\input{pst-3dplot-doc.dat} %% $Id: pst-3dplot-doc.tex 32 2020-10-25 19:18:25Z herbert $ \documentclass[11pt,english,BCOR10mm,DIV12,bibliography=totoc,parskip=false,smallheadings, headexclude,footexclude,oneside,dvipsnames,svgnames]{pst-doc} \listfiles \usepackage{pst-grad,pst-3dplot} \let\pstFV\IIIDplotfileversion \let\belowcaptionskip\abovecaptionskip %\usepackage{pst-grad} %\usepackage{showexpl} %\usepackage{tabularx} %\usepackage{longtable} % \usepackage{biblatex} \addbibresource{\jobname.bib} \makeatletter \renewcommand*\l@subsection{\bprot@dottedtocline{2}{1.5em}{3.6em}} \renewcommand*\l@subsubsection{\bprot@dottedtocline{3}{3.8em}{4.5em}} \makeatother \def\bgImage{% \begin{pspicture}(0,-3)(7,5) \pstThreeDCoor[xMax=2,yMax=13,zMin=0,zMax=6,IIIDticks]% \multido{\rA=2.0+2.5, \rB=0.15+0.20}{5}{% \pstParaboloid[% SegmentColor={[cmyk]% {\rB,0.1,0.11,0.1}}]% (0,\rA,0){5}{1}}% height 5 and radius 1 \pstThreeDLine[linestyle=dashed]{->}(0,0,5)(0,13,5) \end{pspicture} } \lstset{explpreset={pos=l,width=-99pt,overhang=0pt,hsep=\columnsep,vsep=\bigskipamount,rframe={}}, escapechar=?} \def\textat{\char064}% \let\verbI\texttt \begin{document} \author{Herbert Voß} \date{\today} \title{3D plots: pst-3dplot} \subtitle{A PSTricks package for drawing 3d objects, v\pstFV} \maketitle \tableofcontents \clearpage \begin{abstract} The well known \LPack{pstricks} package offers excellent macros to insert more or less complex graphics into a document. \LPack{pstricks} itself is the base for several other additional packages, which are mostly named \nxLPack{pst-xxxx}, like \LPack{pst-3dplot}. % There exist several packages for plotting three dimensional graphical objects. \LPack{pst-3dplot} is similiar to the \LPack{pst-plot} package for two dimensional objects and mathematical functions. This version uses the extended keyval package \LPack{xkeyval}, so be sure that you have installed this package together with the spcecial one \LPack{pst-xkey} for PSTricks. The \LPack{xkeyval} package is available at \href{http://www.dante.de/CTAN/macros/latex/contrib/xkeyval/}{CTAN:/macros/latex/contrib/xkeyval/}. It is also important that after \LPack{pst-3dplot} no package is loaded, which uses the old keyval interface. \vfill\noindent Thanks for feedback and contributions to:\\ Bruce Burlton, Bernhard Elsner, Andreas Fehlner, Christophe Jorssen, Markus Krebs, Chris Kuklewicz, Darrell Lamm, Patrice Mégret, Rolf Niepraschk, Michael Sharpe, Uwe Siart, Thorsten Suhling, Maja Zaloznik \end{abstract} \clearpage \section{The Parallel projection} %\psset{coorType=1} Figure~\ref{Abb0-1} shows a point $P(x,y,z)$ in a three dimensional coordinate system ($x,y,z$) with a transformation into $P^*(x^*,y^*)$, the Point in the two dimensional system ($x_E,y_E$). \begin{figure}[htb] \centering \unitlength1cm \begin{picture}(10,9) \thicklines \put(0,8){\makebox(0,0)[l]{$\alpha$: horizontal rotating angle}} \put(0,7.5){\makebox(0,0)[l]{$\beta$: vertikal rotating