doc-en/.svn/text-base/par-solidespredefinis-en.tex.svn-base

   1 \section {The predefined solids and their parameters}
   2
   3 The basic command is:~
   4 \texttt{\Lcs{psSolid}[object=\textsl{name}]$(x, y ,z)$} which allows us to translate the chosen object to the point with the coordinates $(x, y,
   5 z)$.
   6
   7 The available predefined names for the objects are:
   8 \begin{sloppypar}
   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.}
  14 \end{sloppypar}
  15
  16
  17 The following table gives an example of every one of the above named solids with their specified parameters:
  18
  19 \begin{center}
  20 \begin{tabular}{>{\bfseries\sffamily\color{blue}}lcm{4cm}m{5cm}}
  21   \hline
  22 \toptableau
  23 \\\hline
  24  \Index{Point}&
  25     \begin{tabular}{c}
  26     \texttt{[args=1 1 0]}\\
  27      coordinates
  28     \end{tabular}
  29     &
  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]%
  33 \axesIIID(1.5,1.5,1)
  34 \end{pspicture}
  35  &
  36  \begin{minipage}{5cm}
  37  \begin{verbatim}
  38 \psSolid[object=point,
  39 args=1 1 0]%
  40 \end{verbatim}
  41 \end{minipage}
  42 \\\hline
  43  \Index{Line}&
  44     \begin{tabular}{c}
  45     \texttt{[args=0 -1 0 1 2 2]}\\
  46      coordinates of the\\
  47      end points
  48     \end{tabular}
  49     &
  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]
  53 \axesIIID(1.5,1.5,1)
  54 \end{pspicture}
  55  &
  56 \begin{minipage}{5cm}
  57 \begin{verbatim}
  58 \psSolid[object=line,
  59 args=0 -1 0 1 2 2]
  60 \end{verbatim}
  61 \end{minipage}
  62 \\\hline
  63  \Index{Vector}&
  64     \begin{tabular}{c}
  65     \texttt{[args=1 2 2]}\\
  66      components of\\
  67      the vector
  68     \end{tabular}
  69     &
  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]
  73 \axesIIID(1.5,1.5,1)
  74 \end{pspicture}
  75  &
  76 \begin{minipage}{5cm}
  77 \begin{verbatim}
  78 \psSolid[object=vecteur,
  79 args=1 2 2]
  80 \end{verbatim}
  81 \end{minipage}
  82 \\\hline
  83  \Index{Plane}&
  84     \begin{tabular}{c}
  85     \texttt{[base=-x x -y y]}\\
  86      range of plane\\
  87      \texttt{args={[0 0 1 0]}}\\
  88      equation of plane
  89     \end{tabular}
  90     &
  91  \begin{pspicture}(-2,-2)(2,2)
  92 \psset{lightsrc=10 5 20,viewpoint=50 20 30 rtp2xyz}
  93 \psSolid[object=plan,
  94    definition=equation,
  95    args={[0 0 1 0]},
  96    base=-1 1 -1.5 1.5]
  97 \axesIIID(1.5,1.5,1)
  98 \end{pspicture}
  99  &
 100 \begin{minipage}{5cm}
 101 \begin{verbatim}
 102 \psSolid[object=plan,
 103 definition=equation,
 104 args={[0 0 1 0]},
 105 base=-1 1 -1.5 1.5]
 106 \end{verbatim}
 107 \end{minipage}
 108 \\\hline
 109
 110 \end{tabular}
 111 \end{center}
 112
 113 \begin{center}
 114 \begin{tabular}{>{\bfseries\sffamily\color{blue}}lcm{4cm}m{5cm}}
 115   \hline
 116 \toptableau
 117 \\\hline
 118  \Index{Cube}& \begin{tabular}{c}
 119     \texttt{[a=4]}\\
 120      edge's length
 121     \end{tabular}
 122     &
 123  \begin{pspicture}(-2,-2)(2,2)
 124 \psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
 125  \psset{Decran=60}
 126  \psSolid[
