summaryrefslogtreecommitdiff
path: root/Master/texmf-dist/dvips/pst-solides3d
diff options
context:
space:
mode:
authorKarl Berry <karl@freefriends.org>2008-08-02 23:12:12 +0000
committerKarl Berry <karl@freefriends.org>2008-08-02 23:12:12 +0000
commite64ffb6f004c76b6552fa48978e1ab5a97cdf4db (patch)
treeec554d0aeea6c375082c170705b704735cdfd9e0 /Master/texmf-dist/dvips/pst-solides3d
parent4b522fc9f9bf01716bc73a2f3d23f505bccee883 (diff)
pst-solides3d 4.10 (rename from pst-solide3d) (2aug08)
git-svn-id: svn://tug.org/texlive/trunk@10017 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/dvips/pst-solides3d')
-rw-r--r--Master/texmf-dist/dvips/pst-solides3d/solides.pro11137
1 files changed, 11137 insertions, 0 deletions
diff --git a/Master/texmf-dist/dvips/pst-solides3d/solides.pro b/Master/texmf-dist/dvips/pst-solides3d/solides.pro
new file mode 100644
index 00000000000..7e410935f83
--- /dev/null
+++ b/Master/texmf-dist/dvips/pst-solides3d/solides.pro
@@ -0,0 +1,11137 @@
+%!
+% PostScript prologue for pst-solides3d.tex.
+% Version 4.09, 2008/07/23
+%
+%% COPYRIGHT 2008 by Jean-Paul Vignault
+%%
+%% 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.
+%
+/SolidesDict 100 dict def
+/SolidesbisDict 100 dict def
+SolidesDict begin
+
+%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% %% les variables globales gerees par PSTricks %%
+%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% %% les lignes dessous sont a decommenter si l on veut utiliser le
+%% %% fichier solides.pro independamment du package PSTricks
+%% /Dobs 20 def
+%% /THETA 20 def
+%% /PHI 50 def
+%% /Decran 30 def
+%% /XpointVue {Dobs Cos1Cos2 mul} def
+%% /YpointVue {Dobs Sin1Cos2 mul} def
+%% /ZpointVue {Dobs Sin2 mul} def
+%% /xunit 28.14 def
+%% /solidhollow false def
+%% /solidbiface false def
+%% /xunit 28.45 def
+%% /tracelignedeniveau? true def
+%% /hauteurlignedeniveau 1 def
+%% /couleurlignedeniveau {rouge} def
+%% /linewidthlignedeniveau 4 def
+%% /solidgrid true def
+/aretescachees true def
+/defaultsolidmode 2 def
+
+%% variables globales specifiques a PSTricks
+%% /activationgestioncouleurs true def
+/xmin -10 def
+/xmax 10 def
+/ymin -10 def
+/ymax 10 def
+
+/fillstyle {} def
+/startest false def
+/cm {} def
+/cm_1 {} def
+/yunit {xunit} def
+/angle_repere 90 def
+
+/hadjust 2.5 def
+/vadjust 2.5 def
+/pl@n-en-cours false def
+
+/pointilles {
+ [6.25 3.75] 1.25 setdash
+} def
+/stockcurrentcpath {} def
+/newarrowpath {} def
+/chaine 15 string def
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% choix d une fonte accentuee pour le .ps %%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/ReEncode { exch findfont
+dup length dict begin { 1 index /FID eq {pop pop} {def} ifelse
+}forall /Encoding ISOLatin1Encoding def currentdict end definefont
+pop }bind def
+/Font /Times-Roman /ISOfont ReEncode /ISOfont def
+%Font findfont 10 scalefont setfont
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% extrait de color.pro pour pouvoir recuperer ses couleurs %%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+/GreenYellow{0.15 0 0.69 0 setcmykcolor}def
+/Yellow{0 0 1 0 setcmykcolor}def
+/Goldenrod{0 0.10 0.84 0 setcmykcolor}def
+/Dandelion{0 0.29 0.84 0 setcmykcolor}def
+/Apricot{0 0.32 0.52 0 setcmykcolor}def
+/Peach{0 0.50 0.70 0 setcmykcolor}def
+/Melon{0 0.46 0.50 0 setcmykcolor}def
+/YellowOrange{0 0.42 1 0 setcmykcolor}def
+/Orange{0 0.61 0.87 0 setcmykcolor}def
+/BurntOrange{0 0.51 1 0 setcmykcolor}def
+/Bittersweet{0 0.75 1 0.24 setcmykcolor}def
+/RedOrange{0 0.77 0.87 0 setcmykcolor}def
+/Mahogany{0 0.85 0.87 0.35 setcmykcolor}def
+/Maroon{0 0.87 0.68 0.32 setcmykcolor}def
+/BrickRed{0 0.89 0.94 0.28 setcmykcolor}def
+/Red{0 1 1 0 setcmykcolor}def
+/OrangeRed{0 1 0.50 0 setcmykcolor}def
+/RubineRed{0 1 0.13 0 setcmykcolor}def
+/WildStrawberry{0 0.96 0.39 0 setcmykcolor}def
+/Salmon{0 0.53 0.38 0 setcmykcolor}def
+/CarnationPink{0 0.63 0 0 setcmykcolor}def
+/Magenta{0 1 0 0 setcmykcolor}def
+/VioletRed{0 0.81 0 0 setcmykcolor}def
+/Rhodamine{0 0.82 0 0 setcmykcolor}def
+/Mulberry{0.34 0.90 0 0.02 setcmykcolor}def
+/RedViolet{0.07 0.90 0 0.34 setcmykcolor}def
+/Fuchsia{0.47 0.91 0 0.08 setcmykcolor}def
+/Lavender{0 0.48 0 0 setcmykcolor}def
+/Thistle{0.12 0.59 0 0 setcmykcolor}def
+/Orchid{0.32 0.64 0 0 setcmykcolor}def
+/DarkOrchid{0.40 0.80 0.20 0 setcmykcolor}def
+/Purple{0.45 0.86 0 0 setcmykcolor}def
+/Plum{0.50 1 0 0 setcmykcolor}def
+/Violet{0.79 0.88 0 0 setcmykcolor}def
+/RoyalPurple{0.75 0.90 0 0 setcmykcolor}def
+/BlueViolet{0.86 0.91 0 0.04 setcmykcolor}def
+/Periwinkle{0.57 0.55 0 0 setcmykcolor}def
+/CadetBlue{0.62 0.57 0.23 0 setcmykcolor}def
+/CornflowerBlue{0.65 0.13 0 0 setcmykcolor}def
+/MidnightBlue{0.98 0.13 0 0.43 setcmykcolor}def
+/NavyBlue{0.94 0.54 0 0 setcmykcolor}def
+/RoyalBlue{1 0.50 0 0 setcmykcolor}def
+/Blue{1 1 0 0 setcmykcolor}def
+/Cerulean{0.94 0.11 0 0 setcmykcolor}def
+/Cyan{1 0 0 0 setcmykcolor}def
+/ProcessBlue{0.96 0 0 0 setcmykcolor}def
+/SkyBlue{0.62 0 0.12 0 setcmykcolor}def
+/Turquoise{0.85 0 0.20 0 setcmykcolor}def
+/TealBlue{0.86 0 0.34 0.02 setcmykcolor}def
+/Aquamarine{0.82 0 0.30 0 setcmykcolor}def
+/BlueGreen{0.85 0 0.33 0 setcmykcolor}def
+/Emerald{1 0 0.50 0 setcmykcolor}def
+/JungleGreen{0.99 0 0.52 0 setcmykcolor}def
+/SeaGreen{0.69 0 0.50 0 setcmykcolor}def
+/Green{1 0 1 0 setcmykcolor}def
+/ForestGreen{0.91 0 0.88 0.12 setcmykcolor}def
+/PineGreen{0.92 0 0.59 0.25 setcmykcolor}def
+/LimeGreen{0.50 0 1 0 setcmykcolor}def
+/YellowGreen{0.44 0 0.74 0 setcmykcolor}def
+/SpringGreen{0.26 0 0.76 0 setcmykcolor}def
+/OliveGreen{0.64 0 0.95 0.40 setcmykcolor}def
+/RawSienna{0 0.72 1 0.45 setcmykcolor}def
+/Sepia{0 0.83 1 0.70 setcmykcolor}def
+/Brown{0 0.81 1 0.60 setcmykcolor}def
+/Tan{0.14 0.42 0.56 0 setcmykcolor}def
+/Gray{0 0 0 0.50 setcmykcolor}def
+/Black{0 0 0 1 setcmykcolor}def
+/White{0 0 0 0 setcmykcolor}def
+%% fin de l extrait color.pro
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% autres couleurs %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+/bleu {0 0 1 setrgbcolor} def
+/rouge {1 0 0 setrgbcolor} def
+/vert {0 .5 0 setrgbcolor} def
+/gris {.4 .4 .4 setrgbcolor} def
+/jaune {1 1 0 setrgbcolor} def
+/noir {0 0 0 setrgbcolor} def
+/blanc {1 1 1 setrgbcolor} def
+/orange {1 .65 0 setrgbcolor} def
+/rose {1 .01 .58 setrgbcolor} def
+/cyan {1 0 0 0 setcmykcolor} def
+/magenta {0 1 0 0 setcmykcolor} def
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% definition du point de vue %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% pour la 3D conventionnelle
+%% Dony : graphisme scientifique : page 187
+%% Editeur : Masson
+
+%% calcul des coefficients de la matrice
+%% de transformation
+/Sin1 {THETA sin} def
+/Sin2 {PHI sin} def
+/Cos1 {THETA cos} def
+/Cos2 {PHI cos} def
+/Cos1Sin2 {Cos1 Sin2 mul} def
+/Sin1Sin2 {Sin1 Sin2 mul} def
+/Cos1Cos2 {Cos1 Cos2 mul} def
+/Sin1Cos2 {Sin1 Cos2 mul} def
+
+/3dto2d {
+6 dict begin
+ /Zcote exch def
+ /Yordonnee exch def
+ /Xabscisse exch def
+ /xObservateur
+ Xabscisse Sin1 mul neg Yordonnee Cos1 mul add
+ def
+ /yObservateur
+ Xabscisse Cos1Sin2 mul neg Yordonnee Sin1Sin2 mul sub Zcote Cos2
+ mul add
+ def
+ /zObservateur
+ Xabscisse neg Cos1Cos2 mul Yordonnee Sin1Cos2 mul sub Zcote Sin2
+ mul sub Dobs add
+ def
+ %% maintenant on depose les resultats sur la pile
+ Decran xObservateur mul zObservateur div cm
+ Decran yObservateur mul zObservateur div cm
+end
+} def
+
+/getpointVue {
+ XpointVue
+ YpointVue
+ ZpointVue
+} def
+
+/GetCamPos {
+ getpointVue
+} def
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% jps modifie pour PSTricks %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+/solid {continu} def
+/dashed {pointilles} def
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% geometrie basique %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%% syntaxe~: [x1 y1 ... xn yn] ligne
+/ligne {
+gsave
+ newpath
+ dup 0 getp smoveto
+ ligne_
+ starfill
+ stroke
+grestore
+} def
+
+%% syntaxe~: [x1 y1 ... xn yn] ligne_
+/ligne_ {
+ reversep
+ aload length 2 idiv
+ {
+ slineto
+ } repeat
+} def
+
+%% syntaxe~: [x1 y1 ... xn yn] polygone
+/polygone* {
+1 dict begin
+ /startest {true} def
+ polygone
+end
+} def
+
+/polygone_ {
+ newpath
+ aload length 2 idiv
+ 3 copy pop
+ smoveto
+ {
+ slineto
+ } repeat
+ closepath
+} def
+
+/polygone {
+ gsave
+ polygone_
+ starfill
+ currentlinewidth 0 eq {} {stroke} ifelse
+ grestore
+} def
+
+%% syntaxe : x y point
+/point {
+gsave
+ 1 setlinecap
+ newpath
+ smoveto
+ 0 0 rlineto
+ 5 setlinewidth
+ stroke
+grestore
+} def
+
+/point_ {
+ 1 setlinecap
+ 5 setlinewidth
+ smoveto
+ 0 0 rlineto
+} def
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% %%%%
+%%%% insertion librairie jps %%%%
+%%%% %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% le repere jps %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%% ### AAAopacity ###
+%% les parametres pour la gestion de la transparence
+/setstrokeopacity {
+ /strokeopacity exch def
+} def
+/setfillopacity {
+ /fillopacity exch def
+} def
+%% d apres un code de Jean-Michel Sarlat
+%% http://melusine.eu.org/syracuse/swf/pdf2swf/setdash/
+%% Mise en reserve de la procedure stroke originelle.
+/sysstroke {systemdict /stroke get exec} def
+/sysfill {systemdict /fill get exec} def
+/sysatan {systemdict /atan get exec} def
+/atan {2 copy 0 0 eqp {pop pop 0} {sysatan} ifelse} def
+% Mise en place de la nouvelle procedure
+/stroke {
+ /strokeopacity where {
+ /strokeopacity get
+ } {
+ 1
+ } ifelse
+ .setopacityalpha sysstroke
+} def
+/fill {
+ /fillopacity where {
+ /fillopacity get
+ } {
+ 1
+ } ifelse
+ .setopacityalpha sysfill
+} def
+
+%%%%% ### AAAscale ###
+%%%%%%%%%%%%%%%% les deplacements a l echelle %%%%%%%%%%%%%%%%%%%
+
+ /v@ct_I {xunit 0} def
+ /v@ct_J {angle_repere cos yunit mul angle_repere sin yunit mul} def
+
+/xscale {} def
+/yscale {} def
+
+/xscale-1 {} def
+/yscale-1 {} def
+
+/gtransform {} def
+/gtransform-1 {} def
+
+/jtoppoint {
+2 dict begin
+ gtransform
+ /y exch yscale def
+ /x exch xscale def
+ v@ct_I x mulv
+ v@ct_J y mulv
+ addv
+end
+} def
+
+/rptojpoint {
+ xtranslate ytranslate
+ 3 1 roll %% xA yB yA xB
+ 4 1 roll %% xB xA yB yA
+ sub neg 3 1 roll %% yB-yA xB xA
+ sub neg exch
+ ptojpoint
+} def
+
+/rptoppoint {
+ xtranslate ytranslate
+ 3 1 roll %% xA yB yA xB
+ 4 1 roll %% xB xA yB yA
+ sub neg 3 1 roll %% yB-yA xB xA
+ sub neg exch
+} def
+
+/ptojpoint {
+4 dict begin
+ /Y exch yscale-1 def
+ /X exch xscale-1 def
+ /y Y yunit angle_repere sin mul div def
+ /x X y yunit mul angle_repere cos mul sub xunit div def
+ x y
+ gtransform-1
+end
+} def
+
+/smoveto {
+ jtoppoint
+ moveto
+} def
+
+/srmoveto {
+ jtoppoint
+ rmoveto
+} def
+
+/slineto {
+ jtoppoint
+ lineto
+} def
+
+/srlineto {
+ jtoppoint
+ rlineto
+} def
+
+/stranslate {
+ jtoppoint
+ translate
+} def
+
+%%%%% ### fin insertion ###
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% methodes numeriques %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%% ### solve2nddegre ###
+%% syntaxe : a b c solve2nddegre --> x1 x2
+/solve2nddegre {
+5 dict begin
+ /@c exch def
+ /@b exch def
+ /@a exch def
+ /delt@ @b dup mul 4 @a mul @c mul sub def
+ @b neg delt@ sqrt sub 2 @a mul div
+ @b neg delt@ sqrt add 2 @a mul div
+end
+} def
+
+%%%%% ### fin insertion ###
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% la 2D %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% points %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%% ### tripointangle ###
+%% syntaxe : A B C tripointangle --> angle ABC
+/tripointangle {
+9 dict begin
+ /yC exch def
+ /xC exch def
+ /yB exch def
+ /xB exch def
+ /yA exch def
+ /xA exch def
+ /A {xA yA} def
+ /B {xB yB} def
+ /C {xC yC} def
+ B C angle
+ B A angle
+ sub
+end
+} def
+
+%%%%% ### angle ###
+%% syntaxe : A B angle
+%% --> num, l'angle defini par le vecteur AB dans le repere orthonorme jps
+/angle {
+ vecteur exch atan
+ dup 180 gt
+ {360 sub}
+ if
+} def
+
+%% syntaxe : A B pangle
+%% --> num, l'angle defini par le vecteur AB dans le repere postscript
+/pangle {
+ jtoppoint exchp jtoppoint exchp vecteur exch atan
+ dup 180 gt
+ {360 sub}
+ if
+} def
+
+%%%%% ### setxrange ###
+/setxrange {
+ /xmax exch def
+ /xmin exch def
+} def
+
+%%%%% ### setyrange ###
+/setyrange {
+ /ymax exch def
+ /ymin exch def
+} def
+
+%%%%% ### defpoint ###
+%% syntaxe : xA yA /A defpoint
+/defpoint {
+1 dict begin
+ /t@mp@r@ire exch def
+ [ 3 1 roll ] cvx t@mp@r@ire exch
+end def
+} def
+
+%%%%% ### milieu ###
+%% syntaxe~: A B milieu
+/milieu {
+ %% xA yA xB yB
+ 3 -1 roll %% xA xB yB yA
+ add 2 div %% xA xB yM
+ 3 1 roll %% yM xA xB
+ add 2 div %% yM xM
+ exch
+} def
+
+%%%%% ### parallelopoint ###
+%% syntaxe : A B C parallelopoint --> point D, tel que ABCD parallelogramme
+/parallelopoint {
+11 dict begin
+ /yC exch def
+ /xC exch def
+ /yB exch def
+ /xB exch def
+ /yA exch def
+ /xA exch def
+ /A {xA yA} def
+ /B {xB yB} def
+ /C {xC yC} def
+ /d1 {A B C paral} def
+ /d2 {B C A paral} def
+ d1 d2 interdroite
+end
+} def
+
+%%%%% ### translatepoint ###
+%% syntaxe : A u translatepoint --> B image de A par la translation de vecteur u
+/translatepoint {
+ addv
+} def
+
+%%%%% ### rotatepoint ###
+%% syntaxe : B A r rotatepoint --> C image de B par la rotation de centre A,
+%% d'angle r (en degre)
+%% En prenant les affixes des pts associes, il vient
+%% (zC - zA) = (zB-zA) e^(ir)
+%% soit
+%% zC = (zB-zA) e^(ir) + zA
+/rotatepoint { %% B, A, r
+ 5 copy %% B, A, r, B, A, r
+ cos 5 1 roll %% B, A, r, cos r, B, A
+ 4 1 roll %% B, A, r, cos r, yA, B, xA
+ 4 1 roll %% B, A, r, cos r, A, B
+ vecteur %% B, A, r, cos r, xB-xA, yB-yA
+ 4 -1 roll sin %% B, A, cos r, xB-xA, yB-yA, sin r
+ 4 copy mul %% B, A, cos r, xB-xA, yB-yA, sin r, cos r, xB-xA, (yB-yA) sin r
+ 7 1 roll mul %% B, A, (yB-yA) sin r, cos r, xB-xA, yB-yA, sin r, cos r (xB-xA)
+ 5 1 roll %% B, A, (yB-yA) sin r, cos r (xB-xA), cos r, xB-xA, yB-yA, sin r
+ exch %% B, A, (yB-yA) sin r, cos r (xB-xA), cos r, xB-xA, sin r, yB-yA
+ 4 -1 roll mul %% B, A, (yB-yA) sin r, cos r (xB-xA), xB-xA, sin r, (yB-yA)cos r
+ 3 1 roll mul %% B, A, (yB-yA) sin r, cos r (xB-xA), (yB-yA) cos r, (xB-xA) sin r
+ add %% B, A, (yB-yA) sin r, cos r (xB-xA), (yB-yA) cos r +(xB-xA) sin r
+ 3 1 roll %% B, A, (yB-yA) cos r + (xB-xA) sin r, (yB-yA) sin r, cos r (xB-xA),
+ exch sub %% B, A, (yB-yA) cos r + (xB-xA) sin r, cos r (xB-xA)-(yB-yA) sin r
+ exch %% B, zA, (zB-zA) e^(ir)
+ addv
+ 3 -1 roll pop
+ 3 -1 roll pop
+} def
+
+%%%%% ### hompoint ###
+%% syntaxe : B A alpha hompoint -> le point A' tel que AA' = alpha AB
+/hompoint {
+ 5 copy
+ pop
+ vecteur %% vecteur BA
+ 3 -1 roll
+ neg
+ mulv %% alpha x vecteur AB
+ addv
+ 4 -1 roll
+ 4 -1 roll
+ pop pop
+} def
+
+%%%%% ### orthoproj ###
+%% syntaxe : A D orthoproj --> B, le projete orthogonal de A sur D
+/orthoproj {
+ 6 -1 roll
+ 6 -1 roll %% D A
+ 6 copy %% D A D A
+ 7 -1 roll pop
+ 7 -1 roll pop %% D D A
+ perp
+ interdroite
+} def
+
+%% syntaxe : A projx --> le projete orthogonal de A sur Ox
+/projx {
+ pop 0
+} def
+
+%% syntaxe : A projy --> le projete orthogonal de A sur Oy
+/projy {
+ exch pop 0 exch
+} def
+
+%%%%% ### sympoint ###
+%% syntaxe : A I sympoint --> point A', le symetrique de A par rapport
+%% au point I
+/sympoint {
+ 4 copy
+ pop pop
+ vecteur
+ -2 mulv
+ addv
+} def
+
+%%%%% ### axesympoint ###
+%% syntaxe : A D axesympoint --> point B, le symetrique de A par rapport
+%% a la droite D
+/axesympoint {
+2 dict begin
+ 6 copy
+ pop pop pop pop
+ /yA exch def
+ /xA exch def
+ orthoproj
+ xA yA vecteur
+ -2 mulv
+ xA yA addv
+end
+} def
+
+%%%%% ### cpoint ###
+%% syntaxe : alpha C cpoint -> M, le point du cercle C correspondant a
+%% l'angle alpha
+/cpoint { %% a, xI, yI, r
+1 dict begin
+ dup %% a, xI, yI, r, r
+ 5 -1 roll %% xI, yI, r, r, a
+ /alpha exch def
+ alpha cos mul %% xI, yI, r, r cos a
+ exch
+ alpha sin mul %% xI, yI, r cos a, r sin a
+ 3 -1 roll add %% xI, r cos a, yI + r sin a
+ 3 1 roll %% yI + r sin a, xI, r cos a,
+ add exch %% xI + r cos a, yI + r sin a
+end
+} def
+
+%%%%% ### xdpoint ###
+%% x A B xdpoint : le point de la droite (AB) d'abscisse x
+/xdpoint {
+5 dict begin
+ /pt2 defpoint
+ /pt1 defpoint
+ /x exch def
+ /a pt1 pt2 coeffdir def
+ /b pt1 pt2 ordorig def
+ x dup a mul b add
+end
+} def
+
+%%%%% ### ydpoint ###
+%% y A B ydpoint : le point de la droite (AB) d'ordonnee y
+/ydpoint {
+5 dict begin
+ /pt2 defpoint
+ /pt1 defpoint
+ /y exch def
+ pt1 pt2 verticale?
+ {
+ pt1 pop y
+ }
+ {
+ /a pt1 pt2 coeffdir def
+ /b pt1 pt2 ordorig def
+ y b sub a div y
+ }
+ ifelse
+end
+} def
+
+%%%%% ### ordonnepoints ###
+%% syntaxe : xA yA xB yB ordonnepoints --> idem si yB>yA ou si yB=yA
+%% avec xB>xA, sinon xB yB xA yA
+/ordonnepoints {
+ 4 copy
+ exch pop %% ... xA, yA, yB
+ lt %% yA < yB ?
+ {pop} %% oui, c'est fini
+ { %% non : yA >= yB
+ pop 4 copy
+ exch pop %% ... xA, yA, yB
+ eq %% yA = yB ?
+ {
+ 3 copy %% oui, yA = yB
+ pop pop %% ... xA, xB
+ le %% xA =< xB ?
+ {} %% oui, c'est fini
+ { %% non, on echange A et B
+ 4 -1 roll
+ 4 -1 roll
+ }
+ ifelse
+ }
+ { %% non : yA < yB => on echange A et B
+ pop
+ 4 -1 roll
+ 4 -1 roll
+ }
+ ifelse
+ }
+ ifelse
+} def
+
+%%%%% ### distance ###
+%% syntaxe~: A B distance
+/distance { %% xA yA xB yB
+ vecteur %% x y
+ dup mul exch %% y^2 x
+ dup mul %% y^2 x^2
+ add
+ sqrt
+} def
+
+%%%%% ### dup ###
+/dupp {2 copy} def
+/dupc {3 copy} def
+/dupd {4 copy} def
+
+%%%%% ### fin insertion ###
+/interdroites {interdroite} def
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% vecteurs %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%% ### vecteur ###
+%% syntaxe~: A B vecteur
+/vecteur {
+ %% xA yA xB yB
+ 3 -1 roll %% xA xB yB yA
+ sub %% xA xB yB-yA
+ 3 1 roll %% yB-yA xA xB
+ exch sub %% yB-yA xB-xA
+ exch
+} def
+
+%%%%% ### normalize ###
+%% syntaxe : u normalize -> u / ||u||
+/normalize {
+2 dict begin
+ /u defpoint
+ /n u norme def
+ u 1 n div mulv
+end
+} def
+
+%%%%% ### addv ###
+%% syntaxe : u v addv --> u+v
+/addv { %% xA yA xB yB
+ 3 1 roll %% xA yB yA xB
+ 4 1 roll %% xB xA yB yA
+ add 3 1 roll %% yB+yA xB xA
+ add exch
+} def
+
+%%%%% ### subv ###
+%% syntaxe : u v subv --> u - v
+/subv { %% xA yA xB yB
+ -1 mulv
+ addv
+} def
+
+%%%%% ### mulv ###
+%% syntaxe : u a mulv --> au
+/mulv { %% xA, yA, a
+ dup %% xA, yA, a, a
+ 3 1 roll %% xA, a, yA, a
+ mul 3 1 roll %% ayA, xA, a
+ mul exch
+} def
+
+%%%%% ### scalprod ###
+%% syntaxe : u v scalprod --> le produit scalaire de u par v
+/scalprod {
+2 dict begin
+ /y' exch def
+ exch
+ /y exch def
+ mul y y' mul add
+end
+} def
+
+%%%%% ### normal ###
+%% syntaxe : u normal --> v tel u.v = 0
+/normal {
+ neg exch
+} def
+
+%%%%% ### norme ###
+%% syntaxe : u norme --> |u|
+/norme {
+ dup mul
+ exch
+ dup mul
+ add sqrt
+} def
+
+%%%%% ### oldarrow ###
+%% syntaxe : A B oldarrow --> trace fleche en B, direction AB
+/oldarrow {
+4 dict begin
+gsave
+ /B defpoint
+ /A defpoint
+ oldarrowscale scale
+ oldarrowangle rotate
+ newpath
+ B smoveto
+ A B vecteur normalize /u defpoint
+ u neg exch /v defpoint
+ u oldarrowpointe neg mulv rmoveto %% ainsi c'est la pointe qui est en (0, 0)
+ %% le pt extremal arriere haut
+ u oldarrowplume neg mulv %% l'abscisse
+ v oldarrow@ngle sin oldarrow@ngle cos div oldarrowplume mul mulv addv %% l'ordonnee
+ rlineto
+ u oldarrowplume oldarrowpointe add mulv
+ v oldarrow@ngle sin oldarrow@ngle cos div oldarrowplume mul neg mulv addv
+ rlineto
+ u oldarrowplume oldarrowpointe add neg mulv
+ v oldarrow@ngle sin oldarrow@ngle cos div oldarrowplume mul neg mulv addv
+ rlineto
+ closepath fill
+grestore
+end
+} def
+
+/oldarrowpointe {xunit 5 div} def
+/oldarrowplume {xunit 10 div} def
+/oldarrow@ngle 45 def
+/oldarrowscale {1 1} def
+/oldarrowangle 0 def %% pour l'utilisateur
+
+%%%%% ### drawvecteur ###
+%% syntaxe : A B drawvecteur
+/drawvecteur {
+2 dict begin
+ /B defpoint
+ /A defpoint
+ [A B] ligne
+ A B oldarrow
+end
+} def
+
+%%%%% ### orthovecteur ###
+%% syntaxe : u orthovecteur --> v, vecteur orthogonal a u
+/orthovecteur {
+ neg exch
+} def
+
+%%%%% ### fin insertion ###
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% cercles %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%% ### defcercle ###
+%% syntaxe : A r /d defcercle
+/defcercle {
+1 dict begin
+ /t@mp@r@ire exch def
+ [ 4 1 roll ] cvx t@mp@r@ire exch
+end def
+} def
+
+%%%%% ### interdroitecercle ###
+%% intersection de la droite y = ax+b avec le cercle (x-x0)^2 + (y-y0)^2 = r^2
+%% { -- b - y 2 2 3
+%% { | x = - -----, y = (b + a x0 + a y0 + (2 a b y0 - 2 a b x0 +
+%% { -- a
+%%
+%% 3 2 2 2 2 4 2 2 2 4 2 2
+%% 2 a x0 y0 - a b + a r + a r - a y0 - a x0 )^(1/2)) / (a + 1)
+%%
+%%
+%% --
+%% |,
+%% --
+%% -- b - y 2 2 3
+%% | x = - -----, y = (b + a x0 + a y0 - (2 a b y0 - 2 a b x0 +
+%% -- a
+%%
+%% 3 2 2 2 2 4 2 2 2 4 2 2
+%% 2 a x0 y0 - a b + a r + a r - a y0 - a x0 )^(1/2)) / (a + 1)
+%%
+%% -- }
+%% | }
+%% -- }
+
+%% intersection de la droite x = a avec le cercle (x-x0)^2 + (y-y0)^2 = r^2
+%% 2 2 2 1/2
+%% {[x = a, y = y0 + (2 a x0 - a + r - x0 ) ],
+%%
+%% 2 2 2 1/2
+%% [x = a, y = y0 - (2 a x0 - a + r - x0 ) ]}
+
+%% intersection de la droite y = b avec le cercle (x-x0)^2 + (y-y0)^2 = r^2
+%% 2 2 2 1/2
+%% {[y = b, x = x0 + (2 b y0 - b + r - y0 ) ],
+%%
+%% 2 2 2 1/2
+%% [y = b, x = x0 - (2 b y0 - b + r - y0 ) ]}
+
+%% syntaxe : D I r interdroitecercle
+/interdroitecercle {
+16 dict begin
+ /r exch def
+ /y0 exch def
+ /x0 exch def
+ /yB exch def
+ /xB exch def
+ /yA exch def
+ /xA exch def
+
+ xA yA xB yB verticale?
+
+ %% la droite est verticale
+ {
+ /xpt1 xA def
+ /xpt2 xA def
+ /quantite
+ 2 xA mul x0 mul xA dup mul sub r dup mul add x0 dup mul sub sqrt
+ def
+ /ypt1
+ y0 quantite add
+ def
+ /ypt2
+ y0 quantite sub
+ def
+ }
+
+ %% la droite n'est pas verticale
+ {
+ /a xA yA xB yB coeffdir def
+ /b xA yA xB yB ordorig def
+
+ 0 a eq
+ %% la droite est horizontale
+ {
+ /quantite
+ 2 b mul y0 mul
+ b dup mul sub
+ r dup mul add
+ y0 dup mul sub
+ sqrt
+ def
+ /xpt1
+ x0 quantite add
+ def
+ /xpt2
+ x0 quantite sub
+ def
+ /ypt1 b def
+ /ypt2 b def
+ }
+
+ %% la droite n'est pas horizontale
+ {
+ /quantite1
+ b
+ a x0 mul add
+ a dup mul y0 mul add
+ def
+ /quantite2
+ 2 a dup mul mul b mul y0 mul
+ 2 a 3 exp mul b mul x0 mul sub
+ 2 a 3 exp mul x0 mul y0 mul add
+ a dup mul b dup mul mul sub
+ a dup mul r dup mul mul add
+ a 4 exp r dup mul mul add
+ a dup mul y0 dup mul mul sub
+ a 4 exp x0 dup mul mul sub
+ sqrt
+ def
+ /quantite3
+ a dup mul 1 add
+ def
+ /ypt1
+ quantite1 quantite2 add quantite3 div
+ def
+ /xpt1
+ ypt1 b sub a div
+ def
+ /ypt2
+ quantite1 quantite2 sub quantite3 div
+ def
+ /xpt2
+ ypt2 b sub a div
+ def
+ }
+ ifelse
+ }
+ ifelse
+
+ xpt1 ypt1
+ xpt2 ypt2
+ ordonnepoints
+end
+} def
+
+%%%%% ### intercercle ###
+%% syntaxe : cerc1 cerc2 intercercle --> A B les points d'intersection
+%% des 2 cercles, tries par 'ordonnepoints'
+/intercercle {
+12 dict begin
+ /r2 exch def
+ /y2 exch def
+ /x2 exch def
+ /r1 exch def
+ /y1 exch def
+ /x1 exch def
+
+ %% on translate pour se ramener a (x1, y1) = (0, 0)
+ x2 y2 x1 y1 subv
+ /y2 exch def
+ /x2 exch def
+
+ %% on prepare l'equation du 2nd degre
+
+%% 2 2 2
+%% {y = RootOf((4 x2 + 4 y2 ) _Z
+%%
+%% 3 2 2 2 4
+%% + (-4 y2 - 4 r1~ y2 + 4 y2 r2~ - 4 x2 y2) _Z + x2
+%%
+%% 4 2 2 2 2 2 2 2 2
+%% + r2~ - 2 y2 r2~ + 2 x2 y2 - 2 x2 r2~ - 2 r1~ x2
+%%
+%% 4 4 2 2 2 2
+%% + r1~ + y2 + 2 r1~ y2 - 2 r1~ r2~ ), x = 1/2 (-2 y2
+%%
+%% 2 2 2
+%% RootOf((4 x2 + 4 y2 ) _Z
+%%
+%% 3 2 2 2 4
+%% + (-4 y2 - 4 r1~ y2 + 4 y2 r2~ - 4 x2 y2) _Z + x2
+%%
+%% 4 2 2 2 2 2 2 2 2
+%% + r2~ - 2 y2 r2~ + 2 x2 y2 - 2 x2 r2~ - 2 r1~ x2
+%%
+%% 4 4 2 2 2 2 2 2 2
+%% + r1~ + y2 + 2 r1~ y2 - 2 r1~ r2~ ) + r1~ + x2 + y2
+%%
+%% 2
+%% - r2~ )/x2}
+
+ %% coeff pour le degre 2
+ /a
+ %% 2 2 2
+ %% {y = RootOf((4 x2 + 4 y2 ) _Z
+ 4 x2 dup mul mul
+ 4 y2 dup mul mul add
+ def
+
+ %% coeff pour le degre 1
+ %%
+ /b
+ %% 3 2 2 2
+ %% + (-4 y2 - 4 r1~ y2 + 4 y2 r2~ - 4 x2 y2) _Z
+ -4 y2 3 exp mul
+ 4 r1 dup mul mul y2 mul sub
+ 4 r2 dup mul mul y2 mul add
+ 4 x2 dup mul mul y2 mul sub
+ def
+
+ %% coeff pour le degre 0
+ %%
+ /c {
+ %% 4
+ %% + x2
+ x2 4 exp
+ %%
+ %% 4 2 2 2 2 2 2 2 2
+ %% + r2~ - 2 y2 r2~ + 2 x2 y2 - 2 x2 r2~ - 2 r1~ x2
+ r2 4 exp add
+ 2 y2 dup mul mul r2 dup mul mul sub
+ 2 x2 dup mul mul y2 dup mul mul add
+ 2 x2 dup mul mul r2 dup mul mul sub
+ 2 x2 dup mul mul r1 dup mul mul sub
+ %%
+ %% 4 4 2 2 2 2
+ %% + r1~ + y2 + 2 r1~ y2 - 2 r1~ r2~ )
+ r1 4 exp add
+ y2 4 exp add
+ 2 r1 dup mul mul y2 dup mul mul add
+ 2 r1 dup mul mul r2 dup mul mul sub
+ } def
+
+ a b c solve2nddegre
+ /Y1 exch def
+ /Y0 exch def
+
+ /X0
+ %% x = 1/2 (-2 y2 Y
+ -2 y2 mul Y0 mul
+ %%
+ %% 2 2 2
+ %% + r1~ + x2 + y2
+ r1 dup mul add
+ x2 dup mul add
+ y2 dup mul add
+ %%
+ %% 2
+ %% - r2~ )/x2}
+ r2 dup mul sub
+
+ 2 x2 mul div
+ def
+
+ /X1
+ %% x = 1/2 (-2 y2 Y
+ -2 y2 mul Y1 mul
+ %%
+ %% 2 2 2
+ %% + r1~ + x2 + y2
+ r1 dup mul add
+ x2 dup mul add
+ y2 dup mul add
+ %%
+ %% 2
+ %% - r2~ )/x2}
+ r2 dup mul sub
+
+ 2 x2 mul div
+ def
+
+ %% on depose le resultat, en n'oubliant pas de retranslater en sens
+ %% inverse
+
+ X0 Y0 x1 y1 addv
+ X1 Y1 x1 y1 addv
+ ordonnepoints
+end
+} def
+
+%%%%% ### ABcercle ###
+%% syntaxe : A B C ABcercle --> le cercle passant par A, B, C
+/ABcercle {
+3 dict begin
+ /@3 defpoint
+ /@2 defpoint
+ /@1 defpoint
+ @1 @2 mediatrice
+ @1 @3 mediatrice
+ interdroite
+ dupp
+ @3 distance
+end
+} def
+
+%%%%% ### diamcercle ###
+%% syntaxe : A B diamcercle --> le cercle de diametre [AB]
+/diamcercle {
+ 4 copy
+ distance 2 div
+ 5 1 roll
+ milieu
+ 3 -1 roll
+} def
+
+%%%%% ### fin insertion ###
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% droites %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%% ### horizontale ###
+%% syntaxe : y horizontale
+/horizontale {
+1 dict begin
+ /y exch def
+ xmin y xmax y
+end
+} def
+
+%%%%% ### coeffdir ###
+%% syntaxe~: A B coeffdir
+/coeffdir {
+ vecteur exch div
+} def
+
+%%%%% ### ordorig ###
+%% syntaxe : A B ordorig
+%% attention, la droite est supposee ne pas etre verticale
+/ordorig {
+ /dr@ite 4 array def
+ dr@ite 3 3 -1 roll put
+ dr@ite 2 3 -1 roll put
+ dr@ite 1 3 -1 roll put
+ dr@ite 0 3 -1 roll put
+ dr@ite aload pop coeffdir /c@eff exch def
+ dr@ite aload pop pop pop %% xA yA
+ exch %% yA xA
+ c@eff mul neg add
+} def
+
+%%%%% ### verticale ###
+%% syntaxe~: A B verticale?
