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diff --git a/Master/texmf-dist/doc/generic/pst-solides3d/doc/par-courbeR3.tex b/Master/texmf-dist/doc/generic/pst-solides3d/doc/par-courbeR3.tex new file mode 100644 index 00000000000..f4eb5d768f7 --- /dev/null +++ b/Master/texmf-dist/doc/generic/pst-solides3d/doc/par-courbeR3.tex @@ -0,0 +1,202 @@ +\section {Courbes de fonctions de $R$ vers $R^3$} + +%% \section{Fonctions R --> R\textsuperscript{3}} + +Le tracé de la fonction ainsi définie fait appel à l'objet +\Cadre{courbe} et à l'option \Cadre{function}. + +On pourra réaliser le tracé de l'hélice : + +%% \[ +%% \left\{ +%% \begin{array}{lcl} +%% x&=&3\cos(4t)\\ +%% y&=&3\sin(4t)\\ +%% z&=&t +%% \end{array} +%% \right. +%% \] +en notation algébrique avec la fonction : + +%%\begin{boxedverbatim} +\begin{verbatim} +\defFunction[algebraic]{helice}(t){3*cos(4*t)}{3*sin(4*t)}{t} +\end{verbatim} +%%\end{boxedverbatim} + +%\defFunction[algebraic]{f}(t){t}{(t^2)/10-1}{} +\begin{minipage}{0.4\linewidth} +\psset{unit=0.5} +\psset{lightsrc=10 -20 50,viewpoint=50 -20 20 rtp2xyz,Decran=50} +\begin{pspicture}(-6,-3)(6,8) +\psframe*[linecolor=blue!50](-6,-3)(6,8) +\psSolid[object=grille,base=-4 4 -4 4,linecolor=red,linewidth=0.5\pslinewidth]% +\axesIIID(0,0,0)(4,4,7) +\defFunction[algebraic]{helice}(t){3*cos(4*t)}{3*sin(4*t)}{t} +\psSolid[object=courbe, + r=0, + range=0 6, + linecolor=blue,linewidth=0.1, + resolution=360, + function=helice]% +\end{pspicture} +\end{minipage} +\hfill +\begin{minipage}{0.55\linewidth} +%%\begin{boxedverbatim} +\begin{verbatim} +\defFunction[algebraic]% + {helice}(t){cos(3*t)}{sin(3*t)}{t} +\psSolid[object=courbe, + range=0 6, + r=0, + linecolor=blue, + resolution=360, + function=helice]% +\end{verbatim} +%%\end{boxedverbatim} +\end{minipage} + +\begin{minipage}{0.4\linewidth} +\psset{unit=0.5} +\begin{pspicture}(-6,-3)(6,8) +\psframe*[linecolor=blue!50](-6,-3)(6,8) +\psset{lightsrc=10 -20 50,viewpoint=50 -20 30 rtp2xyz,Decran=50} +\psSolid[object=grille,base=-4 4 -4 4,linecolor=red,linewidth=0.5\pslinewidth]% +\axesIIID(0,0,0)(4,4,7) +\psset{range=-4 4} +\defFunction{CosRad}(t){t 2 mul Cos 4 mul}{t}{0} +\psSolid[object=courbe,linewidth=0.1, + r=0, + linecolor=red, + resolution=360, + function=CosRad]% +\psSolid[object=grille,base=-4 4 -4 4,linecolor=blue,linewidth=0.5\pslinewidth](0,0,3) +\psPoint(0,0,3){O1}\psPoint(0,0,7){Z1}\psline(O1)(Z1)\psline[linestyle=dashed](O1)(O) +\pstVerb{/tmin -4 def /tmax 4 def}% +\defFunction{sinRad}(t){t}{t Sin 3 mul}{3} +\psSolid[object=courbe,linewidth=0.1, + r=0, + linecolor=blue, + resolution=30, + function=sinRad]% +\end{pspicture} +\end{minipage} +\hfill +\begin{minipage}{0.55\linewidth} +%%\begin{boxedverbatim} +\begin{verbatim} +\psset{range=-4 4} +\psSolid[object=grille,base=-4 4 -4 4]% +\defFunction{CosRad}(t){t 2 mul Cos 4 