 127  object=cube,a=2,action=draw*,fillcolor=magenta!20]%
 128  \axesIIID(1,1,1)(1.5,1.5,1.5)
 129  \end{pspicture}
 130  &
 131  \begin{minipage}{5cm}
 132  \begin{verbatim}
 133 \psSolid[
 134    object=cube,
 135    a=2,
 136    action=draw*,
 137    fillcolor=magenta!20]
 138  \end{verbatim}
 139  \end{minipage}
 140 \\\hline
 141  \Index{Cylinder}&
 142     \begin{tabular}{c}
 143      \texttt{[h=6,r=2]}\\
 144      height and radius\\
 145      grid:\\
 146      \texttt{[ngrid=n1 n2]}
 147      \end{tabular}
 148      &
 149  \begin{pspicture}(-2,-2.5)(2,3)
 150 \psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
 151  \psset{Decran=30}
 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)
 154  \end{pspicture}
 155  &
 156  \begin{minipage}{5cm}
 157  \begin{verbatim}
 158 \psSolid[
 159   object=cylindre,
 160   h=5,r=2,
 161   fillcolor=white,
 162   ngrid=4 32]
 163   (0,0,-3)
 164  \end{verbatim}
 165  \end{minipage}
 166 \\\hline
 167  \Index{Hollow Cylinder}&
 168     \begin{tabular}{c}
 169      \texttt{[h=6,r=2]}\\
 170      height and radius\\
 171      grid:\\
 172      \texttt{[ngrid=n1 n2]}
 173      \end{tabular}
 174      &
 175  \begin{pspicture}(-2,-2.5)(2,3)
 176 \psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
 177  \psset{Decran=30}
 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)
 180  \end{pspicture}
 181  &
 182  \begin{minipage}{5cm}
 183  \begin{verbatim}
 184 \psSolid[
 185    object=cylindrecreux,
 186    h=5,r=2,
 187    fillcolor=white,
 188    mode=4,
 189    incolor=green!50]
 190    (0,0,-3)
 191  \end{verbatim}
 192  \end{minipage}
 193  \\\hline
 194 \end{tabular}
 195 \end{center}
 196
 197 \begin{center}
 198 \begin{tabular}{>{\bfseries\sffamily\color{blue}}lcm{4cm}m{5cm}}
 199   \hline
 200 \toptableau
 201 \\\hline
 202  \Index{Cone}&
 203      \begin{tabular}{c}
 204      \texttt{[h=6,r=2]}\\
 205      height and radius\\
 206      grid:\\
 207      \texttt{[ngrid=n1 n2]}
 208      \end{tabular}
 209      &
 210  \begin{pspicture}(-2,-1)(2,4)
 211 \psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
 212  \psset{Decran=30}
 213  \psSolid[object=cone,h=5,r=2,fillcolor=cyan,mode=4]%
 214  \axesIIID(2,2,5)(2.5,2.5,6)
 215  \end{pspicture}
 216  &
 217  \begin{minipage}{5cm}
 218  \begin{verbatim}
 219  \psSolid[
 220     object=cone,
 221     h=5,r=2,
 222     fillcolor=cyan,
 223     mode=4]%
 224  \end{verbatim}
 225  \end{minipage}
 226 \\\hline
 227  \Index{Hollow Cone}&
 228      \begin{tabular}{c}
 229      \texttt{[h=6,r=2]}\\
 230      height and radius\\
 231      grid:\\
 232      \texttt{[ngrid=n1 n2]}
 233      \end{tabular}
 234      &
 235  \begin{pspicture}(-2,-1)(2,4)
 236 \psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
 237  \psset{Decran=30}
 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)
 240  \end{pspicture}
 241  &
 242  \begin{minipage}{5cm}
 243  \begin{verbatim}
 244  \psSolid[
 245     object=conecreux,
 246     h=5,r=2,
 247     RotY=-60,
 248     fillcolor=white,
 249     incolor=green!50,
 250     mode=4]%
 251  \end{verbatim}
 252  \end{minipage}
 253  \\\hline
 254  \Index{Truncated Cone}&