+/verticale? {
+ pop 2 1 roll pop
+ eq
+} def
+
+%% syntaxe : x verticale
+/verticale {
+1 dict begin
+ /x exch def
+ x ymin x ymax
+end
+} def
+
+%%%%% ### droite ###
+%% %% syntaxe : A B droite
+%% /droite {
+%% gsave
+%% 6 dict begin
+%% /yB exch def
+%% /xB exch def
+%% /yA exch def
+%% /xA exch def
+%% xA yA xB yB
+%% eqp
+%% {}
+%% {
+%% xA yA xB yB
+%% verticale?
+%% {
+%% newpath
+%% xA ymin smoveto
+%% xA ymax slineto
+%% stockcurrentcpath
+%% stroke
+%% }
+%% {
+%% newpath
+%% /alpha xA yA xB yB coeffdir def
+%% /beta xA yA xB yB ordorig def
+%% xmin dup alpha mul beta add smoveto
+%% xmax dup alpha mul beta add slineto
+%% stockcurrentcpath
+%% stroke
+%% }
+%% ifelse
+%% }
+%% ifelse
+%% end
+%% grestore
+%% } def
+
+%% syntaxe : A B droite
+/droite {
+gsave
+6 dict begin
+ /B defpoint
+ /A defpoint
+ A pop B pop eq {
+ %% droite verticale
+ newpath
+ A pop ymin smoveto
+ A pop ymax slineto
+ stockcurrentcpath
+ stroke
+ } {
+ %% on cherche le point le + a gauche
+ xmin A B xdpoint /C defpoint
+ C exch pop ymin lt {
+ %% trop a gauche
+ ymin A B ydpoint /C defpoint
+ } if
+ C exch pop ymax gt {
+ %% trop a gauche
+ ymax A B ydpoint /C defpoint
+ } if
+ %% on cherche le point le + a droite
+ xmax A B xdpoint /D defpoint
+ D exch pop ymin lt {
+ %% trop a droite
+ ymin A B ydpoint /D defpoint
+ } if
+ D exch pop ymax gt {
+ %% trop a gauche
+ ymax A B ydpoint /D defpoint
+ } if
+ newpath
+ C smoveto
+ D slineto
+ stockcurrentcpath
+ stroke
+ } ifelse
+end
+grestore
+} def
+
+%%%%% ### defdroite ###
+%% syntaxe : A B /d defdroite
+/defdroite {
+1 dict begin
+ /t@mp@r@ire exch def
+ [ 5 1 roll ] cvx t@mp@r@ire exch
+end def
+} def
+
+%%%%% ### paral ###
+%% syntaxe : D A paral --> droite parallele a D passant par A
+/paral {
+4 dict begin
+ /yA exch def
+ /xA exch def
+ vecteur
+ /u2 exch def
+ /u1 exch def
+ xA yA
+ 2 copy
+ u1 u2 translatepoint
+end
+} def
+
+%%%%% ### interdroite ###
+/interdroite {
+ %% A B C D
+ /dr@ite2 4 array def
+ dr@ite2 3 3 -1 roll put
+ dr@ite2 2 3 -1 roll put
+ dr@ite2 1 3 -1 roll put
+ dr@ite2 0 3 -1 roll put
+ /dr@ite1 4 array def
+ dr@ite1 3 3 -1 roll put
+ dr@ite1 2 3 -1 roll put
+ dr@ite1 1 3 -1 roll put
+ dr@ite1 0 3 -1 roll put
+
+%%% %% trace pour deboguage
+%%% dr@ite1 aload pop droite
+%%% dr@ite2 aload pop droite
+
+%%% Dans tous les cas, on suppose que l'intersection existe
+%%%
+%%% * la 1ere droite est verticale. les equations reduites sont
+%%% x = a1 et y = a2 x + b2
+%%% Le point d'intersection est :
+%%% {{x = a1, y = b2 + a1 a2}}
+%%%
+%%% * la 2eme droite est verticale. les equations reduites sont
+%%% x = a1 x+ b1 et x = a2
+%%% Le point d'intersection est :
+%%% {{x = a2, y = b1 + a1 a2}}
+%%%
+%%% * aucune n'est verticale. Les equations reduites sont
+%%% y = a1 x + b1 et y = a2 x + b2
+%%% Le point d'intersection est :
+%%% { { b2 - b1 a1 b2 - a2 b1 } }
+%%% { { x = -------, y = ------------- } }
+%%% { { a1 - a2 a1 - a2 } }
+
+%%% remarque : pour le moment, je n'arrive pas a rendre mes variables
+%%% locales : elle restent globales. Pour que cela ne soit pas trop
+%%% genant, je les note respectivement @1, @@1, @2 et @@2 au lieu de a1,
+%%% b1, a2 et b2.
+
+ dr@ite1 aload pop verticale?
+ {
+ /@1 {dr@ite1 aload pop pop pop pop} def
+ /@2 {dr@ite2 aload pop coeffdir} def
+ /@@2 {dr@ite2 aload pop ordorig} def
+ @1
+ @1 @2 mul @@2 add
+ }
+ {
+ dr@ite2 aload pop verticale?
+ {
+ /@1 {dr@ite1 aload pop coeffdir} def
+ /@@1 {dr@ite1 aload pop ordorig} def
+ /@2 {dr@ite2 aload pop pop pop pop} def
+ @2
+ @1 @2 mul @@1 add
+ }
+ {
+ /@1 {dr@ite1 aload pop coeffdir} def
+ /@@1 {dr@ite1 aload pop ordorig} def
+ /@2 {dr@ite2 aload pop coeffdir} def
+ /@@2 {dr@ite2 aload pop ordorig} def
+ @@2 @@1 sub @1 @2 sub div
+ @1 @@2 mul @2 @@1 mul sub
+ @1 @2 sub div
+ }
+ ifelse
+ }
+ ifelse
+} def
+
+%%%%% ### perp ###
+%% syntaxe : D A perp --> droite perpendiculaire a D passant par A
+/perp {
+4 dict begin
+ /yA exch def
+ /xA exch def
+ vecteur orthovecteur
+ /u2 exch def
+ /u1 exch def
+ xA yA
+ 2 copy
+ u1 u2 translatepoint
+end
+} def
+
+%%%%% ### mediatrice ###
+%% synaxe : A B mediatrice --> droite
+/mediatrice {
+ 4 copy
+ milieu
+ perp
+} def
+
+%%%%% ### bissectrice ###
+%% syntaxe : A B C bissectrice --> B E ou E est un point de la bissectrice
+/bissectrice {
+10 dict begin
+ /yC exch def
+ /xC exch def
+ /yB exch def
+ /xB exch def
+ /yA exch def
+ /xA exch def
+ /A {xA yA} def
+ /B {xB yB} def
+ /C {xC yC} def
+ /alpha {A B C tripointangle} def
+ B
+ A B alpha rotatepoint
+ A milieu
+end
+} def
+
+%%%%% ### angledroit ###
+ /widthangledroit 5 def
+
+%% syntaxe : A B C angledroit --> dessine un angle droit en B
+/angledroit {
+10 dict begin
+ dup xcheck {
+ /widthangledroit exch def
+ } if
+ /C defpoint
+ /B defpoint
+ /A defpoint
+ B C vecteur normalize widthangledroit 20 div mulv /u defpoint
+ B A vecteur normalize widthangledroit 20 div mulv /v defpoint
+ [B u addv dupp v addv B v addv] ligne
+end
+} def
+
+%%%%% ### translatedroite ###
+%% syntaxe : A B u translatedroite --> C D images resp de A et B par la translation de vecteur u
+/translatedroite { %% A B u
+ 2 copy %% A B u u
+ 6 1 roll
+ 6 1 roll %% A u B u
+ addv %% A u D
+ 6 1 roll
+ 6 1 roll %% D A u
+ addv
+ 4 1 roll
+ 4 1 roll
+} def
+
+%%%%% ### rotatedroite ###
+%% syntaxe : A B O r rotatedroite --> C D images resp de A et B par la
+%% rotation de centre O et d'angle r (en degre)
+/rotatedroite {
+ 5 copy rotatepoint %% A B O r D
+ 6 -1 roll pop %% A xB O r D
+ 6 -1 roll pop %% A O r D
+ 7 1 roll
+ 7 1 roll rotatepoint %% D C
+ 4 1 roll 4 1 roll
+} def
+
+/rotatevecteur {
+ rotatedroite
+} def
+
+/rotatesegment {
+ rotatedroite
+} def
+
+%%%%% ### axesymdroite ###
+%% syntaxe : d D axesymdroite --> droite d', symetrique de la droite d par rapport
+%% a la droite D
+/axesymdroite {
+2 dict begin
+ /D defdroite
+ /B defpoint
+ D axesympoint
+ B D axesympoint
+end
+} def
+
+%%%%% ### fin insertion ###
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% polygones %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%% ### poltransformfile ###
+%% syntaxe : pol u translatepol --> pol'
+/translatepol {
+2 dict begin
+ /uy exch def
+ /ux exch def
+ {ux uy translatepoint} papply
+end
+} def
+
+%% syntaxe : pol u rotatepol --> pol'
+/rotatepol {
+2 dict begin
+ /alpha exch def
+ /I defpoint
+ {I alpha rotatepoint} papply
+end
+} def
+
+%% syntaxe : pol I alpha hompol --> pol'
+/hompol {
+2 dict begin
+ /alpha exch def
+ /I defpoint
+ {I alpha hompoint} papply
+end
+} def
+
+%% syntaxe : pol I sympol --> pol'
+/sympol {
+1 dict begin
+ /I defpoint
+ {I sympoint} papply
+end
+} def
+
+%% syntaxe : pol D axesympol --> pol'
+/axesympol {
+1 dict begin
+ /D defdroite
+ {D axesympoint} papply
+end
+} def
+
+%%%%% ### fin insertion ###
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% les tests %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%% ### isbool ###
+%% syntaxe : any isbool --> booleen
+/isbool {
+ type (booleantype) cvn eq
+} def
+
+%%%%% ### isarray ###
+%% syntaxe : any isarray --> booleen
+/isarray {
+ type (arraytype) cvn eq
+} def
+
+%%%%% ### isstring ###
+%% syntaxe : any isstring --> booleen
+/isstring {
+ type (stringtype) cvn eq
+} def
+
+%%%%% ### isinteger ###
+%% syntaxe : any isinteger --> booleen
+/isinteger {
+ type (integertype) cvn eq
+} def
+
+%%%%% ### isnum ###
+%% syntaxe : any isnum --> booleen
+/isnum {
+ dup isreal
+ exch isinteger or
+} def
+
+%%%%% ### isreal ###
+%% syntaxe : any isreal --> booleen
+/isreal {
+ type (realtype) cvn eq
+} def
+
+%%%%% ### eq ###
+%% syntaxe : A B eqp3d --> booleen = true si les points A et B sont identiques
+/eqp3d {
+ %% x1 y1 z1 x2 y2 z2
+ 4 -1 roll %% x1 y1 x2 y2 z2 z1
+ eq { %% x1 y1 x2 y2
+ eqp
+ } {
+ pop pop pop pop false
+ } ifelse
+} def
+
+%% syntaxe : A B eqp --> booleen = true si les points A et B sont identiques
+/eqp {
+ 3 -1 roll
+ eq
+ {
+ eq
+ {true}
+ {false}
+ ifelse
+ }
+ {pop pop false}
+ ifelse
+} def
+
+%% syntaxe : z z' eqc --> true si z = z', false sinon
+/eqc {
+ eqp
+} def
+
+%%%%% ### eqstring ###
+/eqstring {
+3 dict begin
+ /str2 exch def
+ /str1 exch def
+ str1 length str2 length eq {
+ /i 0 def
+ true
+ str1 length {
+ str1 i get str2 i get eq and
+ /i i 1 add store
+ } repeat
+ } {
+ false
+ } ifelse
+end
+} def
+
+%%%%% ### fin insertion ###
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% conversions de types %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%% ### astr2str ###
+%% syntaxe : array str astr2str --> str
+%% convertit le contenu de array en chaines de caracteres puis les
+%% concatene avec str, en inserant un caractere "space" apres chaque
+%% element du tableau array
+/astr2str {
+5 dict begin
+ /str exch def
+ /table exch def
+ /n table length def
+ n 0 eq {
+ str
+ } {
+ table 0 n 1 sub getinterval
+ table n 1 sub get ( ) cvs
+ ( ) append
+ str append
+ astr2str
+ } ifelse
+end
+} def
+
+%%%%% ### numstr2array ###
+%% syntaxe : str str2num --> num
+/str2num {
+5 dict begin
+ /str exch def
+ /n str length def
+ /signnum 1 def
+ /frct false def
+ /k 0 def
+ 0 1 n 1 sub {
+ /i exch def
+ str i get
+ dup 46 eq {
+ %% il y a un point
+ /frct true def
+ pop
+ i 0 eq {
+ 0
+ } if
+ } {
+ dup 45 eq {
+ /signnum -1 def
+ pop
+ } {
+ frct not {
+ i 1 ge signnum 0 ge and i 2 ge or {
+ exch 10 mul 48 sub add
+ } {
+ 48 sub
+ } ifelse
+ } {
+ 48 sub
+ /k k 1 add store
+ 10 k exp div add
+ } ifelse
+ } ifelse
+ } ifelse
+ } for
+ signnum mul
+end
+} def
+
+/str2num {cvx exec} def
+
+%% syntaxe : str numstr2array -> array
+%% ou str est une chaine de nombres reels separes par des espaces
+%% et array est constitue des elements numeriques de string.
+%% exemple :
+%% (0 -12 .234 54) --> [0 -12 0.234 54]
+/numstr2array {
+6 dict begin
+ /str exch def
+ /n str length def
+ /separateurs [] def
+ [
+ 0 1 n 1 sub {
+ /i exch def
+ str i get
+ 32 eq {
+ /separateurs [separateurs aload pop i] def
+ } if
+ } for
+ /j 0 def
+ /oldsep 0 def
+ 0 1 separateurs length 1 sub {
+ /i exch def
+ str j separateurs i get oldsep sub getinterval str2num
+ /j separateurs i get 1 add def
+ /oldsep separateurs i get 1 add def
+ } for
+ str j n oldsep sub getinterval str2num
+ ]
+end
+} def
+
+%% syntaxe : array numstr2array -> array
+/arraynumstr2arrayarray {
+ {numstr2array} apply
+} def
+
+%%%%% ### fin insertion ###
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% macros de projection %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%% ### projtext ###
+%% syntaxe : str x0 y0 z0 [normal_vect] ultextp3d --> -
+%% syntaxe : str x0 y0 z0 [normal_vect] bool ultextp3d --> -
+%% syntaxe : str x0 y0 plantype ultextp3d --> -
+%% syntaxe : str x0 y0 plantype bool ultextp3d --> -
+%% syntaxe : str1 solid i str2 ultextp3d --> -
+%% syntaxe : str1 solid i str2 bool ultextp3d --> -
+%% syntaxe : str1 solid i alpha str2 bool ultextp3d --> -
+ /initpr@jtext {
+5 dict begin
+ dup isbool {
+ /mybool exch def
+ } {
+ /mybool true def
+ } ifelse
+ dup isplan {
+ /type_plan_proj true def
+ /lepl@n exch def
+ lepl@n plangetbase aload pop
+ /@V defpoint3d
+ /@U defpoint3d
+ lepl@n plangetorigine
+ /z0 exch def
+ /y0 exch def
+ /x0 exch def
+ /table [@U @U @V vectprod3d] def
+ } {
+ dup isarray {
+ %% c est un planprojpath
+ /type_plan_proj true def
+ /table exch def
+ /z0 exch def
+ /y0 exch def
+ /x0 exch def
+ 0 0
+ } {
+ %% c est un solidprojpath
+ /type_plan_proj false def
+ %% y a-t-il un str2
+ dup isstring {
+ /str2 exch def
+ } {
+ /str2 {} def
+ } ifelse
+ %% y a-t-il un alpha
+ 2 copy pop issolid {
+ /alpha 0 def
+ } {
+ /alpha exch def
+ } ifelse
+ /i exch def
+ /solid exch def
+ 0 0
+ } ifelse
+ } ifelse
+} def
+ /closepr@jtext {
+ type_plan_proj {
+ x0 y0 z0 table mybool projpath
+ } {
+ solid i alpha str2 mybool projpath
+ } ifelse
+ fill
+ stroke
+end
+} def
+
+%% syntaxe : str x0 y0 z0 [normal_vect] ultextp3d --> -
+%% syntaxe : str x0 y0 z0 [normal_vect] bool ultextp3d --> -
+%% syntaxe : str1 solid i str2 ultextp3d --> -
+%% syntaxe : str1 solid i str2 bool ultextp3d --> -
+%% syntaxe : str1 solid i alpha str2 bool ultextp3d --> -
+/ultextp3d {initpr@jtext ultext_ closepr@jtext} def
+/cltextp3d {initpr@jtext cltext_ closepr@jtext} def
+/bltextp3d {initpr@jtext bltext_ closepr@jtext} def
+/dltextp3d {initpr@jtext dltext_ closepr@jtext} def
+/ubtextp3d {initpr@jtext ubtext_ closepr@jtext} def
+/cbtextp3d {initpr@jtext cbtext_ closepr@jtext} def
+/bbtextp3d {initpr@jtext bbtext_ closepr@jtext} def
+/dbtextp3d {initpr@jtext dbtext_ closepr@jtext} def
+/uctextp3d {initpr@jtext uctext_ closepr@jtext} def
+/cctextp3d {initpr@jtext cctext_ closepr@jtext} def
+/bctextp3d {initpr@jtext bctext_ closepr@jtext} def
+/dctextp3d {initpr@jtext dctext_ closepr@jtext} def
+/urtextp3d {initpr@jtext urtext_ closepr@jtext} def
+/crtextp3d {initpr@jtext crtext_ closepr@jtext} def
+/brtextp3d {initpr@jtext brtext_ closepr@jtext} def
+/drtextp3d {initpr@jtext drtext_ closepr@jtext} def
+
+%%%%% ### currentppathtransform ###
+%% syntaxe : {f} currentppathtransform --> applique la transformation f
+%% au chemin courant
+/currentppathtransform {
+6 dict begin
+ /warp exch def
+ %% pour remplacer 'move'
+ /warpmove{
+ 2 index {
+ newpath
+ } if
+ warp moveto
+ pop false
+ } def
+
+ %% pour remplacer 'lineto'
+ /warpline {
+ warp lineto
+ } bind def
+
+ %% pour remplacer 'curveto'
+ /warpcurve {
+ 6 2 roll warp
+ 6 2 roll warp
+ 6 2 roll warp
+ curveto
+ } bind def
+
+ true
+ { warpmove } { warpline } { warpcurve } { closepath } pathforall
+ pop
+end
+} def
+
+%% syntaxe : {f} currentpathtransform --> applique la transformation f
+%% au chemin courant
+/currentpathtransform {
+7 dict begin
+ /transform exch def
+ /warp {ptojpoint transform} def
+ %% pour remplacer 'move'
+ /warpmove{
+ 2 index {
+ newpath
+ } if
+ warp smoveto
+ pop false
+ } def
+
+ %% pour remplacer 'lineto'
+ /warpline {
+ warp slineto
+ } bind def
+
+ %% pour remplacer 'curveto'
+ /warpcurve {
+ 6 2 roll warp
+ 6 2 roll warp
+ 6 2 roll warp
+ scurveto
+ } bind def
+
+ true
+ { warpmove } { warpline } { warpcurve } { closepath } pathforall
+ pop
+end
+} def
+
+%%%%% ### normalvect_to_orthobase ###
+%% syntaxe : [normal_vect] normalvect_to_orthobase
+%% --> imI imJ imK
+/normalvect_to_orthobase {
+4 dict begin
+ dup length 3 eq {
+ aload pop normalize3d /normal_vect defpoint3d
+ normal_vect -1 0 0 eqp3d {
+ /imageI {0 -1 0} def
+ /imageK {-1 0 0} def
+ /imageJ {0 0 1} def
+ } {
+ %% on calcule l image de la base (I,J,K)
+ /imageJ {normal_vect 1 0 0 vectprod3d normalize3d} def
+ /imageK {normal_vect} def
+ /imageI {imageJ imageK vectprod3d} def
+ 1 0 0 imageK angle3d 0 eq {
+ 0 1 0 normal_vect vectprod3d /imageI defpoint3d
+ /imageJ {0 1 0} def
+ normal_vect /imageK defpoint3d
+ } if
+ } ifelse
+ } {
+ dup length 6 eq {
+ aload pop
+ normalize3d /imageK defpoint3d
+ normalize3d /imageI defpoint3d
+ imageK imageI vectprod3d /imageJ defpoint3d
+ } {
+ dup length 7 eq {
+ aload pop
+ /alpha exch 2 div def
+ normalize3d /imageK defpoint3d
+ normalize3d /imageI defpoint3d
+ imageK imageI vectprod3d /imageJ defpoint3d
+ %% et ensuite, on fait tourner la base autour de imageK
+ imageI alpha cos mulv3d
+ imageJ alpha sin mulv3d
+ addv3d
+
+ imageI alpha sin neg mulv3d
+ imageJ alpha cos mulv3d
+ addv3d
+
+ /imageJ defpoint3d
+ /imageI defpoint3d
+ } {
+ %% length = 4
+ aload pop
+ /alpha exch def
+ normalize3d /normal_vect defpoint3d
+
+ normal_vect -1 0 0 eqp3d {
+ /imageI {0 -1 0} def
+ /imageK {-1 0 0} def
+ /imageJ {0 0 1} def
+ } {
+ %% on calcule l image de la base (I,J,K)
+ /imageJ {normal_vect 1 0 0 vectprod3d normalize3d} def
+ /imageK {normal_vect} def
+ /imageI {imageJ imageK vectprod3d} def
+ 1 0 0 imageK angle3d 0 eq {
+ 0 1 0 normal_vect vectprod3d /imageI defpoint3d
+ /imageJ {0 1 0} def
+ normal_vect /imageK defpoint3d
+ } if
+ } ifelse
+ } ifelse
+
+ %% et ensuite, on fait tourner la base autour de imageK
+ imageI alpha cos mulv3d
+ imageJ alpha sin mulv3d
+ addv3d
+
+ imageI alpha sin neg mulv3d
+ imageJ alpha cos mulv3d
+ addv3d
+
+ /imageJ defpoint3d
+ /imageI defpoint3d
+ } ifelse
+ } ifelse
+ imageI
+ imageJ
+ imageK
+end
+} def
+
+%%%%% ### projpath ###
+%% syntaxe : x y z [normal] projpath --> planprojpath
+%% syntaxe : x y z [normal] bool projpath --> planprojpath
+%% syntaxe : solid i projpath --> solidprojpath
+%% syntaxe : solid i bool projpath --> solidprojpath
+%% syntaxe : solid i str bool projpath --> solidprojpath
+%% syntaxe : solid i alpha str bool projpath --> solidprojpath
+/projpath {
+2 dict begin
+ dup isbool {
+ /mybool exch def
+ } {
+ /mybool true def
+ } ifelse
+ dup isplan {
+ 3 dict begin
+ /lepl@n exch def
+ lepl@n plangetbase aload pop
+ /@V defpoint3d
+ /@U defpoint3d
+ lepl@n plangetorigine
+ [@U @U @V vectprod3d] mybool planprojpath
+ end
+ } {
+ dup isarray {
+ mybool planprojpath
+ } {
+ mybool solidprojpath
+ } ifelse
+ } ifelse
+end
+} def
+
+
+%% %% syntaxe : x y z [normal] projpath --> planprojpath
+%% %% syntaxe : x y z [normal] bool projpath --> planprojpath
+%% %% syntaxe : solid i projpath --> solidprojpath
+%% %% syntaxe : solid i bool projpath --> solidprojpath
+%% %% syntaxe : solid i str bool projpath --> solidprojpath
+%% %% syntaxe : solid i alpha str bool projpath --> solidprojpath
+%% /projpath {
+%% 2 dict begin
+%% dup isbool {
+%% /mybool exch def
+%% } {
+%% /mybool true def
+%% } ifelse
+%% dup isarray {
+%% mybool planprojpath
+%% } {
+%% mybool solidprojpath
+%% } ifelse
+%% end
+%% } def
+%%
+%% syntaxe : solid i str bool solidprojpath --> -
+%% ou
+%% syntaxe : solid i alpha str bool solidprojpath --> -
+%% projette le chemin courant sur la face i du solide, apres
+%% eventuellement une rotation d angle alpha autour de la normale
+%% bool : pour savoir si on tient compte de la visibilite
+/solidprojpath {
+5 dict begin
+ /visibility exch def
+ dup isstring {
+ /option exch def
+ } if
+ 2 copy pop
+ issolid {
+ /alpha 0 def
+ } {
+ /alpha exch def
+ } ifelse
+ /i exch def
+ /solid exch def
+ solid issolid not {
+ (Error : mauvais type d argument dans solidprojpath) ==
+ } if
+ /n solid solidnombrefaces def
+ i n 1 sub le {
+ visibility not solid i solidfacevisible? or {
+ currentdict /option known {
+ option cvx exec
+ } {
+ solid i solidcentreface
+ } ifelse
+ [
+ solid 0 i solidgetsommetface
+ solid 1 i solidgetsommetface
+ vecteur3d normalize3d
+ solid i solidnormaleface alpha
+ ] false planprojpath
+ } {
+ newpath 0 0 smoveto
+ } ifelse
+ } {
+ (Error : indice trop grand dans solidprojpath) ==
+ quit
+ } ifelse
+end
+} def
+
+%% syntaxe : x y z [normal] bool planprojpath
+/planprojpath {
+6 dict begin
+ /visibility exch def
+ %% on calcule l image de la base (I,J,K)
+ normalvect_to_orthobase
+ /imageK defpoint3d
+ /imageJ defpoint3d
+ /imageI defpoint3d
+ /z exch def
+ /y exch def
+ /x exch def
+
+ visibility not x y z imageK planvisible? or {
+ {ptojpoint 0
+ imageI
+ imageJ
+ imageK
+ transformpoint3d
+ x y z addv3d
+ 3dto2d jtoppoint} currentppathtransform
+ } {
+ newpath
+ } ifelse
+end
+} def
+
+%%%%% ### projscene ###
+%% syntaxe : plantype bool bprojscene ... eprojscene
+/bprojscene {
+10 dict begin
+gsave
+ dup isbool {
+ /mybool exch def
+ } {
+ /mybool true def
+ } ifelse
+ /l@pl@n exch def
+ /savestroke {SolidesDict /stroke get exec} def
+ /stroke {l@pl@n mybool projpath savestroke} def
+ /savefill {SolidesDict /fill get exec} def
+ /fill {l@pl@n mybool projpath savefill} def
+ /masque {} def
+ l@pl@n plangetrange aload pop
+ setyrange setxrange
+ newpath
+%% xmin ymin l@pl@n pointplan smoveto
+%% xmin ymax l@pl@n pointplan slineto
+%% xmax ymax l@pl@n pointplan slineto
+%% xmax ymin l@pl@n pointplan slineto
+%% xmin ymin l@pl@n pointplan smoveto
+%% % closepath
+%% %gsave orange fill grestore
+%% clip
+} def
+/eprojscene {
+grestore
+end
+} def
+
+%%%%% ### fin insertion ###
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% fonctions numeriques %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%% ### courbeparam ###
+/setresolution {
+ /resolution exch def
+} def
+/resolution 200 def
+
+/courbe_dic 2 dict def
+courbe_dic /X {} put
+courbe_dic /Y {} put
+
+%% syntaxe : tmin tmax C@urbeparam_
+ /C@urbeparam_ {
+6 dict begin
+ /tmax@ exch def
+ /tmin@ exch def
+ /t tmin@ def
+ /dt tmax@ tmin@ sub resolution 1 sub div def
+ tmin@ courbe_dic /X get exec
+ pstrickactionR
+ tmin@ courbe_dic /Y get exec
+ pstrickactionR
+ smoveto
+ resolution 1 sub
+ {
+ t courbe_dic /X get exec
+ pstrickactionR
+ t courbe_dic /Y get exec
+ pstrickactionR
+ slineto
+
+ /t t dt add store %% on incremente
+ }
+ repeat
+ tmax@ courbe_dic /X get exec
+ pstrickactionR
+ tmax@ courbe_dic /Y get exec
+ pstrickactionR
+ slineto
+end
+} def
+
+%% syntaxe : tmin tmax {X} {Y} Courbeparam_
+/Courbeparam_ {
+ courbe_dic exch /Y exch put
+ courbe_dic exch /X exch put
+ C@urbeparam_
+} def
+
+%% syntaxe : {X} {Y} courbeparam_
+/courbeparam_ {
+ tmin tmax
+ 4 -1 roll
+ 4 -1 roll
+ Courbeparam_
+} def
+
+%% syntaxe : tmin tmax {X} {Y} Courbeparam
+/Courbeparam {
+gsave
+6 dict begin
+ dup isstring
+ {
+ /option exch def
+ }
+ if
+ courbe_dic exch /Y exch put
+ courbe_dic exch /X exch put
+ /tmax exch def
+ /tmin exch def
+
+ newpath
+ tmin courbe_dic /X get exec
+ pstrickactionR
+ tmin courbe_dic /Y get exec
+ pstrickactionR
+ smoveto %% on commence le chemin
+ tmin tmax C@urbeparam_
+ starfill
+
+ stockcurrentcpath
+ newarrowpath
+ currentdict /option known
+ {
+ /dt tmax tmin sub resolution 1 sub div def
+ tmin dt add courbe_dic /X get exec
+ tmin dt add courbe_dic /Y get exec
+ tmin courbe_dic /X get exec
+ tmin courbe_dic /Y get exec
+ arrowpath0
+ tmax dt sub courbe_dic /X get exec
+ tmax dt sub courbe_dic /Y get exec
+ tmax courbe_dic /X get exec
+ tmax courbe_dic /Y get exec
+ currentdict /dt undef
+ arrowpath1
+ option
+ gere_arrowhead
+ }
+ if
+
+ currentlinewidth 0 eq {} {stroke} ifelse
+
+end
+grestore
+} def
+
+%% syntaxe : {X} {Y} courbeparam
+/courbeparam {
+ dup isstring
+ {
+ tmin tmax
+ 5 -1 roll
+ 5 -1 roll
+ 5 -1 roll
+ }
+ {
+ tmin tmax
+ 4 -1 roll
+ 4 -1 roll
+ }
+ ifelse
+ Courbeparam
+} def
+
+%% syntaxe : tmin tmax {X} {Y} Courbeparam*
+/Courbeparam* {
+1 dict begin
+ /startest {true} def
+ Courbeparam
+end
+} def
+
+%% syntaxe : {X} {Y} courbeparam*
+/courbeparam* {
+1 dict begin
+ /startest {true} def
+ courbeparam
+end
+} def
+
+%%%%% ### courbe ###
+%% syntaxe : {f} courbe
+/courbe {
+ dup isstring %% y a-t-il une option de fin de ligne ?
