%% $Id: pst-3dplot.pro 21 2020-08-04 12:53:07Z herbert $ %% %% This is file `pst-3dplot.pro', %% %% IMPORTANT NOTICE: %% %% Package `pst-3dplot.tex' %% %% Herbert Voss %% %% 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. %% %% DESCRIPTION: %% `pst-3dplot' is a PSTricks package to draw 3d curves and graphical objects %% %% %% version 0.33 / 2017-04-05 Herbert Voss %% with contributions of Darrell Lamm x y z 3 1 roll % h r phi /Phi ED /Radius ED % h->z on stack Radius Phi cos mul exch % x z Radius Phi sin mul exch % x y z } def % /SphericalTo2D { x y z ConvertToCartesian ConvertTo2D } def % /CylinderTo2D { % r phi h x y z ConvCylToCartesian ConvertTo2D } def % /convertStackTo2D { counttomark /n ED /n3 n 3 div cvi def n3 { n -3 roll SphericalCoor { ConvertToCartesian } { saveCoor } ifelse ConvertTo2D x2D xUnit y2D yUnit /n n 1 sub def } repeat } def % % the angle in the parameter equation for an ellipse is not proportional to the real angle! % phi=atan(b*tan(angle)/a)+floor(angle/180+0.5)*180 % /getPhi { % on stack: vecA vecB angle 3 dict begin /angle exch def /vecB exch def /vecA exch def angle cvi 90 mod 0 eq { angle } { vecA angle tan mul vecB atan angle 180 div .5 add floor 180 mul add } ifelse end } def % /RotSet (set ) def % /eulerRotation false def % Matrix multiplication procedure /matmul { /M@tMulDict 20 dict def M@tMulDict begin /m2 ED /m1 ED m1 dup length 2 sub 2 getinterval aload pop /col1max ED /row1max ED m2 dup length 2 sub 2 getinterval aload pop /col2max ED /row2max ED /m3 row1max col2max mul 2 add array def m3 dup length 2 sub row1max col2max 2 array astore putinterval 0 1 row1max 1 sub { /row ED 0 1 col2max 1 sub { /col ED /sum 0 def 0 1 col1max 1 sub{ /rowcol ED sum m1 row col1max mul rowcol add get m2 rowcol col2max mul col add get mul add /sum ED } for m3 row col2max mul col add sum put } for } for m3 end % end of M@tMulDict } def % /SetMQuaternion { /MnewTOold 11 array def /Qu@ternionDict 30 dict def Qu@ternionDict begin /normRotVec xRotVec yRotVec zRotVec 3 array astore VecNorm def normRotVec 0 gt {/xRotVecNorm xRotVec normRotVec div def /yRotVecNorm yRotVec normRotVec div def /zRotVecNorm zRotVec normRotVec div def RotAngle} {/xRotVecNorm 1 def /yRotVecNorm 0 def /zRotVecNorm 0 def 0} ifelse 2 div dup /q0 exch cos def sin dup dup /q1 exch xRotVecNorm mul def /q2 exch yRotVecNorm mul def /q3 exch zRotVecNorm mul def /q0q0 q0 q0 mul def /q0q1 q0 q1 mul def /q0q2 q0 q2 mul def /q0q3 q0 q3 mul def /q1q1 q1 q1 mul def /q1q2 q1 q2 mul def /q1q3 q1 q3 mul def /q2q2 q2 q2 mul def /q2q3 q2 q3 mul def /q3q3 q3 q3 mul def MnewTOold 0 q0q0 q1q1 add q2q2 sub q3q3 sub put MnewTOold 1 q1q2 q0q3 sub 2 mul put MnewTOold 2 q1q3 q0q2 add 2 mul put MnewTOold 3 q1q2 q0q3 add 2 mul put MnewTOold 4 q0q0 q1q1 sub q2q2 add q3q3 sub put MnewTOold 5 q2q3 q0q1 sub 2 mul put MnewTOold 6 q1q3 q0q2 sub 2 mul put MnewTOold 7 q2q3 q0q1 add 2 mul put MnewTOold 8 q0q0 q1q1 sub q2q2 sub q3q3 add put MnewTOold 9 3 put MnewTOold 10 3 put end % end of Qu@ternionDict } def % /SetMxyz { 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 3 3 11 array astore /MnewTOold ED RotSequence cvx exec % Now create a new MnewTOold using xyz, etc. } def % /ConcatMQuaternion { MnewTOold % Push onto stack