 255      \begin{tabular}{c}
 256      \texttt{[h=6,r0=4,r1=1.5]}\\
 257      height and radii\\
 258      grid:\\
 259      \texttt{[ngrid=n1 n2]}
 260      \end{tabular}
 261      &
 262  \begin{pspicture}(-2,-1)(2,4)
 263 \psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
 264  \psset{Decran=30}
 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)
 267  \end{pspicture}
 268  &
 269  \begin{minipage}{5cm}
 270  \begin{verbatim}
 271  \psSolid[
 272     object=tronccone,
 273     r0=2,r1=1.5,h=5,
 274     fillcolor=cyan,
 275     mode=4]%
 276  \end{verbatim}
 277  \end{minipage}
 278 \\\hline
 279      \begin{tabular}{c}
 280      Truncated \\
 281      Hollow Cone
 282      \end{tabular}
 283      &
 284      \begin{tabular}{c}
 285      \texttt{[h=6,r0=4,r1=1.5]}\\
 286      height and radii\\
 287      grid:\\
 288      \texttt{[ngrid=n1 n2]}
 289      \end{tabular}
 290      &
 291  \begin{pspicture}(-2,-1)(2,4)
 292 \psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
 293  \psset{Decran=30}
 294  \psSolid[object=troncconecreux,r0=2,r1=1,h=5,fillcolor=white,mode=4]%
 295  \axesIIID(2,2,5)(2.5,2.5,6)
 296  \end{pspicture}
 297  &
 298  \begin{minipage}{5cm}
 299  \begin{verbatim}
 300 \psSolid[
 301    object=troncconecreux,
 302    r0=2,r1=1,h=5,
 303    fillcolor=white,
 304    mode=4]%
 305  \end{verbatim}
 306  \end{minipage}
 307 \\\hline
 308 \end{tabular}
 309 \end{center}
 310
 311 %\newpage
 312
 313 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 314 \begin{center}
 315 %\begin{tabular}{>{\bfseries\sffamily\color{blue}}lcm{4cm}m{5cm}}
 316 \begin{tabular}{
 317    >{\bfseries\sffamily\color{blue}} l
 318    >{\centering} m{4cm} m{4cm} m{5cm}}
 319   \hline
 320 \toptableau
 321 \\\hline
 322  \Index{Sphere} &
 323      \begin{tabular}{c}
 324      \texttt{[r=2]}\\
 325      radius\\
 326      grid:\\
 327      \texttt{[ngrid=n1 n2]}
 328     \end{tabular}
 329      &
 330  \begin{pspicture}(-2,-2)(2,3)
 331 \psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
 332  \psset{Decran=30}
 333  \psSolid[object=sphere,r=3,fillcolor=red!25,ngrid=18 18,linewidth=0.2\pslinewidth]%
 334  \axesIIID(3,3,3)(4,4,4)
 335  \end{pspicture}
 336  &
 337  \begin{minipage}{5cm}
 338  \begin{verbatim}
 339  \psSolid[
 340     object=sphere,
 341     r=2,fillcolor=red!25,
 342     ngrid=18 18]%
 343  \end{verbatim}
 344  \end{minipage}
 345 \\\hline
 346      \begin{tabular}{c}
 347      Spherical \\
 348      zone
 349      \end{tabular} &
 350      \begin{tabular}{c}
 351      \texttt{[r=2]} \\
 352      radius\\
 353      \texttt{[phi=0,theta=90]} \\
 354      latitude for slicing\\
 355      the zone respectively \\
 356      from the bottom and top \\
 357     \end{tabular}
 358      &
 359 \begin{pspicture}(-2,-3)(5,3)
 360 \psset{unit=0.5cm}
 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)
 365 \end{pspicture}
 366  &
 367  \begin{minipage}{5cm}
 368  \begin{verbatim}
 369 \psSolid[
 370    object=calottesphere,
 371    r=3,ngrid=16 18,
 372    theta=45,phi=-30,
 373    hollow,RotY=-80]%
 374  \end{verbatim}
 375  \end{minipage}
 376 \\\hline
 377  \Index{Torus} &
