doc-en/.svn/text-base/chapter-2-en.tex.svn-base

   1 \section{Choice of the view point}
   2
   3 \begin{center}
   4
   5 \begin{pspicture}(-5,-5.7)(10,7)
   6 \psset{lightsrc=10 20 30,viewpoint=50 30 20 rtp2xyz}
   7 \definecolor{bleuciel}{rgb}{0.78,0.84,0.99}
   8 \psSolid[object=cube,fillcolor=bleuciel,a=2,action=draw*]%%
   9 %\psSolid[object=cubemaillage,fillcolor=bleuciel,a=2]%%
  10 \psSolid[object=grille,base=0 8 0 10,action=draw]%%
  11 \psSolid[object=grille,base=0 7 0 10,action=draw,RotY=90](0,0,7)%
  12 \psSolid[object=grille,base=0 8 0 7,action=draw,RotX=-90](0,0,7)%
  13 \psSolid[object=cube,fillcolor=bleuciel,a=1,action=draw*](0.5,0.5,0.5)%
  14 \psSolid[object=grille,base=-1 1 -1 1,action=draw,linecolor=blue](0,0,1)%
  15 \psSolid[object=grille,base=-1 1 -1 1,action=draw,RotY=90,linecolor=blue](1,0,0)%
  16 \psSolid[object=grille,base=-1 1 -1 1,action=draw,RotX=-90,linecolor=blue](0,1,0)%
  17 \axesIIID(1,1,1)(8,10,7)
  18 \pstVerb{
  19    /dV 12 def % distance V
  20    /dE 6 def % distance \'{e}cran
  21    /Theta 60 def
  22    /Phi 30 def
  23    dV Theta Phi rtp2xyz
  24    /zV exch def
  25    /yV exch def
  26    /xV exch def
  27    dE Theta Phi rtp2xyz
  28    /zE exch def
  29    /yE exch def
  30    /xE exch def
  31          }%
  32 \psPoint(xV,yV,zV){V}
  33 \psPoint(xE,yE,zE){E}
  34 \psPoint(xV,yV,0){Vp}
  35 %
  36 % 5 distance \'{e}cran
  37 %\psPoint(dE Theta  cos mul Phi cos div dE Theta  sin mul Phi cos div 0){Vq}
  38 \psPoint(xV,0,0){Vx}
  39 \psPoint(0,yV,0){Vy}
  40 \psPoint(0,0,zV){Vz}
  41 \psdot(V)
  42 {\psset{linestyle=dashed,linecolor=red}
  43 \psline(V)(Vp)\psline(Vx)(Vp)\psline(Vy)(Vp)\psline(V)(Vz)\psline(V)(O)\psline(Vp)(O)}
  44 %\psSolid[object=grille,base=-5 5 -3 3,action=draw,RotX=-60,linecolor=red](xE,yE,zE)%
  45 \psTransformPoint[RotX=-60](-5 -3 0)(xE,yE,zE){A}
  46 \psTransformPoint[RotX=-60](-5 3 0)(xE,yE,zE){B}
  47 \psTransformPoint[RotX=-60](5 3 0)(xE,yE,zE){C}
  48 \psTransformPoint[RotX=-60](5 -3 0)(xE,yE,zE){D}
  49 \pspolygon[fillstyle=vlines,hatchcolor=yellow!90,hatchwidth=0.02,hatchsep=0.04](A)(B)(C)(D)
  50 %
  51 %
  52 \PointEcran(1,1,1){S1}
  53 \psPoint(1,1,1){s1}
  54 \psline(S1)(V)
  55 \psline[linestyle=dashed](s1)(S1)
  56 %
  57 \PointEcran(1,1,-1){S2}
  58 \psPoint(1,1,-1){s2}
  59 \psline(S2)(V)
  60 \psline[linestyle=dashed](s2)(S2)
  61 %
  62 \PointEcran(-1,1,-1){S3}
  63 \psPoint(-1,1,-1){s3}
  64 \psline(S3)(V)
  65 \psline[linestyle=dashed](s3)(S3)
  66 %
  67 \PointEcran(-1,1,1){S4}
  68 \psPoint(-1,1,1){s4}
  69 \psline(S4)(V)
  70 \psline[linestyle=dashed](s4)(S4)
  71 %
  72 \PointEcran(1,-1,-1){S5}
  73 \psPoint(1,-1,-1){s5}
  74 \psline(S5)(V)
  75 \psline[linestyle=dashed](s5)(S5)
  76 %
