doc-en/par-fusionjps-en.tex

   1 \def\grille{% quadrillage du plan Oxy
   2     \psPoint(-5,-5,0){S1}
   3     \psPoint(-5,5,0){S2}
   4     \psPoint(5,5,0){S3}
   5     \psPoint(5,-5,0){S4}
   6 \pspolygon*[linecolor=gray!20](S1)(S2)(S3)(S4)
   7 \multido{\ix=-5+1}{11}{%
   8     \psPoint(\ix\space,-5,0){A}
   9     \psPoint(\ix\space,5,0){B}
  10     \psline(A)(B)}
  11 \multido{\iy=-5+1}{11}{%
  12     \psPoint(-5,\iy\space,0){A}
  13     \psPoint(5,\iy\space,0){B}
  14     \psline(A)(B)}
  15     \psPoint(0,0,0){O}
  16     \psPoint(5,0,0){X}
  17     \psPoint(0,5,0){Y}
  18     \psPoint(0,0,8){Z}
  19     \psline[arrowsize=0.3,arrowinset=0.2,linecolor=blue]{->}(O)(X)
  20     \psline[arrowsize=0.3,arrowinset=0.2,linecolor=blue]{->}(O)(Y)
  21     \psline[arrowsize=0.3,arrowinset=0.2,linecolor=blue]{->}(O)(Z)
  22     \uput[r](X){\textcolor{blue}{$x$}}\uput[u](Y){\textcolor{blue}{$y$}}%
  23     \uput[r](Z){\textcolor{blue}{$z$}}\uput[u](O){\textcolor{blue}{$O$}}}
  24
  25
  26 \section{Fusing with \textit{jps code}}
  27
  28 We can also \Index{fuse solids} by passing the code directly using
  29 \textit{jps code}. The calculation of the hidden parts is carried
  30 out by the PostScript routines of the \texttt{solides.pro} file,
  31 but the lines of code are ``encapsulated'' within a
  32 \texttt{pspicture} environment thanks to the command
  33 \verb+\codejps{ps code}+.
  34
  35 \subsection{Using \textit{jps code}}
  36
  37 \subsubsection{The choice of object}
  38
  39 \begin{compactitem}
  40   \item \texttt{[section] n newanneau}: choice of a cylindrical ring defined by
  41   the coordinates of the vertices of its intersection with the plane $Oyz$.
  42   \item \texttt{2  1.5  6 [4  16]  newcylindre}: choice of a vertical cylinder
  43 with the following parameters:
  44   \begin{compactitem}
  45     \item \texttt{z0=2}: the position of the base centre on the axis $Oz$;
  46     \item \texttt{radius=1.5}: radius of the cylinder;
  47     \item \texttt{z1=6}: the position of the top centre on the
  48     axis $Oz$;
  49     \item \texttt{[4 16]}: the cylinder is sliced horizontally into 4 pieces and
  50 vertically into 16 sectors.
  51   \end{compactitem}
  52   \end{compactitem}
  53
  54 \subsubsection{The transformations}
  55
  56 \begin{compactitem}
  57   \item \texttt{\{-1  2  5  translatepoint3d\} solidtransform}: the object
  58 previously chosen is translated to the point with the
  59 coordinates $(x=-1,y=2,z=5)$.
  60   \item \texttt{\{90  0  45  rotateOpoint3d\} solidtransform}: the object
  61 previously chosen is rotated around the axes $(Ox,Oy,Oz)$, in
  62 this order: rotation of 90$^\mathsf{o}$ about $(Ox)$ followed
  63 by a rotation of 45$^\mathsf{o}$ about $(Oz)$.
  64 \end{compactitem}
  65
  66 \subsubsection{The choice of object colour}
  67
  68 \begin{compactitem}
  69   \item dup (yellow) outputcolors: a yellow object illuminated in
  70   white light.
  71 \end{compactitem}
  72
  73 \subsubsection{Fusing objects}
  74
  75 \begin{compactitem}
  76   \item The \Index{fusion} is finally made with the instruction \texttt{solidfuz}.
  77 \end{compactitem}
  78
  79 \subsubsection{Designing objects}
  80
  81 \begin{compactitem}
  82   \item There are three drawing options:
  83   \begin{compactitem}
  84     \item \texttt{drawsolid}: only draw edges; hidden edges are drawn dashed;
  85     \item \texttt{drawsolid*}: draw and fill solids in their coded order (not
  86     a very interesting option at first glance); hidden edges are drawn dashed;
  87     \item \texttt{drawsolid**}: draw and fill solids with the
  88     painting algorithm; only those parts seen by the observer are
  89     drawn.