 378      \begin{tabular}{c}
 379      \texttt{[r0=4,r1=1.5]} \\
 380      inner radius\\
 381      mean radius\\
 382      grid:\\
 383      \texttt{[ngrid=n1 n2]}
 384      \end{tabular}
 385      &
 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)
 391  \end{pspicture}
 392  &
 393  \begin{minipage}{5cm}
 394  \begin{verbatim}
 395  \psSolid[
 396     r1=2.5,r0=1.5,
 397     object=tore,
 398     ngrid=18 36,
 399     fillcolor=green!30,
 400     action=draw*]%
 401  \end{verbatim}
 402  \end{minipage}
 403 \\\hline
 404      \begin{tabular}{c}
 405      Cylindric \\
 406      Ring
 407      \end{tabular}
 408       &
 409      \begin{tabular}{c}
 410      \texttt{[R=4,r=3}\\
 411      inner and outer radius\\
 412      \texttt{h=6,section=...]}\\
 413      height\\
 414      cross \\
 415      section
 416      \end{tabular}
 417      &
 418  \begin{pspicture}(-2,-2)(2,2.35)
 419 %\psset{unit=0.44cm}
 420 \psset{lightsrc=42 24 13,viewpoint=50 30 15 rtp2xyz}
 421  \psset{Decran=30}
 422 \psSolid[object=anneau,fillcolor=yellow,h=1.5,R=4,r=3]%
 423  \axesIIID(4,4,0)(5,5,4)
 424  \end{pspicture}
 425  &
 426  \begin{minipage}{5cm}
 427  \begin{verbatim}
 428  \psSolid[
 429     object=anneau,
 430     fillcolor=yellow,
 431     h=1.5,R=4,r=3]%
 432  \end{verbatim}
 433  \end{minipage}
 434 \\\hline
 435 \end{tabular}
 436 \end{center}
 437
 438
 439 \begin{center}
 440 %\begin{tabular}{>{\bfseries\sffamily\color{blue}}lcm{4cm}m{6cm}}
 441 \begin{tabular}{
 442    >{\bfseries\sffamily\color{blue}} l
 443    >{\centering} m{4cm} m{4cm} m{5cm}}
 444   \hline
 445 \toptableau
 446 \\\hline
 447  \Index{Tetrahedron}&
 448      \begin{tabular}{c}
 449      \texttt{[r=2]}\\
 450      radius of the\\
 451      circumscribed sphere
 452      \end{tabular}
 453      &
 454  \begin{pspicture}(-2,-2)(2,2)
 455 \psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
 456  \psset{Decran=30}
 457  \psSolid[object=tetrahedron,r=3,linecolor=blue,action=draw]%
 458  \end{pspicture}
 459  &
 460  \begin{minipage}{5cm}
 461  \begin{verbatim}
 462 \psSolid[
 463    object=tetrahedron,
 464    r=3,
 465    linecolor=blue,
 466    action=draw]%
 467  \end{verbatim}
 468  \end{minipage}
 469 \\\hline
 470 \Index{Octahedron} &
 471      \begin{tabular}{c}
 472      \texttt{[a=2]}\\
 473      radius of the\\
 474      circumscribed sphere
 475      \end{tabular}
 476      &
 477  \begin{pspicture}(-2,-1.85)(2,2.85)
 478 \psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
 479  \psset{Decran=30}
 480  \psSolid[object=octahedron,a=3,linecolor=blue,fillcolor=Turquoise]%
 481  \axesIIID(3,3,3)(4,4,4)
 482  \end{pspicture}
 483  &
 484  \begin{minipage}{5cm}
 485  \begin{verbatim}
 486  \psSolid[
 487     object=octahedron,
 488     a=3,
 489     linecolor=blue,
 490     fillcolor=Turquoise]%
 491  \end{verbatim}
 492  \end{minipage}
 493 \\\hline
 494  \Index{Dodecahedron} &
 495      \begin{tabular}{c}
 496      \texttt{[a=2]}\\
 497      radius of the\\
 498      circumscribed sphere
 499      \end{tabular}
 500      &
 501  \begin{pspicture}(-2,-1.85)(2,1.85)
 502 \psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
