From 9eee0699194e5bdd4a8c0bf41e27b29bc3648559 Mon Sep 17 00:00:00 2001 From: Jean-Michel Sarlat Date: Wed, 19 Oct 2011 21:59:11 +0200 Subject: [PATCH] =?utf8?q?Cr=C3=A9ation=20du=20dossier=20=20avec=20psftopst=20dedans...?= MIME-Version: 1.0 Content-Type: text/plain; charset=utf8 Content-Transfer-Encoding: 8bit --- GILGTEST/eiffel.eps | 2715 ----------------------- GILGTEST/index.xml | 3 - GILGTEST/pst-anamorphosis-doc-part1.pdf | Bin 474646 -> 0 bytes GILGTEST/pst-anamorphosis-doc-part1.tex | 1052 --------- GILGTEST/pst-anamorphosis-doc-part2.pdf | Bin 896879 -> 0 bytes GILGTEST/pst-anamorphosis-doc-part2.tex | 623 ------ GILGTEST/pst-anamorphosis.eps | 912 -------- opt/index.xml | 3 + opt/psftopst.pl | 347 +++ opt/pstopst | 347 +++ 10 files changed, 697 insertions(+), 5305 deletions(-) delete mode 100644 GILGTEST/eiffel.eps delete mode 100644 GILGTEST/index.xml delete mode 100644 GILGTEST/pst-anamorphosis-doc-part1.pdf delete mode 100644 GILGTEST/pst-anamorphosis-doc-part1.tex delete mode 100644 GILGTEST/pst-anamorphosis-doc-part2.pdf delete mode 100644 GILGTEST/pst-anamorphosis-doc-part2.tex delete mode 100644 GILGTEST/pst-anamorphosis.eps create mode 100644 opt/index.xml create mode 100755 opt/psftopst.pl create mode 100755 opt/pstopst diff --git a/GILGTEST/eiffel.eps b/GILGTEST/eiffel.eps deleted file mode 100644 index d8a6e82..0000000 --- a/GILGTEST/eiffel.eps +++ /dev/null @@ -1,2715 +0,0 @@ -%!PS-Adobe-3.0 -%%Title: flattened PostScript generated from file: effel4.eps -%%Creator: pstoedit -%%BoundingBox: (atend) -%%Pages: (atend) -%%EndComments -%%BeginProlog -/setPageSize { pop pop } def -/ntranslate { neg exch neg exch translate } def -/p2esetcolorname { pop } def -/setshowparams { pop pop pop} def -/awidthshowhex { dup length 0 gt { dup /ASCIIHexDecode filter exch length 2 div cvi string readstring pop } if awidthshow } def -/awidthshowhexwithglyphs { true { pop awidthshowhex } { { glyphshow } forall pop } ifelse } def -/backendconstraints { pop pop } def -/pstoedit.newfont { 80 string cvs findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def dup 80 string cvs /FontName exch def currentdict end definefont pop } def -/imagestring 1 string def -%%EndProlog -%%BeginSetup -% pstoedit.textastext pstoedit.doflatten backendconstraints -1 0 backendconstraints -%%EndSetup -%%Page: 1 1 - 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-\pstPutAbs(2.5,-3.75){% -\includegraphics[scale=1]{pst-anamorphosis} -} -\pstPutAbs(2.5,-5.25){% -\LARGE \textbf{\syracuseTitle} -} -\pstPutAbs(2.5,-13.5){% -\begin{pspicture}(0,0)(8,8) -\rput(4,4){\includegraphics[height=8cm]{eiffel}} -%\rput(4,4){\includegraphics[height=8cm]{\syracuseGraphic}} -%\psframe(0,0)(8,8) -\end{pspicture} -} -\pstPutAbs(12.5,-15){% -\parbox{0.4\textwidth}{\Large\raggedleft - {\LARGE\textbf{Contributeurs}}\\[0.2cm] - J\"{u}rgen \textsc{Gilg}\\ - Manuel \textsc{Luque}\\ - Jean-Michel \textsc{Sarlat} -}} -\vfill -\begin{center} -\textcolor{white}{\textbf{\today}}\\[0.3cm] -\textcolor{white}{\url{http://melusine.eu.org/syracuse/G/pstricks/}}\\ -\includegraphics[scale=0.4]{logo_syracuse} -\end{center} - -%% == END == Page de garde ==================================================== - -\newpage - -\section{L'anamorphose cylindrique} - -On place \`{a} l'int\'{e}rieur du cylindre l'image telle qu'elle doit \^{e}tre vue par un observateur regardant dans le miroir cylindrique (on peut la placer \`{a} l'ext\'{e}rieur, mais il faut que les rayons lumineux rencontrent toujours le cylindre, il faut donc veiller aux dimensions). L'objet anamorphique est <<~l'objet d\'{e}form\'{e}~>> dont le miroir reconstituera les proportions r\'{e}elles. - -Objet et image ob\'{e}issent aux lois de la r\'{e}flexion de l'optique g\'{e}om\'{e}trique : -\begin{itemize} - \item rayon incident et rayon r\'{e}fl\'{e}chi appartiennent \`{a} un m\^{e}me plan ; - \item rayon incident et rayon r\'{e}fl\'{e}chi sont sym\'{e}triques par rapport \`{a} la normale au miroir au point d'incidence. -\end{itemize} - -\def\oeil{\psarc[linewidth=2pt](0,2.5){2.5}{215}{270}% -\psarc[linewidth=2pt](0,-2.5){2.5}{90}{140}% -\psarc(-2.5,0){1}{-30}{30}% -\psarc(0,0){1.75}{160}{200} -\psclip{% -\pscircle[linestyle=none](0,0){1.75}} -\pscircle[fillstyle=solid,fillcolor=lightgray](-2.5,0){0.9} -\endpsclip}% -\begin{center} -\psscalebox{0.7}{ -\begin{pspicture}(-2,-6)(15,6) -\psset{Xv=0,Yv=-100} -\newcommand\Rmirror{3} -\psset{viewpoint=-1 -1 1} -\ThreeDput[normal=0 0 1](0,0,0){% -\psaxes{->}(8,4) -\pscircle[doubleline=true]{\Rmirror} -\multido{\i=-2+1,\I=-2+1}{5}{% - \pnode(! \i\space -2){A} - \pnode(! \i\space 2){B} - \psline(A)(B) - \pslineA(A)(B) - \pnode(!-2 \I){A} - \pnode(!2 \I){B} - \pslineA(A)(B) - \psline(A)(B) - } -\input{LouisXIII.pst} -\input{ALouisXIII.pst} -\pstextA[fontsize=28,linecolor=red,fillstyle=solid,fillcolor=yellow!50](0,2){LouisXIII} - } -\FPmul{\largeur}{\Rmirror}{0.1745} -\newcount\n \n=135 - \loop - \FPmul{\tempa}{\FPpi}{\the\n} - \FPdiv{\angle}{\tempa}{180} - \FPsin{\SIN}{\angle}\FPcos{\COS}{\angle} - \FPmul{\xc}{\COS}{\Rmirror} - \FPmul{\yc}{\SIN}{\Rmirror} - \ThreeDput[normal={\COS} {\SIN} 0.0001](\xc,\yc,0){% - \psframe[fillstyle=vlines,hatchangle=0,linestyle=none,hatchcolor=BleuCiel,](0,0)(\largeur,5)} - \ifnum\n<315 \advance\n by 10 -\repeat -\ThreeDput[normal=0.707 -0.707 0.001](2.121,-2.121,0){% -\psline[linewidth=2\pslinewidth](0,5)} -\ThreeDput[normal=0.707 -0.707 0.001](-2.121,2.121,0){% -\psline[linewidth=2\pslinewidth](0,5)} -\ThreeDput[normal=0 0 1](0,0,5){% -\pscircle[doubleline=true]{\Rmirror} -} -\ThreeDput[normal=-1 0 0](0,0,0){% -\psaxes(15,5) -\rput{26.5}(21.5,10.8){\oeil} -\psline[linestyle=dashed,linecolor=blue](20,10)% -\psset{arrowsize=0.5,linecolor=red,linewidth=2\pslinewidth} -\psline{->}(3,1.5)(10,5) -\psline(3,1.5)(20,10) -\psline{->}(6,0)(4.5,0.75) -\psline(6,0)(3,1.5) -\uput[ur](20,10){\color{red}{$V$}} -\uput[u](3,1.5){\color{red}{$I$}} -\uput[u](6,0){\color{red}{$P'$}} -} -\end{pspicture} -} -\end{center} -L'image non d\'{e}form\'{e}e (celle qui est vue dans le miroir) est plac\'{e}e, dans cet exemple, au centre du miroir. Un rayon incident partant de l'objet anamorphique se r\'{e}fl\'{e}chit sur le miroir et apr\`{e}s r\'{e}flexion parvient \`{a} l'{\oe}il de notre observateur. L'observateur a l'illusion que le rayon provient du point image. Il faut donc reconstruire math\'{e}matiquement la marche d'un tel rayon lumineux en partant de l'image dans le miroir. - -L'observateur est suffisamment \'{e}loign\'{e} du miroir pour pouvoir \^{e}tre consid\'{e}r\'{e} comme ponctuel. - -Soit $P$ un point de l'image(not\'{e} $A'$ dans le sch\'{e}ma ci-apr\`{e}s), $V$ l'{\oe}il de l'observateur. Tra\c{c}ons un droite $(PV)$ et d\'{e}terminons le point d'intersection $I$ avec le cylindre : c'est le point d'incidence. -\[ -V(x_V,y_V,z_V)\quad\text{ et }\quad P(x_P,y_P,0) -\] -L'\'{e}quation param\'{e}trique de la droite $(PV)$ s'\'{e}crit $\overrightarrow{IV}=\rho\overrightarrow{PV}$: -\begin{equation}\label{eq:paracyl} -\left\lbrace - \begin{array}{lcl} - x_V-x_I&=&\rho(x_V-x_P)\\ - y_V-y_I&=&\rho(y_V-y_P)\\ - z_V-z_I&=&\rho(z_V-0) - \end{array} - \right. - \Longrightarrow - \left\lbrace - \begin{array}{lcl} - x_I&=&x_V(1-\rho)+\rho x_P\\ - y_I&=&y_V(1-\rho)+\rho y_P\\ - z_I&=&z_V(1-\rho) - \end{array} - \right. -\end{equation} -\begin{center} -\begin{pspicture}(-4,-0.5)(6.5,8) -\pnode(6,7){V} -\uput[0](V){$V$} -\pnode(3,6.5){S} -\pnode(-3,6.5){S'} -\pnode(3,2.8){I} -\pnode(1,0){P} -\pnode(5,0){P'} -\uput[45](P'){$P'$} -\pnode(3,0){G} -\pnode(-3,0){G'} -\pspolygon[fillstyle=solid,fillcolor=lightgray!30](G')(G)(S)(S') -\psaxes[ticks=none,labels=none]{->}(0,0)(-4,0)(6.5,7.5) -\uput[0](6.5,0){$x$} -\uput[90](0,7.5){$z$} -\uput[135](P){$P$} -\uput[-45](G){$G$} -\uput[135](I){$I$} -\psline(V)(P) -\psline(S)(G) -\rput(I){% -\psline[linestyle=dashed](3;0)% -\uput[0](3;0){$N$}% -\psarc[doubleline=true](0,0){1}{-90}{-54.46}% -\psarc[doubleline=true](0,0){1}{54.46}{90} -\uput[72](1.2;72){$\varepsilon$}% -\uput[-72](1.2;-72){$\varepsilon$}% -\rput{-90}(0,0){\psframe(0.3,0.3)} -} -\psline[linecolor=red](V)(I)(P') -\pcline[nodesepB=1.5,linecolor=red,arrowsize=0.175,arrowinset=0.075]{->>}(P')(I) -\pcline[nodesepB=2.5,linecolor=red,arrowsize=0.175,arrowinset=0.075]{->>}(I)(V) -\qdisk(I){2pt} -\qdisk(P){2pt} -\qdisk(V){2pt} -\qdisk(P'){2pt} -\qdisk(G){2pt} -\psline[linewidth=0.5\pslinewidth]{|<->|}(0,-0.2)(1,-0.2) -\uput[-90](0.5,-0.2){$r_P$} -\psline[linewidth=0.5\pslinewidth]{<->}(0,2.8)(3,2.8) -\uput[-90](1.5,2.8){$r_I=R$} -\end{pspicture} -\end{center} -Le