  90   \end{compactitem}
  91 \end{compactitem}
  92 \begin{center}
  93 \psset{lightsrc=50 -50 50,viewpoint=40 16 32 rtp2xyz,Decran=40}
  94 \psset{unit=0.4}
  95 \begin{minipage}{0.3\linewidth}
  96 \begin{pspicture}(-6,-5)(6,7)
  97 \psframe*[linecolor=gray!40](-6,-5)(6,7)
  98 \codejps{
  99 % solide 1
 100  /tour {
 101     -6 1.5 6 [4 16] newcylindre
 102     dup (jaune) outputcolors
 103     } def
 104 % solide 2
 105  /anneau {
 106     [4 -1 4 1 3 1 3 -1] 24 newanneau
 107    {0 0 -1 translatepoint3d} solidtransform
 108     dup (orange) outputcolors
 109     } def
 110 % fusion
 111     tour anneau solidfuz
 112     drawsolid}
 113 \end{pspicture}
 114 \end{minipage}
 115 \hfill
 116 \begin{minipage}{0.3\linewidth}
 117 \begin{pspicture}(-6,-5)(6,7)
 118 \psframe*[linecolor=gray!40](-6,-5)(6,7)
 119 \codejps{
 120 % solide 1
 121  /tour {
 122     -6 1.5 6 [4 16] newcylindre
 123     dup (jaune) outputcolors
 124     } def
 125 % solide 2
 126  /anneau {
 127     [4 -1 4 1 3 1 3 -1] 24 newanneau
 128    {0 0 -1 translatepoint3d} solidtransform
 129     dup (orange) outputcolors
 130     } def
 131 % fusion
 132     tour anneau solidfuz
 133     drawsolid*}
 134 \end{pspicture}
 135 \end{minipage}
 136 \hfill
 137 \begin{minipage}{0.3\linewidth}
 138 \begin{pspicture}(-6,-5)(6,7)
 139 \psframe*[linecolor=gray!40](-6,-5)(6,7)
 140 \codejps{
 141 % solide 1
 142  /tour {
 143     -6 1.5 6 [4 16] newcylindre
 144     dup (jaune) outputcolors
 145     } def
 146 % solide 2
 147  /anneau {
 148     [4 -1 4 1 3 1 3 -1] 24 newanneau
 149    {0 0 -1 translatepoint3d} solidtransform
 150     dup (orange) outputcolors
 151     } def
 152 % fusion
 153     tour anneau solidfuz
 154     drawsolid**}
 155 \psPoint(0,0,8){Z}
 156 \psPoint(0,0,6){Z'}
 157 \psline[arrowsize=0.3,arrowinset=0.2]{->}(Z')(Z)
 158 \uput[u](Z){$z$}
 159 \end{pspicture}
 160 \end{minipage}
 161 \end{center}
 162
 163 \begin{verbatim}
 164 \psset{lightsrc=50 -50 50,viewpoint=50 20 50 rtp2xyz,Decran=50}
 165 \begin{pspicture}(-6,-2)(6,8)
 166 \psframe(-6,-2)(6,8)
 167 \codejps{
 168 % solide 1
 169     /tour{
 170       -6 1.5 6 [4 16] newcylindre
 171       dup (jaune) outputcolors
 172     } def
 173 % solide 2
 174     /anneau{
 175       [4 -1 4 1 3 1 3 -1] 24 newanneau
 176       {0 0 -1 translatepoint3d} solidtransform
 177       dup (orange) outputcolors
 178     } def
 179 % fusion
 180     tour anneau solidfuz
 181     drawsolid**}