+ {
+ xmin xmax
+ {}
+ 5 -1 roll
+ 5 -1 roll
+ }
+ {
+ xmin xmax
+ {}
+ 4 -1 roll
+ }
+ ifelse
+ Courbeparam
+} def
+
+%% syntaxe : mini maxi {f} Courbe
+/Courbe {
+ dup isstring {
+ {}
+ 3 -1 roll
+ 3 -1 roll
+ } {
+ {}
+ 2 -1 roll
+ } ifelse
+ Courbeparam
+} def
+
+%% syntaxe : {f} courbe_
+/courbe_ {
+ xmin xmax
+ {}
+ 4 -1 roll
+ Courbeparam_
+} def
+
+%% syntaxe : mini maxi {f} Courbe_
+/Courbe_ {
+ {}
+ 2 -1 roll
+ Courbeparam_
+} def
+
+%% syntaxe : mini maxi {f} Courbe*
+/Courbe* {
+1 dict begin
+ /startest {true} def
+ Courbe
+end
+} def
+
+%% syntaxe : {f} courbe*
+/courbe* {
+1 dict begin
+ /startest {true} def
+ courbe
+end
+} def
+
+%%%%% ### courbeR2 ###
+%% syntaxe : tmin tmax C@urbeR2_
+ /C@urbeR2_ {
+6 dict begin
+ /tmax@ exch def
+ /tmin@ exch def
+ /t tmin@ def
+ /dt tmax@ tmin@ sub resolution 1 sub div def
+ tmin@ courbe_dic /X get exec
+ pstrickactionR2
+ smoveto
+ /t t dt add store
+ resolution 2 sub
+ {
+ t courbe_dic /X get exec
+ pstrickactionR2
+ slineto
+ /t t dt add store %% on incremente
+ }
+ repeat
+ tmax@ courbe_dic /X get exec
+ pstrickactionR2
+ slineto
+end
+} def
+
+%% syntaxe : tmin tmax {X} CourbeR2_
+/CourbeR2_ {
+ courbe_dic exch /X exch put
+ C@urbeR2_
+} def
+
+%% syntaxe : {X} courbeR2_
+/courbeR2_ {
+ tmin tmax
+ 3 -1 roll
+ 3 -1 roll
+ CourbeR2_
+} def
+
+%% syntaxe : tmin tmax {X} CourbeR2
+/CourbeR2+ {
+2 dict begin
+ /slineto {} def
+ /smoveto {} def
+ CourbeR2
+end
+} bind def
+
+/CourbeR2 {
+gsave
+6 dict begin
+ dup isstring
+ {
+ /option exch def
+ }
+ if
+ courbe_dic exch /X exch put
+ /tmax exch def
+ /tmin exch def
+
+ newpath
+ tmin tmax C@urbeR2_
+ starfill
+ currentlinewidth 0 eq {} {stroke} ifelse
+
+end
+grestore
+} def
+
+%% syntaxe : {X} courbeR2
+/courbeR2 {
+ tmin tmax
+ 3 -1 roll
+ CourbeR2
+} def
+
+%% syntaxe : tmin tmax {X} CourbeR2*
+/CourbeR2* {
+1 dict begin
+ /startest {true} def
+ CourbeR2
+end
+} def
+
+%% syntaxe : {X} {Y} courbeR2*
+/courbeR2* {
+1 dict begin
+ /startest {true} def
+ courbeR2
+end
+} def
+
+%%%%% ### courbeR3 ###
+%% syntaxe : t1 t2 {f} (option) CourbeR3
+/CourbeR3 {
+2 dict begin
+ dup isstring {
+ /option exch def
+ } if
+ /lafonction exch def
+ {lafonction 3dto2d}
+ currentdict /option known
+ {option}
+ if
+ CourbeR2
+end
+} def
+
+%% syntaxe : {f} (option) CourbeR3
+/courbeR3 {
+ tmin tmax 3 -1 roll CourbeR3
+} def
+
+%%%%% ### cercle ###
+%% syntaxe : x0 y0 r cercle
+/cercle {
+3 dict begin
+ /r@y@n exch def
+ /y@ exch def
+ /x@ exch def
+ 0 360 {cos r@y@n mul x@ add} {sin r@y@n mul y@ add} Courbeparam
+end
+} def
+
+%% syntaxe : x0 y0 r cercle_
+/cercle_ {
+3 dict begin
+ /r@y@n exch def
+ /y@ exch def
+ /x@ exch def
+ x@ r@y@n add y@ smoveto
+ 0 360 {cos r@y@n mul x@ add} {sin r@y@n mul y@ add} Courbeparam_
+end
+} def
+
+%% syntaxe : x0 y0 r cercle-_
+/cercle-_ {
+3 dict begin
+ /r@y@n exch def
+ /y@ exch def
+ /x@ exch def
+ x@ r@y@n add y@ smoveto
+ 360 0 {cos r@y@n mul x@ add} {sin r@y@n mul y@ add} Courbeparam_
+end
+} def
+
+%% syntaxe : x0 y0 r cercle*
+/cercle* {
+1 dict begin
+ /startest true def
+ cercle
+end
+} def
+
+%% syntaxe : alpha beta x0 y0 r Cercle
+/Cercle {
+4 dict begin
+ dup isstring
+ {/option exch def}
+ if
+ /r@y@n exch def
+ /y@ exch def
+ /x@ exch def
+ {cos r@y@n mul x@ add} {sin r@y@n mul y@ add}
+ currentdict /option known
+ {option}
+ if
+ Courbeparam
+end
+} def
+
+%% syntaxe : alpha beta x0 y0 r Cercle_
+/Cercle_ {
+3 dict begin
+ /r@y@n exch def
+ /y@ exch def
+ /x@ exch def
+ {cos r@y@n mul x@ add} {sin r@y@n mul y@ add} Courbeparam_
+end
+} def
+
+%% syntaxe : alpha beta x0 y0 r Cercle
+/Cercle* {
+1 dict begin
+ /startest {true} def
+ Cercle
+end
+} def
+
+%%%%% ### fin insertion ###
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% fonctions et constantes mathematiques %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%% ### math ###
+%%%%%%%%%%% constantes mathematiques %%%%%%%%%%%%%%
+
+/pi 3.14159 def
+/e 2.71828 def
+
+%%%%%%%%%%% fonctions mathematiques %%%%%%%%%%%%%%%
+
+/rd {180 pi div mul} def %% transforme des rd en degres
+/deg {pi mul 180 div} def %% transforme des degres en rd
+/log {ln 10 ln div} def
+/Exp {e exch exp} def
+/Cos {rd cos} def
+/Sin {rd sin} def
+/tan {dup sin exch cos div} def
+/cotan {dup cos exch sin div} def
+/Tan {dup Sin exch Cos div} def
+/Cotan {dup Cos exch Sin div} def
+/coTan {Cotan} def
+/arctan {
+dup 0 ge
+ {1 atan}
+ {neg 1 atan neg}
+ifelse
+} def
+/Arctan {arctan deg} def
+/arccos {
+ dup
+ dup mul neg 1 add sqrt
+ exch
+ atan
+} def
+/Arccos {arccos deg} def
+/arcsin {
+ dup 1 eq {
+ 90
+ } {
+ dup
+ dup mul neg 1 add sqrt
+ atan
+ dup 90 lt
+ {}
+ {360 sub}
+ ifelse
+ } ifelse
+} def
+/Arcsin {arcsin deg} def
+/cosh {dup Exp exch neg Exp add 2 div} def
+/sinh {dup Exp exch neg Exp sub 2 div} def
+/tanh {dup sinh exch cosh div} def
+/cotanh {dup cosh exch sinh div} def
+/argcosh {dup dup mul 1 sub sqrt add ln} def
+/argsinh {dup dup mul 1 add sqrt add ln} def
+/argtanh {
+ setxvar
+ x 1 add
+ 1 x sub
+ div
+ ln
+ 2 div
+} def
+/factorielle {
+ dup 0 eq
+ {pop 1}
+ {dup 1 sub factorielle mul}
+ ifelse
+} def
+/Gauss {
+3 dict begin
+ /sigma exch def
+ /m exch def
+ /x exch def
+ x m sub dup mul sigma dup mul 2 mul div neg Exp
+ 2 pi mul sigma dup mul mul sqrt div
+end
+} def
+%% syntaxe : a n modulo
+/modulo {
+2 dict begin
+ /n exch def
+ /a exch def
+ {
+ a 0 lt {
+ /a a n add store
+ } {
+ exit
+ } ifelse
+ } loop
+ a n mod
+end
+} def
+
+%%%%% ### max ###
+/max {
+ 2 copy
+ lt {exch} if
+ pop
+} def
+
+%%%%% ### min ###
+/min {
+2 dict begin
+ dup isarray {
+ duparray /table exch def pop
+ table 0 get
+ 1 1 table length 1 sub {
+ /i exch def
+ table i get
+ min
+ } for
+ } {
+ 2 copy
+ gt {exch} if
+ pop
+ } ifelse
+end
+} def
+
+%%%%% ### setcolor ###
+%% syntaxe : tableau setcolor
+/setcolor {
+ dup length 4 eq
+ {aload pop setcmykcolor}
+ {aload pop setrgbcolor}
+ ifelse
+} def
+
+%%%%% ### in ###
+%% cherche si un elt donne appartient au tableau donne
+%% rque : utilise 3 variables locales
+%% syntaxe : elt array in --> index boolean
+/in {
+3 dict begin
+ /liste exch def
+ /elt exch def
+ /i 0 def
+ false %% la reponse a priori
+ liste length {
+ liste i get elt eq {
+ pop %% en enleve la reponse
+ i true %% pour mettre la bonne
+ exit
+ } if
+ /i i 1 add store
+ } repeat
+end
+} def
+
+%% cherche si un elt donne appartient au tableau donne
+%% syntaxe : elt array in --> boolean
+/In {
+3 dict begin
+ /liste exch def
+ /elt exch def
+ /i 0 def
+ false %% la reponse a priori
+ liste length {
+ liste i get elt eq {
+ pop %% en enleve la reponse
+ true %% pour mettre la bonne
+ exit
+ } if
+ /i i 1 add store
+ } repeat
+end
+} def
+
+%%%%% ### starfill ###
+%% la procedure pour les objets "star"
+%% si c est "star" on fait le fillstyle, sinon non
+/starfill {
+ startest {
+ gsave
+ clip
+ fillstyle
+ grestore
+ /startest false def
+ } if
+} def
+
+%%%%% ### addv ###
+%% syntaxe : u v addv --> u+v
+/addv { %% xA yA xB yB
+ 3 1 roll %% xA yB yA xB
+ 4 1 roll %% xB xA yB yA
+ add 3 1 roll %% yB+yA xB xA
+ add exch
+} def
+
+%%%%% ### continu ###
+/continu {
+ [] 0 setdash
+} def
+
+%%%%% ### trigospherique ###
+%% passage spherique --> cartesiennes
+%% les formules de passage ont été récupérées ici :
+%% http://fr.wikipedia.org/wiki/Coordonn%C3%A9es_polaires
+%% syntaxe : r theta phi rtp2xyz -> x y z
+/rtp2xyz {
+6 dict begin
+ /phi exch def
+ /theta exch def
+ /r exch def
+ /x phi cos theta cos mul r mul def
+ /y phi cos theta sin mul r mul def
+ /z phi sin r mul def
+ x y z
+end
+} def
+
+%% trace d'un arc sur une sphere de centre O
+%% syntaxe : r theta1 phi1 r theta2 phi2 arcspherique
+/arcspherique {
+9 dict begin
+ dup isstring {
+ /option exch def
+ } if
+ /phi2 exch def
+ /theta2 exch def
+ pop
+ /phi1 exch def
+ /theta1 exch def
+ /r exch def
+ /n 12 def
+
+ 1 theta1 phi1 rtp2xyz /u defpoint3d
+ 1 theta2 phi2 rtp2xyz /v defpoint3d
+ u v vectprod3d u vectprod3d dupp3d norme3d 1 exch div mulv3d /w defpoint3d
+
+ /sinalpha u v vectprod3d norme3d def
+ /cosalpha u v scalprod3d def
+ /alpha sinalpha cosalpha atan def
+ /n 12 def
+ /pas alpha n div def
+
+ gsave
+ /t pas neg def
+ [
+ n 1 add {
+ /t t pas add store
+ u t cos r mul mulv3d
+ w t sin r mul mulv3d
+ addv3d
+ } repeat
+ ]
+ currentdict /option known {
+ option
+ } if
+ ligne3d
+ grestore
+end
+} def
+
+%% trace d'un arc sur une sphere de centre O
+%% syntaxe : r theta1 phi1 r theta2 phi2 arcspherique
+/arcspherique_ {
+8 dict begin
+ /phi2 exch def
+ /theta2 exch def
+ pop
+ /phi1 exch def
+ /theta1 exch def
+ /r exch def
+ /n 12 def
+
+ 1 theta1 phi1 rtp2xyz /u defpoint3d
+ 1 theta2 phi2 rtp2xyz /v defpoint3d
+ u v vectprod3d u vectprod3d dupp3d norme3d 1 exch div mulv3d /w defpoint3d
+
+ /sinalpha u v vectprod3d norme3d def
+ /cosalpha u v scalprod3d def
+ /alpha sinalpha cosalpha atan def
+ /n 12 def
+ /pas alpha n div def
+
+ /t pas neg def
+ [
+ n 1 add {
+ /t t pas add store
+ u t cos r mul mulv3d
+ w t sin r mul mulv3d
+ addv3d
+ } repeat
+ ] ligne3d_
+end
+} def
+
+%% trace d'une geodesique sur une sphere de centre O
+%% syntaxe : r theta1 phi1 r theta2 phi2 geodesique_sphere
+/geodesique_sphere {
+13 dict begin
+ /phi2 exch def
+ /theta2 exch def
+ pop
+ /phi1 exch def
+ /theta1 exch def
+ /r exch def
+ /n 360 def
+
+ 1 theta1 phi1 rtp2xyz /u defpoint3d
+ 1 theta2 phi2 rtp2xyz /v defpoint3d
+ u v vectprod3d u vectprod3d dupp3d norme3d 1 exch div mulv3d /w defpoint3d
+
+ /sinalpha u v vectprod3d norme3d def
+ /cosalpha u v scalprod3d def
+ /alpha sinalpha cosalpha atan def
+ /pas 360 n div def
+
+ gsave
+ /t pas neg def
+ [
+ n 1 add {
+ /t t pas add store
+ u t cos r mul mulv3d
+ w t sin r mul mulv3d
+ addv3d
+ } repeat
+ ] ligne3d
+ grestore
+end
+} def
+
+
+%% syntaxe : A B C trianglespherique --> trace le rtiangle ABC
+%% (coordonnees spheriques)
+/trianglespherique* {
+1 dict begin
+ /startest {true} def
+ trianglespherique
+end
+} def
+
+/trianglespherique {
+10 dict begin
+ /C defpoint3d
+ /B defpoint3d
+ /A defpoint3d
+ gsave
+ newpath
+ A rtp2xyz 3dto2d smoveto
+ A B arcspherique_
+ B C arcspherique_
+ C A arcspherique_
+ closepath
+ starfill
+ currentlinewidth 0 eq {} {stroke} ifelse
+ grestore
+end
+} def
+
+%%%%% ### fin insertion ###
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% operations sur les tableaux %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%% ### duparray ###
+/duparray {
+1 dict begin
+ /table exch def
+ table
+ [ table aload pop ]
+end
+} def
+
+%%%%% ### append ###
+%% syntaxe : string1 string2 append --> concatene les 2 chaines ou fusionne 2 tableaux
+/append {
+3 dict begin
+ dup isarray {
+ /tab2 exch def
+ /tab1 exch def
+ [ tab1 aload pop tab2 aload pop ]
+ } {
+ /str2 exch def
+ /str1 exch def
+ /result str1 length str2 length add string def
+ str1 result copy pop
+ result str1 length str2 putinterval
+ result
+ } ifelse
+end
+} def
+
+%%%%% ### rollparray ###
+%% syntaxe : array n rollparray -> array
+%% opere une rotation de n sur les couplets du tableau array
+/rollparray {
+4 dict begin
+ /k exch def
+ /table exch def
+ /n table length def
+ k 0 eq {
+ table
+ } {
+ k 0 ge {
+ [ table aload pop 2 {n 1 roll} repeat ]
+ k 1 sub
+ } {
+ [ table aload pop 2 {n -1 roll} repeat ]
+ k 1 add
+ } ifelse
+ rollparray
+ } ifelse
+end
+} def
+
+%%%%% ### bubblesort ###
+%% syntaxe : 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
+
+%% syntaxe : array1 doublebubblesort --> array2 array3, array3 est
+%% trie par ordre croissant et array2 correspond a la position des
+%% indices de depart, ie si array1 = [3 2 4 1], alors array2 = [3 1 0 2]
+%% code de Bill Casselman, modifie par jpv, 15/08/2006
+%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/
+/doublebubblesort {
+5 dict begin
+ /table exch def
+ /n table length 1 sub def
+ /indices [ 0 1 n {} for ] 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
+ table i get table i 1 add get gt {
+ % if a[i] > a[i+1] swap a[i] and a[i+1]
+ table i 1 add
+ table i get
+ table i table i 1 add get
+ % set new a[i] = old a[i+1]
+ put
+ % set new a[i+1] = old a[i]
+ put
+
+ indices i 1 add
+ indices i get
+ indices i indices 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
+ indices table
+end
+} def
+
+%%%%% ### quicksort ###
+%% src : http://www.math.ubc.ca/~cass/graphics/text/www/code/sort.inc
+%% code de Bill Casselman, modifie par jpv, 18/10/2007
+
+/qsortdict 8 dict def
+
+qsortdict begin
+
+% args: /comp a L R x
+% effect: effects a partition into two pieces [L j] [i R]
+% leaves i j on stack
+
+/partition { 8 dict begin
+/x exch def
+/j exch def
+/i exch def
+/a exch def
+load /comp exch def
+{
+ {
+ a i get x comp exec not {
+ exit
+ } if
+ /i i 1 add def
+ } loop
+ {
+ x a j get comp exec not {
+ exit
+ } if
+ /j j 1 sub def
+ } loop
+
+ i j le {
+ % swap a[i] a[j]
+ a j a i get
+ a i a j get
+ put put
+ indices j indices i get
+ indices i indices j get
+ put put
+ /i i 1 add def
+ /j j 1 sub def
+ } if
+ i j gt {
+ exit
+ } if
+} loop
+i j
+end } def
+
+% args: /comp a L R
+% effect: sorts a[L .. R] according to comp
+
+/subsort {
+% /c a L R
+[ 3 1 roll ] 3 copy
+% /c a [L R] /c a [L R]
+aload aload pop
+% /c a [L R] /c a L R L R
+add 2 idiv
+% /c a [L R] /c a L R (L+R)/2
+3 index exch get
+% /c a [L R] /c a L R x
+partition
+% /c a [L R] i j
+% if j > L subsort(a, L, j)
+dup
+% /c a [L R] i j j
+3 index 0 get gt {
+ % /c a [L R] i j
+ 5 copy
+ % /c a [L R] i j /c a [L R] i j
+ exch pop
+ % /c a [L R] i j /c a [L R] j
+ exch 0 get exch
+ % ... /c a L j
+ subsort
+} if
+% /c a [L R] i j
+pop dup
+% /c a [L R] i i
+% if i < R subsort(a, i, R)
+2 index 1 get lt {
+ % /c a [L R] i
+ exch 1 get
+ % /c a i R
+ subsort
+}{
+ 4 { pop } repeat
+} ifelse
+} def
+
+end
+
+% args: /comp a
+% effect: sorts the array a
+% comp returns truth of x < y for entries in a
+
+/quicksort { qsortdict begin
+dup length 1 gt {
+% /comp a
+dup
+% /comp a a
+length 1 sub
+% /comp a n-1
+0 exch subsort
+} {
+pop pop
+} ifelse
+end } def
+
+% ----------------------------------------
+
+%% fin du code de Bill Casselman
+
+%% syntaxe : array1 doublebubblesort --> array2 array3, array3 est
+%% trie par ordre croissant et array2 correspond a la position des
+%% indices de depart, ie si array1 = [3 2 4 1], alors array2 = [3 1 0 2]
+%% code de Bill Casselman, modifie par jpv, 18/10/2007
+%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/
+/doublequicksort {
+qsortdict begin
+ /comp exch
+ /a exch def
+ a dup length /n exch def
+ /indices [0 1 n 1 sub {} for ] def
+ dup length 1 gt {
+ % /comp a
+ dup
+ % /comp a a
+ length 1 sub
+ % /comp a n-1
+ 0 exch subsort
+ } {
+ pop pop
+ } ifelse
+ indices a
+end
+} def
+
+/comp {lt} def
+
+%%%%% ### apply ###
+%% syntaxe : [x1 ... xn] (f) apply --> [f(x1) ... f(xn)]
+/apply {
+3 dict begin
+ dup isstring
+ {/fonction exch cvx def}
+ {/fonction exch def}
+ ifelse
+ /liste exch def
+ /@i 0 def
+ [
+ liste length {
+ liste @i get fonction
+ /@i @i 1 add store
+ } repeat
+ counttomark
+ 0 eq
+ {pop}
+ {]}
+ ifelse
+end
+} def
+
+%% syntaxe : [x1 ... xn] (f) papply
+/papply {
+3 dict begin
+ dup isstring
+ {/fonction exch cvx def}
+ {/fonction exch def}
+ ifelse
+ /liste exch def
+ /@i 0 def
+ [
+ liste length 2 idiv {
+ liste @i get
+ liste @i 1 add get
+ fonction
+ /@i @i 2 add store
+ } repeat
+ counttomark
+ 0 eq
+ {pop}
+ {]}
+ ifelse
+end
+} def
+
+%% syntaxe : [x1 ... xn] (f) capply
+/capply {
+3 dict begin
+ dup isstring
+ {/fonction exch cvx def}
+ {/fonction exch def}
+ ifelse
+ /liste exch def
+ /@i 0 def
+ [
+ liste length 3 idiv {
+ liste @i get
+ liste @i 1 add get
+ liste @i 2 add get
+ fonction
+ /@i @i 3 add store
+ } repeat
+ counttomark
+ 0 eq
+ {pop}
+ {]}
+ ifelse
+end
+} def
+
+%%%%% ### reverse ###
+%% syntaxe : array reverse --> inverse l ordre des items dans
+%% le tableau
+/reverse {
+3 dict begin
+ /le_tableau exch def
+ /n le_tableau length def
+ /i n 1 sub def
+ [
+ n {
+ le_tableau i get
+ /i i 1 sub store
+ } repeat
+ ]
+end
+} def
+
+%% syntaxe : array_points reversep --> inverse l ordre des points dans
+%% le tableau
+/reversep {
+3 dict begin
+ /le_tableau exch def
+ /n le_tableau length 2 idiv def
+ /i n 1 sub def
+ [
+ n {
+ le_tableau i getp
+ /i i 1 sub store
+ } repeat
+ ]
+end
+} def
+
+%%%%% ### get ###
+%% syntaxe : array_points n getp --> le n-ieme point du tableau de
+%% points array_points
+/getp {
+ 2 copy
+ 2 mul get
+ 3 1 roll
+ 2 mul 1 add get
+} def
+
+%%%%% ### fin insertion ###
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% matrices %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%% ### linear ###
+%% syntaxe : M i j any --> depose any dans M en a_ij
+/put_ij {
+5 dict begin
+ /a exch def
+ /j exch def
+ /i exch def
+ /M exch def
+ /L M i get_Li def
+ L j a put
+ M i L put_Li
+end
+} def
+
+%% syntaxe : M i j get_ij --> le coeff c_ij
+/get_ij {
+ 3 1 roll %% j M i
+ get_Li %% j L_i
+ exch get
+} def
+
+%% syntaxe : M i L put_Li --> remplace dans M la ligne Li par L
+/put_Li {
+ put
+} def
+
+%% syntaxe : M i get_Li --> la ligne Li de M
+/get_Li {
+ get
+} def
+
+%%%%% ### fin insertion ###
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% geometrie 3d (calculs) %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%% ### sortp3d ###
+/sortp3d {
+6 dict begin
+ /M1 defpoint3d
+ /M0 defpoint3d
+ M1
+ /z1 exch def
+ /y1 exch def
+ /x1 exch def
+ M0
+ /z0 exch def
+ /y0 exch def
+ /x0 exch def
+ x0 x1 lt {
+ M0 M1
+ } {
+ x0 x1 gt {
+ M1 M0
+ } {
+ y0 y1 lt {
+ M0 M1
+ } {
+ y0 y1 gt {
+ M1 M0
+ } {
+ z0 z1 lt {
+ M0 M1
+ } {
+ M1 M0
+ } ifelse
+ } ifelse
+ } ifelse
+ } ifelse
+ } ifelse
+end
+} def
+
+%%%%% ### dupp3d ###
+%% duplique le vecteur 3d
+/dupp3d { %% x y z
+ 3 copy
+} def
+/dupv3d {dupp3d} def
+
+%%%%% ### angle3d ###
+%% syntaxe : vect1 vect2 angle3d
+/angle3d {
+4 dict begin
+ normalize3d /vect2 defpoint3d
+ normalize3d /vect1 defpoint3d
+ /cosalpha vect1 vect2 scalprod3d def
+ /sinalpha vect1 vect2 vectprod3d norme3d def
+ sinalpha cosalpha atan
+end
+} def
+
+%%%%% ### transformpoint3d ###
+%% syntaxe : x y z a11 a21 a31 a12 a22 a32 a13 a23 a33
+%% transformpoint3d -> X Y Z
+/transformpoint3d {
+12 dict begin
+ /a33 exch def
+ /a23 exch def
+ /a13 exch def
+ /a32 exch def
+ /a22 exch def
+ /a12 exch def
+ /a31 exch def
+ /a21 exch def
+ /a11 exch def
+ /z exch def
+ /y exch def
+ /x exch def
+ a11 x mul a12 y mul add a13 z mul add
+ a21 x mul a22 y mul add a23 z mul add
+ a31 x mul a32 y mul add a33 z mul add
+end
+} def
+
+%%%%% ### normalize3d ###
+%% rend le vecteur 3d unitaire. Ne fait rien si u=0
+/unitaire3d { %% x y z
+2 dict begin
+ /u defpoint3d
+ /norme u norme3d def
+ norme 0 eq {
+ u
+ } {
+ u 1 norme div mulv3d
+ } ifelse
+end
+} def
+/normalize3d {unitaire3d} def
+
+%%%%% ### geom3d ###
+%% syntaxe : A k1 B k2 barycentre3d -> G, barycentre du systeme
+%% [(A, k1) (B, k2)]
+/barycentre3d {
+4 dict begin
+ /k2 exch def
+ /B defpoint3d
+ /k1 exch def
+ /A defpoint3d
+ A k1 mulv3d
+ B k2 mulv3d
+ addv3d
+ 1 k1 k2 add div mulv3d
+end
+} def
+
+%% syntaxe : array isobarycentre3d --> G
+/isobarycentre3d {
+2 dict begin
+ /table exch def
+ /n table length 3 idiv def
+ table 0 getp3d
+ 1 1 n 1 sub {
+ table exch getp3d
+ addv3d
+ } for
+ 1 n div mulv3d
+end
+} def
+
+%% syntaxe : M A alpha hompoint3d -> le point M' tel que AM' = alpha AM
+/hompoint3d {
+3 dict begin
+ /alpha exch def
+ /A defpoint3d
+ /M defpoint3d
+ A M vecteur3d alpha mulv3d A addv3d
+end
+} def
+
+%% syntaxe : M A sympoint3d -> le point M' tel que AM' = -AM
+/sympoint3d {
+2 dict begin
+ /A defpoint3d
+ /M defpoint3d
+ A M vecteur3d -1 mulv3d A addv3d
+end
+} def
+
+%% syntaxe : A u translatepoint3d --> B image de A par la translation de vecteur u
+/translatepoint3d {
+ addv3d
+} def
+
+/scaleOpoint3d {
+6 dict begin
+ /k3 exch def
+ /k2 exch def
+ /k1 exch def
+ /z exch def
+ /y exch def
+ /x exch def
+ k1 x mul
+ k2 y mul
+ k3 z mul
+end
+} def
+
+% syntaxe : M alpha_x alpha_y alpha_z rotateOpoint3d --> M'
+/rotateOpoint3d {
+21 dict begin
+ /RotZ exch def
+ /RotY exch def
+ /RotX exch def
+ /Zpoint exch def
+ /Ypoint exch def
+ /Xpoint exch def
+ /c1 {RotX cos} bind def
+ /c2 {RotY cos} bind def
+ /c3 {RotZ cos} bind def
+ /s1 {RotX sin} bind def
+ /s2 {RotY sin} bind def
+ /s3 {RotZ sin} bind def
+ /M11 {c2 c3 mul} bind def
+ /M12 {c3 s1 mul s2 mul c1 s3 mul sub} bind def
+ /M13 {c1 c3 mul s2 mul s1 s3 mul add} bind def
+ /M21 {c2 s3 mul} bind def
+ /M22 {s1 s2 mul s3 mul c1 c3 mul add} bind def
+ /M23 {s3 s2 mul c1 mul c3 s1 mul sub} bind def
+ /M31 {s2 neg} bind def
+ /M32 {s1 c2 mul} bind def
+ /M33 {c1 c2 mul} bind def
+ M11 Xpoint mul M12 Ypoint mul add M13 Zpoint mul add
+ M21 Xpoint mul M22 Ypoint mul add M23 Zpoint mul add
+ M31 Xpoint mul M32 Ypoint mul add M33 Zpoint mul add
+end
+} def
+
+%%%%% ### symplan3d ###
+%% syntaxe : M eqplan/plantype symplan3d --> M'
+%% ou M' symetrique de M par rapport au plan P defini par eqplan/plantype
+/symplan3d {
+13 dict begin
+ dup isplan {
+ plan2eq /args exch def
+ } {
+ /args exch def
+ } ifelse
+ /z exch def
+ /y exch def
+ /x exch def
+ args aload pop
+ /d1 exch def
+ /c1 exch def
+ /b1 exch def
+ /a1 exch def
+ /n_U a1 dup mul b1 dup mul add c1 dup mul add sqrt def
+ /a a1 n_U div def
+ /b b1 n_U div def
+ /c c1 n_U div def
+ /d d1 n_U div def
+ /u a x mul b y mul add c z mul add d add def
+ x 2 a mul u mul sub
+ y 2 b mul u mul sub
+ z 2 c mul u mul sub
+end
+} def
+
+%%%%% ### vecteur3d ###
+%% creation du vecteur AB a partir de A et B
+/vecteur3d { %% xA yA zA xB yB zB
+6 dict begin
+ /zB exch def
+ /yB exch def
+ /xB exch def
+ /zA exch def
+ /yA exch def
+ /xA exch def
+ xB xA sub
+ yB yA sub
+ zB zA sub
+end
+}def
+
+%%%%% ### vectprod3d ###
+%% produit vectoriel de deux vecteurs 3d
+/vectprod3d { %% x1 y1 z1 x2 y2 z2
+6 dict begin
+ /zp exch def
+ /yp exch def
+ /xp exch def
+ /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
+
+%%%%% ### scalprod3d ###
+%% produit scalaire de deux vecteurs 3d
+/scalprod3d { %% x1 y1 z1 x2 y2 z2
+6 dict begin
+ /zp exch def
+ /yp exch def
+ /xp exch def
+ /z exch def
+ /y exch def
+ /x exch def
+ x xp mul y yp mul add z zp mul add
+end
+} def
+
+%%%%% ### papply3d ###
+%% syntaxe : [A1 ... An] (f) papply3d --> [f(A1) ... f(An)]
+/papply3d {
+3 dict begin
+ /fonction exch def
+ /liste exch def
+ /i 0 def
+ [
+ liste length 3 idiv {
+ liste i get
+ liste i 1 add get
+ liste i 2 add get
+ fonction
+ /i i 3 add store
+ } repeat
+ counttomark
+ 0 eq
+ {pop}
+ {]}
+ ifelse
+end
+} def
+
+%%%%% ### defpoint3d ###
+%% creation du point A a partir de xA yA yB et du nom /A
+/defpoint3d { %% xA yA zA /nom
+1 dict begin
+ /memo exch def
+ [ 4 1 roll ] cvx memo exch
+end def
+}def
+
+%%%%% ### distance3d ###
+/distance3d { %% A B
+ vecteur3d norme3d
+} def
+
+%%%%% ### get3d ###
+/getp3d { %% [tableau de points 3d] i --> donne le ieme point du tableau
+ 2 copy 2 copy
+ 3 mul get
+ 5 1 roll
+ 3 mul 1 add get
+ 3 1 roll
+ 3 mul 2 add get
+} def
+
+%%%%% ### norme3d ###
+%% norme d un vecteur 3d
+/norme3d { %% x y z
+3 dict begin
+ /z exch def
+ /y exch def
+ /x exch def
+ x dup mul y dup mul add z dup mul add sqrt
+end
+} def
+
+%%%%% ### mulv3d ###
+%% (scalaire)*(vecteur 3d) Attention : dans l autre sens !
+/mulv3d { %% x y z lambda
+4 dict begin
+ /lambda exch def
+ /z exch def
+ /y exch def
+ /x exch def
+ x lambda mul
+ y lambda mul
+ z lambda mul
+end
+} def
+
+%%%%% ### addv3d ###
+%% addition de deux vecteurs 3d
+/addv3d { %% x1 y1 z1 x2 y2 z2
+6 dict begin
+ /zp exch def
+ /yp exch def
+ /xp exch def
+ /z exch def
+ /y exch def
+ /x exch def
+ x xp add
+ y yp add
+ z zp add
+end
+} def
+
+%%%%% ### milieu3d ###
+/milieu3d { %% A B --> I le milieu de [AB]
+ addv3d 0.5 mulv3d
+} def
+
+%%%%% ### exch ###
+/exchp {
+ 4 -1 roll
+ 4 -1 roll
+} def
+/exchc {
+ 6 -1 roll
+ 6 -1 roll
+ 6 -1 roll
+} def
+/exchd {
+ 4 {8 -1 roll} repeat
+} def
+/exchp3d {
+ 6 -1 roll
+ 6 -1 roll
+ 6 -1 roll
+} def
+
+%%%%% ### ABpoint3d ###
+%% syntaxe : A B k ABpoint3d --> M
+%% M tel que vect(AM) = k vect (AB)
+/ABpoint3d {
+3 dict begin
+ /k exch def
+ /B defpoint3d
+ /A defpoint3d
+ A B vecteur3d
+ k mulv3d
+ A addv3d
+end
+} def
+
+%%%%% ### angle3doriente ###
+%% syntaxe : vect1 vect2 vect3 angle3d
+%% vect3 est la normale au plan (vect1, vect2)
+/angle3doriente {
+4 dict begin
+ normalize3d /vect3 defpoint3d
+ normalize3d /vect2 defpoint3d
+ normalize3d /vect1 defpoint3d
+ /cosalpha vect1 vect2 scalprod3d def
+ /sinalpha vect1 vect2 vectprod3d vect3 scalprod3d def
+ sinalpha cosalpha atan
+end
+} def
+
+%%%%% ### points3dalignes ###
+%% syntaxe : A B C points3dalignes -> bool
+/points3dalignes {
+3 dict begin
+ /C defpoint3d
+ /B defpoint3d
+ /A defpoint3d
+ A B vecteur3d /u defpoint3d
+ A C vecteur3d /v defpoint3d
+ u v vectprod3d norme3d 1E-7 lt
+end
+} def
+
+%% syntaxe : M A B point3dsursegment --> true si M in [AB], false sinon
+/point3dsursegment {
+3 dict begin
+ /B defpoint3d
+ /A defpoint3d
+ /M defpoint3d
+ M A B points3dalignes {
+ M A vecteur3d
+ M B vecteur3d
+ scalprod3d 0 lt {
+ true
+ } {
+ false
+ } ifelse
+ } {
+ false
+ } ifelse
+end
+} def
+
+%%%%% ### fin insertion ###
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% geometrie 3d (dessins) %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%% ### point3d ###
+/point3d { %% A
+ 3dto2d point
+} def
+
+/points3d { %% tableau de points3d
+ tab3dto2d points
+} def
+
+%%%%% ### ligne3d ###
+%% [tableau de points3d] option --> trace la ligne brisee
+/ligne3d {
+1 dict begin
+ dup isstring
+ {/option exch def}
+ if
+ tab3dto2d
+ currentdict /option known
+ {option}
+ if
+ ligne
+end
+} def
+
+%% [tableau de points3d] option --> trace la ligne brisee
+/ligne3d_ {
+1 dict begin
+ dup isstring
+ {/option exch def}
+ if
+ tab3dto2d
+ currentdict /option known
+ {option}
+ if
+ ligne_
+end
+} def
+
+%%%%% ### tab3dto2d ###
+%% transforme un tableau de points 3d en tableau de points 2d
+/tab3dto2d {
+2 dict begin
+ /T exch def
+ /n T length def
+ [ T aload pop
+ n 1 sub -1 n 3 idiv 2 mul
+ { 1 dict begin
+ /i exch def
+ 3dto2d i 2 roll
+ end } for ]
+end
+} def
+
+%%%%% ### polygone3d ###
+/polygone3d { %% tableau de points3d
+ tab3dto2d polygone
+} def
+
+/polygone3d* { %% tableau de points3d
+ tab3dto2d polygone*
+} def
+
+%%%%% ### fin insertion ###
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% gestion du texte %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%% ### marks ###
+/xmkstep 1 def % les marques sur Ox
+/xmarkstyle {dctext} def
+/ymarkstyle {(-1 0) bltext} def
+/setxmkstep {
+ /xmkstep exch def
+} def
+/xmark {
+ dup xtick
+ /Courier findfont .8 fontsize mul scalefont setfont
+ dup dup truncate eq {
+ cvi dup chaine cvs exch
+ } {
+ dup chaine cvs exch
+ } ifelse
+ Oy xmarkstyle
+} def
+/xmarks {
+2 dict begin
+ /n xmax xmax xmin sub 1000 div sub xmkstep div truncate cvi
+ xmkstep mul def % mark max
+ /i xmin xmkstep div truncate cvi
+ xmkstep mul def % la 1ere
+ i xmin lt {/i i xmkstep add store} if
+ {
+ i 0 ne {i xmark} if
+ /i i xmkstep abs add store
+ i n gt {exit} if
+ } loop
+end
+} def
+
+/ymkstep 1 def % les marques sur Oy
+/setymkstep {
+ /ymkstep exch def
+} def
+/ymark {
+ dup ytick
+ /Courier findfont .8 fontsize mul scalefont setfont
+ dup chaine cvs exch
+ Ox exch ymarkstyle
+} def
+/ymarks {
+2 dict begin
+ /n ymax ymax ymin sub 1000 div sub ymkstep div truncate cvi
+ ymkstep mul def % mark max
+ /i ymin ymkstep div truncate cvi
+ ymkstep mul def % la 1ere
+ {
+ i 0 ne {i ymark} if
+ /i i ymkstep abs add store
+ i n gt {exit} if
+ } loop
+end
+} def
+
+/setmkstep {
+ setymkstep
+ setxmkstep
+} def
+/marks {
+ xmarks
+ ymarks
+} def
+
+%%%%% ### setfontsize ###
+/setfontsize {
+ /fontsize exch def
+} def
+
+%%%%% ### setCourrier ###
+/Courier findfont
+dup length dict begin
+ {
+ 1 index /FID ne
+ {def}
+ {pop pop}
+ ifelse
+ } forall
+ /Encoding ISOLatin1Encoding def
+ currentdict
+end
+
+/Courier-ISOLatin1 exch definefont pop
+
+/setCourier {
+ /Courier-ISOLatin1 findfont
+ fontsize scalefont
+ setfont
+} def
+
+%%%%% ### pathtext ###
+%% syntaxe : string x y initp@thtext
+ /initp@thtext {
+7 dict begin
+ /y exch def
+ /x exch def
+ /str exch def
+ str 0 0 show_dim
+ /wy exch def
+ /wx exch def
+ /lly exch def
+ /llx exch def
+ pop pop pop
+ newpath
+ x y smoveto
+} def
+ /closep@thtext {
+ str true charpath
+end
+} def
+
+%% syntaxe : string x y cctext_
+/cctext_ {
+ initp@thtext
+ llx wx add lly wy add -.5 mulv rmoveto
+ closep@thtext
+} def
+
+/brtext_ {
+ initp@thtext
+ hadjust 0 rmoveto
+ llx neg 0 rmoveto
+ closep@thtext
+} def
+
+/bbtext_ {
+ initp@thtext
+ 0 0 rmoveto
+ 0 0 rmoveto
+ closep@thtext
+} def
+
+/bltext_ {
+ initp@thtext
+ hadjust neg 0 rmoveto
+ wx neg 0 rmoveto
+ closep@thtext
+} def
+
+/bctext_ {
+ initp@thtext
+ 0 0 rmoveto
+ wx llx add -.5 mul 0 rmoveto
+ closep@thtext
+} def
+
+/ubtext_ {
+ initp@thtext
+ 0 vadjust rmoveto
+ 0 lly neg rmoveto
+ closep@thtext
+} def
+
+/urtext_ {
+ initp@thtext
+ hadjust vadjust rmoveto
+ llx neg lly neg rmoveto
+ closep@thtext
+} def
+
+/ultext_ {
+ initp@thtext
+ hadjust neg vadjust rmoveto
+ wx neg lly neg rmoveto
+ closep@thtext
+} def
+
+/uctext_ {
+ initp@thtext
+ 0 vadjust rmoveto
+ llx wx add -.5 mul lly neg rmoveto
+ closep@thtext
+} def
+
+/drtext_ {
+ initp@thtext
+ hadjust vadjust neg rmoveto
+ llx neg wy neg rmoveto
+ closep@thtext
+} def
+
+/dbtext_ {
+ initp@thtext
+ 0 vadjust neg rmoveto
+ 0 wy neg rmoveto
+ closep@thtext
+} def
+
+/dltext_ {
+ initp@thtext
+ hadjust neg vadjust neg rmoveto
+ wx neg wy neg rmoveto
+ closep@thtext
+} def
+
+/dctext_ {
+ initp@thtext
+ 0 vadjust neg rmoveto
+ llx wx add -2 div wy neg rmoveto
+ closep@thtext
+} def
+
+/crtext_ {
+ initp@thtext
+ hadjust 0 rmoveto
+ llx neg lly wy add -2 div rmoveto
+ closep@thtext
+} def
+
+/cbtext_ {
+ initp@thtext
+ 0 0 rmoveto
+ 0 lly wy add -2 div rmoveto
+ closep@thtext
+} def
+
+/cltext_ {
+ initp@thtext
+ hadjust neg 0 rmoveto
+ wx neg lly wy add -2 div rmoveto
+ closep@thtext
+} def
+
+/cctext_ {
+ initp@thtext
+ 0 0 rmoveto
+ llx wx add lly wy add -.5 mulv rmoveto
+ closep@thtext
+} def
+
+%%%%% ### text3d ###
+%%%% Version 3d des commandes jps TEXTE
+ /pr@p@re3d {
+2 dict begin
+% /vect_echelle [1 1] def
+% /angle_de_rot {0} def
+% dup xcheck
+% {/angle_de_rot exch def}
+% if
+% dup isarray
+% {/vect_echelle exch def}
+% if% CamView vect_echelle {angle_de_rot}
+ 3dto2d
+} def
+
+/bbtext3d {
+ pr@p@re3d
+ bbtext
+end
+} def
+
+/bbtexlabel3d {
+ pr@p@re3d
+ bbtexlabel
+end
+} def
+
+/bctext3d {
+ pr@p@re3d
+ bctext
+end
+} def
+
+/bctexlabel3d {
+ pr@p@re3d
+ bctexlabel
+end
+} def
+
+/bltext3d {
+ pr@p@re3d
+ bltext
+end
+} def
+
+/bltexlabel3d {
+ pr@p@re3d
+ bltexlabel
+end
+} def
+
+/brtext3d {
+ pr@p@re3d
+ brtext
+end
+} def
+
+/brtexlabel3d {
+ pr@p@re3d
+ brtexlabel
+end
+} def
+
+/cbtext3d {
+ pr@p@re3d
+ cbtext
+end
+} def
+
+/cbtexlabel3d {
+ pr@p@re3d
+ cbtexlabel
+end
+} def
+
+/cctext3d {
+ pr@p@re3d
+ cctext
+end
+} def
+
+/cctexlabel3d {
+ pr@p@re3d
+ cctexlabel
+end
+} def
+
+/cltext3d {
+ pr@p@re3d
+ cltext
+end
+} def
+
+/cltexlabel3d {
+ pr@p@re3d
+ cltexlabel
+end
+} def
+
+/crtext3d {
+ pr@p@re3d
+ crtext
+end
+} def
+
+/crtexlabel3d {
+ pr@p@re3d
+ crtexlabel
+end
+} def
+
+/dbtext3d {
+ pr@p@re3d
+ dbtext
+end
+} def
+
+/dbtexlabel3d {
+ pr@p@re3d
+ dbtexlabel
+end
+} def
+
+/dctext3d {
+ pr@p@re3d
+ dctext
+end
+} def
+
+/dctexlabel3d {
+ pr@p@re3d
+ dctexlabel
+end
+} def
+
+/dltext3d {
+ pr@p@re3d
+ dltext
+end
+} def
+
+/dltexlabel3d {
+ pr@p@re3d
+ dltexlabel
+end
+} def
+
+/drtext3d {
+ pr@p@re3d
+ drtext
+end
+} def
+
+/drtexlabel3d {
+ pr@p@re3d
+ drtexlabel
+end
+} def
+
+/ubtext3d {
+ pr@p@re3d
+ ubtext
+end
+} def
+
+/ubtexlabel3d {
+ pr@p@re3d
+ ubtexlabel
+end
+} def
+
+/uctext3d {
+ pr@p@re3d
+ uctext
+end
+} def
+
+/uctexlabel3d {
+ pr@p@re3d
+ uctexlabel
+end
+} def
+
+/ultext3d {
+ pr@p@re3d
+ ultext
+end
+} def
+
+/ultexlabel3d {
+ pr@p@re3d
+ ultexlabel
+end
+} def
+
+/urtext3d {
+ pr@p@re3d
+ urtext
+end
+} def
+
+/urtexlabel3d {
+ pr@p@re3d
+ urtexlabel
+end
+} def
+
+%%%%% ### fin insertion ###
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% bibliotheque sur les solides %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%% ### solide ###
+%% solid = [Sommets Faces Colors_Faces InOut_Table]
+/solidgetsommets {
+ 0 get
+} def
+/solidgetpointstable {solidgetsommets} def
+
+/solidgetfaces {
+ 1 get
+} def
+
+/solidgetface {
+1 dict begin
+ /i exch def
+ solidgetfaces i get
+end
+} def
+
+/solidgetfcolors {
+ 2 get
+} def
+
+%% syntaxe : solid i solidgetfcolor --> str
+/solidgetfcolor {
+1 dict begin
+ /i exch def
+ solidgetfcolors i get
+end
+} def
+
+%% syntaxe : solid i str solidputfcolor --> -
+/solidputfcolor {
+2 dict begin
+ /str exch def
+ /i exch def
+ solidgetfcolors i str put
+end
+} def
+
+/solidgetinouttable {
+ 3 get
+} def
+
+/solidputsommets {
+ 0 exch put
+} def
+/solidputpointstable {solidputsommets} def
+
+/solidputfaces {
+ 1 exch put
+} def
+
+%% syntaxe : solid solidfacesreverse -> -
+/solidfacesreverse {
+5 dict begin
+ /solid exch def
+ /n solid solidnombrefaces def
+ 0 1 n 1 sub {
+ /i exch def
+ /F solid i solidgetface reverse def
+ /m F length def
+ solid i [F aload pop m 0 roll ] solidputface
+ } for
+end
+} def
+
+/solidputfcolors {
+ 2 exch put
+} def
+
+/solidputinouttable {
+ 3 exch put
+} def
+
+%% syntaxe : any issolid --> booleen, vrai si any est de type solid
+/issolid {
+1 dict begin
+ /candidat exch def
+ candidat isarray {
+ candidat length 4 eq {
+ candidat 0 get isarray
+ candidat 1 get isarray and
+ candidat 2 get isarray and
+ candidat 3 get isarray and {
+ /IO candidat 3 get def
+ IO length 4 eq
+ IO 0 get isnum and
+ IO 1 get isnum and
+ IO 2 get isnum and
+ IO 3 get isnum and
+ } {
+ false
+ } ifelse
+ } {
+ false
+ } ifelse
+ } {
+ false
+ } ifelse
+end
+} def
+
+/dupsolid {
+5 dict begin
+ /solid exch def
+ /S solid solidgetsommets def
+ /F solid solidgetfaces def
+ /FC solid solidgetfcolors def
+ /IO solid solidgetinouttable def
+ solid
+ [
+ S duparray exch pop
+ F duparray exch pop
+ FC duparray exch pop
+ IO duparray exch pop
+ ]
+end
+} def
+
+%% syntaxe : solid array solidputinfaces --> -
+/solidputinfaces {
+4 dict begin
+ /facesinternes exch def
+ /solid exch def
+ /n2 facesinternes length def
+ /IO solid solidgetinouttable def
+ /facesexternes solid solidgetoutfaces def
+ /n1 facesexternes length def
+ solid
+ [facesexternes aload pop facesinternes aload pop]
+ solidputfaces
+ IO 0 0 put
+ IO 1 n1 1 sub put
+ IO 2 n1 put
+ IO 3 n1 n2 add 1 sub put
+end
+} def
+
+%% syntaxe : solid array solidputoutfaces --> -
+/solidputoutfaces {
+4 dict begin
+ /facesexternes exch def
+ /solid exch def
+ /n1 facesexternes length def
+ /IO solid solidgetinouttable def
+ /facesinternes solid solidgetinfaces def
+ /n2 facesinternes length def
+ solid
+ [facesexternes aload pop facesinternes aload pop]
+ solidputfaces
+ IO 0 0 put
+ IO 1 n1 1 sub put
+ IO 2 n1 put
+ IO 3 n1 n2 add 1 sub put
+end
+} def
+
+/solidnombreinfaces {
+1 dict begin
+ /solid exch def
+ solid solidwithinfaces {
+ /IO solid solidgetinouttable def
+ IO 3 get IO 2 get sub 1 add
+ } {
+ 0
+ } ifelse
+end
+} def
+
+/solidnombreoutfaces {
+1 dict begin
+ /solid exch def
+ /IO solid solidgetinouttable def
+ IO 1 get IO 0 get sub 1 add
+end
+} def
+
+%% syntaxe : solid solidgetinfaces --> array
+/solidgetinfaces {
+4 dict begin
+ /solid exch def
+ solid issolid not {
+ (Error : mauvais type d argument dans solidgetinfaces) ==
+ quit
+ } if
+ solid solidwithinfaces {
+ /IO solid solidgetinouttable def
+ /F solid solidgetfaces def
+ /n1 IO 2 get def
+ /n2 IO 3 get def
+ /n n2 n1 sub 1 add def
+ F n1 n getinterval
+ } {
+ []
+ } ifelse
+end
+} def
+
+%% syntaxe : solid solidgetoutfaces --> array
+/solidgetoutfaces {
+4 dict begin
+ /solid exch def
+ solid issolid not {
+ (Error : mauvais type d argument dans solidgetoutfaces) ==
+ quit
+ } if
+ /IO solid solidgetinouttable def
+ /F solid solidgetfaces def
+ /n1 IO 0 get def
+ /n2 IO 1 get def
+ /n n2 n1 sub 1 add def
+ F n1 n getinterval
+end
+} def
+
+%% /tracelignedeniveau? false def
+%% /hauteurlignedeniveau 1 def
+%% /couleurlignedeniveau {rouge} def
+%% /linewidthlignedeniveau 4 def
+
+/solidgridOn {
+ /solidgrid true def
+} def
+/solidgridOff {
+ /solidgrid false def
+} def
+
+%% syntaxe : solid i string solidputfcolor
+%% syntaxe : solid str outputcolors
+%% syntaxe : solid str1 str2 inoutputcolors
+%% syntaxe : solid string n solidputncolors
+%% syntaxe : solid array solidputincolors --> -
+%% syntaxe : solid array solidputoutcolors --> -
+%% syntaxe : solid solidgetincolors --> array
+%% syntaxe : solid solidgetoutcolors --> array
+
+%% syntaxe : solid array solidputinfaces --> -
+%% syntaxe : solid array solidputoutfaces --> -
+%% syntaxe : solid solidgetinfaces --> array
+%% syntaxe : solid solidgetoutfaces --> array
+
+%% syntaxe : solid1 solid2 solidfuz -> solid
+
+%% syntaxe : solid i solidgetsommetsface -> array
+%% array = tableau de points 3d
+/solidgetsommetsface {
+1 dict begin
+ /i exch def
+ /solid exch def
+ /F solid i solidgetface def
+ [
+ 0 1 F length 1 sub {
+ /k exch def
+ solid F k get solidgetsommet
+ } for
+ ]
+end
+} def
+
+%% syntaxe : solid index table solidputface -> -
+/solidputface {
+1 dict begin
+ /table exch def
+ /i exch def
+ solidgetfaces i table put
+end
+} def
+
+%% syntaxe : solid table solidaddface -> -
+%% syntaxe : solid table (couleur) solidaddface -> -
+%% on ne se preoccupe pas des faces internes
+/solidaddface {
+6 dict begin
+ dup isstring {
+ /lac@uleur exch def
+ } {
+ /lac@uleur () def
+ } ifelse
+ /table exch def
+ /solid exch def
+ /IO solid solidgetinouttable def
+ /n2 IO 1 get def
+ /FC solid solidgetoutcolors def
+ IO 1 n2 1 add put
+ solid [ solid solidgetfaces aload pop table ] solidputfaces
+ solid IO solidputinouttable
+% solid solidnombrefaces
+ solid [
+ FC aload pop lac@uleur
+ ] solidputoutcolors
+end
+} def
+
+/solidnombrefaces {
+1 dict begin
+ /solid exch def
+ solid solidnombreinfaces
+ solid solidnombreoutfaces
+ add
+end
+} def
+
+%% syntaxe : solid M solidaddsommetexterne -> -
+%% on ajoute le sommet sans se preoccuper de rien
+/solidaddsommetexterne {
+2 dict begin
+ /M defpoint3d
+ /solid exch def
+ solid
+ [ solid solidgetsommets aload pop M ]
+ solidputsommets
+end
+} def
+
+%% syntaxe : solid array solidaddsommets -> -
+/solidaddsommets {
+2 dict begin
+ /table exch def
+ /solid exch def
+ /n table length 3 idiv def
+ 0 1 0 {
+ /i exch def
+ solid table i getp3d solidaddsommet pop
+ } for
+end
+} def
+
+%% syntaxe : solid M solidaddsommet -> k
+%% on ajoute le sommet M. Si il est deja sur une arete,
+%% on l incorpore a la face concernee
+%% s il est deja present, on ne le rajoute pas.