point $I$ appartenant au cylindre, ses coordonn\'{e}es v\'{e}rifient la relation : -\begin{equation}\label{eq:cylindre} -x_I^2+y_I^2=R^2 -\end{equation} -(\ref{eq:paracyl}) en (\ref{eq:cylindre}) et apr\`{e}s d\'{e}veloppement, on obtient l'\'{e}quation du second degr\'{e} en $\rho$: -\begin{gather*} -\left(x_V(1-\rho)+\rho x_P\right)^2+\left(y_V(1-\rho)+\rho y_P\right)^2=R^2\\ -x_V^2(1-2\rho+\rho^2)+2(1-\rho)\rho x_Vx_P+\rho^2 x_P^2+y_V^2(1-2\rho+\rho^2)+2(1-\rho)\rho y_Vy_P+\rho^2 y_P^2=R^2\\ -(x_V^2+y_V^2-2x_Vx_P-2y_Vy_P)\rho^2+2(-x_V^2+x_Vx_P-y_V^2+y_Vy_P)\rho+x_V^2+y_V^2=R^2 -\end{gather*} -Comparaison avec -\[ -a\rho^2+2b'\rho+c=0 -\] -donne : -\[ -\left\lbrace - \begin{array}{lcl} - a&=&(x_V-x_P)^2+(y_V-y_P)^2\\ - 2b'&=&x_Vx_P+y_Vy_P-x_V^2-y_V^2\\ - c&=&x_V^2+y_V^2-R^2 - \end{array} - \right. -\] -La r\'{e}solution de cette \'{e}quation nous donne les solutions classiques: -\[ -\left\lbrace - \begin{array}{lcl} - \rho'&=&\dfrac{-b'+\sqrt{\Delta'}}{a}\\[0.5cm] - \rho''&=&\dfrac{-b'-\sqrt{\Delta'}}{a} - \end{array} - \right. - \qquad \Delta'=b'^2-ac -\] -On retiendra la plus petite valeur positive des deux, que par la suite j'appelle $\rho$. - -$(IV)$ repr\'{e}sente le rayon r\'{e}fl\'{e}chi par le miroir. Le rayon incident est d\'{e}fini par la droite sym\'{e}trique de $(IV)$ par rapport \`{a} la normale au miroir en $I$. Je cherche le sym\'{e}trique de $V$, nomm\'{e} $V'$ par rapport \`{a} cette normale $(IN)$. Ce point $V'$ remplit deux conditions : -\begin{enumerate} - \item $\overrightarrow{IV}+\overrightarrow{IV'}=k\overrightarrow{IN}$ - \item $\overrightarrow{VV'}.\overrightarrow{IN}=0$ -\end{enumerate} -La normale $(IN)$ a pour vecteur directeur $\overrightarrow{IN}(x_I,y_I,0)$ - -La premi\`{e}re condition se traduit par : -\[ -\left\lbrace - \begin{array}{lcl} - x_V-x_I+x_{V'}-x_I&=&kx_I\\ - y_V-x_I+y_{V'}-y_I&=&ky_I\\ - z_V-z_I+z_{V'}-z_I&=&0 - \end{array} - \right. - \Longrightarrow - \left\lbrace - \begin{array}{lcl} - x_{V'}&=&kx_I+2x_I-x_V\\ - y_{V'}&=&ky_I+2y_I-y_V\\ - z_{V'}&=&2z_I-z_V - \end{array} - \right. -\] -La deuxi\`{e}me par : -\[ -(x_{V'}-x_V)x_I+(y_{V'}-y_V)y_I=0 -\] -En rempla\c{c}ant $x_{V'}$ et $y_{V'}$ tir\'{e}s de la premi\`{e}re condition dans la deuxi\`{e}me : -\begin{gather*} -k(x_I^2+y_I^2)+2x_I^2-2x_Vx_I+2y_I^2-2y_Vy_I=0\\ -kR^2+2R^2=2(x_Vx_I+y_Vy_I)\\ -k+2=\dfrac{2}{R^2}(x_Vx_I+y_Vy_I) -\end{gather*} -Les coordonn\'{e}es de $V'$ s'en d\'{e}duisent : -\[ -\left\lbrace - \begin{array}{lcl} - x_{V'}&=&(k+2)x_I-x_V\\ - y_{V'}&=&(k+2)y_I-y_V\\ - z_{V'}&=&z_V(1-2\rho) - \end{array} - \right. -\] -Il reste \`{a} trouver l'intersection de $(IV')$ avec le plan horizontal $z=0$. - -\'Equation param\'{e}trique de $(IV')$, $M$ \'{e}tant un point courant : $\overrightarrow{MV'}=\alpha\overrightarrow{IV'}$ -\[ -\left\lbrace - \begin{array}{lcl} - x_{V'}-x&=&\alpha(x_{V'}-x_I)\\ - y_{V'}-y&=&\alpha(y_{V'}-y_I)\\ - z_{V'}-z&=&\alpha(z_{V'}-z_I) - \end{array} - \right. -\] -$z=0\Longrightarrow \alpha=\dfrac{z_{V'}}{z_{V'}-z_I}$ soit -\[ -\alpha=\dfrac{1-2\rho}{-\rho} -\] -En rempla\c{c}ant $\alpha$ par son expression, nous obtenons les coordonn\'{e}es du point $P'$ de l'objet anamorphique. -\[ -\left\lbrace - \begin{array}{lcl} - x_{P'}&=&x_{V'}-\alpha(x_{V'}-x_I)\\ - y_{P'}&=&y_{V'}-\alpha(y_{V'}-y_I) - \end{array} - \right. -\] -Cette s\'{e}rie de calculs doit \^{e}tre appliqu\'{e}e \`{a} tous les points de l'image <<~normale~>> afin d'obtenir l'objet anamorphique (d\'{e}form\'{e}) dont le miroir <<~redressera~>> la forme. - -On notera que \textit{la cote de l'observateur $z_V$ n'intervient pas}. On le comprend ais\'{e}ment en faisant un dessin du plan vertical passant par l'\oe{}il et l'axe du cylindre miroir. La position de la projection horizontale \'{e}tant fix\'{e}e $(x_V,y_V)$, quelle que soit la valeur de $z_V$, $A$ et $A'$ \'{e}tant sym\'{e}triques par rapport \`{a} la g\'{e}n\'{e}ratrice du miroir appartenant au plan vertical choisi, si $A'$ est donn\'{e} alors $A$ est fix\'{e} quelque soit~$z_V$. - -\newpage - -\section{L'anamorphose conique} - -Le principe est identique \`{a} celui de l'anamorphose cylindrique : imaginons un rayon lumineux provenant de l'objet <<~anamorphique~>>, se r\'{e}fl\'{e}chissant sur le miroir conique et parvenant \`{a} l'{\oe}il de l'observateur plac\'{e} au-dessus et dans l'axe du c\^{o}ne \`{a} une position suffisamment haute pour que l'observateur puisse \^{e}tre consid\'{e}r\'{e} comme ponctuel. Ainsi l'observateur aura l'illusion d'observer l'image reconstitu\'{e}e par le miroir conique. Image et objet sont dans le plan horizontal. - -\begin{center} -\psscalebox{0.7}{ -\begin{pspicture}(-7,-8)(7,9) -\newcommand\R{3} -\newcommand\hauteur{5} -\newcommand\pas{10} -\FPeval{\pasrad}{\pas*\FPpi/180} - \FPmul{\Largeur}{\R}{\pasrad} - \FPdiv{\largeur}{\Largeur}{2} -%Les coordonn\'{e}es de viewpoint -\def\vx{1}\def\vy{-0.8}\def\vz{1} -\FPeval{\RH}{(\R)/(\hauteur)} - \FParctan{\phy}{\RH} - \FPeval{\OH}{sin(\phy)*\hauteur} - \FPeval{\zH}{sin(\phy)*\OH} - \FPeval{\OK}{cos(\phy)*\OH} - \FPeval{\generatrice}{root(2,(\hauteur*\hauteur)+(\R*\R))} -\psset{viewpoint={\vx} {\vy} {\vz}} -\ThreeDput[normal=0 0 1](0,0,0){%% -\psframe*[linecolor=lightgray!25](-10,-10)(10,10) -\psgrid[subgriddiv=0,gridcolor=lightgray,gridlabels=0pt](-10,-10)(10,10) -\psaxes(0,0)(-10,-10)(10,10) -\pscircle[doubleline=true]{3} -\psset{type=conical} -\multido{\n=-1.50+0.50}{7}{% - \pnode(! \n\space -2.50){A} - \pnode(! \n\space -0.50){B} - \psline[linecolor=green](A)(B) - \pslineA[linecolor=green](A)(B) - } -\multido{\N=-2.50+0.50}{5}{% - \pnode(!-1.50 \N){A} - \pnode(!1.50 \N){B} - \pslineA[linecolor=green](A)(B) - \psline[linecolor=green](A)(B) - } -% -\multido{\n=-1.50+0.50}{7}{% - \pnode(! \n\space 2.50){A} - \pnode(! \n\space 0.50){B} - \psline[linecolor=green](A)(B) - \pslineA[linecolor=green](A)(B) - } -\multido{\N=2.50+-0.50}{5}{% - \pnode(!-1.50 \N){A} - \pnode(!1.50 \N){B} - \pslineA[linecolor=green](A)(B) - \psline[linecolor=green](A)(B) - } -\multido{\n=-1.50+0.50}{7}{% - \pnode(! \n\space -2.50){A} - \pnode(! \n\space -0.50){B} - \psline(A)(B) - \pslineA(A)(B) - } -\multido{\N=-2.50+0.50}{5}{% - \pnode(!-1.50 \N){A} - \pnode(!1.50 \N){B} - \pslineA(A)(B) - \psline(A)(B) - } -\multido{\n=-1.50+0.50}{7}{% - \pnode(! \n\space 2.50){A} - \pnode(! \n\space 0.50){B} - \psline(A)(B) - \pslineA(A)(B) - } -\multido{\N=2.50+-0.50}{5}{% - \pnode(!-1.50 \N){A} - \pnode(!1.50 \N){B} - \pslineA(A)(B) - \psline(A)(B) - } -\psanamorphosis[type=conical,scale=-0.7 -0.7](0,1.5){tiger.eps} -\pstextA[fontsize=15,fillcolor=green,scale=1 -1](0,-0.5){Anamorphose} -\pscircle[doubleline=true]{3}} -\newcount\n \n=0 - \loop - \FPmul{\tempa}{\FPpi}{\the\n} - \FPdiv{\angle}{\tempa}{180} - \FPsin{\SIN}{\angle}\FPcos{\COS}{\angle} - \FPmul{\xH}{\COS}{\OK} - \FPmul{\yH}{\SIN}{\OK} - \FPdiv{\grise}{\the\n}{360} - \FPsub{\gris}{1}{\grise} - \FPdiv{\teinte}{\grise}{2} -\definecolor{gris}{cmyk}{\teinte,\teinte,\teinte,0} -%tester les faces visibles -%le produit scalaire du vecteur viewpoint et du vecteur normal \`{a} la face >0 ? -\FPeval{\costest}{(\vx)*\xH+(\vy)*\yH+(\vz)*\zH} - \FPifpos{\costest} - \ThreeDput[normal={\xH} {\yH} \zH](0,0,\hauteur){% - \pspolygon[linecolor=BleuCiel]%[fillstyle=solid,fillcolor=gris,dimen=outer]% - (0,0)(-\largeur,-\generatrice)(\largeur,-\generatrice)}\else{}\fi - \FPifneg{\costest} - \ThreeDput[normal={\xH} {\yH} \zH](0,0,\hauteur){% - \psline[linestyle=dashed,linecolor=gray](0,0)(\largeur,-\generatrice)}\else{}\fi - \ifnum\n<360 \advance\n by \pas -\repeat -%Dessin des faces de dessus et de dessous -%\FPifneg\vz -%face de dessous -%\ThreeDput[normal=0 0 -1](0,0,0){% -%\pscircle[fillstyle=solid,fillcolor=lightgray](0,0){\R}\rput(0,0){\Large\textbf{\textsf{Dessous}}}}\fi -\ThreeDput[normal=1 0 0](0,0,0){% -\psaxes(1,10) -\rput{90}(0,12){\oeil}% -{\boldmath -\red -\pnode(0,10){V} -\uput[0](V){$V$} -\pnode(0,5){S} -\uput[0](S){$S$} -\pnode(-1.5,2.5){I} -\uput[180](I){$I$} -\qdisk(I){2pt} -\pnode(-2,0){P} -\uput[135](P){$P$} -\pnode(-4.545,0){P'} -\uput[135](P'){$P'$} -\psset{linecolor=red} -\psline(V)(I)(P') -\pcline[nodesepB=2,nodesepA=1,linecolor=red,arrowsize=0.175,arrowinset=0.075]{->}(P')(I) -\pcline[nodesepB=4,nodesepA=1,linecolor=red,arrowsize=0.175,arrowinset=0.075]{->}(I)(V) -\psline[linestyle=dashed](I)(P)}}% -\end{pspicture} -} -\end{center} -Il s'agit de d\'{e}terminer en premier, l'intersection de $(VP)$ avec le c\^{o}ne, qu'on appelle $I$ (point d'incidence). Les coordonn\'{e}es de $V$, $S$ et $P$ sont not\'{e}es : $V(0,0,z_V)$, $S(0,0,z_S)$ et $P(x_P,y_P,0)$. - -L'\'{e}quation param\'{e}trique de la droite $(PV)$ s'\'{e}crit $\overrightarrow{IV}=\lambda\overrightarrow{PV}$: -\[ -\left\lbrace - \begin{array}{lcl} - 0-x_I&=&\lambda(0-x_P)\\ - 0-y_I&=&\lambda(0-y_P)\\ - z_V-z_I&=&\lambda(z_V-0) - \end{array} - \right. - \Longrightarrow - \left\lbrace - \begin{array}{lcl} - x_I&=&\lambda x_P\\ - y_I&=&\lambda y_P\\ - z_I&=&(1-\lambda)z_V - \end{array} - \right. -\] -On pose : -\[ - r_I^2=x_I^2+y_I^2\quad\textrm{et}\quad r_P^2=x_P^2+y_P^2\quad\textrm{et}\quad |\overrightarrow{OG}|=R -\] -Le point $I$ appartenant au c\^{o}ne, ses coordonn\'{e}es v\'{e}rifient la relation (th\'{e}or\^{e}me de Thal\`{e}s): -\begin{align*} - \frac{R}{z_S}&=\frac{r_I}{z_S-z_I}\\ - \frac{R}{z_S}&=\frac{\lambda r_P}{z_S-(1-\lambda)z_P}\\ - \lambda&=\frac{R(z_S-z_V)}{r_Pz_S-R z_V} -\end{align*} -\begin{center} -\begin{pspicture}(-4,-1)(6.5,7.75) -\pnode(0,10){V} -\uput[0](V){$V$} -\pnode(0,5){S} -\uput[0](S){$S$} -\pnode(1.5,2.5){I} -\pnode(2,0){P} -\pnode(4.545,0){P'} -\uput[45](P'){$P'$} -\psdots[dotstyle=|](P') -\pnode(3,0){G} -\pnode(-3,0){G'} -\pspolygon[fillstyle=solid,fillcolor=lightgray!30](G')(G)(S) -\psaxes[ticks=none,labels=none]{->}(0,0)(-4,0)(5.5,10.25) -\uput[0](5.5,0){$x$} -\uput[90](0,10.25){$z$} -\uput[45](P){$P$} -\uput[-45](G){$G$} -\uput[70](I){$I$} -\psline(V)(P) -\psline(S)(G) -\rput(I){% -\psline[linestyle=dashed](4;30.96) -\uput[15.5](4;30.1){$N$} -\rput{-59.036}(0,0){\psframe(0.5,0.5)} -\psarc[doubleline=true](0,0){1}{101.31}{120.964} -%\psarc[doubleline=true](0,0){1}{-79.09}{-59.036} -\psarc[doubleline=true](0,0){1.2}{-59.036}{-39.38} -\pnode(1.2;-50){I1} -\pnode(1.2;112){I2} -\uput[-50](I1){$\varepsilon$} -\uput[112](I2){$\varepsilon$} -} -\rput(P'){\pswedge[fillstyle=solid,fillcolor=lightgray](0,0){1}{140.175}{180} -\uput[160](1;160){$\varepsilon'$}} -\rput(S){\psarc[linecolor=gray,linewidth=2\pslinewidth](0,0){1}{-90}{-59.036} -\uput[-75](1;-75){$\theta$}} -\rput(V){\psarc(0,0){2}{-90}{-78.69} -\uput[-80](2;-85){$\beta$}} -\psline[linecolor=red](V)(I)(P') -\pcline[nodesepB=1.5,linecolor=red,arrowsize=0.175,arrowinset=0.075]{->>}(P')(I) -\pcline[nodesepB=4,linecolor=red,arrowsize=0.175,arrowinset=0.075]{->>}(I)(V) -\qdisk(I){2pt} -\qdisk(P){2pt} -\qdisk(S){2pt} -\qdisk(V){2pt} -\qdisk(P'){2pt} -\qdisk(G){2pt} -\psline[linewidth=0.5\pslinewidth]{|<->|}(0,-0.2)(2,-0.2) -\uput[-90](1,-0.2){$r_P$} -\psline[linewidth=0.5\pslinewidth]{|<->|}(0,-0.8)(3,-0.8) -\uput[-90](1.5,-0.8){$R$} -\psline[linewidth=0.5\pslinewidth]{<->}(1.5,2.5)(0,2.5) -\uput[-90](0.75,2.5){$r_I$} -\psline[linewidth=0.5\pslinewidth]{<->|}(-0.2,0)(-0.2,5) -\uput[180](-0.2,2.5){$z_S$} -\psline[linewidth=0.5\pslinewidth]{<->|}(-1,0)(-1,10) -\uput[180](-1,5){$z_V$} -\psline[linewidth=0.5\pslinewidth,linestyle=dashed](1.5,2.5)(1.5,0) -\end{pspicture} -\end{center} -Pour construire le rayon incident, $(P'I)$, $(IV)$ est le rayon r\'{e}fl\'{e}chi, d\'{e}terminons~$\varepsilon'$. - -Un raisonnement g\'{e}om\'{e}trique \'{e}l\'{e}mentaire nous montre que : -\[ - \varepsilon'=90^\circ-2\theta+\beta -\] -avec -\[ - \beta=\arctan\frac{r_P}{z_V} -\] -et -\[ - \theta=\arctan\frac{R}{z_S}\quad\textrm{demi-angle au sommet du c\^{o}ne } -\] -Dans le plan horizontal, les coordonn\'{e}es de $P'$ sont : -\[ -\left\lbrace - \begin{array}{lcl} - x_{P'}&=&x_I+\dfrac{z_I}{\tan \varepsilon'}\\[0.5cm] - y_{P'}&=&y_I+\dfrac{z_I}{\tan \varepsilon'}\\ - \end{array} -\right. -\] - -\newpage - -\section{L'anamorphose sph\'{e}rique} - -On place \`{a} l'int\'{e}rieur de la demi-sph\`{e}re l'image telle qu'elle doit \^{e}tre vue par un observateur regardant dans le miroir sph\'{e}rique (on peut la placer \`{a} l'ext\'{e}rieur, mais il faut que les rayons lumineux rencontrent toujours la sph\`{e}re, il faut donc veiller aux dimensions). L'objet anamorphique est <<~l'objet d\'{e}form\'{e}~>> dont le miroir reconstituera les proportions r\'{e}elles.\par Objet et image ob\'{e}issent aux lois de la r\'{e}flexion de l'optique g\'{e}om\'{e}trique : -\begin{itemize} - \item rayon incident et rayon r\'{e}fl\'{e}chi appartiennent \`{a} un m\^{e}me plan ; - \item rayon incident et rayon r\'{e}fl\'{e}chi sont sym\'{e}triques par rapport \`{a} la normale au miroir au point d'incidence. -\end{itemize} -\begin{center} -\psscalebox{0.67}{ -\begin{pspicture}(-4,-7)(12,4.5) -\psset{lightsrc=viewpoint} -\psset{viewpoint=-100 -100 100,Decran=173.2} -\ThreeDput[normal=0 0 1](0,0,0){%% -\psframe*[linecolor=lightgray!25](-5,-14)(5,5) -\psgrid[subgriddiv=0,gridcolor=lightgray,gridlabels=0pt](-5,-14)(5,5) -\psaxes(0,0)(-5,-14)(5,5) -\psset{type=spherical,Rmirror=5} -\pscircle[doubleline=true]{5} -\multido{\n=-1.00+0.20}{11}{% - \pnode(! \n\space -4.80){A} - \pnode(! \n\space -3.40){B} - \psline(A)(B) - \pslineA(A)(B) - }% -\multido{\N=-4.80+0.20}{8}{% - \pnode(!-1.0 \N){A} - \pnode(!1.0 \N){B} - \pslineA(A)(B) - \psline(A)(B) - }% -\psanamorphosis[scale=0.4 0.4](0,-4){tiger.eps} -\pnode(0,-4){A} -\pnodeA(0,-4){A'} -%\psline(A)(A') - } -\ThreeDput[normal=-1 0 0](0,0,0){% -\pnode(15,5){OE} -\pnode(13.2,4.2){OE'} -\pnode(5,0.4545){I} -\rput{26.5}(OE){\oeil} -} -\psSolid[object=calottesphere,r=5,opacity=0.5, - ngrid=24 36,fillcolor=cyan!50,grid,hollow, - incolor=yellow,theta=90,phi=0,action=draw,linecolor=BleuCiel,linewidth=0.5pt](0,0,0) -\psline[linecolor=red](A')(I)(OE') -\pcline[nodesepB=2.5,linecolor=red,arrowsize=0.175,arrowinset=0.075]{->>}(I)(OE') -\pcline[nodesepB=1,linecolor=red,arrowsize=0.175,arrowinset=0.075]{->>}(A')(I) -\psline(I)(A) -\end{pspicture} -} -\end{center} -L'image non d\'{e}form\'{e}e (celle qui est vue dans le miroir) est plac\'{e}e, dans cet exemple, au centre du miroir. Un rayon incident partant de l'objet anamorphique se r\'{e}fl\'{e}chit sur le miroir et apr\`{e}s r\'{e}flexion parvient \`{a} l'{\oe}il de notre observateur. L'observateur a l'illusion que le rayon provient du point image. Il faut donc reconstruire math\'{e}matiquement la marche d'un tel rayon lumineux en partant de l'image dans le miroir. - -L'observateur est suffisamment \'{e}loign\'{e} du miroir pour pouvoir \^{e}tre consid\'{e}r\'{e} comme ponctuel. - -Soit $P$ un point de l'image, $V$ l'{\oe}il de l'observateur. Tra\c{c}ons un droite $PV$ et d\'{e}terminons le point d'intersection $I$ avec la sph\`{e}re : c'est le point d'incidence. -\[ -V(x_V,y_V,z_V)\quad\text{ et }\quad P(x_P,y_P,0) -\] -\begin{center} -\shorthandoff{!} -\begin{pspicture}(-4,-0.5)(8,5.5) -\pswedge[fillstyle=solid,fillcolor=lightgray!30](0,0){2}{0}{180} -\psaxes[labels=none,ticks=none]{->}(0,0)(-3,0)(7.5,5) -\uput[0](7.5,0){$x$} -\uput[90](0,5){$z$} -\pnode(1.5,0){P} -\pnode(0,0){O}\uput[dl](O){$O$} -\pnode(!