SetMQuaternion % Uses [xyz]RotVec and RotAngle to make MnewToOld MnewTOold matmul /MnewTOold ED } def % /ConcatMxyz { MnewTOold % Push onto stack SetMxyz % Uses RotX, etc. to set MnewTOold MnewTOold matmul /MnewTOold ED } def % /RotatePoint{ MnewTOold x y z 3 1 5 array astore matmul 0 3 getinterval aload pop /z ED /y ED /x ED } def % /makeMoldTOnew { /MoldTOnew 11 array def MoldTOnew 0 MnewTOold 0 get put MoldTOnew 1 MnewTOold 3 get put MoldTOnew 2 MnewTOold 6 get put MoldTOnew 3 MnewTOold 1 get put MoldTOnew 4 MnewTOold 4 get put MoldTOnew 5 MnewTOold 7 get put MoldTOnew 6 MnewTOold 2 get put MoldTOnew 7 MnewTOold 5 get put MoldTOnew 8 MnewTOold 8 get put MoldTOnew 9 3 put MoldTOnew 10 3 put } def % /RotXaxis { eulerRotation {1 0 0} {makeMoldTOnew MoldTOnew 1 0 0 3 1 5 array astore matmul 0 3 getinterval aload pop} ifelse /zRotVec ED /yRotVec ED /xRotVec ED /RotAngle RotX def ConcatMQuaternion } def /RotYaxis { eulerRotation {0 1 0} {makeMoldTOnew MoldTOnew 0 1 0 3 1 5 array astore matmul 0 3 getinterval aload pop} ifelse /zRotVec ED /yRotVec ED /xRotVec ED /RotAngle RotY def ConcatMQuaternion } def /RotZaxis { eulerRotation {0 0 1} {makeMoldTOnew MoldTOnew 0 0 1 3 1 5 array astore matmul 0 3 getinterval aload pop} ifelse /zRotVec ED /yRotVec ED /xRotVec ED /RotAngle RotZ def ConcatMQuaternion } def /xyz { RotXaxis RotYaxis RotZaxis } def /yxz { RotYaxis RotXaxis RotZaxis } def /yzx { RotYaxis RotZaxis RotXaxis } def /xzy { RotXaxis RotZaxis RotYaxis } def /zxy { RotZaxis RotXaxis RotYaxis } def /zyx { RotZaxis RotYaxis RotXaxis } def /quaternion { } def % Null % /VecNorm { 0 exch { dup mul add } forall sqrt } def % /UnitVec { % on stack is [a]; returns a vector with [a][a]/|a|=1 dup VecNorm /norm ED norm 0 lt {/norm 0 def} if { norm div } forall 3 array astore } def % /AxB { % on the stack are the two vectors [a][b] aload pop /b3 ED /b2 ED /b1 ED aload pop /a3 ED /a2 ED /a1 ED a2 b3 mul a3 b2 mul sub a3 b1 mul a1 b3 mul sub a1 b2 mul a2 b1 mul sub 3 array astore } def % /AaddB { % on the stack are the two vectors [a][b] aload pop /b3 ED /b2 ED /b1 ED aload pop /a3 ED /a2 ED /a1 ED a1 b1 add a2 b2 add a3 b3 add 3 array astore } def % /AmulC { % on stack is [a] and c; returns [a] mul c /factor ED { factor mul } forall 3 array astore } def % % /setColorLight { % expects 7 values on stack C M Y K xL yL zL % les rayons de lumi�re xLight dup mul yLight dup mul zLight dup mul add add sqrt /NormeLight ED % the color values /K ED /Yellow ED /Magenta ED /Cyan ED } def % /facetteSphere { newpath /Xpoint Rsphere theta cos mul phi cos mul CX add def /Ypoint Rsphere theta sin mul phi cos mul CY add def /Zpoint Rsphere phi sin mul CZ add def Xpoint Ypoint Zpoint tx@3Ddict begin ProjThreeD end moveto theta 1 theta increment add {% /theta1 ED /Xpoint Rsphere theta1 cos mul phi cos mul CX add def /Ypoint Rsphere theta1 sin mul phi cos mul CY add def /Zpoint Rsphere phi sin mul CZ add def Xpoint Ypoint Zpoint tx@3Ddict begin ProjThreeD end lineto } for phi 1 phi increment add { /phi1 ED /Xpoint Rsphere theta increment add cos mul phi1 cos mul CX add def /Ypoint Rsphere theta increment add sin mul phi1 cos mul CY add def /Zpoint Rsphere phi1 sin mul CZ add def Xpoint Ypoint Zpoint tx@3Ddict begin ProjThreeD