+%% Renvoie l indice du sommet rajoute.
+/solidaddsommet {
+10 dict begin
+ /M defpoint3d
+ /solid exch def
+ /nbf solid solidnombrefaces def
+ /N solid solidnombresommets def
+ /sortie -1 def
+ %% le sommet est-il deja dans la structure
+ 0 1 N 1 sub {
+ /i exch def
+%% (addsommet) ==
+%% solid i solidgetsommet == == ==
+%% M == == ==
+%% solid i solidgetsommet M eqp3d ==
+
+% solid i solidgetsommet M eqp3d {
+ solid i solidgetsommet M distance3d 1e-5 le {
+ %% oui => c est fini
+ /sortie i store
+ } if
+ } for
+ sortie 0 lt {
+ %% non => on le rajoute
+ /sortie N def
+ solid M solidaddsommetexterne
+ %% est il sur une arete deja codee
+ 0 1 nbf 1 sub {
+ %% face d indice i
+ /i exch def
+ solid i solidgetface /F exch def
+ /nbsf F length def
+ 0 1 nbsf 1 sub {
+ /j exch def
+ M
+ solid j i solidgetsommetface
+ solid j 1 add nbsf mod i solidgetsommetface
+ point3dsursegment {
+ %% il est sur l arete concernee
+ solid i [
+ 0 1 j {
+ /k exch def
+ F k get
+ } for
+ N
+ j 1 add nbsf mod dup 0 eq {
+ pop
+ } {
+ 1 nbsf 1 sub {
+ /k exch def
+ F k get
+ } for
+ } ifelse
+ ] solidputface
+ exit
+ } if
+ } for
+ } for
+ } if
+ sortie
+end
+} def
+
+%%%%% ### solidrmsommet ###
+%% syntaxe : solid i solidrmsommet -> -
+/solidrmsommet {
+5 dict begin
+ /i exch def
+ /solid exch def
+ solid issolid not {
+ (Erreur : mauvais type d argument dans solidrmsommet) ==
+ quit
+ } if
+ solid i solidsommetsadjsommet length 0 gt {
+ (Erreur : sommet non isole dans solidrmsommet) ==
+ quit
+ } if
+
+ %% on s occupe des sommets
+ /n solid solidnombresommets def
+ /S [
+ 0 1 n 1 sub {
+ /j exch def
+ j i ne {
+ solid j solidgetsommet
+ } if
+ } for
+ ] def
+ solid S solidputsommets
+ %% on s occupe des faces
+ /n solid solidnombrefaces def
+ /F [
+ 0 1 n 1 sub {
+ %% face d indice j
+ /j exch def
+ /Fj solid j solidgetface def
+ [0 1 Fj length 1 sub {
+ %% sommet d indice k de la face Fj
+ /k exch def
+ Fj k get dup i gt {
+ 1 sub
+ } if
+ } for]
+ } for
+ ] def
+ solid F solidputfaces
+end
+} def
+
+%%%%% ### solidsommetsadjsommet ###
+%% syntaxe : solid i solidsommetsadjsommet --> array
+%% array est le tableau des indices des sommets adjacents au
+%% sommet d indice i
+/solidsommetsadjsommet {
+6 dict begin
+ /no exch def
+ /solid exch def
+ solid no solidfacesadjsommet /facesadj exch def
+ /sommetsadj [] def
+ /nbadj facesadj length def
+ 0 1 nbadj 1 sub {
+ /j exch def
+ %% examen de la jieme face
+ %/j 0 def
+ /F solid facesadj j get solidgetface def
+ /nbsommetsface F length def
+ no F in {
+ /index exch def
+ /i1 F index 1 sub nbsommetsface modulo get def
+ /i2 F index 1 add nbsommetsface mod get def
+ %% si i1 n est pas deja note, on le rajoute
+ i1 sommetsadj in {
+ pop
+ } {
+ /sommetsadj [ sommetsadj aload pop i1 ] store
+ } ifelse
+ %% si i2 n est pas deja note, on le rajoute
+ i2 sommetsadj in {
+ pop
+ } {
+ /sommetsadj [ sommetsadj aload pop i2 ] store
+ } ifelse
+ } {
+ (Error : bug dans solidsommetsadjsommet) ==
+ quit
+ } ifelse
+ } for
+ sommetsadj
+end
+} def
+
+%%%%% ### solidfacesadjsommet ###
+%% syntaxe : solid i solidfacesadjsommet --> array
+%% array est le tableau des indices des faces adjacentes au
+%% sommet d indice i
+/solidfacesadjsommet {
+6 dict begin
+ /no exch def
+ /solid exch def
+ /n solid solidnombrefaces def
+ /indicesfacesadj [] def
+ 0 1 n 1 sub {
+ /j exch def
+ /F solid j solidgetface def
+ no F in {
+ pop
+ /indicesfacesadj [ indicesfacesadj aload pop j ] store
+ } if
+ } for
+ indicesfacesadj
+end
+} def
+
+%%%%% ### ordonnepoints3d ###
+%% syntaxe : array1 M ordonnepoints3d --> array2
+%% array1 = tableau de points 3d coplanaires (plan P)
+%% M = point3d indiquant la direction de la normale a P
+%% array2 = les indices des points de depart, ranges dans le
+%% sens trigo par rapport a la normale
+/ordonnepoints3d {
+5 dict begin
+ /M defpoint3d
+ /table exch def
+ table isobarycentre3d /G defpoint3d
+ %% calcul de la normale
+ table 0 getp3d /ptref defpoint3d
+ table 1 getp3d /A defpoint3d
+ G ptref vecteur3d
+ G A vecteur3d
+ vectprod3d /vecteurnormal defpoint3d
+ vecteurnormal G M vecteur3d scalprod3d 0 lt {
+ vecteurnormal -1 mulv3d /vecteurnormal defpoint3d
+ } if
+ %% la table des angles
+ table duparray exch pop
+ {1 dict begin
+ /M defpoint3d
+ G ptref vecteur3d
+ G M vecteur3d
+ vecteurnormal angle3doriente
+ end} papply3d
+% [0 1 table length 3 idiv 1 sub {} for]
+% exch
+ doublebubblesort pop
+end
+} def
+
+%%%%% ### fin insertion ###
+
+%% /tracelignedeniveau? false def
+%% /hauteurlignedeniveau 1 def
+%% /couleurlignedeniveau {rouge} def
+%% /linewidthlignedeniveau 4 def
+%%
+%% /solidgrid true def
+%% /aretescachees true def
+%% /defaultsolidmode 2 def
+
+%% syntaxe : alpha beta r h newpie --> solid
+/newpie {
+6 dict begin
+ [[/resolution /nbetages] [8 1] [10 1] [12 1] [18 3] [36 5]] gestionsolidmode
+ /h exch def
+ /r exch def
+ /beta exch def
+ /alpha exch def
+ [
+ 0 0
+% alpha cos r mul alpha sin r mul
+ alpha beta {1 dict begin /t exch def t cos r mul t sin r mul end} CourbeR2+
+ ] 0 h [nbetages] newprismedroit
+end
+} def
+
+%%%%% ### newsolid ###
+%% syntaxe : newsolid --> depose le solide nul sur la pile
+/newsolid {
+ [] [] generesolid
+} def
+
+%%%%% ### generesolid ###
+/generesolid {
+2 dict begin
+ /F exch def
+ /S exch def
+ [S F [F length {()} repeat] [0 F length 1 sub -1 -1]]
+end
+} def
+
+%%%%% ### nullsolid ###
+%% syntaxe : solide nullsolid -> booleen, vrai si le solide est nul
+/nullsolid {
+1 dict begin
+ /candidat exch def
+ candidat issolid not {
+ (Error type argument dans "nullsolid") ==
+ quit
+ } if
+ candidat solidgetsommets length 0 eq {
+ true
+ } {
+ false
+ } ifelse
+end
+} def
+
+%%%%% ### solidnombreoutfaces ###
+/solidnombreoutfaces {
+4 dict begin
+ /solid exch def
+ solid issolid not {
+ (Error : mauvais type d argument dans solidnombreoutfaces) ==
+ quit
+ } if
+ solid nullsolid {
+ 0
+ } {
+ /IO solid solidgetinouttable def
+ IO 1 get
+ IO 0 get sub
+ 1 add
+ } ifelse
+end
+} def
+
+%%%%% ### solidnombreinfaces ###
+/solidnombreinfaces {
+4 dict begin
+ /solid exch def
+ solid issolid not {
+ (Error : mauvais type d argument dans solidnombreinfaces) ==
+ quit
+ } if
+ solid solidwithinfaces {
+ /IO solid solidgetinouttable def
+ IO 3 get
+ IO 2 get sub
+ 1 add
+ } {
+ 0
+ } ifelse
+end
+} def
+
+%%%%% ### solidtests ###
+%% syntaxe : solid solidwithinfaces --> bool, true si le solide est vide
+/solidwithinfaces {
+2 dict begin
+ /solid exch def
+ solid issolid not {
+ (Error : mauvais type d argument dans solidwithinfaces) ==
+ quit
+ } if
+ /table solid solidgetinouttable def
+ table 2 get -1 ne {
+ true
+ } {
+ false
+ } ifelse
+end
+} def
+
+%%%%% ### solidgetsommet ###
+%% syntaxe : solid i j solidgetsommetface --> sommet i de la face j
+/solidgetsommetface {
+6 dict begin
+ /j exch def
+ /i exch def
+ /solid exch def
+ solid issolid not {
+ (Error : mauvais type d argument dans solidgetsommetface) ==
+ quit
+ } if
+ /table_faces solid solidgetfaces def
+ /table_sommets solid solidgetsommets def
+ /k table_faces j get i get def
+ table_sommets k getp3d
+end
+} def
+
+%% syntaxe : solid i solidgetsommetsface --> array, tableau des
+%% sommets de la face i du solide
+/solidgetsommetsface {
+6 dict begin
+ /i exch def
+ /solid exch def
+ solid issolid not {
+ (Error : mauvais type d argument dans solidgetsommetsface) ==
+ quit
+ } if
+ /table_faces solid solidgetfaces def
+ /table_sommets solid solidgetsommets def
+ /table_indices table_faces i get def
+ [
+ 0 1 table_indices length 1 sub {
+ /j exch def
+ table_sommets table_indices j get getp3d
+ } for
+ ]
+end
+} def
+
+%% syntaxe : solid i solidgetsommet --> sommet i du solide
+/solidgetsommet {
+3 dict begin
+ /i exch def
+ /solid exch def
+ solid issolid not {
+ (Error : mauvais type d argument dans solidgetsommet) ==
+ quit
+ } if
+ /table_sommets solid solidgetsommets def
+ table_sommets i getp3d
+end
+} def
+
+%%%%% ### solidcentreface ###
+%% syntaxe : solid i solidcentreface --> M
+/solidcentreface {
+ solidgetsommetsface isobarycentre3d
+} def
+
+%%%%% ### solidnombre ###
+/solidnombresommets {
+ solidgetsommets length 3 idiv
+} def
+
+/solidfacenombresommets {
+ solidgetface length
+} def
+
+/solidnombrefaces {
+ solidgetfaces length
+} def
+
+%%%%% ### solidshowsommets ###
+/solidshowsommets {
+8 dict begin
+ dup issolid not {
+ %% on a un argument
+ /option exch def
+ } if
+ /sol exch def
+ /n sol solidnombresommets def
+ /m sol solidnombrefaces def
+ currentdict /option known not {
+ /option [0 1 n 1 sub {} for] def
+ } if
+ 0 1 option length 1 sub {
+ /k exch def
+ option k get /i exch def %% indice du sommet examine
+ sol i solidgetsommet point3d
+ } for
+end
+} def
+
+%%%%% ### solidnumsommets ###
+/solidnumsommets {
+8 dict begin
+% Font findfont 10 scalefont setfont
+ dup issolid not {
+ %% on a un argument
+ /option exch def
+ } if
+ /sol exch def
+ /n sol solidnombresommets def
+ /m sol solidnombrefaces def
+ currentdict /option known not {
+ /option [0 1 n 1 sub {} for] def
+ } if
+ /result [
+ n {false} repeat
+ ] def
+ 0 1 option length 1 sub {
+ /k exch def
+ option k get /i exch def %% indice du sommet examine
+ 0 1 m 1 sub {
+ /j exch def %% indice de la face examinee
+ i sol j solidgetface in {
+ %% le sommet i est dans la face j
+ pop
+ exit
+ } if
+ } for
+ sol i solidgetsommet /S defpoint3d
+ i ( ) cvs
+ m 0 ne {
+ %% le sommet i est dans la face j
+ sol j solidcentreface /G defpoint3d
+ G S vecteur3d normalize3d
+ 15 dup ptojpoint pop
+ mulv3d
+ S addv3d
+ 3dto2d cctext
+ } {
+ S 3dto2d uctext
+ } ifelse
+ } for
+end
+} def
+
+%%%%% ### gestionsolidmode ###
+%% table = [ [vars] [mode0] [mode1] [mode2] [mode3] [mode4] ]
+/gestionsolidmode {
+5 dict begin
+ /table exch def
+ dup xcheck {
+ /mode exch def
+ } {
+ dup isarray {
+ /tableaffectation exch def
+ /mode -1 def
+ } {
+ /mode defaultsolidmode def
+ } ifelse
+ } ifelse
+ /vars table 0 get def
+ /nbvars vars length def
+ mode 0 ge {
+ /tableaffectation table mode 1 add 5 min get def
+ } if
+ 0 1 nbvars 1 sub {
+ /i exch def
+ vars i get
+ tableaffectation i get
+ } for
+ nbvars
+end
+ {def} repeat
+} def
+
+%%%%% ### solidfuz ###
+%% syntaxe : solid1 solid2 solidfuz -> solid
+/solidfuz {
+5 dict begin
+ /solid2 exch def
+ /solid1 exch def
+ /S1 solid1 solidgetsommets def
+ /S2 solid2 solidgetsommets def
+ /n S1 length 3 idiv def
+
+ %% les sommets
+ /S S1 S2 append def
+
+ %% les faces internes et leurs couleurs
+ /FI1 solid1 solidgetinfaces def
+ /FIC1 solid1 solidgetincolors def
+ solid2 solidnombreinfaces 0 eq {
+ /FI2 [] def
+ /FIC2 [] def
+ } {
+ /FI2 solid2 solidgetinfaces {{n add} apply} apply def
+ /FIC2 solid2 solidgetincolors def
+ } ifelse
+ /FI [FI1 aload pop FI2 aload pop] def
+ /FIC [FIC1 aload pop FIC2 aload pop] def
+
+ %% les faces externes et leurs couleurs
+ /FO1 solid1 solidgetoutfaces def
+ /FOC1 solid1 solidgetoutcolors def
+ /FO2 solid2 solidgetoutfaces {{n add} apply} apply def
+ /FOC2 solid2 solidgetoutcolors def
+ /FO [FO1 aload pop FO2 aload pop] def
+ /FOC [FOC1 aload pop FOC2 aload pop] def
+
+ /F [FO aload pop FI aload pop] def
+ /FC [FOC aload pop FIC aload pop] def
+ /IO [
+ 0 FO length 1 sub
+ FI length 0 gt {
+ dup 1 add dup FI length add 1 sub
+ } {
+ -1 -1
+ } ifelse
+ ] def
+
+ S F generesolid
+ dup FC solidputfcolors
+ dup IO solidputinouttable
+end
+} def
+
+%%%%% ### solidnormaleface ###
+%% syntaxe : solid i solidnormaleface --> u, vecteur normale a la
+%% face d indice i du solide
+/solidnormaleface {
+4 dict begin
+ /i exch def
+ /solid exch def
+ solid issolid not {
+ (Error : mauvais type d argument dans solidgetsommetface) ==
+ quit
+ } if
+%% solid 0 i solidgetsommetface /G defpoint3d
+%% G
+%% solid 1 i solidgetsommetface
+%% vecteur3d
+%% G
+%% solid 2 i solidgetsommetface
+%% vecteur3d
+
+ /n solid i solidfacenombresommets def
+ solid i solidcentreface /G defpoint3d
+ %% debug %% G 3dto2d point
+ G
+ solid 0 i solidgetsommetface
+ /A defpoint3d
+ % gsave bleu A point3d grestore
+ A
+ vecteur3d normalize3d
+ G
+ solid 1 i solidgetsommetface
+ /A defpoint3d
+ % gsave orange A point3d grestore
+ A
+ vecteur3d normalize3d
+ vectprod3d
+ /resultat defpoint3d
+ resultat normalize3d
+end
+} def
+
+%%%%% ### solidtransform ###
+%% syntaxe : solid1 {f} solidtransform --> solid2, solid2 est le
+%% transforme de solid1 par la transformation f : R^3 -> R^3
+/solidtransform {
+3 dict begin
+ /@f exch def
+ /solid exch def
+ solid issolid not {
+ (Error : mauvais type d argument dans solidtransform) ==
+ quit
+ } if
+ /les_sommets
+ solid solidgetsommets {@f} papply3d
+ def
+ solid les_sommets solidputsommets
+ solid
+end
+} def
+
+%%%%% ### solidputcolor ###
+%% syntaxe : solid i string solidputfcolor
+/solidputfcolor {
+3 dict begin
+ /str exch def
+ /i exch def
+ /solid exch def
+ /FC solid solidgetfcolors def
+ i FC length lt {
+ FC i str put
+ } if
+end
+} def
+
+%% syntaxe : solid solidgetincolors --> array
+/solidgetincolors {
+3 dict begin
+ /solid exch def
+ solid issolid not {
+ (Error : mauvais type d argument dans solidgetincolors) ==
+ quit
+ } if
+ solid solidwithinfaces {
+ /fcol solid solidgetfcolors def
+ /IO solid solidgetinouttable def
+ /n1 IO 2 get def
+ /n2 IO 3 get def
+ /n n2 n1 sub 1 add def
+ fcol n1 n getinterval
+ } {
+ []
+ } ifelse
+end
+} def
+
+%% syntaxe : solid solidgetoutcolors --> array
+/solidgetoutcolors {
+3 dict begin
+ /solid exch def
+ solid issolid not {
+ (Error : mauvais type d argument dans solidgetoutcolors) ==
+ quit
+ } if
+ /fcol solid solidgetfcolors def
+ /IO solid solidgetinouttable def
+ /n1 IO 0 get def
+ /n2 IO 1 get def
+ /n n2 n1 sub 1 add def
+ fcol n1 n getinterval
+end
+} def
+
+%% syntaxe : solid array solidputincolors --> -
+/solidputincolors {
+4 dict begin
+ /newcolorstable exch def
+ /solid exch def
+ solid issolid not {
+ (Error : mauvais type d argument dans solidputincolors) ==
+ quit
+ } if
+ /n newcolorstable length def
+ n solid solidnombreinfaces ne {
+ (Error : mauvaise longueur de tableau dans solidputincolors) ==
+ quit
+ } if
+ n 0 ne {
+ /FC solid solidgetfcolors def
+ /IO solid solidgetinouttable def
+ /n1 IO 2 get def
+ FC n1 newcolorstable putinterval
+ } if
+end
+} def
+
+%% syntaxe : solid array solidputoutcolors --> -
+/solidputoutcolors {
+4 dict begin
+ /newcolorstable exch def
+ /solid exch def
+ solid issolid not {
+ (Error : mauvais type d argument dans solidputoutcolors) ==
+ quit
+ } if
+ /n newcolorstable length def
+ n solid solidnombreoutfaces ne {
+ (Error : mauvaise longueur de tableau dans solidputoutcolors) ==
+ quit
+ } if
+ n 0 ne {
+ /FC solid solidgetfcolors def
+ /IO solid solidgetinouttable def
+ /n1 IO 0 get def
+ FC n1 newcolorstable putinterval
+ } if
+end
+} def
+
+%% syntaxe : solid str outputcolors
+/outputcolors {
+5 dict begin
+ /color exch def
+ /solid exch def
+ solid issolid not {
+ (Error : mauvais type d argument dans inoutputcolors) ==
+ quit
+ } if
+ /n solid solidnombreoutfaces def
+ solid [ n {color} repeat ] solidputoutcolors
+end
+} def
+
+%% syntaxe : solid str inputcolors
+/inputcolors {
+5 dict begin
+ /color exch def
+ /solid exch def
+ solid issolid not {
+ (Error : mauvais type d argument dans inoutputcolors) ==
+ quit
+ } if
+ /n solid solidnombreinfaces def
+ solid [ n {color} repeat ] solidputincolors
+end
+} def
+
+%% syntaxe : solid str1 str2 inoutputcolors
+/inoutputcolors {
+5 dict begin
+ /colout exch def
+ /colin exch def
+ /solid exch def
+ solid colin inputcolors
+ solid colout outputcolors
+end
+} def
+
+%% syntaxe : solid array solidputoutcolors --> -
+/solidputoutcolors {
+4 dict begin
+ /newcolorstable exch def
+ /solid exch def
+ solid issolid not {
+ (Error : mauvais type d argument dans solidputoutcolors) ==
+ quit
+ } if
+ /n newcolorstable length def
+ n solid solidnombreoutfaces ne {
+ (Error : mauvaise longueur de tableau dans solidputoutcolors) ==
+ quit
+ } if
+ n 0 ne {
+ /FC solid solidgetfcolors def
+ /IO solid solidgetinouttable def
+ /n1 IO 0 get def
+ FC length n n1 add lt {
+ solid newcolorstable solidputfcolors
+ } {
+ FC n1 newcolorstable putinterval
+ } ifelse
+ } if
+end
+} def
+
+/solidputcolors {
+3 dict begin
+ 2 copy pop
+ isstring {
+ inoutputcolors
+ } {
+ outputcolors
+ } ifelse
+end
+} def
+
+%%%%% ### solidputhuecolors ###
+%% syntaxe : solid table solidputhuecolors --> -
+/solidputhuecolors {
+1 dict begin
+ 2 copy pop
+ solidgetinouttable /IO exch def
+ IO 0 get
+ IO 1 get
+ s@lidputhuec@l@rs
+end
+} def
+
+/solidputinhuecolors {
+2 dict begin
+ /table exch def
+ /solid exch def
+ solid solidgetinouttable /IO exch def
+ solid solidwithinfaces {
+ solid table
+ IO 2 get
+ IO 3 get
+ s@lidputhuec@l@rs
+ } if
+end
+} def
+
+/solidputinouthuecolors {
+1 dict begin
+ 2 copy pop
+ solidgetinouttable /IO exch def
+ IO 0 get
+ IO 3 get IO 1 get max
+ s@lidputhuec@l@rs
+end
+} def
+
+%% syntaxe : solid table n1 n2 s@lidputhuec@l@rs --> -
+%% affecte les couleurs des faces d indice n1 a n2 du solid solid, par
+%% un degrade defini par la table.
