1 \section {The predefined solids and their parameters}
4 \texttt{\Lcs{psSolid}[object=\textsl{name}]$(x, y ,z)$} which allows us to translate the chosen object to the point with the coordinates $(x, y,
7 The available predefined names for the objects are:
9 {\ttfamily%\flushleft \hyphenchar\font`\-%
10 point, line, vector, plan, grille, cube, cylindre, cylindrecreux, cone, conecreux, tronccone,
11 troncconecreux, sphere, calottesphere, calottespherecreuse, tore,
12 tetrahedron, octahedron, dodecahedron,
13 isocahedron, anneau, prisme, prismecreux, parallelepiped, face, polygonregulier, ruban, surface, surface*, surfaceparamettree, pie, fusion, geode, load, offfile, objfile, datfile, new.}
17 The following table gives an example of every one of the above named solids with their specified parameters:
20 \begin{tabular}{>{\bfseries\sffamily\color{blue}}lcm{4cm}m{5cm}}
26 \texttt{[args=1 1 0]}\\
30 \begin{pspicture}(-2,-2)(2,2)
31 \psset{lightsrc=10 5 20,viewpoint=50 20 30 rtp2xyz}
32 \psSolid[object=point,args=1 1 0]%
38 \psSolid[object=point,
45 \texttt{[args=0 -1 0 1 2 2]}\\
50 \begin{pspicture}(-2,-2)(2,2)
51 \psset{lightsrc=10 5 20,viewpoint=50 20 30 rtp2xyz}
52 \psSolid[object=line,args=0 -1 0 1 2 2]
65 \texttt{[args=1 2 2]}\\
70 \begin{pspicture}(-2,-2)(2,2)
71 \psset{lightsrc=10 5 20,viewpoint=50 20 30 rtp2xyz}
72 \psSolid[object=vecteur,args=1 2 2]
78 \psSolid[object=vecteur,
85 \texttt{[base=-x x -y y]}\\
87 \texttt{args={[0 0 1 0]}}\\
91 \begin{pspicture}(-2,-2)(2,2)
92 \psset{lightsrc=10 5 20,viewpoint=50 20 30 rtp2xyz}
100 \begin{minipage}{5cm}
102 \psSolid[object=plan,
114 \begin{tabular}{>{\bfseries\sffamily\color{blue}}lcm{4cm}m{5cm}}
118 \Index{Cube}& \begin{tabular}{c}
123 \begin{pspicture}(-2,-2)(2,2)
124 \psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
127 object=cube,a=2,action=draw*,fillcolor=magenta!20]%
128 \axesIIID(1,1,1)(1.5,1.5,1.5)
131 \begin{minipage}{5cm}
137 fillcolor=magenta!20]
146 \texttt{[ngrid=n1 n2]}
149 \begin{pspicture}(-2,-2.5)(2,3)
150 \psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
152 \psSolid[object=cylindre,h=5,r=2,fillcolor=white,ngrid=4 32](0,0,-3)
153 \axesIIID(2,2,2.5)(3,3,3.5)
156 \begin{minipage}{5cm}
167 \Index{Hollow Cylinder}&
172 \texttt{[ngrid=n1 n2]}
175 \begin{pspicture}(-2,-2.5)(2,3)
176 \psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
178 \psSolid[object=cylindrecreux,h=5,r=2,fillcolor=white,mode=4,incolor=green!50](0,0,-2.5)
179 \axesIIID(2,2,2.5)(3,3,4.5)
182 \begin{minipage}{5cm}
185 object=cylindrecreux,
198 \begin{tabular}{>{\bfseries\sffamily\color{blue}}lcm{4cm}m{5cm}}
207 \texttt{[ngrid=n1 n2]}
210 \begin{pspicture}(-2,-1)(2,4)
211 \psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
213 \psSolid[object=cone,h=5,r=2,fillcolor=cyan,mode=4]%
214 \axesIIID(2,2,5)(2.5,2.5,6)
217 \begin{minipage}{5cm}
232 \texttt{[ngrid=n1 n2]}
235 \begin{pspicture}(-2,-1)(2,4)
236 \psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
238 \psSolid[object=conecreux,h=5,r=2,fillcolor=white,mode=4,RotY=-60,incolor=green!50]%
239 \axesIIID(2,2,5)(2.5,2.5,6)
242 \begin{minipage}{5cm}
254 \Index{Truncated Cone}&
256 \texttt{[h=6,r0=4,r1=1.5]}\\
259 \texttt{[ngrid=n1 n2]}