/alpha 15 def /xI 2 alpha cos mul def /yI 2 alpha sin mul def /beta yI xI 1.5 sub atan def xI yI){I} -\psline(P)(I) -\rput(I){\pnode(!beta cos 5 mul beta sin 5 mul){V}} -\psline[linecolor=red](I)(V) -\rput(I){\psarc[doubleline=true](0,0){1}{!alpha}{!beta} -\psarc[doubleline=true](0,0){1.2}{!2 alpha mul beta sub}{!alpha}} -\uput{1.2}[!alpha beta add 2 div](I){$\varepsilon$} -\uput{1.4}[!3 alpha mul beta sub 2 div](I){$\varepsilon$} -\pnode(!yI neg xI 2 alpha mul beta sub tan mul add 2 alpha mul beta sub tan div 0){M} -\psline[linecolor=red](M)(I) -\pcline[nodesepB=0.5,linecolor=red,arrowsize=0.175,arrowinset=0.075]{->>}(M)(I) -\pcline[nodesepB=2,linecolor=red,arrowsize=0.175,arrowinset=0.075]{->>}(I)(V) -\psline[linewidth=0.5\pslinewidth]{<->}(O)(I) -\uput[75](1;15){$R$} -\psline[linewidth=0.5\pslinewidth]{<->}(O)(V) -\uput[75](3,2.7){$r_V$} -\psline[linewidth=0.5\pslinewidth]{|<->|}(0,-0.3)(1.5,-0.3) -\uput[-90](0.75,-0.3){$r_P$} -\rput(I){% -\psline[linestyle=dashed](5;15) -\uput[15](5;15){$N$} -\psline[linewidth=0.5\pslinewidth,linecolor=gray](1.5;105) -\uput[105](1.5;105){$T$} -\psline[linewidth=0.5\pslinewidth,linecolor=gray](1.25;-75) -\rput{-75}(0,0){\psframe(0.3,0.3)} -} -\uput[-45](P){$P$} -\uput[-45](M){$P'$} -\uput[70](I){$I$} -\uput[u](V){$V$} -\psdot(P) -\psdot(I) -\psdot(V) -\psdot(M) -\end{pspicture} -\end{center} -L'\'{e}quation param\'{e}trique de la droite $(PV)$ s'\'{e}crit $\overrightarrow{IV}=\lambda\overrightarrow{PV}$: -\begin{equation}\label{eq:para} -\left\lbrace - \begin{array}{lcl} - x_V-x_I&=&\lambda(x_V-x_P)\\ - y_V-y_I&=&\lambda(y_V-y_P)\\ - z_V-z_I&=&\lambda(z_V-0) - \end{array} - \right. - \Longrightarrow - \left\lbrace - \begin{array}{lcl} - x_I&=&x_V(1-\lambda)+\lambda x_P\\ - y_I&=&y_V(1-\lambda)+\lambda y_P\\ - z_I&=&z_V(1-\lambda) - \end{array} - \right. -\end{equation} -On pose : -\[ -r_V^2=x_V^2+y_V^2+z_V^2\quad\textrm{et}\quad r_P^2=x_P^2+y_P^2 -\] -Le point $I$ appartenant \`{a} la sph\`{e}re, ses coordonn\'{e}es v\'{e}rifient la relation : -\begin{equation}\label{eq:sphere} -x_I^2+y_I^2+z_I^2=R^2 -\end{equation} -(\ref{eq:para}) en (\ref{eq:sphere}) -\begin{gather*} -\left(x_V+\lambda(x_P-x_V)\right)^2+\left(y_V+\lambda(y_P-y_V)\right)^2+\left((1-\lambda)z_V\right)^2=R^2\\ -x_V^2+2\lambda x_V(x_P-x_V)+\lambda^2(x_P-x_V)^2+y_V^2+2\lambda y_V(y_P-y_V) +\lambda^2(y_P-y_V)^2+(1-2\lambda+\lambda^2)z_V^2=R^2 -\end{gather*} -Apr\`{e}s d\'{e}veloppement, on obtient l'\'{e}quation du second degr\'{e} en -$\lambda$: -\begin{gather*} -\lambda^2\left((x_P-x_V)^2+(y_P-y_V)^2+z_V^2\right)+2\lambda\left(x_V(x_P-x_V)+y_V(y_P-y_V)-z_V^2\right)+x_V^2+y_V^2+z_V^2- -R^2=0\\ -\lambda^2\left(x_V^2+y_V^2+z_V^2+x_P^2+y_P^2-2x_Px_V-2y_Py_V\right)+2\lambda\left(-x_V^2-y_V^2-z_V^2+x_Px_V+y_Py_V\right)+x_V^2+y_V^2+z_V^2- -R^2=0 -\end{gather*} -Comparaison avec -\[ -a\lambda^2+2b'\lambda+c=0 -\] -donne pour le coefficient $a$ de $\lambda^2$ : -\[ -a=x_V^2+y_V^2+z_V^2+x_P^2+y_P^2-2x_Px_V-2y_Py_V -\] -Pour le coefficient $2b'$ de $\lambda$ : -\[ -2b'=-x_V^2-y_V^2-z_V^2+x_Px_V+y_Py_V -\] -Pour le coefficient $c$ : -\[ -c=x_V^2+y_V^2+z_V^2-R^2 -\] -Alors -\[ -a\lambda^2+2b'\lambda+c=0 -\] -avec : -\[ -\left\lbrace - \begin{array}{lcl} - a&=&x_V^2+y_V^2+z_V^2+x_P^2+y_P^2-2x_Px_V-2y_Py_V\\ - 2b'&=&-x_V^2-y_V^2-z_V^2+x_Px_V+y_Py_V\\ - c&=&x_V^2+y_V^2+z_V^2-R^2 - \end{array} - \right. -\] -\[\left\lbrace - \begin{array}{lcl} - a&=&r_V^2+r_P^2-2x_Px_V-2y_Py_V\\ - 2b'&=&-r_V^2+x_Px_V+y_Py_V\\ - c&=&r_V^2-R^2 - \end{array} - \right. -\] -La r\'{e}solution de cette \'{e}quation nous donne les solutions classiques: -\[ -\left\lbrace - \begin{array}{lcl} - \lambda'&=&\dfrac{-b'+\sqrt{\Delta'}}{a}\\[0.5cm] - \lambda''&=&\dfrac{-b'-\sqrt{\Delta'}}{a} - \end{array} - \right. - \qquad \Delta'=b'^2-ac -\] -On retiendra la valeur positive.% et \texttt{Coeff1} dans le programme. - -$(IV)$ repr\'{e}sente le rayon r\'{e}fl\'{e}chi par le miroir. Le rayon incident est d\'{e}fini par la droite sym\'{e}trique de $(IV)$ par rapport \`{a} la normale au miroir en $I$. Je cherche le sym\'{e}trique de $V$, nomm\'{e} $V'$ par rapport \`{a} cette normale $(IN)$. Ce point $V'$ remplit deux conditions : -\begin{enumerate} - \item $\overrightarrow{IV}+\overrightarrow{IV'}=k\overrightarrow{IN}$ - \item $\overrightarrow{VV'}.\overrightarrow{IN}=0$ -\end{enumerate} -La normale $(IN)$ a pour vecteur directeur $\overrightarrow{IN}(x_I,y_I,z_I)$ - -La premi\`{e}re condition se traduit par : -\[ -\left\lbrace - \begin{array}{lcl} - x_V-x_I+x_{V'}-x_I&=&kx_I\\ - y_V-x_I+y_{V'}-y_I&=&ky_I\\ - z_V-z_I+z_{V'}-z_I&=&kz_I - \end{array} - \right. - \Longrightarrow - \left\lbrace - \begin{array}{lcl} - x_{V'}&=&kx_I+2x_I-x_V\\ - y_{V'}&=&ky_I+2y_I-y_V\\ - z_{V'}&=&kz_I+2z_I-z_V - \end{array} - \right. -\] -La deuxi\`{e}me par : -\[ -(x_{V'}-x_V)x_I+(y_{V'}-y_V)y_I+(z_{V'}-z_V)z_I=0 -\] -En rempla\c{c}ant $x_{V'}$, $y_{V'}$ et $z_{V'}$ tir\'{e}s de la premi\`{e}re condition dans la deuxi\`{e}me : -\begin{gather*} -k(x_I^2+y_I^2+y_I^2)+2x_I^2-2x_Vx_I+2y_I^2-2y_Vy_I+2z_I^2-2z_Vz_I=0\\ -kR^2+2R^2=2(x_Vx_I+y_Vy_I+z_Vz_I)\\ -k+2=\dfrac{2}{R^2}(x_Vx_I+y_Vy_I+z_Vz_I) -\end{gather*} -Les coordonn\'{e}es de $V'$ s'en d\'{e}duisent : -\[ -\left\lbrace - \begin{array}{lcl} - x_{V'}&=&(k+2)x_I-x_V\\ - y_{V'}&=&(k+2)y_I-y_V\\ - z_{V'}&=&(k+2)z_I-z_V - \end{array} - \right. -\] -Il reste \`{a} trouver l'intersection de $(IV')$ avec le plan horizontal $z=0$. - -\'Equation param\'{e}trique de $(IV')$, $M$ \'{e}tant un point courant : $\overrightarrow{MI}=\alpha\overrightarrow{V'I}$ -\[ -\left\lbrace - \begin{array}{lcl} - x_I-x&=&\alpha(x_I-x_{V'})\\ - y_I-y&=&\alpha(y_I-y_{V'})\\ - z_I-z&=&\alpha(z_I-z_{V'}) - \end{array} - \right. -\] -$z=0\Longrightarrow \alpha=\dfrac{z_{I}}{z_I-z_{V'}}$. - -En rempla\c{c}ant $\alpha$ par son expression, nous obtenons les coordonn\'{e}es du point $P'$ de l'objet anamorphique. -\[ -\left\lbrace - \begin{array}{lcl} - x_{P'}&=&x_I-\alpha(x_I-x_{V'})\\ - y_{P'}&=&y_I-\alpha(y_I-y_{V'})\\ - z_{P'}&=&0 - \end{array} - \right. -\] -Cette s\'{e}rie de calculs doit \^{e}tre appliqu\'{e}e \`{a} tous les points de l'image <<~normale~>> afin d'obtenir l'objet anamorphique (d\'{e}form\'{e}) dont le miroir <<~redressera~>> la forme. - -\textbf{Remarque} : l'image doit se former du c\^{o}t\'{e} de l'observateur \`{a} l'int\'{e}rieur du miroir, plus pr\`{e}s du bord du miroir que du centre. Si on d\'{e}place le point $P$ vers $O$, il arrive un moment o\`{u} le rayon r\'{e}fl\'{e}chi part au-dessus de l'horizontale et ne rencontre plus le plan horizontal. L'anamorphose n'est plus possible et pour les calculs c'est le CRASH ! - -\newpage - -\section{La perspective} - -Dans le livre de Jurgis Baltru\v{s}a\"{\i}tis\footnote{ \textit{Anamorphoses : les perspectives d\'{e}prav\'{e}es} en livre de poche chez Flammarion.}, on trouve le principe de la <<~\textit{costruzione legittima}~>> avec un sch\'{e}ma de L\'{e}onard de Vinci (1492) et des sch\'{e}mas anamorphiques de Niceron (1658). Je cite page 58 : -\begin{quote}\itshape -<<~Rappelons en quelques mots quels ont \'{e}t\'{e} le proc\'{e}d\'{e}s utilis\'{e}s par les artistes pour l'ordonnancement de leurs tableaux en perspective normale. La premi\`{e}re ligne trac\'{e}e est celle de l'horizon \`{a} la hauteur de l'\oe{}il. Deux points y sont ensuite fix\'{e}s : au milieu le point principal vers o\`{u} convergent toutes les lignes droites parall\`{e}les qui s'\'{e}loignent en profondeur ; sur la m\^{e}me horizontale et \`{a} la m\^{e}me distance du point principal que l'\oe{}il, en face de la composition -- le point de distance, vers lequel convergent les diagonales.~>> -\end{quote} -\begin{center} -\begin{pspicture}(-5,-3)(5,14.25) -\psset{ua=2,F=10,D=4,type=perspective} -\psframe*[linecolor=BleuCiel](-5,10)(5,13) -\psframe*[linecolor=OrangePale](-5,2)(5,10) -\psline[arrowinset=0,arrowsize=2mm]{->}(0,14) -\psline[arrowinset=0,arrowsize=2mm]{->}(7,0) -\uput[0](7,0){$x$} -\uput[90](0,14){$y$} -\psline(-5,2)(5,2) -\pnode(4,10){F'} -\pnode(0,10){F} -\uput[ul](F){${F}$} -\uput[ur](F'){${F'}$} -\rput(0,12){\multido{\n=22.5+45.0}{8}{% -\psline[linecolor=yellow](1;\n)}% -\pscircle[linestyle=none,fillstyle=gradient,gradmidpoint=0,gradend=yellow,gradbegin=gray]{0.5}} -\multido{\i=-2+1}{5}{% - \pnode(! \i\space 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-\uput[dr](B){${B}$} -\uput[ul](A'){${A'}$} -\uput[ur](B'){${B'}$} -\uput[dl](C){${C}$} -\uput[dr](D){${D}$} -\uput[ul](P){${P}$} -\uput[u](P'){${P'}$} -\uput[ul](C'){${C'}$} -\uput[ur](D'){${D'}$} -\uput[dl](O){${O}$} -\uput[dr](O'){${O'}$} -\psline{<->|}(-3,2)(-3,10) -\uput[l](-3,6){$f$} -\pcline{|<->|}(F)(F') -\uput[u](2,10){$e$} -\psdots(A)(B)(C)(D)(A')(B')(C')(D')(P)(P')(F)(F')(O)(O') -\psdots[linecolor=blue](N1)(N1') -\uput[dl](N1){$\blue {N_1}$} -\uput[dl](N1'){$\blue {N_1'}$} -\psdots[linecolor=gray](M2)(M2') -\uput[dr](M2){\tiny $\gray {(X,Y)}$} -\uput[dr](M2'){\tiny $\gray {(x',y')}$} -\psdots[linecolor=red](M1') -\uput[dr](M1'){\tiny $\red {(\alpha_1,\beta_1)}$} -\end{pspicture} -\end{center} - -\newpage - -Exemples : -\begin{itemize} - \item $A\longrightarrow A'$ - \item $B\longrightarrow B'$ - \item $C\longrightarrow C'$ - \item $D\longrightarrow D'$ - \item $O\longrightarrow O'$ - \item $M_1\longrightarrow M_1'$ - \item $M_2\longrightarrow M'_2$ -\end{itemize} -D\'{e}terminons les