+ /s@lidputhuec@l@rs {
+9 dict begin
+ /n2 exch def
+ /n1 exch def
+ /table exch def
+ /solid exch def
+ /n n2 n1 sub def
+
+ table length 2 eq {
+ /a0 table 0 get def
+ /a1 table 1 get def
+ a1 isstring {
+ /lacouleurdepart {
+ gsave
+ [a0 cvx exec] length 0 eq {
+ a0 cvx exec currentrgbcolor
+ } {
+ a0 cvx exec
+ } ifelse
+ grestore
+ } def
+ /lacouleurarrivee {
+ gsave
+ [a1 cvx exec] length 0 eq {
+ a1 cvx exec currentrgbcolor
+ } {
+ a1 cvx exec
+ } ifelse
+ grestore
+ } def
+ /table [lacouleurdepart lacouleurarrivee] def
+ } {
+ /A {a0 i a1 a0 sub mul n 1 sub div add} def
+ /B {1} def
+ /C {1} def
+ /D {} def
+ /espacedecouleurs (sethsbcolor) def
+ } ifelse
+ } if
+
+ table length 4 eq {
+ /a0 table 0 get def
+ /a1 table 1 get def
+ /A {a0 i a1 a0 sub mul n 1 sub div add} def
+ /B table 2 get def
+ /C table 3 get def
+ /D {} def
+ /espacedecouleurs (sethsbcolor) def
+ } if
+
+ table length 6 eq {
+ /a0 table 0 get def
+ /b0 table 1 get def
+ /c0 table 2 get def
+ /a1 table 3 get def
+ /b1 table 4 get def
+ /c1 table 5 get def
+ /A {a0 i a1 a0 sub mul n 1 sub div add} def
+ /B {b0 i b1 b0 sub mul n 1 sub div add} def
+ /C {c0 i c1 c0 sub mul n 1 sub div add} def
+ /D {} def
+ /espacedecouleurs (setrgbcolor) def
+ } if
+
+ table length 7 eq {
+ /a0 table 0 get def
+ /b0 table 1 get def
+ /c0 table 2 get def
+ /a1 table 3 get def
+ /b1 table 4 get def
+ /c1 table 5 get def
+ /A {a0 i a1 a0 sub mul n 1 sub div add} def
+ /B {b0 i b1 b0 sub mul n 1 sub div add} def
+ /C {c0 i c1 c0 sub mul n 1 sub div add} def
+ /D {} def
+ /espacedecouleurs (sethsbcolor) def
+ } if
+
+ table length 8 eq {
+ /a0 table 0 get def
+ /b0 table 1 get def
+ /c0 table 2 get def
+ /d0 table 3 get def
+ /a1 table 4 get def
+ /b1 table 5 get def
+ /c1 table 6 get def
+ /d1 table 7 get def
+ /A {a0 i a1 a0 sub mul n 1 sub div add} def
+ /B {b0 i b1 b0 sub mul n 1 sub div add} def
+ /C {c0 i c1 c0 sub mul n 1 sub div add} def
+ /D {d0 i d1 d0 sub mul n 1 sub div add} def
+ /espacedecouleurs (setcmykcolor) def
+ } if
+
+ n1 1 n2 {
+ /i exch def
+ solid i
+ [A B C D] espacedecouleurs astr2str
+ solidputfcolor
+ } for
+
+end
+} def
+
+%%%%% ### solidrmface ###
+%% syntaxe : solid i solidrmface -> -
+/solidrmface {
+5 dict begin
+ /i exch def
+ /solid exch def
+ solid issolid not {
+ (Error : mauvais type d argument dans solidrmface) ==
+ quit
+ } if
+ %% on enleve la face
+ /F solid solidgetfaces def
+ F length 1 sub i lt {
+ (Error : indice trop grand dans solidrmface) ==
+ quit
+ } if
+ [
+ 0 1 F length 1 sub {
+ /j exch def
+ i j ne {
+ F j get
+ } if
+ } for
+ ]
+ /NF exch def
+ solid NF solidputfaces
+ %% on enleve la couleur correspondante
+ /FC solid solidgetfcolors def
+ [
+ 0 1 FC length 1 sub {
+ /j exch def
+ i j ne {
+ FC j get
+ } if
+ } for
+ ]
+ /NFC exch def
+ solid NFC solidputfcolors
+ %% on ajuste la table inout
+ /IO solid solidgetinouttable def
+ solid i solidisoutface {
+ IO 1 IO 1 get 1 sub put
+ solid solidwithinfaces {
+ IO 2 IO 2 get 1 sub put
+ IO 3 IO 3 get 1 sub put
+ } if
+ } if
+ solid i solidisinface {
+ IO 1 IO 1 get 1 sub put
+ IO 2 IO 2 get 1 sub put
+ IO 3 IO 3 get 1 sub put
+ } if
+ solid IO solidputinouttable
+end
+} def
+
+%% syntaxe : solid table solidrmfaces --> -
+/solidrmfaces {
+2 dict begin
+ /table exch bubblesort reverse def
+ /solid exch def
+ table {solid exch solidrmface} apply
+end
+} def
+
+%%%%% ### videsolid ###
+%% syntaxe : solid videsolid -> -
+/videsolid {
+5 dict begin
+ /solid exch def
+ solid issolid not {
+ (Error : mauvais type d argument dans videsolid) ==
+ quit
+ } if
+ solid solidwithinfaces not {
+ /IO solid solidgetinouttable def
+ /FE solid solidgetfaces def
+ /n FE length def
+ IO 2 n put
+ IO 3 2 n mul 1 sub put
+ solid IO solidputinouttable
+ %% on inverse chaque face
+ /FI FE {reverse} apply def
+ solid FE FI append solidputfaces
+ %% et on rajoute autant de couleurs vides que de faces
+ /FEC solid solidgetfcolors def
+% /FIC [FI length {()} repeat] def
+% solid FEC FIC append solidputfcolors
+ solid FEC duparray append solidputfcolors
+ } if
+end
+} def
+
+%%%%% ### solidnumfaces ###
+%% syntaxe : solid array solidnumfaces
+%% syntaxe : solid array bool solidnumfaces
+%% array, le tableau des indices des faces a numeroter, est optionnel
+%% si bool=true, on ne numerote que les faces visibles
+/solidnumfaces {
+5 dict begin
+ dup isbool {
+ /bool exch def
+ } {
+ /bool true def
+ } ifelse
+% setTimes
+ dup issolid not {
+ %% on a un argument
+ /option exch def
+ } if
+ /sol exch def
+ /n sol solidnombrefaces def
+ currentdict /option known not {
+ /option [0 1 n 1 sub {} for] def
+ } if
+
+ 0 1 option length 1 sub {
+ /i exch def
+ /j option i get def
+ j ( ) cvs sol j bool cctextp3d
+ } for
+end
+} def
+
+%%%%% ### creusesolid ###
+%% syntaxe : solid creusesolid -> -
+/creusesolid {
+5 dict begin
+ /solid exch def
+ solid issolid not {
+ (Error : mauvais type d argument dans creusesolid) ==
+ quit
+ } if
+ %% on enleve le fond et le chapeau
+ solid 1 solidrmface
+ solid 0 solidrmface
+ %% on inverse chaque face
+ solid videsolid
+end
+} def
+
+%%%%% ### fin insertion ###
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% dessin des solides %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%% ### solidisinface ###
+%% syntaxe : solid i solidisinface --> bool
+%% true si i est l indice d une face interne, false sinon
+/solidisinface {
+4 dict begin
+ /i exch def
+ solidgetinouttable /IO exch def
+ /n1 IO 2 get def
+ /n2 IO 3 get def
+ n1 i le
+ i n2 le and
+end
+} def
+
+%%%%% ### solidisoutface ###
+%% syntaxe : solid i solidisoutface --> bool
+%% true si i est l indice d une face externe, false sinon
+/solidisoutface {
+4 dict begin
+ /i exch def
+ solidgetinouttable /IO exch def
+ /n1 IO 0 get def
+ /n2 IO 1 get def
+ n1 i le
+ i n2 le and
+end
+} def
+
+%%%%% ### planvisible ###
+%% syntaxe : A k planvisible? --> true si le plan est visible
+/planvisible? {
+4 dict begin
+ /normale_plan defpoint3d
+ /origine defpoint3d
+ /ligne_de_vue {
+ origine
+ GetCamPos
+ vecteur3d
+ } def
+ ligne_de_vue normale_plan scalprod3d 0 gt
+end
+} def
+
+%%%%% ### solidlight ###
+/setlightintensity {
+ /lightintensity exch def
+} def
+
+/setlightsrc {
+ /lightsrc defpoint3d
+} def
+
+/setlight {
+1 dict begin
+gsave
+ exec
+ [ currentrgbcolor ] /lightcolor exch
+grestore
+end
+def
+} def
+
+%%%%% ### drawsolid ###
+/solidlightOn {
+ /s@lidlight true def
+} def
+/solidlightOff {
+ /s@lidlight false def
+} def
+solidlightOff
+
+%% syntaxe : solid i solidfacevisible? --> true si la face est visible
+/solidfacevisible? {
+4 dict begin
+ /i exch def
+ /solid exch def
+ solid issolid not {
+ (Error : mauvais type d argument dans solidgetsommetface) ==
+ quit
+ } if
+ solid i solidgetface length 2 le {
+ true
+ } {
+ /ligne_de_vue {
+ solid i solidcentreface
+ GetCamPos
+ vecteur3d
+ } def
+
+ /normale_face {
+ solid i solidnormaleface
+ } def
+ ligne_de_vue normale_face scalprod3d 0 gt
+ } ifelse
+end
+} def
+
+%% syntaxe : solid i affectecouleursolid_facei --> si la couleur de
+%% la face i est definie, affecte fillstyle a cette couleur
+/affectecouleursolid_facei {
+3 dict begin
+ /i exch def
+ /solid exch def
+ solid solidgetfcolors /FC exch def
+ FC length 1 sub i ge {
+ FC i get length 1 ge {
+ /fillstyle FC i get ( fill) append cvx
+ solidgrid not {
+ FC i get cvx exec
+ } if
+ true
+ } {
+ false
+ } ifelse
+ } {
+ false
+ } ifelse
+end
+{def} if
+} def
+
+%% syntaxe : solid i dessinefacecachee
+/dessinefacecachee {
+11 dict begin
+ /i exch def
+ /solid exch def
+ solid issolid not {
+ (Error : mauvais type d argument dans dessinefacecachee) ==
+ quit
+ } if
+
+ /F solid solidgetfaces def
+ /S solid solidgetsommets def
+
+ %% face cachee => on prend chacune des aretes de la face et on
+ %% la dessine
+ 4 dict begin
+ /n F i get length def %% nb de sommets de la face
+ 0 1 n 1 sub {
+ /k exch def
+ /k1 F i k get_ij def %% indice sommet1
+ /k2 F i k 1 add n mod get_ij def %% indice sommet2
+ gsave
+ currentlinewidth .5 mul setlinewidth
+ pointilles
+ [S k1 getp3d
+ S k2 getp3d sortp3d] ligne3d
+ grestore
+ } for
+
+ %% trace de la ligne de niveau
+ solidintersectiontype 0 ge {
+ /face_a_dessiner [ %% face visible : F [i]
+ 0 1 n 1 sub {
+ /j exch def
+ solid j i solidgetsommetface
+ } for
+ ] def
+ 0 1 solidintersectionplan length 1 sub {
+ /k exch def
+ /lignedeniveau [] def
+ gsave
+ solidintersectiontype 0 eq {
+ pointilles
+ } {
+ continu
+ } ifelse
+ k solidintersectionlinewidth length lt {
+ solidintersectionlinewidth k get setlinewidth
+ } {
+ solidintersectionlinewidth 0 get setlinewidth
+ } ifelse
+ k solidintersectioncolor length lt {
+ solidintersectioncolor k get cvx exec
+ } {
+ solidintersectioncolor 0 get cvx exec
+ } ifelse
+ 0 1 n 1 sub {
+ /j exch def
+ face_a_dessiner j getp3d
+ face_a_dessiner j 1 add n mod getp3d
+ solidintersectionplan k get
+ dup isarray {
+ segment_inter_plan
+ } {
+ segment_inter_planz
+ } ifelse {
+ 1 dict begin
+ /table exch def
+ table length 6 eq {
+ /lignedeniveau table store
+ exit
+ } {
+ /lignedeniveau [
+ lignedeniveau aload pop
+ table 0 getp3d
+ ] store
+ } ifelse
+ end
+ } if
+ } for
+
+ %% dessin de la ligne
+ lignedeniveau length 4 ge {
+ [lignedeniveau aload pop sortp3d] ligne3d
+ } if
+ grestore
+ } for
+ } if
+
+ end
+end
+} def
+
+%% syntaxe : solid i dessinefacevisible
+/dessinefacevisible {
+8 dict begin
+ /i exch def
+ /solid exch def
+ solid issolid not {
+ (Error : mauvais type d argument dans dessinefacevisible) ==
+ quit
+ } if
+ /F solid solidgetfaces def
+ /S solid solidgetsommets def
+
+ /n F i get length def %% nb de sommets de la face
+
+ startest {
+ s@lidlight {
+ /coeff
+ lightintensity
+ solid i solidnormaleface normalize3d
+ solid i solidcentreface lightsrc vecteur3d normalize3d
+ scalprod3d mul
+ 0 max 1 min
+ def
+ /lightcolor where {
+ pop
+ /lacouleur lightcolor def
+ } {
+ /lacouleur [
+ gsave
+ solid solidgetfcolors i get cvx exec currentrgbcolor
+ grestore
+ ] def
+ } ifelse
+ /fillstyle {
+ lacouleur {coeff mul} apply setcolor fill
+ } def
+ solidgrid not {
+ lacouleur {coeff mul} apply setcolor
+ } if
+ } {
+ n 2 eq {
+ 1 dict begin
+ solidgridOff
+ solid i affectecouleursolid_facei
+ end
+ } {
+ solid i affectecouleursolid_facei
+ } ifelse
+ } ifelse
+ } if
+
+ /face_a_dessiner [ %% face visible : F [i]
+ 0 1 n 1 sub {
+ /j exch def
+ solid j i solidgetsommetface
+ } for
+ ] def
+ face_a_dessiner polygone3d
+
+ %% trace de la ligne de niveau
+ solidintersectiontype 0 ge {
+ 0 1 solidintersectionplan length 1 sub {
+ /k exch def
+ /lignedeniveau [] def
+ gsave
+ k solidintersectionlinewidth length lt {
+ solidintersectionlinewidth k get setlinewidth
+ } {
+ solidintersectionlinewidth 0 get setlinewidth
+ } ifelse
+ k solidintersectioncolor length lt {
+ solidintersectioncolor k get cvx exec
+ } {
+ solidintersectioncolor 0 get cvx exec
+ } ifelse
+ 0 1 n 1 sub {
+ /j exch def
+ face_a_dessiner j getp3d
+ face_a_dessiner j 1 add n mod getp3d
+ solidintersectionplan k get
+ dup isarray {
+ segment_inter_plan
+ } {
+ segment_inter_planz
+ } ifelse {
+ 1 dict begin
+ /table exch def
+ /lignedeniveau [
+ lignedeniveau aload pop
+ table 0 getp3d
+ table length 4 ge {
+ table 1 getp3d
+ } if
+ ] store
+ end
+ } if
+ } for
+
+ %% dessin de la ligne
+ lignedeniveau length 4 ge {
+ solid i solidisinface solidintersectiontype 0 eq and {
+ pointilles
+ } if
+ lignedeniveau ligne3d
+ } if
+ grestore
+ } for
+ } if
+
+end
+} def
+
+/drawsolid* {
+1 dict begin
+ /startest {true} def
+ drawsolid
+end
+} def
+
+/peintrealgorithme false def
+
+/drawsolid** {
+2 dict begin
+ /aretescachees false def
+ /peintrealgorithme true def
+ drawsolid*
+end
+} def
+
+%% syntaxe : solid array drawsolid
+%% array est en option, il indique les faces triees
+/drawsolid {
+8 dict begin
+ dup issolid not {
+ /ordre exch def
+ } if
+ /solid exch def
+ solid issolid not {
+ (Error : mauvais type d argument dans drawsolid) ==
+ quit
+ } if
+ solid nullsolid not {
+ solid solidgetfaces
+ /F exch def
+ solid solidgetsommets
+ /S exch def
+ /n S length 3 idiv def
+
+ currentdict /ordre known not {
+ peintrealgorithme {
+ %% tri des indices des faces par distance decroissante
+ [
+ 0 1 F length 1 sub {
+ /i exch def
+ solid i solidcentreface
+ GetCamPos
+ distance3d
+ } for
+ ] doublequicksort pop reverse
+ } {
+ [
+ 0 1 F length 1 sub {
+ } for
+ ]
+ } ifelse
+ /ordre exch def
+ } if
+
+ 0 1 F length 1 sub {
+ /k exch def
+ /i ordre k get def
+ gsave
+ solid i solidfacevisible? {
+ solid i dessinefacevisible
+ } if
+ grestore
+ } for
+ aretescachees {
+ 0 1 F length 1 sub {
+ /k exch def
+ /i ordre k get def
+ gsave
+ solid i solidfacevisible? not {
+ solid i dessinefacecachee
+ } if
+ grestore
+ } for
+ } if
+
+%% %% si on veut repasser les traits des faces visibles
+%% 0 1 F length 1 sub {
+%% /k exch def
+%% /i ordre k get def
+%% gsave
+%% 1 dict begin
+%% /startest false def
+%% solid i solidfacevisible? {
+%% solid i dessinefacevisible
+%% } if
+%% end
+%% grestore
+%% } for
+ } if
+end
+} def
+
+%%%%% ### segment_inter_planz ###
+%% syntaxe : A B k segment_inter_planz --> array true ou false
+/segment_inter_planz {
+4 dict begin
+ /k exch def
+ /B defpoint3d
+ /A defpoint3d
+ A /zA exch def pop pop
+ B /zB exch def pop pop
+ zA k sub zB k sub mul dup 0 gt {
+ %% pas d intersection
+ pop
+ false
+ } {
+ 0 eq {
+ %% intersection en A ou en B
+ [
+ zA k eq {A} if
+ zB k eq {B} if
+ ] true
+ } {
+ %% intersection entre A et B
+ [
+ A B vecteur3d
+ k zA sub zB zA sub div mulv3d
+ A addv3d
+ ] true
+ } ifelse
+ } ifelse
+end
+} def
+
+%%%%% ### fin insertion ###
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% plans affines %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%% ### planaffine ###
+%% plan : origine, base, range, ngrid
+%% [0 0 0 [1 0 0 0 1 0] [-3 3 -2 2] [1. 1.] ]
+
+/explan [0 0 0 [1 0 0 0 1 0 0 0 1] [-3 3 -2 2] [1. 1.] ] def
+
+%% syntaxe : any isplan --> bool
+/isplan {
+1 dict begin
+ /candidat exch def
+ candidat isarray {
+ candidat length 6 eq {
+ candidat 3 get isarray {
+ candidat 4 get isarray {
+ candidat 5 get isarray
+ } {
+ false
+ } ifelse
+ } {
+ false
+ } ifelse
+ } {
+ false
+ } ifelse
+ } {
+ false
+ } ifelse
+end
+} def
+
+/newplanaffine {
+ [0 0 0 [1 0 0 0 1 0] [-3 3 -2 2] [1 1]]
+} def
+
+/dupplan {
+4 dict begin
+ /leplan exch def
+ /result newplanaffine def
+ result leplan plangetorigine planputorigine
+ result leplan plangetbase planputbase
+ result leplan plangetrange planputrange
+ result leplan plangetngrid planputngrid
+ result
+end
+} def
+
+%% syntaxe : plantype getorigine --> x y z
+/plangetorigine {
+1 dict begin
+ /plan exch def
+ plan isplan not {
+ (Erreur : mauvais type d argument dans plangetorigine) ==
+ Error
+ } if
+ plan 0 get
+ plan 1 get
+ plan 2 get
+end
+} def
+
+%% syntaxe : plantype getbase --> [u v w]
+%% ou u, v et w vecteurs de R^3
+/plangetbase {
+1 dict begin
+ /plan exch def
+ plan isplan not {
+ (Erreur : mauvais type d argument dans plangetbase) ==
+ Error
+ } if
+ plan 3 get
+end
+} def
+
+%% syntaxe : plantype getrange --> array
+%% ou array = [xmin xmax ymin ymax]
+/plangetrange {
+1 dict begin
+ /plan exch def
+ plan isplan not {
+ (Erreur : mauvais type d argument dans plangetrange) ==
+ Error
+ } if
+ plan 4 get
+end
+} def
+
+%% syntaxe : plantype getngrid --> array
+%% ou array = [n1 n2]
+/plangetngrid {
+1 dict begin
+ /plan exch def
+ plan isplan not {
+ (Erreur : mauvais type d argument dans plangetngrid) ==
+ Error
+ } if
+ plan 5 get
+end
+} def
+
+%% ===================
+
+%% syntaxe : plantype x y z putorigine --> -
+/planputorigine {
+4 dict begin
+ /z exch def
+ /y exch def
+ /x exch def
+ /plan exch def
+ plan isplan not {
+ (Erreur : mauvais type d argument dans planputorigine) ==
+ Error
+ } if
+ plan 0 x put
+ plan 1 y put
+ plan 2 z put
+end
+} def
+
+%% syntaxe : plantype [u v w] putbase --> -
+%% ou u, v et w vecteurs de R^3
+/planputbase {
+2 dict begin
+ /base exch def
+ /plan exch def
+ plan isplan not {
+ (Erreur : mauvais type d argument dans planputbase) ==
+ Error
+ } if
+ plan 3 base put
+end
+} def
+
+%% syntaxe : plantype array putrange --> -
+%% ou array = [xmin xmax ymin ymax]
+/planputrange {
+2 dict begin
+ /table exch def
+ /plan exch def
+ plan isplan not {
+ (Erreur : mauvais type d argument dans planputrange) ==
+ Error
+ } if
+ plan 4 table put
+end
+} def
+
+%% syntaxe : plantype array putngrid --> -
+%% ou array = [n1 n2]
+/planputngrid {
+2 dict begin
+ /table exch def
+ /plan exch def
+ plan isplan not {
+ (Erreur : mauvais type d argument dans planputngrid) ==
+ quit
+ } if
+ plan 5 table put
+end
+} def
+
+%% -3 3 -2 2 1. 1. newgrille
+%% drawsolid
+
+%orange
+
+%% plan : origine, base, range, ngrid
+
+%% syntaxe : plantype drawplanaffine --> -
+/drawplanaffine {
+5 dict begin
+ /plan exch def
+ plan plangetbase
+ aload pop
+ /imK defpoint3d
+ /imJ defpoint3d
+ /imI defpoint3d
+ newpath
+ plan plangetrange plan plangetngrid aload pop quadrillagexOy_
+ plan plangetorigine [imI imK] false planprojpath
+ stroke
+end
+} def
+
+
+%% %% syntaxe : [a b c d] (x0 y0 z0) alpha defeqplanaffine --> plantype
+%% %% plan defini par l equation ax+by+cz+d=0,
+%% %% rotation de alpha autour de la normale (alpha est optionnel)
+%% %% origine (x0, y0, z0). l origine est optionnelle
+%% /defeqplanaffine {
+%% 5 dict begin
+%% dup isarray {
+%% /alpha 0 def
+%% } {
+%% dup isstring {
+%% /alpha 0 def
+%% } {
+%% /alpha exch def
+%% } ifelse
+%% } ifelse
+%% dup isstring {
+%% cvx /origine exch def
+%% } if
+%% /table exch def
+%% table length 4 ne {
+%% (Erreur : mauvais type d argument dans defeqplanaffine) ==
+%% Error
+%% } if
+%% table 0 get /a exch def
+%% table 1 get /b exch def
+%% table 2 get /c exch def
+%% table 3 get /d exch def
+%% /resultat newplanaffine def
+%% [a b c alpha] normalvect_to_orthobase
+%% /imK defpoint3d
+%% /imJ defpoint3d
+%% /imI defpoint3d
+%% resultat [imI imJ imK] planputbase
+%% currentdict /origine known {
+%% origine /z exch def /y exch def /x exch def
+%% a x mul b y mul add c z mul add d add 0 ne {
+%% (Erreur : mauvaise origine dans defeqplanaffine) ==
+%% Error
+%% } if
+%% resultat origine planputorigine
+%% } {
+%% c 0 ne {
+%% resultat 0 0 d neg c div planputorigine
+%% } {
+%% a 0 ne {
+%% resultat d neg a div 0 0 planputorigine
+%% } {
+%% resultat 0 d neg b div 0 planputorigine
+%% } ifelse
+%% } ifelse
+%% } ifelse
+%% resultat
+%% end
+%% } def
+
+%% /explan [0 0 0 [1 0 0 0 1 0 0 0 1] [-3 3 -2 2] [1 1] ] def
+%% explan drawplanaffine
+%% noir
+%% /explan [0 0 2 [1 0 0 0 1 0 0 0 1] [-3 3 -2 2] [1 .5] ] def
+%% explan drawplanaffine
+
+%% orange
+%% [0 0 1 -2] defeqplanaffine
+%% drawplanaffine
+%% noir
+%% [0 0 1 0] defeqplanaffine
+%% drawplanaffine
+%% bleu
+%% [1 1 1 0] (1 -1 0) defeqplanaffine
+%% drawplanaffine
+%%
+
+/dessinebase {
+4 dict begin
+gsave
+ /V3 defpoint3d
+ /V2 defpoint3d
+ /V1 defpoint3d
+ /M0 defpoint3d
+ rouge
+ V3 newvecteur
+ {M0 translatepoint3d} solidtransform
+ drawsolid**
+ bleu
+ V2 newvecteur
+ {M0 translatepoint3d} solidtransform
+ drawsolid**
+ orange
+ V1 newvecteur
+ {M0 translatepoint3d} solidtransform
+ drawsolid**
+grestore
+end
+} def
+
+%% syntaxe : solid i solidface2eqplan --> [a b c d]
+%% equation cartesienne de la face d'indice i du solide solid
+/solidface2eqplan {
+8 dict begin
+ /i exch def
+ /solid exch def
+ solid i solidnormaleface
+ /c exch def
+ /b exch def
+ /a exch def
+ solid 0 i solidgetsommetface
+ /z exch def
+ /y exch def
+ /x exch def
+ [a b c a x mul b y mul add c z mul add neg]
+end
+} def
+
+
+%% syntaxe : plantype newplan --> solid
+/newplan {
+5 dict begin
+ /lepl@n exch def
+ lepl@n plangetbase /@base exch def
+ @base 0 getp3d /@U defpoint3d
+ @base 1 getp3d /@V defpoint3d
+ lepl@n plangetorigine /@M defpoint3d
+ lepl@n plangetrange /@range exch def
+ lepl@n plangetngrid /@ngrid exch def
+ /@F {
+ 2 dict begin
+ /@y exch def
+ /@x exch def
+ @U @x mulv3d
+ @V @y mulv3d
+ addv3d
+ @M addv3d
+ end
+ } def
+ @range aload pop @ngrid {@F} newsurfaceparametree
+end
+} def
+
+%% syntaxe : M eqplan --> real
+%% image de M par la fonction definie par l equation eqplan
+/pointeqplan {
+8 dict begin
+ /eqplan exch def
+ /@z exch def
+ /@y exch def
+ /@x exch def
+ /@a eqplan 0 get def
+ /@b eqplan 1 get def
+ /@c eqplan 2 get def
+ /@d eqplan 3 get def
+ @a @x mul @b @y mul add @c @z mul add @d add
+end
+} def
+
+/plan2eq {
+6 dict begin
+ /leplan exch def
+ leplan plangetbase aload pop vectprod3d
+ /c exch def
+ /b exch def
+ /a exch def
+ leplan plangetorigine
+ /z0 exch def
+ /y0 exch def
+ /x0 exch def
+ [a b c a x0 mul b y0 mul add c z0 mul add neg]
+end
+} def
+
+%% syntaxe : [a b c d] (x0 y0 z0) alpha defeqplanaffine --> plantype
+%% plan defini par l equation ax+by+cz+d=0,
+%% rotation de alpha autour de la normale (alpha est optionnel)
+%% origine (x0, y0, z0). l origine est optionnelle
+/eq2plan {
+5 dict begin
+ dup isarray {
+ /alpha 0 def
+ } {
+ dup isstring {
+ /alpha 0 def
+ } {
+ /alpha exch def
+ } ifelse
+ } ifelse
+ dup isstring {
+ cvx /origine exch def
+ } if
+ /table exch def
+ table length 4 ne {
+ (Erreur : mauvais type d argument dans eq2plan) ==
+ quit
+ } if
+ table 0 get /a exch def
+ table 1 get /b exch def
+ table 2 get /c exch def
+ table 3 get /d exch def
+ /resultat newplanaffine def
+ [a b c alpha] normalvect_to_orthobase
+ /imK defpoint3d
+ /imJ defpoint3d
+ /imI defpoint3d
+ resultat [imI imJ] planputbase
+ currentdict /origine known {
+ origine /z exch def /y exch def /x exch def
+ a x mul b y mul add c z mul add d add 0 ne {
+ (Erreur : mauvaise origine dans eq2plan) ==
+ quit
+ } if
+ resultat origine planputorigine
+ } {
+ c 0 ne {
+ resultat 0 0 d neg c div planputorigine
+ } {
+ a 0 ne {
+ resultat d neg a div 0 0 planputorigine
+ } {
+ b 0 ne {
+ resultat 0 d neg b div 0 planputorigine
+ } {
+ (Error dans eq2plan : (a,b,c) = (0,0,0)) ==
+ } ifelse
+ } ifelse
+ } ifelse
+ } ifelse
+ resultat
+end
+} def
+
+/points2eqplan {
+10 dict begin
+ /C defpoint3d
+ /B defpoint3d
+ /A defpoint3d
+ A B vecteur3d
+ A C vecteur3d
+ vectprod3d
+ normalize3d
+ /c exch def
+ /b exch def
+ /a exch def
+ A
+ /zA exch def
+ /yA exch def
+ /xA exch def
+ [a b c a xA mul b yA mul add c zA mul add neg]
+end
+} def
+
+%% /monplan
+%% %[0 0 -2 [1 0 0 0 1 0 0 0 1] [-3 3 -2 2] [1. 1.]]
+%% [0 0 1 1] 30 eq2plan
+%% def
+%%
+%% [0 0 1 -2] eq2plan newplan
+%% dup (blanc) outputcolors
+%% monplan newplan
+%% dup (blanc) outputcolors
+%% solidfuz
+%% drawsolid**
+%% monplan plangetorigine
+%% monplan plangetbase aload pop dessinebase
+
+%% syntaxe : x0 y0 z0 [normalvect] norm2plan
+/norm2plan {
+9 dict begin
+ normalvect_to_orthobase
+ /imK defpoint3d
+ /imJ defpoint3d
+ /imI defpoint3d
+ imK
+ /c exch def
+ /b exch def
+ /a exch def
+ /z0 exch def
+ /y0 exch def
+ /x0 exch def
+ [a b c a x0 mul b y0 mul add c z0 mul add neg] eq2plan
+ dup x0 y0 z0 planputorigine
+ dup [imI imJ] planputbase
+end
+} def
+
+%% syntaxe : plantype planxmarks
+/planxmarks {
+5 dict begin
+ dup isbool {
+ /mybool exch def
+ } {
+ /mybool true def
+ } ifelse
+ /leplan exch def
+ leplan plangetrange aload pop
+ /ymax exch def
+ /ymin exch def
+ /xmax exch def
+ /xmin exch def
+ newpath
+ xmin truncate cvi 0 smoveto
+ xmax truncate cvi 0 slineto
+ leplan mybool projpath
+ stroke
+ xmin truncate cvi xmkstep xmax truncate cvi {
+ dup 0 ne {
+ /x exch def
+ x
+ x x truncate eq {
+ cvi
+ } if
+ dup chaine cvs exch 0 leplan mybool dctextp3d
+ newpath
+ x 0 smoveto
+ 0 2.5 rmoveto
+ 0 -5 rlineto
+ leplan mybool projpath
+ stroke
+ } {
+ pop (0) 0 0 leplan mybool dltextp3d
+ } ifelse
+ } for
+end
+} def
+
+%% syntaxe : plantype planymarks
+/planymarks {
+5 dict begin
+ dup isbool {
+ /mybool exch def
+ } {
+ /mybool true def
+ } ifelse
+ /leplan exch def
+ leplan plangetrange aload pop
+ /ymax exch def
+ /ymin exch def
+ /xmax exch def
+ /xmin exch def
+ newpath
+ 0 ymin truncate cvi smoveto
+ 0 ymax truncate cvi slineto
+ leplan mybool projpath
+ stroke
+ ymin truncate cvi ymkstep ymax truncate cvi {
+ dup 0 ne {
+ /y exch def
+ y
+ y y truncate eq {
+ cvi
+ } if
+ dup chaine cvs exch 0 exch leplan mybool cltextp3d
+ newpath
+ 0 y smoveto
+ 2.5 0 rmoveto
+ -5 0 rlineto
+ leplan mybool projpath
+ stroke
+ } {
+ pop (0) 0 0 leplan mybool dltextp3d
+ } ifelse
+ } for
+end
+} def
+
+%% syntaxe : plantype planmarks
+/planmarks {
+1 dict begin
+ dup isbool {
+ /mybool exch def
+ } {
+ /mybool true def
+ } ifelse
+ dup mybool planxmarks mybool planymarks
+end
+} def
+
+%% bleu
+%% [-3 3 -2 2] quadrillagexOy_
+%% stroke
+%% noir
+
+%% syntaxe : [xmin xmax ymin ymax] dx dy quadrillagexOy_
+/quadrillagexOy_ {
+4 dict begin
+ dup isarray {
+ /dx 1 def
+ /dy 1 def
+ } {
+ /dy exch def
+ dup isarray {
+ /dx dy def
+ } {
+ /dx exch def
+ } ifelse
+ } ifelse
+ /table exch def
+ table 0 get /xmin exch def
+ table 1 get /xmax exch def
+ table 2 get /ymin exch def
+ table 3 get /ymax exch def
+ ymin dy ymax {
+ /y exch def
+ xmin y smoveto
+ xmax y slineto
+ } for
+ xmin dx xmax {
+ /x exch def
+ x ymin smoveto
+ x ymax slineto
+ } for
+end
+} def
+
+%% syntaxe : plan [ngrid] planquadrillage
+/planquadrillage {
+4 dict begin
+ dup isbool {
+ /mybool exch def
+ } {
+ /mybool true def
+ } ifelse
+ dup isplan {
+ /ngrid [1 1] def
+ } {
+ /ngrid exch def
+ } ifelse
+ /leplan exch def
+ /dx ngrid 0 get def
+ /dy ngrid 1 get def
+ /table leplan plangetrange def
+ table 0 get cvi truncate /xmin exch def
+ table 1 get cvi truncate /xmax exch def
+ table 2 get cvi truncate /ymin exch def
+ table 3 get cvi truncate /ymax exch def
+ newpath
+ ymin dy ymax {
+ /y exch def
+ xmin y smoveto
+ xmax y slineto
+ } for
+ xmin dx xmax {
+ /x exch def
+ x ymin smoveto
+ x ymax slineto
+ } for
+ leplan mybool projpath
+ stroke
+end
+} def
+
+%% syntaxe : plantype str1 str2 planshowbase -> -
+%% syntaxe : plantype str2 planshowbase -> -
+%% syntaxe : plantype planshowbase -> -
+/planshowbase {
+3 dict begin
+ dup isbool {
+ /mybool exch def
+ } {
+ /mybool true def
+ } ifelse
+ dup isstring {
+ /couleur2 exch def
+ dup isstring {
+ /couleur1 exch def
+ } {
+ /couleur1 (rouge) def
+ } ifelse
+ } {
+ /couleur1 (rouge) def
+ /couleur2 (vert) def
+ } ifelse
+ mybool bprojscene
+ couleur1 cvx exec
+ newpath
+ 0 0 smoveto
+ 1 0 slineto
+ stroke
+ 0 0 1 0 oldarrow
+ couleur2 cvx exec
+ newpath
+ 0 0 smoveto
+ 0 1 slineto
+ stroke
+ 0 0 0 1 oldarrow
+ eprojscene
+end
+} def
+
+%% syntaxe : plantype str1 str2 str3 planshowbase3d -> -
+%% syntaxe : plantype str2 str3 planshowbase3d -> -
+%% syntaxe : plantype str3 planshowbase3d -> -
+%% syntaxe : plantype planshowbase3d -> -
+%% syntaxe : plantype str1 str2 str3 array planshowbase3d -> -
+%% syntaxe : plantype str2 str3 array planshowbase3d -> -
+%% syntaxe : plantype str3 array planshowbase3d -> -
+%% syntaxe : plantype array planshowbase3d -> -
+/planshowbase3d {
+7 dict begin
+ dup isbool {
+ /mybool exch def
+ } {
+ /mybool true def
+ } ifelse
+ dup dup isarray exch isplan not and {
+ /table exch def
+ } {
+ /table {} def
+ } ifelse
+ dup isstring {
+ /couleur3 exch def
+ dup isstring {
+ /couleur2 exch def
+ dup isstring {
+ /couleur1 exch def
+ } {
+ /couleur1 (rouge) def
+ } ifelse
+ } {
+ /couleur2 (vert) def
+ /couleur1 (rouge) def
+ } ifelse
+ } {
+ /couleur1 (rouge) def
+ /couleur2 (vert) def
+ /couleur3 (bleu) def
+ } ifelse
+ /plan exch def
+ plan couleur1 couleur2 mybool planshowbase
+ plan plangetorigine /I defpoint3d
+ plan plangetbase
+ dup 0 getp3d /u defpoint3d
+ 1 getp3d /v defpoint3d
+ u v vectprod3d table newvecteur
+ {I addv3d} solidtransform
+ dup couleur3 solidputcolors
+ solidgridOff
+ drawsolid**
+end
+} def
+
+%% syntaxe : plantype x y z plantranslate --> -
+/plantranslate {
+4 dict begin
+ /M defpoint3d
+ /plan exch def
+ plan isplan not {
+ (Erreur : mauvais type d argument dans plantranslate) ==
+ quit
+ } if
+ plan plan plangetorigine M addv3d planputorigine
+end
+} def
+
+% syntaxe : alpha_x alpha_y alpha_z rotateOpplan --> -
+/rotateOplan {
+4 dict begin
+ /Rxyz defpoint3d
+ /plan exch def
+ plan isplan not {
+ (Erreur : mauvais type d argument dans rotateOplan) ==
+ quit
+ } if
+ plan plan plangetorigine Rxyz rotateOpoint3d planputorigine
+
+ plan plangetbase 0 getp3d /U defpoint3d
+ plan plangetbase 1 getp3d /V defpoint3d
+ plan [
+ U Rxyz rotateOpoint3d
+ V Rxyz rotateOpoint3d
+ ] planputbase
+end
+} def
+
+%% syntaxe : plantype phi rotateplan --> -
+/rotateplan {
+5 dict begin
+ /phi exch def
+ /leplan exch def
+ leplan plangetbase 0 getp3d /U defpoint3d
+ leplan plangetbase 1 getp3d /V defpoint3d
+ U phi cos mulv3d
+ V phi sin mulv3d addv3d /U0 defpoint3d
+ U phi sin neg mulv3d
+ V phi cos mulv3d addv3d /V0 defpoint3d
+ leplan [U0 V0] planputbase
+end
+} def
+
+%% syntaxe : solid i solidface2plan --> plantype
+%% syntaxe : solid i I solidface2plan --> plantype
+/solidface2plan {
+5 dict begin
+ 2 copy pop issolid {
+ /i exch def
+ /solid exch def
+ solid i solidcentreface /I defpoint3d
+ } {
+ /I defpoint3d
+ /i exch def
+ /solid exch def
+ } ifelse
+ /result newplanaffine def
+ solid i solidcentreface /G defpoint3d
+ solid i solidnormaleface /K defpoint3d
+ solid 0 i solidgetsommetface
+ solid 1 i solidgetsommetface
+ milieu3d /A defpoint3d
+ G A vecteur3d normalize3d /U defpoint3d
+ K U vectprod3d /V defpoint3d
+ result [U V] planputbase
+ result I planputorigine
+ result
+end
+} def
+
+%%%%% ### fin insertion ###
+%% syntaxe : x y plantype pointplan --> X Y Z
+/pointplan {
+5 dict begin
+ /leplan exch def
+ /y exch def
+ /x exch def
+ leplan plangetbase 0 getp3d /U defpoint3d
+ leplan plangetbase 1 getp3d /V defpoint3d
+ U x mulv3d V y mulv3d addv3d
+end
+} def
+
+%%%%% ### fin insertion ###
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% operations sur des solides particuliers %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+/piedist {
+4 dict begin
+ /mypie exch def
+ mypie 0 solidgetface length /n exch def
+ mypie n 2 idiv solidgetsommet /A defpoint3d
+ mypie n 2 idiv 1 add solidgetsommet /B defpoint3d
+ A B milieu3d GetCamPos distance3d
+end
+} def
+
+/sortpieset {
+5 dict begin
+ dup issolid {
+ ]
+ } if
+ /table exch def
+ [
+ 0 1 table length 1 sub {
+ /i exch def
+ table i get piedist
+ } for
+ ]
+ doublequicksort pop reverse
+ /result exch def
+ [
+ 0 1 result length 1 sub {
+ /i exch def
+ table result i get get
+ } for
+ ]
+end
+} def
+
+/drawpieset {
+1 dict begin
+ /startest true def
+ sortpieset dup {drawsolid**} apply {0 dessinefacevisible} apply
+end
+} def
+
+%%%%% ### solidchanfreine ###
+%% syntaxe : solid coeff solidchanfreine --> solid
+/solidchanfreine {
+10 dict begin
+ /coeff exch def
+ /solid exch def
+ /result newsolid def
+ solid issolid not {
+ (Erreur : mauvais type d argument dans solidchanfreine) ==
+ quit
+ } if
+ /n solid solidnombresommets def
+ /nf solid solidnombrefaces def
+
+ %% ajout des faces reduites
+ 0 1 nf 1 sub {
+ /i exch def
+ /Fsommets solid i solidgetsommetsface def
+ /Findex solid i solidgetface def
+ /ns Fsommets length 3 idiv def
+ /couleurfaceorigine solid i solidgetfcolor def
+ Fsommets isobarycentre3d /G defpoint3d
+ %% on ajoute les nouveaux sommets
+ /Sindex [] def
+ 0 1 ns 1 sub {
+ /j exch def
+ /Sindex [ Sindex aload pop
+ Fsommets j getp3d /M defpoint3d
+ result M G coeff hompoint3d solidaddsommet
+ ] store
+ } for
+ %% Sindex contient les indices des nouveaux sommets
+ result Sindex couleurfaceorigine solidaddface
+ } for
+
+ %% ajout des faces rectangulaires entre faces d'origines adjacentes
+ %% pour chaque face de depart
+ 0 1 nf 2 sub {
+ /i exch def
+ /F solid i solidgetface def
+ /couleurfaceorigine solid i solidgetfcolor def
+ /Fres result i solidgetface def
+ %% pour chaque arete de la face
+ 0 1 F length 1 sub {
+ /j exch def
+ /trouve false def
+ /indice1 F j get def
+ /indice2 F j 1 add F length mod get def
+ /a1 j def
+ /a2 j 1 add F length mod def
+ %% on regarde toutes les autres faces
+ i 1 add 1 nf 1 sub {
+ /k exch def
+ /Ftest solid k solidgetface def
+ indice1 Ftest in {pop true} {false} ifelse
+ indice2 Ftest in {pop true} {false} ifelse
+ and {
+ /indiceFadj k def
+ indice1 Ftest in pop /k1 exch def
+ indice2 Ftest in pop /k2 exch def
+ /trouve true def
+ exit
+ } if
+ } for
+ trouve {
+ /Fadj solid indiceFadj solidgetface def
+ result [
+ Fres a1 get
+ result indiceFadj solidgetface k1 get
+ result indiceFadj solidgetface k2 get
+ Fres a2 get
+ ] couleurfaceorigine solidaddface
+ } if
+ } for
+ } for
+
+ %% pour chaque face
+ 0 1 nf 2 sub {
+ /i exch def
+ /F solid i solidgetface def
+ /couleurfaceorigine solid i solidgetfcolor def
+ %% et pour chaque sommet de cette face
+ 0 1 F length 1 sub {
+ /j exch def
+ /k F j get def
+ solid k solidfacesadjsommet /adj exch def
+ %% adj est le tableau des indices des faces adjacentes
+ %% au sommet d'indice k
+ %% rque : toutes les faces d'indice strict inferieur a i
+ %% sont deja traitees
+ %% Pour chaque face adjacente, on repere l'indice du sommet concerne dans
+ %% la face
+ adj min i lt not {
+ /indadj [] def
+ 0 1 adj length 1 sub {
+ /m exch def
+ k solid adj m get solidgetface in {
+ /ok exch def
+ /indadj [indadj aload pop ok] store
+ } if
+ } for
+
+ /aajouter [
+ 0 1 adj length 1 sub {
+ /m exch def
+ result adj m get solidgetface indadj m get get
+ } for
+ ] def
+
+ %% la table des sommets
+ [0 1 aajouter length 1 sub {
+ /m exch def
+ result aajouter m get solidgetsommet
+ } for]
+ solid k solidgetsommet %% le point indiquant la direction de la normale
+ ordonnepoints3d
+ /indicestries exch def
+
+ result [
+ 0 1 indicestries length 1 sub {
+ /m exch def
+ aajouter indicestries m get get
+ } for
+ ] couleurfaceorigine solidaddface
+ } if
+ } for
+ } for
+
+ result
+end
+} def
+
+%%%%% ### solidplansection ###
+%% syntaxe : M eqplan --> real
+%% image de M par la fonction definie par l equation eqplan
+/pointeqplan {
+8 dict begin
+ /@qplan exch def
+ /@z exch def
+ /@y exch def
+ /@x exch def
+ /@a @qplan 0 get def
+ /@b @qplan 1 get def
+ /@c @qplan 2 get def
+ /@d @qplan 3 get def
+ @a @x mul @b @y mul add @c @z mul add @d add
+end
+} def
+
+%% syntaxe : A B eqplan segment_inter_plan --> array true ou false
+%% array contient 1 point M si [AB] inter plan = {M}
+%% array contient les 2 points A et B si [AB] inter plan = [AB]
+/segment_inter_plan {
+4 dict begin
+ dup isplan {plan2eq} if
+ /plan exch def
+ plan aload pop
+ /d exch def
+ /c exch def
+ /b exch def
+ /a exch def
+ /B defpoint3d
+ /A defpoint3d
+ A
+ /zA exch def
+ /yA exch def
+ /xA exch def
+ B
+ /zB exch def
+ /yB exch def
+ /xB exch def
+ /imA a xA mul b yA mul add c zA mul add d add def
+ /imB a xB mul b yB mul add c zB mul add d add def
+ imA imB mul dup 0 gt {
+ %% pas d intersection
+ pop
+ false
+ } {
+ 0 eq {
+ %% intersection en A ou en B
+ [
+ imA 0 eq {A} if
+ imB 0 eq {B} if
+ ] true
+ } {
+ %% intersection entre A et B
+ /k
+ imA neg
+ xB xA sub a mul
+ yB yA sub b mul add
+ zB zA sub c mul add
+ dup 0 eq {
+ (Error dans segment_inter_plan) ==
+ quit
+ } if
+ div
+ def
+ [
+ A B vecteur3d
+ k mulv3d
+ A addv3d
+ ] true
+ } ifelse
+ } ifelse
+end
+} def
+
+%% syntaxe : solid i solidface2eqplan --> [a b c d]
+%% equation cartesienne de la face d'indice i du solide solid
+/solidface2eqplan {
+8 dict begin
+ /i exch def
+ /solid exch def
+ solid i solidnormaleface
+ /c exch def
+ /b exch def
+ /a exch def
+ solid 0 i solidgetsommetface
+ /z exch def
+ /y exch def
+ /x exch def
+ [a b c a x mul b y mul add c z mul add neg]
+end
+} def
+
+%% syntaxe : array1 arrayrmdouble --> array2
+%% remplace 2 elts identiques consecutifs par 1 elt
+/arrayrmdouble {
+5 dict begin
+ /table exch def
+ /result [table 0 get] def
+ /j 0 def
+ 1 1 table length 1 sub {
+ /i exch def
+ table i get
+ result j get
+ eq not {
+ /result [result aload pop table i get] store
+ /j j 1 add store
+ } if
+ } for
+ result
+end
+} def
+
+%% syntaxe : solid eqplan/plantype solidplansection --> solid2
+/solidplansection {
+10 dict begin
+ dup isbool {
+ /tr@nsmit exch def
+ } {
+ /tr@nsmit false def
+ } ifelse
+ dup isplan {
+ plan2eqplan
+ /eqplan exch def
+ } {
+ /eqplan exch def
+ } ifelse
+ dupsolid /result exch def
+ /solid exch def
+ /aenlever [] def
+ /indnouveauxsommets [] def
+ /nouvellesaretes [] def
+
+ %% pour chaque face d'indice i
+ 0 1 solid solidnombrefaces 1 sub {
+ /i exch def
+ /lacouleur solid i solidgetfcolor def
+ /F solid i solidgetface def %% table des indices des sommets
+ /n F length def %% nb d'aretes
+ /k1 -1 def
+ /k2 -1 def
+ /k3 -1 def
+ /k4 -1 def
+ /k3a -3 def
+ /k4a -3 def
+ %% pour chaque arete [AB]
+ 0 1 n 1 sub {
+ /j exch def
+ %% arete testee : [j, j+1 mod n] (indices relatifs a la face i)
+ solid j i solidgetsommetface /A defpoint3d
+ solid j 1 add n mod i solidgetsommetface /B defpoint3d
+ %% y a-t-il intersection
+ A B eqplan segment_inter_plan {
+ %% il y a intersection
+ dup length 6 eq {
+ %% l'intersection, c'est [AB]
+ /k1 -1 def
+ /k2 -1 def
+ /k3 -1 def
+ /k4 -1 def
+ /k3a -1 def
+ /k4a -1 def
+ dup 0 getp3d /A defpoint3d
+ 1 getp3d /B defpoint3d
+ result A solidaddsommet /a1 exch def
+ result B solidaddsommet /a2 exch def
+ /indnouveauxsommets [
+ indnouveauxsommets aload pop a1 a2
+ ] store
+ /nouvellesaretes [
+ [a1 a2]
+ nouvellesaretes aload pop
+ ] store
+ exit %% c est deja scinde
+ } if
+ %% il y a intersection <> [AB]
+ k1 0 lt {
+ %% 1ere intersection de la face
+ /k1 j def %% sommet precedent intersection 1
+ result exch aload pop solidaddsommet
+ /k1a exch def %% sommet intersection 1
+ } {
+ k2 0 lt {
+ %% 2eme intersection de la face
+ /k2 j def %% sommet precedent intersection 2
+ result exch aload pop solidaddsommet
+ /k2a exch def %% sommet intersection 2
+ } {
+ k3 0 lt {
+ %% 3eme intersection de la face
+ /k3 j def %% sommet precedent intersection 3
+ result exch aload pop solidaddsommet
+ /k3a exch def %% sommet intersection 3
+ } {
+ %% 4eme intersection de la face
+ /k4 j def %% sommet precedent intersection 4
+ result exch aload pop solidaddsommet
+ /k4a exch def %% sommet intersection 4
+ } ifelse
+ } ifelse
+ } ifelse
+ } if
+ } for
+
+ %% y a-t-il eu une coupe ?