 503  \psset{Decran=30}
 504  \psSolid[object=dodecahedron,a=2.5,RotZ=90,action=draw*,fillcolor=OliveGreen]%
 505  \end{pspicture}
 506  &
 507  \begin{minipage}{5cm}
 508  \begin{verbatim}
 509  \psSolid[
 510     object=dodecahedron,
 511     a=2.5,RotZ=90,
 512     action=draw*,
 513     fillcolor=OliveGreen]%
 514  \end{verbatim}
 515  \end{minipage}
 516 \\ \hline
 517 \Index{Icosahedron} &
 518      \begin{tabular}{c}
 519      \texttt{[a=2]}\\
 520      radius of the\\
 521      circumscribed sphere
 522      \end{tabular}
 523      &
 524  \begin{pspicture}(-2,-1.85)(2,2.85)
 525 \psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
 526  \psset{Decran=30}
 527  \psSolid[object=icosahedron,a=3,action=draw*,fillcolor=green!50]%
 528  \axesIIID(3,3,3)(4,4,4)
 529  \end{pspicture}
 530  &
 531  \begin{minipage}{5cm}
 532  \begin{verbatim}
 533 \psSolid[
 534    object=icosahedron,
 535    a=3,
 536    action=draw*,
 537    fillcolor=green!50]%
 538  \end{verbatim}
 539  \end{minipage}
 540 \\\hline
 541      \Index{Prism}
 542       &
 543      \begin{tabular}{c}
 544      \texttt{[axe=0 0 1]}\\
 545      direction of the axis\\
 546      \texttt{[base=}\\
 547      \texttt{-1 -1 1 -1 0 1]}\\
 548      coordinates of\\
 549      the vertices\\
 550      of the base\\
 551      \texttt{[h=6]}\\
 552      height
 553      \end{tabular}
 554      &
 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)
 561  \end{pspicture}
 562  &
 563  \begin{minipage}{5cm}
 564  \begin{verbatim}
 565 \psSolid[
 566    object=prisme,
 567    action=draw*,
 568    linecolor=red,
 569    h=4]%
 570  \end{verbatim}
 571  \end{minipage}
 572  \\\hline
 573 \end{tabular}
 574 \end{center}
 575
 576 %\newpage
 577 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 578 \begin{center}
 579 %\psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
 580 %\begin{tabular}{>{\bfseries\sffamily\color{blue}}lcm{4cm}m{6cm}}
 581 \begin{tabular}{
 582    >{\bfseries\sffamily\color{blue}} l
 583    >{\centering} m{4cm} m{4cm} m{5cm}}
 584   \hline
 585 \toptableau
 586 \\\hline
 587      \Index{Grid}
 588       &
 589      \begin{tabular}{c}
 590      \texttt{[base=-X +X -Y +Y]}
 591      \end{tabular}
 592      &
 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)
 598  \end{pspicture}
 599  &
 600  \begin{minipage}{5cm}
 601  \begin{verbatim}
 602 \psSolid[
 603    object=grille,
 604    base=-5 5 -3 3]%
 605  \end{verbatim}
 606  \end{minipage}
 607 \\\hline
 608 %
 609    \Index{Cuboid}
 610       &
 611      \begin{tabular}{c}
 612      \texttt{[a=4,b=3,c=2]}\\
 613      edge lenghts\\
 614      with center in $O$
 615      \end{tabular}
 616      &
 617  \begin{pspicture}(-1.5,-2)(2,3)
 618  \psset{lightsrc=10 20 30,viewpoint=50 20 30 rtp2xyz}
 619  \psset{Decran=30}
 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)
 625  \end{pspicture}
 626  &
 627  \begin{minipage}{5cm}
 628  \begin{verbatim}
 629 \psSolid[
 630    object=parallelepiped,%
 631    a=5,b=6,c=2,
 632    fillcolor=yellow]%
 633    (0,0,c 2 div)
 634  \end{verbatim}
 635  \end{minipage}
 636 \\\hline
 637 %