  77 \PointEcran(1,-1,1){S6}
  78 \psPoint(1,-1,1){s6}
  79 \psline(S6)(V)
  80 \psline[linestyle=dashed](s6)(S6)
  81 %
  82 \PointEcran(-1,-1,1){S7}
  83 \psPoint(-1,-1,1){s7}
  84 \psline(S7)(V)
  85 \psline[linestyle=dashed](s7)(S7)
  86 \psset{solidmemory}
  87 \psSolid[object=plan,
  88    definition=equation,
  89    args={[0 0 1 0]},
  90    base=-5 5 -3 3,
  91    RotX=-60,
  92 %   showBase,
  93    action=none,
  94    name=planbase,
  95 ]
  96 %% here, we define the plantype object "Ecran"
  97 \codejps{
  98    planbase
  99    dup xE yE zE planputorigine
 100    dup -180 rotateplan
 101    /Ecran exch def
 102 }%
 103 %% uncomment follow line to draw "Ecran"
 104 %\psSolid[object=plan,args=Ecran,showBase,planmarks]
 105 \psProjection[object=texte,
 106    plan=Ecran,
 107    fontsize=20,
 108    text=Projection Screen](-2,2)
 109
 110 %
 111 \psset{linecolor=red,fillstyle=vlines,hatchsep=0.04,hatchwidth=0.02}
 112 \pspolygon[hatchcolor=red!60](S1)(S2)(S3)(S4)
 113 \pspolygon[,hatchcolor=red!60](S1)(S2)(S5)(S6)
 114 \pspolygon[hatchcolor=red!10](S1)(S4)(S7)(S6)
 115 \psdots(s1)(s2)(s3)(s4)(s5)(s6)(s7)(S1)(S2)(S3)(S4)(S5)(S6)(S7)
 116 \psbrace[ref=lC,linecolor=black](V)(E){$D$}
 117 \uput[45](V){View Point}
 118 \end{pspicture}
 119 \end{center}
 120
 121 The coordinates of the object, in this case the bluish cube, are setup in the axes of coordinates $Oxyz$.  The \Index{coordinates} of the \Index{view point} ($V$), are setup in the same axes of coordinates, either in \Index{spherical coordinates}---with the adding option \verb+[rtp2xyz]+, or in Cartesian coordinates---which is the default option.
 122
 123 Example: \verb+[viewpoint=50 30 20  rtp2xyz]+ \qquad (here the notation with spherical coordinates)
 124
 125
 126 See some examples:
 127
 128 \def\decor{%
 129 \psset{solidmemory}
 130  \psSolid[object=plan,
 131    definition=equation,
 132    base=-5 5 -5 5,
 133    args={[0 0 1 0] 180},
 134    name=P1]%
 135 \psset{fontsize=28.45,plan=P1}
 136 \psSolid[object=plan,
 137    args=P1,
 138    plangrid,action=none]
 139 \psProjection[object=texte,
 140    linecolor=red,
 141    text=pst-solides3d](0,3.5)
 142  \psSolid[object=sphere,r=1,fillcolor=red!25,ngrid=18 36](4,4,1)
 143  \psSolid[object=cone,h=3,r=1,fillcolor=cyan,mode=5](-4,4,0)
 144  \psSolid[object=cube,a=2,fillcolor=magenta!20](-4,-4,1)
 145  \psSolid[object=cylindre,r=1,h=4,fillcolor=blue!20,ngrid=4 16](4,-4,0)
 146 \axesIIID(0,0,0)(6,6,6)
 147 \psPoint(0,0,0){O}
 148 \psdot(O)}
 149
 150 \begin{pspicture}(-3,-3)(3,3)
 151 %\psframe(-5,-3)(4,4)
 152  \psset{viewpoint=20 25 15,Decran=20,lightsrc=viewpoint,unit=0.9}
 153 \decor
 154 \rput(0,-4){\texttt{viewpoint=20 25 15}}
 155  \end{pspicture}\qquad\qquad\qquad\qquad