262 \begin{pspicture}(-2,-1)(2,4)
263 \psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
265 \psSolid[object=tronccone,r0=2,r1=1.5,h=5,fillcolor=cyan,mode=4]%
266 \axesIIID(2,2,5)(2.5,2.5,6)
269 \begin{minipage}{5cm}
285 \texttt{[h=6,r0=4,r1=1.5]}\\
288 \texttt{[ngrid=n1 n2]}
291 \begin{pspicture}(-2,-1)(2,4)
292 \psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
294 \psSolid[object=troncconecreux,r0=2,r1=1,h=5,fillcolor=white,mode=4]%
295 \axesIIID(2,2,5)(2.5,2.5,6)
298 \begin{minipage}{5cm}
301 object=troncconecreux,
313 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
315 %\begin{tabular}{>{\bfseries\sffamily\color{blue}}lcm{4cm}m{5cm}}
317 >{\bfseries\sffamily\color{blue}} l
318 >{\centering} m{4cm} m{4cm} m{5cm}}
327 \texttt{[ngrid=n1 n2]}
330 \begin{pspicture}(-2,-2)(2,3)
331 \psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
333 \psSolid[object=sphere,r=3,fillcolor=red!25,ngrid=18 18,linewidth=0.2\pslinewidth]%
334 \axesIIID(3,3,3)(4,4,4)
337 \begin{minipage}{5cm}
341 r=2,fillcolor=red!25,
353 \texttt{[phi=0,theta=90]} \\
354 latitude for slicing\\
355 the zone respectively \\
356 from the bottom and top \\
359 \begin{pspicture}(-2,-3)(5,3)
361 \psset{lightsrc=42 24 13,viewpoint=50 30 15 rtp2xyz,Decran=50}
362 \psSolid[object=calottesphere,r=3,ngrid=16 18,
363 fillcolor=cyan!50,incolor=yellow,theta=45,phi=-30,hollow,RotY=-80]%
364 \axesIIID(0,3,3)(6,5,4)
367 \begin{minipage}{5cm}
370 object=calottesphere,
379 \texttt{[r0=4,r1=1.5]} \\
383 \texttt{[ngrid=n1 n2]}
386 \begin{pspicture}(-2,-2)(2,2.35)
387 \psset{lightsrc=42 24 13,viewpoint=50 30 15 rtp2xyz}
388 \psset{Decran=30,unit=0.9cm}
389 \psSolid[r1=2.5,r0=1.5,object=tore,ngrid=18 36,fillcolor=green!30,action=draw**]%
390 \axesIIID(4,4,0)(5,5,4)
393 \begin{minipage}{5cm}
411 inner and outer radius\\
412 \texttt{h=6,section=...]}\\
418 \begin{pspicture}(-2,-2)(2,2.35)
420 \psset{lightsrc=42 24 13,viewpoint=50 30 15 rtp2xyz}
422 \psSolid[object=anneau,fillcolor=yellow,h=1.5,R=4,r=3]%
423 \axesIIID(4,4,0)(5,5,4)
426 \begin{minipage}{5cm}
440 %\begin{tabular}{>{\bfseries\sffamily\color{blue}}lcm{4cm}m{6cm}}
442 >{\bfseries\sffamily\color{blue}} l
443 >{\centering} m{4cm} m{4cm} m{5cm}}
454 \begin{pspicture}(-2,-2)(2,2)
455 \psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
457 \psSolid[object=tetrahedron,r=3,linecolor=blue,action=draw]%
460 \begin{minipage}{5cm}
477 \begin{pspicture}(-2,-1.85)(2,2.85)
478 \psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
480 \psSolid[object=octahedron,a=3,linecolor=blue,fillcolor=Turquoise]%
481 \axesIIID(3,3,3)(4,4,4)
484 \begin{minipage}{5cm}
490 fillcolor=Turquoise]%
494 \Index{Dodecahedron} &
501 \begin{pspicture}(-2,-1.85)(2,1.85)
502 \psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
504 \psSolid[object=dodecahedron,a=2.5,RotZ=90,action=draw*,fillcolor=OliveGreen]%
507 \begin{minipage}{5cm}
513 fillcolor=OliveGreen]%
517 \Index{Icosahedron} &
524 \begin{pspicture}(-2,-1.85)(2,2.85)
525 \psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
527 \psSolid[object=icosahedron,a=3,action=draw*,fillcolor=green!50]%
528 \axesIIID(3,3,3)(4,4,4)
531 \begin{minipage}{5cm}
544 \texttt{[axe=0 0 1]}\\
545 direction of the axis\\