 182 \end{pspicture}
 183 \end{verbatim}
 184
 185 \newpage
 186
 187 \subsection{A \Index{chloride ion}}
 188 \begin{LTXexample}[width=6cm]
 189 \begin{pspicture}(-3,-4)(3,4)
 190 \psset{lightsrc=100 -50 -10,lightintensity=3,viewpoint=200 20 10 rtp2xyz,Decran=20}
 191 {\psset{linewidth=0.5\pslinewidth}
 192 \codejps{/Cl {9.02  [18 16] newsphere
 193 {-90 0 0 rotateOpoint3d} solidtransform
 194  dup (Green) outputcolors} def
 195 /Cl1 { Cl {10.25 10.25 10.25 translatepoint3d} solidtransform } def
 196 /Cl2 { Cl {10.25 -10.25 10.25 translatepoint3d} solidtransform } def
 197 /Cl3 { Cl {-10.25 -10.25 10.25 translatepoint3d} solidtransform } def
 198 /Cl4 { Cl {-10.25 10.25 10.25 translatepoint3d} solidtransform } def
 199 /Cl5 { Cl {10.25 10.25 -10.25 translatepoint3d} solidtransform } def
 200 /Cl6 { Cl {10.25 -10.25 -10.25 translatepoint3d} solidtransform } def
 201 /Cl7 { Cl {-10.25 -10.25 -10.25 translatepoint3d} solidtransform } def
 202 /Cl8 { Cl {-10.25 10.25 -10.25 translatepoint3d} solidtransform } def
 203 /Cs {8.38  [18 16] newsphere
 204  dup (White) outputcolors} def
 205 /Cl12{ Cl1 Cl2 solidfuz} def
 206 /Cl123{ Cl12 Cl3 solidfuz} def
 207 /Cl1234{ Cl123 Cl4 solidfuz} def
 208 /Cl12345{ Cl1234 Cl5 solidfuz} def
 209 /Cl123456{ Cl12345 Cl6 solidfuz} def
 210 /Cl1234567{ Cl123456 Cl7 solidfuz} def
 211 /Cl12345678{ Cl1234567 Cl8 solidfuz} def
 212 /C_Cs { Cl12345678 Cs solidfuz} def
 213 C_Cs  drawsolid**}}%
 214 \psPoint(0,0,0){P}
 215 \psPoint(10.25,10.25,10.25){Cl1}
 216 \psPoint(10.25,-10.25,10.25){Cl2}
 217 \psPoint(-10.25,-10.25,10.25){Cl3}
 218 \psPoint(-10.25,10.25,10.25){Cl4}
 219 \psPoint(10.25,10.25,-10.25){Cl5}
 220 \psPoint(10.25,-10.25,-10.25){Cl6}
 221 \psPoint(-10.25,-10.25,-10.25){Cl7}
 222 \psPoint(-10.25,10.25,-10.25){Cl8}
 223 \pspolygon[linestyle=dashed](Cl1)(Cl2)(Cl3)(Cl4)
 224 \pspolygon[linestyle=dashed](Cl5)(Cl6)(Cl7)(Cl8)
 225 \psline[linestyle=dashed](Cl2)(Cl6)
 226 \psline[linestyle=dashed](Cl3)(Cl7)
 227 \psline[linestyle=dashed](Cl1)(Cl5)
 228 \psline[linestyle=dashed](Cl4)(Cl8)
 229 \pcline[offset=0.5]{<->}(Cl2)(Cl1)
 230 \aput{:U}{a}
 231 \pcline[offset=0.5]{<->}(Cl6)(Cl2)
 232 \aput{:U}{a}
 233 \end{pspicture}
 234 \end{LTXexample}
 235
 236 We define the chloride ion $\mathrm{Cl^-}$:
 237 \begin{verbatim}
 238 /Cl {9.02  [12 8] newsphere
 239  {-90 0 0 rotateOpoint3d} solidtransform
 240  dup (Green) outputcolors} def
 241 \end{verbatim}
 242 which we shift to each vertex of a cube:
 243 \begin{verbatim}
 244 /Cl1 { Cl {10.25 10.25 10.25 translatepoint3d} solidtransform } def
 245 /Cl2 { Cl {10.25 -10.25 10.25 translatepoint3d} solidtransform } def
 246 /Cl3 { Cl {-10.25 -10.25 10.25 translatepoint3d} solidtransform } def
 247 /Cl4 { Cl {-10.25 10.25 10.25 translatepoint3d} solidtransform } def
 248 /Cl5 { Cl {10.25 10.25 -10.25 translatepoint3d} solidtransform } def
 249 /Cl6 { Cl {10.25 -10.25 -10.25 translatepoint3d} solidtransform } def
 250 /Cl7 { Cl {-10.25 -10.25 -10.25 translatepoint3d} solidtransform } def
 251 /Cl8 { Cl {-10.25 10.25 -10.25 translatepoint3d} solidtransform } def
 252 \end{verbatim}
 253 Then a caesium ion $\mathrm{Cs^+}$ is placed in the center:
 254 \begin{verbatim}
 255 /Cs {8.38  [12 8] newsphere
 256  dup (White) outputcolors} def
 257 \end{verbatim}
 258 Finally we fuse the separate spheres in pairs.
 259
 260 \vfill
 261
 262
 263 \subsection{A prototype of a \Index{vehicle}}
 264 \begin{center}
 265 \psset{lightsrc=100 0 100,viewpoint=25 10 10,Decran=30}
 266 \begin{pspicture}(-6,-4)(6,8)
 267 \pstVerb{/Pneu {
 268    /m {90 4 div} bind def
 269    /Scos {m cos 2 m mul cos add 3 m mul cos add} bind def
 270    /Z0 {h 4 div} bind def
 271    /c {Z0 Scos div} bind def
 272    /Z1 {Z0 c m cos mul add} bind def
 273    /Z2 {Z1 c m 2 mul cos mul add} bind def
 274    /R1 {R c m sin mul sub} bind def
 275    /R2 {R1 c m 2 mul sin mul sub} bind def
 276    /R3 {R2 c m 3 mul sin mul sub} bind def
 277    R h 4 div neg % 1
 278    R h 4 div % 2
 279    R1 Z1 % 3
 280    R2 Z2 % 4
 281    R3 h 2 div % 5
 282    r h 2 div  % 6
 283    r h 2 div neg  % 7
 284    R3 h 2 div neg % 8
 285    R2 Z2 neg % 9
 286    R1 Z1 neg % 10
 287    } def}%
 288 \grille
 289 \codejps{
 290 /roue12 {
 291 % solide 1
 292     /R 2 def /r 1 def /h 1 def
 293     [Pneu] 36 newanneau
 294      {90 0 90 rotateOpoint3d} solidtransform
 295      {3 4 2 translatepoint3d} solidtransform
 296      dup (White) outputcolors
 297 % solide 2
 298     [Pneu] 36 newanneau
 299     {90 0 90 rotateOpoint3d} solidtransform
 300    {-3 4 2 translatepoint3d} solidtransform
 301     dup (White) outputcolors
 302 % fusion
 303     solidfuz } def
 304 /axe12{
 305 0 0.1 6 [4 16] newcylindre
 306 {90 0 90 rotateOpoint3d} solidtransform
 307 {-3 4 2  translatepoint3d} solidtransform
 308 dup (White) outputcolors
 309 } def
 310 /roue12axes {
 311 roue12 axe12 solidfuz } def
 312 /roue34 {
 313 % solide 3
 314    /R 1.5 def /r 1 def /h 1 def
 315     [Pneu] 36 newanneau
 316     {90 0 110 rotateOpoint3d} solidtransform
 317    {3 -4 1.5 translatepoint3d} solidtransform
 318     dup (White) outputcolors
 319 % solide 4
 320     [Pneu] 36 newanneau
 321    {90 0 110 rotateOpoint3d} solidtransform
 322    {-3 -4 1.5 translatepoint3d} solidtransform
 323     dup (White) outputcolors
 324 % fusion
 325     solidfuz } def
 326 /axe34{
 327 0 0.1 6  [16 16] newcylindre
 328 {90 0 90 rotateOpoint3d} solidtransform
 329 {-3 -4 1.5  translatepoint3d} solidtransform
 330 dup (White) outputcolors
 331 } def
 332 /roue34axes34 {
 333 roue34 axe34 solidfuz } def
 334 /roues {roue34axes34 roue12axes solidfuz} def
 335 /chassis {
 336 0 1 8  [4 16] newcylindre
 337 {100 0 0 rotateOpoint3d} solidtransform
 338 {0 4 2.5  translatepoint3d} solidtransform
 339 dup (White) outputcolors
 340 } def
 341 roues chassis solidfuz
 342     drawsolid**}
 343 \psPoint(0,0,2.7){Z'}
 344 \psline[arrowsize=0.3,arrowinset=0.2,linecolor=blue]{->}(Z')(Z)
 345 \end{pspicture}
 346 \end{center}
 347 We have to operate in several steps to fuse the solids in pairs:
 348 \begin{compactitem}
 349   \item We first fuse the two front wheels \texttt{roue12}:
 350   \begin{verbatim}
 351 /roue12 {
 352 % solide 1
 353     /R 2 def /r 1 def /h 1 def
 354     [Pneu] 36 newanneau
 355      {90 0 90 rotateOpoint3d} solidtransform
 356      {3 4 2 translatepoint3d} solidtransform
 357      dup (White) outputcolors
 358 % solide 2
 359     [Pneu] 36 newanneau
 360     {90 0 90 rotateOpoint3d} solidtransform
 361    {-3 4 2 translatepoint3d} solidtransform
 362     dup (White) outputcolors
 363 % fusion
 364     solidfuz } def
 365   \end{verbatim}
 366   \item Then the two wheels and their axis:
 367   \begin{verbatim}
 368 /axe12{
 369 0 0.1 6  [4 16] newcylindre
 370 {90 0 90 rotateOpoint3d} solidtransform
 371 {-3 4 2  translatepoint3d} solidtransform