 638    \Index{Face}
 639       &
 640      \begin{tabular}{l}
 641      \texttt{[base=x0 y0 x1 y1}\\
 642      \texttt{~     x2 y2 etc.]}\\
 643      the coordinates \\
 644      of the vertices
 645      \end{tabular}
 646      &
 647 \begin{pspicture}(-2,-2)(3,2)
 648 \psset{unit=0.4cm}
 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,
 652       incolor=blue,
 653       base=0 0 3 0 1.5 3
 654       ](0,1,0)
 655 \psSolid[object=face,fillcolor=yellow,
 656       incolor=blue,
 657       base=0 0 3 0 1.5 3,
 658       RotX=180](0,-1,0)
 659 \axesIIID(0,0,0)(6,6,3)
 660 \end{pspicture}
 661  &
 662  \begin{minipage}{5cm}
 663  \begin{verbatim}
 664 \psSolid[
 665    object=face,
 666    fillcolor=yellow,
 667    incolor=blue,
 668    base=0 0 3 0 1.5 3
 669    ](0,1,0)
 670 \psSolid[
 671    object=face,
 672    fillcolor=yellow,
 673    incolor=blue,
 674    base=0 0 3 0 1.5 3,
 675    RotX=180](0,-1,0)
 676  \end{verbatim}
 677  \end{minipage}
 678 \\\hline
 679 %
 680    \Index{Strip}
 681       &
 682      \begin{tabular}{l}
 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\\
 690      of the strip
 691      \end{tabular}
 692      &
 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,
 698       num=0 1 2 3,
 699       show=0 1 2 3,
 700       ngrid=3]%
 701 \axesIIID(0,2,0)(6,6,6)
 702 \end{pspicture}
 703  &
 704  \begin{minipage}{5cm}
 705  \begin{verbatim}
 706 \psSolid[
 707    object=ruban,h=3,
 708    fillcolor=red!50,
 709    base=0 0 2 2 4 0 6 2,
 710    num=0 1 2 3,
 711    show=0 1 2 3,
 712    ngrid=3])
 713  \end{verbatim}
 714  \end{minipage}
 715 \\\hline
 716 \end{tabular}
 717 \end{center}
 718
 719 %\newpage
 720
 721 %\begin{center}
 722 %\psset{lightsrc=10 20 30,SphericalCoor,viewpoint=50 20 30}
 723 %%\begin{tabular}{>{\bfseries\sffamily\color{blue}}lcm{4cm}m{6cm}}
 724 %\begin{tabular}{
 725 %   >{\bfseries\sffamily\color{blue}} l
 726 %   >{\centering} m{4cm} m{4cm} m{5cm}}
 727 %  \hline
 728 %\toptableau
 729 %%    chemin
 730 %%       &
 731 %%      \begin{tabular}{l}
 732 %%      dessine un chemin\\
 733 %%      d\'{e}fini en postscript\\
 734 %%      sur un plan
 735 %%      \end{tabular}
 736 %%      &
 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,
 743 %%             normal=1 1 2 180,
 744 %%             path=newpath
 745 %%                 -4 -4 smoveto
 746 %%                 -4 4 slineto
 747 %%                 4 4 slineto
 748 %%                 4 -4 slineto
 749 %%                 closepath
 750 %%             ](1,1,2)
 751 %% \psProjection[object=chemin,
 752 %%       linewidth=.02,
 753 %%       normal=1 1 2 180,
 754 %%       path=newpath
 755 %%           -4 1 4
 756 %%           {-4 exch smoveto
 757 %%            8 0 srlineto} for
 758 %%            -4 1 4
 759 %%           {-4 smoveto
 760 %%            0 8 srlineto} for
 761 %%             ](1,1,2)
 762 %% \psProjection[object=chemin,fillstyle=hlines,hatchcolor=yellow,
 763 %%             linecolor=red,
 764 %%             normal=1 1 2 180,
 765 %%             path=newpath
 766 %%             2 0 moveto
 767 %%             0 2 360 {
 768 %%                 /x exch def