mul}{t}{0} +\psSolid[object=courbe,linewidth=0.1, + r=0, + linecolor=red, + resolution=360, + function=CosRad]% +\defFunction{sinRad}(t){t}{t Sin 3 mul}{3} +\psSolid[object=grille,base=-4 4 -4 4](0,0,3) +\psSolid[object=courbe, + r=0, + linecolor=blue, + resolution=360, + function=sinRad] +\end{verbatim} +%%\end{boxedverbatim} +\end{minipage} + +\begin{minipage}{0.4\linewidth} +\psset{unit=0.5} +\begin{pspicture}(-5,0)(7,9) +\psset{lightsrc=10 -20 50,viewpoint=50 -20 20 rtp2xyz,Decran=50} +\psSolid[object=grille,base=-4 4 -4 4,linecolor=lightgray,linewidth=0.5\pslinewidth]% +\psSolid[object=grille,base=-4 4 0 8,linecolor=lightgray,RotX=90,linewidth=0.5\pslinewidth](0,4,0) +\psSolid[object=grille,base=-4 4 -4 4,linecolor=lightgray,RotY=90,linewidth=0.5\pslinewidth](-4,0,4) +\defFunction[algebraic]{helice}% +(t){1.3*(1-cos(2.5*t))*cos(6*t)}{1.3*(1-cos(2.5*t))*sin(6*t)}{t} +\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} +\defFunction[algebraic]{helice_xz}(t){1.3*(1-cos(2.5*t))*cos(6*t)}{4}{t} +\defFunction[algebraic]{helice_yz}(t){-4}{1.3*(1-cos(2.5*t))*sin(6*t)}{t} +\psset{range=0 8} +\psSolid[object=courbe, + r=0, + linecolor=blue, + linewidth=0.05, + resolution=360, + normal=0 0 1, + function=helice_xy]% +\psSolid[object=courbe, + r=0, + linecolor=green, + linewidth=0.05, + resolution=360, + normal=0 0 1, + function=helice_xz]% +\psSolid[object=courbe, + r=0, + linewidth=0.05, + resolution=360, + normal=0 0 1, + function=helice_yz]% +\psSolid[object=courbe, + r=0, + linecolor=red, + linewidth=0.1, + resolution=360, + function=helice]% + \end{pspicture} +\end{minipage} +\hfill +\begin{minipage}{0.55\linewidth} +\footnotesize +%%\begin{boxedverbatim} +\begin{verbatim} +\psSolid[object=grille,base=-4 4 -4 4]% +\psSolid[object=grille,base=-4 4 0 8](0,4,0) +\psSolid[object=grille,base=-4 4 -4 4](-4,0,4) +\defFunction[algebraic]{helice}% + (t){1.3*(1-cos(2.5*t))*cos(6*t)} + {1.3*(1-cos(2.5*t))*sin(6*t)}{t} +\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} +\defFunction[algebraic]{helice_xz}% + (t){1.3*(1-cos(2.5*t))*cos(6*t)}{4}{t} +\defFunction[algebraic]{helice_yz}% + (t){-4}{1.3*(1-cos(2.5*t))*sin(6*t)}{t} +\psset{range=0 8} +\psSolid[object=courbe, + r=0, + linecolor=blue, + linewidth=0.05, + resolution=360, + normal=0 0 1, + function=helice_xy]% +\psSolid[object=courbe, + r=0, + linecolor=green, + linewidth=0.05, + resolution=360, + normal=0 0 1, + function=helice_xz]% +\psSolid[object=courbe, + r=0, + linewidth=0.05, + resolution=360, + normal=0 0 1, + function=helice_yz]% +\psSolid[object=courbe, + r=0, + linecolor=red, + linewidth=0.1, + resolution=360, + function=helice]% +\end{verbatim} +%%\end{boxedverbatim} +\end{minipage} + +Ces dernières courbes se trouvent sous forme d'animations sur la page : + +\centerline{\url{http://melusine.eu.org/syracuse/pstricks/pst-solides3d/animations/}} + + |