end lineto } for theta increment add -1 theta {% /theta1 ED /Xpoint Rsphere theta1 cos mul phi increment add cos mul CX add def /Ypoint Rsphere theta1 sin mul phi increment add cos mul CY add def /Zpoint Rsphere phi increment add sin mul CZ add def Xpoint Ypoint Zpoint tx@3Ddict begin ProjThreeD end lineto } for phi increment add -1 phi { /phi1 ED /Xpoint Rsphere theta cos mul phi1 cos mul CX add def /Ypoint Rsphere theta sin mul phi1 cos mul CY add def /Zpoint Rsphere phi1 sin mul CZ add def Xpoint Ypoint Zpoint tx@3Ddict begin ProjThreeD end lineto } for closepath } def % /MaillageSphere { % on stack must be x y z Radius increment C M Y K setColorLight /increment ED /Rsphere ED /CZ ED /CY ED /CX ED /StartTheta 0 def /condition { PSfacetteSphere 0 ge } def -90 increment 90 increment sub {% /phi ED StartTheta increment 360 StartTheta add increment sub {% /theta ED % Centre de la facette /Xpoint Rsphere theta increment 2 div add cos mul phi increment 2 div add cos mul CX add def /Ypoint Rsphere theta increment 2 div add sin mul phi increment 2 div add cos mul CY add def /Zpoint Rsphere phi increment 2 div add sin mul CZ add def % normale a la facette /nXfacette Xpoint CX sub def /nYfacette Ypoint CY sub def /nZfacette Zpoint CZ sub def % test de visibilite /PSfacetteSphere vX nXfacette mul vY nYfacette mul add vZ nZfacette mul add def condition { gsave facetteSphere /cosV { 1 xLight nXfacette mul yLight nYfacette mul zLight nZfacette mul add add NormeLight nXfacette dup mul nYfacette dup mul nZfacette dup mul add add sqrt mul div sub } bind def Cyan cosV mul Magenta cosV mul Yellow cosV mul K cosV mul setcmykcolor fill grestore % 0 setgray showgrid { facetteSphere stroke } if } if } for % /StartTheta StartTheta increment 2 div add def } for } def % %---------------------- Cylinder --------------------------- % /PlanCoupeCylinder { % /TableauxPoints [ 0 1 359 { /phi ED [ Radius phi Height ConvCyl2d ] % on décrit le cercle } for ] def newpath TableauxPoints 0 get aload pop moveto 1 1 359 { TableauxPoints exch get aload pop lineto } for closepath } def % /facetteCylinder { % newpath Radius phi currentHeight ConvCyl2d moveto phi 1 phi dAngle add { % loop variable on stack Radius exch currentHeight ConvCyl2d lineto } for phi dAngle add -1 phi { % fill dHeight Radius exch currentHeight dHeight add ConvCyl2d lineto } for closepath } def % facette % /MaillageCylinder { % on stack true or false for saving values { setColorLight % expects 4 values on stack C M Y K /dHeight ED /dAngle ED /Height ED /Radius ED /CZ ED /CY ED /CX ED } if % 0 dHeight Height dHeight sub { /currentHeight ED 0 dAngle 360 dAngle sub { /phi ED % Normal vector of the center /nXfacetteCylinder Radius phi dAngle 2 div add cos mul CX add def /nYfacetteCylinder Radius phi dAngle 2 div add sin mul CY add def /nZfacetteCylinder currentHeight dHeight 2 div add CZ add def /NormeN nXfacetteCylinder dup mul nYfacetteCylinder dup mul nZfacetteCylinder dup mul add add sqrt def NormeN 0 eq { /NormeN 1e-10 def } if % test de visibilité /PSfacetteCylinder vX nXfacetteCylinder mul vY nYfacetteCylinder mul add vZ nZfacetteCylinder mul add def condition { facetteCylinder /cosV 1 xLight nXfacetteCylinder mul yLight nYfacetteCylinder mul zLight