angle}} % \put(5.25,9){\makebox(0,0){z}} \put(5,0){\vector(0,1){9}} \put(6,5.5){\vector(-2,-1){5.5}} \put(9.5,3){\makebox(0,0){y}} \put(4,5.5){\vector(+2,-1){5.5}} \put(0.5,3){\makebox(0,0){x}} \thinlines \put(0,5){\vector(+1,0){10}} \put(5,5.02){\line(+1,0){1}} \put(10,4.5){\makebox(0,0){$x_E$}} \put(5.25,8.5){\makebox(0,0){$y_E$}} \put(5.3,4.5){\makebox(0,0){$\alpha$}} \put(2.6,3.6){\makebox(0,0){$\alpha$}} % \put(2,3.5){\line(+2,-1){5}} \put(9,3){\line(-2,-1){3.5}} \put(6,1.5){\line(0,1){5}} \put(6,6.5){\circle*{0.2}} \put(6.2,6.7){\makebox(0,0)[l]{$P(x,y,z)$}} \put(6.2,6.3){\makebox(0,0)[l]{$P^*(x^*,y^*)$}} \put(6.2,5.3){\makebox(0,0)[l]{$x^*$}} % \put(5,3){\line(+1,0){4}} \put(7,2.7){\makebox(0,0){$y\cdot\sin\alpha$}} \put(2,3.5){\line(+1,0){3}} \put(3.5,3.2){\makebox(0,0){$x\cdot\cos\alpha$}} \thicklines \put(5,1.5){\line(+1,0){1}} \put(5,1.52){\line(+1,0){1}} \thinlines \put(4.2,4.8){\makebox(0,0){$\alpha$}} \thicklines \put(5.03,5){\line(0,-1){2}} \put(5.1,4){\makebox(0,0)[l]{$y\cdot\cos\alpha$}} \put(4.97,5){\line(0,-1){1.5}} \put(4.9,4.2){\makebox(0,0)[r]{$x\cdot\sin\alpha$}} \thinlines \put(5.5,0.5){\vector(0,+1){1}} \put(5.5,0.5){\line(1,0){0.5}} \put(6.2,0.5){\makebox(0,0)[l]{$y\cdot\sin\alpha-x\cdot\cos\alpha$}} %\put(4.5,3.25){\vector(1,0){0.5}} %\put(4.5,3.25){\line(-1,-2){1}} %\put(3.5,1.25){\line(-1,0){0.5}} \put(4.9,1.5){\makebox(0,0)[r]{$y\cdot\cos\alpha+x\cdot\sin\alpha$}} \end{picture}% \caption{Lengths in a three dimensional System}\label{Abb0-1} \end{figure} The angle $\alpha$ is the horizontal rotation with positive values for anti clockwise rotations of the 3D coordinates. The angle $\beta$ is the vertical rotation (orthogonal to the paper plane). In figure~\ref{Abb0-2} we have $\alpha=\beta=0$. The y-axis comes perpendicular out of the paper plane. Figure~\ref{Abb0-3} shows the same for another angle with a view from the side, where the x-axis shows into the paper plane and the angle $\beta$ is greater than $0$ degrees. \begin{figure}[htb] \centering \unitlength1cm \begin{picture}(2,2.5) \thicklines \put(2.2,2){\makebox(0,0){$z$}} \put(2,0.5){\vector(0,1){2}} \put(2,0.5){\vector(-1,0){2}} \put(0.5,0.7){\makebox(0,0){$x$}} \put(2,0.5){\circle*{0.2}} \put(2,0.5){\circle{0.5}} \put(2.3,0.7){\makebox(0,0)[l]{$y$}} \end{picture} \caption{Coordinate System for $\alpha=\beta=0$ ($y$-axis comes out of the paper plane)}\label{Abb0-2} \end{figure} The two dimensional x coordinate $x^*$ is the difference of the two horizontal lengths $y\cdot\sin\alpha$ und $x\cdot\cos\alpha$ (figure \ref{Abb0-1}): \begin{equation} x^{*}=-x\cdot\cos\alpha+y\cdot\sin\alpha \end{equation} The z-coordinate is unimportant, because the rotation comes out of the paper plane, so we have only a different $y^*$ value for the two dimensional coordinate but no other $x^*$ value. The $\beta$ angle is well seen in figure \ref{Abb0-3} which derives from figure \ref{Abb0-2}, if the coordinate system is rotated by $90$\textdegree\ horizontally to the left and vertically by $\beta$ also to the left. \begin{figure}[htbp] \unitlength1cm \centering \begin{picture}(1,3) \thicklines \put(1.5,2.9){\makebox(0,0){z}} \put(2,1){\vector(-1,2){1}} \put(2,1){\vector(-2,-1){2}} \put(0,0.3){\makebox(0,0){y}} \put(2,1){\circle{0.5}} \put(1.8,0.8){\line(1,1){0.4}} \put(1.8,1.2){\line(1,-1){0.4}} \put(2.3,1.2){\makebox(0,0)[l]{x}} \thinlines \put(2,1){\line(-1,0){2}} \put(2,1){\line(0,1){2}} \put(1.7,2){\makebox(0,0){$\beta$}} \put(1.3,0.8){\makebox(0,0){$\beta$}} \put(2,2.5){\line(-1,0){0.75}} \put(2.2,2.5){\makebox(0,0)[l]{$z*_1=z\cdot\cos\beta$}} \put(1,1){\line(0,-1){0.5}} \put(1.3,0.5){\makebox(0,0)[l]{$y\cdot\cos\alpha+x\cdot\sin\alpha$}} \put(0.9,0.7){\makebox(0,0)[r]{$-(y\cdot\cos\alpha+x\cdot\sin\alpha)\cdot\sin\beta$}} \end{picture} \caption{Coordinate System for $\alpha=0$ and $\beta>0$ ($x$-axis goes into the paper plane)}\label{Abb0-3} \end{figure} The value of the perpendicular projected z coordinate is $z^{*}=z\cdot cos\beta$. With figure~\ref{Abb0-3} we see, that the point $P(x,y,z)$ runs on an elliptical curve when $\beta$ is constant and $\alpha$ changes continues. The vertical alteration of $P$ is the difference of the two "`perpendicular"' lines $y\cdot\cos\alpha$ and $x\cdot\sin\alpha$. These lines are rotated by the angle $\beta$, so we have them to multiply with $\sin\beta$ to get the vertical part. We get the following transformation equations: \begin{equation} \begin{array}{lll} x_{E} & = & -x\cos\alpha+y\sin\alpha\\ y_{E} & = & -(x\sin\alpha+y\cos\alpha)\cdot\sin\beta+z\cos\beta \end{array} \end{equation} \noindent or written in matrix form: {\footnotesize\addtolength{\arraycolsep}{-2pt} \begin{equation} \begin{pmatrix}x_E\\y_E\end{pmatrix}= \begin{pmatrix} -\cos\alpha & \sin\alpha & 0\\ -\sin\alpha\sin\beta & -\cos\alpha\sin\beta & \cos\beta \end{pmatrix}\cdot \begin{pmatrix}x\\y\\z\end{pmatrix} \end{equation}% \addtolength{\arraycolsep}{2pt}% } All following figures show a grid, which has only the sense to make things clearer. \section{Options} All options which are set with \Lcs{psset} are global and all which are passed with the optional argument of a macro are local for this macro. This is an important fact for setting the angles \Lkeyword{Alpha} and \Lkeyword{Beta}. Mostly all macro need these values, this is the reason why they should be set with \Lcs{psset} and not part of an optional argument. \section{Coordinates and Axes} \LPack{pst-3dplot} accepts cartesian or spherical coordinates. In both cases there must be three parameters: \verb+(x,y,z)+ or alternatively ($r$,$\phi$,$\theta$), where $r$ is the radius, $\phi$ the \Index{longitude angle} and $\theta$ the \Index{lattitude angle}. For the spherical coordinates set the option \Lkeyword{SphericalCoor}=\true. Spherical coordinates are possible for all macros where three dimensional coordinates are expected, except for the plotting functions (math functions and data records). Maybe that this is also interesting for someone, then let me know. Unlike coordinates in two dimensions, three dimensional coordinates may be specified using PostScript code, which need not be preceded by \Lnotation{!