (f(u))'=u'f'(u) -/EvalFunc { - 4 2 roll 4 index (1) ne - { AddOpPar 4 index StrConcat (\)*) StrConcat } if - (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Func derivative -> Eval<func> -/EvalFunc_sin {% - PreCommonFunc - { (cos\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_cos {% - PreCommonFunc - { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_tan {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if - PostCommonFunc } def -/EvalFunc_asin {% - PreCommonFunc - { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_acos {% - PreCommonFunc - { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_atg {% - PreCommonFunc - { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_ln {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_exp {% - PreCommonFunc - { (exp\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_sqrt {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_Fact {% - PreCommonFunc { ERROR_no_variable_expression_in_Fact } if - PostCommonFunc } def -/EvalFunc_sh {% - PreCommonFunc - { (ch\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_ch {% - PreCommonFunc - { (sh\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_th {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if - PostCommonFunc } def -/EvalFunc_Argsh {% - PreCommonFunc - { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_Argch {% - PreCommonFunc - { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_Argth {% - PreCommonFunc - { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -/PreCommonFunc { - 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop - 4 2 roll 4 index (0) eq - { (0) StrConcat false } - { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse -} def -/PostCommonFunc { - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -/EvalFunc_Derive {% - 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs - 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add - 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar - 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval - exch 6 2 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% literal switch -> func call, vector, variables -/EvalFunc_Sum {% - 1 add NextNonBlankChar pop - %% read the variable name - ReadLiteral pop 3 -1 roll pop NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if - %% read the initial value - 1 add NextNonBlankChar pop ReadNumber pop - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - %% read the increment value - 1 add NextNonBlankChar pop ReadNumber pop - 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if - %% read the limit value - 1 add NextNonBlankChar pop ReadNumber pop - 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if - 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop - 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat - 4 index StrConcat AddClPar - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% literal switch -> func call, vector, variables -/EvalFunc_IfTE {% - 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond - NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if - 1 add NextNonBlankChar pop dup 5 1 roll - AnalyzeExpr NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if - 1 add NextNonBlankChar pop - AnalyzeExpr 1 add NextNonBlankChar pop - 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat - 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% advance in str until a comma is found (no error detection!) -%% str index -> str index' -/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Convert to radians if trigo function call -%% (name) -> -/TrigoFunc { - dup (cos) eq 1 index (sin) eq or exch (tan) eq or - { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add - array astore def - } if -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% No derivative for condition.... -/EvalCondOp { 3 -1 roll pop } bind def -/PutIntervalOneAdd {putinterval 1 add} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add open parenthesis in string at the given index -%% str index -> str index+1 -/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add close parenthesis in string at the given index -%% str index -> str index+1 -/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add 0 in string at the given index -%% str index -> str index+1 -/AddZero {2 copy (0) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add open parenthesis in string at the given index -%% str index -> str index+1 -/AddMul {2 copy (*) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add open parenthesis in string at the given index -%% str index -> str index+1 -/AddDiv {2 copy (/) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add a plus sign in string at the given index -%% str index -> str index+1 -/AddAdd {2 copy (+) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add a minus sign in string at the given index -%% str index -> str index+1 -/AddSub {2 copy (-) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add a pipe sign in string at the given index -%% str index -> str index+1 -/AddPipe {2 copy (|) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% H O O K S -/AnalyzePreHook { dup 5 1 roll } bind def -/PreEvalHook {} def -/AnalyzePostHook { 7 -1 roll pop } bind def -/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def -/RollOp { 5 1 roll } bind def -end%%%tx@CoreAnalyzerDict -/tx@AddMathFunc 12 dict def tx@AddMathFunc begin -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% NEW FUNC -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) -%% x -> theta -/asin {% - dup abs 1 gt { EQDFasinrangeerror } if - dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad -} def -%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) -%% x -> theta -/acos {% - dup abs 1 gt { EQDFacosrangeerror } if - dup dup mul 1 exch sub sqrt exch atan DegtoRad -} def -%% function arctangent in radians -%% x -> theta -/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def -%% HYPERBOLIC FUNCTIONS -/sh { dup Ex exch neg Ex sub 2 div } def -/ch { dup Ex exch neg Ex add 2 div } def -/th { dup sh exch ch div } def -/Argsh { dup dup mul 1 add sqrt add ln } def -/Argch { dup dup mul 1 sub sqrt add ln } def -/Argth { dup 1 add exch 1 exch sub div ln 2 div } def -%% modified exponential funtion for 0 -%% x n -> x^n -/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def -%% modified exponential funtion for 0 -%% x -> e^x -/Ex { Euler exch exp } bind def -%% -%% factorial function -%% n -> n! -/Fact { 1 exch 2 exch 1 exch { mul } for } bind def -/fact { Fact } bind def -end - -% END pstricks.pro - -%%EndProcSet -%%BeginProcSet: pst-dots.pro 0 0 -% $Id: pst-dots.pro 26 2008-06-14 11:50:02Z herbert $ -% -%% PostScript prologue for pstricks.tex. -%% Version 2.02, 2008/04/18 -%% -%% For distribution, see pstricks.tex. -%% -%% Timothy Van Zandt <tvz@Princeton.EDU> -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -%% -%% Modified by Etienne Riga - Dec. 16, 1999 -%% Modified by Etienne Riga - 2005/01/01 (er) -%% to add /Diamond, /SolidDiamond and /BoldDiamond -%% Modified by Herbert Voss (hv) - 2008/04/17 -% -10 dict dup begin % hold local - /FontType 3 def - /FontMatrix [.001 0 0 .001 0 0] def - /FontBBox [-571.5 -742.5 571.5 742.5] def -% /FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph - /Encoding 256 array def - 0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef - Encoding % replace with given dot names - dup (b) 0 get /Bullet put % get the numerical position of b in ASCII -% % and save /Bullet at this place in Encoding - dup (c) 0 get /Circle put - dup (C) 0 get /BoldCircle put % 67 - dup (u) 0 get /SolidTriangle put - dup (t) 0 get /Triangle put - dup (T) 0 get /BoldTriangle put - dup (r) 0 get /SolidSquare put - dup (s) 0 get /Square put - dup (S) 0 get /BoldSquare put - dup (q) 0 get /SolidPentagon put - dup (p) 0 get /Pentagon put - dup (P) 0 get /BoldPentagon put -%%% - dup (k) 0 get /Asterisk put - dup (K) 0 get /BoldAsterisk put - dup (J) 0 get /SolidAsterisk put - dup (h) 0 get /Hexagon put - dup (H) 0 get /BoldHexagon put - dup (G) 0 get /SolidHexagon put - dup (f) 0 get /Octogon put % 2008-04-18 hv - dup (F) 0 get /BoldOctogon put % 2008-04-18 hv - dup (g) 0 get /SolidOctogon put % 2008-04-18 hv - dup (a) 0 get /Add put - dup (A) 0 get /BoldAdd put % 65 - dup (x) 0 get /Mul put - dup (X) 0 get /BoldMul put - dup (m) 0 get /Oplus put - dup (M) 0 get /BOplus put - dup (e) 0 get /SolidOplus put - dup (n) 0 get /Otimes put - dup (N) 0 get /BOtimes put - dup (E) 0 get /SolidOtimes put - dup (i) 0 get /Bar put - dup (I) 0 get /BoldBar put - dup (l) 0 get /SolidDiamond put - dup (d) 0 get /Diamond put - (D) 0 get /BoldDiamond put -%%% -/CharProcs 47 dict def -CharProcs begin - /CirclePath {0 0 500 0 360 arc closepath} def - /Bullet {CirclePath fill} def - /Circle {CirclePath .9 .9 scale CirclePath eofill} def - /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def - /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def - /SolidTriangle {TrianglePath fill} def - /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def - /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def - /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def - /SolidSquare {SquarePath fill} def - /Square {SquarePath .89 .89 scale SquarePath eofill} def - /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def - /PentagonPath { - -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto - 0 574.7 lineto -546.6 177.6 lineto closepath - } def - /SolidPentagon {PentagonPath fill} def - /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def - /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def -%-------------- hv begin 2004/07/25 from: er 2003/03/24 - /HexagonPath { - 0 550 moveto -476 275 lineto -476 -275 lineto - 0 -550 lineto 476 -275 lineto 476 275 lineto closepath - } def - /SolidHexagon {HexagonPath fill} def - /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def - /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def -% 2008-04-18 hv - /OctogonPath { - 550 dup 22.5 tan mul dup neg dup add /xMove exch def - exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def - /SolidOctogon { OctogonPath fill } def - /Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def - /BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def -% - /AsteriskPath { - 20 0 moveto 10 250 180 500 0 500 curveto - -180 500 -10 250 -20 0 curveto closepath - } def - /Asterisk { - AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath - 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill - } def -% - /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def - /BoldAsteriskPath { - 50 30 cos 100 mul moveto Basterp - 60 rotate Basterp 60 rotate Basterp - 60 rotate Basterp 60 rotate Basterp - 60 rotate Basterp closepath - } def - /BoldAsterisk {BoldAsteriskPath fill} def - /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def - /CrossPath { - 40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto - -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto - 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath - } def - /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto - -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto - 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath - } def - /Add {CrossPath fill} def - /Mul {45 rotate CrossPath fill} def - /BoldAdd {BoldCrossPath fill} def - /BoldMul {45 rotate BoldCrossPath fill} def - /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def - /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def - /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def - /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def - /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def - /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def - /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def - /Bar {BarPath fill} def - /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def - /BoldBar {BoldBarPath fill} def - /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath} def - /SolidDiamond {DiamondPath fill} def - /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def - /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def -%%% - /.notdef { } def -end -% -/BuildGlyph { - exch - begin -% Metrics 1 index get exec 0 - 0 0 -% BBoxes 3 index get exec - -1000 -1000 1000 1000 -% -571.5 -742.5 571.5 742.5 - setcachedevice - CharProcs begin load exec end - end -} def -% -/BuildChar { - 1 index /Encoding get exch get - 1 index /BuildGlyph get exec -} bind def - -end -/PSTricksDotFont exch definefont pop - -%% end - -%%EndProcSet -%%BeginProcSet: pst-node.pro 0 0 -% $Id: pst-node.pro 26 2008-06-14 11:50:02Z herbert $ -%% -%% PostScript prologue for pst-node.tex. -%% Version 1.00, 2008/01/01. -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -% -/tx@NodeDict 400 dict def tx@NodeDict begin -tx@Dict begin % from main pstricks dict - /T /translate load def -end -/NewNode { % on stack: { x y } boolean N@name type InitXnode - gsave - /next ED % { x y } boolean N@name type - dict dup % { x y } boolean N@name dict dict - 3 1 roll def % { x y } boolean dict N@name dict def - exch { dup 3 1 roll def } if % { x y } dict boolean - begin % { x y } dict begin - tx@Dict begin - STV CP T exec % set scaling - end - /NodeMtrx CM def % save CM - next % InitXNode - end - grestore -} def -% -/InitPnode { - /Y ED /X ED - /NodePos { NodeSep Cos mul NodeSep Sin mul } def -} def -% -/InitCnode { - /r ED /Y ED /X ED - /NodePos { NodeSep r add dup Cos mul exch Sin mul } def -} def -% -/GetRnodePos { - Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse - Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse - dx Sin mul abs dy - Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse -} def -% -/InitRnode { - /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED - /NodePos { GetRnodePos } def -} def -% -/DiaNodePos { - w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup - Cos mul exch Sin mul -} def -% -/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h -mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul -} ifelse } def -/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d -ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d -sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan -sin def /NodePos { TriNodePos } def } def -/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos -hh mul Atan dup cos ww mul exch sin hh mul } def -/GetCenter { begin X Y NodeMtrx transform CM itransform end } def -% -/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist - Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } - { 0 Dist Sin mul } ifelse } ifelse Do -} def -/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform - exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx - dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop - XYPos } ifelse -} def -/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 -roll sin mul sub exch } ifelse } def -/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA -AddOffset yA add /yA1 ED xA add /xA1 ED } def -/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB -AddOffset yB add /yB1 ED xB add /xB1 ED } def -/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA -AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED -ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED -} ifelse } def -/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB -AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED -ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED -} ifelse } def -/InitNC { - /b ED /a ED % second and first node - /NodeSepTypeB ED /NodeSepTypeA ED - /NodeSepB ED /NodeSepA ED - /OffsetB ED /OffsetA ED - tx@NodeDict a known tx@NodeDict b known and dup { - /NodeA a load def - /NodeB b load def - NodeA GetCenter /yA ED /xA ED - NodeB GetCenter /yB ED /xB ED } if -} def -% -/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub -mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def -/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt -{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop -} repeat LPutLine cleartomark } def -/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED -/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 -mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx -sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul -add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add -y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul -mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def -/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def -} def -/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def -/NAngle yyB yyA sub xxB xxA sub Atan def } def -/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def -/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def -} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit -} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd -} def -/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def -} def -/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def -/NAngle yyB yyA sub xxB xxA sub Atan def } def -/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def -/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def -} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { -exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark -VPosEnd } def -/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 -roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx -def grestore exec /LPutVar /SaveLPutVar load def } def -/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def -GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { -LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { -LPutVar VPutLine } def LPutVar } def -/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop -end } def -/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub -Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan -/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 -yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { -LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } -ifelse } def -/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 -roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA -GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict -begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] -cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines -} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def -% -/NCAngles { - GetEdgeA GetEdgeB GetArmA GetArmB - /mtrx AngleA matrix rotate def - xA2 yA2 mtrx transform pop - xB2 yB2 mtrx transform exch pop - mtrx itransform - /y0 ED /x0 ED - mark ArmB 0 ne { xB1 yB1 } if - xB2 yB2 x0 y0 xA2 yA2 - ArmA 0 ne { xA1 yA1 } if - tx@Dict begin false Line end - /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def - /LPutPos { LPutLines } def - /HPutPos { HPutLines } def - /VPutPos { VPutLines } def } def -% -/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 -yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform -/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 -tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] -cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { -VPutLines } def } def -/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def -xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx -transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } -{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB -0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict -begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx -def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { -VPutLines } def } def -/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if -xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end -/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { -LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } -def -/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED -GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin -false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { -LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } -def -/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate -def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 -mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 -mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 -xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false -Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] -cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { -VPutLines } def } def -% DG/SR modification begin - May 9, 1997 - Patch 1 -%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r -%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add -%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 -%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED -/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r -r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add -exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 -mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED -% DG/SR modification end -} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add -AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r -Div def /y ED /x ED } def -/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB -180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos -mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def -/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy -add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos -{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar -tx@Dict begin false Polygon end } def -/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan -def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 -mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def -/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div -def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def -GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul -sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 -eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } -{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def -0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 -roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 -0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 -roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } -ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos -{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { -r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } -{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add -add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub -mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t -sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse -y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { -LPutPos } def } def -/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB -sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 -ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB -w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos -{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } -{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } -def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin -/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def - -/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg -exch X sub neg exch moveto setmatrix CP grestore } def - -/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 -def } ifelse LPutCoor } def -/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } -if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } -ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } -def -/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if -r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } -ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } -def -end -% END pst-node.pro - -%%EndProcSet -%%BeginProcSet: pstricks-add.pro 0 0 -%% $Id: pstricks-add.pro 49 2008-10-13 10:59:27Z herbert $ -% PostScript prologue for pstricks-add.tex. -% Version 0.21, 2008/10/15 -% For distribution, see pstricks.tex. -% -% HISTORY -> see file Changes -% -/tx@addDict 410 dict def tx@addDict begin -%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -/GTriangle { - gsave - /mtrx CM def - /colorA ED /colorB ED /colorC ED % save the colors - /yA ED /xA ED % save the origin - xA yA translate - rotate % \psk@gangle - /yB ED /xB ED /yC ED /xC ED % save other coordinates - /ds [ % save data in a array - 0 0 0 colorA aload pop % fd x y xr xg xb - 0 xB xA sub yB yA sub colorB aload pop - 0 xC xA sub yC yA sub colorC aload pop -% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD - ] def - newpath - << - /ShadingType 4 % single Gouraud - /ColorSpace [ /DeviceRGB ] - /DataSource ds - >> - shfill - closepath - mtrx - setmatrix grestore} def -% -/RGBtoCMYK { % on stack r g b -> C M Y K - 3 dict begin - /Blue ED /Green ED /Red ED - 1 Red sub % Cyan - 1 Green sub % Magenta - 1 Blue sub % Yellow - 0 % Black - end -} def -% -/CMYKtoGRAY { % on stack c m y k -> gray - exch 0.11 mul add - exch 0.59 mul add - exch 0.3 mul add - dup 1 gt { pop 1 } if - neg 1 add -} def -% -/RGBtoGRAY { % on stack r g b -> gray - 0.11 mul - exch 0.59 mul add - exch 0.3 mul add -} def -% -/HSBtoGRAY { - 6 dict begin - /b exch def - /s exch def 6 mul dup cvi dup - /i exch def sub - /f exch def - /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def - F i get { s mul neg 1 add b mul} forall - 0.11 mul - exch 0.59 mul add - exch 0.3 mul add - end -} def -% -%% convertisseur longueur d'onde ->R,G,B Manuel Luque -%% lambda max=780 nanometres -%% lambda min=380 nanometres -%% adaptation de : -%% http://www.physics.sfasu.edu/astro/color.html -%% www.efg2.com/lab -% -/Gamma 0.8 def -/calculateRGB { - lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if - lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if - lambda 380 ge {lambda 439 le { - /R {lambda 440 sub neg 440 380 sub div} def - /Red R factor mul Gamma exp def - /G 0 def - /Green G factor mul Gamma exp def - /B 1 def - /Blue B factor mul Gamma exp def} if - } if - lambda 440 ge { lambda 489 le { - /G {lambda 440 sub 490 440 sub div} def - /Green G factor mul Gamma exp def - /R 0 def /Red 0 def - /B 1 def - /Blue B factor mul Gamma exp def } if - } if - lambda 490 ge {lambda 509 le { - /B {lambda 510 sub neg 510 490 sub div} def - /Blue B factor mul Gamma exp def - /R 0 def /Red 0 def - /G 1 def - /Green G factor mul Gamma exp def } if - } if - lambda 510 ge {lambda 579 le { - /R {lambda 510 sub 580 510 sub div } def - /Red R factor mul Gamma exp def - /Blue 0 def - /G 1 def - /Green G factor mul Gamma exp def } if - } if - lambda 580 ge {lambda 644 le { - /G {lambda 645 sub neg 645 580 sub div } def - /Green G factor mul Gamma exp def - /Blue 0 def - /R 1 def - /Red R factor mul Gamma exp def } if - } if - lambda 645 ge { lambda 780 le { - /Red 1 factor mul Gamma exp def - /Blue 0 def - /Green 0 def } if - } if -} def -% -/factor { - lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if - lambda 420 ge {lambda 700 le { 1 } if } if - lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if -} def -% -/wavelengthToRGB { % the wavelength in nm must be on top of the stack - 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x1 y1 - moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto - Lineto pop pop closepath } ifelse } def -/Diamond { - /mtrx CM def - T rotate - /h ED - /w ED - dup 0 eq { pop } { CLW mul neg - /d ED - /a w h Atan def - /h d a sin Div h add def - /w d a cos Div w add def } ifelse - mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div - /ArrowA { moveto } def - /ArrowB { } def - false Line - closepath mtrx setmatrix } def -% DG modification begin - Jan. 15, 1997 -%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { -%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 -%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 -%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx -%setmatrix } def -/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup -CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 -div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 -d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx -% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) -% setmatrix } def -setmatrix pop } def -% DG/SR modification end -% -/CCA { - /y ED /x ED - 2 copy y sub /dy1 ED - x sub /dx1 ED - /l1 dx1 dy1 Pyth def -} def -% -/CC { - /l0 l1 def - /x1 x dx sub def - /y1 y dy sub def - /dx0 dx1 def - /dy0 dy1 def - CCA - /dx dx0 l1 c exp mul dx1 l0 c exp mul add def - /dy dy0 l1 c exp mul dy1 l0 c exp mul add def - /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def - /x2 x l0 dx mul m mul sub def - /y2 y l0 dy mul m mul sub def - /dx l1 dx mul m mul neg def - /dy l1 dy mul m mul neg def -} def -% -/IC { - /c c 1 add def - c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse - /a a 2 mul 3 div 45 cos b exp div def - CCA - /dx 0 def - /dy 0 def -} def -% -/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def -/NC { CC x1 y1 x2 y2 x y curveto } def -/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def -/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def -/NAC { x2 y2 x y curveto CC x1 y1 } def -/EAC { x2 y2 x y ArrowB curveto pop pop } def -% -/OpenCurve { - NArray n 3 lt - { n { pop pop } repeat } - { BOC /n n 3 sub def n { NC } repeat EOC } ifelse -} def -% -/AltCurve { - { false NArray n 2 mul 2 roll - [ n 2 mul 3 sub 1 roll ] aload - /Points ED - n 2 mul -2 roll } - { false NArray } ifelse - n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse -} def -% -/ClosedCurve { - NArray n 3 lt - { n { pop pop } repeat } - { n 3 gt { CheckClosed } if - 6 copy n 2 mul 6 add 6 roll - IC CC x y moveto n { NC } repeat - closepath pop pop - } ifelse -} def -% -/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def -/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def -/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } -def -/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix -rotate matrix concatmatrix exch findfont exch makefont setfont } def -/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto -x1 y1 lineto closepath } def -/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 -y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div -exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse -/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto -x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } -ifelse } def -/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add -/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { -pop pop Rect } { OvalFrame } ifelse } def -% -/BezierNArray { - /f ED - counttomark 2 div dup cvi /n ED - n eq not { exch pop } if - n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat - f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse -} def -% -/OpenBezier { - BezierNArray - n 1 eq - { pop pop } - { ArrowA n 4 sub 3 idiv - { 6 2 roll 4 2 roll curveto } repeat - 6 2 roll 4 2 roll ArrowB curveto } ifelse -} def -% -/ClosedBezier { - BezierNArray - n 1 eq - { pop pop } - { moveto n 1 sub 3 idiv - { 6 2 roll 4 2 roll curveto } repeat - closepath } ifelse -} def -% -/BezierShowPoints { - gsave - Points aload length 2 div cvi /n ED - moveto - n 1 sub { lineto } repeat - CLW 2 div SLW [ 4 4 ] 0 setdash stroke - grestore -} def -% -/Parab { - /y0 ED /x0 ED /y1 ED /x1 ED - /dx x0 x1 sub 3 div def - /dy y0 y1 sub 3 div def - x0 dx sub y0 dy add x1 y1 ArrowA - x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB - curveto - /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def -} def -% -/Grid { - newpath - /a 4 string def - /b ED /c ED /n ED - cvi dup 1 lt { pop 1 } if - /s ED - s div dup 0 eq { pop 1 } if - /dy ED s div dup 0 eq { pop 1 } if - /dx ED dy div round dy mul - /y0 ED dx div round dx mul - /x0 ED dy div round cvi - /y2 ED dx div round cvi - /x2 ED dy div round cvi - /y1 ED dx div round cvi - /x1 ED - /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def - /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def - b 0 gt { - /z1 b 4 div CLW 2 div add def -% /Helvetica findfont b scalefont setfont - /b b .95 mul CLW 2 div add def } if - systemdict /setstrokeadjust known - { true setstrokeadjust /t { } def } - { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add - exch itransform } bind def } ifelse - gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse - /i x1 def - /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def - /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def - x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if - { i dx mul dup y0 moveto - b 0 gt - { gsave c i a cvs dup stringwidth pop - /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse - h 0 gt {b neg}{z1} ifelse - rmoveto show grestore } if - dup t f moveto - g t L stroke - /i i w add def - } repeat - grestore - gsave - n 0 gt - % DG/SR modification begin - Nov. 7, 1997 - Patch 1 - %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } - { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } - % DG/SR modification end - { 2 setlinecap } ifelse - /i y1 def - /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def - /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def - y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if - { newpath i dy mul dup x0 exch moveto - b 0 gt { gsave c i a cvs dup stringwidth pop - /z2 ED - w 0 gt {z1 z2 add neg} {z1} ifelse - h 0 gt {z1} {b neg} ifelse - rmoveto show grestore } if - dup f exch t moveto - g exch t L stroke - /i i h add def - } repeat - grestore -} def -% -/ArcArrow { - /d ED /b ED /a ED - gsave - newpath 0 -1000 moveto clip - newpath - 0 1 0 0 b - grestore - c mul - /e ED - pop pop pop r a e d PtoC y add exch x add - exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c - mul neg d -} def -% -/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def -% -/ArcAdjust { %%%% Vincent Guirardel -% given a target length (targetLength) and an initial angle (angle0) [in the stack], -% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). -% This computes an angle t such that (x0,y0) is at distance -% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). -% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 -% contrary to TvZ's code. -% To achieve, this, one iterates the following process: start with some angle t, -% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. -% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. -% -% Another difference with TvZ's code is that we need d (=add/sub) to be defined. -% the value of d = add/sub is used to know on which side we have to move. -% It is only used in the initialisation of the angle before the iteration. -% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% Input stack: 1: target length 2: initial angle -% variables used : rx, ry, d (=add/sub) -% - /targetLength ED /angle0 ED - /x0 rx angle0 cos mul def - /y0 ry angle0 sin mul def -% we are looking for an angle t such that (x0,y0) is at distance targetLength -% from the point M(t)=(rx*cos(t),ry*sin(t))) -%initialisation of angle (using 1st order approx = TvZ's code) - targetLength 57.2958 mul - angle0 sin rx mul dup mul - angle0 cos ry mul dup mul - add sqrt div -% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees -% (if the ellipse is very curved at the point where we draw the arrow, % -% the value can be much more than 360 degrees !) -% this should avoid going on the wrong side (more than 180 degrees) or go near -% a bad attractive point (at 180 degrees) - dup 90 ge { pop 90 } if - angle0 exch d % add or sub -% maximum number of times to iterate the iterative procedure: -% iterative procedure: takes an angle t on top of stack, computes a -% better angle (and put it on top of stack) - 30 { dup -% compute distance D between (x0,y0) and M(t) - dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt -% if D almost equals targetLength, we stop - dup targetLength sub abs 1e-5 le { pop exit } if -% stack now contains D t -% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: -% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) - exch dup cos rx mul x0 sub exch sin ry mul y0 sub -% stack contains: y(t)-y0, x(t)-x0, d - 2 index Div targetLength mul y0 add ry Div exch - 2 index Div targetLength mul x0 add rx Div -% stack contains x(t')/rx , y(t')/ry , d -% now compute t', and remove D from stack - atan exch pop - } repeat -% we don't look at what happened... in particular, if targetLength is greater -% than the diameter of the ellipse... -% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... -% after iteration, stack contains an angle t such that M(t) is the tail of the arrow -% to give back the result as a an angle relative to angle0 we could add the following line: -% angle0 sub 0 exch d -% -% begin bug fix 2006-01-11 -% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 -%(we don't want to make the ellipse turn more or less than it should)... -dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse -% end bug fix -} def -% -/EllipticArcArrow { - /d ED % is add or sub - /b ED % arrow procedure - /a1 ED % angle - gsave - newpath - 0 -1000 moveto - clip % Set clippath far from arrow. - newpath - 0 1 0 0 b % Draw arrow to determine length. - grestore -% Length of arrow is on top of stack. Next 3 numbers are junk. -% - a1 exch ArcAdjust % Angular position of base of arrow. - /a2 ED - pop pop pop - a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig - a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig - a1 cos rx mul xOrig add % - a1 sin ry mul yOrig add % -% Now arrow tip coor and base coor are on stack. - b pop pop pop pop % Draw arrow, and discard coordinates. - a2 CLW 8 div -% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) - 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse - ArcAdjust -% resets original value of d - 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. -} def -%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% -% -/Rot { CP CP translate 3 -1 roll neg rotate NET } def -% -/RotBegin { - tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if - /TMatrix [ TMatrix CM ] cvx def - /a ED - a Rot /RAngle [ RAngle dup a add ] cvx def -} def -% -/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def -% -/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def -/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def -/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def -/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s -abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b -div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { -h1 abs h sub dup s mul abs } ifelse } def -/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s -mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q -{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add -exch } def -/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible -/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def -} if } ifelse } def -/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def -/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit -neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def -/IfVisible true def } def -end -%-----------------------------------------------------------------------------% - -% END pstricks.pro - -%%EndProcSet -%%BeginProcSet: pst-algparser.pro 0 0 -% $Id: pst-algparser.pro 26 2008-06-14 11:50:02Z herbert $ -%% -%% PostScript prologue for PSTricks algorithm parser -%% Version 0.01, 2008/01/01 -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -%% -%%-----------------------------------------------------------------------------% -% -/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez -% -/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin -% -% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 -% E->T|E+T -% T->FS|T*FS -% FS -> F | +FS | -FS -% F->P|F^SF -% P->(E)|literal -% literal->number|var|var[E]|func(params) -% params->E|E,param -% number->TOBEFINISHED -% -%% E expression, T term, SF signed factor, F factor, P power -% -%% parser -% -%% str -% -%% C->E<condition_operators>E -%% STR index -> STR index+lenExpr -/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def -% -%% analyze Expression List (separator , or | ) -%% STR index -> STR index+lenExpr -%% /AnalyzeListOfE { -%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar -%% NextNonBlankChar dup 0 eq { pop exit } if -%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if -%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop -%% AnalyzeListOfEPostHook -%% } def -/AnalyzeListOfE { - /NotFirst false def - { NextNonBlankChar pop AnalyzeExpr - NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse - dup Strlen eq { exit } if NextNonBlankChar - dup 44 ne 1 index 124 ne and - { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } - if pop 1 add } loop - AnalyzeListOfEPostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% E->T|E+T -%% STR index -> STR index+lenExpr -/AnalyzeExpr { - AnalyzePreHook AnalyzeTerm IsEndingExpr - { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } - { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } - ifelse - AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% T->FS|T*FS -%% STR index -/AnalyzeTerm { - AnalyzePreHook AnalyzeSignedFactor IsEndingTerm - { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } - { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } - ifelse - AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% FS -> F | +FS | -FS -%% STR index -/AnalyzeSignedFactor { - AnalyzePreHook 2 copy get dup IsUnaryOp - { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } - { pop AnalyzeFactor } - ifelse AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% F->P|F^P -%% STR index -/AnalyzeFactor { - AnalyzePreHook AnalyzePower IsEndingFactor - { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } - { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } - ifelse AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% P->(E)|literal -%% STR index -/AnalyzePower { - %% depending of first char either a number, or a literal - 2 copy get dup 40 eq%%an open par - { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } - { AnalyzeLiteral } - ifelse -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index STR[index] -> STR index -%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def -/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% recognize + or - -%% chr -> T/F -/IsUnaryOp { dup 43 eq exch 45 eq or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a number can contain only : 0123456789. -%% chr -> T/F -/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index -> STR index number -%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? -%% STR index -> STR index' number -/ReadNumber { - exch dup 3 -1 roll dup 3 1 roll - %%read mantissa - { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop - dup 101 eq exch 69 eq or - %%% there is a "e" or "E" -> read exponant - { 1 add 2 copy get dup IsUnaryOp - { pop 1 add 2 copy get } if - { IsNumber not { exit } if 1 add 2 copy get } loop } - if - dup 4 1 roll - 3 -1 roll exch 1 index sub getinterval -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a number can contain only : 0123456789. -%% chr -> T/F -/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index -> STR index number -%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? -%% STR index -> STR index' number -/ReadCondOp { - NextNonBlankChar 1 index 4 1 roll - { IsCondOp not { exit } if 1 add 2 copy get } loop - 2 copy 5 -1 roll - exch 1 index sub getinterval 3 1 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a literal can contain only : 0123456789. -%% chr -> T/F -/IsLiteral {% - dup 48 ge exch dup 57 le 3 -1 roll and exch - dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch - dup 97 ge exch 122 le and or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? -%% STR index -> literal STR index' nextchr -/ReadLiteral { - exch dup 3 -1 roll dup 3 1 roll - %%read literal core - { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop - 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or a clpar -%% STR index -> STR index STR[index] T/F -/IsEndingExpr {% - 2 copy dup Strlen eq - %% if end of str is reached -> end ! - { pop pop 0 true } - %% ending chr -> clpar, comma, |, <, >, =, !, - {get dup dup 41 eq - exch dup 124 eq - exch dup 93 eq - exch dup 44 eq - exch dup 30 eq - exch dup 60 ge exch 62 le and or or or or or} - ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or a +- -%% STR index -> STR index STR[index] T/F -/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or */ -%% STR index -> STR index STR[index] T/F -/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or ^ -%% STR index -> STR index STR[index] T/F -/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index -> STR index STR[index] -/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def -/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def -%%%%%%%%%%%%%%%%%%%%%%%% -%% DEBUG -/BRK {false} def -/BRKtrue {/BRK true def} def -/BRKStop {BRK {BRKtoto} if } def -/BRKEvalStop {BRK exch if } def -/BRKBRK2true {BRK {BRK2true} if } def -/BRK2 {false} def -/BRK2true {/BRK2 true def} def -/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def -end -% -%-------------------------------------------------------------------------------% -% -/tx@AlgToPs 12 dict def tx@AlgToPs begin -% -%% algExpr -> PSVector -/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def -/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def -/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def -/Strlen 0 def -/EvalListOfExpr {} def% -/EvalNumber {% - ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx - exch 1 add array astore def NextNonBlankChar pop } def -/EvalAddSub {% - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll - 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def -} def -/EvalMulDiv {% - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll - 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def -} def -/EvalPower {% - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll - pop /exp cvx exch 1 add array astore def -} def -/EvalLiteral {% - ReadLiteral - dup 40 eq%%% there is an open par -> function call - { pop 2 index - dup (Sum) eq { EvalSum } - { dup (IfTE) eq { EvalCond } - { dup (Derive) eq { pop EvalDerive } - { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx - exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } - { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def - dup 91 eq%%% there is an open bracket -> vector element - { pop 1 add NextNonBlankChar pop AnalyzeExpr - /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } - { pop NextNonBlankChar pop } - ifelse} - ifelse -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% the derive function : Derive(n,f(x)) -%% firstparindex lastparindex -> -/EvalDerive { - %% manage the function descripiton - 1 add ReadNumber 3 1 roll NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - 1 add NextNonBlankChar pop - 3 -1 roll cvi - dup 0 eq - { pop AnalyzeExpr 3 -1 roll pop 1 add } - { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll - { (x) tx@Derive begin Derive end } repeat - ExpressionVector exch /ExpressionVector [] def - AlgToPs aload length - /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def - l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add - 1 index length /Strlen exch def } ifelse -} def -/EvalSum {% - pop 1 add NextNonBlankChar pop - %% read the variable name - ReadLiteral pop NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if - %% read the initial value - 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - %% read the increment value - 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - %% read the limit value - 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll - 5 -1 roll 4 add array astore def - %% keep ExpressionVector for later and create a new one for internal Sum computation - ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def - 1 add NextNonBlankChar pop AnalyzeExpr - %% add each term - /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def - /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add - array astore def 3 -1 roll pop 1 add -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Convert to radians if trigo function call -%% (name) -> -/TrigoFunc { - dup (cos) eq 1 index (sin) eq or exch (tan) eq or - { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add - array astore def - } if -} def -/EvalCond {% - pop 1 add AnalyzeCond NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if - ExpressionVector 3 1 roll /ExpressionVector [] def - 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def - NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if - 1 add AnalyzeExpr - NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if - ExpressionVector - /ExpressionVector 6 -1 roll aload length dup - 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def - 1 add 3 -1 roll pop -} def -%% CondOp STR index -/EvalCondOp {% - 3 -1 roll - dup (=) eq { /eq } {% - dup (<) eq { /lt } {% - dup (>) eq { /gt } {% - dup (>=) eq { /ge } {% - dup (<=) eq { /ge } {% - dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } - ifelse } ifelse } ifelse } ifelse } ifelse } ifelse - cvx exch pop - /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def -/EvalUnaryOp { - 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% H O O K S -/AnalyzePreHook {} bind def -/PreEvalHook {} bind def -/AnalyzeListOfEPostHook {} bind def -/AnalyzePostHook {} def -/RollOp { 3 1 roll } bind def -end %tx@CoreAnalyzerDict -% -%--------------------------------------------------------------------% -% -/tx@Derive 41 dict def tx@Derive begin -%%increase ^^ for each function added -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% algExpr variable -> PSVector -/Derive {% - 10240 string 3 1 roll 0 3 1 roll - /Variable exch def - tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end -} def -/Strlen 0 def -/InitParser { dup length /Strlen exch def 0 } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% algExpr variable index -> PSVector -/DeriveIndexed {% - 3 1 roll 10240 string 3 1 roll 0 3 1 roll - /Variable exch def - tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u,v)'=-(u',v') -/EvalListOfExpr {% - 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe - 2 copy 7 -1 roll dup length 4 1 roll putinterval add - 6 -2 roll pop pop - 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (-u)'=-(u') -/EvalUnaryOp { - 4 -2 roll 4 index (0) eq - { (0) StrConcat 7 -1 roll pop } - { 7 -1 roll 45 eq - { AddSub AddOpPar true } { false } ifelse - 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (number)'=0 -/EvalNumber { ReadNumber (0) 6 2 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u+v)'=u'+v' -/EvalAddSub {% - 7 index dup (0) eq - { pop true }%% du=0 nothing added - { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } - ifelse - 5 index dup (0) eq - { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 - { exch - { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added - { 5 -2 roll 7 index 43 eq%%something yet added - { AddAdd false } { AddSub AddOpPar true } ifelse } - ifelse 11 1 roll - 3 -1 roll StrConcat 10 -1 roll { AddClPar } if - 2 copy pop 0 6 2 roll GetIntervalNewStr } - ifelse - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u*v)' or (u/v)' -/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u*v)'=u'*v+u*v' -/EvalMul {% - 4 -2 roll 7 index dup (0) eq - { pop false }%%du=0 - { (1) eq%%du=1 - { false } - { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse - 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if - true }%%du!=0 - ifelse - 5 1 roll 5 index (0) eq - { 5 -1 roll not { (0) StrConcat } if }%%dv=0 - { 5 -1 roll { AddAdd } if - 4 index (1) eq - { 8 index StrConcat } - { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } - ifelse - }%%dv!=0 - ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u/v)'=(u'*v-u*v')/v^2 -/EvalDiv {% - 4 -2 roll - 4 index (0) eq%%dv=0 -> u'/v - { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } - { 7 index dup (0) eq - { pop }%%du=0 - { (1) eq%%du=1 - { false } - { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse - 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 - ifelse - AddSub - 4 index (1) eq - { 8 index StrConcat } - { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } - ifelse - %}%%dv!=0 - 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar - AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } - ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% str1 index str2 -> str1 index -/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def -/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) -/EvalPower {% - 4 -2 roll 7 index (0) eq - {%%if du=0 then (u^v)'=v'ln(u)u^v - 4 index (0) eq - { (0) StrConcat }%%if dv=0 then (u^v)'=0 - { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if - 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if - AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse - } - {%%du!