1 \section {Courbes de fonctions de $R$ vers $R^3$}
3 %% \section{Fonctions R --> R\textsuperscript{3}}
5 Le tracé de la fonction ainsi définie fait appel à l'objet
6 \Cadre{courbe} et à l'option \Cadre{function}.
8 On pourra réaliser le tracé de l'hélice :
19 en notation algébrique avec la fonction :
21 %%\begin{boxedverbatim}
23 \defFunction[algebraic]{helice}(t){3*cos(4*t)}{3*sin(4*t)}{t}
27 %\defFunction[algebraic]{f}(t){t}{(t^2)/10-1}{}
28 \begin{minipage}{0.4\linewidth}
30 \psset{lightsrc=10 -20 50,viewpoint=50 -20 20 rtp2xyz,Decran=50}
31 \begin{pspicture}(-6,-3)(6,8)
32 \psframe*[linecolor=blue!50](-6,-3)(6,8)
33 \psSolid[object=grille,base=-4 4 -4 4,linecolor=red,linewidth=0.5\pslinewidth]%
34 \axesIIID(0,0,0)(4,4,7)
35 \defFunction[algebraic]{helice}(t){3*cos(4*t)}{3*sin(4*t)}{t}
36 \psSolid[object=courbe,
39 linecolor=blue,linewidth=0.1,
45 \begin{minipage}{0.55\linewidth}
46 %%\begin{boxedverbatim}
48 \defFunction[algebraic]%
49 {helice}(t){cos(3*t)}{sin(3*t)}{t}
50 \psSolid[object=courbe,
60 \begin{minipage}{0.4\linewidth}
62 \begin{pspicture}(-6,-3)(6,8)
63 \psframe*[linecolor=blue!50](-6,-3)(6,8)
64 \psset{lightsrc=10 -20 50,viewpoint=50 -20 30 rtp2xyz,Decran=50}
65 \psSolid[object=grille,base=-4 4 -4 4,linecolor=red,linewidth=0.5\pslinewidth]%
66 \axesIIID(0,0,0)(4,4,7)
68 \defFunction{CosRad}(t){t 2 mul Cos 4 mul}{t}{0}
69 \psSolid[object=courbe,linewidth=0.1,
74 \psSolid[object=grille,base=-4 4 -4 4,linecolor=blue,linewidth=0.5\pslinewidth](0,0,3)
75 \psPoint(0,0,3){O1}\psPoint(0,0,7){Z1}\psline(O1)(Z1)\psline[linestyle=dashed](O1)(O)
76 \pstVerb{/tmin -4 def /tmax 4 def}%
77 \defFunction{sinRad}(t){t}{t Sin 3 mul}{3}
78 \psSolid[object=courbe,linewidth=0.1,
86 \begin{minipage}{0.55\linewidth}
87 %%\begin{boxedverbatim}
90 \psSolid[object=grille,base=-4 4 -4 4]%
91 \defFunction{CosRad}(t){t 2 mul Cos 4 mul}{t}{0}
92 \psSolid[object=courbe,linewidth=0.1,
97 \defFunction{sinRad}(t){t}{t Sin 3 mul}{3}
98 \psSolid[object=grille,base=-4 4 -4 4](0,0,3)
99 \psSolid[object=courbe,
105 %%\end{boxedverbatim}
108 \begin{minipage}{0.4\linewidth}
110 \begin{pspicture}(-5,0)(7,9)
111 \psset{lightsrc=10 -20 50,viewpoint=50 -20 20 rtp2xyz,Decran=50}
112 \psSolid[object=grille,base=-4 4 -4 4,linecolor=lightgray,linewidth=0.5\pslinewidth]%
113 \psSolid[object=grille,base=-4 4 0 8,linecolor=lightgray,RotX=90,linewidth=0.5\pslinewidth](0,4,0)
114 \psSolid[object=grille,base=-4 4 -4 4,linecolor=lightgray,RotY=90,linewidth=0.5\pslinewidth](-4,0,4)
115 \defFunction[algebraic]{helice}%
116 (t){1.3*(1-cos(2.5*t))*cos(6*t)}{1.3*(1-cos(2.5*t))*sin(6*t)}{t}
117 \defFunction[algebraic]{helice_xy}(t){1.3*(1-cos(2.5*t))*cos(6*t)}{1.3*(1-cos(2.5*t))*sin(6*t)}{0}
118 \defFunction[algebraic]{helice_xz}(t){1.3*(1-cos(2.5*t))*cos(6*t)}{4}{t}
119 \defFunction[algebraic]{helice_yz}(t){-4}{1.3*(1-cos(2.5*t))*sin(6*t)}{t}
121 \psSolid[object=courbe,
128 \psSolid[object=courbe,
135 \psSolid[object=courbe,
141 \psSolid[object=courbe,
150 \begin{minipage}{0.55\linewidth}
152 %%\begin{boxedverbatim}
154 \psSolid[object=grille,base=-4 4 -4 4]%
155 \psSolid[object=grille,base=-4 4 0 8](0,4,0)
156 \psSolid[object=grille,base=-4 4 -4 4](-4,0,4)
157 \defFunction[algebraic]{helice}%
158 (t){1.3*(1-cos(2.5*t))*cos(6*t)}
159 {1.3*(1-cos(2.5*t))*sin(6*t)}{t}
160 \defFunction[algebraic]{helice_xy}%
161 (t){1.3*(1-cos(2.5*t))*cos(6*t)}
162 {1.3*(1-cos(2.5*t))*sin(6*t)}{0}
163 \defFunction[algebraic]{helice_xz}%
164 (t){1.3*(1-cos(2.5*t))*cos(6*t)}{4}{t}
165 \defFunction[algebraic]{helice_yz}%
166 (t){-4}{1.3*(1-cos(2.5*t))*sin(6*t)}{t}
168 \psSolid[object=courbe,
175 \psSolid[object=courbe,
182 \psSolid[object=courbe,
188 \psSolid[object=courbe,
195 %%\end{boxedverbatim}
198 Ces dernières courbes se trouvent sous forme d'animations sur la page :
200 \centerline{\url{http://melusine.eu.org/syracuse/pstricks/pst-solides3d/animations/}}