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

   1 \section{Curves of real-valued and \Index{parameterised functions}}
   2
   3 \subsection{Curve of a real-valued function}
   4
   5 The object \Lkeyword{courbe} allows us to draw a curve, where the
   6 name is given with the option \Lkeyword{function}. This \Index{function},
   7 with values in $\mathbb{R}$, has to be defined by the macro
   8 \verb+\defFunction+ (see the appropriate paragraph for more
   9 details).
  10
  11 We can define this function either in algebraic notation, with the
  12 option \Lkeyword{algebraic}, or in Reverse Polish Notation (RPN),
  13 with variables like $(x,u,t\ldots)$, using an expression of the
  14 following form:
  15
  16
  17 \begin{verbatim}
  18 \defFunction[algebraic]{nom_fonction}(x){x*sin(x)}{}{}
  19 \end{verbatim}
  20
  21 \begin{verbatim}
  22 \defFunction{nom_fonction}(x){x dup sin mul}{}{}
  23 \end{verbatim}
  24
  25
  26 \encadre{This expression needs to be included within a
  27 \texttt{pspicture} environment.}
  28
  29 The limits of the variables are defined by the option
  30 \texttt{\Lkeyword{range}=$xmin$ $xmax$}, and the option \texttt{argument=$n$}
  31 defines the number of points to be plotted when drawing the \Index{curve}.
  32
  33 \begin{LTXexample}[width=7.5cm]
  34 \begin{pspicture}(-3,-3)(4,3.5)%
  35 \psframe*[linecolor=blue!50](-3,-3)(4,3.5)
  36 \psset{lightsrc=50 20 20,viewpoint=50 30 15,Decran=60}
  37 \psset{solidmemory}
  38 \defFunction[algebraic]{1_sin}(x){2*sin(1/x)}{}{}
  39 \psSolid[object=grille,
  40    base=-3 0 -3 3,
  41    linewidth=0.5\pslinewidth,linecolor=gray,]
  42 %% definition du plan de projection
  43 \psSolid[object=plan,
  44    definition=equation,
  45    args={[1 0 0 0] 90},
  46    base=-3.2 3.2 -2.2 2.2,
  47    planmarks,
  48    showBase,
  49    name=monplan]
  50 \psset{plan=monplan}
  51 \psSolid[object=plan,
  52    args=monplan,
  53    linecolor=gray!40,
  54    plangrid,
  55    action=none]
  56 \psProjection[object=courbe,
  57    linecolor=red,
  58    range=-3 3,resolution=720,
  59    function=1_sin]
  60 \composeSolid
  61 \axesIIID(4,2,2)(5,4,3)
  62 \end{pspicture}
  63 \end{LTXexample}
  64
  65 \subsection{\Index{Parameterised curves}}
  66
  67 The technique used here is analogous to the above, with the
  68 difference that the values now come from $\mathbb{R}^2$, and the
  69 object for the macro \Lcs{psProjection} is now \Lkeyword{courbeR2}.
  70
  71 For example, to draw a circle of radius $3$ and centre $O$, we
  72 type:
  73
  74 \begin{verbatim}
  75 \defFunction[algebraic]{cercle}(t){3*cos(t)}{3*sin(t)}{}
  76 \end{verbatim}
  77
  78
  79 Another example: \Index{Lissajous} curves.
  80
  81
  82 \begin{LTXexample}[width=7.5cm]
  83 \begin{pspicture}(-3,-3)(4,3.5)%
  84 \psframe*[linecolor=blue!50](-3,-3)(4,3.5)
  85 \psset{lightsrc=50 20 20,viewpoint=50 30 15,Decran=60}
  86 \psset{solidmemory}
  87 \defFunction[algebraic]{F}(t){2*sin(0.57735*t)}{2*sin(0.707*t)}{}
  88 \psSolid[object=grille,
  89    base=-3 0 -3 3,
  90    linewidth=0.5\pslinewidth,linecolor=gray,]
  91 %% definition du plan de projection
  92 \psSolid[object=plan,
  93    definition=equation,
  94    args={[1 0 0 0] 90},
  95    base=-3.2 3.2 -2.2 2.2,
  96    name=monplan,
  97    planmarks,
  98    showBase]
  99 \psset{plan=monplan}
 100 \psSolid[object=plan,
 101    args=monplan,
 102    linecolor=gray!40,
 103    plangrid,
 104    action=none]
 105 \psProjection[object=courbeR2,
 106    range=-25.12 25.12,resolution=720,
 107    normal=1 1 2,linecolor=red,
 108    function=F]
 109 \composeSolid
 110 \axesIIID(4,2,2)(5,4,3)
 111 \end{pspicture}
 112 \end{LTXexample}
 113
 114 \endinput