coordonn\'{e}es $(\alpha_1,\beta_1)$ de l'intersection de $(PF)$ avec $(AF')$. - -Posons que les coordonn\'{e}es des points essentiels sont : -\begin{itemize} - \item $F(0,f)$ - \item $F'(e,f)$ - \item $A(-a,a)$ - \item $B(a,a)$ - \item $C(a,-a)$ - \item $D(-a,-a)$ - \item $P(X,a)$ -\end{itemize} -\'Equation de $(AF')$ : -\[ -\frac{y-f}{x-e}=\frac{a-f}{-a-e}\Longrightarrow x(a-f)+y(a+e)-a(f+e)=0 -\] -\'Equation de $(PF)$ : -\[ -\frac{x-0}{y-f}=\frac{X-0}{a-f}\Longrightarrow x(a-f)-yX+fX=0 -\] -Intersection $(PF)\bigcap (AF')$ -\[ -\alpha_1=\frac{Xe}{X+a+e}\qquad\beta_1=\frac{a(f+e)+fX}{X+a+e} -\] -Si on prend maintenant, un point d'ordonn\'{e}e $Y\neq X$ par exemple $N_1$ dont l'image $N'_1$ se situe toujours sur $(PF)$, mais \`{a} l'intersection de $PF$ avec la parall\`{e}le \`{a} $x'Ox$ men\'{e}e par le point-image du point de coordonn\'{e}e $(Y,Y)$ (ici $O'$ qui est l'image de $O(0,0)$). - -Il s'agit de d\'{e}terminer l'intersection de $(PF)$ avec la droite d'\'{e}quation : -\[ -y=\beta_2=\frac{a(f+e)+fY}{Y+a+e} -\] -Apr\`{e}s calculs et simplifications, on trouve pour l'abscisse : -\[ -\alpha_2=\frac{Xe}{Y+a+e} -\] -En r\'{e}sum\'{e} si dans le rep\`{e}re $Oxy$, on appelle $({\red X},{\red Y})$ les coordonn\'{e}es d'un point-objet et $({\blue x'},{\blue y'})$ les coordonn\'{e}es du point image dans la transformation \textit{anamorphose oblique} ou \textit{perspective}, les formules qui permettent de passer de l'objet \`{a} l'image s'\'{e}crivent : -\[ -\left\lbrace - \begin{array}{lcl} - {\blue x'}&=&\displaystyle\frac{{\red X}e}{{\red Y}+a+e}\\[0.5cm] - {\blue y'}&=&\displaystyle\frac{a(f+e)+f{\red Y}}{{\red Y}+a+e} - \end{array} -\right. -\] -\end{document} \ No newline at end of file diff --git a/GILGTEST/pst-anamorphosis-doc-part2.pdf b/GILGTEST/pst-anamorphosis-doc-part2.pdf deleted file mode 100644 index a42015d788392f3a847a6842c15c99c68abd25e1..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 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-\psset{ua=3,F=14,D=3,type=inverseperspective,linewidth=0.5\pslinewidth} -\multido{\i=-3+1}{7}{% - \pnode(! \i\space -3){A} - \pnode(! \i\space 3){B} - \psline(A)(B) - \pslineA(A)(B) - }% -\multido{\i=-3+1}{7}{% - \pnode(!-3 \i){A} - \pnode(!3 \i){B} - \pslineA(A)(B) - \psline(A)(B) - }% -\psanamorphosis{tiger.eps} -\psset{fillcolor={[cmyk]{0.2 0.55 0.85 0.0}},linecolor={[cmyk]{0.2 0.55 0.85 0.0}},fontsize=40,scale=1.32 1} -\pstextA(0,2){TIGRE*} -\pstextA(-2.48,1){I} -\pstextA(-2.48,0){G} -\pstextA(-2.48,-1){R} -\pstextA(-2.48,-2){E} -\pstextA(-2.48,-3){*} -\end{pspicture} -} -\end{center} -\begin{lstlisting} -\begin{pspicture}(-3,-4)(3,3) -\psgrid[subgriddiv=0,gridcolor=lightgray,griddots=10,gridlabels=6pt](-3,-3)(3,-6) -\psset{ua=3,F=14,D=3,type=inverseperspective,linewidth=0.5\pslinewidth} -\multido{\i=-3+1}{7}{% - \pnode(! \i\space -3){A} - \pnode(! \i\space 3){B} - \psline(A)(B) - \pslineA(A)(B) - }% -\multido{\i=-3+1}{7}{% - \pnode(!-3 \i){A} - \pnode(!3 \i){B} - \pslineA(A)(B) - \psline(A)(B) - }% -\psanamorphosis{tiger.eps} -\psset{fillcolor={[cmyk]{0.2 0.55 0.85 0.0}},linecolor={[cmyk]{0.2 0.55 0.85 0.0}},fontsize=40,scale=1.32 1} -\pstextA(0,2){TIGRE!} -\pstextA(-2.48,1){I} -\pstextA(-2.48,0){G} -\pstextA(-2.48,-1){R} -\pstextA(-2.48,-2){E} -\pstextA(-2.48,-3){!} -\end{pspicture} -\end{lstlisting} - -\section{Les fichiers pst} - -\begin{center} -\begin{pspicture}[showgrid](-5,-6)(5,3) -\rput(0,-1.3333){% -\psscalebox{0.6667}{% -\begin{pspicture}(-6,-8)(6,4) -\psset{Xv=0,Yv=-100} -\pscircle[doubleline=true,linecolor=black]{3} -\input{luckyluke.pst} -\AFP{luckyluke.pst} -\psset{linewidth=0.5\pslinewidth} -\multido{\n=-2.00+0.50}{9}{% - \pnode(! \n\space -2.00){A} - \pnode(! \n\space 2.00){B} - \psline(A)(B) - \pslineA(A)(B) - } -\multido{\N=-2.00+0.50}{9}{% - \pnode(!-2.0 \N){A} - \pnode(!2.0 \N){B} - \pslineA(A)(B) - \psline(A)(B) - } -\end{pspicture} -}} -\end{pspicture} -\end{center} -\begin{lstlisting} -\begin{pspicture}(-6,-8)(6,4) -\psset{Xv=0,Yv=-100} -\pscircle[doubleline=true,linecolor=black]{3} -\input{luckyluke.pst} -\AFP{luckyluke.pst} -\psset{linewidth=0.5\pslinewidth} -\multido{\n=-2.00+0.50}{9}{% - \pnode(! \n\space -2.00){A} - \pnode(! \n\space 2.00){B} - \psline(A)(B) - \pslineA(A)(B) - } -\multido{\N=-2.00+0.50}{9}{% - \pnode(!-2.0 \N){A} - \pnode(!2.0 \N){B} - \pslineA(A)(B) - \psline(A)(B) - } -\end{pspicture} -\end{lstlisting} -Les fichiers \textsf{.pst} sont des fichiers de commandes PSTricks obtenues par conversion d'un fichier \textsf{.eps} au moyen d'un script \'{e}crit par Jean-Michel \textsc{Sarlat}. - -L'anamorphose d'une telle image est obtenue \`{a} l'aide d'une seule commande \verb+\AFP{luckyluke.pst}+ (AFP $=$ \textbf{A}namorphose \`{a} partir d'un \textbf{F}ichier \textbf{P}STricks). De tels fichiers pourront donc \^{e}tre obtenues au moyen du script ou bien directement sur le serveur de \textsf{syracuse} (adresse \`{a} pr\'{e}ciser). - -En fonction de la complexit\'{e} du fichier (du nombre de lignes de commandes qu'il contient) il sera n\'{e}cessaire d'allouer un suppl\'{e}ment de m\'{e}moire \`{a} \TeX. Par exemple, sous Windows, \`{a} partir de MiK\TeX~2.8, Alexander \textsc{Grahn} donne la proc\'{e}dure \`{a} suivre dans la documentation de son package : `\textsf{animate}' -\begin{lstlisting} -1. Open a DOS command prompt window (execute `cmd.exe' via `Start'! `Run'). -2. At the DOS prompt, enter -initexmf --edit-config-file=latex -3. Type -main_memory=10000000 -into the editor window that opens, save the file and quit the editor. -4. To rebuild the format, enter -initexmf --dump=latex -5. Repeat steps 2-4 with config - -initexmf --edit-config-file=pdflatex -main_memory=10000000 -initexmf --dump=pdflatex - -initexmf --edit-config-file=xelatex -main_memory=10000000 -initexmf --dump=xelatex -\end{lstlisting} - -\section{Normalisation d'une image au format \textsf{.eps}} - -Il est souvent n\'{e}cessaire de ``pr\'{e}parer'' l'image \`{a} anamorphoser. Voici le d\'{e}tail de la proc\'{e}dure suivie \`{a} partir d'une image de Donald Duck captur\'{e}e sur un site de coloriage. - -\url{http://www.waouo.com/wp-content/uploads/2011/06/coloriagedonaldduck.jpg} - -\begin{enumerate} - \item Transformer l'image au format \textsf{bmp} avec \textsf{The Gimp} (par exemple). - \item Vectoriser l'image avec \textsf{Potrace}, en ligne de commande : \textsf{potrace donald.bmp -o donald2.eps} - \item Avec \textsf{pstoedit} convertir au format vectoriel ps simplifi\'{e} avec courbes. On peut op\'{e}rer en ligne de commande : \textsf{pstoedit -f ps donald2.eps donald1.eps} ou bien avec \textsf{GSview} dans le menu Edition, cliquer sur \textsf{Conversion vers un format vectoriel} et choisir \textsf{ps : Simplified Postscript with curves}, on enregistre sous le nom \textsf{donald1.eps}. - \item Avec votre \'{e}diteur de texte rechercher \`{a} la fin du fichier la ligne qui donne les dimensions de la bo\^{\i}te : \verb+%%BoundingBox: 4 7 453 640+ . - \item La hauteur de l'image eps est $640-7 =633$\,pts, c'est la plus grande dimension. Supposons que votre image finale doive poss\'{e}der une longueur de 4\,cm dans sa plus grande dimension. Sachant que 1\,cm vaut 28.45274\,pts, il faut donc lui appliquer un facteur d'\'{e}chelle \'{e}gal \`{a} $\dfrac{4\times28.45274}{633}$. -\item Ensuite il faut d\'{e}placer cette image pour que le centre de celle-ci soit \`{a} l'origine $(0,0)$, il faut donc appliquer la translation $-\dfrac{453+4}{2},\,-\dfrac{640+7}{2}$, ce qui convertit en postscript se traduira par l'ajout de ces deux lignes dans le fichier \textsf{donald1.eps}, au d\'{e}but du fichier juste apr\`{e}s la ligne : \verb+%%Page: 1 1+ -\begin{lstlisting} - 4 28.45274 mul 633 div dup scale - 4 453 add 2 div neg 640 7 add 2 div neg translate -\end{lstlisting} - On enregistre ce fichier. -\item \textsf{pstoedit} intervient \`{a} nouveau, avec les m\^{e}mes options, et on enregistre le fichier final sous le nom : \textsf{donald.eps}. -\end{enumerate} -\begin{center} -\begin{pspicture}[showgrid](-8,-4)(8,10) -\pscircle[doubleline=true]{3} -\psset{Yv=100,linestyle=dotted} -\psanamorphosis[scale=1 -1](0,0){donald.eps} -\multido{\n=-2.00+0.50}{9}{% - 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390.473 23.7031 393.582 24.7969 395.879 27.0 curveto - 