 769 %%                 x cos 2 mul
 770 %%              x sin 2 mul
 771 %%                 slineto
 772 %%          } for
 773 %%             ](1,1,2)
 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,
 779 %%       linewidth=.1,
 780 %%       linecolor=green,
 781 %%       normal=1 1 2 180,
 782 %%       path=
 783 %%          newpath
 784 %%             0 0 smoveto
 785 %%             1 0 slineto](1,1,2)
 786 %% \psProjection[object=chemin,
 787 %%       linewidth=.1,
 788 %%       linecolor=blue,
 789 %%       normal=1 1 2 180,
 790 %%       path=
 791 %%          newpath
 792 %%             0 0 smoveto
 793 %%             0 1 slineto](1,1,2)
 794 %% \axesIIID(4,4,2)(5,5,6)
 795 %% \end{pspicture}
 796 %%  &
 797 %%  \begin{minipage}{6cm}
 798 %%  \begin{verbatim}
 799 %%     \psProjection[object=chemin,
 800 %%     fillstyle=hlines,
 801 %%     hatchcolor=yellow,
 802 %%     linecolor=red,
 803 %%     normal=1 1 2 180,
 804 %%     path=newpath
 805 %%     2 0 smoveto
 806 %%     0 2 360 {
 807 %%      /x exch def
 808 %%      x cos 2 mul
 809 %%      x sin 2 mul
 810 %%      slineto
 811 %%     } for
 812 %%     ](1,1,2)
 813 %%  \end{verbatim}
 814 %%  \end{minipage}
 815 %\end{tabular}
 816 %\end{center}
 817
 818 %\newpage
 819 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 820 \begin{center}
 821 %\begin{tabular}{>{\bfseries\sffamily\color{blue}}lcm{4cm}m{6cm}}
 822 \begin{tabular}{
 823    >{\bfseries\sffamily\color{blue}} l
 824    >{\centering} m{4cm} m{4cm} m{5cm}}
 825   \hline
 826 \toptableau
 827 \\\hline
 828    \Index{Surface}
 829       &
 830      \begin{tabular}{l}
 831      see the related \\
 832      paragraph in the \\
 833      documentation
 834      \end{tabular}
 835      &
 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}
 840 \end{pspicture}
 841  &
 842  \begin{minipage}{5cm}
 843  \begin{verbatim}
 844 \psSurface[ngrid=.25 .25,
 845   incolor=white,axesboxed]
 846   (-4,-4)(4,4){%
 847   x dup mul y dup mul 3 mul
 848   sub x mul 32 div}
 849  \end{verbatim}
 850  \end{minipage}
 851 \\\hline
 852 %
 853    \Index{New}
 854       &
 855      \begin{tabular}{l}
 856      solid defined\\
 857      by the coordinates \\
 858      of the vertices\\
 859      and the vertices\\
 860      of each face
 861      \end{tabular}
 862      &
 863
 864 \begin{pspicture}(-2,-2)(2,4)
 865 \psset{unit=0.4cm}
 866 \psset{viewpoint=50 -20 30 rtp2xyz,Decran=50}
 867 \psSolid[object=new,
 868          action=draw,
 869          sommets=
 870          2  4  3
 871         -2  4  3
 872         -2 -4  3
 873          2 -4  3
 874          2  4  0
 875         -2  4  0
 876         -2 -4  0
 877          2 -4  0
 878          0  4  5
 879          0 -4  5,
 880     faces={
 881         [0 1 2 3]
 882         [7 6 5 4]
 883         [0 3 7 4]
 884         [3 9 2]
 885         [1 8 0]
 886         [8 9 3 0]
 887         [9 8 1 2]
 888         [6 7 3 2]
 889         [2 1 5 6]},
 890         num=all,
 891       show=all]%
 892 \axesIIID(0,0,0)(5,5,7)
 893 \end{pspicture}
 894  &
 895  \begin{minipage}{5cm}
 896  \begin{verbatim}
 897  \psSolid[object=new,