 372 dup (White) outputcolors
 373 } def
 374 /roue12axes {
 375 roue12 axe12 solidfuz } def
 376 \end{verbatim}
 377   \item After that the rear wheels and their axis:
 378   \begin{verbatim}
 379 /roue34 {
 380 % solide 3
 381    /R 1.5 def /r 1 def /h 1 def
 382     [Pneu] 36 newanneau
 383     {90 0 110 rotateOpoint3d} solidtransform
 384    {3 -4 1.5 translatepoint3d} solidtransform
 385     dup (White) outputcolors
 386 % solide 4
 387     [Pneu] 36 newanneau
 388    {90 0 110 rotateOpoint3d} solidtransform
 389    {-3 -4 1.5 translatepoint3d} solidtransform
 390     dup (White) outputcolors
 391 % fusion
 392     solidfuz } def
 393 /axe34{
 394 0 0.1 6 [16 16] newcylindre
 395 {90 0 90 rotateOpoint3d} solidtransform
 396 {-3 -4 1.5  translatepoint3d} solidtransform
 397 dup (White) outputcolors
 398 } def
 399 /roue34axes34 {
 400 roue34 axe34 solidfuz } def
 401 \end{verbatim}
 402
 403 \item Then fuse the two wheel assemblies:
 404 \begin{verbatim}
 405 /roues {roue34axes34 roue12axes solidfuz} def
 406 \end{verbatim}
 407
 408 \item The final step is to fuse the previously generated solid with
 409 the chassis:
 410 \begin{verbatim}
 411 /chassis {
 412 0 1 8  [4 16] newcylindre
 413 {100 0 0 rotateOpoint3d} solidtransform
 414 {0 4 2.5  translatepoint3d} solidtransform
 415 dup (White) outputcolors
 416 } def
 417 roues chassis solidfuz
 418     drawsolid**}
 419 \end{verbatim}
 420 \end{compactitem}
 421
 422
 423 \subsection{A \Index{wheel} -- or a space station}
 424
 425 \begin{center}
 426 \begin{pspicture}(-6,-5)(6,6)
 427 \psset{lightsrc=50 -50 50,viewpoint=40 50 60,Decran=60,linewidth=0.5\pslinewidth}
 428 %\psframe*[linecolor=black](-6,-5)(6,5)
 429 \codejps{
 430  /rayon0 {
 431      1 0.2 6 [4 16] newcylindre
 432      {90 0 0 rotateOpoint3d} solidtransform
 433       dup (White) outputcolors
 434    } def
 435 36 36 360 {
 436     /angle exch def
 437   /rayon1 {
 438      1 0.2 6  [4 16] newcylindre
 439      {90 0 angle rotateOpoint3d} solidtransform
 440       dup (White) outputcolors
 441    } def
 442   /rayons {rayon0 rayon1 solidfuz} def
 443   /rayon0 rayons def
 444   } for
 445  /moyeu { -2 1 2  [4 10] newcylindre dup (jaune) outputcolors} def
 446  /rayonsmoyeu {rayons  moyeu solidfuz} def
 447  /pneu {2 7 [18 36] newtore dup (White) outputcolors} def
 448  /ROUE {pneu rayonsmoyeu solidfuz} def
 449   ROUE  drawsolid**}
 450 \end{pspicture}
 451 \end{center}
 452 We define the first spoke:
 453 \begin{verbatim}
 454  /rayon0 {
 455      1 0.2 6 [4 16] newcylindre
 456      {90 0 0 rotateOpoint3d} solidtransform
 457       dup (White) outputcolors
 458    } def
 459 \end{verbatim}
 460 Then, with a loop, we fuse all the spokes of the wheel:
 461 \begin{verbatim}
 462 36 36 360 {
 463     /angle exch def
 464   /rayon1 {
 465      1 0.2 6  [4 16] newcylindre
 466      {90 0 angle rotateOpoint3d} solidtransform
 467       dup (White) outputcolors
 468    } def
 469   /rayons {rayon0 rayon1 solidfuz} def
 470   /rayon0 rayons def
 471   } for
 472 \end{verbatim}
 473 After that, we draw the hub and the tyre of the wheel, and finally
 474 fuse all of them:
 475 \begin{verbatim}
 476  /moyeu { -0.5 1 0.5  [4 10] newcylindre dup (White) outputcolors} def
 477  /rayonsmoyeu {rayons  moyeu solidfuz} def
 478  /pneu {2 7 [18 36] newtore dup (jaune) outputcolors} def
 479  /ROUE {pneu rayonsmoyeu solidfuz} def
 480   ROUE  drawsolid**
 481 \end{verbatim}
 482
 483
 484 \subsection{Intersection of two cylinders}
 485
 486 \begin{LTXexample}[width=8cm]
 487 \begin{pspicture}(-4,-3)(6,3)
 488 \psset{lightsrc=50 -50 50,viewpoint=100 -30
 489 40,Decran=100,linewidth=0.5\pslinewidth, unit=0.5}
 490 \codejps{
 491  /cylindre1 {
 492      -6 2 6 [36 36] newcylindrecreux %newcylindre
 493      {90 0 0 rotateOpoint3d} solidtransform
 494       dup (Yellow) (White) inoutputcolors
 495    } def
 496  /cylindre2 {
 497      -6 2 6 [36 36] newcylindrecreux %newcylindre
 498      {90 0 90 rotateOpoint3d} solidtransform
 499       dup (Yellow) (White) inoutputcolors
 500    } def
 501  /UnionCylindres {cylindre1 cylindre2 solidfuz} def
 502   UnionCylindres  drawsolid**}
 503 \end{pspicture}
 504 \end{LTXexample}
 505
 506
 507 \subsection{Intersection between a sphere and a cylinder}
 508
 509 This time we draw the curve of intersection using
 510 \verb+\psSolid[object=courbe]+.