398.176 29.2031 399.379 32.0938 399.379 35.7969 curveto - closepath - 413.176 85.2656 moveto - 413.176 86.7656 412.676 87.9688 411.785 88.9688 curveto - 410.879 90.0625 409.676 90.5625 408.379 90.5625 curveto - 407.082 90.5625 405.988 90.0625 405.082 88.9688 curveto - 404.176 87.875 403.676 86.6719 403.676 85.1719 curveto - 403.676 83.7656 404.176 82.5625 405.082 81.5781 curveto - 405.988 80.4688 407.082 79.9688 408.379 79.9688 curveto - 409.676 79.9688 410.879 80.4688 411.785 81.5781 curveto - 412.676 82.5625 413.176 83.7656 413.176 85.2656 curveto - closepath - 416.082 25.0 moveto - 416.082 26.5 lineto - 413.879 27.0 412.785 28.3906 412.785 30.8906 curveto - 412.785 69.9844 lineto - 409.082 67.2812 405.176 65.6719 401.082 64.9844 curveto - 401.082 63.4844 lineto - 402.785 63.0781 403.879 62.2812 404.285 60.9844 curveto - 404.379 60.4844 404.488 58.9844 404.488 56.6875 curveto - 404.488 30.8906 lineto - 404.488 28.5 403.379 27.0 401.082 26.5 curveto - 401.082 25.0 lineto - 416.082 25.0 lineto - closepath - 439.477 35.7969 moveto - 439.477 38.5938 438.664 41.2969 437.07 43.7969 curveto - 435.57 46.3906 432.773 49.4844 428.773 53.1875 curveto - 425.383 56.2812 423.68 59.0781 423.68 61.6875 curveto - 423.68 63.375 424.18 64.6719 425.086 65.7812 curveto - 425.977 66.7812 427.18 67.2812 428.68 67.2812 curveto - 432.18 67.2812 434.367 64.6719 435.18 59.4844 curveto - 435.477 57.4844 lineto - 435.68 56.6875 lineto - 437.367 56.6875 lineto - 437.367 67.9844 lineto - 434.367 68.6719 431.883 68.9844 429.883 68.9844 curveto - 426.383 68.9844 423.477 67.9844 421.273 65.7812 curveto - 418.977 63.7812 417.883 61.0781 417.883 57.7812 curveto - 417.883 55.0781 418.883 52.5781 420.883 50.1875 curveto - 422.273 48.4844 424.383 46.2812 427.273 43.4844 curveto - 429.977 40.9844 431.57 39.1875 432.07 38.2969 curveto - 432.977 36.8906 433.367 35.0938 433.367 33.0 curveto - 433.367 28.2969 431.477 25.9062 427.68 25.9062 curveto - 423.586 25.9062 420.977 29.8906 419.977 37.8906 curveto - 418.289 37.8906 lineto - 418.289 25.5 lineto - 421.586 24.2969 424.383 23.7031 426.68 23.7031 curveto - 430.57 23.7031 433.68 24.7969 435.977 27.0 curveto - 438.273 29.2031 439.477 32.0938 439.477 35.7969 curveto - closepath - 440.383 25.0 moveto -eofill -gsave %{ - grestore %} - grestore %} - grestore %} - grestore %} - showpage -%%BoundingBox: 0 7 440 92 -showpage -%%EOF diff --git a/opt/index.xml b/opt/index.xml new file mode 100644 index 0000000..7697097 --- /dev/null +++ b/opt/index.xml @@ -0,0 +1,3 @@ + + Scripts d'appoint + diff --git a/opt/psftopst.pl b/opt/psftopst.pl new file mode 100755 index 0000000..e127258 --- /dev/null +++ b/opt/psftopst.pl @@ -0,0 +1,347 @@ +eval '(exit $?0)' && eval 'exec perl -S $0 ${1+"$@"}' && eval 'exec perl -S $0 $argv:q' + if 0; +use strict; +# ============================================================================== +# psftopdf +# Version 1.0 (Mercredi 19 octobre 2011) Jean-Michel Sarlat +# Ce script fait partie du projet pst-anamorphosis (Gilg, Luque, Sarlat) +# http://melusine.eu.org/syracuse/G/pst-anamorphosis Checkout +# http://melusine.eu.org/syracuse/G/git/?p=pst-anamorphosis.git git +# ============================================================================== + +our $windows_pstoedit = ""; + +our $on_windows = $^O =~ /^MSWin/; +our $GS = $on_windows ? "gswin32c" : "gs"; +our $PS = $on_windows ? $windows_pstoedit : "pstoedit"; + + +# === Acquisition des options de la ligne de commande ------------------------- +$::opt_dimmax = 4; # Dimension maximale : 4 cm par défaut +$::opt_t = 0; # Transformation initiale par pstoedit +use Getopt::Long; +GetOptions( + "dimmax=s", + "t" +); + +our $debug = 1; + +our $GSBBOX = "$GS -sDEVICE=bbox -dBATCH -dNOPAUSE -dNOSAFER -P -c save pop -f"; + +our $cm = 28.3464567; + +our $Fichier = $ARGV[0]; +-f $Fichier or die "Fichier <$Fichier> introuvable !\n"; + +our ($Nom, $Dir, $Ext) = &FichierNRE($Fichier); + +# === Transformation éventuelle par pstoedit ----------------------------------- +if ($::opt_t) { + use File::Copy; + my $f = "$Nom-original$Ext"; + copy($Fichier, $f); + my @a = ($PS, "-f ps", $f, $Fichier); + $debug and print STDERR "Processing by pstoedit...\n"; + system(@a) == 0 or die "Running pstoedit failed\nCommand :".join(" ",@a)."\n"; + $debug and print STDERR "Ok!\n"; +} +# ============================================================================== + +our $ps = &FichierListe($Fichier); +our $table = []; +our @Bbox = (); + +our $cmyk = {}; +our $centrex = 0; +our $centrey = 0; + +our $facteur = 1; +our $DimMax = $::opt_dimmax; + +our $PageSizeX = 0; +our $PageSizeY = 0; + +our @currentpoint = (); +our @lastpoint = (); +our $dmax = 0; + +# ============================================================================== +# === Analyse +# ============================================================================== +$$table[0] = { + fichier => $Fichier, + source => &FichierScalaire($Fichier), + createur => "psftopst" +}; +&LecturePostScript($table, $ps); +$$table[0]->{bbox} = \@Bbox; +# ============================================================================== +# === Production +# ============================================================================== +our $pst = &EcritureFichierPST($table, $Nom); +open PST, ">$Nom.pst" and print PST $pst and close PST; +# ============================================================================== + +sub EcritureFichierPST { + my ($r, $n) = @_; + my $c = $$r[0]->{cmyk}; + my $nc = 1; + my $out = "%\@PATRON:pstricks\n"; + $out .= "\\makeatletter\n\\def\\psfs\@asolid{\\pst\@fill{\\pst\@usecolor\\psfillcolor eofill}}\n\\makeatother\n"; + # Définition des couleurs dans le fichier pstricks + # Elles sont reprises dans la table représentant le fichier ps + $out .= "%\@COULEURS:\n"; + foreach (@$c) { + my $roman = &Roman($nc); + $$cmyk{$_} = "Couleur$roman"; + s/\s/\,/g; + $out .= "\\definecolor{Couleur$roman}{cmyk}{$_}\n"; + $nc++; + } + # Acquisition du centre de l'image + my $b = $$r[0]->{bbox}; + $out .= "%\@BOUNDINGBOX: " . join(" ", @$b) . "\n"; + $centrex = ($$b[2] + $$b[0]) / 2; + $centrey = ($$b[3] + $$b[1]) / 2; + $out .= "%\@TRANSLATION: -($centrex,$centrey)\n"; + my $l = ($$b[2] - $$b[0]); + my $h = ($$b[3] - $$b[1]); + my $max = $l; $max = $h if $h > $l; + $facteur = ($DimMax * $cm) / $max; + $out .= "%\@FACTEUR: $facteur\n"; + my $abox = &xy_couple_modifie($b); + $out .= "%\@PSPICTURE:\n"; + $out .= "% \\begin{pspicture}$abox\n"; + if ($PageSizeX) { + my $clipframe = &xy_couple_modifie([0, 0, $PageSizeX, $PageSizeY]); + $out .= "%\@CLIPPING: $PageSizeX $PageSizeY\n"; + $out .= "% \\begin{psclip}{\\psframe[linestyle=none]$clipframe}\n"; + } + $out .= "%\@PICTURE:\n"; + # Éléments de construction + for (my $i = 1; $i < scalar @$r; $i++) { + if ($$r[$i]->{path}) { + $out .= "%% Path : $i\n"; + my $couleur = $$cmyk{$$r[$i]->{setcmykcolor}}; + my $epaisseur = $$r[$i]->{setlinewidth}; $epaisseur = sprintf("linewidth=%0.5fpt", $epaisseur / $facteur); + my $t = $$r[$i]->{type}; + $t eq "fill" and $out .= "\\pscustom[fillstyle=solid,fillcolor=$couleur,linestyle=none]{\n"; + $t eq "eofill" and $out .= "\\pscustom[fillstyle=asolid,fillcolor=$couleur,linestyle=none]{\n"; + $t eq "clip" and $out .= "\\psclip{\\psframe[fillstyle=none,linestyle=none]$abox}\%\n\\pscustom{\n"; + $t eq "stroke" and $out .= "\\pscustom[$epaisseur,linecolor=$couleur]{\n"; + my $p = $$r[$i]->{path}; + my $n = $$r[$i]->{closepath}; + foreach (@$p) { + my %e = %$_; + $e{t} eq "moveto" and $out .= "\\moveto".&xy_couple_modifie($e{p}); + $e{t} eq "lineto" and $out .= "\\psline".&xy_couple_modifie($e{p}); + $e{t} eq "curveto" and $out .= "\\psbezier".&xy_couple_modifie($e{p}); + $e{t} eq "closepath" and $out .= "\\closepath"; + $out .= "\n"; + @lastpoint = @currentpoint; + } + $out .= "}\n"; + $$r[$i]->{type} eq "clip" and $out .= "\\endpsclip\n"; + } + } + $out .= "%\@---\n"; + $out .= "% \\end{psclip}\n" if $PageSizeX; + $out .= "% \\end{pspicture}\n"; +} + + +sub LecturePostScript { + my ($t, $p) = @_; + my $pathnumber = 0; + my $natpath = ""; + my $path = []; + my $fpath = 0; + my $niveau = 0; + my $nclosepath = 0; # Nombre de closepath rencontrés + foreach (@$p) { + /^\%\s*(\d+)\s+pathnumber/ and $pathnumber = $1 and $$t[$pathnumber] = {}; + /^\s*gsave/ and $niveau++; + /^\s*grestore/ and $niveau--; + s/setPageSize\s*$// and &setPageSize($_); + /^\%\%BoundingBox\: ([\d\.