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-\section{Generalization of the notion of a cylinder and a cone}
-
-\subsection{Cylinder or \Index{cylindric area}}
-
-This paragraph generalizes the notion of a cylinder, or a cylindric
-area\footnote{This was written by
-Maxime \textsc{Chupin}, as a result of a question on the list
-\url{http://melusine.eu.org/cgi-bin/mailman/listinfo/syracuse}}.
-A \textit{routing} curve has to be defined by a function and the
-direction of the \textit{cylinder} axis needs to be arranged. In
-the example below the routing curve is sinusoidal, situated in the plane $z=-2$:
-\begin{verbatim}
-\defFunction[algebraic]{G1}(t){t}{2*sin(t)}{-2}
-\end{verbatim}
-The direction of the cylinder is defined by the components of a vector
-\texttt{\Lkeyword{axe}=0 1 1}. The drawing calls \Lkeyword{object}=\Lkeyval{cylindre} which
-in addition to the usual parameters---which is the height \texttt{\Lkeyword{h}=4}---
-is about the \textbf{length of the generator} and not of the distance
-between the two base planes, and needs to define the routing curve
-\texttt{\Lkeyword{function}=G1} and the interval of the variable $t$ \texttt{\Lkeyword{range}=-3 3}.
-
-\begin{verbatim}
-\psSolid[object=cylindre,
- h=4,function=G1,
- range=-3 3,
- ngrid=3 16,
- axe=0 1 1,
- incolor=green!50,
- fillcolor=yellow!50]
-\end{verbatim}
-
-
-\begin{center}
-\psset{unit=0.75}
-\begin{pspicture}(-5,-4)(5,4)
-\psset{lightsrc=viewpoint,viewpoint=100 10 20 rtp2xyz,Decran=100}
-\psSolid[object=grille,base=-4 4 -6 6,linecolor={[rgb]{0.72 0.72 0.5}},action=draw](0,0,-2)
-\defFunction[algebraic]{G1}(t){t}{2*sin(t)}{-2}
-\defFunction[algebraic]{G2}(t){t}{2*sin(t)+4}{2}
-\psSolid[object=courbe,function=G1,
- range=-3 3,r=0,
- linecolor=blue,
- linewidth=2pt]
-\psSolid[object=cylindre,
- h=5.65685,function=G1,
- range=-3 3,
- ngrid=3 16,
- axe=0 1 1,
- incolor=green!50,
- fillcolor=yellow!50]
-\psSolid[object=courbe,function=G2,
- range=-3 3,r=0,
- linecolor=blue,
- linewidth=2pt]
-\psSolid[object=parallelepiped,
- a=8,b=12,c=4,action=draw](0,0,0)
-\psSolid[object=plan,action=draw,
- definition=equation,
- args={[0 0 1 -2] 90},
- base=-6 6 -4 4,planmarks,showBase]
-\psSolid[object=plan,action=draw,
- definition=equation,
- args={[0 1 0 -6] 180},
- base=-4 4 -2 2,planmarks,showBase]
-\psSolid[object=plan,action=draw,
- definition=equation,
- args={[1 0 0 -4] 90},
- base=-6 6 -2 2,planmarks,showBase]
-\psSolid[object=vecteur,
- linecolor=red,
- args=0 3 3]
-\end{pspicture}
-\end{center}
-
-In the following example, before drawing the horizontal planes, we calculate the
-distance between these two planes.