547 \texttt{-1 -1 1 -1 0 1]}\\
555 \begin{pspicture}(-2,-2)(2,3)
556 \psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
557 \psset{Decran=30,unit=0.9cm}
558 \psSolid[object=prisme,action=draw*,linecolor=red,h=4,fillcolor=gray!50]%
559 \psSolid[object=grille,base=-3 3 -3 3,action=draw]%
560 \axesIIID(3,3,4)(5,5,5)
563 \begin{minipage}{5cm}
577 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
579 %\psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
580 %\begin{tabular}{>{\bfseries\sffamily\color{blue}}lcm{4cm}m{6cm}}
582 >{\bfseries\sffamily\color{blue}} l
583 >{\centering} m{4cm} m{4cm} m{5cm}}
590 \texttt{[base=-X +X -Y +Y]}
593 \begin{pspicture}(-1.5,-2)(2,3)
594 \psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
595 \psset{Decran=30,unit=0.9cm}
596 \psSolid[object=grille,base=-5 5 -3 3]%
597 \axesIIID(5,3,0)(6,4,4)
600 \begin{minipage}{5cm}
612 \texttt{[a=4,b=3,c=2]}\\
617 \begin{pspicture}(-1.5,-2)(2,3)
618 \psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
620 \psSolid[object=parallelepiped,a=5,b=6,c=2,fillcolor=bleuciel,axe=1 1 1](0,0,c 2 div)
621 \psSolid[object=grille,base=-2.5 2.5 -3 3,action=draw](0,0,2)
622 \psSolid[object=grille,base=-1 1 -3 3,RotY=90,action=draw](2.5,0,1)
623 \psSolid[object=grille,base=-2.5 2.5 -1 1,RotX=-90,action=draw](0,3,1)
624 \axesIIID(2.5,3,2)(3.5,4,4)
627 \begin{minipage}{5cm}
630 object=parallelepiped,%
641 \texttt{[base=x0 y0 x1 y1}\\
642 \texttt{~ x2 y2 etc.]}\\
647 \begin{pspicture}(-2,-2)(3,2)
649 \psset{viewpoint=50 -20 30 rtp2xyz,Decran=50}
650 \psSolid[object=grille,base=-4 6 -4 4,action=draw,linecolor=gray](0,0,0)
651 \psSolid[object=face,fillcolor=yellow,
655 \psSolid[object=face,fillcolor=yellow,
659 \axesIIID(0,0,0)(6,6,3)
662 \begin{minipage}{5cm}
683 \texttt{[base=x0 y0 x1 y1}\\
684 \texttt{~ x2 y2 etc.]}\\
685 \texttt{[h=height]}\\
686 \texttt{[ngrid=value]}\\
687 number of gridlines\\
688 \texttt{[axe=0 0 1]}\\
689 direction of inclination\\
693 \begin{pspicture}(-2,-2)(5,3)
694 \psset{lightsrc=10 0 10,viewpoint=50 -20 30 rtp2xyz,Decran=50,unit=0.5cm}
695 \psSolid[object=grille,base=-4 6 -2 4,action=draw,linecolor=gray](0,0,0)
696 \psSolid[object=ruban,h=3,fillcolor=red!50,
697 base=0 0 2 2 4 0 6 2,
701 \axesIIID(0,2,0)(6,6,6)
704 \begin{minipage}{5cm}
709 base=0 0 2 2 4 0 6 2,
722 %\psset{lightsrc=10 20 30,SphericalCoor,viewpoint=50 20 30}
723 %%\begin{tabular}{>{\bfseries\sffamily\color{blue}}lcm{4cm}m{6cm}}
725 % >{\bfseries\sffamily\color{blue}} l
726 % >{\centering} m{4cm} m{4cm} m{5cm}}
731 %% \begin{tabular}{l}
732 %% dessine un chemin\\
733 %% d\'{e}fini en postscript\\
737 %% \psset{unit=0.4cm}
738 %% \begin{pspicture}(-2,-5)(6,8)%
739 %% \psframe*[linecolor=blue!50](-6,-5)(6,7)
740 %% \psset{lightsrc=50 20 20,viewpoint=50 30 15,Decran=60}
741 %% \psProjection[object=chemin,fillstyle=solid,fillcolor=white,
742 %% linewidth=.05,linecolor=red,
751 %% \psProjection[object=chemin,
762 %% \psProjection[object=chemin,fillstyle=hlines,hatchcolor=yellow,
774 %% \psPoint(0,0,0){O}
775 %% \psPoint(1,1,2){O1}\psPoint(1.4,1.4,2.8){K}
776 %% \psline[linewidth=.1,linecolor=red](O1)(K)
777 %% \psline[linestyle=dashed](O)(O1)
778 %% \psProjection[object=chemin,
785 %% 1 0 slineto](1,1,2)