=0 - 4 index (0) eq - {%%if dv=0 then (u^v)'=vu'u^(v-1) - 5 index dup IsStrNumber - { dup (0) eq - { StrConcat } - { dup dup (1) eq exch (1.0) eq or - { StrConcat } - { StrConcat - 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 - { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 - (*\() StrConcat 8 index StrConcat (\)) StrConcat - 5 index dup dup (2) eq exch (2.0) eq or - { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } - { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat - 5 index StrConcat (-1\)) StrConcat } ifelse - } - {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) - 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if - AddOpPar 5 index StrConcat (\)*\() StrConcat - 8 index StrConcat (\)^\() StrConcat - 5 index StrConcat (-1\)+\() StrConcat - 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if - 8 index StrConcat (\)^\() StrConcat - 5 index StrConcat (\)*ln\() StrConcat - 8 index StrConcat AddClPar - } ifelse - } ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% str -> true/false -/IsStrNumber {% - true exch - { dup 48 lt exch dup 57 gt 3 -1 roll or - exch dup 46 ne%%. - exch dup 43 ne%%+ - exch 45 ne%%- - and and and { pop false } if } forall -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% literal switch -> func call, vector, variables -/EvalLiteral {% - ReadLiteral dup 40 eq%%% there is an open par -> function call - { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } - { dup 91 eq%%% there is an open bracket -> vector element - { ERROR_vector_not_yet_implemented } - { pop EvalVariable } - ifelse } - ifelse -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% first last parpos Expr[first:parpos-1] -> -/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (f(u))'=u'f'(u) -/EvalFunc { - 4 2 roll 4 index (1) ne - { AddOpPar 4 index StrConcat (\)*) StrConcat } if - (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Func derivative -> Eval<func> -/EvalFunc_sin {% - PreCommonFunc - { (cos\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_cos {% - PreCommonFunc - { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_tan {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if - PostCommonFunc } def -/EvalFunc_asin {% - PreCommonFunc - { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_acos {% - PreCommonFunc - { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_atg {% - PreCommonFunc - { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_ln {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_exp {% - PreCommonFunc - { (exp\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_sqrt {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_Fact {% - PreCommonFunc { ERROR_no_variable_expression_in_Fact } if - PostCommonFunc } def -/EvalFunc_sh {% - PreCommonFunc - { (ch\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_ch {% - PreCommonFunc - { (sh\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_th {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if - PostCommonFunc } def -/EvalFunc_Argsh {% - PreCommonFunc - { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_Argch {% - PreCommonFunc - { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_Argth {% - PreCommonFunc - { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -/PreCommonFunc { - 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop - 4 2 roll 4 index (0) eq - { (0) StrConcat false } - { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse -} def -/PostCommonFunc { - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -/EvalFunc_Derive {% - 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs - 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add - 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar - 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval - exch 6 2 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% literal switch -> func call, vector, variables -/EvalFunc_Sum {% - 1 add NextNonBlankChar pop - %% read the variable name - ReadLiteral pop 3 -1 roll pop NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if - %% read the initial value - 1 add NextNonBlankChar pop ReadNumber pop - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - %% read the increment value - 1 add NextNonBlankChar pop ReadNumber pop - 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if - %% read the limit value - 1 add NextNonBlankChar pop ReadNumber pop - 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if - 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop - 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat - 4 index StrConcat AddClPar - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% literal switch -> func call, vector, variables -/EvalFunc_IfTE {% - 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond - NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if - 1 add NextNonBlankChar pop dup 5 1 roll - AnalyzeExpr NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if - 1 add NextNonBlankChar pop - AnalyzeExpr 1 add NextNonBlankChar pop - 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat - 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% advance in str until a comma is found (no error detection!) -%% str index -> str index' -/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Convert to radians if trigo function call -%% (name) -> -/TrigoFunc { - dup (cos) eq 1 index (sin) eq or exch (tan) eq or - { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add - array astore def - } if -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% No derivative for condition.... -/EvalCondOp { 3 -1 roll pop } bind def -/PutIntervalOneAdd {putinterval 1 add} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add open parenthesis in string at the given index -%% str index -> str index+1 -/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add close parenthesis in string at the given index -%% str index -> str index+1 -/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add 0 in string at the given index -%% str index -> str index+1 -/AddZero {2 copy (0) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add open parenthesis in string at the given index -%% str index -> str index+1 -/AddMul {2 copy (*) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add open parenthesis in string at the given index -%% str index -> str index+1 -/AddDiv {2 copy (/) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add a plus sign in string at the given index -%% str index -> str index+1 -/AddAdd {2 copy (+) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add a minus sign in string at the given index -%% str index -> str index+1 -/AddSub {2 copy (-) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add a pipe sign in string at the given index -%% str index -> str index+1 -/AddPipe {2 copy (|) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% H O O K S -/AnalyzePreHook { dup 5 1 roll } bind def -/PreEvalHook {} def -/AnalyzePostHook { 7 -1 roll pop } bind def -/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def -/RollOp { 5 1 roll } bind def -end%%%tx@CoreAnalyzerDict -/tx@AddMathFunc 12 dict def tx@AddMathFunc begin -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% NEW FUNC -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) -%% x -> theta -/asin {% - dup abs 1 gt { EQDFasinrangeerror } if - dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad -} def -%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) -%% x -> theta -/acos {% - dup abs 1 gt { EQDFacosrangeerror } if - dup dup mul 1 exch sub sqrt exch atan DegtoRad -} def -%% function arctangent in radians -%% x -> theta -/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def -%% HYPERBOLIC FUNCTIONS -/sh { dup Ex exch neg Ex sub 2 div } def -/ch { dup Ex exch neg Ex add 2 div } def -/th { dup sh exch ch div } def -/Argsh { dup dup mul 1 add sqrt add ln } def -/Argch { dup dup mul 1 sub sqrt add ln } def -/Argth { dup 1 add exch 1 exch sub div ln 2 div } def -%% modified exponential funtion for 0 -%% x n -> x^n -/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def -%% modified exponential funtion for 0 -%% x -> e^x -/Ex { Euler exch exp } bind def -%% -%% factorial function -%% n -> n! -/Fact { 1 exch 2 exch 1 exch { mul } for } bind def -/fact { Fact } bind def -end - -% END pstricks.pro - -%%EndProcSet -%%BeginProcSet: pst-dots.pro 0 0 -% $Id: pst-dots.pro 26 2008-06-14 11:50:02Z herbert $ -% -%% PostScript prologue for pstricks.tex. -%% Version 2.02, 2008/04/18 -%% -%% For distribution, see pstricks.tex. -%% -%% Timothy Van Zandt <tvz@Princeton.EDU> -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -%% -%% Modified by Etienne Riga - Dec. 16, 1999 -%% Modified by Etienne Riga - 2005/01/01 (er) -%% to add /Diamond, /SolidDiamond and /BoldDiamond -%% Modified by Herbert Voss (hv) - 2008/04/17 -% -10 dict dup begin % hold local - /FontType 3 def - /FontMatrix [.001 0 0 .001 0 0] def - /FontBBox [-571.5 -742.5 571.5 742.5] def -% /FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph - /Encoding 256 array def - 0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef - Encoding % replace with given dot names - dup (b) 0 get /Bullet put % get the numerical position of b in ASCII -% % and save /Bullet at this place in Encoding - dup (c) 0 get /Circle put - dup (C) 0 get /BoldCircle put % 67 - dup (u) 0 get /SolidTriangle put - dup (t) 0 get /Triangle put - dup (T) 0 get /BoldTriangle put - dup (r) 0 get /SolidSquare put - dup (s) 0 get /Square put - dup (S) 0 get /BoldSquare put - dup (q) 0 get /SolidPentagon put - dup (p) 0 get /Pentagon put - dup (P) 0 get /BoldPentagon put -%%% - dup (k) 0 get /Asterisk put - dup (K) 0 get /BoldAsterisk put - dup (J) 0 get /SolidAsterisk put - dup (h) 0 get /Hexagon put - dup (H) 0 get /BoldHexagon put - dup (G) 0 get /SolidHexagon put - dup (f) 0 get /Octogon put % 2008-04-18 hv - dup (F) 0 get /BoldOctogon put % 2008-04-18 hv - dup (g) 0 get /SolidOctogon put % 2008-04-18 hv - dup (a) 0 get /Add put - dup (A) 0 get /BoldAdd put % 65 - dup (x) 0 get /Mul put - dup (X) 0 get /BoldMul put - dup (m) 0 get /Oplus put - dup (M) 0 get /BOplus put - dup (e) 0 get /SolidOplus put - dup (n) 0 get /Otimes put - dup (N) 0 get /BOtimes put - dup (E) 0 get /SolidOtimes put - dup (i) 0 get /Bar put - dup (I) 0 get /BoldBar put - dup (l) 0 get /SolidDiamond put - dup (d) 0 get /Diamond put - (D) 0 get /BoldDiamond put -%%% -/CharProcs 47 dict def -CharProcs begin - /CirclePath {0 0 500 0 360 arc closepath} def - /Bullet {CirclePath fill} def - /Circle {CirclePath .9 .9 scale CirclePath eofill} def - /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def - /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def - /SolidTriangle {TrianglePath fill} def - /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def - /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def - /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def - /SolidSquare {SquarePath fill} def - /Square {SquarePath .89 .89 scale SquarePath eofill} def - /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def - /PentagonPath { - -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto - 0 574.7 lineto -546.6 177.6 lineto closepath - } def - /SolidPentagon {PentagonPath fill} def - /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def - /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def -%-------------- hv begin 2004/07/25 from: er 2003/03/24 - /HexagonPath { - 0 550 moveto -476 275 lineto -476 -275 lineto - 0 -550 lineto 476 -275 lineto 476 275 lineto closepath - } def - /SolidHexagon {HexagonPath fill} def - /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def - /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def -% 2008-04-18 hv - /OctogonPath { - 550 dup 22.5 tan mul dup neg dup add /xMove exch def - exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def - /SolidOctogon { OctogonPath fill } def - /Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def - /BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def -% - /AsteriskPath { - 20 0 moveto 10 250 180 500 0 500 curveto - -180 500 -10 250 -20 0 curveto closepath - } def - /Asterisk { - AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath - 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill - } def -% - /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def - /BoldAsteriskPath { - 50 30 cos 100 mul moveto Basterp - 60 rotate Basterp 60 rotate Basterp - 60 rotate Basterp 60 rotate Basterp - 60 rotate Basterp closepath - } def - /BoldAsterisk {BoldAsteriskPath fill} def - /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def - /CrossPath { - 40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto - -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto - 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath - } def - /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto - -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto - 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath - } def - /Add {CrossPath fill} def - /Mul {45 rotate CrossPath fill} def - /BoldAdd {BoldCrossPath fill} def - /BoldMul {45 rotate BoldCrossPath fill} def - /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def - /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def - /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def - /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def - /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def - /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def - /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def - /Bar {BarPath fill} def - /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def - /BoldBar {BoldBarPath fill} def - /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath} def - /SolidDiamond {DiamondPath fill} def - /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def - /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def -%%% - /.notdef { } def -end -% -/BuildGlyph { - exch - begin -% Metrics 1 index get exec 0 - 0 0 -% BBoxes 3 index get exec - -1000 -1000 1000 1000 -% -571.5 -742.5 571.5 742.5 - setcachedevice - CharProcs begin load exec end - end -} def -% -/BuildChar { - 1 index /Encoding get exch get - 1 index /BuildGlyph get exec -} bind def - -end -/PSTricksDotFont exch definefont pop - -%% end - -%%EndProcSet -%%BeginProcSet: pst-node.pro 0 0 -% $Id: pst-node.pro 26 2008-06-14 11:50:02Z herbert $ -%% -%% PostScript prologue for pst-node.tex. -%% Version 1.00, 2008/01/01. -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -% -/tx@NodeDict 400 dict def tx@NodeDict begin -tx@Dict begin % from main pstricks dict - /T /translate load def -end -/NewNode { % on stack: { x y } boolean N@name type InitXnode - gsave - /next ED % { x y } boolean N@name type - dict dup % { x y } boolean N@name dict dict - 3 1 roll def % { x y } boolean dict N@name dict def - exch { dup 3 1 roll def } if % { x y } dict boolean - begin % { x y } dict begin - tx@Dict begin - STV CP T exec % set scaling - end - /NodeMtrx CM def % save CM - next % InitXNode - end - grestore -} def -% -/InitPnode { - /Y ED /X ED - /NodePos { NodeSep Cos mul NodeSep Sin mul } def -} def -% -/InitCnode { - /r ED /Y ED /X ED - /NodePos { NodeSep r add dup Cos mul exch Sin mul } def -} def -% -/GetRnodePos { - Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse - Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse - dx Sin mul abs dy - Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse -} def -% -/InitRnode { - /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED - /NodePos { GetRnodePos } def -} def -% -/DiaNodePos { - w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup - Cos mul exch Sin mul -} def -% -/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h -mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul -} ifelse } def -/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d -ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d -sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan -sin def /NodePos { TriNodePos } def } def -/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos -hh mul Atan dup cos ww mul exch sin hh mul } def -/GetCenter { begin X Y NodeMtrx transform CM itransform end } def -% -/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist - Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } - { 0 Dist Sin mul } ifelse } ifelse Do -} def -/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform - exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx - dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop - XYPos } ifelse -} def -/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 -roll sin mul sub exch } ifelse } def -/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA -AddOffset yA add /yA1 ED xA add /xA1 ED } def -/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB -AddOffset yB add /yB1 ED xB add /xB1 ED } def -/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA -AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED -ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED -} ifelse } def -/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB -AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED -ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED -} ifelse } def -/InitNC { - /b ED /a ED % second and first node - /NodeSepTypeB ED /NodeSepTypeA ED - /NodeSepB ED /NodeSepA ED - /OffsetB ED /OffsetA ED - tx@NodeDict a known tx@NodeDict b known and dup { - /NodeA a load def - /NodeB b load def - NodeA GetCenter /yA ED /xA ED - NodeB GetCenter /yB ED /xB ED } if -} def -% -/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub -mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def -/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt -{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop -} repeat LPutLine cleartomark } def -/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED -/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 -mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx -sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul -add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add -y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul -mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def -/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def -} def -/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def -/NAngle yyB yyA sub xxB xxA sub Atan def } def -/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def -/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def -} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit -} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd -} def -/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def -} def -/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def -/NAngle yyB yyA sub xxB xxA sub Atan def } def -/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def -/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def -} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { -exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark -VPosEnd } def -/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 -roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx -def grestore exec /LPutVar /SaveLPutVar load def } def -/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def -GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { -LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { -LPutVar VPutLine } def LPutVar } def -/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop -end } def -/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub -Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan -/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 -yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { -LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } -ifelse } def -/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 -roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA -GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict -begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] -cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines -} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def -% -/NCAngles { - GetEdgeA GetEdgeB GetArmA GetArmB - /mtrx AngleA matrix rotate def - xA2 yA2 mtrx transform pop - xB2 yB2 mtrx transform exch pop - mtrx itransform - /y0 ED /x0 ED - mark ArmB 0 ne { xB1 yB1 } if - xB2 yB2 x0 y0 xA2 yA2 - ArmA 0 ne { xA1 yA1 } if - tx@Dict begin false Line end - /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def - /LPutPos { LPutLines } def - /HPutPos { HPutLines } def - /VPutPos { VPutLines } def } def -% -/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 -yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform -/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 -tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] -cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { -VPutLines } def } def -/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def -xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx -transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } -{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB -0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict -begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx -def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { -VPutLines } def } def -/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if -xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end -/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { -LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } -def -/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED -GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin -false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { -LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } -def -/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate -def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 -mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 -mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 -xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false -Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] -cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { -VPutLines } def } def -% DG/SR modification begin - May 9, 1997 - Patch 1 -%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r -%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add -%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 -%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED -/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r -r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add -exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 -mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED -% DG/SR modification end -} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add -AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r -Div def /y ED /x ED } def -/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB -180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos -mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def -/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy -add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos -{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar -tx@Dict begin false Polygon end } def -/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan -def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 -mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def -/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div -def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def -GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul -sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 -eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } -{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def -0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 -roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 -0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 -roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } -ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos -{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { -r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } -{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add -add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub -mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t -sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse -y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { -LPutPos } def } def -/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB -sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 -ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB -w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos -{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } -{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } -def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin -/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def - -/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg -exch X sub neg exch moveto setmatrix CP grestore } def - -/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 -def } ifelse LPutCoor } def -/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } -if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } -ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } -def -/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if -r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } -ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } -def -end -% END pst-node.pro - -%%EndProcSet -%%BeginProcSet: pstricks-add.pro 0 0 -%% $Id: pstricks-add.pro 49 2008-10-13 10:59:27Z herbert $ -% PostScript prologue for pstricks-add.tex. -% Version 0.21, 2008/10/15 -% For distribution, see pstricks.tex. -% -% HISTORY -> see file Changes -% -/tx@addDict 410 dict def tx@addDict begin -%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -/GTriangle { - gsave - /mtrx CM def - /colorA ED /colorB ED /colorC ED % save the colors - /yA ED /xA ED % save the origin - xA yA translate - rotate % \psk@gangle - /yB ED /xB ED /yC ED /xC ED % save other coordinates - /ds [ % save data in a array - 0 0 0 colorA aload pop % fd x y xr xg xb - 0 xB xA sub yB yA sub colorB aload pop - 0 xC xA sub yC yA sub colorC aload pop -% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD - ] def - newpath - << - /ShadingType 4 % single Gouraud - /ColorSpace [ /DeviceRGB ] - /DataSource ds - >> - shfill - closepath - mtrx - setmatrix grestore} def -% -/RGBtoCMYK { % on stack r g b -> C M Y K - 3 dict begin - /Blue ED /Green ED /Red ED - 1 Red sub % Cyan - 1 Green sub % Magenta - 1 Blue sub % Yellow - 0 % Black - end -} def -% -/CMYKtoGRAY { % on stack c m y k -> gray - exch 0.11 mul add - exch 0.59 mul add - exch 0.3 mul add - dup 1 gt { pop 1 } if - neg 1 add -} def -% -/RGBtoGRAY { % on stack r g b -> gray - 0.11 mul - exch 0.59 mul add - exch 0.3 mul add -} def -% -/HSBtoGRAY { - 6 dict begin - /b exch def - /s exch def 6 mul dup cvi dup - /i exch def sub - /f exch def - /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def - F i get { s mul neg 1 add b mul} forall - 0.11 mul - exch 0.59 mul add - exch 0.3 mul add - end -} def -% -%% convertisseur longueur d'onde ->R,G,B Manuel Luque -%% lambda max=780 nanometres -%% lambda min=380 nanometres -%% adaptation de : -%% http://www.physics.sfasu.edu/astro/color.html -%% www.efg2.com/lab -% -/Gamma 0.8 def -/calculateRGB { - lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if - lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if - lambda 380 ge {lambda 439 le { - /R {lambda 440 sub neg 440 380 sub div} def - /Red R factor mul Gamma exp def - /G 0 def - /Green G factor mul Gamma exp def - /B 1 def - /Blue B factor mul Gamma exp def} if - } if - lambda 440 ge { lambda 489 le { - /G {lambda 440 sub 490 440 sub div} def - /Green G factor mul Gamma exp def - /R 0 def /Red 0 def - /B 1 def - /Blue B factor mul Gamma exp def } if - } if - lambda 490 ge {lambda 509 le { - /B {lambda 510 sub neg 510 490 sub div} def - /Blue B factor mul Gamma exp def - /R 0 def /Red 0 def - /G 1 def - /Green G factor mul Gamma exp def } if - } if - lambda 510 ge {lambda 579 le { - /R {lambda 510 sub 580 510 sub div } def - /Red R factor mul Gamma exp def - /Blue 0 def - /G 1 def - /Green G factor mul Gamma exp def } if - } if - lambda 580 ge {lambda 644 le { - /G {lambda 645 sub neg 645 580 sub div } def - /Green G factor mul Gamma exp def - /Blue 0 def - /R 1 def - /Red R factor mul Gamma exp def } if - } if - lambda 645 ge { lambda 780 le { - /Red 1 factor mul Gamma exp def - /Blue 0 def - /Green 0 def } if - } if -} def -% -/factor { - lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if - lambda 420 ge {lambda 700 le { 1 } if } if - lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if -} def -% -/wavelengthToRGB { % the wavelength in nm must be on top of the stack - 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x1 0 gt y1 0 gt or x 0 gt or y 0 gt and - { [ y x y1 x1 ] 1 a sub y mul } - { [ 1 0 ] 0 } ifelse - setdash stroke -} def -%%-------------- DG end patch 15 ---------------%% -/DotLine { - /b PathLength def - /a ED /z ED /y CLW def - /z y z add def - a 0 gt { - /b b a div def - }{ - a 0 eq { - /b b y sub def - }{ a -3 eq { - /b b y add def } if - } ifelse - } ifelse - [ 0 b b z Div round Div dup 0 le { pop 1 } if ] - a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse - setdash 1 setlinecap stroke -} def -% -/LineFill { % hv ------------ patch 7 ------------- - gsave - abs /hatchWidthInc ED - abs /hatchSepInc ED - abs CLW add /a ED - a 0 dtransform round exch round exch - 2 copy idtransform - exch Atan rotate - idtransform pop /a ED - .25 .25 itransform pathbbox - /y2 ED - a Div ceiling cvi /x2 ED /y1 ED - a Div cvi /x1 ED /y2 y2 y1 sub def - clip - newpath - 2 setlinecap - systemdict - /setstrokeadjust known { true setstrokeadjust } if - x2 x1 sub 1 add { - x1 a mul y1 moveto 0 y2 rlineto stroke - /x1 x1 1 add - hatchWidthInc 0 gt { CLW add } if - def - hatchSepInc 0 gt hatchWidthInc 0 gt or { - /a a hatchSepInc add def - CLW hatchWidthInc add SLW - } if - } repeat - grestore - pop pop } def -% -/PenroseFill {% on stack: scaling factor - dup dup scale - 1 exch div round /penroseFactor ED - a 0 dtransform round