-
- \begin{verbatim}
-\pstVerb{/ladistance 2 sqrt 2 mul def}
- \end{verbatim}
-
-{\psset{unit=0.75,lightsrc=viewpoint,viewpoint=100 -10 20 rtp2xyz,Decran=100}
-\begin{LTXexample}[pos=t]
-\begin{pspicture}(-1.5,-3)(6.5,6)
-\psSolid[object=grille,base=-3 3 -1 8,action=draw]
-\pstVerb{/ladistance 2 sqrt 2 mul def}
-\defFunction[algebraic]{G3}(t){6*(cos(t))^3*sin(t)}{4*(cos(t))^2}{0}
-\defFunction[algebraic]{G4}(t){6*(cos(t))^3*sin(t)}{4*(cos(t))^2+ladistance}{ladistance}
-\psSolid[object=courbe,function=G3,range=0 6.28,r=0,linecolor=blue,linewidth=2pt]
-\psSolid[object=cylindre,range=0 -6.28,h=4,function=G3,axe=0 1 1,ngrid=3 36,
- fillcolor=green!50,incolor=yellow!50]
-\psSolid[object=courbe,function=G4,range=0 6.28,r=0,linecolor=blue,linewidth=2pt]
-\psSolid[object=vecteur,linecolor=red,args=0 ladistance dup]
-\psSolid[object=plan,action=draw,definition=equation,args={[0 0 1 ladistance neg] 90},
- base=-1 8 -3 3,planmarks,showBase]
-\axesIIID(0,4.5,0)(4,8,5)
-\rput(0,-3){\texttt{axe=0 1 1}}
-\end{pspicture}
-\end{LTXexample}}
-
-
-\begin{LTXexample}[width=8cm]
-\psset{unit=0.75,lightsrc=viewpoint,
- viewpoint=100 -10 20 rtp2xyz,Decran=100}
-\begin{pspicture}(-1.5,-3)(6.5,6)
-\psSolid[object=grille,base=-3 3 -1 6,action=draw]
-\defFunction[algebraic]{G5}(t)
- {t}{0.5*t^2}{0}
-\defFunction[algebraic]{G6}(t)
- {t}{0.5*t^2}{4}
-\psSolid[object=courbe,function=G5,
- range=-3 2,r=0,linecolor=blue,
- linewidth=2pt]
-\psSolid[object=cylindre,
- range=-3 2,h=4,
- function=G5,
- axe=0 0 1, %% valeur par d\'{e}faut
- incolor=green!50,
- fillcolor=yellow!50,
- ngrid=3 8]
-\psSolid[object=courbe,function=G6,
- range=-3 2,r=0,linecolor=blue,
- linewidth=2pt]
-\axesIIID(0,4.5,0)(4,6,5)
-\psSolid[object=vecteur,
- linecolor=red,args=0 0 4]
-\psSolid[object=plan,action=draw,
- definition=equation,
- args={[0 0 1 -4] 90},
- base=-1 6 -3 3,planmarks,showBase]
-\end{pspicture}
-\end{LTXexample}
-
-\begin{LTXexample}[width=8cm]
-\psset{unit=0.75,lightsrc=viewpoint,
- viewpoint=100 -10 20 rtp2xyz,Decran=100}
-\begin{pspicture}(-3.5,-3)(6.5,6)
-\psset{lightsrc=viewpoint,viewpoint=100 45 45,Decran=100}
-\psSolid[object=grille,base=-3 3 -2 7,fillcolor=gray!30]
-\defFunction[algebraic]{G7}(t)
- {2*cos(t)}{2*sin(t)}{0}
-\defFunction[algebraic]{G8}(t)
- {2*cos(t)}{2*sin(t)+4}{4}
-\psSolid[object=courbe,function=G7,
- range=0 6.28,r=0,
- linecolor=blue,linewidth=2pt]
-\psSolid[object=cylindre,
- range=0 6.28,h=5.65685,
- function=G7,axe=0 1 1,
- incolor=green!20,
- fillcolor=yellow!50,
- ngrid=3 36]
-\psSolid[object=courbe,function=G8,
- range=0 6.28,r=0,linecolor=blue,
- linewidth=2pt]
-\axesIIID(2,4.5,2)(4,8,5)
-\psSolid[object=vecteur,
- linecolor=red,args=0 1 1](0,4,4)
-\psSolid[object=plan,action=draw,
- definition=equation,
- args={[0 0 1 -4] 90},
- base=-2 7 -3 3,planmarks,showBase]
-\end{pspicture}
-\end{LTXexample}
-
-
-\encadre{The routing curve can be any curve and need not necessarily be a plane horizontal.}
-
-\begin{LTXexample}[width=8cm]
-\begin{pspicture}(-3.5,-2)(4,5)
-\psset{unit=0.75,lightsrc=viewpoint,viewpoint=100 -5 10 rtp2xyz,Decran=100}
-\psSolid[object=grille,base=-4 4 -4 4,ngrid=8. 8.](0,0,-1)
-\defFunction[algebraic]{G9}(t)
- {3*cos(t)}{3*sin(t)}{1*cos(5*t)}
-\psSolid[object=cylindre,
- range=0 6.28,h=5,function=G9,
- axe=0 0 1,incolor=green!50,
- fillcolor=yellow!50,
- ngrid=4 72,grid]
-\end{pspicture}
-\end{LTXexample}
-
-\subsection{Cone or \Index{conic area}}
-This paragraph generalizes the notion of a cone, or a conic
-area\footnote{This was written by
-Maxime \textsc{Chupin}, as the result of a question on the list
-\url{http://melusine.eu.org/cgi-bin/mailman/listinfo/syracuse}}.