+ %% si oui, il faut scinder la face d'indice i en cours
+ k1 0 ge {
+%% (coupe) ==
+%% (n) == n ==
+%% k1 == k2 == k3 == k4 ==
+%% (a) ==
+%% k1a == k2a == k3a == k4a ==
+ k1a k2a eq k3 0 lt and {
+ %% 1 pt d'intersection
+ } {
+ %% il y a coupe, on cherche a eliminer les
+ %% doublons dans {k1a, k2a, k3a, k4a}
+ k1a k2a eq k3 0 ge and {
+ %% 2 pts d'intersection
+ /k2a k3a def
+ /k2 k3 def
+ } if
+ k1a k3a eq k4 0 ge and {
+ %% 2 pts d'intersection
+ /k2a k4a def
+ /k2 k4 def
+ } if
+ /nouvellesaretes [
+ [k1a k2a]
+ nouvellesaretes aload pop
+ ] store
+ [
+ k1a F k1 1 add n mod get ne {
+ k1a
+ } if
+ k1 1 add n mod 1 k2 {F exch get} for
+ k2a F k2 get ne {
+ k2a
+ } if
+ ]
+ result exch lacouleur solidaddface
+ /indnouveauxsommets [indnouveauxsommets aload pop k1a k2a] store
+ [
+ k2a F k2 1 add n mod get ne {
+ k2a
+ } if
+ k2 1 add n ne {
+ k2 1 add n mod 1 n 1 sub {F exch get} for
+ } if
+ 0 1 k1 {F exch get} for
+ k1a F k1 get ne {
+ k1a
+ } if
+ ]
+ result exch lacouleur solidaddface
+ /aenlever [aenlever aload pop i] store
+ } ifelse
+ } if
+ } for
+ result aenlever solidrmfaces
+
+ nouvellesaretes separe_composantes
+ /composantes exch def
+
+ %% pour chacune des composantes
+ 0 1 composantes length 1 sub {
+ %% on oriente et on ajoute la face
+ /icomp exch def
+ %indnouveauxsommets bubblesort arrayrmdouble
+ /indnouveauxsommets composantes icomp get def
+ %% maintenant, on ajoute la face de plan de coupe
+ /nouveauxsommets [
+ 0 1 indnouveauxsommets length 1 sub {
+ /i exch def
+ result indnouveauxsommets i get solidgetsommet
+ } for
+ ] def
+
+ 0 0 0 eqplan pointeqplan 0 eq {
+ /ptref {0 1 1} def
+ } {
+ /ptref {0 0 0} def
+ } ifelse
+
+ %% restera a traiter le cas limite ou la nouvelle face existe deja
+ %% tester si max(indicestries) < nb sommets avant section
+ nouveauxsommets ptref ordonnepoints3d
+ /indicestries exch def
+ /nvelleface [
+ 0 1 indicestries length 1 sub {
+ /m exch def
+ indnouveauxsommets indicestries m get get
+ } for
+ ] def
+ /F result solidgetfaces def
+ /FC result solidgetfcolors def
+ /IO result solidgetinouttable def
+ /n1 IO 1 get def
+ IO 1 n1 1 add put
+ result IO solidputinouttable
+ result [nvelleface F aload pop] solidputfaces
+ result [lacouleur FC aload pop] solidputfcolors
+ } for
+ result
+ tr@nsmit {
+ composantes length
+ } if
+end
+} def
+
+%% syntaxe : elt array compteoccurences
+%% ou array est un tableau du type [ [a1 a2] [b1 b2] [c1 c2] ... ]
+/compteoccurences {
+5 dict begin
+ /table exch def
+ /elt exch def
+ /n 0 def
+ 0 1 table length 1 sub {
+ /i exch def
+ elt table i get in {
+ pop
+ /n n 1 add store
+ } if
+ } for
+ n
+end
+} def
+
+/separe_composantes {
+10 dict begin
+ /result [] def %% les composantes deja faites
+ /table exch def %% ce qui reste a faire
+
+% (recu) == table {==} apply
+ {
+ /ext1 table 0 get 1 get def
+ /ext0 table 0 get 0 get def
+ /composante [] def
+
+ { %% maintenant on suit les extremites et on epluche une composante
+ /change false def
+ /aenlever [] def
+ 0 1 table length 1 sub {
+ /i exch def
+ ext1 table i get In
+ ext0 table i get In or {
+ /aenlever [aenlever aload pop i] store
+ /change true store
+ %% l'arete i contient l'extremite ext0 ou ext1
+ ext0 table i get in {
+ %% index = 0 ou 1
+ neg 1 add table i get exch get
+ /ext0 exch store
+ ext0 composante In not {
+ /composante [composante aload pop ext0] store
+ } if
+ %% on verifie que ext0 est legitime
+ ext0 table compteoccurences 2 gt {
+ /ext0 -1 store
+ } if
+ } if
+ ext1 table i get in {
+ %% index = 0 ou 1
+ neg 1 add table i get exch get
+ /ext1 exch store
+ ext1 composante In not {
+ /composante [composante aload pop ext1] store
+ } if
+ %% on verifie que ext1 est legitime
+ ext1 table compteoccurences 2 gt {
+ /ext1 -1 store
+ } if
+ } if
+ } if
+ } for
+ %% il faut reconstruire table
+ /table [
+ 0 1 table length 1 sub {
+ /i exch def
+ i aenlever in {
+ pop
+ } {
+ table i get
+ } ifelse
+ } for
+ ] store
+ change not {exit} if
+ } loop
+ %% on vient de finir une composante
+ /result [result aload pop composante] store
+ %% (nouvelle comp) == composante {==} apply
+ table length 0 eq {exit} if
+ } loop
+ result
+% (renvoie) == result {==} apply
+end
+} def
+
+/solideqplansepare {solidplansepare} def
+
+%% syntaxe : solid eqplan/plantype solidplansepare --> solid1 solid2
+/solidplansepare {
+10 dict begin
+ dup isplan {
+ plan2eq
+ /eqplan exch def
+ } {
+ /eqplan exch def
+ } ifelse
+ eqplan true solidplansection
+ /nbcomposantes exch def
+ /solid exch def
+ /n solid solidnombrefaces def
+
+ /F [] def
+ /FC [] def
+ %% on retire les faces de coupe
+ 0 1 nbcomposantes 1 sub {
+ /i exch def
+ /F [F aload pop solid i solidgetface] store
+ /FC [FC aload pop solid i solidgetfcolor] store
+ } for
+ solid [0 1 nbcomposantes 1 sub {} for] solidrmfaces
+ /n n nbcomposantes sub store
+
+ %% on separe les autres faces en 2 parties
+ /lesneg [] def %% indices des faces "positives"
+ /lespos [] def %% indices des faces negatives"
+ 0 1 n 1 sub {
+ /i exch def
+ solid i solidcentreface /G defpoint3d
+ G eqplan pointeqplan dup 0 gt {
+ pop
+ /lespos [lespos aload pop i] store
+ } {
+ 0 lt {
+ /lesneg [lesneg aload pop i] store
+ } {
+% /lesneg [lesneg aload pop i] store
+% /lespos [lespos aload pop i] store
+ } ifelse
+ } ifelse
+ } for
+ solid
+ dupsolid dup lesneg solidrmfaces
+ /result1 exch def
+ dupsolid dup lespos solidrmfaces
+ /result2 exch def
+ pop
+
+ 0 1 nbcomposantes 1 sub {
+ /i exch def
+ /facecoupe F i get def
+ /couleurfacecoupe FC i get def
+ /lesfaces1 result1 solidgetfaces def
+ /lescouleurs1 result1 solidgetfcolors def
+ /IO1 result1 solidgetinouttable def
+ /lesfaces2 result2 solidgetfaces def
+ /lescouleurs2 result2 solidgetfcolors def
+ /IO2 result2 solidgetinouttable def
+ %% on rajoute maintenant la face du plan de coupe
+% result1 facecoupe couleurfacecoupe solidaddface
+ result1 [facecoupe lesfaces1 aload pop] solidputfaces
+ result1 [couleurfacecoupe lescouleurs1 aload pop] solidputfcolors
+ result1 IO1 dup dup 1 get 1 add 1 exch put solidputinouttable
+ %% et on verifie l'orientation
+% result1 dup solidnombrefaces 1 sub solidnormaleface
+% result1 dup solidnombrefaces 1 sub solidcentreface addv3d
+ result1 0 solidnormaleface
+ result1 0 solidcentreface addv3d
+ eqplan pointeqplan 0 gt {
+ %% l'orientation est mauvaise
+ result1 0 solidrmface
+ result2 [facecoupe lesfaces2 aload pop] solidputfaces
+ result2 [couleurfacecoupe lescouleurs2 aload pop] solidputfcolors
+ result2 IO2 dup dup 1 get 1 add 1 exch put solidputinouttable
+ result1 [facecoupe reverse lesfaces1 aload pop] solidputfaces
+ result1 [couleurfacecoupe lescouleurs1 aload pop] solidputfcolors
+ result1 dup solidgetinouttable dup dup 1 get 1 add 1 exch put solidputinouttable
+ } {
+ %% l'orientation est ok
+ result2 IO2 dup dup 1 get 1 add 1 exch put solidputinouttable
+ result2 [facecoupe reverse lesfaces2 aload pop] solidputfaces
+ result2 [couleurfacecoupe lescouleurs2 aload pop] solidputfcolors
+ } ifelse
+ } for
+
+ %% maintenant on enleve les sommets isoles
+ /sommetspos [] def
+ /sommetsneg [] def
+ %% pour chaque face du cote negatif
+ 0 1 lesneg length 1 sub {
+ lesneg exch get /i exch def
+ /F solid i solidgetface def
+ %% pour chaque sommet de cette face
+ 0 1 F length 1 sub {
+ /j exch def
+ /sommet F j get def
+ %% si le sommet n'est pas encore note
+ sommet sommetsneg in not {
+ %% et s'il est isole, on peut l'enlever
+ result1 sommet solidsommetsadjsommet length 0 eq {
+ /sommetsneg [sommetsneg aload pop sommet] store
+ } if
+ } {
+ pop
+ } ifelse
+ } for
+ } for
+ sommetsneg bubblesort reverse {result1 exch solidrmsommet} apply
+
+ %% pour chaque face du cote positif
+ 0 1 lespos length 1 sub {
+ lespos exch get /i exch def
+ /F solid i solidgetface def
+ %% pour chaque sommet de cette face
+ 0 1 F length 1 sub {
+ /j exch def
+ /sommet F j get def
+ %% si le sommet n'est pas encore note
+ sommet sommetspos in not {
+ %% et s'il est isole, on peut l'enlever
+ result2 sommet solidsommetsadjsommet length 0 eq {
+ /sommetspos [sommetspos aload pop sommet] store
+ } if
+ } {
+ pop
+ } ifelse
+ } for
+ } for
+ sommetspos bubblesort reverse {result2 exch solidrmsommet} apply
+
+ result1 result2
+end
+} def
+
+%%%%% ### solidaffine ###
+%% syntaxe : solid coeff i solidaffine -> -
+%% syntaxe : solid coeff array solidaffine -> -
+%% syntaxe : solid coeff solidaffine -> -
+%% syntaxe : solid coeff str solidaffine -> -
+%% syntaxe : solid coeff bool solidaffine -> -
+/solidaffine {
+10 dict begin
+ dup isbool {
+ /rmfacecentrale exch def
+ } {
+ /rmfacecentrale true def
+ } ifelse
+ dup isstring {
+ /couleurface exch def
+ } if
+ 2 copy pop issolid {
+ %% 2 arguments --> on affine tout
+ 2 copy pop solidnombrefaces /n exch def
+ /table [n 1 sub -1 0 {} for] def
+ } {
+ %% 1 tableau --> il donne les faces a enlever
+ dup isarray {
+ /table exch bubblesort reverse def
+ } {
+ %% 1 seule face a enlever
+ [ exch ] /table exch def
+ } ifelse
+ } ifelse
+ /coeff exch def
+ /solid exch def
+ 0 1 table length 1 sub {
+ /i exch def
+ solid coeff table i get
+ currentdict /couleurface known {
+ couleurface
+ } if
+ rmfacecentrale s@lidaffineface
+ } for
+end
+} def
+
+%% syntaxe : solid coeff i s@lidaffineface
+ /s@lidaffineface {
+10 dict begin
+ /rmfacecentrale exch def
+ dup isstring {
+ /couleurface exch def
+ } if
+ /indice_a_chamfreiner exch def
+ /i indice_a_chamfreiner def
+ /coeff exch def
+ /solid exch def
+ solid issolid not {
+ (Erreur : mauvais type d argument dans affine) ==
+ quit
+ } if
+ /n solid solidnombresommets def
+ /F solid i solidgetsommetsface def
+ /Findex solid i solidgetface def
+ /ni F length 3 idiv def
+ /couleurfaceorigine solid i solidgetfcolor def
+ F isobarycentre3d /G defpoint3d
+ %% on ajoute les nouveaux sommets
+ /Sindex [] def
+ 0 1 ni 1 sub {
+ /j exch def
+ /Sindex [ Sindex aload pop
+ solid G F j getp3d vecteur3d coeff mulv3d G addv3d solidaddsommet
+ ] store
+ } for
+ %% Sindex contient les indices des nouveaux sommets
+ %% on prepare les faces a ajouter
+ /facestoadd [] def
+ /facestoadd [facestoadd aload pop
+ 0 1 ni 1 sub {
+ /j exch def
+ [Findex j get
+ Findex j 1 add ni mod get
+ Sindex j 1 add ni mod get
+ Sindex j get]
+ } for
+ ] store
+ 0 1 ni 1 sub {
+ /i exch def
+ solid facestoadd i get solidaddface
+ } for
+ %% on enleve la face d origine
+ solid indice_a_chamfreiner solidrmface
+ %% on ajuste les couleurs des nouvelles faces
+ /N solid solidnombrefaces def
+ 0 1 ni 1 sub {
+ /i exch def
+ solid N 1 sub i sub couleurfaceorigine solidputfcolor
+ } for
+ %% puis on ajoute eventuellement la face centrale
+ rmfacecentrale not {
+ solid
+ [0 1 ni 1 sub {
+ /j exch def
+ Sindex j get
+ } for]
+ solidaddface
+ %% en ajustant la couleur de cette derniere
+ solid N
+ currentdict /couleurface known {
+ couleurface
+ } {
+ couleurfaceorigine
+ } ifelse
+ solidputfcolor
+ } if
+end
+} def
+
+%%%%% ### solidtronque ###
+%% syntaxe : solid indicesommet k solidtronque --> solid
+%% syntaxe : solid array k solidtronque --> solid
+%% syntaxe : solid k solidtronque --> solid
+%% k entier > 0, array = tableau des indices des sommets
+/solidtronque {
+10 dict begin
+ /coeff exch def
+ dup issolid {
+ dup solidnombresommets /N exch def
+ /table [0 1 N 1 sub {} for] def
+ } {
+ dup isarray {
+ /table exch def
+ } {
+ [ exch ] /table exch def
+ } ifelse
+ } ifelse
+ /solid exch def
+ solid dupsolid /result exch def pop
+ /n solid solidnombrefaces def
+ 0 1 table length 1 sub {
+ table exch get /no exch def
+ result no solidgetsommet /sommetvise defpoint3d
+ %% on recup les sommets adjacents au sommet vise
+ /sommetsadj solid no solidsommetsadjsommet def
+ %% on calcule les nouveaux sommets
+ /nouveauxsommets [
+ 0 1 sommetsadj length 1 sub {
+ /i exch def
+ solid sommetsadj i get solidgetsommet
+ } for
+ ] {sommetvise exchp3d coeff ABpoint3d} papply3d def
+ %% on pose G = barycentre de ces points
+ nouveauxsommets isobarycentre3d /G defpoint3d
+ %% il faut ordonner ces sommets
+ nouveauxsommets 0 getp3d /ptref defpoint3d
+ G result no solidgetsommet vecteur3d /vecteurnormal defpoint3d
+ %% on construit le tableau des angles ordonnes par rapport
+ %% a la normale
+ nouveauxsommets duparray exch pop
+ {1 dict begin
+ /M defpoint3d
+ G ptref vecteur3d
+ G M vecteur3d
+ vecteurnormal angle3doriente
+ end} papply3d
+ doublebubblesort pop
+ %% nos sommets sont tries
+ /indicesommetstries exch def
+ %% on rajoute les sommets au solide, et on note les nouveaux indices
+ /nouveauxindices [
+ 0 1 nouveauxsommets length 3 idiv 1 sub {
+ /k exch def
+ result nouveauxsommets k getp3d solidaddsommet
+ } for
+ ] def
+ %% on ajoute la face concernee
+ result [
+ 0 1 indicesommetstries length 1 sub {
+ /k exch def
+ nouveauxindices indicesommetstries k get get
+ } for
+ ] solidaddface
+ result no solidfacesadjsommet /lesfaces exch def
+ %% on examine la face d indice i, et on elimine le
+ %% sommet vise
+ 0 1 lesfaces length 1 sub {
+ /i exch def
+ /j lesfaces i get def
+ /F result j solidgetface def
+ result [
+ 0 1 F length 1 sub {
+ /k exch def
+ F k get dup no eq {pop} if
+ } for
+ ] j exch solidputface
+ } for
+ } for
+ table bubblesort reverse {result exch solidrmsommet} apply
+ result
+end
+} def
+
+%%%%% ### dualpolyedre ###
+%% syntaxe : solid dualpolyedreregulier --> solid
+%% syntaxe : solid r dualpolyedreregulier --> solid
+%% si le nombre r est present, projette les nouveaux sommets sur la sphere de centre O , de rayon r
+/dualpolyedreregulier {
+20 dict begin
+ dup isnum {
+ /r exch def
+ /projection true def
+ } {
+ /projection false def
+ } ifelse
+ /solid exch def
+ solid dupsolid /result exch def pop
+ /n solid solidnombrefaces def
+ /N solid solidnombresommets def
+ /facesaenlever [] def
+ %% pour chacun des sommets
+ 0 1 N 1 sub {
+ %% sommet d indice i
+ /i exch def
+ %% indicesfacesadj = liste des indices des faces ou on trouve le sommet i
+ /indicesfacesadj solid i solidfacesadjsommet def
+ %% on recupere les centres des faces concernees
+ /nouveauxsommets [
+ 0 1 indicesfacesadj length 1 sub {
+ /k exch def
+ solid indicesfacesadj k get solidgetsommetsface isobarycentre3d
+ } for
+ ] def
+ %% et on pose G = barycentre de ces points
+ nouveauxsommets isobarycentre3d /G defpoint3d
+ %% il faut ordonner ces sommets
+ nouveauxsommets 0 getp3d /ptref defpoint3d
+ G solid i solidgetsommet vecteur3d /vecteurnormal defpoint3d
+ nouveauxsommets duparray exch pop
+ {1 dict begin
+ /M defpoint3d
+ G ptref vecteur3d
+ G M vecteur3d
+ vecteurnormal angle3doriente
+ end} papply3d
+ doublebubblesort pop
+ %% nos sommets sont tries
+ /indicesommetstries exch def
+ projection {
+ %% on projette les sommets sur la sphere
+ /nouveauxsommets [ nouveauxsommets {normalize3d r mulv3d} papply3d aload pop ] store
+ } if
+ %% puis on les rajoute au solide
+ /nouveauxindices [
+ 0 1 nouveauxsommets length 3 idiv 1 sub {
+ /k exch def
+ result nouveauxsommets k getp3d solidaddsommet
+ } for
+ ] def
+ %% ainsi que la face concernee
+ result [
+ 0 1 indicesommetstries length 1 sub {
+ /k exch def
+ nouveauxindices indicesommetstries k get get
+ } for
+ ] solidaddface
+ /facesaenlever [ facesaenlever aload pop indicesfacesadj aload pop ] store
+ } for
+ result [0 1 n 1 sub {} for] solidrmfaces
+ [N 1 sub -1 0 {} for] {result exch solidrmsommet} apply
+ result
+end
+} def
+
+%%%%% ### newgeode ###
+%% syntaxe : solid r newgeode --> solid
+%% syntaxe : N r newgeode --> solid
+%% N in {3,4,5} -> polyhedre de depart, r = niveau de recursion
+/newgeode {
+2 dict begin
+ /r exch def
+ dup issolid not {
+ /N exch def
+ N 3 eq {
+ 1 newtetraedre
+ } {
+ N 4 eq {
+ 1 newoctaedre
+ } {
+ 1 newicosaedre
+ } ifelse
+ } ifelse
+ } if
+
+ r {
+ 15 dict begin
+ /solid exch def
+ solid dupsolid /result exch def pop
+ /n solid solidnombrefaces def
+ n 1 sub -1 0 {
+ /i exch def
+ %% la face d indice i
+ solid i solidgetface /F exch def
+ /i0 F 0 get def
+ /i1 F 1 get def
+ /i2 F 2 get def
+ solid i0 solidgetsommet /A0 defpoint3d
+ solid i1 solidgetsommet /A1 defpoint3d
+ solid i2 solidgetsommet /A2 defpoint3d
+ A0 A1 milieu3d normalize3d /A01 defpoint3d
+ A1 A2 milieu3d normalize3d /A12 defpoint3d
+ A2 A0 milieu3d normalize3d /A20 defpoint3d
+ result A01 solidaddsommet /i01 exch def
+ result A12 solidaddsommet /i12 exch def
+ result A20 solidaddsommet /i20 exch def
+ result i solidrmface
+ result [i0 i01 i20] solidaddface
+ result [i01 i1 i12] solidaddface
+ result [i01 i12 i20] solidaddface
+ result [i20 i12 i2] solidaddface
+ } for
+ result
+ end
+ } repeat
+end
+} def
+
+%% syntaxe : N r newdualgeode --> solid
+/newdualgeode {
+ newgeode 1
+ dualpolyedreregulier
+} def
+
+%%%%% ### fin insertion ###
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% quelques solides precalcules %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%% ### newface ###
+%% syntaxe : array newmonoface -> solid
+%% ou array = tableau de points 2d
+/newmonoface {
+4 dict begin
+ /table exch def
+ /n table length 2 idiv def
+ /S table {0} papply def
+
+ /F [
+ [0 1 n 1 sub {} for]
+ ] def
+ S F generesolid
+end
+} def
+
+%% syntaxe : array newbiface -> solid
+%% ou array = tableau de points 2d
+/newbiface {
+ newmonoface
+ dup videsolid
+} def
+
+%%%%% ### newpolreg ###
+%% syntaxe : r n newpolreg --> solid
+/newpolreg {
+5 dict begin
+ /n exch def
+ /r exch def
+ /S [
+ 0 360 n div 360 360 n div sub {
+ /theta exch def
+ theta cos r mul
+ theta sin r mul
+ 0
+ } for
+ ] def
+ /F [
+ [0 1 n 1 sub {} for]
+ ] def
+
+ S F generesolid
+ dup videsolid
+end
+} def
+
+%%%%% ### newgrille ###
+%% syntaxe : xmin xmax ymin ymax [dx dy] newgrille -> solid
+%% syntaxe : xmin xmax ymin ymax [nx ny] newgrille -> solid
+%% syntaxe : xmin xmax ymin ymax {mode} newgrille -> solid
+%% syntaxe : xmin xmax ymin ymax newgrille -> solid
+/newgrille {
+10 dict begin
+ [[/nx /ny] [1 1] [1. 1.] [1. 1.] [1. 1.] [.5 .5]] gestionsolidmode
+ %% ny nb d etages en y
+ %% nx nb d etages en x
+ /biface false def
+ [nx ny] {0} newsurfaceparametree
+end
+} def
+
+%% %% syntaxe : xmin xmax ymin ymax [dx dy] {f} newsurface -> solid
+%% %% f : R^2 -> R
+/newsurface {
+ true newsurfaceparametree
+} def
+
+/biface true def
+
+/newsurfaceparametree {
+10 dict begin
+ dup isbool {
+ pop /surfz true def
+ } {
+ /surfz false def
+ } ifelse
+ /f_surface exch def
+ [[/nx /ny] [2 2] [4 4] [1. 1.] [1. 1.] [.25 .25]] gestionsolidmode
+ %% ny nb d etages en y
+ %% nx nb d etages en x
+ /ymax exch def
+ /ymin exch def
+ /xmax exch def
+ /xmin exch def
+
+ nx isinteger not {
+ %% alors nx est un dx
+ /nx xmax xmin sub nx div cvi store
+ } if
+ ny isinteger not {
+ %% alors ny est un dy
+ /ny ymax ymin sub ny div cvi store
+ } if
+ /dy ymax ymin sub ny div def %% le pas sur y
+ /dx xmax xmin sub nx div def %% le pas sur x
+
+ /S [
+ 0 1 nx {
+ /i exch def
+ 0 1 ny {
+ /j exch def
+ /u xmin i dx mul add def
+ /v ymin j dy mul add def
+ u v
+ surfz {2 copy} if
+ f_surface
+ pstrickactionR3
+ } for
+ } for
+ ] def
+
+ /F [
+ 0 1 nx 1 sub {
+ /i exch def
+ 0 1 ny 1 sub {
+ /j exch def
+ [
+ j 1 add i ny 1 add mul add
+ j i ny 1 add mul add
+ j ny 1 add add i ny 1 add mul add
+ j ny 2 add add i ny 1 add mul add
+ ]
+ } for
+ } for
+%% 0 1 0 {%nx 1 sub {
+%% /i exch def
+%% 0 1 0 {%ny 2 sub {
+%% /j exch def
+%% [
+%% j 1 add %% i ny mul add
+%% j %% i ny mul add
+%% ny 1 add j add %% i ny mul add
+%% ny 2 add j add %% i ny mul add
+%% ]
+%% } for
+%% } for
+ ] def
+ S F generesolid
+ biface pl@n-en-cours not and {dup videsolid} if
+end
+} def
+
+%%%%% ### newgrillecirculaire ###
+%% syntaxe : r option newgrillecirculaire -> solid
+/newgrillecirculaire {
+6 dict begin
+ [[/K /N] [6 6] [6 8] [10 8] [16 12] [16 36]] gestionsolidmode
+
+ %% N = nb de meridiens (diviseur de 360 = 2^4 * 3^2 * 5)
+ %% K = nb d horizontales (diviseur de 160 = 2^5 * 5)
+
+ /r exch def
+ /F [
+ %% 1er etage
+ 1 1 N {
+ /i exch def
+ [0 i i N mod 1 add]
+ } for
+ %% etages suivants
+ 0 1 K 2 sub {
+ /j exch def
+ 1 1 N {
+ /i exch def
+ [i j N mul add
+ i N add j N mul add
+ i N mod N add 1 add j N mul add
+ i N mod 1 add j N mul add]
+ } for
+ } for
+ ] def
+
+ %% tableau des sommets
+ /S [
+ 0 0 0
+ 1 1 K {
+ /j exch def
+ 1 1 N {
+ /i exch def
+ /theta i 360 mul N div def
+ theta cos r j mul K div mul
+ theta sin r j mul K div mul
+ 0 %2 copy f %exch atan 90 div
+ } for
+ } for
+ ] def
+
+ S F generesolid
+end
+} def
+
+%% syntaxe : r [dx dy] {f} newsurface* -> solid
+/newsurface* {
+7 dict begin
+ /f_surface exch def
+ [[/nx /ny] [6 6] [6 8] [10 8] [16 12] [16 36]] gestionsolidmode
+
+ nx isinteger not {
+ %% alors nx est un dx
+ /nx xmax xmin sub nx div cvi store
+ } if
+ ny isinteger not {
+ %% alors ny est un dy
+ /ny ymax ymin sub ny div cvi store
+ } if
+ /dy ymax ymin sub ny div def %% le pas sur y
+ /dx xmax xmin sub nx div def %% le pas sur x
+
+ %% ny = nb de meridiens
+ %% nx = nb d horizontales
+
+ /r exch def
+ /F [
+ %% 1er etage
+ 1 1 ny {
+ /i exch def
+ [0 i i ny mod 1 add]
+ } for
+ %% etages suivants
+ 0 1 nx 2 sub {
+ /j exch def
+ 1 1 ny {
+ /i exch def
+ [i j ny mul add
+ i ny add j ny mul add
+ i ny mod ny add 1 add j ny mul add
+ i ny mod 1 add j ny mul add]
+ } for
+ } for
+ ] def
+
+ %% tableau des sommets
+ /S [
+ 0 0 0
+ 1 1 nx {
+ /j exch def
+ 1 1 ny {
+ /i exch def
+ /theta i 360 mul ny div def
+ theta cos r j mul nx div mul
+ theta sin r j mul nx div mul
+ 2 copy f_surface
+ } for
+ } for
+ ] def
+
+ S F generesolid
+end
+} def
+
+%%%%% ### newruban ###
+%% syntaxe : array h u [n] newruban -> solid d axe (O, u), de maillage vertical n
+%% syntaxe : array h u newruban -> solid d axe (O, u),
+%% syntaxe : array h newruban -> solid d axe (O, k),
+%% ou array tableau de points 2d
+/newruban {
+7 dict begin
+ %% N = nb d etages
+ [[/N] [1] [1] [1] [3] [4]] gestionsolidmode
+ 2 copy pop isarray {
+ /u {0 0 1} def
+ } {
+ /u defpoint3d
+ } ifelse
+ u 0 eq {
+ (Error : 3eme composante nulle dans le vecteur pour newruban) ==
+ quit
+ } if
+ pop pop
+ /h exch def
+ /table exch def
+ %% n = indice du dernier point
+ /n table length 2 idiv 1 sub def
+ %% vecteur de translation
+ u
+ h u norme3d div
+ mulv3d /v defpoint3d
+
+ %% tableau des sommets
+ /S [
+ 0 1 N {
+ /j exch def
+ 0 1 n {
+ /i exch def
+ table i getp
+ 0
+ v N j sub N div mulv addv3d
+ } for
+ } for
+ ] def
+
+ /F [
+ %% faces etage
+ 1 1 N {
+ /j exch def
+ 1 1 n {
+ /i exch def
+ [i j 1 sub n 1 add mul add
+ i 1 sub j 1 sub n 1 add mul add
+ n 1 add i add 1 sub j 1 sub n 1 add mul add
+ n 1 add i add j 1 sub n 1 add mul add]
+ } for
+ } for
+ ] def
+
+ S F generesolid
+ dup videsolid
+end
+} def
+
+%%%%% ### newicosaedre ###
+/newicosaedre {
+3 dict begin
+ /a exch def
+ /S [
+ 0.8944271 0 0.4472137
+ 0.2763932 0.8506507 0.4472137
+ -0.7236067 0.5257311 0.4472137
+ -0.7236067 -0.5257311 0.4472137
+ 0.2763932 -0.8506507 0.4472137
+ 0 0 1
+ 0 0 -1
+ -0.8944271 0 -0.4472137
+ -0.2763932 -0.8506507 -0.4472137
+ 0.7236067 -0.5257311 -0.4472137
+ 0.7236067 0.5257311 -0.4472137
+ -0.2763932 0.8506507 -0.4472137
+ ] {a mulv3d} papply3d def
+
+ /F [
+ [0 1 5] %% 1 2 6 ]
+ [1 2 5] %% 2 3 6 ]
+ [2 3 5] %% 3 4 6 ]
+ [3 4 5] %% 4 5 6 ]
+ [4 0 5] %% 5 1 6 ]
+ [9 0 4] %% 10 1 5 ]
+ [0 9 10] %% 1 10 11]
+ [10 1 0] %% 11 2 1 ]
+ [1 10 11] %% 2 11 12]
+ [11 2 1] %% 12 3 2 ]
+ [2 11 7] %% 3 12 8 ]
+ [2 7 3] %% 3 8 4 ]
+ [3 7 8] %% 4 8 9 ]
+ [3 8 4] %% 4 9 5 ]
+ [4 8 9] %% 5 9 10 ]
+ [6 7 11] %% 7 8 12 ]
+ [6 8 7] %% 7 9 8 ]
+ [6 9 8] %% 7 10 9 ]
+ [6 10 9] %% 7 11 10]
+ [6 11 10] %% 7 12 11]
+ ] def
+
+ S F generesolid
+end
+} def
+
+%%%%% ### newdodecaedre ###
+/newdodecaedre {
+3 dict begin
+ /a exch def
+ /S [
+ 0 0.607062 0.7946545
+ -0.5773503 0.1875925 0.7946545
+ -0.3568221 -0.4911235 0.7946545
+ 0.3568221 -0.4911235 0.7946545
+ 0.5773503 0.1875925 0.7946545
+ 0 0.982247 0.1875925
+ -0.9341724 0.303531 0.1875925
+ -0.5773503 -0.7946645 0.1875925
+ 0.5773503 -0.7946645 0.1875925
+ 0.9341724 0.303531 0.1875925
+ 0 -0.982247 -0.1875925
+ 0.9341724 -0.303531 -0.1875925
+ 0.5773503 0.7946545 -0.1875925
+ -0.5773503 0.7946545 -0.1875925
+ -0.9341724 -0.303531 -0.1875925
+ -0.5773503 -0.1875925 -0.7946545
+ -0.3568221 0.4911235 -0.7946545
+ 0.3568221 0.4911235 -0.7946545
+ 0.5773503 -0.1875925 -0.7946545
+ 0 -0.607062 -0.7946545
+ ] {a mulv3d} papply3d def
+
+ /F [
+ [0 1 2 3 4]
+ [4 3 8 11 9]
+ [4 9 12 5 0]
+ [0 5 13 6 1]
+ [1 6 14 7 2]
+ [2 7 10 8 3]
+ [10 19 18 11 8]
+ [11 18 17 12 9]
+ [12 17 16 13 5]
+ [13 16 15 14 6]
+ [14 15 19 10 7]
+ [15 16 17 18 19]
+ ] def
+ S F generesolid
+end
+} def
+
+%%%%% ### newoctaedre ###
+/newoctaedre {
+3 dict begin
+ /a exch def
+ %%Sommets
+ /S [
+ 0 0 1
+ 1 0 0
+ 0 1 0
+ -1 0 0
+ 0 -1 0
+ 0 0 -1
+ ] {a mulv3d} papply3d def
+
+ /F [
+ [0 4 1]
+ [1 2 0]
+ [0 2 3]
+ [3 4 0]
+ [1 5 2]
+ [2 5 3]
+ [3 5 4]
+ [4 5 1]
+ ] def
+
+ S F generesolid
+end
+} def
+
+%%%%% ### newtetraedre ###
+/newtetraedre {
+3 dict begin
+ /r exch def
+ %%Tetraedre
+ /S [
+ 0 0 1
+ -0.4714045 -0.8164965 -1 3 div
+ 0.942809 0 -1 3 div
+ -0.4714045 0.8164965 -1 3 div
+ ] {r mulv3d} papply3d def
+
+ /F [
+ [0 1 2]
+ [0 2 3]
+ [0 3 1]
+ [1 3 2]
+ ] def
+
+ S F generesolid
+end
+} def
+
+%%%%% ### newcube ###
+/newcube {
+3 dict begin
+ [[/n] [1] [1] [1] [3] [4]] gestionsolidmode
+ /a exch 2 div def
+
+ n 1 le {
+ /F [
+ [0 1 2 3]
+ [0 4 5 1]
+ [1 5 6 2]
+ [2 6 7 3]
+ [0 3 7 4]
+ [4 7 6 5]
+ ] def
+
