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

   1 \section{\Index{Transformations} to a point}
   2
   3 Given is an initial point $A(x,y,z)$. Now we make some
   4 rotations around the axes $Ox$, $Oy$ and $Oz$ with the appropriate angles (in degrees):
   5 \verb+[RotX=valueX,RotY=valueY,RotZ=valueZ]+, in this order,
   6 then translate it with the vector $(v_x,v_y,v_z)$. The problem is to get back
   7 the coordinates of the image (final point) $A'(x',y',z')$.
   8
   9 The code
  10 \texttt{\textbackslash psTransformPoint[RotX=valueX,RotY=valueY,
  11  RotZ=valueZ](x y z)(vx,vy,vz)\{A'\}}\\
  12 now allows us to save the node $A'$, the coordinates of the transformed point.
  13
  14 In the following example, $A(2,2,2)$ is one of the vertices of the initial
  15 cube, where the centre is placed at the origin.
  16
  17 \begin{verbatim}
  18 \psSolid[object=cube,a=4,action=draw*,linecolor=red]%
  19 \end{verbatim}
  20
  21 Some transformations are applied to the cube:
  22
  23 \begin{verbatim}
  24 \psSolid[object=cube,a=4,action=draw*,RotX=-30,RotY=60,RotZ=-60](7.5,11.25,10)%
  25 \end{verbatim}
  26
  27 To obtain the image of $A$, we use the following command:
  28
  29
  30 \begin{verbatim}
  31 \psTransformPoint[RotX=-30,RotY=60,RotZ=-60](2 2 2)(7.5,11.25,10){A'}
  32 \end{verbatim}
  33
  34 This allows us, for example, to name these points and then draw the vector $\overrightarrow{AA'}$.
  35 \begin{center}
  36 \begin{pspicture}(-2,-4)(6,6)
  37 \psframe(-3,-4)(9,6)
  38 \psset{viewpoint=50 20 30 rtp2xyz,Decran=50,unit=0.5}
  39 \psSolid[object=cube,a=4,action=draw*,linecolor=red]%
  40 \psPoint(2,2,2){A}\psdot(A)
  41 \psSolid[object=cube,a=4,action=draw*,RotX=-30,RotY=60,RotZ=-60](7.5,11.25,10)%
  42 \psTransformPoint[RotX=-30,RotY=60,RotZ=-60](2 2 2)(7.5,11.25,10){A'}
  43 \psdot(A')\psline[linecolor=blue,arrowsize=0.3]{{o-v}}(A)(A')
  44 \uput[u](A'){$A'$}\uput[u](A){$A$}
  45 \psset{solidmemory,action=none}
  46 \psSolid[object=cube,a=4,name=A1,](0,0,0)
  47 \psSolid[object=plan,definition=solidface,args=A1 0,name=P0]
  48 \psSolid[object=plan,definition=solidface,args=A1 1,name=P1]
  49 \psSolid[object=plan,definition=solidface,args=A1 4,name=P4]
  50 \psset{fontsize=100}
  51 \psProjection[object=texte,linecolor=red,text=A,plan=P0]
  52 \psProjection[object=texte,linecolor=red,text=B,plan=P1]
  53 \psProjection[object=texte,linecolor=red,text=E,plan=P4]
  54 \psSolid[object=cube,a=4,RotX=-30,RotY=60,RotZ=-60,name=A2,](7.5,11.25,10)
  55 \psSolid[object=plan,definition=solidface,args=A2 0,name=P'0]
  56 \psSolid[object=plan,definition=solidface,args=A2 1,name=P'1]
  57 \psSolid[object=plan,definition=solidface,args=A2 2,name=P'2]
  58 \psProjection[object=texte,text=A,plan=P'0]
  59 \psProjection[object=texte,text=B,plan=P'1]
  60 \psProjection[object=texte,text=C,plan=P'2]
  61 \axesIIID(2,2,2)(10,10,8)
  62 \end{pspicture}
  63 \end{center}
  64
  65
  66 \endinput