 156 \begin{pspicture}(-3,-3)(3,3)
 157 %\psframe(-5,-3)(4,4)
 158  \psset{viewpoint=-10 0 30,Decran=20,lightsrc=viewpoint,unit=0.9}
 159 \decor
 160 \rput(0,-4){\texttt{viewpoint=-10 0 30}}
 161  \end{pspicture}
 162
 163
 164 \begin{pspicture}(-3,-3)(3,4.5)
 165 %\psframe(-5,-3)(4,4)
 166  \psset{viewpoint=-20 0 10,Decran=10,lightsrc=viewpoint,unit=0.9}
 167 \decor
 168 \rput(0,-4){\texttt{viewpoint=-20 0 10}}
 169  \end{pspicture}\qquad\qquad\qquad\qquad
 170  \begin{pspicture}(-3,-3)(3,4.5)
 171 %\psframe(-5,-3)(4,4)
 172  \psset{viewpoint=-20 -10 25,Decran=20,lightsrc=viewpoint,unit=0.9}
 173 \decor
 174 \rput(0,-4){\texttt{viewpoint=-20 -10 25}}
 175  \end{pspicture}
 176
 177 \section{The definition of the option \texttt{\Index{Decran}}}
 178 The \Index{projection screen} is placed perpendicular to the direction $OV$---central
 179 perspective, at a distance $D$ from the view point $V$: We call that distance
 180 `Decran', with the default value of \texttt{\Lkeyword{Decran}=50}; this value can
 181 either be positive or negative.
 182
 183
 184
 185 The following examples show the behaviour of the parameter \Lkeyword{Decran}.
 186
 187 \begin{center}
 188 \begin{pspicture}(-2,-3)(2.5,3)
 189 \psaxes[yAxis=false](-2,-2)(2,2)
 190 \psset{viewpoint=0 0 5,Decran=5}
 191 \psSolid[object=grille,base=-2 2 -2 2]
 192 \psSolid[object=vecteur,args=0 0 0  2 2 0,linecolor=red,linewidth=2pt]
 193 \axesIIID(3,3,3)\pnode(2,-2){B}\pnode(2,2){A}
 194 \end{pspicture}
 195 \qquad
 196 \begin{pspicture}(-0.5,-3)(5,3)
 197 \psaxes[yAxis=false](0,-2)(5,2)
 198 \psset{viewpoint=5 0 5,Decran=5,RotX=-90}
 199 \psSolid[object=grille,base=-2 2 -2 2,RotX=89.9]
 200 \axesIIID[axisnames={x,z,y}](3,3,0)
 201 \psdot(5,0)\uput[0](5,0){V}
 202 \psline[tbarsize=3mm 5]{<->|}(0,-0.5)(5,-0.5)\rput*(2.5,-0.5){$D=V$}
 203 \psline[linestyle=dashed](0,2)(5,0)\psline[linestyle=dashed](0,-2)(5,0)
 204 \uput[-90](0,-2.5){Original}\uput[-90](0,-2.85){Image}
 205 \psline[linestyle=dotted](A)(0,2)
 206 \psline[linestyle=dotted](B)(0,-2)
 207 \rput(-1,2.75){Rotation: }
 208 \rput(-1,2.25){90$^\circ$ around $x$}
 209 \psSolid[object=vecteur,args=0 0 0  2 2 0,linecolor=red,linewidth=2pt]
 210 \end{pspicture}\\[\normalbaselineskip]
 211 %
 212 \begin{pspicture}(-2,-3)(2.5,3)
 213 \psaxes[yAxis=false](-2,-2)(2,2)
 214 \psset{viewpoint=0 0 5,Decran=2.5}
 215 \psSolid[object=grille,base=-2 2 -2 2]
 216 \psSolid[object=vecteur,args=0 0 0  2 2 0,linecolor=red,linewidth=2pt]
 217 \axesIIID(3,3,3)\pnode(1,-1){B}\pnode(1,1){A}
 218 \end{pspicture}
 219 \qquad
 220 \begin{pspicture}(-0.5,-3)(5,3)
 221 \psaxes[yAxis=false](0,-2)(5,2)
 222 \psset{viewpoint=5 0 5,Decran=2.5,RotX=-90}
 223 \psline[linewidth=1pt](0,2)(0,-2)
