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diff --git a/Master/texmf-dist/doc/generic/pst-solides3d/text/par-cylindres-cones-en.tex b/Master/texmf-dist/doc/generic/pst-solides3d/text/par-cylindres-cones-en.tex new file mode 100644 index 00000000000..4a8330bbccb --- /dev/null +++ b/Master/texmf-dist/doc/generic/pst-solides3d/text/par-cylindres-cones-en.tex @@ -0,0 +1,276 @@ +\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 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.} + +\url{http://melusine.eu.org/lab/bpst/pst-solides3d/cone/cone-dir_02.pst} + +\endinput |