exch round exch - 2 copy idtransform - exch Atan rotate - idtransform pop /a ED - .25 .25 itransform pathbbox - /y2 ED - a Div ceiling cvi /x2 ED /y1 ED - a Div cvi /x1 ED /y2 y2 y1 sub def - clip - newpath - systemdict - /setstrokeadjust known { true setstrokeadjust } if - /I/S/L/W/G/+/Z/F/E/D[/def/exch/for{E D}/add{s E get mul} - { Z -36.2001 1 33 }{25 E S rlineto}{/q Z dup q G E q 1 + G}{Z 2 2}]{cvx def}forall - [0 72 1008 {dup sin E cos }F ]1 setlinejoin/s W{/a W{/b I 10{/i I 4{/m I moveto - i m +/j I 10{/l Z b m l + G a l G sub s m get div .2 + floor .3 + 25 - mul j l + S rmoveto}F i L j L stroke }F}F}F}F - grestore - pop pop -} def -% -%gsave abs CLW add /a ED a 0 dtransform round exch round exch -%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 -%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 -%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a -%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a -%% DG/SR modification end -%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict -%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 -%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) -%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } -%% def -%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore -%pop pop } def -%% DG/SR modification end -% -/BeginArrow { - ADict begin % hold it local, for end see EndArrow - /@mtrx CM def - gsave - 2 copy T - 2 index sub neg exch - 3 index sub exch Atan - rotate newpath -} def -% -/EndArrow { @mtrx setmatrix CP grestore end } def % end the ADict -% -/Arrow { - CLW mul add dup - 2 div /w ED - mul dup /h ED - mul /a ED - { 0 h T 1 -1 scale } if - w neg h moveto - 0 0 L w h L w neg a neg rlineto - gsave fill grestore -} def -% -/ArrowD { % the sides are drawn as curves (hv 20071211) - CLW mul add dup - 2 div /w ED - mul dup /h ED - mul /Inset ED - { 0 h T 1 -1 scale } if % changes the direction -% we use y=w/h^2 * x^2 as equation for the control points -% for the coordinates the arrow is seen from top to bottom -% the bottom (tip) is (0;0) - w neg h moveto % lower left of > - w 9 div 4 mul neg h 3 div 2 mul - w 9 div neg h 3 div - 0 0 curveto % tip of > - w 9 div h 3 div - w 9 div 4 mul h 3 div 2 mul - w h curveto % upper left of > - w neg Inset neg rlineto % move to x=0 and inset - gsave fill grestore -} def -% -/Tbar { - CLW mul add /z ED - z -2 div CLW 2 div moveto - z 0 rlineto stroke - 0 CLW moveto -} def -% -/Bracket { - CLW mul add dup CLW sub 2 div - /x ED mul CLW add /y ED /z CLW 2 div def - x neg y moveto - x neg CLW 2 div L x CLW 2 div L x y L stroke - 0 CLW moveto -} def -% -/RoundBracket { - CLW mul add dup 2 div - /x ED mul /y ED /mtrx CM def - 0 CLW 2 div T x y mul 0 ne { x y scale } if - 1 1 moveto - .85 .5 .35 0 0 0 curveto - -.35 0 -.85 .5 -1 1 curveto - mtrx setmatrix stroke 0 CLW moveto -} def -% -/SD { 0 360 arc fill } def -% -/EndDot { % DS is the dot size - { /z DS def } { /z 0 def } ifelse - /b ED 0 z DS SD b { 0 z DS CLW sub SD } if - 0 DS z add CLW 4 div sub moveto } def -% -/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { - /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto - load } if ] cvx newpath 3 1 roll T exec } def -% -%/NArray { -% aload length 2 div dup dup cvi eq not { exch pop } if /n exch -% cvi def -%} def -% -/NArray { % holds the coordinates and on top of stack the showpoints boolean - /showpoints ED - counttomark 2 div dup cvi /n ED - n eq not { exch pop } if - showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse -} def -% -/Line { - NArray n 0 eq not - { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def - n { Lineto } repeat - CP 4 2 roll ArrowB L pop pop - } if -} def -% -/Arcto { - /a [ 6 -2 roll ] cvx def - a r - /arcto load stopped { 5 } { 4 } ifelse { pop } repeat - a -} def -% -/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq - and { pop pop /n n 1 sub def } if } def -/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } - repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 - ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 - moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto - Lineto pop pop closepath } ifelse } def -/Diamond { - /mtrx CM def - T rotate - /h ED - /w ED - dup 0 eq { pop } { CLW mul neg - /d ED - /a w h Atan def - /h d a sin Div h add def - /w d a cos Div w add def } ifelse - mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div - /ArrowA { moveto } def - /ArrowB { } def - false Line - closepath mtrx setmatrix } def -% DG modification begin - Jan. 15, 1997 -%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { -%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 -%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 -%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx -%setmatrix } def -/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup -CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 -div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 -d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx -% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) -% setmatrix } def -setmatrix pop } def -% DG/SR modification end -% -/CCA { - /y ED /x ED - 2 copy y sub /dy1 ED - x sub /dx1 ED - /l1 dx1 dy1 Pyth def -} def -% -/CC { - /l0 l1 def - /x1 x dx sub def - /y1 y dy sub def - /dx0 dx1 def - /dy0 dy1 def - CCA - /dx dx0 l1 c exp mul dx1 l0 c exp mul add def - /dy dy0 l1 c exp mul dy1 l0 c exp mul add def - /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def - /x2 x l0 dx mul m mul sub def - /y2 y l0 dy mul m mul sub def - /dx l1 dx mul m mul neg def - /dy l1 dy mul m mul neg def -} def -% -/IC { - /c c 1 add def - c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse - /a a 2 mul 3 div 45 cos b exp div def - CCA - /dx 0 def - /dy 0 def -} def -% -/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def -/NC { CC x1 y1 x2 y2 x y curveto } def -/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def -/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def -/NAC { x2 y2 x y curveto CC x1 y1 } def -/EAC { x2 y2 x y ArrowB curveto pop pop } def -% -/OpenCurve { - NArray n 3 lt - { n { pop pop } repeat } - { BOC /n n 3 sub def n { NC } repeat EOC } ifelse -} def -% -/AltCurve { - { false NArray n 2 mul 2 roll - [ n 2 mul 3 sub 1 roll ] aload - /Points ED - n 2 mul -2 roll } - { false NArray } ifelse - n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse -} def -% -/ClosedCurve { - NArray n 3 lt - { n { pop pop } repeat } - { n 3 gt { CheckClosed } if - 6 copy n 2 mul 6 add 6 roll - IC CC x y moveto n { NC } repeat - closepath pop pop - } ifelse -} def -% -/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def -/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def -/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } -def -/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix -rotate matrix concatmatrix exch findfont exch makefont setfont } def -/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto -x1 y1 lineto closepath } def -/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 -y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div -exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse -/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto -x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } -ifelse } def -/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add -/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { -pop pop Rect } { OvalFrame } ifelse } def -% -/BezierNArray { - /f ED - counttomark 2 div dup cvi /n ED - n eq not { exch pop } if - n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat - f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse -} def -% -/OpenBezier { - BezierNArray - n 1 eq - { pop pop } - { ArrowA n 4 sub 3 idiv - { 6 2 roll 4 2 roll curveto } repeat - 6 2 roll 4 2 roll ArrowB curveto } ifelse -} def -% -/ClosedBezier { - BezierNArray - n 1 eq - { pop pop } - { moveto n 1 sub 3 idiv - { 6 2 roll 4 2 roll curveto } repeat - closepath } ifelse -} def -% -/BezierShowPoints { - gsave - Points aload length 2 div cvi /n ED - moveto - n 1 sub { lineto } repeat - CLW 2 div SLW [ 4 4 ] 0 setdash stroke - grestore -} def -% -/Parab { - /y0 ED /x0 ED /y1 ED /x1 ED - /dx x0 x1 sub 3 div def - /dy y0 y1 sub 3 div def - x0 dx sub y0 dy add x1 y1 ArrowA - x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB - curveto - /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def -} def -% -/Grid { - newpath - /a 4 string def - /b ED /c ED /n ED - cvi dup 1 lt { pop 1 } if - /s ED - s div dup 0 eq { pop 1 } if - /dy ED s div dup 0 eq { pop 1 } if - /dx ED dy div round dy mul - /y0 ED dx div round dx mul - /x0 ED dy div round cvi - /y2 ED dx div round cvi - /x2 ED dy div round cvi - /y1 ED dx div round cvi - /x1 ED - /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def - /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def - b 0 gt { - /z1 b 4 div CLW 2 div add def -% /Helvetica findfont b scalefont setfont - /b b .95 mul CLW 2 div add def } if - systemdict /setstrokeadjust known - { true setstrokeadjust /t { } def } - { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add - exch itransform } bind def } ifelse - gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse - /i x1 def - /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def - /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def - x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if - { i dx mul dup y0 moveto - b 0 gt - { gsave c i a cvs dup stringwidth pop - /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse - h 0 gt {b neg}{z1} ifelse - rmoveto show grestore } if - dup t f moveto - g t L stroke - /i i w add def - } repeat - grestore - gsave - n 0 gt - % DG/SR modification begin - Nov. 7, 1997 - Patch 1 - %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } - { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } - % DG/SR modification end - { 2 setlinecap } ifelse - /i y1 def - /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def - /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def - y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if - { newpath i dy mul dup x0 exch moveto - b 0 gt { gsave c i a cvs dup stringwidth pop - /z2 ED - w 0 gt {z1 z2 add neg} {z1} ifelse - h 0 gt {z1} {b neg} ifelse - rmoveto show grestore } if - dup f exch t moveto - g exch t L stroke - /i i h add def - } repeat - grestore -} def -% -/ArcArrow { - /d ED /b ED /a ED - gsave - newpath 0 -1000 moveto clip - newpath - 0 1 0 0 b - grestore - c mul - /e ED - pop pop pop r a e d PtoC y add exch x add - exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c - mul neg d -} def -% -/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def -% -/ArcAdjust { %%%% Vincent Guirardel -% given a target length (targetLength) and an initial angle (angle0) [in the stack], -% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). -% This computes an angle t such that (x0,y0) is at distance -% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). -% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 -% contrary to TvZ's code. -% To achieve, this, one iterates the following process: start with some angle t, -% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. -% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. -% -% Another difference with TvZ's code is that we need d (=add/sub) to be defined. -% the value of d = add/sub is used to know on which side we have to move. -% It is only used in the initialisation of the angle before the iteration. -% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% Input stack: 1: target length 2: initial angle -% variables used : rx, ry, d (=add/sub) -% - /targetLength ED /angle0 ED - /x0 rx angle0 cos mul def - /y0 ry angle0 sin mul def -% we are looking for an angle t such that (x0,y0) is at distance targetLength -% from the point M(t)=(rx*cos(t),ry*sin(t))) -%initialisation of angle (using 1st order approx = TvZ's code) - targetLength 57.2958 mul - angle0 sin rx mul dup mul - angle0 cos ry mul dup mul - add sqrt div -% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees -% (if the ellipse is very curved at the point where we draw the arrow, % -% the value can be much more than 360 degrees !) -% this should avoid going on the wrong side (more than 180 degrees) or go near -% a bad attractive point (at 180 degrees) - dup 90 ge { pop 90 } if - angle0 exch d % add or sub -% maximum number of times to iterate the iterative procedure: -% iterative procedure: takes an angle t on top of stack, computes a -% better angle (and put it on top of stack) - 30 { dup -% compute distance D between (x0,y0) and M(t) - dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt -% if D almost equals targetLength, we stop - dup targetLength sub abs 1e-5 le { pop exit } if -% stack now contains D t -% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: -% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) - exch dup cos rx mul x0 sub exch sin ry mul y0 sub -% stack contains: y(t)-y0, x(t)-x0, d - 2 index Div targetLength mul y0 add ry Div exch - 2 index Div targetLength mul x0 add rx Div -% stack contains x(t')/rx , y(t')/ry , d -% now compute t', and remove D from stack - atan exch pop - } repeat -% we don't look at what happened... in particular, if targetLength is greater -% than the diameter of the ellipse... -% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... -% after iteration, stack contains an angle t such that M(t) is the tail of the arrow -% to give back the result as a an angle relative to angle0 we could add the following line: -% angle0 sub 0 exch d -% -% begin bug fix 2006-01-11 -% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 -%(we don't want to make the ellipse turn more or less than it should)... -dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse -% end bug fix -} def -% -/EllipticArcArrow { - /d ED % is add or sub - /b ED % arrow procedure - /a1 ED % angle - gsave - newpath - 0 -1000 moveto - clip % Set clippath far from arrow. - newpath - 0 1 0 0 b % Draw arrow to determine length. - grestore -% Length of arrow is on top of stack. Next 3 numbers are junk. -% - a1 exch ArcAdjust % Angular position of base of arrow. - /a2 ED - pop pop pop - a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig - a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig - a1 cos rx mul xOrig add % - a1 sin ry mul yOrig add % -% Now arrow tip coor and base coor are on stack. - b pop pop pop pop % Draw arrow, and discard coordinates. - a2 CLW 8 div -% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) - 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse - ArcAdjust -% resets original value of d - 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. -} def -%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% -% -/Rot { CP CP translate 3 -1 roll neg rotate NET } def -% -/RotBegin { - tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if - /TMatrix [ TMatrix CM ] cvx def - /a ED - a Rot /RAngle [ RAngle dup a add ] cvx def -} def -% -/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def -% -/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def -/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def -/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def -/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s -abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b -div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { -h1 abs h sub dup s mul abs } ifelse } def -/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s -mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q -{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add -exch } def -/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible -/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def -} if } ifelse } def -/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def -/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit -neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def -/IfVisible true def } def -end -%-----------------------------------------------------------------------------% - -% END pstricks.pro - -%%EndProcSet -%%BeginProcSet: pst-algparser.pro 0 0 -% $Id: pst-algparser.pro 26 2008-06-14 11:50:02Z herbert $ -%% -%% PostScript prologue for PSTricks algorithm parser -%% Version 0.01, 2008/01/01 -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -%% -%%-----------------------------------------------------------------------------% -% -/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez -% -/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin -% -% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 -% E->T|E+T -% T->FS|T*FS -% FS -> F | +FS | -FS -% F->P|F^SF -% P->(E)|literal -% literal->number|var|var[E]|func(params) -% params->E|E,param -% number->TOBEFINISHED -% -%% E expression, T term, SF signed factor, F factor, P power -% -%% parser -% -%% str -% -%% C->E<condition_operators>E -%% STR index -> STR index+lenExpr -/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def -% -%% analyze Expression List (separator , or | ) -%% STR index -> STR index+lenExpr -%% /AnalyzeListOfE { -%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar -%% NextNonBlankChar dup 0 eq { pop exit } if -%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if -%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop -%% AnalyzeListOfEPostHook -%% } def -/AnalyzeListOfE { - /NotFirst false def - { NextNonBlankChar pop AnalyzeExpr - NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse - dup Strlen eq { exit } if NextNonBlankChar - dup 44 ne 1 index 124 ne and - { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } - if pop 1 add } loop - AnalyzeListOfEPostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% E->T|E+T -%% STR index -> STR index+lenExpr -/AnalyzeExpr { - AnalyzePreHook AnalyzeTerm IsEndingExpr - { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } - { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } - ifelse - AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% T->FS|T*FS -%% STR index -/AnalyzeTerm { - AnalyzePreHook AnalyzeSignedFactor IsEndingTerm - { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } - { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } - ifelse - AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% FS -> F | +FS | -FS -%% STR index -/AnalyzeSignedFactor { - AnalyzePreHook 2 copy get dup IsUnaryOp - { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } - { pop AnalyzeFactor } - ifelse AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% F->P|F^P -%% STR index -/AnalyzeFactor { - AnalyzePreHook AnalyzePower IsEndingFactor - { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } - { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } - ifelse AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% P->(E)|literal -%% STR index -/AnalyzePower { - %% depending of first char either a number, or a literal - 2 copy get dup 40 eq%%an open par - { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } - { AnalyzeLiteral } - ifelse -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index STR[index] -> STR index -%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def -/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% recognize + or - -%% chr -> T/F -/IsUnaryOp { dup 43 eq exch 45 eq or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a number can contain only : 0123456789. -%% chr -> T/F -/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index -> STR index number -%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? -%% STR index -> STR index' number -/ReadNumber { - exch dup 3 -1 roll dup 3 1 roll - %%read mantissa - { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop - dup 101 eq exch 69 eq or - %%% there is a "e" or "E" -> read exponant - { 1 add 2 copy get dup IsUnaryOp - { pop 1 add 2 copy get } if - { IsNumber not { exit } if 1 add 2 copy get } loop } - if - dup 4 1 roll - 3 -1 roll exch 1 index sub getinterval -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a number can contain only : 0123456789. -%% chr -> T/F -/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index -> STR index number -%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? -%% STR index -> STR index' number -/ReadCondOp { - NextNonBlankChar 1 index 4 1 roll - { IsCondOp not { exit } if 1 add 2 copy get } loop - 2 copy 5 -1 roll - exch 1 index sub getinterval 3 1 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a literal can contain only : 0123456789. -%% chr -> T/F -/IsLiteral {% - dup 48 ge exch dup 57 le 3 -1 roll and exch - dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch - dup 97 ge exch 122 le and or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? -%% STR index -> literal STR index' nextchr -/ReadLiteral { - exch dup 3 -1 roll dup 3 1 roll - %%read literal core - { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop - 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or a clpar -%% STR index -> STR index STR[index] T/F -/IsEndingExpr {% - 2 copy dup Strlen eq - %% if end of str is reached -> end ! - { pop pop 0 true } - %% ending chr -> clpar, comma, |, <, >, =, !, - {get dup dup 41 eq - exch dup 124 eq - exch dup 93 eq - exch dup 44 eq - exch dup 30 eq - exch dup 60 ge exch 62 le and or or or or or} - ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or a +- -%% STR index -> STR index STR[index] T/F -/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or */ -%% STR index -> STR index STR[index] T/F -/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or ^ -%% STR index -> STR index STR[index] T/F -/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index -> STR index STR[index] -/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def -/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def -%%%%%%%%%%%%%%%%%%%%%%%% -%% DEBUG -/BRK {false} def -/BRKtrue {/BRK true def} def -/BRKStop {BRK {BRKtoto} if } def -/BRKEvalStop {BRK exch if } def -/BRKBRK2true {BRK {BRK2true} if } def -/BRK2 {false} def -/BRK2true {/BRK2 true def} def -/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def -end -% -%-------------------------------------------------------------------------------% -% -/tx@AlgToPs 12 dict def tx@AlgToPs begin -% -%% algExpr -> PSVector -/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def -/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def -/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def -/Strlen 0 def -/EvalListOfExpr {} def% -/EvalNumber {% - ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx - exch 1 add array astore def NextNonBlankChar pop } def -/EvalAddSub {% - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll - 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def -} def -/EvalMulDiv {% - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll - 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def -} def -/EvalPower {% - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll - pop /exp cvx exch 1 add array astore def -} def -/EvalLiteral {% - ReadLiteral - dup 40 eq%%% there is an open par -> function call - { pop 2 index - dup (Sum) eq { EvalSum } - { dup (IfTE) eq { EvalCond } - { dup (Derive) eq { pop EvalDerive } - { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx - exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } - { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def - dup 91 eq%%% there is an open bracket -> vector element - { pop 1 add NextNonBlankChar pop AnalyzeExpr - /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } - { pop NextNonBlankChar pop } - ifelse} - ifelse -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% the derive function : Derive(n,f(x)) -%% firstparindex lastparindex -> -/EvalDerive { - %% manage the function descripiton - 1 add ReadNumber 3 1 roll NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - 1 add NextNonBlankChar pop - 3 -1 roll cvi - dup 0 eq - { pop AnalyzeExpr 3 -1 roll pop 1 add } - { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll - { (x) tx@Derive begin Derive end } repeat - ExpressionVector exch /ExpressionVector [] def - AlgToPs aload length - /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def - l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add - 1 index length /Strlen exch def } ifelse -} def -/EvalSum {% - pop 1 add NextNonBlankChar pop - %% read the variable name - ReadLiteral pop NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if - %% read the initial value - 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - %% read the increment value - 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - %% read the limit value - 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll - 5 -1 roll 4 add array astore def - %% keep ExpressionVector for later and create a new one for internal Sum computation - ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def - 1 add NextNonBlankChar pop AnalyzeExpr - %% add each term - /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def - /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add - array astore def 3 -1 roll pop 1 add -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Convert to radians if trigo function call -%% (name) -> -/TrigoFunc { - dup (cos) eq 1 index (sin) eq or exch (tan) eq or - { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add - array astore def - } if -} def -/EvalCond {% - pop 1 add AnalyzeCond NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if - ExpressionVector 3 1 roll /ExpressionVector [] def - 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def - NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if - 1 add AnalyzeExpr - NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if - ExpressionVector - /ExpressionVector 6 -1 roll aload length dup - 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def - 1 add 3 -1 roll pop -} def -%% CondOp STR index -/EvalCondOp {% - 3 -1 roll - dup (=) eq { /eq } {% - dup (<) eq { /lt } {% - dup (>) eq { /gt } {% - dup (>=) eq { /ge } {% - dup (<=) eq { /ge } {% - dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } - ifelse } ifelse } ifelse } ifelse } ifelse } ifelse - cvx exch pop - /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def -/EvalUnaryOp { - 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% H O O K S -/AnalyzePreHook {} bind def -/PreEvalHook {} bind def -/AnalyzeListOfEPostHook {} bind def -/AnalyzePostHook {} def -/RollOp { 3 1 roll } bind def -end %tx@CoreAnalyzerDict -% -%--------------------------------------------------------------------% -% -/tx@Derive 41 dict def tx@Derive begin -%%increase ^^ for each function added -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% algExpr variable -> PSVector -/Derive {% - 10240 string 3 1 roll 0 3 1 roll - /Variable exch def - tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end -} def -/Strlen 0 def -/InitParser { dup length /Strlen exch def 0 } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% algExpr variable index -> PSVector -/DeriveIndexed {% - 3 1 roll 10240 string 3 1 roll 0 3 1 roll - /Variable exch def - tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u,v)'=-(u',v') -/EvalListOfExpr {% - 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe - 2 copy 7 -1 roll dup length 4 1 roll putinterval add - 6 -2 roll pop pop - 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (-u)'=-(u') -/EvalUnaryOp { - 4 -2 roll 4 index (0) eq - { (0) StrConcat 7 -1 roll pop } - { 7 -1 roll 45 eq - { AddSub AddOpPar true } { false } ifelse - 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (number)'=0 -/EvalNumber { ReadNumber (0) 6 2 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u+v)'=u'+v' -/EvalAddSub {% - 7 index dup (0) eq - { pop true }%% du=0 nothing added - { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } - ifelse - 5 index dup (0) eq - { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 - { exch - { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added - { 5 -2 roll 7 index 43 eq%%something yet added - { AddAdd false } { AddSub AddOpPar true } ifelse } - ifelse 11 1 roll - 3 -1 roll StrConcat 10 -1 roll { AddClPar } if - 2 copy pop 0 6 2 roll GetIntervalNewStr } - ifelse - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u*v)' or (u/v)' -/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u*v)'=u'*v+u*v' -/EvalMul {% - 4 -2 roll 7 index dup (0) eq - { pop false }%%du=0 - { (1) eq%%du=1 - { false } - { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse - 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if - true }%%du!