 898          action=draw,
 899          sommets=
 900          2  4  3
 901         -2  4  3
 902         -2 -4  3
 903          2 -4  3
 904          2  4  0
 905         -2  4  0
 906         -2 -4  0
 907          2 -4  0
 908          0  4  5
 909          0 -4  5,
 910     faces={
 911         [0 1 2 3]
 912         [7 6 5 4]
 913         [0 3 7 4]
 914         [3 9 2]
 915         [1 8 0]
 916         [8 9 3 0]
 917         [9 8 1 2]
 918         [6 7 3 2]
 919         [2 1 5 6]}]%
 920  \end{verbatim}
 921  \end{minipage}
 922 \\\hline
 923 %
 924    \Index{Curve}
 925       &
 926      \begin{tabular}{l}
 927      curve of a function\\
 928      $\mathbb{R} \rightarrow \mathbb{R}^3$\\
 929      defined by its\\
 930      paramterised equations\\
 931      \end{tabular}
 932      &
 933
 934 \begin{pspicture}(-2,-1)(1.75,2.7)
 935 \psset{unit=0.35cm}
 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,
 942         range=0 6,
 943         linecolor=blue,linewidth=0.1,
 944         resolution=360,
 945         function=helice]%
 946 \end{pspicture}
 947  &
 948  \begin{minipage}{5cm}
 949 % \footnotesize
 950  \begin{verbatim}
 951 \defFunction[algebraic]%
 952    {helice}(t)
 953    {3*cos(4*t)}{3*sin(4*t)}{t}
 954 \psSolid[object=courbe,r=0,
 955    range=0 6,
 956    linecolor=blue,
 957    linewidth=0.1,
 958    resolution=360,
 959    function=helice]%
 960  \end{verbatim}
 961  \end{minipage}
 962 \\\hline
 963 %%    courbeR2
 964 %%       &
 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\\
 970 %%      \end{tabular}
 971 %%      &
 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,
 984 %%       linewidth=.1,
 985 %%       linecolor=blue,
 986 %%       normal=0 1 0 1 0 0,
 987 %%       path=
 988 %%          newpath
 989 %%             0 0 moveto
 990 %%             1 0 lineto]
 991 %% \psProjection[object=chemin,
 992 %%       linewidth=.1,
 993 %%       linecolor=red,
 994 %%       normal=0 1 0 1 0 0,
 995 %%       path=
 996 %%          newpath
 997 %%             0 0 moveto
 998 %%             0 1 lineto]
 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,
1004 %%    range=-2 2,
1005 %%    linecolor=green,
1006 %%    normal=0 1 0 1 0 0,
1007 %%    function=parabole]
1008 %% \psProjection[object=courbeR2,
1009 %%    range=-2 2 ,
1010 %%    linecolor=red,
1011 %%    normal=0 1 0 1 0 0,
1012 %%    function=droite]
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\}\{\}}}}
1016 %% \end{pspicture}
1017 %%  &
1018 %%  \begin{minipage}{6cm}
1019 %%  \footnotesize
1020 %%  \begin{verbatim}
1021 %% \psProjection[object=courbeR2,
1022 %%    range=-2 2,
1023 %%    linecolor=green,
1024 %%    normal=0 1 0 1 0 0,
1025 %%    function=parabole]
1026 %%  \end{verbatim}
1027 %%  \end{minipage}
1028 %% \\\hline
1029 \end{tabular}
1030 \end{center}
1031
1032 Some information about rings and parallelepipeds is available in the documents:
1033 \begin{itemize}
1034   \item \texttt{doc-grille-parallelepiped.tex(.pdf)};
1035   \item \texttt{doc-anneau.tex(.pdf).}
1036 \end{itemize}
1037 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1038 %\newpage
1039
1040 \endinput