 224 \psline[linewidth=1.5pt,linecolor=red]{->}(0,0)(0,-2)
 225 \psdot(5,0)\uput[0](5,0){V}
 226 \psline[tbarsize=3mm 5]{<->|}(0,1.5)(5,1.5)\rput*(2.5,1.5){$V$}
 227 \psline[linestyle=dashed](0,2)(5,0)\psline[linestyle=dashed](0,-2)(5,0)
 228 \psline[tbarsize=3mm 5]{|<->|}(2.5,-1.5)(5,-1.5)\rput*(3.75,-1.5){$D$}
 229 \psline[linewidth=1.5pt](2.5,1)(2.5,-1)
 230 \psline[linewidth=1.5pt,linecolor=red]{->}(2.5,0)(2.5,-1)
 231 \psline{->}(2.5,0)(3.5,0)\uput[0](3.5,0){$z$}
 232 \uput[-90](0,-2.5){Original}\uput[-90](2.5,-2.5){Image}
 233 \psline[linestyle=dotted](A)(2.5,1)
 234 \psline[linestyle=dotted](B)(2.5,-1)
 235 \rput(-1.5,1.75){Rotation:}
 236 \rput(-1.5,1.25){90$^\circ$ around $x$}
 237 \end{pspicture}
 238 \end{center}
 239
 240
 241 If you keep the view point and make the \Lkeyword{Decran} value smaller, then the
 242 image gets smaller. If you make the \Lkeyword{Decran} value larger, then the image gets larger.
 243
 244 Here are some examples, where we keep the same object, the same view point
 245 and just vary the \Lkeyword{Decran} value:
 246
 247 \begin{center}
 248 \begin{pspicture}(-2,-2)(2,2)
 249 %\psgrid
 250 \psset{solidmemory}
 251 \psset{viewpoint=0 50 0,Decran=50}
 252 %\psSolid[object=sphere,r=2,ngrid=18 36]
 253 \psSolid[object=plan,definition=normalpoint,plangrid,linecolor=red,
 254          base=-2 2 -2 2,args={0 0 0 [0 1 0 180]},name=monplan]
 255 \psset{plan=monplan}
 256 \psProjection[object=texte,
 257               linecolor=red,
 258               fontsize=105.35,
 259               text=PS]%
 260 \composeSolid
 261 \rput*(0,-1.75){\texttt{Decran=50}}
 262 \end{pspicture}\qquad
 263 \begin{pspicture}(-2,-2)(2,2)
 264 %\psgrid
 265 \psset{solidmemory}
 266 \psset{viewpoint=0 50 0,Decran=25}
 267 %\psSolid[object=sphere,r=2,ngrid=18 36]
 268 \psSolid[object=plan,definition=normalpoint,plangrid,linecolor=red,
 269          base=-2 2 -2 2,args={0 0 0 [0 1 0 180]},name=monplan]
 270 \psset{plan=monplan}
 271 \psProjection[object=texte,
 272               linecolor=red,
 273               fontsize=105.35,
 274               text=PS]%
 275 \composeSolid
 276 \rput*(0,-1.75){\texttt{Decran=25}}
 277 \end{pspicture}\qquad
 278 \begin{pspicture}(-2,-2)(2,2)
 279 %\psgrid
 280 \psset{solidmemory}
 281 \psset{viewpoint=0 50 0,Decran=-50}
 282 \psSolid[object=plan,definition=normalpoint,plangrid,linecolor=red,
 283          base=-2 2 -2 2,args={0 0 0 [0 1 0 180]},name=monplan]
 284 \psset{plan=monplan}
 285 \psProjection[object=texte,
 286               linecolor=red,
 287               fontsize=105.35,
 288               text=PS]%
 289 \composeSolid
 290 \rput*(0,-1.75){\texttt{Decran=-50}}
 291 \end{pspicture}
 292 \end{center}
 293
 294
 295 \endinput
 296
 297