=0 - ifelse - 5 1 roll 5 index (0) eq - { 5 -1 roll not { (0) StrConcat } if }%%dv=0 - { 5 -1 roll { AddAdd } if - 4 index (1) eq - { 8 index StrConcat } - { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } - ifelse - }%%dv!=0 - ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u/v)'=(u'*v-u*v')/v^2 -/EvalDiv {% - 4 -2 roll - 4 index (0) eq%%dv=0 -> u'/v - { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } - { 7 index dup (0) eq - { pop }%%du=0 - { (1) eq%%du=1 - { false } - { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse - 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 - ifelse - AddSub - 4 index (1) eq - { 8 index StrConcat } - { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } - ifelse - %}%%dv!=0 - 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar - AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } - ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% str1 index str2 -> str1 index -/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def -/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) -/EvalPower {% - 4 -2 roll 7 index (0) eq - {%%if du=0 then (u^v)'=v'ln(u)u^v - 4 index (0) eq - { (0) StrConcat }%%if dv=0 then (u^v)'=0 - { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if - 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if - AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse - } - {%%du!=0 - 4 index (0) eq - {%%if dv=0 then (u^v)'=vu'u^(v-1) - 5 index dup IsStrNumber - { dup (0) eq - { StrConcat } - { dup dup (1) eq exch (1.0) eq or - { StrConcat } - { StrConcat - 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 - { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 - (*\() StrConcat 8 index StrConcat (\)) StrConcat - 5 index dup dup (2) eq exch (2.0) eq or - { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } - { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat - 5 index StrConcat (-1\)) StrConcat } ifelse - } - {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) - 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if - AddOpPar 5 index StrConcat (\)*\() StrConcat - 8 index StrConcat (\)^\() StrConcat - 5 index StrConcat (-1\)+\() StrConcat - 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if - 8 index StrConcat (\)^\() StrConcat - 5 index StrConcat (\)*ln\() StrConcat - 8 index StrConcat AddClPar - } ifelse - } ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% str -> true/false -/IsStrNumber {% - true exch - { dup 48 lt exch dup 57 gt 3 -1 roll or - exch dup 46 ne%%. - exch dup 43 ne%%+ - exch 45 ne%%- - and and and { pop false } if } forall -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% literal switch -> func call, vector, variables -/EvalLiteral {% - ReadLiteral dup 40 eq%%% there is an open par -> function call - { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } - { dup 91 eq%%% there is an open bracket -> vector element - { ERROR_vector_not_yet_implemented } - { pop EvalVariable } - ifelse } - ifelse -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% first last parpos Expr[first:parpos-1] -> -/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (f(u))'=u'f'(u) -/EvalFunc { - 4 2 roll 4 index (1) ne - { AddOpPar 4 index StrConcat (\)*) StrConcat } if - (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Func derivative -> Eval<func> -/EvalFunc_sin {% - PreCommonFunc - { (cos\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_cos {% - PreCommonFunc - { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_tan {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if - PostCommonFunc } def -/EvalFunc_asin {% - PreCommonFunc - { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_acos {% - PreCommonFunc - { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_atg {% - PreCommonFunc - { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_ln {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_exp {% - PreCommonFunc - { (exp\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_sqrt {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_Fact {% - PreCommonFunc { ERROR_no_variable_expression_in_Fact } if - PostCommonFunc } def -/EvalFunc_sh {% - PreCommonFunc - { (ch\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_ch {% - PreCommonFunc - { (sh\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_th {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if - PostCommonFunc } def -/EvalFunc_Argsh {% - PreCommonFunc - { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_Argch {% - PreCommonFunc - { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_Argth {% - PreCommonFunc - { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -/PreCommonFunc { - 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop - 4 2 roll 4 index (0) eq - { (0) StrConcat false } - { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse -} def -/PostCommonFunc { - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -/EvalFunc_Derive {% - 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs - 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add - 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar - 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval - exch 6 2 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% literal switch -> func call, vector, variables -/EvalFunc_Sum {% - 1 add NextNonBlankChar pop - %% read the variable name - ReadLiteral pop 3 -1 roll pop NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if - %% read the initial value - 1 add NextNonBlankChar pop ReadNumber pop - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - %% read the increment value - 1 add NextNonBlankChar pop ReadNumber pop - 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if - %% read the limit value - 1 add NextNonBlankChar pop ReadNumber pop - 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if - 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop - 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat - 4 index StrConcat AddClPar - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% literal switch -> func call, vector, variables -/EvalFunc_IfTE {% - 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond - NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if - 1 add NextNonBlankChar pop dup 5 1 roll - AnalyzeExpr NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if - 1 add NextNonBlankChar pop - AnalyzeExpr 1 add NextNonBlankChar pop - 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat - 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% advance in str until a comma is found (no error detection!) -%% str index -> str index' -/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Convert to radians if trigo function call -%% (name) -> -/TrigoFunc { - dup (cos) eq 1 index (sin) eq or exch (tan) eq or - { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add - array astore def - } if -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% No derivative for condition.... -/EvalCondOp { 3 -1 roll pop } bind def -/PutIntervalOneAdd {putinterval 1 add} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add open parenthesis in string at the given index -%% str index -> str index+1 -/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add close parenthesis in string at the given index -%% str index -> str index+1 -/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add 0 in string at the given index -%% str index -> str index+1 -/AddZero {2 copy (0) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add open parenthesis in string at the given index -%% str index -> str index+1 -/AddMul {2 copy (*) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add open parenthesis in string at the given index -%% str index -> str index+1 -/AddDiv {2 copy (/) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add a plus sign in string at the given index -%% str index -> str index+1 -/AddAdd {2 copy (+) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add a minus sign in string at the given index -%% str index -> str index+1 -/AddSub {2 copy (-) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add a pipe sign in string at the given index -%% str index -> str index+1 -/AddPipe {2 copy (|) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% H O O K S -/AnalyzePreHook { dup 5 1 roll } bind def -/PreEvalHook {} def -/AnalyzePostHook { 7 -1 roll pop } bind def -/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def -/RollOp { 5 1 roll } bind def -end%%%tx@CoreAnalyzerDict -/tx@AddMathFunc 12 dict def tx@AddMathFunc begin -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% NEW FUNC -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) -%% x -> theta -/asin {% - dup abs 1 gt { EQDFasinrangeerror } if - dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad -} def -%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) -%% x -> theta -/acos {% - dup abs 1 gt { EQDFacosrangeerror } if - dup dup mul 1 exch sub sqrt exch atan DegtoRad -} def -%% function arctangent in radians -%% x -> theta -/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def -%% HYPERBOLIC FUNCTIONS -/sh { dup Ex exch neg Ex sub 2 div } def -/ch { dup Ex exch neg Ex add 2 div } def -/th { dup sh exch ch div } def -/Argsh { dup dup mul 1 add sqrt add ln } def -/Argch { dup dup mul 1 sub sqrt add ln } def -/Argth { dup 1 add exch 1 exch sub div ln 2 div } def -%% modified exponential funtion for 0 -%% x n -> x^n -/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def -%% modified exponential funtion for 0 -%% x -> e^x -/Ex { Euler exch exp } bind def -%% -%% factorial function -%% n -> n! -/Fact { 1 exch 2 exch 1 exch { mul } for } bind def -/fact { Fact } bind def -end - -% END pstricks.pro - -%%EndProcSet -%%BeginProcSet: pst-dots.pro 0 0 -% $Id: pst-dots.pro 26 2008-06-14 11:50:02Z herbert $ -% -%% PostScript prologue for pstricks.tex. -%% Version 2.02, 2008/04/18 -%% -%% For distribution, see pstricks.tex. -%% -%% Timothy Van Zandt <tvz@Princeton.EDU> -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -%% -%% Modified by Etienne Riga - Dec. 16, 1999 -%% Modified by Etienne Riga - 2005/01/01 (er) -%% to add /Diamond, /SolidDiamond and /BoldDiamond -%% Modified by Herbert Voss (hv) - 2008/04/17 -% -10 dict dup begin % hold local - /FontType 3 def - /FontMatrix [.001 0 0 .001 0 0] def - /FontBBox [-571.5 -742.5 571.5 742.5] def -% /FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph - /Encoding 256 array def - 0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef - Encoding % replace with given dot names - dup (b) 0 get /Bullet put % get the numerical position of b in ASCII -% % and save /Bullet at this place in Encoding - dup (c) 0 get /Circle put - dup (C) 0 get /BoldCircle put % 67 - dup (u) 0 get /SolidTriangle put - dup (t) 0 get /Triangle put - dup (T) 0 get /BoldTriangle put - dup (r) 0 get /SolidSquare put - dup (s) 0 get /Square put - dup (S) 0 get /BoldSquare put - dup (q) 0 get /SolidPentagon put - dup (p) 0 get /Pentagon put - dup (P) 0 get /BoldPentagon put -%%% - dup (k) 0 get /Asterisk put - dup (K) 0 get /BoldAsterisk put - dup (J) 0 get /SolidAsterisk put - dup (h) 0 get /Hexagon put - dup (H) 0 get /BoldHexagon put - dup (G) 0 get /SolidHexagon put - dup (f) 0 get /Octogon put % 2008-04-18 hv - dup (F) 0 get /BoldOctogon put % 2008-04-18 hv - dup (g) 0 get /SolidOctogon put % 2008-04-18 hv - dup (a) 0 get /Add put - dup (A) 0 get /BoldAdd put % 65 - dup (x) 0 get /Mul put - dup (X) 0 get /BoldMul put - dup (m) 0 get /Oplus put - dup (M) 0 get /BOplus put - dup (e) 0 get /SolidOplus put - dup (n) 0 get /Otimes put - dup (N) 0 get /BOtimes put - dup (E) 0 get /SolidOtimes put - dup (i) 0 get /Bar put - dup (I) 0 get /BoldBar put - dup (l) 0 get /SolidDiamond put - dup (d) 0 get /Diamond put - (D) 0 get /BoldDiamond put -%%% -/CharProcs 47 dict def -CharProcs begin - /CirclePath {0 0 500 0 360 arc closepath} def - /Bullet {CirclePath fill} def - /Circle {CirclePath .9 .9 scale CirclePath eofill} def - /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def - /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def - /SolidTriangle {TrianglePath fill} def - /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def - /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def - /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def - /SolidSquare {SquarePath fill} def - /Square {SquarePath .89 .89 scale SquarePath eofill} def - /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def - /PentagonPath { - -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto - 0 574.7 lineto -546.6 177.6 lineto closepath - } def - /SolidPentagon {PentagonPath fill} def - /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def - /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def -%-------------- hv begin 2004/07/25 from: er 2003/03/24 - /HexagonPath { - 0 550 moveto -476 275 lineto -476 -275 lineto - 0 -550 lineto 476 -275 lineto 476 275 lineto closepath - } def - /SolidHexagon {HexagonPath fill} def - /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def - /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def -% 2008-04-18 hv - /OctogonPath { - 550 dup 22.5 tan mul dup neg dup add /xMove exch def - exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def - /SolidOctogon { OctogonPath fill } def - /Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def - /BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def -% - /AsteriskPath { - 20 0 moveto 10 250 180 500 0 500 curveto - -180 500 -10 250 -20 0 curveto closepath - } def - /Asterisk { - AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath - 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill - } def -% - /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def - /BoldAsteriskPath { - 50 30 cos 100 mul moveto Basterp - 60 rotate Basterp 60 rotate Basterp - 60 rotate Basterp 60 rotate Basterp - 60 rotate Basterp closepath - } def - /BoldAsterisk {BoldAsteriskPath fill} def - /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def - /CrossPath { - 40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto - -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto - 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath - } def - /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto - -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto - 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath - } def - /Add {CrossPath fill} def - /Mul {45 rotate CrossPath fill} def - /BoldAdd {BoldCrossPath fill} def - /BoldMul {45 rotate BoldCrossPath fill} def - /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def - /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def - /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def - /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def - /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def - /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def - /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def - /Bar {BarPath fill} def - /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def - /BoldBar {BoldBarPath fill} def - /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath} def - /SolidDiamond {DiamondPath fill} def - /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def - /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def -%%% - /.notdef { } def -end -% -/BuildGlyph { - exch - begin -% Metrics 1 index get exec 0 - 0 0 -% BBoxes 3 index get exec - -1000 -1000 1000 1000 -% -571.5 -742.5 571.5 742.5 - setcachedevice - CharProcs begin load exec end - end -} def -% -/BuildChar { - 1 index /Encoding get exch get - 1 index /BuildGlyph get exec -} bind def - -end -/PSTricksDotFont exch definefont pop - -%% end - -%%EndProcSet -%%BeginProcSet: pst-node.pro 0 0 -% $Id: pst-node.pro 26 2008-06-14 11:50:02Z herbert $ -%% -%% PostScript prologue for pst-node.tex. -%% Version 1.00, 2008/01/01. -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -% -/tx@NodeDict 400 dict def tx@NodeDict begin -tx@Dict begin % from main pstricks dict - /T /translate load def -end -/NewNode { % on stack: { x y } boolean N@name type InitXnode - gsave - /next ED % { x y } boolean N@name type - dict dup % { x y } boolean N@name dict dict - 3 1 roll def % { x y } boolean dict N@name dict def - exch { dup 3 1 roll def } if % { x y } dict boolean - begin % { x y } dict begin - tx@Dict begin - STV CP T exec % set scaling - end - /NodeMtrx CM def % save CM - next % InitXNode - end - grestore -} def -% -/InitPnode { - /Y ED /X ED - /NodePos { NodeSep Cos mul NodeSep Sin mul } def -} def -% -/InitCnode { - /r ED /Y ED /X ED - /NodePos { NodeSep r add dup Cos mul exch Sin mul } def -} def -% -/GetRnodePos { - Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse - Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse - dx Sin mul abs dy - Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse -} def -% -/InitRnode { - /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED - /NodePos { GetRnodePos } def -} def -% -/DiaNodePos { - w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup - Cos mul exch Sin mul -} def -% -/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h -mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul -} ifelse } def -/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d -ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d -sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan -sin def /NodePos { TriNodePos } def } def -/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos -hh mul Atan dup cos ww mul exch sin hh mul } def -/GetCenter { begin X Y NodeMtrx transform CM itransform end } def -% -/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist - Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } - { 0 Dist Sin mul } ifelse } ifelse Do -} def -/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform - exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx - dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop - XYPos } ifelse -} def -/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 -roll sin mul sub exch } ifelse } def -/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA -AddOffset yA add /yA1 ED xA add /xA1 ED } def -/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB -AddOffset yB add /yB1 ED xB add /xB1 ED } def -/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA -AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED -ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED -} ifelse } def -/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB -AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED -ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED -} ifelse } def -/InitNC { - /b ED /a ED % second and first node - /NodeSepTypeB ED /NodeSepTypeA ED - /NodeSepB ED /NodeSepA ED - /OffsetB ED /OffsetA ED - tx@NodeDict a known tx@NodeDict b known and dup { - /NodeA a load def - /NodeB b load def - NodeA GetCenter /yA ED /xA ED - NodeB GetCenter /yB ED /xB ED } if -} def -% -/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub -mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def -/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt -{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop -} repeat LPutLine cleartomark } def -/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED -/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 -mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx -sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul -add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add -y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul -mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def -/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def -} def -/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def -/NAngle yyB yyA sub xxB xxA sub Atan def } def -/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def -/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def -} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit -} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd -} def -/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def -} def -/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def -/NAngle yyB yyA sub xxB xxA sub Atan def } def -/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def -/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def -} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { -exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark -VPosEnd } def -/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 -roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx -def grestore exec /LPutVar /SaveLPutVar load def } def -/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def -GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { -LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { -LPutVar VPutLine } def LPutVar } def -/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop -end } def -/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub -Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan -/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 -yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { -LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } -ifelse } def -/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 -roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA -GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict -begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] -cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines -} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def -% -/NCAngles { - GetEdgeA GetEdgeB GetArmA GetArmB - /mtrx AngleA matrix rotate def - xA2 yA2 mtrx transform pop - xB2 yB2 mtrx transform exch pop - mtrx itransform - /y0 ED /x0 ED - mark ArmB 0 ne { xB1 yB1 } if - xB2 yB2 x0 y0 xA2 yA2 - ArmA 0 ne { xA1 yA1 } if - tx@Dict begin false Line end - /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def - /LPutPos { LPutLines } def - /HPutPos { HPutLines } def - /VPutPos { VPutLines } def } def -% -/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 -yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform -/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 -tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] -cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { -VPutLines } def } def -/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def -xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx -transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } -{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB -0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict -begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx -def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { -VPutLines } def } def -/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if -xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end -/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { -LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } -def -/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED -GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin -false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { -LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } -def -/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate -def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 -mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 -mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 -xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false -Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] -cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { -VPutLines } def } def -% DG/SR modification begin - May 9, 1997 - Patch 1 -%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r -%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add -%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 -%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED -/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r -r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add -exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 -mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED -% DG/SR modification end -} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add -AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r -Div def /y ED /x ED } def -/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB -180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos -mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def -/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy -add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos -{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar -tx@Dict begin false Polygon end } def -/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan -def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 -mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def -/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div -def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def -GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul -sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 -eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } -{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def -0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 -roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 -0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 -roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } -ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos -{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { -r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } -{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add -add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub -mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t -sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse -y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { -LPutPos } def } def -/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB -sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 -ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB -w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos -{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } -{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } -def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin -/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def - -/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg -exch X sub neg exch moveto setmatrix CP grestore } def - -/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 -def } ifelse LPutCoor } def -/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } -if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } -ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } -def -/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if -r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } -ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } -def -end -% END pst-node.pro - -%%EndProcSet -%%BeginProcSet: pstricks-add.pro 0 0 -%% $Id: pstricks-add.pro 49 2008-10-13 10:59:27Z herbert $ -% PostScript prologue for pstricks-add.tex. -% Version 0.21, 2008/10/15 -% For distribution, see pstricks.tex. -% -% HISTORY -> see file Changes -% -/tx@addDict 410 dict def tx@addDict begin -%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -/GTriangle { - gsave - /mtrx CM def - /colorA ED /colorB ED /colorC ED % save the colors - /yA ED /xA ED % save the origin - xA yA translate - rotate % \psk@gangle - /yB ED /xB ED /yC ED /xC ED % save other coordinates - /ds [ % save data in a array - 0 0 0 colorA aload pop % fd x y xr xg xb - 0 xB xA sub yB yA sub colorB aload pop - 0 xC xA sub yC yA sub colorC aload pop -% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD - ] def - newpath - << - /ShadingType 4 % single Gouraud - /ColorSpace [ /DeviceRGB ] - /DataSource ds - >> - shfill - closepath - mtrx - setmatrix grestore} def -% -/RGBtoCMYK { % on stack r g b -> C M Y K - 3 dict begin - /Blue ED /Green ED /Red ED - 1 Red sub % Cyan - 1 Green sub % Magenta - 1 Blue sub % Yellow - 0 % Black - end -} def -% -/CMYKtoGRAY { % on stack c m y k -> gray - exch 0.11 mul add - exch 0.59 mul add - exch 0.3 mul add - dup 1 gt { pop 1 } if - neg 1 add -} def -% -/RGBtoGRAY { % on stack r g b -> gray - 0.11 mul - exch 0.59 mul add - exch 0.3 mul add -} def -% -/HSBtoGRAY { - 6 dict begin - /b exch def - /s exch def 6 mul dup cvi dup - /i exch def sub - /f exch def - /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def - F i get { s mul neg 1 add b mul} forall - 0.11 mul - exch 0.59 mul add - exch 0.3 mul add - end -} def -% -%% convertisseur longueur d'onde ->R,G,B Manuel Luque -%% lambda max=780 nanometres -%% lambda min=380 nanometres -%% adaptation de : -%% http://www.physics.sfasu.edu/astro/color.html -%% www.efg2.com/lab -% -/Gamma 0.8 def -/calculateRGB { - lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if - lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if - lambda 380 ge {lambda 439 le { - /R {lambda 440 sub neg 440 380 sub div} def - /Red R factor mul Gamma exp def - /G 0 def - /Green G factor mul Gamma exp def - /B 1 def - /Blue B factor mul Gamma exp def} if - } if - lambda 440 ge { lambda 489 le { - /G {lambda 440 sub 490 440 sub div} def - /Green G factor mul Gamma exp def - /R 0 def /Red 0 def - /B 1 def - /Blue B factor mul Gamma exp def } if - } if - lambda 490 ge {lambda 509 le { - /B {lambda 510 sub neg 510 490 sub div} def - /Blue B factor mul Gamma exp def - /R 0 def /Red 0 def - /G 1 def - /Green G factor mul Gamma exp def } if - } if - lambda 510 ge {lambda 579 le { - /R {lambda 510 sub 580 510 sub div } def - /Red R factor mul Gamma exp def - /Blue 0 def - /G 1 def - /Green G factor mul Gamma exp def } if - } if - lambda 580 ge {lambda 644 le { - /G {lambda 645 sub neg 645 580 sub div } def - /Green G factor mul Gamma exp def - /Blue 0 def - /R 1 def - /Red R factor mul Gamma exp def } if - } if - lambda 645 ge { lambda 780 le { - /Red 1 factor mul Gamma exp def - /Blue 0 def - /Green 0 def } if - } if -} def -% -/factor { - lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if - lambda 420 ge {lambda 700 le { 1 } if } if - lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if -} def -% -/wavelengthToRGB { % the wavelength in nm must be on top of the stack - 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1 gt {1.0 1. 