-A \textit{routing} curve needs to be defined by a function which
-defines the base of the cone, and the vertex of the \textit{cone}
-which is by default \texttt{\Lkeyword{origine}=0 0 0}. The parts above and
-below the cone are symmetric concerning the vertice. In the example
-below, the routing curve is a parabolic arc, situated in the plane $z=-2$.
-
-\begin{LTXexample}[width=7.5cm]
-\begin{pspicture}(-3,-4)(4.5,6)
-\psset{unit=0.75,lightsrc=viewpoint,viewpoint=100 10 10 rtp2xyz,Decran=100}
-\psSolid[object=grille,base=-4 4 -3 3,action=draw](0,0,-2)
-\defFunction[algebraic]{G1}(t){t}{0.25*t^2}{-2}
-\defFunction[algebraic]{G2}(t){-t}{-0.25*t^2}{2}
-\psSolid[object=courbe,function=G1,
- range=-3.46 3,r=0,
- linecolor=blue,linewidth=2pt]
-\psSolid[object=cone,function=G1,
- range=-3.46 3,ngrid=3 16,
- incolor=green!50,
- fillcolor=yellow!50,
- origine=0 0 0]
-\psSolid[object=courbe,
- function=G2,range=-3.46 3,
- r=0,linecolor=blue,
- linewidth=2pt]
-\psPoint(0,0,0){I}
-\uput[l](I){\red$(0,0,0)$}
-\psdot[linecolor=red](I)
-\gridIIID[Zmin=-2,Zmax=2,spotX=r](-4,4)(-3,3)
-\end{pspicture}
-\end{LTXexample}
-
-\begin{LTXexample}[width=7.5cm]
-\begin{pspicture}(-3,-4)(4.5,6)
-\psset{unit=0.7,lightsrc=viewpoint,viewpoint=100 -10 20 rtp2xyz,Decran=100}
-\psSolid[object=grille,base=-4 4 -3 3,
- linecolor={[rgb]{0.72 0.72 0.5}},action=draw](0,0,-2)
-\defFunction[algebraic]{G1}(t){t}{2*sin(t)}{-2}
-\defFunction[algebraic]{G2}(t){-t}{-2*sin(t)}{2}
-\psSolid[object=courbe,function=G1,
- range=-3.14 3.14,r=0,
- linecolor=blue,
- linewidth=2pt]
-\psSolid[object=cone,function=G1,
- range=-3.14 3.14,ngrid=3 16,
- incolor=green!50,
- fillcolor=yellow!50,
- origine=0 0 0]
-\psSolid[object=courbe,
- function=G2,range=-3.14 3.14,
- r=0,linecolor=blue,
- linewidth=2pt]
-\psPoint(0,0,0){I} \uput[l](I){\red$(0,0,0)$}
-\psdot[linecolor=red](I)
-\gridIIID[Zmin=-2,Zmax=2,spotX=r](-4,4)(-3,3)
-\end{pspicture}
-\end{LTXexample}
-
-\begin{LTXexample}[width=7.5cm]
-\begin{pspicture}(-3,-4)(4.5,6)
-\psset{unit=0.7,lightsrc=viewpoint,viewpoint=100 -10 20 rtp2xyz,Decran=100}
-\psSolid[object=grille,base=-4 4 -4 4,linecolor={[rgb]{0.72 0.72 0.5}},action=draw](0,0,-2)
-\defFunction[algebraic]{G1}(t){t}{2*sin(t)}{-2}
-\defFunction[algebraic]{G2}(t){-t}{-2*sin(t)-2}{2}
-\psSolid[object=courbe,function=G1,
- range=-3.14 3.14,r=0,
- linecolor=blue,
- linewidth=2pt]
-\psSolid[object=cone,
- function=G1,range=-3.14 3.14,
- ngrid=3 16,incolor=green!50,
- fillcolor=yellow!50,
- origine=0 -1 0]
-\psSolid[object=courbe,
- function=G2,range=-3.14 3.14,
- r=0,linecolor=blue,
- linewidth=2pt]
-\psPoint(0,-1,0){I}\uput[l](I){\red$(0,-1,0)$}
-\psdot[linecolor=red](I)
-\gridIIID[Zmin=-2,Zmax=2,spotX=r](-4,4)(-4,4)
-\end{pspicture}
-\end{LTXexample}
-
-\encadre{For the cones as well, the routing curve can be any curve and need not necessarily
-be a plane horizontal curve, as the following example, written by Maxime
-\textsc{Chupin}, will show.}
-
-\centerline{\url{http://melusine.eu.org/lab/bpst/pst-solides3d/cone/cone-dir_02.pst}}
-
-\endinput