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author | Karl Berry <karl@freefriends.org> | 2010-04-12 17:36:45 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2010-04-12 17:36:45 +0000 |
commit | d68dc2a80b6149839a67b6498294f1b774687157 (patch) | |
tree | b846801b3f2b0a1c6590dda241807d9f38f0e3b8 /Master/texmf-dist/doc/generic/pst-solides3d/doc-src/par-anneaux-en.tex | |
parent | eb5da0fa2dab043786ca8eca9ed5df4453633c4f (diff) |
pst-solides3d 4.18 (11apr10)
git-svn-id: svn://tug.org/texlive/trunk@17821 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/generic/pst-solides3d/doc-src/par-anneaux-en.tex')
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diff --git a/Master/texmf-dist/doc/generic/pst-solides3d/doc-src/par-anneaux-en.tex b/Master/texmf-dist/doc/generic/pst-solides3d/doc-src/par-anneaux-en.tex new file mode 100644 index 00000000000..8a12bc143a6 --- /dev/null +++ b/Master/texmf-dist/doc/generic/pst-solides3d/doc-src/par-anneaux-en.tex @@ -0,0 +1,397 @@ + +\section{Solid rings} + +This paragraph discusses the cylindric \Index{rings}. Within the macro +\Lcs{psSolid}, this object is passed with the option: +\texttt{\Lkeyword{object}=\Lkeyval{anneau}}, that comes with 3 parameters: +\begin{itemize} + \item the inner radius \texttt{\Lkeyword{r}=1.5} (value by default); + \item the outer radius \texttt{\Lkeyword{R}=4} (value by default); + \item the height \texttt{\Lkeyword{h}=6} (value by default). +\end{itemize} + +The argument \Lkeyword{ngrid} defines the number of sections used to make a complete +rotation of $360$~degrees. Its default value is $24$. + +The section of the ring, whose shape is \textit{rectangular} was chosen as default, +and can be redesigned by the user. +We will discuss different examples of sections for rings. + +\subsection{Predefined command: the ring with a rectangular section} + +This section is defined in the plane $Oyz$, it is parameterized with the +triple $(r, R, h)$. The values of the outer radius $R$, inner radius $r$ and the +height $h$ are passed in the macro \Lcs{psSolid}. By default, one has a ring with +a variable rectangular section, and the definition takes place at the time +of the transmission of the values $(r, R, h)$ into the options of \Lcs{psSolid}. + +If the user redefines the \TeX {} macro \verb+\Section+ with some numeric values +instead of the parameters $r$, $R$ and $h$, then +the ring won't be variable anymore and it is not necessary to transmit the +values $r$, $R$, and $h$ into the options of \Lcs{psSolid}. + +\begin{minipage}{0.45\linewidth} +\begin{verbatim} +\newcommand\Section{% +% y z + R h 2 div neg % sommet 1 + % S1 (R,-h/2) + R h 2 div % sommet 2 + % S2 (r,h/2) + r h 2 div % sommet 3 + % S3 (r,h/2) + r h 2 div neg % sommet 4 + % S4 (r,-h/2) + } +\end{verbatim} +\end{minipage} +\hfill +\begin{minipage}{0.45\linewidth} +\psset{unit=0.5} +\begin{pspicture}(-5,-3)(5,3) +\pstVerb{/R 4 def /r 2 def /h 2 def}% +\newcommand\RectangularSection{% + \pspolygon[fillstyle=vlines,linewidth=2\pslinewidth]% + (!R h 2 div neg)(!R h 2 div)(!r h 2 div)(!r h 2 div neg)} +\rput(0,0){\RectangularSection}\rput(-6,0){\RectangularSection} +\psline(-2,1)(2,1)\psline(-2,-1)(2,-1) +\psline[linestyle=dashed,dash=1 0.2 0.05 0.2]{->}(0,-3)(0,3) +\psline[linestyle=dashed]{->}(-4,0)(4.2,0) +\uput[u](0,3){$z$}\uput[r](4.1,0){$y$}\uput[dl](0,0){$O$} +\psline{->}(0,1.5)(2,1.5)\uput[u](1,1.5){$r$} +\psline{->}(0,2.5)(4,2.5)\uput[u](2,2.5){$R$} +\psline{<->}(5,-1)(5,1)\uput[r](5,0){$h$} +\uput[dr](!R h 2 div neg){1} +\uput[ur](!R h 2 div ){2} +\uput[ul](!r h 2 div ){3} +\uput[dl](!r h 2 div neg){4} +\end{pspicture} +\end{minipage} +\newpage +\begin{LTXexample}[width=6cm] +\psset{unit=0.5} +\begin{pspicture}(-5,-4)(5,4) +\psset[pst-solides3d]{viewpoint=50 20 40 rtp2xyz, + Decran=25,lightsrc=10 20 20} +\psSolid[object=anneau,fillcolor=cyan, + h=3,R=8,r=6,ngrid=4,RotX=10](0,0,0) +\end{pspicture}\\ +\begin{pspicture}(-5,-4)(5,4) +\psset[pst-solides3d]{viewpoint=50 -20 -40 rtp2xyz, + Decran=25,lightsrc=-10 -20 -20} +\psSolid[object=anneau, +fillcolor=yellow,h=3,R=8,r=6, +RotX=90,RotZ=10](0,0,0) +\end{pspicture} +\end{LTXexample} + + + +\subsection{Example 1: a simple ring with a triangular section} + +Below is a very simple ring with a fixed triangular section. + The section is defined by $3$~points $(6, -2)$, $(10, 0)$ +and $(6, 2)$ within the option \Lkeyword{section} of \Lcs{psSolid}. + +\begin{LTXexample}[width=6cm] +\psset{unit=0.5} +\begin{pspicture}(-5,-6)(5,6) +\psset[pst-solides3d]{viewpoint=50 20 40 rtp2xyz,Decran=25, + lightsrc=10 20 20} +\psSolid[object=anneau, + section=6 -2 10 0 6 2, + fillcolor=cyan,RotX=10]% +\end{pspicture} +\end{LTXexample} + +%\newpage + +\subsection{Example 2: a ring with a variable triangular section} + +\newcommand\SectionTriangulaire{ + R h 2 div neg % sommet 1 + R r add 2 div h 2 div % sommet 2 + r h 2 div neg % sommet 3 +} + +\begin{minipage}{0.45\linewidth} +\begin{verbatim} +\newcommand\SectionTriangulaire{ +% y <----z----> + R h 2 div neg + % S1 (R,-h/2) + R r add 2 div h 2 div + % S2 ((R+r)/2,h/2) + r h 2 div neg + % S3 (r,-h/2) +} +\end{verbatim} +\end{minipage} +\hfill +\begin{minipage}{0.45\linewidth} +\psset{unit=0.5} +\begin{pspicture}(-5,-3)(5,3) +%\psgrid +\pstVerb{/R 4 def /r 2 def /h 2 def}% +\newcommand\TriangularSection{% + \pspolygon[fillstyle=vlines,linewidth=2\pslinewidth]% + (!R h 2 div neg)(!R r add 2 div