1.0 add div }{ 0.5 } ifelse def 1. cvi { /ArrowPos -ArrowPos dArrowPos add def x12 x11 sub ArrowPos mul x11 add y12 y11 -sub ArrowPos mul y11 add currentdict /ArrowInside known { ArrowInside -} if pop pop } repeat } ifelse pop pop Lineto } def n { 4 copy /y11 -ED /x11 ED /y12 ED /x12 ED drawArrows } repeat x1 y1 x0 y0 6 4 roll -2 copy /y11 ED /x11 ED /y12 y0 def /x12 x0 def drawArrows /y11 y0 def -/x11 x0 def /y12 yy1 def /x12 xx1 def drawArrows pop pop closepath -} ifelse gsave 1 1 1 setrgbcolor 1. .setopacityalpha fill grestore -gsave 0.1 SLW 0 0 0 setrgbcolor 1. .setopacityalpha 0 setlinecap -stroke grestore end - -@endspecial @beginspecial -@setspecial - tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def -/ArrowInside { } def 0.1 SLW 0 0 0 setrgbcolor [ 1.20709 1.20709 -8.53546 0.0 0.0 0.0 /Lineto /lineto load def false 1 setlinejoin -NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } repeat }{ -n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 ED /x1 -ED /xx1 x1 def /yy1 y1 def x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 -add 2 div def x1 y1 moveto /n n 2 sub def /drawArrows { x11 y11 0.5 - 1 gt { /Alpha y12 y11 sub x12 x11 sub atan def /ArrowPos 0. def /Length -x12 x11 sub y12 y11 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos -ArrowPos dArrowPos add def ArrowPos Length gt { exit } if x11 Alpha -cos ArrowPos mul add y11 Alpha sin ArrowPos mul add currentdict /ArrowInside -known { ArrowInside } if pop pop } loop }{ /ArrowPos 0. def /dArrowPos -1. 1 gt {1.0 1. 1.0 add div }{ 0.5 } ifelse def 1. cvi { /ArrowPos -ArrowPos dArrowPos add def x12 x11 sub ArrowPos mul x11 add y12 y11 -sub ArrowPos mul y11 add currentdict /ArrowInside known { ArrowInside -} if pop pop } repeat } ifelse pop pop Lineto } def n { 4 copy /y11 -ED /x11 ED /y12 ED /x12 ED drawArrows } repeat x1 y1 x0 y0 6 4 roll -2 copy /y11 ED /x11 ED /y12 y0 def /x12 x0 def drawArrows /y11 y0 def -/x11 x0 def /y12 yy1 def /x12 xx1 def drawArrows pop pop closepath -} ifelse gsave 0 0 0 setrgbcolor 1. .setopacityalpha fill grestore -gsave 0.1 SLW 0 0 0 setrgbcolor 1. .setopacityalpha 0 setlinecap -stroke grestore end - -@endspecial @beginspecial @setspecial - tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def -/ArrowInside { } def 0.1 SLW 0 0 0 setrgbcolor [ 1.20709 -1.20709 -8.53546 0.0 0.0 0.0 /Lineto /lineto load def false 1 setlinejoin -NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } repeat }{ -n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 ED /x1 -ED /xx1 x1 def /yy1 y1 def x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 -add 2 div def x1 y1 moveto /n n 2 sub def /drawArrows { x11 y11 0.5 - 1 gt { /Alpha y12 y11 sub x12 x11 sub atan def /ArrowPos 0. def /Length -x12 x11 sub y12 y11 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos -ArrowPos dArrowPos add def ArrowPos Length gt { exit } if x11 Alpha -cos ArrowPos mul add y11 Alpha sin ArrowPos mul add currentdict /ArrowInside -known { ArrowInside } if pop pop } loop }{ /ArrowPos 0. def /dArrowPos -1. 1 gt {1.0 1. 1.0 add div }{ 0.5 } ifelse def 1. cvi { /ArrowPos -ArrowPos dArrowPos add def x12 x11 sub ArrowPos mul x11 add y12 y11 -sub ArrowPos mul y11 add currentdict /ArrowInside known { ArrowInside -} if pop pop } repeat } ifelse pop pop Lineto } def n { 4 copy /y11 -ED /x11 ED /y12 ED /x12 ED drawArrows } repeat x1 y1 x0 y0 6 4 roll -2 copy /y11 ED /x11 ED /y12 y0 def /x12 x0 def drawArrows /y11 y0 def -/x11 x0 def /y12 yy1 def /x12 xx1 def drawArrows pop pop closepath -} ifelse gsave 1 1 1 setrgbcolor 1. .setopacityalpha fill grestore -gsave 0.1 SLW 0 0 0 setrgbcolor 1. .setopacityalpha 0 setlinecap -stroke grestore end - -@endspecial -@beginspecial @setspecial - tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def -/ArrowInside { } def 0.1 SLW 0 0 0 setrgbcolor [ -1.20709 1.20709 -0.0 8.53546 0.0 0.0 /Lineto /lineto load def false 1 setlinejoin -NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } repeat }{ -n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 ED /x1 -ED /xx1 x1 def /yy1 y1 def x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 -add 2 div def x1 y1 moveto /n n 2 sub def /drawArrows { x11 y11 0.5 - 1 gt { /Alpha y12 y11 sub x12 x11 sub atan def /ArrowPos 0. def /Length -x12 x11 sub y12 y11 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos -ArrowPos dArrowPos add def ArrowPos Length gt { exit } if x11 Alpha -cos ArrowPos mul add y11 Alpha sin ArrowPos mul add currentdict /ArrowInside -known { ArrowInside } if pop pop } loop }{ /ArrowPos 0. def /dArrowPos -1. 1 gt {1.0 1. 1.0 add div }{ 0.5 } ifelse def 1. cvi { /ArrowPos -ArrowPos dArrowPos add def x12 x11 sub ArrowPos mul x11 add y12 y11 -sub ArrowPos mul y11 add currentdict /ArrowInside known { ArrowInside -} if pop pop } repeat } ifelse pop pop Lineto } def n { 4 copy /y11 -ED /x11 ED /y12 ED /x12 ED drawArrows } repeat x1 y1 x0 y0 6 4 roll -2 copy /y11 ED /x11 ED /y12 y0 def /x12 x0 def drawArrows /y11 y0 def -/x11 x0 def /y12 yy1 def /x12 xx1 def drawArrows pop pop closepath -} ifelse gsave 0 0 0 setrgbcolor 1. .setopacityalpha fill grestore -gsave 0.1 SLW 0 0 0 setrgbcolor 1. .setopacityalpha 0 setlinecap -stroke grestore end - -@endspecial @beginspecial -@setspecial - tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def -/ArrowInside { } def 0.1 SLW 0 0 0 setrgbcolor [ 1.20709 1.20709 -0.0 8.53546 0.0 0.0 /Lineto /lineto load def false 1 setlinejoin -NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } repeat }{ -n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 ED /x1 -ED /xx1 x1 def /yy1 y1 def x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 -add 2 div def x1 y1 moveto /n n 2 sub def /drawArrows { x11 y11 0.5 - 1 gt { /Alpha y12 y11 sub x12 x11 sub atan def /ArrowPos 0. def /Length -x12 x11 sub y12 y11 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos -ArrowPos dArrowPos add def ArrowPos Length gt { exit } if x11 Alpha -cos ArrowPos mul add y11 Alpha sin ArrowPos mul add currentdict /ArrowInside -known { ArrowInside } if pop pop } loop }{ /ArrowPos 0. def /dArrowPos -1. 1 gt {1.0 1. 1.0 add div }{ 0.5 } ifelse def 1. cvi { /ArrowPos -ArrowPos dArrowPos add def x12 x11 sub ArrowPos mul x11 add y12 y11 -sub ArrowPos mul y11 add currentdict /ArrowInside known { ArrowInside -} if pop pop } repeat } ifelse pop pop Lineto } def n { 4 copy /y11 -ED /x11 ED /y12 ED /x12 ED drawArrows } repeat x1 y1 x0 y0 6 4 roll -2 copy /y11 ED /x11 ED /y12 y0 def /x12 x0 def drawArrows /y11 y0 def -/x11 x0 def /y12 yy1 def /x12 xx1 def drawArrows pop pop closepath -} ifelse gsave 1 1 1 setrgbcolor 1. .setopacityalpha fill grestore -gsave 0.1 SLW 0 0 0 setrgbcolor 1. .setopacityalpha 0 setlinecap -stroke grestore end - -@endspecial @beginspecial @setspecial - tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def -/ArrowInside { } def 0.1 SLW 0 0 0 setrgbcolor [ -1.20709 -1.20709 --8.53546 0.0 0.0 0.0 /Lineto /lineto load def false 1 setlinejoin -NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } repeat }{ -n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 ED /x1 -ED /xx1 x1 def /yy1 y1 def x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 -add 2 div def x1 y1 moveto /n n 2 sub def /drawArrows { x11 y11 0.5 - 1 gt { /Alpha y12 y11 sub x12 x11 sub atan def /ArrowPos 0. def /Length -x12 x11 sub y12 y11 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos -ArrowPos dArrowPos add def ArrowPos Length gt { exit } if x11 Alpha -cos ArrowPos mul add y11 Alpha sin ArrowPos mul add currentdict /ArrowInside -known { ArrowInside } if pop pop } loop }{ /ArrowPos 0. def /dArrowPos -1. 1 gt {1.0 1. 1.0 add div }{ 0.5 } ifelse def 1. cvi { /ArrowPos -ArrowPos dArrowPos add def x12 x11 sub ArrowPos mul x11 add y12 y11 -sub ArrowPos mul y11 add currentdict /ArrowInside known { ArrowInside -} if pop pop } repeat } ifelse pop pop Lineto } def n { 4 copy /y11 -ED /x11 ED /y12 ED /x12 ED drawArrows } repeat x1 y1 x0 y0 6 4 roll -2 copy /y11 ED /x11 ED /y12 y0 def /x12 x0 def drawArrows /y11 y0 def -/x11 x0 def /y12 yy1 def /x12 xx1 def drawArrows pop pop closepath -} ifelse gsave 0 0 0 setrgbcolor 1. .setopacityalpha fill grestore -gsave 0.1 SLW 0 0 0 setrgbcolor 1. .setopacityalpha 0 setlinecap -stroke grestore end - -@endspecial -@beginspecial @setspecial - tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def -/ArrowInside { } def 0.1 SLW 0 0 0 setrgbcolor [ -1.20709 1.20709 --8.53546 0.0 0.0 0.0 /Lineto /lineto load def false 1 setlinejoin -NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } repeat }{ -n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 ED /x1 -ED /xx1 x1 def /yy1 y1 def x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 -add 2 div def x1 y1 moveto /n n 2 sub def /drawArrows { x11 y11 0.5 - 1 gt { /Alpha y12 y11 sub x12 x11 sub atan def /ArrowPos 0. def /Length -x12 x11 sub y12 y11 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos -ArrowPos dArrowPos add def ArrowPos Length gt { exit } if x11 Alpha -cos ArrowPos mul add y11 Alpha sin ArrowPos mul add currentdict /ArrowInside -known { ArrowInside } if pop pop } loop }{ /ArrowPos 0. def /dArrowPos -1. 1 gt {1.0 1. 1.0 add div }{ 0.5 } ifelse def 1. cvi { /ArrowPos -ArrowPos dArrowPos add def x12 x11 sub ArrowPos mul x11 add y12 y11 -sub ArrowPos mul y11 add currentdict /ArrowInside known { ArrowInside -} if pop pop } repeat } ifelse pop pop Lineto } def n { 4 copy /y11 -ED /x11 ED /y12 ED /x12 ED drawArrows } repeat x1 y1 x0 y0 6 4 roll -2 copy /y11 ED /x11 ED /y12 y0 def /x12 x0 def drawArrows /y11 y0 def -/x11 x0 def /y12 yy1 def /x12 xx1 def drawArrows pop pop closepath -} ifelse gsave 1 1 1 setrgbcolor 1. .setopacityalpha fill grestore -gsave 0.1 SLW 0 0 0 setrgbcolor 1. .setopacityalpha 0 setlinecap -stroke grestore end - -@endspecial @beginspecial -@setspecial - tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def -/ArrowInside { } def 0.1 SLW 0 0 0 setrgbcolor [ 1.20709 -1.20709 -0.0 -8.53546 0.0 0.0 /Lineto /lineto load def false 1 setlinejoin -NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } repeat }{ -n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 ED /x1 -ED /xx1 x1 def /yy1 y1 def x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 -add 2 div def x1 y1 moveto /n n 2 sub def /drawArrows { x11 y11 0.5 - 1 gt { /Alpha y12 y11 sub x12 x11 sub atan def /ArrowPos 0. def /Length -x12 x11 sub y12 y11 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos -ArrowPos dArrowPos add def ArrowPos Length gt { exit } if x11 Alpha -cos ArrowPos mul add y11 Alpha sin ArrowPos mul add currentdict /ArrowInside -known { ArrowInside } if pop pop } loop }{ /ArrowPos 0. def /dArrowPos -1. 1 gt {1.0 1. 1.0 add div }{ 0.5 } ifelse def 1. cvi { /ArrowPos -ArrowPos dArrowPos add def x12 x11 sub ArrowPos mul x11 add y12 y11 -sub ArrowPos mul y11 add currentdict /ArrowInside known { ArrowInside -} if pop pop } repeat } ifelse pop pop Lineto } def n { 4 copy /y11 -ED /x11 ED /y12 ED /x12 ED drawArrows } repeat x1 y1 x0 y0 6 4 roll -2 copy /y11 ED /x11 ED /y12 y0 def /x12 x0 def drawArrows /y11 y0 def -/x11 x0 def /y12 yy1 def /x12 xx1 def drawArrows pop pop closepath -} ifelse gsave 0 0 0 setrgbcolor 1. .setopacityalpha fill grestore -gsave 0.1 SLW 0 0 0 setrgbcolor 1. .setopacityalpha 0 setlinecap -stroke grestore end - -@endspecial @beginspecial @setspecial - tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def -/ArrowInside { } def 0.1 SLW 0 0 0 setrgbcolor [ -1.20709 -1.20709 -0.0 -8.53546 0.0 0.0 /Lineto /lineto load def false 1 setlinejoin -NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } repeat }{ -n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 ED /x1 -ED /xx1 x1 def /yy1 y1 def x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 -add 2 div def x1 y1 moveto /n n 2 sub def /drawArrows { x11 y11 0.5 - 1 gt { /Alpha y12 y11 sub x12 x11 sub atan def /ArrowPos 0. def /Length -x12 x11 sub y12 y11 sub Pyth def /dArrowPos 0.5 abs def { /ArrowPos -ArrowPos dArrowPos add def ArrowPos Length gt { exit } if x11 Alpha -cos ArrowPos mul add y11 Alpha sin ArrowPos mul add currentdict /ArrowInside -known { ArrowInside } if pop pop } loop }{ /ArrowPos 0. def /dArrowPos -1. 1 gt {1.0 1. 1.0 add div }{ 0.5 } ifelse def 1. cvi { /ArrowPos -ArrowPos dArrowPos add def x12 x11 sub ArrowPos mul x11 add y12 y11 -sub ArrowPos mul y11 add currentdict /ArrowInside known { ArrowInside -} if pop pop } repeat } ifelse pop pop Lineto } def n { 4 copy /y11 -ED /x11 ED /y12 ED /x12 ED drawArrows } repeat x1 y1 x0 y0 6 4 roll -2 copy /y11 ED /x11 ED /y12 y0 def /x12 x0 def drawArrows /y11 y0 def -/x11 x0 def /y12 yy1 def /x12 xx1 def drawArrows pop pop closepath -} ifelse gsave 1 1 1 setrgbcolor 1. .setopacityalpha fill grestore -gsave 0.1 SLW 0 0 0 setrgbcolor 1. .setopacityalpha 0 setlinecap -stroke grestore end - -@endspecial -eop end -%%Trailer - -userdict /end-hook known{end-hook}if -%%EOF diff --git a/Master/texmf-dist/doc/latex/bclogo/bcrosevents.pdf b/Master/texmf-dist/doc/latex/bclogo/bcrosevents.pdf Binary files differdeleted file mode 100644 index 6caa0169851..00000000000 --- a/Master/texmf-dist/doc/latex/bclogo/bcrosevents.pdf +++ /dev/null diff --git a/Master/texmf-dist/doc/latex/bclogo/bcsoleil.eps b/Master/texmf-dist/doc/latex/bclogo/bcsoleil.eps deleted file mode 100644 index a4eaaa6809d..00000000000 --- a/Master/texmf-dist/doc/latex/bclogo/bcsoleil.eps +++ /dev/null @@ -1,2542 +0,0 @@ -%!PS-Adobe-2.0 EPSF-2.0 -%%Creator: dvips(k) 5.96dev Copyright 2007 Radical Eye Software -%%Title: CompileEps.dvi -%%CreationDate: Sat Sep 19 14:18:02 2009 -%%BoundingBox: 71 701 90 721 -%%EndComments -%DVIPSWebPage: (www.radicaleye.com) -%DVIPSCommandLine: dvips -E -o -%+ C:\Users\Alain_2\Documents\LaTeX\Logos\bcsoleil.eps CompileEps.dvi -%DVIPSParameters: dpi=600 -%DVIPSSource: TeX output 2009.09.19:1418 -%%BeginProcSet: tex.pro 0 0 -%! -/TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S -N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 -mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 -0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ -landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize -mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ -matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round -exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ -statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] -N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin -/FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array -/BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 -array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N -df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A -definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get -}B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} -B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr -1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S -/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy -setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask -restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn -/BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put -}if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ -bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A -mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ -SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ -userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X -1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 -index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N -/p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ -/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) -(LaserWriter 16/600)]{A length product length le{A length product exch 0 -exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse -end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask -grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} -imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round -exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto -fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p -delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} -B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ -p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S -rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end - -%%EndProcSet -%%BeginProcSet: pstricks.pro 0 0 -% $Id: pstricks.pro 34 2008-06-25 17:20:01Z herbert $ -% -%% PostScript prologue for pstricks.tex. -%% Version 1.05, 2008/06/25 -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -% -% -% Define the follwing gs-functions if not known, eg when using distiller -% -systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if -systemdict /.setblendmode known not {/.setblendmode { pop } def } if -systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if -% -/tx@Dict 200 dict def % the main PSTricks dictionary -tx@Dict begin -/ADict 25 dict def % The arrow dictionaray -/CM { matrix currentmatrix } bind def -/SLW /setlinewidth load def -/CLW /currentlinewidth load def -/CP /currentpoint load def -/ED { exch def } bind def -/L /lineto load def -/T /translate load def -/TMatrix { } def -/RAngle { 0 } def -/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments -/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known -/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) -/Div { dup 0 eq { pop } { div } ifelse } def % control the division -/tan { dup cos abs 1.e-10 lt - { pop 1.e10 } % return 1.e10 as infinit - { dup sin exch cos div } ifelse % default sin/cos -} def -/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees -/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root - pop pop 0 }{ sqrt exch atan} ifelse } def -/NET { neg exch neg exch T } def % change coordinate system to the negative one -/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter -/Pyth2 { % Pythagoras, xA yA xB yB - 3 -1 roll % xA xB yB yA - sub % xA xB yB-yA - 3 1 roll % yB-yA xA xB - sub % yB-yA xA-xB - Pyth } def -/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian -/Rand { rand 4294967295 div } def % a real random number -%----------------- hv added 20050516 --------------- -/PiDiv2 1.57079632680 def -/Pi 3.14159265359 def -/TwoPi 6.28318530718 def -/Euler 2.71828182846 def -%/e Euler bind def -/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees -/DegtoRad { Pi mul 180 div } bind def % viceversa -%----------------- hv end--------------------------- -/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def -/PathLength { - flattenpath /z 0 def - { /y1 ED /x1 ED /y2 y1 def /x2 x1 def } - { /y ED /x ED PathLength@ } - {} - { /y y2 def /x x2 def PathLength@ } - /pathforall load stopped { pop pop pop pop } if - z -} def -% -/STP { .996264 dup scale } def % BP/PT scaling -/STV { SDict begin normalscale end STP } def % -% -%%-------------- DG begin patch 15 ---------------%% -%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def -%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y -%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul -%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] -%0 } ifelse setdash stroke } def -/DashLine { - dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse - /b ED /x1 ED /y1 ED /x ED /y ED - /z y x add y1 add x1 add def - /Coef b a .5 sub 2 mul y mul sub z Div round - z mul a .5 sub 2 mul y mul add b exch Div def - /y y Coef mul def - /x x Coef mul def - /y1 y1 Coef mul def - /x1 x1 Coef mul def - x1 0 gt y1 0 gt or x 0 gt or y 0 gt and - { [ y x y1 x1 ] 1 a sub y mul } - { [ 1 0 ] 0 } ifelse - setdash stroke -} def -%%-------------- DG end patch 15 ---------------%% -/DotLine { - /b PathLength def - /a ED /z ED /y CLW def - /z y z add def - a 0 gt { - /b b a div def - }{ - a 0 eq { - /b b y sub def - }{ a -3 eq { - /b b y add def } if - } ifelse - } ifelse - [ 0 b b z Div round Div dup 0 le { pop 1 } if ] - a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse - setdash 1 setlinecap stroke -} def -% -/LineFill { % hv ------------ patch 7 ------------- - gsave - abs /hatchWidthInc ED - abs /hatchSepInc ED - abs CLW add /a ED - a 0 dtransform round exch round exch - 2 copy idtransform - exch Atan rotate - idtransform pop /a ED - .25 .25 itransform pathbbox - /y2 ED - a Div ceiling cvi /x2 ED /y1 ED - a Div cvi /x1 ED /y2 y2 y1 sub def - clip - newpath - 2 setlinecap - systemdict - /setstrokeadjust known { true setstrokeadjust } if - x2 x1 sub 1 add { - x1 a mul y1 moveto 0 y2 rlineto stroke - 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Dec. 12, 1997 - Patch 2 -%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a -%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a -%% DG/SR modification end -%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict -%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 -%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) -%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } -%% def -%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore -%pop pop } def -%% DG/SR modification end -% -/BeginArrow { - ADict begin % hold it local, for end see EndArrow - /@mtrx CM def - gsave - 2 copy T - 2 index sub neg exch - 3 index sub exch Atan - rotate newpath -} def -% -/EndArrow { @mtrx setmatrix CP grestore end } def % end the ADict -% -/Arrow { - CLW mul add dup - 2 div /w ED - mul dup /h ED - mul /a ED - { 0 h T 1 -1 scale } if - w neg h moveto - 0 0 L w h L w neg a neg rlineto - gsave fill grestore -} def -% -/ArrowD { % the sides are drawn as curves (hv 20071211) - CLW mul add dup - 2 div /w ED - mul dup /h ED - mul /Inset ED - { 0 h T 1 -1 scale } if % changes the direction -% we use y=w/h^2 * x^2 as equation for the control points -% for the coordinates the arrow is seen from top to bottom -% the bottom (tip) is (0;0) - w neg h moveto % lower left of > - w 9 div 4 mul neg h 3 div 2 mul - w 9 div neg h 3 div - 0 0 curveto % tip of > - w 9 div h 3 div - w 9 div 4 mul h 3 div 2 mul - w h curveto % upper left of > - w neg Inset neg rlineto % move to x=0 and inset - gsave fill grestore -} def -% -/Tbar { - CLW mul add /z ED - z -2 div CLW 2 div moveto - z 0 rlineto stroke - 0 CLW moveto -} def -% -/Bracket { - CLW mul add dup CLW sub 2 div - /x ED mul CLW add /y ED /z CLW 2 div def - x neg y moveto - x neg CLW 2 div L x CLW 2 div L x y L stroke - 0 CLW moveto -} def -% -/RoundBracket { - CLW mul add dup 2 div - /x ED mul /y ED /mtrx CM def - 0 CLW 2 div T x y mul 0 ne { x y scale } if - 1 1 moveto - .85 .5 .35 0 0 0 curveto - -.35 0 -.85 .5 -1 1 curveto - mtrx setmatrix stroke 0 CLW moveto -} def -% -/SD { 0 360 arc fill } def -% -/EndDot { % DS is the dot size - { /z DS def } { /z 0 def } ifelse - /b ED 0 z DS SD b { 0 z DS CLW sub SD } if - 0 DS z add CLW 4 div sub moveto } def -% -/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { - /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto - load } if ] cvx newpath 3 1 roll T exec } def -% -%/NArray { -% aload length 2 div dup dup cvi eq not { exch pop } if /n exch -% cvi def -%} def -% -/NArray { % holds the coordinates and on top of stack the showpoints boolean - /showpoints ED - counttomark 2 div dup cvi /n ED - n eq not { exch pop } if - showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse -} def -% -/Line { - NArray n 0 eq not - { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def - n { Lineto } repeat - CP 4 2 roll ArrowB L pop pop - } if -} def -% -/Arcto { - /a [ 6 -2 roll ] cvx def - a r - /arcto load stopped { 5 } { 4 } ifelse { pop } repeat - a -} def -% -/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq - and { pop pop /n n 1 sub def } if } def -/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } - repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 - ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 - moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto - Lineto pop pop closepath } ifelse } def -/Diamond { - /mtrx CM def - T rotate - /h ED - /w ED - dup 0 eq { pop } { CLW mul neg - /d ED - /a w h Atan def - /h d a sin Div h add def - /w d a cos Div w add def } ifelse - mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div - /ArrowA { moveto } def - /ArrowB { } def - false Line - closepath mtrx setmatrix } def -% DG modification begin - Jan. 15, 1997 -%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { -%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 -%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 -%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx -%setmatrix } def -/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup -CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 -div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 -d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx -% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) -% setmatrix } def -setmatrix pop } def -% DG/SR modification end -% -/CCA { - /y ED /x ED - 2 copy y sub /dy1 ED - x sub /dx1 ED - /l1 dx1 dy1 Pyth def -} def -% -/CC { - /l0 l1 def - /x1 x dx sub def - /y1 y dy sub def - /dx0 dx1 def - /dy0 dy1 def - CCA - /dx dx0 l1 c exp mul dx1 l0 c exp mul add def - /dy dy0 l1 c exp mul dy1 l0 c exp mul add def - /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def - /x2 x l0 dx mul m mul sub def - /y2 y l0 dy mul m mul sub def - /dx l1 dx mul m mul neg def - /dy l1 dy mul m mul neg def -} def -% -/IC { - /c c 1 add def - c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse - /a a 2 mul 3 div 45 cos b exp div def - CCA - /dx 0 def - /dy 0 def -} def -% -/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def -/NC { CC x1 y1 x2 y2 x y curveto } def -/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def -/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def -/NAC { x2 y2 x y curveto CC x1 y1 } def -/EAC { x2 y2 x y ArrowB curveto pop pop } def -% -/OpenCurve { - NArray n 3 lt - { n { pop pop } repeat } - { BOC /n n 3 sub def n { NC } repeat EOC } ifelse -} def -% -/AltCurve { - { false NArray n 2 mul 2 roll - [ n 2 mul 3 sub 1 roll ] aload - /Points ED - n 2 mul -2 roll } - { false NArray } ifelse - n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse -} def -% -/ClosedCurve { - NArray n 3 lt - { n { pop pop } repeat } - { n 3 gt { CheckClosed } if - 6 copy n 2 mul 6 add 6 roll - IC CC x y moveto n { NC } repeat - closepath pop pop - } ifelse -} def -% -/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def -/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def -/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } -def -/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix -rotate matrix concatmatrix exch findfont exch makefont setfont } def -/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto -x1 y1 lineto closepath } def -/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 -y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div -exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse -/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto -x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } -ifelse } def -/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add -/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { -pop pop Rect } { OvalFrame } ifelse } def -% -/BezierNArray { - /f ED - counttomark 2 div dup cvi /n ED - n eq not { exch pop } if - n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat - f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse -} def -% -/OpenBezier { - BezierNArray - n 1 eq - { pop pop } - { ArrowA n 4 sub 3 idiv - { 6 2 roll 4 2 roll curveto } repeat - 6 2 roll 4 2 roll ArrowB curveto } ifelse -} def -% -/ClosedBezier { - BezierNArray - n 1 eq - { pop pop } - { moveto n 1 sub 3 idiv - { 6 2 roll 4 2 roll curveto } repeat - closepath } ifelse -} def -% -/BezierShowPoints { - gsave - Points aload length 2 div cvi /n ED - moveto - n 1 sub { lineto } repeat - CLW 2 div SLW [ 4 4 ] 0 setdash stroke - grestore -} def -% -/Parab { - /y0 ED /x0 ED /y1 ED /x1 ED - /dx x0 x1 sub 3 div def - /dy y0 y1 sub 3 div def - x0 dx sub y0 dy add x1 y1 ArrowA - x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB - curveto - /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def -} def -% -/Grid { - newpath - /a 4 string def - /b ED /c ED /n ED - cvi dup 1 lt { pop 1 } if - /s ED - s div dup 0 eq { pop 1 } if - /dy ED s div dup 0 eq { pop 1 } if - /dx ED dy div round dy mul - /y0 ED dx div round dx mul - /x0 ED dy div round cvi - /y2 ED dx div round cvi - /x2 ED dy div round cvi - /y1 ED dx div round cvi - /x1 ED - /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def - /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def - b 0 gt { - /z1 b 4 div CLW 2 div add def -% /Helvetica findfont b scalefont setfont - /b b .95 mul CLW 2 div add def } if - systemdict /setstrokeadjust known - { true setstrokeadjust /t { } def } - { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add - exch itransform } bind def } ifelse - gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse - /i x1 def - /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def - /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def - x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if - { i dx mul dup y0 moveto - b 0 gt - { gsave c i a cvs dup stringwidth pop - /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse - h 0 gt {b neg}{z1} ifelse - rmoveto show grestore } if - dup t f moveto - g t L stroke - /i i w add def - } repeat - grestore - gsave - n 0 gt - % DG/SR modification begin - Nov. 7, 1997 - Patch 1 - %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } - { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } - % DG/SR modification end - { 2 setlinecap } ifelse - /i y1 def - /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def - /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def - y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if - { newpath i dy mul dup x0 exch moveto - b 0 gt { gsave c i a cvs dup stringwidth pop - /z2 ED - w 0 gt {z1 z2 add neg} {z1} ifelse - h 0 gt {z1} {b neg} ifelse - rmoveto show grestore } if - dup f exch t moveto - g exch t L stroke - /i i h add def - } repeat - grestore -} def -% -/ArcArrow { - /d ED /b ED /a ED - gsave - newpath 0 -1000 moveto clip - newpath - 0 1 0 0 b - grestore - c mul - /e ED - pop pop pop r a e d PtoC y add exch x add - exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c - mul neg d -} def -% -/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def -% -/ArcAdjust { %%%% Vincent Guirardel -% given a target length (targetLength) and an initial angle (angle0) [in the stack], -% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). -% This computes an angle t such that (x0,y0) is at distance -% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). -% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 -% contrary to TvZ's code. -% To achieve, this, one iterates the following process: start with some angle t, -% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. -% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. -% -% Another difference with TvZ's code is that we need d (=add/sub) to be defined. -% the value of d = add/sub is used to know on which side we have to move. -% It is only used in the initialisation of the angle before the iteration. -% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% Input stack: 1: target length 2: initial angle -% variables used : rx, ry, d (=add/sub) -% - /targetLength ED /angle0 ED - /x0 rx angle0 cos mul def - /y0 ry angle0 sin mul def -% we are looking for an angle t such that (x0,y0) is at distance targetLength -% from the point M(t)=(rx*cos(t),ry*sin(t))) -%initialisation of angle (using 1st order approx = TvZ's code) - targetLength 57.2958 mul - angle0 sin rx mul dup mul - angle0 cos ry mul dup mul - add sqrt div -% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees -% (if the ellipse is very curved at the point where we draw the arrow, % -% the value can be much more than 360 degrees !) -% this should avoid going on the wrong side (more than 180 degrees) or go near -% a bad attractive point (at 180 degrees) - dup 90 ge { pop 90 } if - angle0 exch d % add or sub -% maximum number of times to iterate the iterative procedure: -% iterative procedure: takes an angle t on top of stack, computes a -% better angle (and put it on top of stack) - 30 { dup -% compute distance D between (x0,y0) and M(t) - dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt -% if D almost equals targetLength, we stop - dup targetLength sub abs 1e-5 le { pop exit } if -% stack now contains D t -% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: -% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) - exch dup cos rx mul x0 sub exch sin ry mul y0 sub -% stack contains: y(t)-y0, x(t)-x0, d - 2 index Div targetLength mul y0 add ry Div exch - 2 index Div targetLength mul x0 add rx Div -% stack contains x(t')/rx , y(t')/ry , d -% now compute t', and remove D from stack - atan exch pop - } repeat -% we don't look at what happened... in particular, if targetLength is greater -% than the diameter of the ellipse... -% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... -% after iteration, stack contains an angle t such that M(t) is the tail of the arrow -% to give back the result as a an angle relative to angle0 we could add the following line: -% angle0 sub 0 exch d -% -% begin bug fix 2006-01-11 -% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 -%(we don't want to make the ellipse turn more or less than it should)... -dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse -% end bug fix -} def -% -/EllipticArcArrow { - /d ED % is add or sub - /b ED % arrow procedure - /a1 ED % angle - gsave - newpath - 0 -1000 moveto - clip % Set clippath far from arrow. - newpath - 0 1 0 0 b % Draw arrow to determine length. - grestore -% Length of arrow is on top of stack. Next 3 numbers are junk. -% - a1 exch ArcAdjust % Angular position of base of arrow. - /a2 ED - pop pop pop - a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig - a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig - a1 cos rx mul xOrig add % - a1 sin ry mul yOrig add % -% Now arrow tip coor and base coor are on stack. - b pop pop pop pop % Draw arrow, and discard coordinates. - a2 CLW 8 div -% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) - 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse - ArcAdjust -% resets original value of d - 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. -} def -%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% -% -/Rot { CP CP translate 3 -1 roll neg rotate NET } def -% -/RotBegin { - tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if - /TMatrix [ TMatrix CM ] cvx def - /a ED - a Rot /RAngle [ RAngle dup a add ] cvx def -} def -% -/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def -% -/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def -/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def -/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def -/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s -abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b -div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { -h1 abs h sub dup s mul abs } ifelse } def -/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s -mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q -{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add -exch } def -/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible -/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def -} if } ifelse } def -/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def -/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit -neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def -/IfVisible true def } def -end -%-----------------------------------------------------------------------------% - -% END pstricks.pro - -%%EndProcSet -%%BeginProcSet: pst-algparser.pro 0 0 -% $Id: pst-algparser.pro 26 2008-06-14 11:50:02Z herbert $ -%% -%% PostScript prologue for PSTricks algorithm parser -%% Version 0.01, 2008/01/01 -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -%% -%%-----------------------------------------------------------------------------% -% -/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez -% -/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin -% -% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 -% E->T|E+T -% T->FS|T*FS -% FS -> F | +FS | -FS -% F->P|F^SF -% P->(E)|literal -% literal->number|var|var[E]|func(params) -% params->E|E,param -% number->TOBEFINISHED -% -%% E expression, T term, SF signed factor, F factor, P power -% -%% parser -% -%% str -% -%% C->E<condition_operators>E -%% STR index -> STR index+lenExpr -/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def -% -%% analyze Expression List (separator , or | ) -%% STR index -> STR index+lenExpr -%% /AnalyzeListOfE { -%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar -%% NextNonBlankChar dup 0 eq { pop exit } if -%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if -%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop -%% AnalyzeListOfEPostHook -%% } def -/AnalyzeListOfE { - /NotFirst false def - { NextNonBlankChar pop AnalyzeExpr - NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse - dup Strlen eq { exit } if NextNonBlankChar - dup 44 ne 1 index 124 ne and - { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } - if pop 1 add } loop - AnalyzeListOfEPostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% E->T|E+T -%% STR index -> STR index+lenExpr -/AnalyzeExpr { - AnalyzePreHook AnalyzeTerm IsEndingExpr - { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } - { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } - ifelse - AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% T->FS|T*FS -%% STR index -/AnalyzeTerm { - AnalyzePreHook AnalyzeSignedFactor IsEndingTerm - { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } - { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } - ifelse - AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% FS -> F | +FS | -FS -%% STR index -/AnalyzeSignedFactor { - AnalyzePreHook 2 copy get dup IsUnaryOp - { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } - { pop AnalyzeFactor } - ifelse AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% F->P|F^P -%% STR index -/AnalyzeFactor { - AnalyzePreHook AnalyzePower IsEndingFactor - { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } - { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } - ifelse AnalyzePostHook -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% P->(E)|literal -%% STR index -/AnalyzePower { - %% depending of first char either a number, or a literal - 2 copy get dup 40 eq%%an open par - { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } - { AnalyzeLiteral } - ifelse -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index STR[index] -> STR index -%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def -/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% recognize + or - -%% chr -> T/F -/IsUnaryOp { dup 43 eq exch 45 eq or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a number can contain only : 0123456789. -%% chr -> T/F -/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index -> STR index number -%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? -%% STR index -> STR index' number -/ReadNumber { - exch dup 3 -1 roll dup 3 1 roll - %%read mantissa - { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop - dup 101 eq exch 69 eq or - %%% there is a "e" or "E" -> read exponant - { 1 add 2 copy get dup IsUnaryOp - { pop 1 add 2 copy get } if - { IsNumber not { exit } if 1 add 2 copy get } loop } - if - dup 4 1 roll - 3 -1 roll exch 1 index sub getinterval -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a number can contain only : 0123456789. -%% chr -> T/F -/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index -> STR index number -%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? -%% STR index -> STR index' number -/ReadCondOp { - NextNonBlankChar 1 index 4 1 roll - { IsCondOp not { exit } if 1 add 2 copy get } loop - 2 copy 5 -1 roll - exch 1 index sub getinterval 3 1 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a literal can contain only : 0123456789. -%% chr -> T/F -/IsLiteral {% - dup 48 ge exch dup 57 le 3 -1 roll and exch - dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch - dup 97 ge exch 122 le and or } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? -%% STR index -> literal STR index' nextchr -/ReadLiteral { - exch dup 3 -1 roll dup 3 1 roll - %%read literal core - { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop - 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or a clpar -%% STR index -> STR index STR[index] T/F -/IsEndingExpr {% - 2 copy dup Strlen eq - %% if end of str is reached -> end ! - { pop pop 0 true } - %% ending chr -> clpar, comma, |, <, >, =, !, - {get dup dup 41 eq - exch dup 124 eq - exch dup 93 eq - exch dup 44 eq - exch dup 30 eq - exch dup 60 ge exch 62 le and or or or or or} - ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or a +- -%% STR index -> STR index STR[index] T/F -/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or */ -%% STR index -> STR index STR[index] T/F -/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% expr is ended by end of str or ^ -%% STR index -> STR index STR[index] T/F -/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% STR index -> STR index STR[index] -/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def -/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def -%%%%%%%%%%%%%%%%%%%%%%%% -%% DEBUG -/BRK {false} def -/BRKtrue {/BRK true def} def -/BRKStop {BRK {BRKtoto} if } def -/BRKEvalStop {BRK exch if } def -/BRKBRK2true {BRK {BRK2true} if } def -/BRK2 {false} def -/BRK2true {/BRK2 true def} def -/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def -end -% -%-------------------------------------------------------------------------------% -% -/tx@AlgToPs 12 dict def tx@AlgToPs begin -% -%% algExpr -> PSVector -/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def -/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def -/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def -/Strlen 0 def -/EvalListOfExpr {} def% -/EvalNumber {% - ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx - exch 1 add array astore def NextNonBlankChar pop } def -/EvalAddSub {% - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll - 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def -} def -/EvalMulDiv {% - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll - 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def -} def -/EvalPower {% - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll - pop /exp cvx exch 1 add array astore def -} def -/EvalLiteral {% - ReadLiteral - dup 40 eq%%% there is an open par -> function call - { pop 2 index - dup (Sum) eq { EvalSum } - { dup (IfTE) eq { EvalCond } - { dup (Derive) eq { pop EvalDerive } - { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc - /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx - exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } - { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def - dup 91 eq%%% there is an open bracket -> vector element - { pop 1 add NextNonBlankChar pop AnalyzeExpr - /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } - { pop NextNonBlankChar pop } - ifelse} - ifelse -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% the derive function : Derive(n,f(x)) -%% firstparindex lastparindex -> -/EvalDerive { - %% manage the function descripiton - 1 add ReadNumber 3 1 roll NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - 1 add NextNonBlankChar pop - 3 -1 roll cvi - dup 0 eq - { pop AnalyzeExpr 3 -1 roll pop 1 add } - { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll - { (x) tx@Derive begin Derive end } repeat - ExpressionVector exch /ExpressionVector [] def - AlgToPs aload length - /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def - l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add - 1 index length /Strlen exch def } ifelse -} def -/EvalSum {% - pop 1 add NextNonBlankChar pop - %% read the variable name - ReadLiteral pop NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if - %% read the initial value - 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - %% read the increment value - 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - %% read the limit value - 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll - 5 -1 roll 4 add array astore def - %% keep ExpressionVector for later and create a new one for internal Sum computation - ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def - 1 add NextNonBlankChar pop AnalyzeExpr - %% add each term - /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def - /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add - array astore def 3 -1 roll pop 1 add -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Convert to radians if trigo function call -%% (name) -> -/TrigoFunc { - dup (cos) eq 1 index (sin) eq or exch (tan) eq or - { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add - array astore def - } if -} def -/EvalCond {% - pop 1 add AnalyzeCond NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if - ExpressionVector 3 1 roll /ExpressionVector [] def - 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def - NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if - 1 add AnalyzeExpr - NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if - ExpressionVector - /ExpressionVector 6 -1 roll aload length dup - 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def - 1 add 3 -1 roll pop -} def -%% CondOp STR index -/EvalCondOp {% - 3 -1 roll - dup (=) eq { /eq } {% - dup (<) eq { /lt } {% - dup (>) eq { /gt } {% - dup (>=) eq { /ge } {% - dup (<=) eq { /ge } {% - dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } - ifelse } ifelse } ifelse } ifelse } ifelse } ifelse - cvx exch pop - /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def -/EvalUnaryOp { - 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% H O O K S -/AnalyzePreHook {} bind def -/PreEvalHook {} bind def -/AnalyzeListOfEPostHook {} bind def -/AnalyzePostHook {} def -/RollOp { 3 1 roll } bind def -end %tx@CoreAnalyzerDict -% -%--------------------------------------------------------------------% -% -/tx@Derive 41 dict def tx@Derive begin -%%increase ^^ for each function added -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% algExpr variable -> PSVector -/Derive {% - 10240 string 3 1 roll 0 3 1 roll - /Variable exch def - tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end -} def -/Strlen 0 def -/InitParser { dup length /Strlen exch def 0 } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% algExpr variable index -> PSVector -/DeriveIndexed {% - 3 1 roll 10240 string 3 1 roll 0 3 1 roll - /Variable exch def - tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u,v)'=-(u',v') -/EvalListOfExpr {% - 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe - 2 copy 7 -1 roll dup length 4 1 roll putinterval add - 6 -2 roll pop pop - 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (-u)'=-(u') -/EvalUnaryOp { - 4 -2 roll 4 index (0) eq - { (0) StrConcat 7 -1 roll pop } - { 7 -1 roll 45 eq - { AddSub AddOpPar true } { false } ifelse - 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (number)'=0 -/EvalNumber { ReadNumber (0) 6 2 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u+v)'=u'+v' -/EvalAddSub {% - 7 index dup (0) eq - { pop true }%% du=0 nothing added - { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } - ifelse - 5 index dup (0) eq - { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 - { exch - { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added - { 5 -2 roll 7 index 43 eq%%something yet added - { AddAdd false } { AddSub AddOpPar true } ifelse } - ifelse 11 1 roll - 3 -1 roll StrConcat 10 -1 roll { AddClPar } if - 2 copy pop 0 6 2 roll GetIntervalNewStr } - ifelse - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u*v)' or (u/v)' -/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u*v)'=u'*v+u*v' -/EvalMul {% - 4 -2 roll 7 index dup (0) eq - { pop false }%%du=0 - { (1) eq%%du=1 - { false } - { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse - 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if - true }%%du!=0 - ifelse - 5 1 roll 5 index (0) eq - { 5 -1 roll not { (0) StrConcat } if }%%dv=0 - { 5 -1 roll { AddAdd } if - 4 index (1) eq - { 8 index StrConcat } - { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } - ifelse - }%%dv!=0 - ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u/v)'=(u'*v-u*v')/v^2 -/EvalDiv {% - 4 -2 roll - 4 index (0) eq%%dv=0 -> u'/v - { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } - { 7 index dup (0) eq - { pop }%%du=0 - { (1) eq%%du=1 - { false } - { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse - 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 - ifelse - AddSub - 4 index (1) eq - { 8 index StrConcat } - { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } - ifelse - %}%%dv!=0 - 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar - AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } - ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% str1 index str2 -> str1 index -/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def -/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) -/EvalPower {% - 4 -2 roll 7 index (0) eq - {%%if du=0 then (u^v)'=v'ln(u)u^v - 4 index (0) eq - { (0) StrConcat }%%if dv=0 then (u^v)'=0 - { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if - 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if - AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse - } - {%%du!