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diff --git a/Master/texmf-dist/doc/generic/pst-3d/pst-3d-doc.tex b/Master/texmf-dist/doc/generic/pst-3d/pst-3d-doc.tex new file mode 100644 index 00000000000..0211848e590 --- /dev/null +++ b/Master/texmf-dist/doc/generic/pst-3d/pst-3d-doc.tex @@ -0,0 +1,783 @@ +%% $Id: pst-3d-doc.tex 289 2010-02-13 14:35:35Z herbert $ +\documentclass[11pt,english,BCOR10mm,DIV12,bibliography=totoc,parskip=false,smallheadings + headexclude,footexclude,oneside,dvipsnames,svgnames]{pst-doc} +\listfiles + +\usepackage[utf8]{inputenc} +\usepackage{pst-3d} +\SpecialCoor +\let\pstFV\fileversion +\let\belowcaptionskip\abovecaptionskip +% +\makeatletter +\renewcommand*\l@subsection{\bprot@dottedtocline{2}{1.5em}{3.6em}} +\renewcommand*\l@subsubsection{\bprot@dottedtocline{3}{3.8em}{4.5em}} +\makeatother +\def\bgImage{} +\lstset{explpreset={pos=l,width=-99pt,overhang=0pt,hsep=\columnsep,vsep=\bigskipamount,rframe={}}, + escapechar=?} +\def\textat{\char064}% +\usepackage{shortvrb} +\MakeShortVerb{|} +\def\la{<} +\def\ra{>} +\def\arc{\mathrm{arc}} +\def\sign{\mathrm{sign}} +\def\PiCTeX{\texttt{PiCTeX}} +\def\endmacro{} + +\begin{document} +\title{\texttt{pst-3d}\\basic three dimension functions \\\small v.\pstFV} +\docauthor{Herbert Vo\ss} +\author{Timothy Van Zandt\\Herbert Vo\ss} +\date{\today} + +\maketitle + +\begin{abstract} +This version of \LPack{pst-3d} uses the extended keyval handling +of \LPack{pst-xkey}. + +\vfill +\noindent +Thanks to: +\end{abstract} + +\clearpage +\tableofcontents + +\clearpage + +\section[PostScript]{PostScript functions \nxLps{SetMatrixThreeD},\nxLps{ProjThreeD}, and \nxLps{SetMatrixEmbed}} + \xLps{SetMatrixThreeD}\xLps{ProjThreeD}\xLps{SetMatrixEmbed} +The \Index{viewpoint} for 3D coordinates is given by three angles: $\alpha$, $\beta$ and + $\gamma$. $\alpha$ and $\beta$ determine the direction from which one is + looking. $\gamma$ then determines the orientation of the observing. + + When $\alpha$, $\beta$ and $\gamma$ are all zero, the observer is looking + from the negative part of the $y$-axis, and sees the $xz$-plane the way in + 2D one sees the $xy$ plan. Hence, to convert the 3D coordinates to their 2D + project, $\la x, y, z\ra$ map to $\la x, z\ra$. + + When the orientation is different, we rotate the coordinates, and then + perform the same projection. + + We move up to latitude $\beta$, over to longitude $\alpha$, and then rotate + by $\gamma$. This means that we first rotate around $y$-axis by $\gamma$, + then around $x$-axis by $\beta$, and the around $z$-axis by $\alpha$. + + Here are the matrices: + \begin{eqnarray*} + R_z(\alpha) & = & \left[ + \begin{array}{ccc} + \cos \alpha & -\sin \alpha & 0 \\ + \sin \alpha & cos \alpha & 0 \\ + 0 & 0 & 1 + \end{array} \right] \\ + R_x(\beta) & = & \left[ + \begin{array}{ccc} + 1 & 0 & 0 \\ + 0 & \cos \beta & \sin \beta \\ + 0 & -\sin \beta & \cos \beta + \end{array} \right] \\ + R_y(\gamma) & = & \left[ + \begin{array}{ccc} + \cos \gamma & 0 & -\sin \gamma \\ + 0 & 1 & 0 \\ + \sin \gamma & 0 & \cos \gamma + \end{array} \right] + \end{eqnarray*} + + The rotation of a coordinate is then performed by the matrix $R_z(\alpha) + R_x(\beta) R_y(\gamma)$. The first and third columns of the matrix are the + basis vectors of the plan upon which the 3D coordinates are project (the old + basis vectors were $\la 1, 0, 0\ra$ and $\la 0, 0, 1$\ra; rotating these + gives the first and third columns of the matrix). + + These new basis vectors are: + \begin{eqnarray*} + \tilde{x} & = & \left[ + \begin{array}{c} + \cos\alpha \cos\gamma - \sin\beta \sin\alpha \sin\gamma \\ + \sin\alpha \cos\gamma + \sin\beta \cos\alpha \sin\gamma \\ + \cos\beta \sin\gamma + \end{array} \right] \\ + \tilde{z} & = & \left[ + \begin{array}{c} + -\cos\alpha \sin\gamma - \sin\beta \sin\alpha \cos\gamma \\ + -\sin\alpha \sin\gamma + \sin\beta \cos\alpha \cos\gamma \\ + \cos\beta \cos\gamma + \end{array} \right] + \end{eqnarray*} + + Rather than specifying the angles $\alpha$ and $\beta$, the user gives a + vector indicating where the viewpoint is. This new viewpoint is the rotation + o the old viewpoint. The old viewpoint is $\la 0, -1, 0\ra$, and so the new + viewpoint is + \[ + R_z(\alpha) R_x(\beta) \left[ \begin{array}{c} 0\\-1\\0 \end{array} \right] + \, = \, + \left[ \begin{array}{c} + \cos\beta \sin\alpha \\ + -\cos\beta \cos\alpha \\ + \sin\beta + \end{array} \right] + \, = \, + \left[ \begin{array}{c} v_1 \\ v_2 \\ v_3 \end{array} \right] + \] + Therefore, + \begin{eqnarray*} + \alpha & = & \arc\tan (v_1 / -v_2) \\ + \beta & = & \arc\tan (v_3 \sin\alpha / v_1) + \end{eqnarray*} + Unless $p_1=p_2=0$, in which case $\alpha=0$ and $\beta=\sign(p_3)90$, or + $p_1=p_3=0$, in which case $\beta=0$. + + + +The syntax of \Lps{SetMatrixThreeD} is + $v_1$ $v_2$ $v_3$ $\gamma$ SetMatrixThreeD + +\Lps{SetMatrixThreeD} first computes + \[ + \begin{array}{ll} + a=\sin\alpha & b=\cos\alpha\\ + c=\sin\beta & d=\cos\beta\\ + e=\sin\gamma & f=\cos\gamma + \end{array} + \] + and then sets \Lps{Matrix3D} to |[|$\tilde{x}$ $\tilde{z}$|]|. + + +\begin{lstlisting} +/SetMatrixThreeD { + dup sin /e ED cos /f ED + /p3 ED /p2 ED /p1 ED + p1 0 eq + { /a 0 def /b p2 0 le { 1 } { -1 } ifelse def + p3 p2 abs + } + { p2 0 eq + { /a p1 0 lt { -1 } { 1 } ifelse def /b 0 def + p3 p1 abs + } + { p1 dup mul p2 dup mul add sqrt dup + p1 exch div /a ED + p2 exch div neg /b ED + p3 p1 a div + } + ifelse + } + ifelse + atan dup sin /c ED cos /d ED + /Matrix3D + [ + b f mul c a mul e mul sub + a f mul c b mul e mul add + d e mul + b e mul neg c a mul f mul sub + a e mul neg c