-]+) ([\d\.-]+) ([\d\.-]+) ([\d\.-]+)/ and &setBbox($1,$2,$3,$4); + if ($pathnumber) { + /^\%\s*filledpath/ and $natpath = "filledpath" and next; + /^\%\s*eofilledpath/ and $natpath = "eofilledpath" and next; + /^\%\s*strokedpath/ and $natpath = "strokedpath" and next; + /^\%\s*clippath/ and $natpath = "clippath" and next; + /setlinewidth$/ and $$t[$pathnumber]->{setlinewidth} = &setlinewidth($_) and next; + /setcmykcolor$/ and $$t[$pathnumber]->{setcmykcolor} = &setcmykcolor($_) and next; + /^newpath/ and $fpath = 1 and $path = [] and next; + if ($fpath) { + s/moveto\s*$// and push(@$path, {t => "moveto", p => &xy($_)}); + s/lineto\s*$// and push(@$path, {t => "lineto", p => &xy($_)}); + s/curveto\s*$// and push(@$path, {t => "curveto", p => &xy($_)}); + /closepath/ and push(@$path, {t => "closepath", p => 1}) and $nclosepath++; + if (/(stroke)/ or /(eofill)/ or /(fill)/ or /(clip)/) { + $fpath = 0; + $$t[$pathnumber]->{path} = $path; + $$t[$pathnumber]->{type} = $1; + $$t[$pathnumber]->{niveau} = $niveau; + $$t[$pathnumber]->{closepath} = $nclosepath; + $pathnumber = 0; + $nclosepath = 0; + } + } + } + } + $$t[0]->{cmyk} = []; + foreach (keys %$cmyk) { + push @{$$t[0]->{cmyk}}, $_; + } +} + +sub setPageSize { + my $s = shift; + $s =~ s/^\s*|\s*$//g; + ($PageSizeX, $PageSizeY) = split /\s+/, $s; +} + +sub setlinewidth { + my $s = shift; + $s =~ s/^\s*|\s+setlinewidth$//g; + return $s; +} + +sub setcmykcolor { + my $s = shift; + $s =~ s/^\s*|\s+setcmykcolor$//g; + $$cmyk{$s} = 1; + return $s; +} + +sub xy { + my $s = shift; + $s =~ s/^\s*|\s*$//g; + my @xy = split /\s+/, $s; + return \@xy; +} + +sub xy_couple_modifie { + my $xy = shift; + my @l = @$xy; @currentpoint = ($l[-2],$l[-1]); + my $s = ""; + while (my ($x, $y) = splice(@l, 0, 2)) { + $s .= sprintf("(%0.8f,%0.8f)", ($x - $centrex) * $facteur, ($y - $centrey) * $facteur); + } + return $s; +} + +# === Contenu d'un fichier et éléments du nom ---------------------------------- +# ------------------------------------------------------------------------------ +# Contenu sous forme d'une liste de lignes +sub FichierListe { + my $f = shift; + open(FICH, $f) or die "Le fichier $f est introuvable !\n"; + my @l = ; + close FICH; + chomp @l; + return \@l; +} +# Contenu en un seul élément +sub FichierScalaire { + my $f = shift; + local $/; + open(FICH, $f) or die "Le fichier $f est introuvable !\n"; + my $c = ; + close FICH; + return $c; +} +# Nom, Repertoire et Extension d'un fichier +sub FichierNRE { + my $f = shift; + use File::Basename; + my ($n, $r, $e) = fileparse($f,qw{\..*}); + $e =~ s/^\.//; + return ($n, $r, $e); +} +# === Acquisition de la BoundingBox -------------------------------------------- +sub setBbox { + @Bbox = @_; +} + +# === Écriture d'un nombre en chiffres romains --------------------------------- +# Code emprunté au module Roman.pm ; http://search.cpan.org/dist/Roman +# AUTEURS: +# OZAWA Sakuro 1995-1997 +# Alexandr Ciornii, C<< >> 2007 +# ------------------------------------------------------------------------------ +sub Roman { + my $arg = shift; + 0 < $arg and $arg < 4000 or return undef; + my %roman_digit = qw(1 IV 10 XL 100 CD 1000 MMMMMM); + my @figure = reverse sort keys %roman_digit; + $roman_digit{$_} = [split(//, $roman_digit{$_}, 2)] foreach @figure; + my($x, $roman); + foreach (@figure) { + my($digit, $i, $v) = (int($arg / $_), @{$roman_digit{$_}}); + if (1 <= $digit and $digit <= 3) { + $roman .= $i x $digit; + } elsif ($digit == 4) { + $roman .= "$i$v"; + } elsif ($digit == 5) { + $roman .= $v; + } elsif (6 <= $digit and $digit <= 8) { + $roman .= $v . $i x ($digit - 5); + } elsif ($digit == 9) { + $roman .= "$i$x"; + } + $arg -= $digit * $_; + $x = $i; + } + return $roman; +} +# === Wanda -------------------------------------------------------------------- +sub WandaExecutePlugin { + my ($cnf, $elm, $args) = @_; +} +sub WandaAnalyseLignes { + my $cnf = shift; + my $l = shift; + my $c = {}; + my $e = "CORPS"; + my @p = (); + # Traitement + for(my $i=0; $i < scalar @$l; $i++) { + if ($$l[$i] =~ /^%@([\da-zA-Z_]+)\s*:\s*(.+?)\s*$/) { + # Affectation simple : la valeur suit le nom dans la ligne ----- + $$c{$1} = $2; + } elsif ($$l[$i] =~ /^%@([\da-zA-Z_]+)\s*:\s*$/) { + # Affectation bloc : la valeur est constituée du bloc à suivre - + push @p, $e; $e = $1; + } elsif ($$l[$i] =~ /^%@\-\-\-/) { + # On ferme l'élément en cours... ------------------------------- + $e = pop @p; + } elsif ($$l[$i] =~ /^%@\@lib:\s*(.+?)\s+$/) { + # On ajoute le contenu d'un fichier de la librairie ------------ + if (-f "$$cnf{DIR}/lib/$1") { + $$c{$e} .= qx{cat "$$cnf{DIR}/lib/$1"} if $e; + } + } elsif ($$l[$i] =~ /^%@\@inc:\s*(.+?)\s+$/) { + # On ajoute le contenu d'un fichier local ---------------------- + if (-f $1) { + $$c{$e} .= qx{cat $1} if $e; + } + } elsif ($$l[$i] =~ /^%@\@exec:\s*(.+?)\s+$/) { + # On éxécute un plugin ----------------------------------------- + $$c{$e} .= &WandaExecutePlugin($cnf, $c, $1); + } else { + # La ligne est enregistrée dans l'éventuel élément en cours ---- + $$c{$e} .= $$l[$i] if $e; + } + } + return $c; +} +sub WandaAnalyseContenu { + my ($cnf, $fichier) = @_; + open(SRC, $fichier); my @LIGNES = ; close(SRC); + return &WandaAnalyseLignes($cnf, \@LIGNES); +} + + + diff --git a/opt/pstopst b/opt/pstopst new file mode 100755 index 0000000..e127258 --- /dev/null +++ b/opt/pstopst @@ -0,0 +1,347 @@ +eval '(exit $?0)' && eval 'exec perl -S $0 ${1+"$@"}' && eval 'exec perl -S $0 $argv:q' + if 0; +use strict; +# ============================================================================== +# psftopdf +# Version 1.0 (Mercredi 19 octobre 2011) Jean-Michel Sarlat +# Ce script fait partie du projet pst-anamorphosis (Gilg, Luque, Sarlat) +# http://melusine.eu.org/syracuse/G/pst-anamorphosis Checkout +# http://melusine.eu.org/syracuse/G/git/?p=pst-anamorphosis.git git +# ============================================================================== + +our $windows_pstoedit = ""; + +our $on_windows = $^O =~ /^MSWin/; +our $GS = $on_windows ? "gswin32c" : "gs"; +our $PS = $on_windows ? $windows_pstoedit : "pstoedit"; + + +# === Acquisition des options de la ligne de commande ------------------------- +$::opt_dimmax = 4; # Dimension maximale : 4 cm par défaut +$::opt_t = 0; # Transformation initiale par pstoedit +use Getopt::Long; +GetOptions( + "dimmax=s", + "t" +); + +our $debug = 1; + +our $GSBBOX = "$GS -sDEVICE=bbox -dBATCH -dNOPAUSE -dNOSAFER -P -c save pop -f"; + +our $cm = 28.3464567; + +our $Fichier = $ARGV[0]; +-f $Fichier or die "Fichier <$Fichier> introuvable !\n"; + +our ($Nom, $Dir, $Ext) = &FichierNRE($Fichier); + +# === Transformation éventuelle par pstoedit ----------------------------------- +if ($::opt_t) { + use File::Copy; + my $f = "$Nom-original$Ext"; + copy($Fichier, $f); + my @a = ($PS, "-f ps", $f, $Fichier); + $debug and print STDERR "Processing by pstoedit...\n"; + system(@a) == 0 or die "Running pstoedit failed\nCommand :".join(" ",@a)."\n"; + $debug and print STDERR "Ok!\n"; +} +# ============================================================================== + +our $ps = &FichierListe($Fichier); +our $table = []; +our @Bbox = (); + +our $cmyk = {}; +our $centrex = 0; +our $centrey = 0; + +our $facteur = 1; +our $DimMax = $::opt_dimmax; + +our $PageSizeX = 0; +our $PageSizeY = 0; + +our @currentpoint = (); +our @lastpoint = (); +our $dmax = 0; + +# ============================================================================== +# === Analyse +# ============================================================================== +$$table[0] = { + fichier => $Fichier, + source => &FichierScalaire($Fichier), + createur => "psftopst" +}; +&LecturePostScript($table, $ps); +$$table[0]->{bbox} = \@Bbox; +# ============================================================================== +# === Production +# ============================================================================== +our $pst = &EcritureFichierPST($table, $Nom); +open PST, ">$Nom.pst" and print PST $pst and close PST; +# ============================================================================== + +sub EcritureFichierPST { + my ($r, $n) = @_; + my $c = $$r[0]->{cmyk}; + my $nc = 1; + my $out = "%\@PATRON:pstricks\n"; + $out .