 511
 512 \begin{LTXexample}[width=8cm]
 513 \psset{unit=0.5,lightsrc=50 -50 50,viewpoint=100 0 0 rtp2xyz,Decran=110,linewidth=0.5\pslinewidth}
 514 \begin{pspicture}(-7,-6)(5,6)
 515 \defFunction{F}(t){t cos dup mul 5 mul}{t cos t sin mul 5 mul}{t sin 5 mul}
 516 \codejps{%
 517    /cylindre1 {
 518        -5 2.5 5 [36 36] newcylindre
 519        {2.5 0 0 translatepoint3d} solidtransform
 520         dup (White) outputcolors
 521    } def
 522    /sphere1 {
 523         5 [36 72] newsphere
 524         dup (White) outputcolors
 525    } def
 526    /CS {cylindre1 sphere1 solidfuz} def
 527    CS drawsolid**}
 528 \psPoint(0,0,0){O}
 529 \psSolid[object=courbe,r=0,
 530    function=F,
 531    range=0 360,
 532    linecolor=red,linewidth=4\pslinewidth]
 533 \end{pspicture}
 534 \end{LTXexample}
 535
 536
 537 \subsection{Two linked \Index{rings}}
 538
 539 \begin{LTXexample}[width=8cm]
 540 \begin{pspicture}(-5,-4)(3,3)
 541 \psset{lightsrc=50 50 50,viewpoint=40 50 60,Decran=30,unit=0.85}
 542 \codejps{
 543  /anneau1 {1 7 [12 36] newtore
 544  {0 0 0 translatepoint3d} solidtransform
 545  dup (Yellow) outputcolors} def
 546  /anneau2 {1 7 [12 36] newtore
 547  {90 0 0 rotateOpoint3d} solidtransform
 548  {7 0 0 translatepoint3d} solidtransform
 549  dup (White) outputcolors} def
 550  /collier {anneau1 anneau2 solidfuz} def
 551   collier  drawsolid**}
 552 \end{pspicture}
 553 \end{LTXexample}
 554
 555
 556
 557 \subsection{The \Index{methane molecule}: wooden model}
 558
 559 \begin{LTXexample}[width=8cm]
 560 \begin{pspicture}(-4.5,-4)(3.2,5)
 561 \psset{lightsrc=50 50 10,lightintensity=2,viewpoint=100 50 20 rtp2xyz,
 562 Decran=30}
 563 \psset{linecolor={[cmyk]{0,0.72,1,0.45}},linewidth=0.5\pslinewidth,
 564   unit=1}
 565 %\psframe[fillstyle=solid,fillcolor=green!20](-4,-4)(3.2,5)
 566 \pstVerb{/hetre {0.764 0.6 0.204 setrgbcolor} def
 567          /chene {0.568 0.427 0.086 setrgbcolor} def
 568          /bois {0.956 0.921 0.65 setrgbcolor} def
 569          }%
 570 \codejps{
 571  /H1 {
 572  2  [18 16] newsphere
 573  {-90 0 0 rotateOpoint3d} solidtransform
 574  {0 10.93 0 translatepoint3d} solidtransform
 575  dup (hetre) outputcolors} def
 576   /L1 {
 577      0 0.25 10  [12 10] newcylindre
 578      {-90 0 0 rotateOpoint3d} solidtransform
 579       dup (bois) outputcolors
 580    } def
 581 /HL1{ H1 L1  solidfuz} def
 582 /HL2 { HL1 {0 0 -109.5 rotateOpoint3d} solidtransform } def
 583 /HL3 { HL2 {0 -120 0 rotateOpoint3d} solidtransform } def
 584 /HL4 { HL2 {0 120 0 rotateOpoint3d} solidtransform } def
 585  /C {3  [18 16] newsphere
 586   {90 0 0 rotateOpoint3d} solidtransform
 587    dup (chene) outputcolors} def
 588 /HL12 { HL1 HL2 solidfuz} def
 589 /HL123 { HL12 HL3 solidfuz} def
 590 /HL1234 { HL123 HL4 solidfuz} def
 591 /methane { HL1234 C solidfuz} def
 592   methane  drawsolid**}