b mul f mul add + d f mul + ] def +} def +\end{lstlisting} + +The syntax of \Lps{ProjThreeD} is $x$ $y$ $z$ \Lps{ProjThreeD} $x'$ $y'$ +where $x'=\la x, y, z\ra \cdot \tilde{x}$ and $y'=\la x, y, z\ra \cdot +\tilde{z}$. + +\begin{lstlisting} +/ProjThreeD { + /z ED /y ED /x ED + Matrix3D aload pop + z mul exch y mul add exch x mul add + 4 1 roll + z mul exch y mul add exch x mul add + exch +} def +\end{lstlisting} + + To embed 2D $\la x, y\ra$ coordinates in 3D, the user specifies the normal + vector and an angle. If we decompose this normal vector into an angle, as + when converting 3D coordinates to 2D coordinates, and let $\hat\alpha$, + $\hat\beta$ and $\hat\gamma$ be the three angles, then when these angles are + all zero the coordinate $\la x, y\ra$ gets mapped to $\la x, 0, y\ra$, and + otherwise $\la x, y\ra$ gets mapped to + \[ + R_z(\hat\alpha) R_x(\hat\beta) R_y(\hat\gamma) + \left[ \begin{array}{c} x \\ 0 \\ y \end{array} \right] + \, = \, + \left[ \begin{array}{c} + \hat{x}_1 x + \hat{z}_1 y\\ + \hat{x}_2 x + \hat{z}_2 y\\ + \hat{x}_3 x + \hat{z}_3 y + \end{array} \right] + \] + where $\hat{x}$ and $\hat{z}$ are the first and third columns of + $R_z(\hat\alpha) R_x(\hat\beta) R_y(\hat\gamma)$. + + Now add on a 3D-origin: + \[ + \left[ \begin{array}{c} + \hat{x}_1 x + \hat{z}_1 y + x_0\\ + \hat{x}_2 x + \hat{z}_2 y + y_0\\ + \hat{x}_3 x + \hat{z}_3 y + z_0 + \end{array} \right] + \] + + Now when we project back onto 2D coordinates, we get + \begin{eqnarray*} + x' & = & \tilde{x}_1(\hat{x}_1 x + \hat{z}_1 y + x_0) + + \tilde{x}_2(\hat{x}_2 x + \hat{z}_2 y + y_0) + + \tilde{x}_3(\hat{x}_3 x + \hat{z}_3 y + z_0)\\ + & = & + (\tilde{x}_1\hat{x}_1 + \tilde{x}_2\hat{x}_2 + \tilde{x}_3\hat{x}_3) x\\ + + (\tilde{x}_1\hat{z}_1 + \tilde{x}_2\hat{z}_2 + \tilde{x}_3\hat{z}_3) y\\ + + \tilde{x}_1 x_0 + \tilde{x}_2 y_0 + \tilde{z}_3 z_0 + y' & = & \tilde{z}_1(\hat{x}_1 x + \hat{z}_1 y + x_0) + + \tilde{z}_2(\hat{x}_2 x + \hat{z}_2 y + y_0) + + \tilde{z}_3(\hat{x}_3 x + \hat{z}_3 y + z_0)\\ + & = & + (\tilde{z}_1\hat{x}_1 + \tilde{z}_2\hat{x}_2 + \tilde{z}_3\hat{x}_3) x\\ + + (\tilde{z}_1\hat{z}_1 + \tilde{z}_2\hat{z}_2 + \tilde{z}_3\hat{z}_3) y\\ + + \tilde{z}_1 x_0 + \tilde{z}_2 y_0 + \tilde{z}_3 z_0 + \end{eqnarray*} + Hence, the transformation matrix is: + \[ + \left[ \begin{array}{c} + \tilde{x}_1\hat{x}_1 + \tilde{x}_2\hat{x}_2 + \tilde{x}_3\hat{x}_3) \\ + \tilde{z}_1\hat{x}_1 + \tilde{z}_2\hat{x}_2 + \tilde{z}_3\hat{x}_3) \\ + \tilde{x}_1\hat{z}_1 + \tilde{x}_2\hat{z}_2 + \tilde{x}_3\hat{z}_3) \\ + \tilde{z}_1\hat{z}_1 + \tilde{z}_2\hat{z}_2 + \tilde{z}_3\hat{z}_3) \\ + \tilde{x}_1 x_0 + \tilde{x}_2 y_0 + \tilde{z}_3 z_0 \\ + \tilde{z}_1 x_0 + \tilde{z}_2 y_0 + \tilde{z}_3 z_0 + \end{array} \right] + \] + +The syntax of \Lps{SetMatrixEmbed} is + $x_0$ $y_0$ $z_0$ $\hat{v_1}$ $\hat{v_2}$ $\hat{v_3}$ $\hat{\gamma}$ + $v_1$ $v_2$ $v_3$ $\gamma$ \Lps{SetMatrixEmbed} + +\Lps{SetMatrixEmbed} first sets |<x1 x2 x3 y1 y2 y3>| to the basis vectors for + the viewpoint projection (the tilde stuff above). Then it sets |Matrix3D| to + the basis vectors for the embedded plane. Finally, it sets the + transformation matrix to the matrix given above. + +\begin{lstlisting} +/SetMatrixEmbed { + SetMatrixThreeD + Matrix3D aload pop + /z3 ED /z2 ED /z1 ED /x3 ED /x2 ED /x1 ED + SetMatrixThreeD + [ + Matrix3D aload pop + z3 mul exch z2 mul add exch z1 mul add 4 1 roll + z3 mul exch z2 mul add exch z1 mul add + Matrix3D aload pop + x3 mul exch x2 mul add exch x1 mul add 4 1 roll + x3 mul exch x2 mul add exch x1 mul add + 3 -1 roll 3 -1 roll 4 -1 roll 8 -3 roll 3 copy + x3 mul exch x2 mul add exch x1 mul add 4 1 roll + z3 mul exch z2 mul add exch z1 mul add + ] + concat +} def +\end{lstlisting} + + +\section{Keywords} +\subsection{\nxLkeyword{viewpoint}} + +\begin{lstlisting} +\let\pssetzlength\pssetylength +\define@key[psset]{pst-3d}{viewpoint}{% + \pst@expandafter\psset@@viewpoint#1 {} {} {} \@nil + \let\psk@viewpoint\pst@tempg} +\def\psset@@viewpoint#1 #2 #3 #4\@nil{% + \begingroup + \pssetxlength\pst@dima{#1}% + \pssetylength\pst@dimb{#2}% + \pssetzlength\pst@dimc{#3}% + \xdef\pst@tempg{% + \pst@number\pst@dima \pst@number\pst@dimb \pst@number\pst@dimc}% + \endgroup} +\psset[pst-3d]{viewpoint=1 -1 1} +\end{lstlisting} + +\subsection{\nxLkeyword{viewangle}} + +\begin{lstlisting} +\define@key[psset]{pst-3d}{viewangle}{\pst@getangle{#1}\psk@viewangle} +\psset[pst-3d]{viewangle=0} +\end{lstlisting} + +\subsection{\nxLkeyword{normal}} + +\begin{lstlisting} +\define@key[psset]{pst-3d}{normal}{% + \pst@expandafter\psset@@viewpoint#1 {} {} {} \@nil + \let\psk@normal\pst@tempg} +\psset[pst-3d]{normal=0 0 1} +\end{lstlisting} + + +\subsection{\nxLkeyword{embedangle}} +\begin{lstlisting} +\define@key[psset]{pst-3d}{embedangle}{\pst@getangle{#1}\psk@embedangle} +\psset[pst-3d]{embedangle=0} +\end{lstlisting} + + +\section{Transformation matrix} + +\begin{lstlisting} +/TMSave { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if end + /TMatrix [ TMatrix CM ] cvx def +} def +/TMRestore { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/TMChange { + TMSave + /cp [ currentpoint ] cvx def % ??? Check this later. + CM +} def +\end{lstlisting} + Set standard coor. system , with |pt| units and origin at \Index{currentpoint}. + This let's us rotate, or whatever, around \TeX's current point, without + having to worry about strange coordinate systems that the dvi-to-ps + driver might be using. +\begin{lstlisting} +CP T STV +\end{lstlisting} + + Let M = old matrix (on stack), and M' equal current matrix. Then + go from M' to M by applying M