+ %% tableau des sommets
+ /S [
+ 1 1 1 %% 0
+ -1 1 1 %% 1
+ -1 -1 1 %% 2
+ 1 -1 1 %% 3
+ 1 1 -1 %% 4
+ -1 1 -1 %% 5
+ -1 -1 -1 %% 6
+ 1 -1 -1 %% 7
+ ] {a mulv3d} papply3d def
+ S F generesolid
+ } {
+ /dl 2 n div def
+ /N n dup mul n add 4 mul def
+ /n1 n 1 sub dup mul def %% nb sommets centre d une face
+
+ %% tableau des sommets
+ /S1 [
+ 0 1 n 1 sub {
+ /j exch def
+ 0 1 n {
+ /i exch def
+ -1 i dl mul add
+ -1 j dl mul add
+ 1
+ } for
+ } for
+ ] def
+
+ /S2 S1 {-90 0 0 rotateOpoint3d} papply3d def
+ /S3 S2 {-90 0 0 rotateOpoint3d} papply3d def
+ /S4 S3 {-90 0 0 rotateOpoint3d} papply3d def
+
+ /S5 [
+ 1 1 n 1 sub {
+ /j exch def
+ 1 1 n 1 sub {
+ /i exch def
+ 1
+ -1 i dl mul add
+ -1 j dl mul add
+ } for
+ } for
+ ] def
+
+ /S6 [
+ 1 1 n 1 sub {
+ /j exch def
+ 1 1 n 1 sub {
+ /i exch def
+ -1
+ -1 i dl mul add
+ -1 j dl mul add
+ } for
+ } for
+ ] def
+
+ %% tableau des faces
+ /F1 [
+ 0 1 n 1 sub {
+ /j exch def
+ 0 1 n 1 sub {
+ /i exch def
+ [
+ i n 1 add j mul add
+ dup 1 add
+ dup n 1 add add
+ dup 1 sub
+ ]
+ } for
+ } for
+ ] def
+
+ %% syntaxe : i sommettourgauche --> l indice du i-eme sommet du tour
+ %% de la face gauche (en commencant par l indice 0). ATTENTION :
+ %% utilise la variable globale n = nb d etages
+ /sommettourgauche {
+ 1 dict begin
+ /i exch def
+ i 4 n mul ge {
+ i
+ (Error: indice trop grand dans sommettourgauche) ==
+ exit
+ } if
+ n n 1 add i mul add
+ end
+ } def
+
+ %% syntaxe : i sommetcentregauche --> l indice du i-eme sommet du centre
+ %% de la face gauche (en commencant par l indice 0). ATTENTION :
+ %% utilise les variables globales n = nb d etages, et N = nb sommets
+ %% des 4 1eres faces
+ /sommetcentregauche {
+ 1 dict begin
+ /i exch def
+ i n 1 sub dup mul ge {
+ i
+ (Error: indice trop grand dans sommetcentregauche) ==
+ exit
+ } if
+ N i add
+ end
+ } def
+
+ /F5 [
+ %%%%% la face gauche %%%%%
+ %% le coin superieur gauche
+ [
+ 1 sommettourgauche
+ 0 sommettourgauche
+ n 4 mul 1 sub sommettourgauche
+ n1 n 1 sub sub sommetcentregauche
+ ]
+
+ %% la bande superieure (i from 1 to n-2)
+ 1 1 n 2 sub {
+ /i exch def
+ [
+ i 1 add sommettourgauche
+ i sommettourgauche
+ n1 n sub i add sommetcentregauche
+ n1 n sub i 1 add add sommetcentregauche
+ ]
+ } for
+
+ %% le coin superieur droit
+ [
+ n sommettourgauche
+ n 1 sub sommettourgauche
+ n1 1 sub sommetcentregauche
+ n 1 add sommettourgauche
+ ]
+
+ %% la descente gauche
+ %% j from 1 to n-2
+ 1 1 n 2 sub {
+ /j exch def
+ [
+ n1 n 1 sub j mul sub sommetcentregauche
+ n 4 mul j sub sommettourgauche
+ n 4 mul j 1 add sub sommettourgauche
+ n1 n 1 sub j 1 add mul sub sommetcentregauche
+ ]
+ } for
+
+ %% les bandes centrales (j from 1 to n-2 et i from 1 to n-2)
+ 1 1 n 2 sub {
+ /j exch def
+ 1 1 n 2 sub {
+ /i exch def
+ [
+ n1 i n 1 sub j 1 sub mul add sub sommetcentregauche
+ n1 i 1 add n 1 sub j 1 sub mul add sub sommetcentregauche
+ n1 i 1 add n 1 sub j mul add sub sommetcentregauche
+ n1 i n 1 sub j mul add sub sommetcentregauche
+ ]
+ } for
+ } for
+
+ %% la descente droite
+ 1 1 n 2 sub {
+ /j exch def
+ [
+ n j add sommettourgauche
+ n1 1 sub j 1 sub n 1 sub mul sub sommetcentregauche
+ n1 1 sub j n 1 sub mul sub sommetcentregauche
+ n j 1 add add sommettourgauche
+ ]
+ } for
+
+ %% le coin inferieur gauche
+ [
+ 0 sommetcentregauche
+ n 3 mul 1 add sommettourgauche
+ n 3 mul sommettourgauche
+ n 3 mul 1 sub sommettourgauche
+ ]
+
+ %% la bande inferieure (i from 1 to n-2)
+ 1 1 n 2 sub {
+ /i exch def
+ [
+ i sommetcentregauche
+ i 1 sub sommetcentregauche
+ n 3 mul i sub sommettourgauche
+ n 3 mul i sub 1 sub sommettourgauche
+ ]
+ } for
+
+ %% le coin inferieur droit
+ [
+ n 2 mul 1 sub sommettourgauche
+ n 2 sub sommetcentregauche
+ n 2 mul 1 add sommettourgauche
+ n 2 mul sommettourgauche
+ ]
+ ] def
+
+ %% syntaxe : i sommettourdroit --> l indice du i-eme sommet du tour
+ %% de la face droit (en commencant par l indice 0). ATTENTION :
+ %% utilise la variable globale n = nb d etages
+ /sommettourdroit {
+ 1 dict begin
+ /i exch def
+ i 4 n mul ge {
+ i
+ (Error: indice trop grand dans sommettourdroit) ==
+ exit
+ } if
+ n 1 add i mul
+ end
+ } def
+
+ %% syntaxe : i sommetcentredroit --> l indice du i-eme sommet du centre
+ %% de la face droit (en commencant par l indice 0). ATTENTION :
+ %% utilise les variables globales n = nb d etages, et N = nb sommets
+ %% des 4 1eres faces
+ /sommetcentredroit {
+ 1 dict begin
+ /i exch def
+ i n 1 sub dup mul ge {
+ i
+ (Error: indice trop grand dans sommetcentredroit) ==
+ exit
+ } if
+ N n1 add i add
+ end
+ } def
+
+ /F6 [
+ %% coin superieur droit
+ [
+ 0 sommettourdroit
+ 1 sommettourdroit
+ n1 n 1 sub sub sommetcentredroit
+ 4 n mul 1 sub sommettourdroit
+ ]
+ %% coin superieur gauche
+ [
+ n 1 sub sommettourdroit
+ n sommettourdroit
+ n 1 add sommettourdroit
+ n1 1 sub sommetcentredroit
+ ]
+ %% coin inferieur gauche
+ [
+ n 2 sub sommetcentredroit
+ 2 n mul 1 sub sommettourdroit
+ 2 n mul sommettourdroit
+ 2 n mul 1 add sommettourdroit
+ ]
+ %% coin inferieur droit
+ [
+ 3 n mul 1 add sommettourdroit
+ 0 sommetcentredroit
+ 3 n mul 1 sub sommettourdroit
+ 3 n mul sommettourdroit
+ ]
+ %% bande superieure
+ 1 1 n 2 sub {
+ /i exch def
+ [
+ i sommettourdroit
+ i 1 add sommettourdroit
+ n 1 sub n 2 sub mul i add sommetcentredroit
+ n 1 sub n 2 sub mul i 1 sub add sommetcentredroit
+ ]
+ } for
+ %% bande inferieure
+ 1 1 n 2 sub {
+ /i exch def
+ [
+ i 1 sub sommetcentredroit
+ i sommetcentredroit
+ 3 n mul 1 sub i sub sommettourdroit
+ 3 n mul i sub sommettourdroit
+ ]
+ } for
+ %% descente gauche
+ 1 1 n 2 sub {
+ /i exch def
+ [
+ n1 1 sub i 1 sub n 1 sub mul sub sommetcentredroit
+ n i add sommettourdroit
+ n i 1 add add sommettourdroit
+ n1 1 sub i n 1 sub mul sub sommetcentredroit
+ ]
+ } for
+ %% descente droite
+ 1 1 n 2 sub {
+ /i exch def
+ [
+ 4 n mul i sub sommettourdroit
+ n 1 sub n 1 sub i sub mul sommetcentredroit
+ n 1 sub n 2 sub i sub mul sommetcentredroit
+ 4 n mul i sub 1 sub sommettourdroit
+ ]
+ } for
+ %% bandes interieures
+ 1 1 n 2 sub {
+ /j exch def
+ 1 1 n 2 sub {
+ /i exch def
+ [
+ n 1 sub j mul i 1 sub add sommetcentredroit
+ n 1 sub j mul i add sommetcentredroit
+ n 1 sub j 1 sub mul i add sommetcentredroit
+ n 1 sub j 1 sub mul i 1 sub add sommetcentredroit
+ ]
+ } for
+ } for
+
+ ] def
+
+ /F2 F1 {{n dup mul n add add} apply} apply def
+ /F3 F2 {{n dup mul n add add} apply} apply def
+ /F4 F3 {{n dup mul n add add} apply} apply def
+
+
+ S1 S2 append S3 append S4 append S5 append S6 append {a mulv3d} papply3d
+ F1 F2 append F3 append F4 append {{N mod} apply} apply F5 append F6 append
+ generesolid
+ } ifelse
+end
+} def
+
+%%%%% ### newparallelepiped ###
+% 14 octobre 2006
+/newparallelepiped {
+2 dict begin
+ /c exch 2 div def
+ /b exch 2 div def
+ /a exch 2 div def
+ /F [
+ [0 1 2 3]
+ [0 4 5 1]
+ [1 5 6 2]
+ [2 6 7 3]
+ [0 3 7 4]
+ [4 7 6 5]
+ ] def
+
+ %% tableau des sommets
+ /S [
+ a b c %% 0
+ a neg b c %% 1
+ a neg b neg c %% 2
+ a b neg c %% 3
+ a b c neg %% 4
+ a neg b c neg %% 5
+ a neg b neg c neg %% 6
+ a b neg c neg %% 7
+ ] def
+ S F generesolid
+} def
+
+%%%%% ### newcylindre ###
+%% syntaxe : z0 r0 z1 newcylindre -> solide
+%% syntaxe : z0 r0 z1 {mode} newcylindre -> solide
+%% syntaxe : z0 r0 z1 [n1 n2] newcylindre -> solide
+%% syntaxe : a b {f} {u} h [n1 n2] newcylindre
+/newcylindre {
+2 dict begin
+ [[/n2 /n1] [1 6] [1 8] [1 10] [3 12] [5 18]] gestionsolidmode
+ 2 copy pop xcheck {
+ %% cylindre cas general
+ /h exch def
+ /U exch def
+ U normalize3d /u defpoint3d
+ /lafonction exch def
+ /b exch def
+ /a exch def
+ /pas b a sub n1 div def
+ /vpas h n2 div def
+ /S [
+ 0 1 n2 {
+ /j exch def
+ 0 1 n1 {
+ /i exch def
+ a i pas mul add lafonction
+ u j vpas mul mulv3d addv3d
+ } for
+ } for
+ ] def
+ /F [
+ 0 1 n2 1 sub {
+ /j exch def
+ 0 1 n1 1 sub {
+ /i exch def
+ [
+ i n1 1 add j mul add
+ dup 1 add
+ dup n1 1 add add
+ dup 1 sub
+ ]
+ } for
+ } for
+ ] def
+
+ S F generesolid
+% dup videsolid
+ } {
+ %% cylindre de revolution
+ 2 copy pop [n2 n1] newtronccone
+ } ifelse
+end
+} def
+
+%% syntaxe : z0 r0 z1 newcylindrecreux -> solide
+/newcylindrecreux {
+ newcylindre
+ dup creusesolid
+} def
+
+%%%%% ### newtronccone ###
+%% syntaxe : z0 r0 z1 r1 newtronccone -> solid
+/newtronccone {
+11 dict begin
+ [[/n /N] [1 6] [1 8] [1 10] [3 12] [5 18]] gestionsolidmode
+
+ /r1 exch def
+ /z1 exch def
+ /r0 exch def
+ /z0 exch def
+ /dz z1 z0 sub n div def
+ /dr r1 r0 sub n div def
+
+ /FE [
+ [0 1 N 1 sub {} for]
+ [n 1 add N mul 1 sub -1 n N mul {} for]
+
+ 0 1 n 1 sub {
+ /k exch def
+ k N mul 1 add 1 k 1 add N mul 1 sub {
+ /i exch def
+ [i i 1 sub N i add 1 sub N i add]
+ } for
+ [k N mul k 1 add N mul 1 sub k 2 add N mul 1 sub k 1 add N mul]
+ } for
+
+ ] def
+
+ %% tableau des sommets
+ /S [
+ n -1 0 {
+ /k exch def
+ 0 1 N 1 sub {
+ /i exch def
+ 360 N idiv i mul cos r0 dr k mul add mul
+ 360 N idiv i mul sin r0 dr k mul add mul
+ z0 dz k mul add
+ } for
+ } for
+ ] def
+ S FE generesolid
+end
+} def
+
+%% syntaxe : z0 r0 z1 r1 newtroncconecreux -> solid
+/newtroncconecreux {
+ newtronccone
+ dup creusesolid
+} def
+
+%%%%% ### newcone ###
+%% syntaxe : z0 r0 z1 newcone -> solid
+%% syntaxe : z0 r0 z1 {mode} newcone -> solid
+%% syntaxe : z0 r0 z1 [n1 n2] newcone -> solid
+%% syntaxe : a b {f} {sommet} [n1 n2] newcone -> solid
+/newcone {
+11 dict begin
+ [ [/n /N] [1 6] [1 8] [1 10] [3 12] [5 18] ] gestionsolidmode
+ dup xcheck {
+ %% cas general
+ /sommet exch def
+ /lafonction exch def
+ /b exch def
+ /a exch def
+
+ /pas b a sub N div def
+ /S [
+ sommet
+ 0 1 n 1 sub {
+ /j exch def
+ 0 1 N {
+ /i exch def
+ a i pas mul add lafonction
+ dupp3d sommet vecteur3d j n div mulv3d addv3d
+ } for
+ } for
+ 1 1 n {
+ /j exch def
+ 0 1 N {
+ /i exch def
+ a i pas mul add lafonction
+ sommet vecteur3d j n div mulv3d sommet addv3d
+ } for
+ } for
+ ] def
+
+ /F [
+ %% les etages inferieurs
+ 0 1 n 2 sub {
+ /j exch def
+ 1 1 N {
+ /i exch def
+ [
+ i j N 1 add mul add
+ dup 1 add
+ dup N add 1 add
+ dup 1 sub
+ ]
+ } for
+ } for
+ %% dernier etage inferieur
+ 1 1 N {
+ /i exch def
+ [
+ i N 1 add n 1 sub mul add
+ dup 1 add
+ 0
+ ]
+ } for
+ %% premier etage superieur
+ 1 1 N {
+ /i exch def
+ [
+ i N 1 add n mul add
+ dup 1 add
+ 0
+ exch
+ ]
+ } for
+ %% les etages superieurs
+ n 1 n 2 mul 2 sub {
+ /j exch def
+ 1 1 N {
+ /i exch def
+ [
+ i j N 1 add mul add
+ dup 1 add
+ dup N add 1 add
+ dup 1 sub
+ ]
+ } for
+ } for
+ ] def
+
+ S F generesolid
+% dup videsolid
+ } {
+ %% cylindre de revolution
+ /z1 exch def
+ /r0 exch def
+ /z0 exch def
+ /dz z1 z0 sub n div def
+ /dr r0 n div def
+
+ /F [
+ %% la base
+ [N 1 sub -1 0 {} for]
+ %% le dernier etage
+ n 1 sub N mul 1 add 1 n N mul 1 sub {
+ /i exch def
+ [i 1 sub i n N mul]
+ } for
+ [n N mul 1 sub n 1 sub N mul n N mul]
+ %% les autres etages
+ 0 1 n 2 sub {
+ /j exch def
+ 0 N j mul add 1 N N j mul add 2 sub {
+ /i exch def
+ [i i 1 add dup N add dup 1 sub]
+ } for
+ [N N j mul add 1 sub N j mul dup N add dup N add 1 sub]
+ } for
+ ] def
+
+ %% tableau des sommets
+ /S [
+ %% etage no j (in [1; n])
+ 0 1 n 1 sub {
+ /j exch def
+ 0 1 N 1 sub {
+ /i exch def
+ 360 N idiv i mul cos r0 dr j mul sub mul
+ 360 N idiv i mul sin r0 dr j mul sub mul
+ z0 dz j mul add
+ } for
+ } for
+ 0 0 z1
+ ] def
+ S F generesolid
+ } ifelse
+end
+} def
+
+%% %% syntaxe : z0 r0 z1 newconecreux -> solid
+ /newconecreux {
+ newcone
+ dup 0 solidrmface
+ dup videsolid
+ } def
+
+%%%%% ### newtore ###
+%% syntaxe : r R newtore -> solid
+/newtore {
+10 dict begin
+ [[/n1 /n2] [4 5] [6 10] [8 12] [9 18] [18 36]] gestionsolidmode
+ /n2 n2 3 max store
+ /n1 n1 2 max store
+ /R exch def
+ /r exch def
+ /S [
+ 0 1 n1 1 sub {
+ /i exch def
+ 360 n1 div i mul cos r mul R add
+ 360 n1 div i mul sin r mul
+ } for
+ ]
+ def
+ S [n2] newanneau
+end
+} def
+
+%%%%% ### newprisme ###
+%% syntaxe : array z0 z1 newprisme -> solid d axe (O, u),
+/newprismedroit {
+ [[/N] [1] [1] [1] [3] [6]] gestionsolidmode
+ 0 0 1 [N] newprisme
+} def
+
+%% syntaxe : array z0 z1 u newprisme -> solid d axe (O, u),
+%% ou array tableau de points 2d
+/newprisme {
+7 dict begin
+ [[/N] [1] [1] [1] [3] [6]] gestionsolidmode
+ dup 0 eq {
+ (Error : 3eme composante nulle dans le vecteur pour newprisme) ==
+ quit
+ } if
+ /u defpoint3d
+ /z1 exch def
+ /z0 exch def
+ %% N = nb d etages
+ /table exch def
+ %% n = indice du dernier point
+ /n table length 2 idiv 1 sub def
+ %% vecteur de translation
+ u
+ z1 z0 sub u norme3d div
+ mulv3d /v defpoint3d
+
+ %% tableau des sommets
+ /S [
+ 0 1 N {
+ /j exch def
+ 0 1 n {
+ /i exch def
+ table i getp
+ z0
+ v N j sub N div mulv addv3d
+ } for
+ } for
+ ] def
+
+ /F [
+ %% face superieure
+ [0 1 n {} for]
+ %% base
+ [N 1 add n 1 add mul 1 sub -1 N n 1 add mul {} for]
+ %% faces etage
+ 1 1 N {
+ /j exch def
+ 1 1 n {
+ /i exch def
+ [i j 1 sub n 1 add mul add
+ i 1 sub j 1 sub n 1 add mul add
+ n 1 add i add 1 sub j 1 sub n 1 add mul add
+ n 1 add i add j 1 sub n 1 add mul add]
+ } for
+ [0 j 1 sub n 1 add mul add
+ n j 1 sub n 1 add mul add
+ 2 n mul 1 add j 1 sub n 1 add mul add
+ n 1 add j 1 sub n 1 add mul add]
+ } for
+ ] def
+
+ S F generesolid
+end
+} def
+
+%%%%% ### newsphere ###
+%% syntaxe : r option newsphere -> solid
+/newsphere {
+2 dict begin
+ [[/K /N] [6 6] [8 8] [10 12] [16 12] [16 36]] gestionsolidmode
+ -90 90 [K N] newcalottesphere
+end
+} def
+
+%% syntaxe : r phi theta option newcalottesphere -> solid
+/newcalottesphere {
+6 dict begin
+ [[/K /N] [6 6] [8 8] [10 12] [16 12] [16 36]] gestionsolidmode
+
+ %% test de beta (ex-theta)
+ dup 90 eq {
+ /beta exch def
+ /idebut 1 def
+ } {
+ /beta exch 80 min -80 max def
+ /idebut 0 def
+ } ifelse
+ %% test de alpha (ex-phi)
+ dup -90 eq {
+ /alpha exch def
+ } {
+ /alpha exch beta min -80 max def
+ } ifelse
+ /r exch def
+ beta 90 eq {
+ alpha -90 eq {
+ /ifin K def
+ /db alpha beta sub K 1 add div def
+ } {
+ /ifin K def
+ /db alpha beta sub K div def
+ } ifelse
+ } {
+ alpha -90 eq {
+ /ifin K 1 sub def
+ /db alpha beta sub K div def
+ } {
+ /ifin K 1 sub def
+ /db alpha beta sub K 1 sub div def
+ } ifelse
+ } ifelse
+
+ %% nombre de sommets -2
+ /nb N K mul def
+
+ %% tableau des sommets
+ /S [
+ idebut 1 ifin {
+ /j exch def
+ /phi beta j db mul add def
+ phi cos r mul /r_tmp exch def
+ 0 1 N 1 sub {
+ /i exch def
+ 360 N idiv i mul cos r_tmp mul
+ 360 N idiv i mul sin r_tmp mul
+ phi sin r mul
+ } for
+ } for
+ 0 0 r neg
+ 0 0 r
+ ] def
+
+ /F [
+ %% calotte inferieure
+ alpha -90 eq {
+ 1 1 N 1 sub {
+ /i exch def
+ [
+ nb
+ nb i sub
+ nb i 1 add sub
+ ]
+ } for
+ [nb nb N sub nb 1 sub]
+ } {
+ [nb 1 sub -1 nb N sub {} for ]
+ } ifelse
+
+ %% calotte superieure
+ beta 90 eq {
+ 0 1 N 1 sub {
+ /i exch def
+ [i i 1 add N mod N K mul 1 add]
+ } for
+ } {
+ [0 1 N 1 sub {} for]
+ } ifelse
+
+ 1 1 K 1 sub {
+ /j exch def
+ [
+ j N mul
+ j N mul 1 add
+ j 1 sub N mul 1 add
+ j 1 sub N mul
+ ]
+ N 2 sub {dup {1 add} apply} repeat
+ [
+ j 1 add N mul 1 sub
+ j N mul
+ j 1 sub N mul
+ j N mul 1 sub
+ ]
+ } for
+ ] def
+
+ S F generesolid
+end
+} def
+
+%% syntaxe : r phi theta option newcalottespherecreuse -> solid
+/newcalottespherecreuse {
+6 dict begin
+ [[/K /N] [6 6] [8 8] [10 12] [16 12] [16 36]] gestionsolidmode
+
+ %% test de beta (ex-theta)
+ dup 90 eq {
+ /beta exch def
+ /idebut 1 def
+ } {
+ /beta exch 80 min -80 max def
+ /idebut 0 def
+ } ifelse
+ %% test de alpha (ex-phi)
+ dup -90 eq {
+ /alpha exch def
+ } {
+ /alpha exch beta min -80 max def
+ } ifelse
+ /r exch def
+ beta 90 eq {
+ alpha -90 eq {
+ /ifin K def
+ /db alpha beta sub K 1 add div def
+ } {
+ /ifin K def
+ /db alpha beta sub K div def
+ } ifelse
+ } {
+ alpha -90 eq {
+ /ifin K 1 sub def
+ /db alpha beta sub K div def
+ } {
+ /ifin K 1 sub def
+ /db alpha beta sub K 1 sub div def
+ } ifelse
+ } ifelse
+
+ %% nombre de sommets -2
+ /nb N K mul def
+
+ %% tableau des sommets
+ /S [
+ idebut 1 ifin {
+ /j exch def
+ /phi beta j db mul add def
+ phi cos r mul /r_tmp exch def
+ 0 1 N 1 sub {
+ /i exch def
+ 360 N idiv i mul cos r_tmp mul
+ 360 N idiv i mul sin r_tmp mul
+ phi sin r mul
+ } for
+ } for
+ 0 0 r neg
+ 0 0 r
+ ] def
+
+ /F [
+ %% calotte inferieure
+ alpha -90 eq {
+ 1 1 N 1 sub {
+ /i exch def
+ [
+ nb
+ nb i sub
+ nb i 1 add sub
+ ]
+ } for
+ [nb nb N sub nb 1 sub]
+ } {
+% [nb 1 sub -1 nb N sub {} for ]
+ } ifelse
+
+ %% calotte superieure
+ beta 90 eq {
+ 0 1 N 1 sub {
+ /i exch def
+ [i i 1 add N mod N K mul 1 add]
+ } for
+ } {
+% [0 1 N 1 sub {} for]
+ } ifelse
+
+ 1 1 K 1 sub {
+ /j exch def
+ [
+ j N mul
+ j N mul 1 add
+ j 1 sub N mul 1 add
+ j 1 sub N mul
+ ]
+ N 2 sub {dup {1 add} apply} repeat
+ [
+ j 1 add N mul 1 sub
+ j N mul
+ j 1 sub N mul
+ j N mul 1 sub
+ ]
+ } for
+ ] def
+
+ S F generesolid
+ dup videsolid
+end
+} def
+
+%%%%% ### newanneau ###
+%% syntaxe : array n newanneau --> solid
+%% syntaxe : array {mode} newanneau --> solid
+%% ou array est un tableau de points de R^2 et n un nombre entier positif
+/newanneau {
+10 dict begin
+ dup isnum {
+ /n exch def
+ [n]
+ } if
+ [[/n2] [6] [12] [24] [32] [36]] gestionsolidmode
+ /n2 n2 3 max store
+ %% on plonge la section dans R^3 par projection sur yOz
+ /S1 exch {0 3 1 roll} papply def
+ %% nombre de sommets
+ /n1 S1 length 3 idiv def
+
+ /S S1
+ n2 {
+ duparray
+ {0 0 360 n2 div rotateOpoint3d} papply3d
+ } repeat
+ n2 {append} repeat
+ def
+
+ /F [
+ 0 1 n2 1 sub {
+ /j exch def
+ n1 j mul 1 j 1 add n1 mul 2 sub {
+ /i exch def
+ [i 1 add i dup n1 add i n1 1 add add]
+ } for
+ [n1 j mul j 1 add n1 mul 1 sub j 2 add n1 mul 1 sub j 1 add n1 mul]
+ } for
+ ] def
+
+ S F generesolid
+end
+} def
+
+%%%%% ### newvecteur ###
+%% syntaxe : x y z newvecteur
+%% syntaxe : x y z array newvecteur
+/newvecteur {
+4 dict begin
+ dup isarray {
+ /table exch def
+ /h@uteur table 1 get def
+ /r@y@n table 0 get def
+ } {
+ /h@uteur .3 def
+ /r@y@n .1 def
+ } ifelse
+ /A defpoint3d
+ %%Sommets
+ /S [0 0 0 A] def
+ /F [
+ [0 1]
+ ] def
+ S F generesolid
+ [ A ]
+ normalvect_to_orthobase
+ /imK defpoint3d
+ /imJ defpoint3d
+ /imI defpoint3d
+
+ A norme3d /z exch h@uteur sub def
+ 0 r@y@n h@uteur [1 8] newcone
+ dup (noir) outputcolors
+ {0 0 z translatepoint3d} solidtransform
+ {imI imJ imK transformpoint3d} solidtransform
+ solidfuz
+end
+} def
+
+%%%%% ### readsolidfile ###
+%% syntaxe : str readsolidfile -> solid
+/readsolidfile {
+1 dict begin
+ /str exch def
+ [str (-sommets.dat) append run]
+ [str (-faces.dat) append run]
+ generesolid
+ dup [str (-couleurs.dat) append run] solidputfcolors
+ dup [str (-io.dat) append run] solidputinouttable
+end
+} def
+
+%%%%% ### writesolidfile ###
+%% syntaxe : solid str writesolidfile -> -
+/writesolidfile {
+10 dict begin
+ /str exch def
+ /solid exch def
+ solid issolid not {
+ (Error : mauvais type d argument dans writesolidfile) ==
+ quit
+ } if
+ str (-sommets.dat) append (w) file /lefichiersommets exch def
+ str (-faces.dat) append (w) file /lefichierfaces exch def
+ str (-couleurs.dat) append (w) file /lefichiercouleurs exch def
+ str (-io.dat) append (w) file /lefichierio exch def
+
+ /S solid solidgetsommets def
+ 0 1 S length 3 idiv 1 sub {
+ /i exch def
+ solid i solidgetsommet
+ /z exch def
+ /y exch def
+ /x exch def
+ lefichiersommets x chaine cvs writestring
+ lefichiersommets 32 write %% espace
+ lefichiersommets y chaine cvs writestring
+ lefichiersommets 32 write %% espace
+ lefichiersommets z chaine cvs writestring
+ lefichiersommets 10 write %% CR
+ } for
+ lefichiersommets closefile
+
+ /F solid solidgetfaces def
+ 0 1 F length 1 sub {
+ /i exch def
+ /Fi solid i solidgetface def
+ lefichierfaces 91 write %% [
+ 0 1 Fi length 1 sub {
+ /j exch def
+ lefichierfaces Fi j get chaine cvs writestring
+ lefichierfaces 32 write %% espace
+ } for
+ lefichierfaces 93 write %% ]
+ lefichierfaces 10 write %% CR
+ } for
+ lefichierfaces closefile
+
+ /C solid solidgetfcolors def
+ 0 1 C length 1 sub {
+ /i exch def
+ lefichiercouleurs 40 write %% (
+ lefichiercouleurs C i get writestring
+ lefichiercouleurs 41 write %% )
+ lefichiercouleurs 10 write %% CR
+ } for
+ lefichiercouleurs closefile
+
+ /IO solid solidgetinouttable def
+ 0 1 3 {
+ /i exch def
+ lefichierio IO i get chaine cvs writestring
+ lefichierio 32 write %% space
+ } for
+ lefichierio closefile
+end
+} def
+
+%%%%% ### writeobjfile ###
+%% syntaxe : solid str writeobjfile -> -
+/writeobjfile {
+10 dict begin
+ /str exch (.obj) append def
+ /solid exch def
+ solid issolid not {
+ (Erreur : mauvais type d argument dans writeobjfile) ==
+ quit
+ } if
+ /n solid solidnombresommets def
+ str (w) file /lefichier exch def
+ 0 1 n 1 sub {
+ /i exch def
+ solid i solidgetsommet
+ /z exch def
+ /y exch def
+ /x exch def
+ lefichier (v ) writestring
+ lefichier x chaine cvs writestring
+ lefichier 32 write %% espace
+ lefichier y chaine cvs writestring
+ lefichier 32 write %% espace
+ lefichier z chaine cvs writestring
+ lefichier 10 write %% CR
+ } for
+ /n solid solidnombrefaces def
+ 0 1 n 1 sub {
+ /i exch def
+ lefichier (f ) writestring
+ /F solid i solidgetface {1 add} apply def
+ F {
+ lefichier exch
+ chaine cvs writestring
+ lefichier 32 write %% espace
+ } apply
+ lefichier 10 write %% CR
+ } for
+ lefichier closefile
+end
+} def
+
+%%%%% ### writeofffile ###
+%% syntaxe : solid str writeobjfile -> -
+/writeofffile {
+12 dict begin
+ /str exch (.off) append def
+ /solid exch def
+ solid issolid not {
+ (Erreur : mauvais type d argument dans writeofffile) ==
+ quit
+ } if
+ /n solid solidnombresommets def
+ /nf solid solidnombrefaces def
+ str (w) file /lefichier exch def
+ lefichier (OFF) writestring
+ lefichier 10 write %% CR
+ lefichier n chaine cvs writestring
+ lefichier 32 write %% espace
+ lefichier nf chaine cvs writestring
+ lefichier 32 write %% espace
+ lefichier 0 chaine cvs writestring
+ lefichier 10 write %% CR
+ 0 1 n 1 sub {
+ /i exch def
+ solid i solidgetsommet
+ /z exch def
+ /y exch def
+ /x exch def
+ lefichier x chaine cvs writestring
+ lefichier 32 write %% espace
+ lefichier y chaine cvs writestring
+ lefichier 32 write %% espace
+ lefichier z chaine cvs writestring
+ lefichier 10 write %% CR
+ } for
+ 0 1 nf 1 sub {
+ /i exch def
+ /F solid i solidgetface def
+ lefichier F length chaine cvs writestring
+ lefichier 32 write %% espace
+ F {
+ lefichier exch
+ chaine cvs writestring
+ lefichier 32 write %% espace
+ } apply
+ lefichier 10 write %% CR
+ } for
+ lefichier closefile
+end
+} def
+
+%%%%% ### newobjfile ###
+/newobjfile {
+3 dict begin
+ /objfilename exch (.obj) append def
+ /v {} def
+ /ok true def
+ /f {
+ ok {
+ %% 1ere fois
+ ] %% ferme les sommets
+ [ [ %% ouvre les faces
+ /ok false store
+ } {
+ %% les autres fois
+ ] %% ferme la face
+ [ %% ouvre la nouvelle
+ } ifelse
+ } def
+ [ 0 0 0 %% sommet fantome pour respecter l'indexation (a partir de l'indice 1)
+ objfilename run
+ ]]
+ /F exch def
+ /S exch def
+
+ S F generesolid
+% dup videsolid
+end
+} def
+
+%%%%% ### newofffile ###
+/newofffile {
+3 dict begin
+ /str 35 string def
+ /offfilename exch (.off) append def
+ offfilename (r) file
+ /offfile exch def
+ offfile str readline pop pop
+ offfile str readline pop
+ numstr2array
+ dup 0 get /ns exch def
+ 1 get /nf exch def
+ [ns {
+ offfile str readline pop numstr2array aload pop
+% 3 1 roll
+ } repeat]
+ /S exch def
+ [nf {
+ [
+ offfile str readline pop numstr2array
+ /table exch def
+ 1 1 table length 1 sub {
+ /i exch def
+ table i get
+ } for
+ ]
+ } repeat]
+ /F exch def
+
+ S F generesolid
+% dup videsolid
+end
+} def
+
+%%%%% ### newtube ###
+ /tub@dernierk1 [1 0 0] def
+ /tub@dernierk2 [0 1 0] def
+ /tub@dernierk3 [0 0 1] def
+
+/inittube {
+2 dict begin
+ normalize3d /vect3 defpoint3d
+ normalize3d /vect2 defpoint3d
+ normalize3d /vect1 defpoint3d
+ vect1 norme3d 0 eq {
+ vect2 vect3 vectprod3d /vect1 defpoint3d
+ } if
+ vect2 norme3d 0 eq {
+ vect3 vect1 vectprod3d /vect2 defpoint3d
+ } if
+ vect3 norme3d 0 eq {
+ vect1 vect2 vectprod3d /vect3 defpoint3d
+ } if
+ /tub@dernierk1 [vect1] store
+ /tub@dernierk2 [vect2] store
+ /tub@dernierk3 [vect3] store
+end
+} def
+
+%% syntaxe : tmin tmax (f) array r newtube -> solid
+%% array = [K N]
+/newtube {
+10 dict begin
+ /table exch def
+ /K table 0 get def %% nb d etages
+ /N table 1 get def %% nb de points sur le perimetre
+ /@r exch def %% le rayon du tube
+ /str exch def
+ /lafonction str cvx def
+ /laderivee str (') append cvx def
+%% /laderivee2nd str ('') append cvx def
+ /tmax exch def
+ /tmin exch def
+ /pas tmax tmin sub K 1 sub div def
+
+ %% definition des sommets
+ [
+ /@k 0 def
+ K {
+ /a0 tmin @k pas mul add def
+
+ %% definition du repere de Frenet (k1, k2, k3) au point f(a)
+ a0 lafonction /M defpoint3d
+
+ str (') append cvlit where {
+ pop
+ a0 laderivee normalize3d /k1 defpoint3d
+% pop /avecderiv true def
+ } {
+ M a0 pas 100 div add lafonction vecteur3d normalize3d /k1 defpoint3d
+% /avecderiv false
+ } ifelse
+
+ k1 baseplannormal /K3 defpoint3d /K2 defpoint3d
+% a0 laderivee2nd normalize3d /k2 defpoint3d
+
+ %% projete orthogonal du dernier rayon sur le plan actuel
+ %% (normal a la vitesse)
+ K2 tub@dernierk2 aload pop K2 scalprod3d mulv3d
+ K3 tub@dernierk2 aload pop K3 scalprod3d mulv3d addv3d /k2 defpoint3d
+% M k1 K2 K3 dessinebase
+ k1 norme3d 0 eq {
+ tub@dernierk1 aload pop /k1 defpoint3d
+ } {
+ /tub@dernierk1 [k1] store
+ } ifelse