nZfacetteCylinder mul add add NormeLight NormeN mul div sub def Cyan Magenta Yellow K cosV mul 4 1 roll cosV mul 4 1 roll cosV dup mul mul 4 1 roll cosV dup mul mul 4 1 roll setcmykcolor fill showgrid { 0 setgray facetteCylinder % drawing the segments stroke } if } if } for } for } def % %------------------------ Cylinder type II ----------------------- % /MoveTo { Conv3D2D moveto } def /LineTo { Conv3D2D lineto } def /IIIDEllipse { % x y z rA rB startAngle endAngle Wedge /dAngle 1 def /isWedge ED /endAngle ED /startAngle ED /radiusB ED /radiusA ED startAngle cos radiusA mul startAngle sin radiusB mul 0 isWedge { 0 0 moveto LineTo }{ MoveTo } ifelse /Angle startAngle def startAngle dAngle endAngle { /Angle ED Angle cos radiusA mul Angle sin radiusB mul 0 LineTo } for isWedge { 0 0 lineto } if } def /IIIDCircle { % x y z r startAngle endAngle Wedge 7 3 roll % startAngle endAngle Wedge x y z r dup % startAngle endAngle Wedge x y z r r 8 -3 roll IIIDEllipse } def /IIIDWedge { % x y z r startAngle endAngle true IIIDCircle } def /IIIDCylinder {% x y z r h start end wedge /isWedge ED /increment ED /endAngle ED /startAngle ED /height ED /radius ED startAngle increment endAngle { /Angle ED radius Angle 0 ConvCylToCartesian MoveTo radius Angle height ConvCylToCartesian LineTo } for stroke } def % %---------------------- Box --------------------------- % /PlanCoupeBox { % x y z /TableauxPoints [ [ CX CY CZ Height add ConvBox2d ] % top or bottom [ CX CY Depth add CZ Height add ConvBox2d ] [ CX Width add CY Depth add CZ Height add ConvBox2d ] [ CX Width add CY CZ Height add ConvBox2d ] [ CX CY CZ Height add ConvBox2d ] % bottom ] def newpath TableauxPoints 0 get aload pop moveto 0 1 3 { TableauxPoints exch get aload pop lineto } for closepath } def % /facetteBox { % newpath dup 1 eq { % back CX CY CZ ConvBox2d moveto CX CY CZ Height add ConvBox2d lineto CX Width add CY CZ Height add ConvBox2d lineto CX Width add CY CZ ConvBox2d lineto CX CY CZ ConvBox2d lineto } if dup 2 eq { % right CX CY CZ ConvBox2d moveto CX CY CZ Height add ConvBox2d lineto CX CY Depth add CZ Height add ConvBox2d lineto CX CY Depth add CZ ConvBox2d lineto CX CY CZ ConvBox2d lineto } if dup 3 eq { % left CX Width add CY CZ ConvBox2d moveto CX Width add CY Depth add CZ ConvBox2d lineto CX Width add CY Depth add CZ Height add ConvBox2d lineto CX Width add CY CZ Height add ConvBox2d lineto CX Width add CY CZ ConvBox2d lineto } if 4 eq { % front CX CY Depth add CZ ConvBox2d moveto CX CY Depth add CZ Height add ConvBox2d lineto CX Width add CY Depth add CZ Height add ConvBox2d lineto CX Width add CY Depth add CZ ConvBox2d lineto CX CY Depth add CZ ConvBox2d lineto } if closepath } def % facette % /TestPlane { % on stack x y z of the plane center and # of plane /nZfacetteBox ED /nYfacetteBox ED /nXfacetteBox ED /Plane ED /NormeN nXfacetteBox dup mul nYfacetteBox dup mul nZfacetteBox dup mul add add sqrt def NormeN 0 eq { /NormeN 1e-10 def } if % test de visibilite /PSfacetteBox vX nXfacetteBox mul vY nYfacetteBox mul add vZ nZfacetteBox mul add def condition { Plane facetteBox /cosV 1 xLight nXfacetteBox mul yLight nYfacetteBox mul zLight nZfacetteBox mul add add NormeLight NormeN mul div sub def Cyan Magenta Yellow K cosV mul 4 1 roll