=0 - 4 index (0) eq - {%%if dv=0 then (u^v)'=vu'u^(v-1) - 5 index dup IsStrNumber - { dup (0) eq - { StrConcat } - { dup dup (1) eq exch (1.0) eq or - { StrConcat } - { StrConcat - 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 - { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 - (*\() StrConcat 8 index StrConcat (\)) StrConcat - 5 index dup dup (2) eq exch (2.0) eq or - { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } - { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat - 5 index StrConcat (-1\)) StrConcat } ifelse - } - {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) - 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if - AddOpPar 5 index StrConcat (\)*\() StrConcat - 8 index StrConcat (\)^\() StrConcat - 5 index StrConcat (-1\)+\() StrConcat - 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if - 8 index StrConcat (\)^\() StrConcat - 5 index StrConcat (\)*ln\() StrConcat - 8 index StrConcat AddClPar - } ifelse - } ifelse - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% str -> true/false -/IsStrNumber {% - true exch - { dup 48 lt exch dup 57 gt 3 -1 roll or - exch dup 46 ne%%. - exch dup 43 ne%%+ - exch 45 ne%%- - and and and { pop false } if } forall -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% literal switch -> func call, vector, variables -/EvalLiteral {% - ReadLiteral dup 40 eq%%% there is an open par -> function call - { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } - { dup 91 eq%%% there is an open bracket -> vector element - { ERROR_vector_not_yet_implemented } - { pop EvalVariable } - ifelse } - ifelse -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% first last parpos Expr[first:parpos-1] -> -/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% (f(u))'=u'f'(u) -/EvalFunc { - 4 2 roll 4 index (1) ne - { AddOpPar 4 index StrConcat (\)*) StrConcat } if - (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Func derivative -> Eval<func> -/EvalFunc_sin {% - PreCommonFunc - { (cos\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_cos {% - PreCommonFunc - { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_tan {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if - PostCommonFunc } def -/EvalFunc_asin {% - PreCommonFunc - { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_acos {% - PreCommonFunc - { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_atg {% - PreCommonFunc - { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_ln {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_exp {% - PreCommonFunc - { (exp\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_sqrt {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_Fact {% - PreCommonFunc { ERROR_no_variable_expression_in_Fact } if - PostCommonFunc } def -/EvalFunc_sh {% - PreCommonFunc - { (ch\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_ch {% - PreCommonFunc - { (sh\() StrConcat 5 index StrConcat AddClPar } if - PostCommonFunc } def -/EvalFunc_th {% - PreCommonFunc - { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if - PostCommonFunc } def -/EvalFunc_Argsh {% - PreCommonFunc - { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_Argch {% - PreCommonFunc - { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if - PostCommonFunc } def -/EvalFunc_Argth {% - PreCommonFunc - { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if - PostCommonFunc } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -/PreCommonFunc { - 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop - 4 2 roll 4 index (0) eq - { (0) StrConcat false } - { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse -} def -/PostCommonFunc { - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -/EvalFunc_Derive {% - 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs - 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add - 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar - 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval - exch 6 2 roll } def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% literal switch -> func call, vector, variables -/EvalFunc_Sum {% - 1 add NextNonBlankChar pop - %% read the variable name - ReadLiteral pop 3 -1 roll pop NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if - %% read the initial value - 1 add NextNonBlankChar pop ReadNumber pop - 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if - %% read the increment value - 1 add NextNonBlankChar pop ReadNumber pop - 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if - %% read the limit value - 1 add NextNonBlankChar pop ReadNumber pop - 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if - 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop - 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat - 4 index StrConcat AddClPar - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% literal switch -> func call, vector, variables -/EvalFunc_IfTE {% - 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond - NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if - 1 add NextNonBlankChar pop dup 5 1 roll - AnalyzeExpr NextNonBlankChar - 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if - 1 add NextNonBlankChar pop - AnalyzeExpr 1 add NextNonBlankChar pop - 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat - 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar - 2 copy pop 0 6 2 roll GetIntervalNewStr - mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% advance in str until a comma is found (no error detection!) -%% str index -> str index' -/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Convert to radians if trigo function call -%% (name) -> -/TrigoFunc { - dup (cos) eq 1 index (sin) eq or exch (tan) eq or - { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add - array astore def - } if -} def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% No derivative for condition.... -/EvalCondOp { 3 -1 roll pop } bind def -/PutIntervalOneAdd {putinterval 1 add} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add open parenthesis in string at the given index -%% str index -> str index+1 -/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add close parenthesis in string at the given index -%% str index -> str index+1 -/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add 0 in string at the given index -%% str index -> str index+1 -/AddZero {2 copy (0) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add open parenthesis in string at the given index -%% str index -> str index+1 -/AddMul {2 copy (*) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add open parenthesis in string at the given index -%% str index -> str index+1 -/AddDiv {2 copy (/) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add a plus sign in string at the given index -%% str index -> str index+1 -/AddAdd {2 copy (+) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add a minus sign in string at the given index -%% str index -> str index+1 -/AddSub {2 copy (-) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% Add a pipe sign in string at the given index -%% str index -> str index+1 -/AddPipe {2 copy (|) PutIntervalOneAdd} bind def -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% H O O K S -/AnalyzePreHook { dup 5 1 roll } bind def -/PreEvalHook {} def -/AnalyzePostHook { 7 -1 roll pop } bind def -/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def -/RollOp { 5 1 roll } bind def -end%%%tx@CoreAnalyzerDict -/tx@AddMathFunc 12 dict def tx@AddMathFunc begin -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% NEW FUNC -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) -%% x -> theta -/asin {% - dup abs 1 gt { EQDFasinrangeerror } if - dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad -} def -%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) -%% x -> theta -/acos {% - dup abs 1 gt { EQDFacosrangeerror } if - dup dup mul 1 exch sub sqrt exch atan DegtoRad -} def -%% function arctangent in radians -%% x -> theta -/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def -%% HYPERBOLIC FUNCTIONS -/sh { dup Ex exch neg Ex sub 2 div } def -/ch { dup Ex exch neg Ex add 2 div } def -/th { dup sh exch ch div } def -/Argsh { dup dup mul 1 add sqrt add ln } def -/Argch { dup dup mul 1 sub sqrt add ln } def -/Argth { dup 1 add exch 1 exch sub div ln 2 div } def -%% modified exponential funtion for 0 -%% x n -> x^n -/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def -%% modified exponential funtion for 0 -%% x -> e^x -/Ex { Euler exch exp } bind def -%% -%% factorial function -%% n -> n! -/Fact { 1 exch 2 exch 1 exch { mul } for } bind def -/fact { Fact } bind def -end - -% END pstricks.pro - -%%EndProcSet -%%BeginProcSet: pst-dots.pro 0 0 -% $Id: pst-dots.pro 26 2008-06-14 11:50:02Z herbert $ -% -%% PostScript prologue for pstricks.tex. -%% Version 2.02, 2008/04/18 -%% -%% For distribution, see pstricks.tex. -%% -%% Timothy Van Zandt <tvz@Princeton.EDU> -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -%% -%% Modified by Etienne Riga - Dec. 16, 1999 -%% Modified by Etienne Riga - 2005/01/01 (er) -%% to add /Diamond, /SolidDiamond and /BoldDiamond -%% Modified by Herbert Voss (hv) - 2008/04/17 -% -10 dict dup begin % hold local - /FontType 3 def - /FontMatrix [.001 0 0 .001 0 0] def - /FontBBox [-571.5 -742.5 571.5 742.5] def -% /FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph - /Encoding 256 array def - 0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef - Encoding % replace with given dot names - dup (b) 0 get /Bullet put % get the numerical position of b in ASCII -% % and save /Bullet at this place in Encoding - dup (c) 0 get /Circle put - dup (C) 0 get /BoldCircle put % 67 - dup (u) 0 get /SolidTriangle put - dup (t) 0 get /Triangle put - dup (T) 0 get /BoldTriangle put - dup (r) 0 get /SolidSquare put - dup (s) 0 get /Square put - dup (S) 0 get /BoldSquare put - dup (q) 0 get /SolidPentagon put - dup (p) 0 get /Pentagon put - dup (P) 0 get /BoldPentagon put -%%% - dup (k) 0 get /Asterisk put - dup (K) 0 get /BoldAsterisk put - dup (J) 0 get /SolidAsterisk put - dup (h) 0 get /Hexagon put - dup (H) 0 get /BoldHexagon put - dup (G) 0 get /SolidHexagon put - dup (f) 0 get /Octogon put % 2008-04-18 hv - dup (F) 0 get /BoldOctogon put % 2008-04-18 hv - dup (g) 0 get /SolidOctogon put % 2008-04-18 hv - dup (a) 0 get /Add put - dup (A) 0 get /BoldAdd put % 65 - dup (x) 0 get /Mul put - dup (X) 0 get /BoldMul put - dup (m) 0 get /Oplus put - dup (M) 0 get /BOplus put - dup (e) 0 get /SolidOplus put - dup (n) 0 get /Otimes put - dup (N) 0 get /BOtimes put - dup (E) 0 get /SolidOtimes put - dup (i) 0 get /Bar put - dup (I) 0 get /BoldBar put - dup (l) 0 get /SolidDiamond put - dup (d) 0 get /Diamond put - (D) 0 get /BoldDiamond put -%%% -/CharProcs 47 dict def -CharProcs begin - /CirclePath {0 0 500 0 360 arc closepath} def - /Bullet {CirclePath fill} def - /Circle {CirclePath .9 .9 scale CirclePath eofill} def - /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def - /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def - /SolidTriangle {TrianglePath fill} def - /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def - /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def - /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def - /SolidSquare {SquarePath fill} def - /Square {SquarePath .89 .89 scale SquarePath eofill} def - /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def - /PentagonPath { - -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto - 0 574.7 lineto -546.6 177.6 lineto closepath - } def - /SolidPentagon {PentagonPath fill} def - /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def - /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def -%-------------- hv begin 2004/07/25 from: er 2003/03/24 - /HexagonPath { - 0 550 moveto -476 275 lineto -476 -275 lineto - 0 -550 lineto 476 -275 lineto 476 275 lineto closepath - } def - /SolidHexagon {HexagonPath fill} def - /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def - /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def -% 2008-04-18 hv - /OctogonPath { - 550 dup 22.5 tan mul dup neg dup add /xMove exch def - exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def - /SolidOctogon { OctogonPath fill } def - /Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def - /BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def -% - /AsteriskPath { - 20 0 moveto 10 250 180 500 0 500 curveto - -180 500 -10 250 -20 0 curveto closepath - } def - /Asterisk { - AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath - 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill - } def -% - /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def - /BoldAsteriskPath { - 50 30 cos 100 mul moveto Basterp - 60 rotate Basterp 60 rotate Basterp - 60 rotate Basterp 60 rotate Basterp - 60 rotate Basterp closepath - } def - /BoldAsterisk {BoldAsteriskPath fill} def - /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def - /CrossPath { - 40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto - -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto - 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath - } def - /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto - -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto - 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath - } def - /Add {CrossPath fill} def - /Mul {45 rotate CrossPath fill} def - /BoldAdd {BoldCrossPath fill} def - /BoldMul {45 rotate BoldCrossPath fill} def - /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def - /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def - /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def - /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def - /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def - /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def - /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def - /Bar {BarPath fill} def - /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def - /BoldBar {BoldBarPath fill} def - /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath} def - /SolidDiamond {DiamondPath fill} def - /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def - /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def -%%% - /.notdef { } def -end -% -/BuildGlyph { - exch - begin -% Metrics 1 index get exec 0 - 0 0 -% BBoxes 3 index get exec - -1000 -1000 1000 1000 -% -571.5 -742.5 571.5 742.5 - setcachedevice - CharProcs begin load exec end - end -} def -% -/BuildChar { - 1 index /Encoding get exch get - 1 index /BuildGlyph get exec -} bind def - -end -/PSTricksDotFont exch definefont pop - -%% end - -%%EndProcSet -%%BeginProcSet: pst-node.pro 0 0 -% $Id: pst-node.pro 26 2008-06-14 11:50:02Z herbert $ -%% -%% PostScript prologue for pst-node.tex. -%% Version 1.00, 2008/01/01. -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -% -/tx@NodeDict 400 dict def tx@NodeDict begin -tx@Dict begin % from main pstricks dict - /T /translate load def -end -/NewNode { % on stack: { x y } boolean N@name type InitXnode - gsave - /next ED % { x y } boolean N@name type - dict dup % { x y } boolean N@name dict dict - 3 1 roll def % { x y } boolean dict N@name dict def - exch { dup 3 1 roll def } if % { x y } dict boolean - begin % { x y } dict begin - tx@Dict begin - STV CP T exec % set scaling - end - /NodeMtrx CM def % save CM - next % InitXNode - end - grestore -} def -% -/InitPnode { - /Y ED /X ED - /NodePos { NodeSep Cos mul NodeSep Sin mul } def -} def -% -/InitCnode { - /r ED /Y ED /X ED - /NodePos { NodeSep r add dup Cos mul exch Sin mul } def -} def -% -/GetRnodePos { - Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse - Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse - dx Sin mul abs dy - Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse -} def -% -/InitRnode { - /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED - /NodePos { GetRnodePos } def -} def -% -/DiaNodePos { - w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup - Cos mul exch Sin mul -} def -% -/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h -mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul -} ifelse } def -/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d -ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d -sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan -sin def /NodePos { TriNodePos } def } def -/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos -hh mul Atan dup cos ww mul exch sin hh mul } def -/GetCenter { begin X Y NodeMtrx transform CM itransform end } def -% -/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist - Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } - { 0 Dist Sin mul } ifelse } ifelse Do -} def -/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform - exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx - dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop - XYPos } ifelse -} def -/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 -roll sin mul sub exch } ifelse } def -/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA -AddOffset yA add /yA1 ED xA add /xA1 ED } def -/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB -AddOffset yB add /yB1 ED xB add /xB1 ED } def -/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA -AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED -ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED -} ifelse } def -/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB -AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED -ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED -} ifelse } def -/InitNC { - /b ED /a ED % second and first node - /NodeSepTypeB ED /NodeSepTypeA ED - /NodeSepB ED /NodeSepA ED - /OffsetB ED /OffsetA ED - tx@NodeDict a known tx@NodeDict b known and dup { - /NodeA a load def - /NodeB b load def - NodeA GetCenter /yA ED /xA ED - NodeB GetCenter /yB ED /xB ED } if -} def -% -/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub -mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def -/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt -{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop -} repeat LPutLine cleartomark } def -/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED -/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 -mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx -sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul -add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add -y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul -mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def -/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def -} def -/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def -/NAngle yyB yyA sub xxB xxA sub Atan def } def -/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def -/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def -} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit -} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd -} def -/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def -} def -/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def -/NAngle yyB yyA sub xxB xxA sub Atan def } def -/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def -/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def -} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { -exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark -VPosEnd } def -/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 -roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx -def grestore exec /LPutVar /SaveLPutVar load def } def -/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def -GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { -LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { -LPutVar VPutLine } def LPutVar } def -/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop -end } def -/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub -Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan -/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 -yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { -LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } -ifelse } def -/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 -roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA -GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict -begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] -cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines -} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def -% -/NCAngles { - GetEdgeA GetEdgeB GetArmA GetArmB - /mtrx AngleA matrix rotate def - xA2 yA2 mtrx transform pop - xB2 yB2 mtrx transform exch pop - mtrx itransform - /y0 ED /x0 ED - mark ArmB 0 ne { xB1 yB1 } if - xB2 yB2 x0 y0 xA2 yA2 - ArmA 0 ne { xA1 yA1 } if - tx@Dict begin false Line end - /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def - /LPutPos { LPutLines } def - /HPutPos { HPutLines } def - /VPutPos { VPutLines } def } def -% -/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 -yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform -/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 -tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] -cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { -VPutLines } def } def -/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def -xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx -transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } -{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB -0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict -begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx -def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { -VPutLines } def } def -/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if -xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end -/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { -LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } -def -/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED -GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin -false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { -LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } -def -/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate -def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 -mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 -mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 -xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false -Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] -cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { -VPutLines } def } def -% DG/SR modification begin - May 9, 1997 - Patch 1 -%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r -%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add -%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 -%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED -/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r -r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add -exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 -mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED -% DG/SR modification end -} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add -AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r -Div def /y ED /x ED } def -/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB -180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos -mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def -/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy -add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos -{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar -tx@Dict begin false Polygon end } def -/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan -def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 -mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def -/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div -def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def -GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul -sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 -eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } -{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def -0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 -roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 -0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 -roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } -ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos -{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { -r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } -{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add -add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub -mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t -sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse -y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { -LPutPos } def } def -/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB -sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 -ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB -w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos -{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } -{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } -def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin -/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def - -/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg -exch X sub neg exch moveto setmatrix CP grestore } def - -/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 -def } ifelse LPutCoor } def -/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } -if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } -ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } -def -/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if -r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } -ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } -def -end -% END pst-node.pro - -%%EndProcSet -%%BeginProcSet: pstricks-add.pro 0 0 -%% $Id: pstricks-add.pro 49 2008-10-13 10:59:27Z herbert $ -% PostScript prologue for pstricks-add.tex. -% Version 0.21, 2008/10/15 -% For distribution, see pstricks.tex. -% -% HISTORY -> see file Changes -% -/tx@addDict 410 dict def tx@addDict begin -%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -/GTriangle { - gsave - /mtrx CM def - /colorA ED /colorB ED /colorC ED % save the colors - /yA ED /xA ED % save the origin - xA yA translate - rotate % \psk@gangle - /yB ED /xB ED /yC ED /xC ED % save other coordinates - /ds [ % save data in a array - 0 0 0 colorA aload pop % fd x y xr xg xb - 0 xB xA sub yB yA sub colorB aload pop - 0 xC xA sub yC yA sub colorC aload pop -% 1 xC xB add yB colorA aload pop % for use with 4 points ABCD - ] def - newpath - << - /ShadingType 4 % single Gouraud - /ColorSpace [ /DeviceRGB ] - /DataSource ds - >> - shfill - closepath - mtrx - setmatrix grestore} def -% -/RGBtoCMYK { % on stack r g b -> C M Y K - 3 dict begin - /Blue ED /Green ED /Red ED - 1 Red sub % Cyan - 1 Green sub % Magenta - 1 Blue sub % Yellow - 0 % Black - end -} def -% -/CMYKtoGRAY { % on stack c m y k -> gray - exch 0.11 mul add - exch 0.59 mul add - exch 0.3 mul add - dup 1 gt { pop 1 } if - neg 1 add -} def -% -/RGBtoGRAY { % on stack r g b -> gray - 0.11 mul - exch 0.59 mul add - exch 0.3 mul add -} def -% -/HSBtoGRAY { - 6 dict begin - /b exch def - /s exch def 6 mul dup cvi dup - /i exch def sub - /f exch def - /F [[0 1 f sub 1][f 0 1][1 0 1 f sub][1 f 0][1 f sub 1 0][0 1 f][0 1 1]] def - F i get { s mul neg 1 add b mul} forall - 0.11 mul - exch 0.59 mul add - exch 0.3 mul add - end -} def -% -%% convertisseur longueur d'onde ->R,G,B Manuel Luque -%% lambda max=780 nanometres -%% lambda min=380 nanometres -%% adaptation de : -%% http://www.physics.sfasu.edu/astro/color.html -%% www.efg2.com/lab -% -/Gamma 0.8 def -/calculateRGB { - lambda 379 le {/Red 0 def /Green 0 def /Blue 0 def} if - lambda 781 ge {/Red 0 def /Green 0 def /Blue 0 def} if - lambda 380 ge {lambda 439 le { - /R {lambda 440 sub neg 440 380 sub div} def - /Red R factor mul Gamma exp def - /G 0 def - /Green G factor mul Gamma exp def - /B 1 def - /Blue B factor mul Gamma exp def} if - } if - lambda 440 ge { lambda 489 le { - /G {lambda 440 sub 490 440 sub div} def - /Green G factor mul Gamma exp def - /R 0 def /Red 0 def - /B 1 def - /Blue B factor mul Gamma exp def } if - } if - lambda 490 ge {lambda 509 le { - /B {lambda 510 sub neg 510 490 sub div} def - /Blue B factor mul Gamma exp def - /R 0 def /Red 0 def - /G 1 def - /Green G factor mul Gamma exp def } if - } if - lambda 510 ge {lambda 579 le { - /R {lambda 510 sub 580 510 sub div } def - /Red R factor mul Gamma exp def - /Blue 0 def - /G 1 def - /Green G factor mul Gamma exp def } if - } if - lambda 580 ge {lambda 644 le { - /G {lambda 645 sub neg 645 580 sub div } def - /Green G factor mul Gamma exp def - /Blue 0 def - /R 1 def - /Red R factor mul Gamma exp def } if - } if - lambda 645 ge { lambda 780 le { - /Red 1 factor mul Gamma exp def - /Blue 0 def - /Green 0 def } if - } if -} def -% -/factor { - lambda 380 ge {lambda 419 le { 0.3 0.7 lambda 380 sub mul 420 380 sub div add} if } if - lambda 420 ge {lambda 700 le { 1 } if } if - lambda 701 ge {lambda 780 le { 0.3 0.7 780 lambda sub mul 780 700 sub div add} if } if -} def -% -/wavelengthToRGB { % the wavelength in nm must be on top of the stack - cvi /lambda exch def % no floating point here - calculateRGB -} def % now the colors are saved in Red Green Blue -% -/wavelengthToCMYK { % the wavelength in nm must be on top of the stack - cvi /lambda exch def % no floating point here - gsave - calculateRGB Red Green Blue RGBtoCMYK - /Black ED /Yellow ED /Magenta ED /Cyan ED - grestore -} def % now the colors are saved in Cyan Magenta Yellow Black -% -/axfill { - 8 dict begin - /xw exch def /nl exch def - /C1 exch def /y1 exch def/x1 exch def - /C0 exch def /y0 exch def/x0 exch def - << /ShadingType 2 - /ColorSpace /DeviceRGB - /Coords [ x0 y0 x1 y1 ] - /EmulatorHints [ xw 2 div dup ] - /Function << - /FunctionType 2 - /Domain [0 1] - /C0 C0 - /C1 C1 - /N 1 - >> - >> shfill - end -} bind def -% -%%%%% ### bubblesort ### -%% syntax : array bubblesort --> array2 trie par ordre croissant -%% code de Bill Casselman -%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/ -/bubblesort { -4 dict begin - /a exch def - /n a length 1 sub def - 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