1 \section{Curves of real-valued and \Index{parameterised functions}}
3 \subsection{Curve of a real-valued function}
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
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
18 \defFunction[algebraic]{nom_fonction}(x){x*sin(x)}{}{}
22 \defFunction{nom_fonction}(x){x dup sin mul}{}{}
26 \encadre{This expression needs to be included within a
27 \texttt{pspicture} environment.}
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}.
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}
38 \defFunction[algebraic]{1_sin}(x){2*sin(1/x)}{}{}
39 \psSolid[object=grille,
41 linewidth=0.5\pslinewidth,linecolor=gray,]
42 %% definition du plan de projection
46 base=-3.2 3.2 -2.2 2.2,
56 \psProjection[object=courbe,
58 range=-3 3,resolution=720,
61 \axesIIID(4,2,2)(5,4,3)
65 \subsection{\Index{Parameterised curves}}
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}.
71 For example, to draw a circle of radius $3$ and centre $O$, we
75 \defFunction[algebraic]{cercle}(t){3*cos(t)}{3*sin(t)}{}
79 Another example: \Index{Lissajous} curves.
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}
87 \defFunction[algebraic]{F}(t){2*sin(0.57735*t)}{2*sin(0.707*t)}{}
88 \psSolid[object=grille,
90 linewidth=0.5\pslinewidth,linecolor=gray,]
91 %% definition du plan de projection
95 base=-3.2 3.2 -2.2 2.2,
100 \psSolid[object=plan,
105 \psProjection[object=courbeR2,
106 range=-25.12 25.12,resolution=720,
107 normal=1 1 2,linecolor=red,
110 \axesIIID(4,2,2)(5,4,3)