h 2 div)(!r h 2 div neg)} +\rput(0,0){\TriangularSection}\rput(-6,0){\TriangularSection} +\psline(-3,1)(3,1)\psline(-4,-1)(4,-1) +\psline[linestyle=dashed,dash=1 0.2 0.05 0.2]{->}(0,-3)(0,3) +\uput[u](0,3){$z$}\uput[r](4.1,0){$y$}\uput[dl](0,0){$O$} +\psline[linestyle=dashed](2,-1)(2,1.5) +\psline[linestyle=dashed](4,-1)(4,2.5) +\psline[linestyle=dashed]{->}(-4,0)(4.2,0) +\psline{->}(0,1.5)(2,1.5)\uput[u](1,1.5){$r$} +\psline{->}(0,2.5)(4,2.5)\uput[u](2,2.5){$R$} +\psline{<->}(5,-1)(5,1)\uput[r](5,0){$h$} +\uput[dr](!R h 2 div neg){1} +\uput[u](!R r add 2 div h 2 div){2} +\uput[dl](!r h 2 div neg){3} +\end{pspicture} +\end{minipage} +\begin{center} +%% +\psset{unit=0.5} +\begin{pspicture}(-5,-6)(5,6) +\psframe(-5,-4)(5,4) +\psset[pst-solides3d]{viewpoint=50 20 40 rtp2xyz,Decran=25,lightsrc=10 20 20} +\psSolid[object=anneau,section=\SectionTriangulaire,fillcolor=cyan,h=3,R=8,r=4,RotX=10]% +\end{pspicture} +%% +\begin{pspicture}(-5,-6)(5,5) +\psframe(-5,-4)(5,4) +\psset[pst-solides3d]{viewpoint=50 -20 -40 rtp2xyz,Decran=25,lightsrc=-10 -20 -20} +\psSolid[object=anneau,section=\SectionTriangulaire,fillcolor=yellow,h=3,R=8,r=4,RotX=-90,RotZ=10]% +\end{pspicture} +\end{center} + +\begin{verbatim} +\psSolid[object=anneau,section=\SectionTriangulaire,% + fillcolor=cyan,h=3,R=8,r=4,RotX=10](0,0,0) +\psSolid[object=anneau,section=\SectionTriangulaire,% + fillcolor=yellow,h=3,R=8,r=4,RotX=-90,RotZ=10](0,0,0) +\end{verbatim} + +%%\newpage + +\newcommand\SectionPneu{ + /m {90 4 div} bind def + /Scos {m cos 2 m mul cos add 3 m mul cos add} bind def + /Z0 {h 4 div} bind def + /c {Z0 Scos div} bind def + /Z1 {Z0 c m cos mul add} bind def + /Z2 {Z1 c m 2 mul cos mul add} bind def + /R1 {R c m sin mul sub} bind def + /R2 {R1 c m 2 mul sin mul sub} bind def + /R3 {R2 c m 3 mul sin mul sub} bind def + R h 4 div neg % 1 + R h 4 div % 2 + R1 Z1 % 3 + R2 Z2 % 4 + R3 h 2 div % 5 + r h 2 div % 6 + r h 2 div neg % 7 + R3 h 2 div neg % 8 + R2 Z2 neg % 9 + R1 Z1 neg % 10 + } + +\subsection{Example 3: a ring with a``tyre''-like section: cylindric ring with chamfered edges} + +\begin{minipage}{0.45\linewidth} +{\small +\begin{verbatim} +\renewcommand\SectionPneu{ + /m {90 4 div} bind def + /Scos {m cos 2 m mul cos add 3 m mul cos add} bind def + /Z0 {h 4 div} bind def + /c {Z0 Scos div} bind def + /Z1 {Z0 c m cos mul add} bind def + /Z2 {Z1 c m 2 mul cos mul add} bind def + /R1 {R c m sin mul sub} bind def + /R2 {R1 c m 2 mul sin mul sub} bind def + /R3 {R2 c m 3 mul sin mul sub} bind def + R h 4 div neg % 1 + R h 4 div % 2 + R1 Z1 % 3 + R2 Z2 % 4 + R3 h 2 div % 5 + r h 2 div % 6 + r h 2 div neg % 7 + R3 h 2 div neg % 8 + R2 Z2 neg % 9 + R1 Z1 neg % 10 + } +\end{verbatim}} +\end{minipage} +\hfill +\begin{minipage}{0.45\linewidth} +%\psset{unit=0.65} +\begin{pspicture}(-2,-3)(5,6) +%\psgrid +\pstVerb{/R 4 def /r 2 def /h 2 def}% +\pstVerb{/m {90 4 div} bind def + /Scos {m cos 2 m mul cos add 3 m mul cos add} bind def + /Z0 {h 4 div} bind def + /c {Z0 Scos div} bind def + /Z1 {Z0 c m cos mul add} bind def + /Z2 {Z1 c m 2 mul cos mul add} bind def + /R1 {R c m sin mul sub} bind def + /R2 {R1 c m 2 mul sin mul sub} bind def + /R3 {R2 c m 3 mul sin mul sub} bind def}% +\pnode(!R h 4 div neg){S1} +\pnode(!R h 4 div){S2} +\pnode(!R1 Z1){S3} +\pnode(!R2 Z2){S4} +\pnode(!R3 h 2 div){S5} +\pnode(!r h 2 div){S6} +\pnode(!r h 2 div neg){S7} +\pnode(!R3 h 2 div neg){S8} +\pnode(!R2 Z2 neg){S9} +\pnode(!R1 Z1 neg){S10} +\newcommand\pneuSection{\pspolygon[fillstyle=vlines,linewidth=2\pslinewidth]% + (S1)(S2)(S3)(S4)(S5)(S6)(S7)(S8)(S9)(S10)} +\rput(0,0){\pneuSection}\rput{180}{\pspolygon[fillstyle=vlines,linewidth=2\pslinewidth]% + (!R h 4 div neg)(!R h 4 div)(!R1 Z1)(!R2 Z2)(!R3 h 2 div)(!r h 2 div)(!r h 2 div neg)(!R3 h 2 div neg)(!R2 Z2 neg)(!R1 Z1 neg)} +\psline(-3,1)(3,1)\psline(-3,-1)(3,-1) +\psline[linestyle=dashed,dash=1 0.2 0.05 0.2]{->}(0,-3)(0,3) +\uput[u](0,3){$z$}\uput[r](4.1,0){$y$}\uput[dl](0,0){$O$} +\psline[linestyle=dashed](2,-1)(2,1.5) +\psline[linestyle=dashed](4,-1)(4,2.5) +\psline[linestyle=dashed]{->}(-4,0)(4.2,0) +\psline{->}(0,1.5)(2,1.5)\uput[u](1,1.5){$r$} +\psline{->}(0,2.5)(4,2.5)\uput[u](2,2.5){$R$} +\psline{<->}(5,-1)(5,1)\uput[r](5,0){$h$} +\uput[r](S1){1} +\uput[r](S2){2} +\uput[u](S3){3} +\uput[u](S4){4} +\uput[u](S5){5} +\uput[ul](S6){6} +\uput[dl](S7){7} +\uput[dl](S8){8} +\uput[dr](S9){9} +\uput[r](S10){10} +\psdots[linecolor=red](S1)(S2)(S3)(S4)(S5)(S6)(S7)(S8)(S9)(S10) +\end{pspicture} +\end{minipage} + +%\iffalse +\begin{center} +\psset{unit=0.7} +\begin{pspicture}(-5,-5)(5,4) +\psframe(-5,-4)(5,4) +\psset[pst-solides3d]{viewpoint=50 20 40 rtp2xyz,Decran=25,lightsrc=10 20 20} +\psSolid[object=anneau,section=\SectionPneu,fillcolor=cyan,h=3,R=8,r=4,RotX=10]% +\end{pspicture} +%% +\begin{pspicture}(-5,-5)(5,4) +\psframe(-5,-4)(5,4) +\psset[pst-solides3d]{viewpoint=50 -20 -40 rtp2xyz,Decran=25,lightsrc=-10 -20 -20} +\psSolid[object=anneau,section=\SectionPneu,fillcolor=yellow,h=3,R=8,r=4,RotX=-90,RotZ=10]% +\end{pspicture} +\end{center} +%% + +\begin{verbatim} +\psSolid[object=anneau,section=\SectionPneu,% + fillcolor=cyan,h=3,R=8,r=4,RotX=10](0,0,0) +\psSolid[object=anneau,section=\SectionPneu,% + fillcolor=yellow,h=3,R=8,r=4,RotX=-90,RotZ=10]% +\end{verbatim} + +%\fi +\newpage + +\subsection{Example 4: an empty bobbin} + +\newcommand\SectionBobine{ + r h 2 div % 1 + r h 2 div neg % 2 + R h 2 div neg % 3 + R h 3 