+ k2 norme3d 0 eq {
+ tub@dernierk2 aload pop /k2 defpoint3d
+ } {
+ /tub@dernierk2 [k2] store
+ } ifelse
+ k1 k2 vectprod3d normalize3d /k3 defpoint3d
+ k3 norme3d 0 eq {
+ tub@dernierk3 aload pop /k3 defpoint3d
+ } {
+ /tub@dernierk3 [k3] store
+ } ifelse
+ k3 k1 vectprod3d normalize3d /k2 defpoint3d
+%% M k1 k2 k3 dessinebase
+ /tub@dernierk2 [k2] store
+ /@n 360 N div def %% le pas angulaire
+ 0 @n 360 @n sub {
+ /@i exch def
+ M
+ k2 @i cos @r mul mulv3d addv3d
+ k3 @i sin @r mul mulv3d addv3d
+ } for
+ /@k @k 1 add store
+ } repeat
+ ]
+
+ dup length 3 idiv /nb exch def
+ %% definition des faces
+ [
+ %% face de depart
+ [N 1 sub -1 0 {} for]
+ %% face d arrivee
+ [nb 1 sub N 1 sub {dup 1 sub} repeat] reverse
+
+ %% les etages
+ /j 0 def
+ K 1 sub {
+ 0 1 N 1 sub {
+ /i exch def
+ [
+ i N j mul add
+ i 1 add N mod N j mul add
+ i 1 add N mod N add N j mul add
+ i N add N j mul add
+ ]
+ } for
+ /j j 1 add store
+ } repeat
+ ]
+ generesolid
+end
+} def
+
+%%%%% ### newcourbe ###
+%% syntaxe : a b {f} array newcourbe --> solid
+/newcourbe {
+10 dict begin
+ dup xcheck not {
+ 0 get /n exch def
+ } {
+ /n 80 def
+ } ifelse
+ /l@f@nct exch def
+ /b exch def
+ /a exch def
+ /pas b a sub n 1 sub div def
+ /S [
+ 0 1 n 1 sub {
+ /@i exch def
+ a @i pas mul add
+ l@f@nct
+ pstrickactionR3
+ } for
+ ] def
+ /@F [
+ 0 1 n 2 sub {
+ /@i exch def
+ [@i @i 1 add]
+ } for
+ ] def
+ S @F generesolid
+end
+} def
+
+%%%%% ### baseplannormal ###
+%% syntaxe : x y z baseplannormal -> x1 y1 z1 x2 y2 z2
+/baseplannormal {
+5 dict begin
+ /K defpoint3d
+ 1 0 0 K vectprod3d normalize3d /U defpoint3d
+ U norme3d 0 eq {
+ 0 1 0 K vectprod3d normalize3d /U defpoint3d
+ } if
+ K U vectprod3d normalize3d /V defpoint3d
+ U V
+end
+} def
+
+%%%%% ### fin insertion ###
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% %%%%
+%%%% fin insertion librairie jps %%%%
+%%%% %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% gestion de chaine de caracteres %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+/Times-Roman findfont
+dup length dict begin
+ {
+ 1 index /FID ne
+ {def}
+ {pop pop}
+ ifelse
+ } forall
+ /Encoding ISOLatin1Encoding def
+ currentdict
+end
+/Times-Roman-ISOLatin1 exch definefont pop
+
+/setTimesRoman {
+ /Times-Roman-ISOLatin1 findfont
+ fontsize scalefont
+ setfont
+} def
+
+/setTimes {
+ setTimesRoman
+} def
+
+%% syntaxe : string x y cctext
+/cctext {
+5 dict begin
+ /y exch def
+ /x exch def
+ /str exch def
+ str stringwidth
+ /wy exch def
+ /wx exch def
+ gsave
+ x y smoveto
+ wx -2 div wy -2 div rmoveto
+ str show
+ grestore
+end
+} def
+
+/dbtext {gsave newpath dbtext_ fill grestore} def
+/dctext {gsave newpath dctext_ fill grestore} def
+/dltext {gsave newpath dltext_ fill grestore} def
+/drtext {gsave newpath drtext_ fill grestore} def
+
+/bbtext {gsave newpath bbtext_ fill grestore} def
+/bctext {gsave newpath bctext_ fill grestore} def
+/bltext {gsave newpath bltext_ fill grestore} def
+/brtext {gsave newpath brtext_ fill grestore} def
+
+/cbtext {gsave newpath cbtext_ fill grestore} def
+/cctext {gsave newpath cctext_ fill grestore} def
+/cltext {gsave newpath cltext_ fill grestore} def
+/crtext {gsave newpath crtext_ fill grestore} def
+
+/ubtext {gsave newpath ubtext_ fill grestore} def
+/uctext {gsave newpath uctext_ fill grestore} def
+/ultext {gsave newpath ultext_ fill grestore} def
+/urtext {gsave newpath urtext_ fill grestore} def
+
+
+%% syntaxe : str x y show_dim --> str x y llx lly wx wy
+%% attention, doit laisser la pile intacte
+/show_dim {
+ 3 copy pop pop
+ newpath
+ 0 0 moveto
+ true charpath flattenpath pathbbox
+ closepath
+ newpath
+} def
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% procedures pour PSTricks %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%% les 3 procedures utilisees pour transformer les depots de AlgToPs en nombres
+/pstrickactionR3 {
+3 dict begin
+ /len@3 exch def
+ /len@2 exch def
+ /len@1 exch def
+ len@1 exec
+ len@2 exec
+ len@3 exec
+end
+} def
+
+/pstrickactionR2 {
+ exec exch exec exch
+} def
+
+/pstrickactionR {
+ exec
+} def
+
+/gere_pst-deffunction {
+ counttomark
+ dup 1 eq {
+ pop
+ pstrickactionR
+ ] aload pop
+ } {
+ 2 eq {
+ pstrickactionR2
+ ] aload pop
+ } {
+ pstrickactionR3
+ ] aload pop
+ } ifelse
+ } ifelse
+} def
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% procedures pour \psSolid %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+/all (all) def
+
+/draw {drawsolid} def
+/draw* {drawsolid*} def
+/draw** {drawsolid**} def
+/writeobj {solidfilename writeobjfile} def
+/writesolid {solidfilename writesolidfile} def
+/writeoff {solidfilename writeofffile} def
+/none {pop} def
+/vecteur_en_c@urs false def
+
+/gere_pstricks_color_inout {
+ gsave
+ dup [fillincolor] (setrgbcolor) astr2str
+ [fillcolor] (setrgbcolor) astr2str inoutputcolors
+ grestore
+} def
+
+/gere_pstricks_color_out {
+ gsave
+ dup [fillcolor] (setrgbcolor) astr2str outputcolors
+ grestore
+} def
+
+/gere_pstfont {
+ fontsize mul setfontsize
+ %setTimes
+ PSfont dup /Symbol ne isolatin and {
+ /ISO-Font ReEncode /ISO-Font
+ } if
+ findfont fontsize scalefont setfont
+} def
+
+/gere_pstricks_opt {
+% /CourbeR2 {CourbeR2+} def
+ 1 gere_pstfont
+ linecolor
+ linestyle
+ solidlinewidth setlinewidth
+ solidtrunc length 0 ne {
+ solidtrunc 0 get isstring {
+ dup trunccoeff solidtronque
+ } {
+ dup solidtrunc trunccoeff solidtronque
+ } ifelse
+ } if
+ solidgeode {
+ 1 newgeode
+ } if
+ soliddualreg {
+ dualpolyedreregulier
+ } if
+ chanfrein {
+ dup chanfreincoeff solidchanfreine
+ } if
+ RotX 0 ne RotY 0 ne or RotZ 0 ne or {
+ {RotX RotY RotZ rotateOpoint3d} solidtransform
+ } if
+ CX 0 ne CY 0 ne or CZ 0 ne or {
+ {CX CY CZ translatepoint3d} solidtransform
+ } if
+ plansection length 0 gt {
+ 0 1 plansection length 1 sub {
+ /i exch def
+ plansection i get solidplansection
+ dup 0 solidrmface
+ } for
+ } if
+ /rmfaces rmfaces bubblesort reverse store
+ 0 1 rmfaces length 1 sub {
+ /i exch def
+ dup rmfaces i get solidrmface
+ } for
+ tx@Dict /pst-transformoption known {
+ dup {pst-transformoption} solidtransform
+ } if
+ solidaffinage length 0 ne {
+ %% si on affine, il faut colorier avant
+ activationgestioncouleurs {
+ gere_pstricks_color_out
+ } if
+ solidaffinage 0 get isstring {
+ dup affinagecoeff
+ /solidfcolor where {
+ pop
+ solidfcolor
+ } if
+ affinagerm solidaffine
+ } {
+ dup affinagecoeff solidaffinage
+ /solidfcolor where {
+ pop
+ solidfcolor
+ } if
+ affinagerm solidaffine
+ } ifelse
+ %% et il faut evider et coloriier l'interieur si necessaire
+ solidhollow {
+ dup videsolid
+ activationgestioncouleurs {
+ gsave
+ dup [fillincolor] (setrgbcolor) astr2str inputcolors
+ grestore
+ } if
+ } if
+ /activationgestioncouleurs false def
+ } if
+ tx@Dict /plansepare known {
+ plansepare solidplansepare
+ tx@Dict /plansepare undef
+ tx@Dict /solidname known {
+ solidname (1) append cvlit exch def
+ dup solidname (0) append cvlit exch def
+ %%
+ solidname (1) append cvx exec
+ solidhollow {
+ dup videsolid
+ } if
+ activationgestioncouleurs {
+ dup solidwithinfaces {
+ gere_pstricks_color_inout
+ } {
+ gere_pstricks_color_out
+ } ifelse
+ } if
+ solidinouthue length 0 gt {
+ dup solidinouthue solidputinouthuecolors
+ } {
+ solidhue length 0 gt {
+ dup solidhue solidputhuecolors
+ } if
+ solidinhue length 0 gt {
+ dup solidinhue solidputinhuecolors
+ } if
+ } ifelse
+ pop
+ tx@Dict /solidname undef
+ } {
+ /solid1 exch def
+ /solid2 exch def
+ } ifelse
+ } if
+ solidhollow {
+ dup videsolid
+ } if
+ activationgestioncouleurs {
+ dup solidwithinfaces {
+ gere_pstricks_color_inout
+ } {
+ gere_pstricks_color_out
+ } ifelse
+ solidinouthue length 0 gt {
+ dup solidinouthue solidputinouthuecolors
+ } {
+ solidhue length 0 gt {
+ dup solidhue solidputhuecolors
+ } if
+ solidinhue length 0 gt {
+ dup solidinhue solidputinhuecolors
+ } if
+ } ifelse
+ } if
+
+ 0 1 fcol length 2 idiv 1 sub {
+ /i exch def
+ dup fcol 2 i mul get fcol 2 i mul 1 add get solidputfcolor
+ } for
+ vecteur_en_c@urs not {
+ /lightsrc where {pop solidlightOn} if
+ } {
+ /vecteur_en_c@urs false def
+ } ifelse
+ dup action cvx exec
+ noir
+ solidnumf length 0 ne {
+ solidnumf 0 get isstring {
+ dup projectionsifacevisible solidnumfaces
+ } {
+ dup solidnumf projectionsifacevisible solidnumfaces
+ } ifelse
+ } if
+ solidshow length 0 ne {
+ solidshow 0 get isstring {
+ dup solidshowsommets
+ } {
+ dup solidshow solidshowsommets
+ } ifelse
+ } if
+ solidnum length 0 ne {
+ solidnum 0 get isstring {
+ .8 gere_pstfont
+ dup solidnumsommets
+ } {
+ dup solidnum solidnumsommets
+ } ifelse
+ } {
+ %% pop
+ } ifelse
+ tx@Dict /solidname known {
+ solidname cvlit exch bind def
+ tx@Dict /solidname undef
+ } {
+ pop
+ } ifelse
+} def
+
+/pst-octahedron {
+ a newoctaedre
+ gere_pstricks_opt
+} def
+
+/pst-dodecahedron {
+ a newdodecaedre
+ gere_pstricks_opt
+} def
+
+/pst-icosahedron {
+ a newicosaedre
+ gere_pstricks_opt
+} def
+
+/pst-cube {
+ a
+ ngrid length 1 eq {
+ ngrid
+ } {
+ {Mode}
+ } ifelse
+ newcube
+%% solidhollow {
+%% dup videsolid
+%% } if
+ gere_pstricks_opt
+} def
+
+/pst-parallelepiped {
+ a b c
+ newparallelepiped
+ gere_pstricks_opt
+} def
+
+/pst-tetrahedron {
+ r newtetraedre
+ gere_pstricks_opt
+} def
+
+/pst-tore {
+ r0 r1
+ ngrid length 2 eq {
+ ngrid
+ } {
+ {Mode}
+ } ifelse
+ newtore
+ gere_pstricks_opt
+} def
+
+/pst-sphere {
+ % rayon
+ % mode
+ % r {Mode} newsphere
+ r
+ ngrid length 2 eq {
+ ngrid
+ } {
+ {Mode}
+ } ifelse
+ newsphere
+ gere_pstricks_opt
+} def
+
+/pst-cylindre {
+ /save-cylinderhollow solidhollow def
+ tx@Dict /function known {
+ range aload pop function cvx {axe} h ngrid newcylindre
+ tx@Dict /function undef
+ /solidhollow true def
+ } {
+ % rayon
+ % mode
+ 0 r h
+ ngrid length 2 eq {
+ ngrid
+ } {
+ {Mode}
+ } ifelse
+ newcylindre
+ solidhollow {
+ dup creusesolid
+ } if
+ } ifelse
+ gere_pstricks_opt
+ /solidhollow save-cylinderhollow store
+} def
+
+/pst-cylindrecreux {
+ % rayon
+ % mode
+ 0 r h
+ ngrid length 2 eq {
+ ngrid
+ } {
+ {Mode}
+ } ifelse
+ newcylindre
+ dup creusesolid
+ gere_pstricks_opt
+} def
+
+/pst-cone {
+ /save-conehollow solidhollow def
+ tx@Dict /function known {
+ range aload pop function cvx {origin} ngrid newcone
+ tx@Dict /function undef
+ /solidhollow true def
+ } {
+ % rayon
+ % mode
+ 0 r h
+ ngrid length 2 eq {
+ ngrid
+ } {
+ {Mode}
+ } ifelse
+ solidhollow {
+ newconecreux
+ } {
+ newcone
+ } ifelse
+ } ifelse
+ gere_pstricks_opt
+ /solidhollow save-conehollow store
+} def
+
+/pst-tronccone {
+ % rayon
+ % mode
+ 0 r0 h r1
+ ngrid length 2 eq {
+ ngrid
+ } {
+ {Mode}
+ } ifelse
+ solidhollow {
+ newtroncconecreux
+ } {
+ newtronccone
+ } ifelse
+ gere_pstricks_opt
+} def
+
+/pst-troncconecreux {
+ % rayon
+ % mode
+ 0 r0 h r1
+ ngrid length 2 eq {
+ ngrid
+ } {
+ {Mode}
+ } ifelse
+ newtroncconecreux
+ gere_pstricks_opt
+} def
+
+/pst-conecreux {
+ % rayon
+ % mode
+ 0 r h
+ ngrid length 2 eq {
+ ngrid
+ } {
+ {Mode}
+ } ifelse
+ newconecreux
+ gere_pstricks_opt
+} def
+
+/pst-anneau {
+ [ section ]
+ ngrid length 1 ge {
+ [ngrid 0 get]
+ } {
+ [24]
+ } ifelse
+ newanneau
+ gere_pstricks_opt
+} def
+
+
+/pst-prisme {
+ % tableau des points de la base
+ % h hauteur du prisme
+ % axe : vecteur direction de l axe
+ base decal rollparray
+ 0 h axe
+ ngrid length 1 ge {
+ [ngrid 0 get]
+ } if
+ newprisme
+ solidhollow {
+ dup creusesolid
+ } if
+ gere_pstricks_opt
+} def
+
+/pst-prismecreux {
+ % tableau des points de la base
+ % h hauteur du prisme
+ % axe : vecteur direction de l axe
+ base
+ 0 h axe
+ ngrid length 1 ge {
+ [ngrid 0 get]
+ } if
+ newprisme
+ dup creusesolid
+ gere_pstricks_opt
+} def
+
+/pst-grille {
+ base aload pop
+ ngrid length 2 ge {
+ [ngrid 0 get ngrid 1 get]
+ } {
+ ngrid length 1 eq {
+ [ngrid 0 get dup]
+ } if
+ } ifelse
+ newgrille
+ gere_pstricks_opt
+} def
+
+%% syntaxe : array N h u newruban -> solid d axe (O, u),
+/pst-ruban {
+ % tableau des points de la base
+ % h hauteur du prisme
+ % axe : vecteur direction de l axe
+ base
+ h axe
+ ngrid length 1 ge {
+ [ngrid 0 get]
+ } if
+ newruban
+ gere_pstricks_opt
+} def
+
+%% syntaxe : r phi option newcalottesphere -> solid
+/pst-calottesphere {
+ % rayon
+ % mode
+ % r phi theta option newcalottesphere
+ r
+ phi theta
+ ngrid length 2 eq {
+ ngrid
+ } {
+ {Mode}
+ } ifelse
+ solidhollow {
+ newcalottespherecreuse
+ } {
+ newcalottesphere
+ } ifelse
+ gere_pstricks_opt
+} def
+
+%% syntaxe : r phi option newcalottesphere -> solid
+/pst-calottespherecreuse {
+ % rayon
+ % mode
+ % r phi theta option newcalottespherecreuse
+ r
+ phi theta
+ ngrid length 2 eq {
+ ngrid
+ } {
+ {Mode}
+ } ifelse
+ newcalottespherecreuse
+ gere_pstricks_opt
+} def
+
+/pointtest{2 2 2} def
+
+/pst-face {
+ % tableau des points de la base
+ % h hauteur du prisme
+ % axe : vecteur direction de l axe
+ base
+ solidbiface {
+ newbiface
+ } {
+ newmonoface
+ } ifelse
+ gere_pstricks_opt
+} def
+
+/pst-Surface {
+ base
+ base aload pop
+ ngrid length 2 ge {
+ [ngrid 0 get ngrid 1 get]
+ } {
+ ngrid length 1 eq {
+ [ngrid 0 get dup]
+ } ifelse
+ } ifelse
+ {f} newsurface
+ solidbiface {
+ dup videsolid
+ } if
+ gere_pstricks_opt
+} def
+
+/pst-surface {
+ base
+ base aload pop
+ ngrid length 2 ge {
+ [ngrid 0 get ngrid 1 get]
+ } {
+ ngrid length 1 eq {
+ [ngrid 0 get dup]
+ } ifelse
+ } ifelse
+ { function cvx exec } newsurface
+ solidbiface {
+ dup videsolid
+ } if
+ gere_pstricks_opt
+} def
+
+/pst-polygoneregulier {
+ r ngrid 0 get
+ newpolreg
+ solidbiface {
+ } {
+ dup 1 solidrmface
+ } ifelse
+ gere_pstricks_opt
+} def
+
+/pst-fusion {
+1 dict begin
+ /activationgestioncouleurs false def
+ /n base length def
+ base aload pop n 1 sub {solidfuz} repeat
+ gere_pstricks_opt
+end
+} def
+
+/pst-new {
+ sommets faces
+ generesolid
+%% solidhollow {
+%% dup videsolid
+%% } if
+ gere_pstricks_opt
+} def
+
+/pst-courbe {
+ solidlinewidth setlinewidth
+ r 0 eq {
+ range aload pop function cvx [resolution] newcourbe
+ gere_pstricks_opt
+ } {
+ range aload pop function r
+ ngrid length 2 lt {
+ [300 4]
+ } {
+ ngrid
+ } ifelse
+ newtube
+ gere_pstricks_opt %% r function [36 12] newtube
+ } ifelse
+} def
+
+/pst-surfaceparametree {
+ base aload pop
+ ngrid length 2 ge {
+ [ngrid 0 get ngrid 1 get]
+ } {
+ ngrid length 1 eq {
+ [ngrid 0 get dup]
+ } if
+ } ifelse
+ { function cvx exec } newsurfaceparametree
+ dup videsolid
+ gere_pstricks_opt
+} def
+
+/pst-surface* {
+ r
+ ngrid length 2 ge {
+ [ngrid 0 get ngrid 1 get]
+ } {
+ ngrid length 1 eq {
+ [ngrid 0 get dup]
+ } if
+ } ifelse
+ { function cvx exec } newsurface*
+ dup videsolid
+ gere_pstricks_opt
+} def
+
+/pst-vecteur {
+gsave
+ /activationgestioncouleurs false def
+ /vecteur_en_c@urs true def
+ solidlinewidth setlinewidth
+ 2 setlinejoin
+ 1 setlinecap
+ linecolor
+ linestyle
+ tx@Dict /solidname known {
+ texte args definition cvx exec
+ solidname cvlit exch defpoint3d
+ tx@Dict /solidname undef
+ } if
+ args definition cvx exec newvecteur
+ dup
+ gsave
+ [linecolor currentrgbcolor] ( ) astr2str (setrgbcolor) append
+ outputcolors
+ grestore
+ gere_pstricks_opt
+grestore
+} def
+
+%/pst-vect- {} def
+%/pst-vect-2points {vecteur3d} def
+/pst-line {
+ gsave
+ linestyle
+ linecolor
+ [args] ligne3d
+ grestore
+} def
+
+/pst-objfile {
+ solidfilename newobjfile
+ gere_pstricks_opt
+} def
+
+/pst-offfile {
+ solidfilename newofffile
+ gere_pstricks_opt
+} def
+
+/pst-datfile {
+ solidfilename readsolidfile
+% /activationgestioncouleurs false def
+ gere_pstricks_opt
+} def
+
+/pst-plantype {
+% args definition
+ args (pst-plan-) definition append cvx exec
+ dup phi rotateplan
+ base length 4 eq {
+ dup base planputrange
+ } if
+ origin eqpl@n pointeqplan 0 eq {
+ dup origin planputorigine
+ } if
+ ngrid length 0 ne {
+ dup ngrid planputngrid
+ } if
+ tx@Dict /solidname known {
+ solidname cvlit exch bind def
+ tx@Dict /solidname undef
+ } {
+ pop
+ } ifelse
+} def
+/pst-plan- {pst-plan-plantype} def
+
+%x0 y0 z0 [normalvect] norm2plan
+/pst-plan-plantype {
+ dup plan2eq /eqpl@n exch def
+ /plan-@k true def
+} def
+
+/pst-plan {
+% args definition
+ args (pst-plan-) definition append cvx exec
+ /pl@n-en-cours true def
+ definition length 0 ne {
+% plan-@k not {
+ dup
+ base 0 get base 1 get lt
+ base 2 get base 3 get lt and {
+ base
+ } {
+ [-3 3 -2 2] %pop base %aload pop boum
+ } ifelse
+ planputrange
+ origin eqpl@n pointeqplan 0 eq {
+ dup origin planputorigine
+ } if
+ CX isreal
+ CX 0 eq and
+ CY isreal and
+ CY 0 eq and
+ CZ isreal and
+ CZ 0 eq and not {
+ dup CX CY CZ planputorigine
+ } if
+ /CX 0. def
+ /CY 0. def
+ /CZ 0. def
+ ngrid length 0 ne {
+ dup ngrid planputngrid
+ } if
+ } if
+% dup RotX RotY RotZ rotateOplan
+ dup phi rotateplan
+ /l@pl@n exch def
+ tx@Dict /solidname known {
+ l@pl@n solidname cvlit exch bind def
+ /solidname solidname (_s) append store
+ } if
+ l@pl@n newplan
+ gere_pstricks_opt
+ /pl@n-en-cours false def
+% action ==
+% noir
+ l@pl@n RotX RotY RotZ rotateOplan
+% l@pl@n CX CY CZ plantranslate
+% fontsize setfontsize
+% setTimes
+ 1 gere_pstfont
+ solidplanmarks {l@pl@n projectionsifacevisible planmarks} if
+ solidplangrid {linecolor l@pl@n projectionsifacevisible planquadrillage} if
+ solidshowbase {l@pl@n projectionsifacevisible planshowbase} if
+ solidshowbase3d {l@pl@n projectionsifacevisible planshowbase3d} if
+} def
+
+
+/pst-plan-normalpoint {
+ /plan-@k false def
+ norm2plan
+ dup plan2eq /eqpl@n exch def
+} def
+
+/pst-plan-equation {
+ /plan-@k false def
+ dup isarray {
+ dup /eqpl@n exch def
+ } {
+ 2 copy pop /eqpl@n exch def
+ } ifelse
+ eq2plan
+} def
+
+/pst-plan-solidface {
+ /plan-@k false def
+ solidface2plan
+ CX isreal
+ CX 0 eq and
+ CY isreal and
+ CY 0 eq and
+ CZ isreal and
+ CZ 0 eq and not {
+ dup CX CY CZ planputorigine
+ } if
+
+% dup plangetrange aload pop boum
+% dup origin planputorigine
+ dup plan2eq /eqpl@n exch def
+} def
+
+/pst-geode {
+ ngrid aload pop newgeode
+ gere_pstricks_opt
+} def
+
+/pst-load {
+ solidloadname
+% /activationgestioncouleurs false def
+ gere_pstricks_opt
+} def
+
+/pst-point {
+gsave
+ linecolor
+ 1 gere_pstfont
+ action (none) eqstring not {
+ args definition cvx exec point3d
+ } if
+ texte args definition cvx exec pos (text3d) append cvx exec
+ tx@Dict /solidname known {
+ texte args definition cvx exec
+ solidname cvlit defpoint3d
+ tx@Dict /solidname undef
+ } if
+grestore
+} def
+
+%% syntaxe : alpha beta r h newpie --> solid
+/pst-pie {
+ phi theta r h
+ ngrid length 2 ge {
+ [ngrid 0 get ngrid 1 get]
+ } if
+ newpie
+ gere_pstricks_opt
+} def
+
+/pst-trigospherique {
+3 dict begin
+gsave
+ solidlinewidth setlinewidth
+ linecolor
+ linestyle
+ args definition cvx exec
+grestore
+end
+} def
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%% procedures pour \psProjection %%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+/gere_pstricks_proj_opt {
+ /planprojpst where {
+ pop
+ planprojpst projectionsifacevisible projpath
+% /planprojpst where pop /planprojpst undef
+ } {
+ /solidprojname where {
+ /solidprojname get noface phi
+ xorigine 0 eq
+ yorigine 0 eq and
+ zorigine 0 eq and
+ xorigine isinteger not and
+ yorigine isinteger not and
+ yorigine isinteger not and {
+ } {
+ [xorigine yorigine zorigine] ( ) astr2str
+ } ifelse
+ projectionsifacevisible solidprojpath
+ } {
+ xorigine yorigine zorigine [ normale ] projectionsifacevisible planprojpath
+ } ifelse
+ } ifelse
+} def
+
+/proj-pst-chemin {
+ solidlinewidth setlinewidth
+ 1 dict begin
+ newpath
+ /cercle {cercle_} def
+ path
+ linecolor
+ gere_pstricks_proj_opt
+ end
+} def
+
+/proj-pst-courbeR2 {
+ l@pl@n plangetrange aload pop
+ setyrange setxrange
+ newpath
+ xmin ymin l@pl@n pointplan smoveto
+ xmin ymax l@pl@n pointplan slineto
+ xmax ymax l@pl@n pointplan slineto
+ xmax ymin l@pl@n pointplan slineto
+ xmin ymin l@pl@n pointplan slineto
+ planprojpst projpath
+ clip
+ solidlinewidth setlinewidth
+ newpath
+ linecolor
+ range aload pop { function cvx exec } CourbeR2_
+ gere_pstricks_proj_opt
+} def
+
+/proj-pst-courbe {
+ l@pl@n plangetrange aload pop
+ setyrange setxrange
+ newpath
+ xmin ymin l@pl@n pointplan smoveto
+ xmin ymax l@pl@n pointplan slineto
+ xmax ymax l@pl@n pointplan slineto
+ xmax ymin l@pl@n pointplan slineto
+ xmin ymin l@pl@n pointplan slineto
+ planprojpst projpath
+ clip
+ solidlinewidth setlinewidth
+ newpath
+ linecolor
+ range aload pop {} { function cvx exec } Courbeparam_
+ gere_pstricks_proj_opt
+} def
+
+/proj-pst-point {
+ [proj-args] length 0 eq {
+ xorigine yorigine /proj-args defpoint
+ } if
+ /projname where {
+ pop
+ [proj-args proj-definition cvx exec]
+ dup 0 getp projname cvlit defpoint
+ dup length 2 gt {
+ 1 getp projname (0) append cvlit defpoint
+ } if
+ /projname where pop /projname undef
+ } if
+ proj-action (none) eqstring not {
+ solidlinewidth setlinewidth
+ linecolor
+ [proj-args proj-definition cvx exec] 0 getp point_
+ gere_pstricks_proj_opt
+ stroke
+ } if
+% 1 1 0 0 1 1 Diamond
+ texte length 0 gt {
+ proj-fontsize setfontsize
+ %setTimes
+ solidlinewidth setlinewidth
+ newpath
+ linecolor
+ texte [proj-args proj-definition cvx exec 0 0 phi neg rotatepoint] 0 getp
+ pos (text_) append cvx exec
+%% /planprojpst where {
+%% planprojpst dupplan dup phi rotateplan /planprojpst exch def
+%% pop
+%% xorigine yorigine
+%% 0 0 phi neg rotatepoint
+%% } {
+%% 0 0
+%% } ifelse
+ %gere_pstricks_proj_opt
+ planprojpst dupplan dup phi rotateplan projectionsifacevisible projpath
+ fill
+ } if
+} def
+
+/proj-pst-vecteur {
+ proj-action (none) eqstring not {
+ planprojpst bprojscene
+ solidlinewidth setlinewidth
+ linestyle
+ linecolor
+ xorigine yorigine 2 copy proj-args proj-definition cvx exec addv drawvecteur
+ eprojscene
+ } if
+ /projname where {
+ pop
+ proj-args proj-definition cvx exec projname cvlit defpoint
+ /projname where pop /projname undef
+ } if
+} def
+
+/proj-pst-droite {
+ proj-action (none) eqstring not {
+ l@pl@n plangetrange aload pop
+ setyrange setxrange
+%% newpath
+%% xmin ymin l@pl@n pointplan smoveto
+%% xmin ymax l@pl@n pointplan slineto
+%% xmax ymax l@pl@n pointplan slineto
+%% xmax ymin l@pl@n pointplan slineto
+%% xmin ymin l@pl@n pointplan smoveto
+%% planprojpst projpath
+%% clip
+ planprojpst bprojscene
+ solidlinewidth setlinewidth
+ linestyle
+ linecolor
+ proj-args proj-definition cvx exec droite
+ eprojscene
+ } if
+ /projname where {
+ pop
+ proj-args proj-definition cvx exec projname cvlit defdroite
+ /projname where pop /projname undef
+ } if
+} def
+
+/proj-pst-polygone {
+ proj-action (none) eqstring not {
+ l@pl@n plangetrange aload pop
+ setyrange setxrange
+ newpath
+ xmin ymin l@pl@n pointplan smoveto
+ xmin ymax l@pl@n pointplan slineto
+ xmax ymax l@pl@n pointplan slineto
+ xmax ymin l@pl@n pointplan slineto
+ xmin ymin l@pl@n pointplan slineto
+ planprojpst projpath
+ clip
+ solidlinewidth setlinewidth
+ linestyle
+ linecolor
+ proj-definition length 0 eq {
+ [proj-args]
+ } {
+ proj-args
+ } ifelse
+ proj-definition cvx exec polygone_
+ planprojpst projectionsifacevisible projpath
+ } if
+ /projname where {
+ pop
+ proj-definition length 0 eq {
+ [proj-args]
+ } {
+ proj-args
+ } ifelse
+ proj-definition cvx exec projname cvlit exch def
+ /projname where pop /projname undef
+ } if
+} def
+
+/proj-pst-cercle {
+ /projname where {
+ pop
+ proj-args proj-definition cvx exec projname cvlit defcercle
+ /projname where pop /projname undef
+ } if
+ proj-action (none) eqstring not {
+ l@pl@n plangetrange aload pop
+ setyrange setxrange
+ newpath
+ xmin ymin l@pl@n pointplan smoveto
+ xmin ymax l@pl@n pointplan slineto
+ xmax ymax l@pl@n pointplan slineto
+ xmax ymin l@pl@n pointplan slineto
+ xmin ymin l@pl@n pointplan slineto
+ planprojpst projpath
+ clip
+ solidlinewidth setlinewidth
+ linestyle
+ linecolor
+ newpath
+ range aload pop proj-args
+ proj-definition cvx exec Cercle_
+ planprojpst projectionsifacevisible projpath
+ } if
+} def
+
+/proj-pst-line {
+ proj-action (none) eqstring not {
+ l@pl@n plangetrange aload pop
+ setyrange setxrange
+ newpath
+ xmin ymin l@pl@n pointplan smoveto
+ xmin ymax l@pl@n pointplan slineto
+ xmax ymax l@pl@n pointplan slineto
+ xmax ymin l@pl@n pointplan slineto
+ xmin ymin l@pl@n pointplan slineto
+ planprojpst projpath
+ clip
+ planprojpst bprojscene
+ solidlinewidth setlinewidth
+ linestyle
+ linecolor
+ proj-definition length 0 eq {
+ [proj-args]
+ } {
+ proj-args
+ } ifelse
+ proj-definition cvx exec ligne
+ eprojscene
+ } if
+ /projname where {
+ pop
+ proj-definition length 0 eq {
+ [proj-args]
+ } {
+ proj-args
+ } ifelse
+ proj-definition cvx exec projname cvlit exch def
+ /projname where pop /projname undef
+ } if
+} def
+
+/proj-pst-rightangle {
+ proj-action (none) eqstring not {
+ planprojpst bprojscene
+ solidlinewidth setlinewidth
+ linestyle
+ linecolor
+ proj-args proj-definition cvx exec angledroit
+ eprojscene
+ } if
+} def
+
+/proj-pst-texte {
+2 dict begin
+ proj-fontsize setfontsize
+ %setTimes
+ 1 gere_pstfont
+ solidlinewidth setlinewidth
+ newpath
+ linecolor
+ texte
+ /planprojpst where {
+ planprojpst dupplan dup phi rotateplan /planprojpst exch def
+ pop
+ xorigine yorigine
+ 0 0 phi neg rotatepoint
+ } {
+ 0 0
+ } ifelse
+ pos (text_) append cvx exec
+ gere_pstricks_proj_opt
+fill
+end
+} def
+
+% END solides.pro
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-04 05:59:25 +0000