doc-en/.svn/text-base/par-courbeR3-en.tex.svn-base

   1 \section[Curves of functions from R in R\textsuperscript{3}]%
   2 {Curves of functions from $\mathbb{R}$ in $\mathbb{R}^3$} %$
   3
   4 %% \section{Fonctions R --> R\textsuperscript{3}}
   5
   6 The line of a defined \Index{function} calls the object \Lkeyval{courbe} and the option \Lkeyword{function}.
   7 We can realize a helix in algebraic notation with the function:
   8
   9 \begin{verbatim}
  10 \defFunction[algebraic]{helice}(t){3*cos(4*t)}{3*sin(4*t)}{t}
  11 \end{verbatim}
  12
  13 \psset{lightsrc=10 -20 50,viewpoint=50 -20 20 rtp2xyz,Decran=50}
  14 \begin{LTXexample}[width=6.5cm]
  15 \psset{unit=0.5}
  16 \begin{pspicture}(-6,-3)(6,8)
  17 \psframe*[linecolor=blue!50](-6,-3)(6,8)
  18 \psSolid[object=grille,base=-4 4 -4 4,linecolor=red,linewidth=0.5\pslinewidth]%
  19 \axesIIID(0,0,0)(4,4,7)
  20 \defFunction[algebraic]{helice}(t){3*cos(4*t)}{3*sin(4*t)}{t}
  21 \psSolid[object=courbe,
  22         r=0,
  23         range=0 6,
  24         linecolor=blue,linewidth=0.1,
  25         resolution=360,
  26         function=helice]%
  27 \end{pspicture}
  28 \end{LTXexample}
  29
  30 \begin{LTXexample}[width=6.5cm]
  31 \psset{unit=0.5}
  32 \begin{pspicture}(-6,-3)(6,8)
  33 \psframe*[linecolor=blue!50](-6,-3)(6,8)
  34 \psset{lightsrc=10 -20 50,viewpoint=50 -20 30 rtp2xyz,Decran=50}
  35 \psSolid[object=grille,base=-4 4 -4 4,linecolor=red,linewidth=0.5\pslinewidth]%
  36 \axesIIID(0,0,0)(4,4,7)
  37 \psset{range=-4 4}
  38 \defFunction{cosRad}(t){ t 2 mul Cos 4 mul }{ t }{ 0 }
  39 \psSolid[object=courbe,linewidth=0.1,
  40   r=0,linecolor=red,
  41   resolution=360,
  42   function=cosRad]
  43 \psSolid[object=grille,base=-4 4 -4 4,linecolor=blue,linewidth=0.5\pslinewidth](0,0,3)
  44 \psPoint(0,0,3){O1}\psPoint(0,0,7){Z1}\psline(O1)(Z1)\psline[linestyle=dashed](O1)(O)
  45 \pstVerb{/tmin -4 def /tmax 4 def}%
  46 \defFunction{sinRad}(t){ t }{ t Sin 3 mul }{ 3 }
  47 \psSolid[object=courbe,linewidth=0.1,
  48   r=0,linecolor=blue,
  49   resolution=30,
  50   function=sinRad]
  51 \end{pspicture}
  52 \end{LTXexample}
  53
  54 \begin{LTXexample}[width=6.5cm]
  55 \psset{unit=0.5}
  56 \begin{pspicture}(-6.5,-3)(7,11)
  57 \psset{lightsrc=10 -20 50,viewpoint=50 -20 20 rtp2xyz,Decran=50}
  58 \psSolid[object=grille,base=-4 4 -4 4,
  59   linecolor=lightgray,linewidth=0.5\pslinewidth]%
  60 \psSolid[object=grille,base=-4 4 0 8,
  61   linecolor=lightgray,RotX=90,
  62   linewidth=0.5\pslinewidth](0,4,0)
  63 \psSolid[object=grille,base=-4 4 -4 4,
  64   linecolor=lightgray,RotY=90,
  65   linewidth=0.5\pslinewidth](-4,0,4)
  66 \defFunction[algebraic]{helice}(t)%
  67   {1.3*(1-cos(2.5*t))*cos(6*t)}
  68   {1.3*(1-cos(2.5*t))*sin(6*t)}{t}
  69 \defFunction[algebraic]{helice_xy}(t)%
  70   {1.3*(1-cos(2.5*t))*cos(6*t)}
  71   {1.3*(1-cos(2.5*t))*sin(6*t)}{0}
  72 \defFunction[algebraic]{helice_xz}%
  73   (t){1.3*(1-cos(2.5*t))*cos(6*t)}{4}{t}
  74 \defFunction[algebraic]{helice_yz}%
  75   (t){-4}{1.3*(1-cos(2.5*t))*sin(6*t)}{t}
  76 \psset{range=0 8}
  77 \psSolid[object=courbe,r=0,linecolor=blue,
  78   linewidth=0.05,resolution=360,
  79   normal=0 0 1,function=helice_xy]
  80 \psSolid[object=courbe,r=0,
  81   linecolor=green,linewidth=0.05,
  82   resolution=360,normal=0 0 1,
  83   function=helice_xz]
  84 \psSolid[object=courbe,r=0,
  85   linewidth=0.05,resolution=360,
  86   normal=0 0 1,function=helice_yz]
  87 \psSolid[object=courbe,r=0,
  88   linecolor=red,linewidth=0.1,
  89   resolution=360,function=helice]
  90  \end{pspicture}
  91 \end{LTXexample}
  92
  93
  94 These last function lines are found in an animated form on the website:
  95
  96 \centerline{\url{http://melusine.eu.org/syracuse/pstricks/pst-solides3d/animations/}}
  97
  98
  99 \endinput