= "\\makeatletter\n\\def\\psfs\@asolid{\\pst\@fill{\\pst\@usecolor\\psfillcolor eofill}}\n\\makeatother\n"; + # Définition des couleurs dans le fichier pstricks + # Elles sont reprises dans la table représentant le fichier ps + $out .= "%\@COULEURS:\n"; + foreach (@$c) { + my $roman = &Roman($nc); + $$cmyk{$_} = "Couleur$roman"; + s/\s/\,/g; + $out .= "\\definecolor{Couleur$roman}{cmyk}{$_}\n"; + $nc++; + } + # Acquisition du centre de l'image + my $b = $$r[0]->{bbox}; + $out .= "%\@BOUNDINGBOX: " . join(" ", @$b) . "\n"; + $centrex = ($$b[2] + $$b[0]) / 2; + $centrey = ($$b[3] + $$b[1]) / 2; + $out .= "%\@TRANSLATION: -($centrex,$centrey)\n"; + my $l = ($$b[2] - $$b[0]); + my $h = ($$b[3] - $$b[1]); + my $max = $l; $max = $h if $h > $l; + $facteur = ($DimMax * $cm) / $max; + $out .= "%\@FACTEUR: $facteur\n"; + my $abox = &xy_couple_modifie($b); + $out .= "%\@PSPICTURE:\n"; + $out .= "% \\begin{pspicture}$abox\n"; + if ($PageSizeX) { + my $clipframe = &xy_couple_modifie([0, 0, $PageSizeX, $PageSizeY]); + $out .= "%\@CLIPPING: $PageSizeX $PageSizeY\n"; + $out .= "% \\begin{psclip}{\\psframe[linestyle=none]$clipframe}\n"; + } + $out .= "%\@PICTURE:\n"; + # Éléments de construction + for (my $i = 1; $i < scalar @$r; $i++) { + if ($$r[$i]->{path}) { + $out .= "%% Path : $i\n"; + my $couleur = $$cmyk{$$r[$i]->{setcmykcolor}}; + my $epaisseur = $$r[$i]->{setlinewidth}; $epaisseur = sprintf("linewidth=%0.5fpt", $epaisseur / $facteur); + my $t = $$r[$i]->{type}; + $t eq "fill" and $out .= "\\pscustom[fillstyle=solid,fillcolor=$couleur,linestyle=none]{\n"; + $t eq "eofill" and $out .= "\\pscustom[fillstyle=asolid,fillcolor=$couleur,linestyle=none]{\n"; + $t eq "clip" and $out .= "\\psclip{\\psframe[fillstyle=none,linestyle=none]$abox}\%\n\\pscustom{\n"; + $t eq "stroke" and $out .= "\\pscustom[$epaisseur,linecolor=$couleur]{\n"; + my $p = $$r[$i]->{path}; + my $n = $$r[$i]->{closepath}; + foreach (@$p) { + my %e = %$_; + $e{t} eq "moveto" and $out .= "\\moveto".&xy_couple_modifie($e{p}); + $e{t} eq "lineto" and $out .= "\\psline".&xy_couple_modifie($e{p}); + $e{t} eq "curveto" and $out .= "\\psbezier".&xy_couple_modifie($e{p}); + $e{t} eq "closepath" and $out .= "\\closepath"; + $out .= "\n"; + @lastpoint = @currentpoint; + } + $out .= "}\n"; + $$r[$i]->{type} eq "clip" and $out .= "\\endpsclip\n"; + } + } + $out .= "%\@---\n"; + $out .= "% \\end{psclip}\n" if $PageSizeX; + $out .= "% \\end{pspicture}\n"; +} + + +sub LecturePostScript { + my ($t, $p) = @_; + my $pathnumber = 0; + my $natpath = ""; + my $path = []; + my $fpath = 0; + my $niveau = 0; + my $nclosepath = 0; # Nombre de closepath rencontrés + foreach (@$p) { + /^\%\s*(\d+)\s+pathnumber/ and $pathnumber = $1 and $$t[$pathnumber] = {}; + /^\s*gsave/ and $niveau++; + /^\s*grestore/ and $niveau--; + s/setPageSize\s*$// and &setPageSize($_); + /^\%\%BoundingBox\: ([\d\.-]+) ([\d\.-]+) ([\d\.-]+) ([\d\.-]+)/ and &setBbox($1,$2,$3,$4); + if ($pathnumber) { + /^\%\s*filledpath/ and $natpath = "filledpath" and next; + /^\%\s*eofilledpath/ and $natpath = "eofilledpath" and next; + /^\%\s*strokedpath/ and $natpath = "strokedpath" and next; + /^\%\s*clippath/ and $natpath = "clippath" and next; + /setlinewidth$/ and $$t[$pathnumber]->{setlinewidth} = &setlinewidth($_) and next; + /setcmykcolor$/ and $$t[$pathnumber]->{setcmykcolor} = &setcmykcolor($_) and next; + /^newpath/ and $fpath = 1 and $path = [] and next; + if ($fpath) { + s/moveto\s*$// and push(@$path, {t => "moveto", p => &xy($_)}); + s/lineto\s*$// and push(@$path, {t => "lineto", p => &xy($_)}); + s/curveto\s*$// and push(@$path, {t => "curveto", p => &xy($_)}); + /closepath/ and push(@$path, {t => "closepath", p => 1}) and $nclosepath++; + if (/(stroke)/ or /(eofill)/ or /(fill)/ or /(clip)/) { + $fpath = 0; + $$t[$pathnumber]->{path} = $path; + $$t[$pathnumber]->{type} = $1; + $$t[$pathnumber]->{niveau} = $niveau; + $$t[$pathnumber]->{closepath} = $nclosepath; + $pathnumber = 0; + $nclosepath = 0; + } + } + } + } + $$t[0]->{cmyk} = []; + foreach (keys %$cmyk) { + push @{$$t[0]->{cmyk}}, $_; + } +} + +sub setPageSize { + my $s = shift; + $s =~ s/^\s*|\s*$//g; + ($PageSizeX, $PageSizeY) = split /\s+/, $s; +} + +sub setlinewidth { + my $s = shift; + $s =~ s/^\s*|\s+setlinewidth$//g; + return $s; +} + +sub setcmykcolor { + my $s = shift; + $s =~ s/^\s*|\s+setcmykcolor$//g; + $$cmyk{$s} = 1; + return $s; +} + +sub xy { + my $s = shift; + $s =~ s/^\s*|\s*$//g; + my @xy = split /\s+/, $s; + return \@xy; +} + +sub xy_couple_modifie { + my $xy = shift; + my @l = @$xy; @currentpoint = ($l[-2],$l[-1]); + my $s = ""; + while (my ($x, $y) = splice(@l, 0, 2)) { + $s .= sprintf("(%0.8f,%0.8f)", ($x - $centrex) * $facteur, ($y - $centrey) * $facteur); + } + return $s; +} + +# === Contenu d'un fichier et éléments du nom ---------------------------------- +# ------------------------------------------------------------------------------ +# Contenu sous forme d'une liste de lignes +sub FichierListe { + my $f = shift; + open(FICH, $f) or die "Le fichier $f est introuvable !\n"; + my @l = ; + close FICH; + chomp @l; + return \@l; +} +# Contenu en un seul élément +sub FichierScalaire { + my $f = shift; + local $/; + open(FICH, $f) or die "Le fichier $f est introuvable !\n"; + my $c = ; + close FICH; + return $c; +} +# Nom, Repertoire et Extension d'un fichier +sub FichierNRE { + my $f = shift; + use File::Basename; + my ($n, $r, $e) = fileparse($f,qw{\..*}); + $e =~ s/^\.//; + return ($n, $r, $e); +} +# === Acquisition de la BoundingBox -------------------------------------------- +sub setBbox { + @Bbox = @_; +} + +# === Écriture d'un nombre en chiffres romains --------------------------------- +# Code emprunté au module Roman.pm ; http://search.cpan.org/dist/Roman +# AUTEURS: +# OZAWA Sakuro 1995-1997 +# Alexandr Ciornii, C<< >> 2007 +# ------------------------------------------------------------------------------ +sub Roman { + my $arg = shift; + 0 < $arg and $arg < 4000 or return undef; + my %roman_digit = qw(1 IV 10 XL 100 CD 1000 MMMMMM); + my @figure = reverse sort keys %roman_digit; + $roman_digit{$_} = [split(//, $roman_digit{$_}, 2)] foreach @figure; + my($x, $roman); + foreach (@figure) { + my($digit, $i, $v) = (int($arg / $_), @{$roman_digit{$_}}); + if (1 <= $digit and $digit <= 3) { + $roman .= $i x $digit; + } elsif ($digit == 4) { + $roman .= "$i$v"; + } elsif ($digit == 5) { + $roman .= $v; + } elsif (6 <= $digit and $digit <= 8) { + $roman .= $v . $i x ($digit - 5); + } elsif ($digit == 9) { + $roman .= "$i$x"; + } + $arg -= $digit * $_; + $x = $i; + } + return $roman; +} +# === Wanda -------------------------------------------------------------------- +sub WandaExecutePlugin { + my ($cnf, $elm, $args) = @_; +} +sub WandaAnalyseLignes { + my $cnf = shift; + my $l = shift; + my $c = {}; + my $e = "CORPS"; + my @p = (); + # Traitement + for(my $i=0; $i < scalar @$l; $i++) { + if ($$l[$i] =~ /^%@([\da-zA-Z_]+)\s*:\s*(.+?)\s*$/) { + # Affectation simple : la valeur suit le nom dans la ligne ----- + $$c{$1} = $2; + } elsif ($$l[$i] =~ /^%@([\da-zA-Z_]+)\s*:\s*$/) { + # Affectation bloc : la valeur est constituée du bloc à suivre - + push @p, $e; $e = $1; + } elsif ($$l[$i] =~ /^%@\-\-\-/) { + # On ferme l'élément en cours... ------------------------------- + $e = pop @p; + } elsif ($$l[$i] =~ /^%@\@lib:\s*(.+?)\s+$/) { + # On ajoute le contenu d'un fichier de la librairie ------------ + if (-f "$$cnf{DIR}/lib/$1") { + $$c{$e} .= qx{cat "$$cnf{DIR}/lib/$1"} if $e; + } + } elsif ($$l[$i] =~ /^%@\@inc:\s*(.+?)\s+$/) { + # On ajoute le contenu d'un fichier local ---------------------- + if (-f $1) { + $$c{$e} .= qx{cat $1} if $e; + } + } elsif ($$l[$i] =~ /^%@\@exec:\s*(.+?)\s+$/) { + # On éxécute un plugin ----------------------------------------- + $$c{$e} .= &WandaExecutePlugin($cnf, $c, $1); + } else { + # La ligne est enregistrée dans l'éventuel élément en cours ---- + $$c{$e} .= $$l[$i] if $e; + } + } + return $c; +} +sub WandaAnalyseContenu { + my ($cnf, $fichier) = @_; + open(SRC, $fichier); my @LIGNES = ; close(SRC); + return &WandaAnalyseLignes($cnf, \@LIGNES); +} + + + -- 2.20.1

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