 593 \end{pspicture}
 594 \end{LTXexample}
 595
 596
 597 \subsection{The \Index{thiosulphate ion}}
 598
 599 \begin{center}
 600 \begin{pspicture}(-4,-3)(4.5,5.5)
 601 \psset{lightsrc=100 10 -20,lightintensity=3,viewpoint=200 30
 602 20 rtp2xyz,Decran=40}
 603 %\psframe(-4,-3)(4.5,5.5)
 604 {\psset{linewidth=0.5\pslinewidth}
 605 \codejps{
 606 /Soufre1 {3.56  [20 16] newsphere
 607  dup (Yellow) outputcolors} def
 608 /Soufre2 {3.56  [20 16] newsphere
 609  {0 0.000 20.10 translatepoint3d} solidtransform
 610  dup (Yellow) outputcolors} def
 611 % Liaison simple
 612 /LiaisonR {
 613      7.5 0.5 15  [10 10] newcylindre
 614       dup (Red) outputcolors
 615    } def
 616 /LiaisonY {
 617      0 0.5 7.5  [10 10] newcylindre
 618       dup (Yellow) outputcolors
 619    } def
 620 % fin Liaison simple
 621 /Liaison{LiaisonR LiaisonY solidfuz} def
 622 /Ox {2.17  [20 16] newsphere
 623      {0 0 15 translatepoint3d} solidtransform
 624      dup (Red) outputcolors} def
 625 /LO { Liaison Ox solidfuz} def
 626 /LO1 { LO  {0 -109.5 0 rotateOpoint3d} solidtransform } def
 627 /LOx1 { LO1  {0 0 120 rotateOpoint3d} solidtransform } def
 628 % fin liaison simple S-O
 629 % Liaison double S=O
 630 /LiaisonD1 {Liaison {-0.75 0 0 translatepoint3d} solidtransform} def
 631 /LiaisonD2 {Liaison {0.75 0 0 translatepoint3d} solidtransform} def
 632 /LiaisonDD { LiaisonD1 LiaisonD2 solidfuz} def
 633 /LiaisonDOx {LiaisonDD Ox solidfuz} def
 634 /LiaisonDOx1 {LiaisonDOx {0 -109.5 0 rotateOpoint3d} solidtransform } def
 635 /LiaisonDOx2 {LiaisonDOx1 {0  0 -120 rotateOpoint3d} solidtransform } def
 636 /LO12 { LiaisonDOx1 LiaisonDOx2 solidfuz} def
 637 /LO123 {LO12 LOx1 solidfuz} def
 638 % liaison simple S-S
 639 /L4 { 0 0.5 20.10  [16 10] newcylindre
 640       dup (Yellow) outputcolors
 641     } def
 642 /S1L4{ Soufre1 L4 solidfuz} def
 643 /S1S2L4{ S1L4 Soufre2 solidfuz} def
 644 /S2O3 { S1S2L4 LO123 solidfuz} def
 645 S2O3  drawsolid**}
 646 \axesIIID(0,0,0)(25,20,25)}
 647 \psPoint(0,0,20.1){S2}
 648 \psPoint(-14.14,0,-5){O1}
 649 \psPoint(7.07,-12.24,-5 ){O2}
 650 \psPoint(7.07,12.24,-5 ){O3}
 651 \pcline[linestyle=dotted]{<->}(O2)(O)
 652 \aput{:U}{15 pm}
 653 \pcline[linestyle=dotted]{<->}(O)(S2)
 654 \aput{:U}{\small 20,1 pm}
 655 \pcline[linestyle=dotted]{<->}(O2)(O3)
 656 \lput*{:U}{\small 24,5 pm}
 657 \pcline[linestyle=dotted]{<->}(O2)(S2)
 658 \lput*{:U}{\small 28,8 pm}
 659 \pstMarkAngle[arrows=<->,MarkAngleRadius=0.8,linestyle=dotted]{O2}{O}{O3}{\footnotesize 109,4$^{\mathrm{o}}$}
 660 \pstMarkAngle[arrows=<->,MarkAngleRadius=0.8,linestyle=dotted]{O1}{O}{S2}{\footnotesize 109,5$^{\mathrm{o}}$}
 661 \rput(0,-2.5){$\mathrm{S_2^{\phantom{2}}O_3^{2-}}$}
 662 \end{pspicture}
 663 \end{center}
 664
 665 We first define the two sulphur atoms and place them on the $Oz$
 666 axis. $\mathrm{S_1}$ is placed at the origin $O$.