786 %% \psProjection[object=chemin,
793 %% 0 1 slineto](1,1,2)
794 %% \axesIIID(4,4,2)(5,5,6)
797 %% \begin{minipage}{6cm}
799 %% \psProjection[object=chemin,
801 %% hatchcolor=yellow,
819 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
821 %\begin{tabular}{>{\bfseries\sffamily\color{blue}}lcm{4cm}m{6cm}}
823 >{\bfseries\sffamily\color{blue}} l
824 >{\centering} m{4cm} m{4cm} m{5cm}}
836 \begin{pspicture}(-2,-3)(3,3)
837 \psset{unit=0.4cm,lightsrc=30 30 25,viewpoint=50 40 30 rtp2xyz,Decran=50}
838 \psSurface[ngrid=.25 .25,incolor=white,axesboxed](-4,-4)(4,4){%
839 x dup mul y dup mul 3 mul sub x mul 32 div}
842 \begin{minipage}{5cm}
844 \psSurface[ngrid=.25 .25,
845 incolor=white,axesboxed]
847 x dup mul y dup mul 3 mul
857 by the coordinates \\
864 \begin{pspicture}(-2,-2)(2,4)
866 \psset{viewpoint=50 -20 30 rtp2xyz,Decran=50}
892 \axesIIID(0,0,0)(5,5,7)
895 \begin{minipage}{5cm}
927 curve of a function\\
928 $\mathbb{R} \rightarrow \mathbb{R}^3$\\
930 paramterised equations\\
934 \begin{pspicture}(-2,-1)(1.75,2.7)
936 \psset{lightsrc=10 -20 50,viewpoint=50 -20 20 rtp2xyz,Decran=50}
937 %\psframe*[linecolor=blue!50](-6,-3)(6,8)
938 \psSolid[object=grille,base=-4 4 -4 4,linecolor=red,linewidth=0.5\pslinewidth]%
939 \axesIIID(0,0,0)(4,4,7)
940 \defFunction[algebraic]{helice}(t){3*cos(4*t)}{3*sin(4*t)}{t}
941 \psSolid[object=courbe,r=0,
943 linecolor=blue,linewidth=0.1,
948 \begin{minipage}{5cm}
951 \defFunction[algebraic]%
953 {3*cos(4*t)}{3*sin(4*t)}{t}
954 \psSolid[object=courbe,r=0,
965 %% \begin{tabular}{l}
966 %% trac\'{e} d'une fonction\\
967 %% R --> R\textsuperscript{2}\\
968 %% d\'{e}finie par ses\\
969 %% \'{e}quations param\'{e}triques\\
972 %% \psset{unit=0.4cm}
973 %% \begin{pspicture}(-6,-7)(6,6)
974 %% \psframe*[linecolor=yellow!50](-6,-6)(6,6)
975 %% \psset{SphericalCoor,viewpoint=50 -20 30,Decran=50}
976 %% {\psset{linewidth=0.5\pslinewidth,linecolor=gray}
977 %% \psSolid[object=grille,base=-4 4 -4 0,RotX=90,RotZ=90]%
978 %% \psSolid[object=grille,base=-4 4 -4 4]%
979 %% \psSolid[object=grille,base=-4 4 0 4,RotX=90,RotZ=90]}
980 %% \defFunction{parabole}(t){t}{t dup mul}{}
981 %% \defFunction{droite}(t){t}{t 2 add }{}
982 %% \axesIIID(0,0,0)(4,4,4)
983 %% \psProjection[object=chemin,
986 %% normal=0 1 0 1 0 0,
991 %% \psProjection[object=chemin,
994 %% normal=0 1 0 1 0 0,
999 %% \psProjection[object=courbeR2,
1000 %% range=-1 2,fillstyle=vlines,hatchwidth=0.5\pslinewidth,
1001 %% normal=0 1 0 1 0 0,
1002 %% function=parabole]
1003 %% \psProjection[object=courbeR2,
1006 %% normal=0 1 0 1 0 0,
1007 %% function=parabole]
1008 %% \psProjection[object=courbeR2,
1011 %% normal=0 1 0 1 0 0,
1013 %% \psPoint(0,0,4.15){Z1}
1014 %% \uput*[60](Z1){$z=y^2$}
1015 %% \rput(0,-6.5){\psframebox[linecolor=yellow!50]{\texttt{$\backslash${}defFunction\{parabole\}(t)\{t\}\{t dup mul\}\{\}}}}
1018 %% \begin{minipage}{6cm}
1021 %% \psProjection[object=courbeR2,
1024 %% normal=0 1 0 1 0 0,
1025 %% function=parabole]
1032 Some information about rings and parallelepipeds is available in the documents:
1034 \item \texttt{doc-grille-parallelepiped.tex(.pdf)};
1035 \item \texttt{doc-anneau.tex(.pdf).}
1037 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%