cosV mul 4 1 roll cosV dup mul mul 4 1 roll cosV dup mul mul 4 1 roll setcmykcolor fill 0 setgray Plane facetteBox % drawing the segments stroke } if } def % /MaillageBox { % on stack true or false for saving values { setColorLight % expects 4 values on stack C M Y K /Depth ED /Height ED /Width ED /CZ ED /CY ED /CX ED } if % % Normal vector of the box center /PlaneSet [ [ Width 2 div CX add CY Height 2 div CZ add ] % normal back [ CX Depth 2 div CY add Height 2 div CZ add ] % normal right [ Width CX add Depth 2 div CY add Height 2 div CZ add ] % normal left [ Width 2 div CX add Depth CY add Height 2 div CZ add ] % normal front ] def PlaneSequence length 0 eq { % user defined? Alpha abs cvi 360 mod /iAlpha ED iAlpha 90 lt { [ 1 2 3 4 ] }{ iAlpha 180 lt { [ 2 4 1 3 ] }{ iAlpha 270 lt { [ 3 4 1 2 ] }{ [ 3 1 4 2] } ifelse } ifelse } ifelse }{ PlaneSequence } ifelse { dup 1 sub PlaneSet exch get aload pop TestPlane } forall } def % %--------------------------- Paraboloid ----------------------------- /PlanCoupeParaboloid { /Z height store /V {Z sqrt} bind def /TableauxPoints [ 0 1 359 { /U ED [ U U Z V calculate2DPoint ] % on decrit le cercle } for ] def newpath TableauxPoints 0 get aload pop moveto 0 1 359 { /compteur ED TableauxPoints compteur get aload pop lineto } for closepath } def % /facetteParaboloid{ newpath U U Z V calculate2DPoint moveto U 1 U increment add {% /U1 ED U1 U1 Z V calculate2DPoint lineto } for Z pas10 Z pas add pas10 add{ /Z1 ED /V {Z1 sqrt} bind def U1 U1 Z1 V calculate2DPoint lineto } for U increment add -1 U {% /U2 ED U2 U2 Z pas add V calculate2DPoint lineto } for Z pas add pas10 sub pas10 neg Z pas10 sub { /Z2 ED /V Z2 abs sqrt def U U Z2 V calculate2DPoint lineto } for closepath } def % facette % /MaillageParaboloid { % on stack true or false for saving values { setColorLight % expects 7 values on stack C M Y K xL yL zL % /CZ ED /CY ED /CX ED } if 0 pas height pas sub {% /Z ED /V Z sqrt def 0 increment 360 increment sub {% /U ED % Centre de la facette /Ucentre U increment 2 div add def /Vcentre Z pas 2 div add sqrt def % normale à la facette /nXfacetteParaboloid 2 Vcentre dup mul mul Ucentre cos mul radius mul def /nYfacetteParaboloid 2 Vcentre dup mul mul Ucentre sin mul radius mul def /nZfacetteParaboloid Vcentre neg radius dup mul mul def /NormeN { nXfacetteParaboloid dup mul nYfacetteParaboloid dup mul nZfacetteParaboloid dup mul add add sqrt} bind def NormeN 0 eq {/NormeN 1e-10 def} if % test de visibilit� /PSfacetteParaboloid vX nXfacetteParaboloid mul vY nYfacetteParaboloid mul add vZ nZfacetteParaboloid mul add def condition { facetteParaboloid /cosV 1 xLight nXfacetteParaboloid mul yLight nYfacetteParaboloid mul zLight nZfacetteParaboloid mul add add NormeLight NormeN mul div sub def Cyan Magenta Yellow K cosV mul 4 1 roll cosV mul 4 1 roll cosV dup mul mul 4 1 roll cosV dup mul mul 4 1 roll setcmykcolor fill showgrid { 0 setgray facetteParaboloid stroke } if } if } for } for } def % % ------------------------------------ math stuff ---------------------------------- % % Matrix A in arrays of rows A[[row1][row2]...] % with [row1]=[a11 a12 ... b1] % returns on stack solution vector X=[x1 x2 ... xn] /SolveLinEqSystem { % on stack matrix M=[A,b] (A*x=b) 