 667 \begin{verbatim}
 668 \codejps{
 669 /Soufre1 {3.56  [20 16] newsphere
 670  dup (Yellow) outputcolors} def
 671 /Soufre2 {3.56  [20 16] newsphere
 672  {0 0.000 20.10 translatepoint3d} solidtransform
 673  dup (Yellow) outputcolors} def
 674 \end{verbatim}
 675 Then the single bond \textsf{S-O} using the following convention:
 676 half red---the half connected to \textsf{O}, and half yellow---the half connected to \textsf{S}.
 677 \begin{verbatim}
 678 /LiaisonR {
 679      7.5 0.5 15  [10 10] newcylindre
 680       dup (Red) outputcolors
 681    } def
 682 /LiaisonY {
 683      0 0.5 7.5  [10 10] newcylindre
 684       dup (Yellow) outputcolors
 685    } def
 686 /Liaison{LiaisonR LiaisonY solidfuz} def
 687 \end{verbatim}
 688 The oxygen atom, its bond, and the setting of the combined unit:
 689 \begin{verbatim}
 690 /Ox {2.17  [20 16] newsphere
 691      {0 0 15 translatepoint3d} solidtransform
 692      dup (Red) outputcolors} def
 693 /LO { Liaison Ox solidfuz} def
 694 /LO1 { LO  {0 -109.5 0 rotateOpoint3d} solidtransform } def
 695 /LOx1 { LO1  {0 0 120 rotateOpoint3d} solidtransform } def
 696 % fin liaison simple S-O
 697 \end{verbatim}
 698 For the double bond \textsf{S=O}, we take the single bond above
 699 and duplicate it with shifts of 0.75~cm along the $Ox$ axis.
 700 \begin{verbatim}
 701 % Liaison double S=O
 702 /LiaisonD1 {Liaison {-0.75 0 0 translatepoint3d} solidtransform} def
 703 /LiaisonD2 {Liaison {0.75 0 0 translatepoint3d} solidtransform} def
 704 /LiaisonDD { LiaisonD1 LiaisonD2 solidfuz} def
 705 \end{verbatim}
 706 Connecting it to the \textsf{O} atom:
 707 \begin{verbatim}
 708 /LiaisonDOx {LiaisonDD Ox solidfuz} def
 709 \end{verbatim}
 710 and with two successive rotations we position the two bonds
 711 \textsf{=O}:
 712 \begin{verbatim}
 713 /LiaisonDOx1 {LiaisonDOx {0 -109.5 0 rotateOpoint3d} solidtransform } def
 714 /LiaisonDOx2 {LiaisonDOx1 {0  0 -120 rotateOpoint3d} solidtransform } def
 715 \end{verbatim}
 716 The following step consists of fusing the two connections:
 717 \begin{verbatim}
 718 /LO12 { LiaisonDOx1 LiaisonDOx2 solidfuz} def
 719 /LO123 {LO12 LOx1 solidfuz} def
 720 \end{verbatim}
 721 Then the single bond \textsf{S-S} is created:
 722 \begin{verbatim}
 723 % liaison simple S-S
 724 /L4 { 0 0.5 20.10  [16 10] newcylindre
 725       dup (Yellow) outputcolors
 726     } def
 727 \end{verbatim}
 728 and fused with the two atoms \textsf{S-S}:
 729 \begin{verbatim}
 730 /S1L4{ Soufre1 L4 solidfuz} def
 731 /S1S2L4{ S1L4 Soufre2 solidfuz} def
 732 \end{verbatim}
 733 The last step will be to fuse the two \textsf{S-S} and the three
 734 \textsf{O} already equipped with their bonds:
 735 \begin{verbatim}
 736 /S2O3 { S1S2L4 LO123 solidfuz} def
 737 S2O3  drawsolid**}
 738 \end{verbatim}
 739
 740 \endinput