div neg % 4 + R h 4 div sub h 3 div neg % 5 + R h 4 div sub h 3 div % 6 + R h 3 div % 7 + R h 2 div % 8 + } + +\begin{minipage}{0.45\linewidth} +\begin{verbatim} +\newcommand\SectionBobine{ + r h 2 div % 1 + r h 2 div neg % 2 + R h 2 div neg % 3 + R h 3 div neg % 4 + R h 4 div sub h 3 div neg % 5 + R h 4 div sub h 3 div % 6 + R h 3 div % 7 + R h 2 div % 8 + } +\end{verbatim} +\end{minipage} +\hfill +\begin{minipage}{0.45\linewidth} +\begin{pspicture}(-2,-2)(5,2) +\pstVerb{/RB 4 def /rB 2 def /hB 3 def}% +\pnode(!rB hB 2 div){S1} +\pnode(!rB hB 2 div neg){S2} +\pnode(!RB hB 2 div neg){S3} +\pnode(!RB hB 3 div neg){S4} +\pnode(!RB hB 4 div sub hB 3 div neg){S5} +\pnode(!RB hB 4 div sub hB 3 div){S6} +\pnode(!RB hB 3 div){S7} +\pnode(!RB hB 2 div){S8} +\newcommand\pneuSection{\pspolygon[fillstyle=vlines,linewidth=2\pslinewidth]% + (S1)(S2)(S3)(S4)(S5)(S6)(S7)(S8)} +\rput(0,0){\pneuSection}\rput{180}{\pspolygon[fillstyle=vlines,linewidth=2\pslinewidth]% + (!rB hB 2 div)(!rB hB 2 div neg)(!RB hB 2 div neg)(!RB hB 3 div neg)(!RB hB 4 div sub hB 3 div neg)(!RB hB 4 div sub hB 3 div)(!RB hB 3 div)(!RB hB 2 div)} +\psline(-3,1.5)(3,1.5)\psline(-3,-1.5)(3,-1.5) +\psline[linestyle=dashed,dash=1 0.2 0.05 0.2]{->}(0,-3)(0,3) +\uput[u](0,3){$z$}\uput[r](4.1,0){$y$}\uput[dl](0,0){$O$} +\psline[linestyle=dashed](2,-1)(2,1.5) +\psline[linestyle=dashed](4,-1)(4,2.5) +\psline[linestyle=dashed](-4,-1)(4,-1) +\psline[linestyle=dashed](-4,1)(4,1) +\psline[linestyle=dashed]{->}(-4,0)(4.2,0) +\psline{->}(0,1.8)(2,1.8)\uput[u](1,1.8){$r$} +\psline{->}(0,2.5)(4,2.5)\uput[u](2,2.5){$R$} +\psline{<->}(5,-1.5)(5,1.5)\uput[r](5,0){$h$} +\uput[u](S1){1} +\uput[d](S2){2} +\uput[d](S3){3} +\uput[r](S4){4} +\uput[ur](S5){5} +\uput[dr](S6){6} +\uput[r](S7){7} +\uput[r](S8){8} +\psdots[linecolor=red](S1)(S2)(S3)(S4)(S5)(S6)(S7)(S8) +\end{pspicture} +\end{minipage} +\begin{center} +\begin{pspicture}(-5,-6)(5,5) +\psframe*[linecolor=blue!50](-5,-5)(5,4) +\psset[pst-solides3d]{viewpoint=70 40 10 rtp2xyz,Decran=25,lightsrc=0 30 100} +\psSolid[object=grille,base=-15 15 -15 15,fillcolor=yellow!30!black!10](0,0,-8) +%\psSolid[object=prisme,h=2,base=-15 1 -15 -1 15 -1 15 1](0,0,-8) +\psSolid[object=anneau,section=\SectionBobine,fillcolor=gray!50,h=6,R=8,r=4,RotX=90,linecolor=gray]% +\end{pspicture} +\end{center} +\begin{verbatim} +\psSolid[object=grille,base=-15 15 -15 15,fillcolor=yellow!30](0,0,-8) +\psSolid[object=anneau,section=\SectionBobine,% + fillcolor=gray!50,h=6,R=8,r=4,RotX=90,linecolor=gray]% +\end{verbatim} + + + +\subsection{Some other rings} + +Three other examples are available on the website: + +\centerline{\url{http://syracuse.eu.org/lab/bpst/pst-solides3d/anneaux}} + + +\endinput |