10 dict begin % hold all ocal /A exch def /Rows A length def % Rows = number of rows /Cols A 0 get length def % Cols = number of columns /Index [ 0 1 Rows 1 sub { } for ] def % Index = [0 1 2 ... Rows-1] /col 0 def /row 0 def /PR Rows array def % PR[c] = pivot row for row row { % starts the loop, find pivot entry in row r col Cols ge row Rows ge or { exit } if % col < Cols and row < Rows else exit /pRow row def % pRow = pivot row /max A row get col get abs def % get A[row[col]], first A[0,0] row 1 add 1 Rows 1 sub { % starts for loop 1 1 Rows-1 /j exch def % index counter /x A j get col get abs def % get A[j[r]] x max gt { % x>max, then save position /pRow j def /max x def } if } for % now we have the row with biggest A[0,1] % with pRow = the pivot row max 0 gt { % swap entries pRow and row in i /tmp Index row get def Index row Index pRow get put Index pRow tmp put % and columns pRow and row in A /tmp A row get def A row A pRow get put A pRow tmp put % pivot /row0 A row get def % the pivoting row /p0 row0 col get def % the pivot value row 1 add 1 Rows 1 sub { % start for loop /j exch def /c1 A j get def /p c1 col get p0 div def c1 col p put % subtract (p1/p0)*row[i] from row[j] col 1 add 1 Cols 1 sub { % start for loop /i exch def c1 dup i exch % c1 i c1 i get row0 i get p mul sub put } for } for PR row col put /col col 1 add def /row row 1 add def }{ % all zero entries /row row 1 add def % continue loop with same row } ifelse } loop /X A def % solution vector A Rows 1 sub get dup Cols 1 sub get exch Cols 2 sub get div X Rows 1 sub 3 -1 roll put % X[n] Rows 2 sub -1 0 { % for loop to calculate X[i] /xi exch def % current index A xi get % i-th row /Axi exch def /sum 0 def Cols 2 sub -1 xi 1 add { /n exch def /sum sum Axi n get X n get mul add def } for Axi Cols 1 sub get % b=Axi[Cols-1] sum sub % b-sum Axi xi get div % b-sum / Axi[xi] X xi 3 -1 roll put % X[xi] } for X end } def % % u -> e_u with |e_u|=1 /vector-unit { 1 dict begin dup vector-length 1 exch div vector-scale end } def % % u v -> u+v /vector-add { 1 dict begin /v exch def [ exch 0 % u i exch { % i u[i] v % i u[i] v 2 index get add % i u[i]+v[i] exch 1 add % i } forall pop ] end } def % % u v -> u-v /vector-sub { 1 dict begin /v exch def [ exch 0 % u i exch { % i u[i] v % i u[i] v 2 index get sub % i u[i]+v[i] exch 1 add % i } forall pop ] end } def % % [v] c -> [c.v] /vector-scale { 1 dict begin /c exch def [ exch { % s i u[i] c mul % s i u[i] v } forall ] end } def % % % [u] [v] -> [u x v] /vector-prod { %% x1 y1 z1 x2 y2 z2 6 dict begin aload pop /zp exch def /yp exch def /xp exch def aload pop /z exch def /y exch def /x exch def [ y zp mul z yp mul sub z xp mul x zp mul sub x yp mul y xp mul sub ] end } def % % [u] [v] -> u.v /vector-mul { %% x1 y1 z1 x2 y2 z2 6 dict begin aload pop /zp exch def /yp exch def /xp exch def aload pop /z exch def /y exch def /x exch def x xp mul y yp mul add z zp mul add end } def % % [x y z ... ] -> r % watch out for overflow /vector-length { 1 dict begin dup % find maximum entry /max 0 def { % max abs dup max gt { % if abs gt max /max exch def } { pop } ifelse } forall max 0 ne { 0 exch { % 0 v[i] max div dup mul add } forall sqrt max mul } { pop 0 } ifelse end } def % end % tx@3DPlotDict %