Inv(M'). +\begin{lstlisting} +CM matrix invertmatrix % Inv(M') +matrix concatmatrix % M Inv(M') +\end{lstlisting} + Now modify transformation matrix: +\begin{lstlisting} +exch exec +\end{lstlisting} +Now apply M Inv(M') +\begin{lstlisting} +concat cp moveto +\end{lstlisting} + + +\section{Macros} +\subsection{\nxLcs{ThreeDput}} + +\begin{lstlisting} +\def\ThreeDput{\pst@object{ThreeDput}} +\def\ThreeDput@i{\@ifnextchar({\ThreeDput@ii}{\ThreeDput@ii(\z@,\z@,\z@)}} +\def\ThreeDput@ii(#1,#2,#3){% + \pst@killglue\pst@makebox{\ThreeDput@iii(#1,#2,#3)}} +\def\ThreeDput@iii(#1,#2,#3){% + \begingroup + \use@par + \if@star\pst@starbox\fi + \pst@makesmall\pst@hbox + \pssetxlength\pst@dima{#1}% + \pssetylength\pst@dimb{#2}% + \pssetzlength\pst@dimc{#3}% + \leavevmode + \hbox{% + \pst@Verb{% + { \pst@number\pst@dima + \pst@number\pst@dimb + \pst@number\pst@dimc + \psk@normal + \psk@embedangle + \psk@viewpoint + \psk@viewangle + \tx@SetMatrixEmbed + } \tx@TMChange}% + \box\pst@hbox + \pst@Verb{\tx@TMRestore}}% + \endgroup + \ignorespaces} +\end{lstlisting} + +\section{Arithmetic}\label{Arithmetic} + + {\verb+\pst@divide+} + This is adapted from Donald Arseneau's |shapepar.sty|. + Syntax: + \begin{verbatim} + \pst@divide{<numerator>}{<denominator>}{<command>} + \pst@@divide{<numerator>}{<denominator>} + \end{verbatim} + <numerator> and <denominator> should be dimensions. |\pst@divide| sets + <command> to <num>/<den> (in points). |\pst@@divide| sets |\pst@dimg| to + <num>/<den>. + \begin{lstlisting} + \def\pst@divide#1#2#3{% + \pst@@divide{#1}{#2}% + \pst@dimtonum\pst@dimg{#3}} + \def\pst@@divide#1#2{% + \pst@dimg=#1\relax + \pst@dimh=#2\relax + \pst@cntg=\pst@dimh + \pst@cnth=67108863 + \pst@@@divide\pst@@@divide\pst@@@divide\pst@@@divide + \divide\pst@dimg\pst@cntg} + \end{lstlisting} + The number 16 is the level of uncertainty. Use a lower power of 2 for more + accuracy (2 is most precise). But if you change it, you must change the + repetions of |\pst@@@divide| in |\pst@@divide| above: + \[ + \mbox{precision}^{\mbox{repetitions}} = 65536 + \] + (E.g., $16^4 = 65536$). +\begin{lstlisting} + \def\pst@@@divide{% + \ifnum + \ifnum\pst@dimg<\z@-\fi\pst@dimg<\pst@cnth + \multiply\pst@dimg\sixt@@n + \else + \divide\pst@cntg\sixt@@n + \fi} +\end{lstlisting} + + {\verb+\pst@pyth+} + Syntax: + \begin{verbatim} + \pst@pyth{<dim1>}{<dim2>}{<dimen register>} + \end{verbatim} + <dimen register> is set to $((dim1)^2+(dim2)^2)^{1/2}$. + + The algorithm is copied from \PiCTeX, by Michael Wichura (with permission). + Here is his description: + \begin{quote} + Suppose $x>0$, $y>0$. Put $s = x+y$. Let $z = (x^2+y^2)^{1/2}$. Then $z = + s\times f$, where + \[ + f = (t^2 + (1-t)^2)^{1/2} = ((1+\tau^2)/2)^{1/2} + \] + and $t = x/s$ and $\tau = 2(t-1/2)$. + \end{quote} + \begin{lstlisting} +\def\pst@pyth#1#2#3{% + \begingroup + \pst@dima=#1\relax + \ifnum\pst@dima<\z@\pst@dima=-\pst@dima\fi % dima=abs(x) + \pst@dimb=#2\relax + \ifnum\pst@dimb<\z@\pst@dimb=-\pst@dimb\fi % dimb=abs(y) + \advance\pst@dimb\pst@dima % dimb=s=abs(x)+abs(y) + \ifnum\pst@dimb=\z@ + \global\pst@dimg=\z@ % dimg=z=sqrt(x^2+y^2) + \else + \multiply\pst@dima 8\relax % dima= 8abs(x) + \pst@@divide\pst@dima\pst@dimb % dimg =8t=8abs(x)/s + \advance\pst@dimg -4pt % dimg = 4tau = (8t-4) + \multiply\pst@dimg 2 + \pst@dimtonum\pst@dimg\pst@tempa + \pst@dima=\pst@tempa\pst@dimg % dima=(8tau)^2 + \advance\pst@dima 64pt % dima=u=[64+(8tau)^2]/2 + \divide\pst@dima 2\relax % =(8f)^2 + \pst@dimd=7pt % initial guess at sqrt(u) + \pst@@pyth\pst@@pyth\pst@@pyth % dimd=sqrt(u) + \pst@dimtonum\pst@dimd\pst@tempa + \pst@dimg=\pst@tempa\pst@dimb + \global\divide\pst@dimg 8 % dimg=z=(8f)*s/8 + \fi + \endgroup + #3=\pst@dimg} +\def\pst@@pyth{% dimd = g <-- (g + u/g)/2 + \pst@@divide\pst@dima\pst@dimd + \advance\pst@dimd\pst@dimg + \divide\pst@dimd 2\relax} + \end{lstlisting} + + + {\verb+\pst@sinandcos+} + Syntax: + \begin{verbatim} + \pst@sinandcos{<dim>}{<int>} + \end{verbatim} + <dim>, in |sp| units, should equal 100,000 times the angle, in degrees + between 0 and 90. <int> should equal the angle's quadrant (0, 1, 2 or 3). + |\pst@dimg| is set to $\sin(\theta)$ and |\pst@dimh| is set to + $\cos(\theta)$ (in pt's). + + The algorithms uses the usual McLaurin expansion. + \begin{lstlisting} +\def\pst@sinandcos#1{% + \begingroup + \pst@dima=#1\relax + \pst@dima=.366022\pst@dima %Now 1pt=1/32rad + \pst@dimb=\pst@dima % dimb->32sin(angle) in pts + \pst@dimc=32\p@ % dimc->32cos(angle) in pts + \pst@dimtonum\pst@dima\pst@tempa + \pst@cntb=\tw@ + \pst@cntc=-\@ne + \pst@cntg=32 + \loop + \ifnum\pst@dima>\@cclvi % 256 + \pst@dima=\pst@tempa\pst@dima + \divide\pst@dima\pst@cntg + \divide\pst@dima\pst@cntb + \ifodd\pst@cntb + \advance\pst@dimb \pst@cntc\pst@dima + \pst@cntc=-\pst@cntc + \else + \advance\pst@dimc by \pst@cntc\pst@dima + \fi + \advance\pst@cntb\@ne + \repeat + \divide\pst@dimb\pst@cntg + \divide\pst@dimc\pst@cntg + \global\pst@dimg\pst@dimb + \global\pst@dimh\pst@dimc + \endgroup} + \end{lstlisting} + + + {\verb+\pst@getsinandcos+} + |\pst@getsinandcos| normalizes the angle to be in the first quadrant, sets + |\pst@quadrant| to 0 for the first quadrant, 1 for the second, 2 for the + third, and 3 for the fourth, invokes |\pst@sinandcos|, and sets |\pst@sin| + to the sine and |\pst@cos| to the cosine. + \begin{lstlisting} +\def\pst@getsinandcos#1{% + \pst@dimg=100000sp + \pst@dimg=#1\pst@dimg + \pst@dimh=36000000sp + \pst@cntg=0 + \loop + \ifnum\pst@dimg<\z@ + \advance\pst@dimg\pst@dimh + \repeat + \loop + \ifnum\pst@dimg>\pst@dimh + \advance\pst@dimg-\pst@dimh + \repeat + \pst@dimh=9000000sp + \def\pst@tempg{% + \ifnum\pst@dimg<\pst@dimh\else + \advance\pst@dimg-\pst@dimh + \advance\pst@cntg\@ne + \ifnum\pst@cntg>\thr@@ \advance\pst@cntg-4 \fi + \expandafter\pst@tempg + \fi}% + \pst@tempg + \chardef\pst@quadrant\pst@cntg + \ifdim\pst@dimg=\z@ + \def\pst@sin{0}% + \def\pst@cos{1}% + \else + \pst@sinandcos\pst@dimg + \pst@dimtonum\pst@dimg\pst@sin + \pst@dimtonum\pst@dimh\pst@cos + \fi} + \end{lstlisting} + + + \section{Tilting} + + {\verb+\pstilt+} + \begin{lstlisting} +\def\pstilt#1{\pst@makebox{\pstilt@{#1}}} +\def\pstilt@#1{% + \begingroup + \leavevmode + \pst@getsinandcos{#1}% + \hbox{% + \ifcase\pst@quadrant + \kern\pst@cos\dp\pst@hbox + \pst@dima=\pst@cos\ht\pst@hbox + \ht\pst@hbox=\pst@sin\ht\pst@hbox + \dp\pst@hbox=\pst@sin\dp\pst@hbox + \or + \kern\pst@sin\ht\pst@hbox + \pst@dima=\pst@sin\dp\pst@hbox + \ht\pst@hbox=\pst@cos\ht\pst@hbox + \dp\pst@hbox=\pst@cos\dp\pst@hbox + \or + \kern\pst@cos\ht\pst@hbox + \pst@dima=\pst@sin\dp\pst@hbox + \pst@dimg=\pst@sin\ht\pst@hbox + \ht\pst@hbox=\pst@sin\dp\pst@hbox + \dp\pst@hbox=\pst@dimg + \or + \kern\pst@sin\dp\pst@hbox + \pst@dima=\pst@sin\ht\pst@hbox + \pst@dimg=\pst@cos\ht\pst@hbox + \ht\pst@hbox=\pst@cos\dp\pst@hbox + \dp\pst@hbox=\pst@dimg + \fi + \pst@Verb{% + { [ 1 0 + \pst@cos\space \ifnum\pst@quadrant>\@ne neg \fi + \pst@sin\space + \ifnum\pst@quadrant>\z@\ifnum\pst@quadrant<\thr@@ neg \fi\fi + \ifodd\pst@quadrant exch \fi + 0 0 + ] concat + } \tx@TMChange}% + \box\pst@hbox + \pst@Verb{\tx@TMRestore}% + \kern\pst@dima}% + \endgroup} + \end{lstlisting} + + + {\verb+\psTilt+} + \begin{lstlisting} +\def\psTilt#1{\pst@makebox{\psTilt@{#1}}} +\def\psTilt@#1{% + \begingroup + \leavevmode + \pst@getsinandcos{#1}% + \hbox{% + \ifodd\pst@quadrant + \pst@@divide{\dp\pst@hbox}{\pst@cos\p@}% + \ifnum\pst@quadrant=\thr@@\kern\else\pst@dima=\fi\pst@sin\pst@dimg + \pst@@divide{\ht\pst@hbox}{\pst@cos\p@}% + \ifnum\pst@quadrant=\@ne\kern\else\pst@dima=\fi\pst@sin\pst@dimg + \else + \ifdim\pst@sin\p@=\z@ + \@pstrickserr{\string\psTilt\space angle cannot be 0 or 180}\@ehpa + \def\pst@sin{.7071}% + \def\pst@cos{.7071}% + \fi + \pst@@divide{\dp\pst@hbox}{\pst@sin\p@}% + \ifnum\pst@quadrant=\z@\kern\else\pst@dima=\fi\pst@cos\pst@dimg + \pst@@divide{\ht\pst@hbox}{\pst@sin\p@}% + \ifnum\pst@quadrant=\tw@\kern\else\pst@dima=\fi\pst@cos\pst@dimg + \fi + \ifnum\pst@quadrant>\@ne + \pst@dimg=\ht\pst@hbox + \ht\pst@hbox=\dp\pst@hbox + \dp\pst@hbox=\pst@dimg + \fi + \pst@Verb{% + { [ 1 0 + \pst@cos\space \pst@sin\space + \ifodd\pst@quadrant exch \fi + \tx@Div + \ifnum\pst@quadrant>\z@\ifnum\pst@quadrant<\thr@@ neg \fi\fi + \ifnum\pst@quadrant>\@ne -1 \else 1 \fi + 0 0 + ] concat + } \tx@TMChange}% + \box\pst@hbox + \pst@Verb{\tx@TMRestore}% + \kern\pst@dima}% + \endgroup} + \end{lstlisting} + + + {\verb+\psset@Tshadowsize,\psTshadowsize+} +\begin{lstlisting} +\define@key[psset]{pst-3d}{Tshadowsize}{% + \pst@checknum{#1}\psTshadowsize} +\psset[pst-3d]{Tshadowsize=1} +\end{lstlisting} + + +{\verb+\psset@Tshadowangle,\psk@Tshadowangle+} +\begin{lstlisting} +\define@key[psset]{pst-3d}{Tshadowangle}{% + \pst@getangle{#1}\psk@Tshadowangle} +\psset[pst-3d]{Tshadowangle=60} +\end{lstlisting} + + + {\verb+\psset@Tshadowcolor,\psTshadowcolor+} +\begin{lstlisting} +\define@key[psset]{pst-3d}{Tshadowcolor}{% + \pst@getcolor{#1}\psTshadowcolor} +\psset[pst-3d]{Tshadowcolor=lightgray} +\end{lstlisting} + + + {\verb+\psshadow+} +\begin{lstlisting} +\def\psshadow{\def\pst@par{}\pst@object{psshadow}} +\def\psshadow@i{\pst@makebox{\psshadow@ii}} +\def\psshadow@ii{% + \begingroup + \use@par + \leavevmode + \pst@getsinandcos{\psk@Tshadowangle}% + \hbox{% + \lower\dp\pst@hbox\hbox{% + \pst@Verb{% + { [ 1 0 + \pst@cos\space \psTshadowsize mul + \ifnum\pst@quadrant>\@ne neg \fi + \pst@sin\space \psTshadowsize mul + \ifnum\pst@quadrant>\z@\ifnum\pst@quadrant<\thr@@ neg \fi\fi + \ifodd\pst@quadrant exch \fi + 0 0 + ] concat + } \tx@TMChange}}% + \hbox to\z@{{\@nameuse{\psTshadowcolor}\copy\pst@hbox\hss}}% + \pst@Verb{\tx@TMRestore}% + \box\pst@hbox}% + \endgroup} + \end{lstlisting} + +\section{Affin Transformations} + +\begin{BDef} +\Lcs{psAffinTransform}\OptArgs\Largb{transformation matrix}\Largb{object} +\end{BDef} + +\begin{LTXexample}[width=3cm] +\pspicture(3,6)\psset{linewidth=4pt,arrows=->} +\psline(0,0)(1.5,0)(3,3)\rput*(2.25,1.5){foo} +\psAffinTransform{0.5 0 0 2 0 0}{\color{red}% + \psline[linecolor=red](0,0)(1.5,0)(3,3)\rput*(2.25,1.5){foo}}% +\endpspicture +\end{LTXexample} + +The transformation matrix must be a list of 6 values divided by a space. +For a translation modify the last two values of $1 0 0 1 dx dy$. The values for +$dx$ and $dy$ must be of the unit pt! For a rotation +we have the transformation matrix + +\begin{align} +\left[\begin{aligned} \cos(\alpha) & \sin(\alpha) & 0 \\ +-\sin(\alpha) & \cos(\alpha) & 0 \\ +0 & 0 & 1\end{aligned}\right] +\end{align} + +For \Lcs{psAffinTransform} the four values have to be modifies \texttt{a cos a sin a sin neg a cos 0 0}. +Tilting can be done with $sx 0 0 sy 0 0$. All effects can be combined. + +\begin{LTXexample}[width=3cm] +\pspicture(3,6)\psset{linewidth=4pt,arrows=->} +\psline(0,0)(1.5,0)(3,3)\rput*(2.25,1.5){foo} +\psAffinTransform{0.5 0.8 0.3 2 20 -20}{\color{red}% + \psline[linecolor=red](0,0)(1.5,0)(3,3)\rput*(2.25,1.5){foo}}% +\endpspicture +\end{LTXexample} + + +\clearpage +\section{List of all optional arguments for \texttt{pst-3d}} + +\xkvview{family=pst-3d,columns={key,type,default}} + + + + + +\nocite{*} +\bgroup +\RaggedRight +\bibliographystyle{plain} +\bibliography{pst-3d-doc} +\egroup + +\printindex + + + + + +\end{document} |