}. For example, assuming \verb+\def\nA{2}+, (1,0,2) and \verb+(90 cos, 100 100 sub, \nA\space 2 div 1 add)+ specify the same point. (Recall that a \Lcs{space} is required after a macro that will be expanded into PostScript code, as \TeX\ absorbs the space following a macro.) The syntax for drawing the coordinate axes is \begin{BDef} \Lcs{pstThreeDCoor}\OptArgs \end{BDef} The only special option is \Lkeyword{drawing}\texttt{=true|false}, which enables the drawing of the coordinate axes. The default is true. In nearly all cases the \Lcs{pstThreeDCoor} macro must be part of any drawing to initialize the 3d-system. If \Lkeyword{drawing} is set to \verb+false+, then all ticklines options are also disabled. Without any options we get the default view with the in table~\ref{tab:coor} listed options with the predefined values. { \begin{longtable}{@{}l>{\ttfamily}lll@{}} \caption{All new parameters for \texttt{pst-3dplot}\label{tab:coor}}\\ \textrm{name} & \textrm{type} & \textrm{Default} & \emph{page}\\\hline \endfirsthead \textrm{name} & \textrm{type} & \textrm{Default} & \emph{page}\\\hline \endhead \Lkeyword{Alpha} & & 45 & \pageref{exa:Alpha}\\ \Lkeyword{Beta} & & 30 & \pageref{exa:Beta}\\ \Lkeyword{xMin} & & -1 & \pageref{exa:xMin}\\ %ok \Lkeyword{xMax} & & 4 & \pageref{exa:xMax}\\ %ok \Lkeyword{yMin} & & -1 & \pageref{exa:yMin}\\ %ok \Lkeyword{yMax} & & 4 & \pageref{exa:yMax}\\ %ok \Lkeyword{zMin} & & -1 & \pageref{exa:zMin}\\ %ok \Lkeyword{zMax} & & 4 & \pageref{exa:zMax}\\ %ok \Lkeyword{nameX} & & \$x\$ & \pageref{exa:nameX}\\ \Lkeyword{spotX} & & 180 & \pageref{exa:spotX}\\ \Lkeyword{nameY} & & \$y\$ & \pageref{exa:nameY}\\ \Lkeyword{spotY} & & 0 & \pageref{exa:spotY}\\ \Lkeyword{nameZ} & & \$z\$ & \pageref{exa:nameZ}\\ \Lkeyword{spotZ} & & 90 & \pageref{exa:spotZ}\\ \Lkeyword{IIIDticks} & false|true & false & \pageref{exa:IIIDticks}\\ \Lkeyword{IIIDlabels} & false|true & false& \pageref{exa:IIIDlabels}\\ \Lkeyword{Dx} & & 1 & \pageref{exa:Dx}\\ \Lkeyword{Dy} & & 1 & \pageref{exa:Dy}\\ \Lkeyword{Dz} & & 1 & \pageref{exa:Dz}\\ \Lkeyword{IIIDxTicksPlane} & xy|xz|yz & xy & \pageref{exa:IIIDxTicksPlane}\\ \Lkeyword{IIIDyTicksPlane} & xy|xz|yz & yz & \pageref{exa:IIIDyTicksPlane}\\ \Lkeyword{IIIDzTicksPlane} & xy|xz|yz & yz & \pageref{exa:IIIDzTicksPlane}\\ \Lkeyword{IIIDticksize} & & 0.1 & \pageref{exa:IIIDticksize}\\ \Lkeyword{IIIDxticksep} & & -0.4 & \pageref{exa:IIIDxticksep}\\ \Lkeyword{IIIDyticksep} & & -0.2 & \pageref{exa:IIIDyticksep}\\ \Lkeyword{IIIDzticksep} & & 0.2 & \pageref{exa:IIIDzticksep}\\ \Lkeyword{RotX} & & 0 & \pageref{exa:RotX}\\ \Lkeyword{RotY} & & 0 & \pageref{exa:RotY}\\ \Lkeyword{RotZ} & & 0 & \pageref{exa:RotZ}\\ \Lkeyword{RotAngle} & & 0 & \pageref{exa:RotAngle}\\ \Lkeyword{xRotVec} & & 0 & \pageref{exa:xRotVec}\\ \Lkeyword{yRotVec} & & 0 & \pageref{exa:yRotVec}\\ \Lkeyword{zRotVec} & & 0 & \pageref{exa:zRotVec}\\ \Lkeyword{RotSequence} & xyz|xzy|yxz|yzx|zxy|zyx|quaternion & xyz & \pageref{exa:RotSequence}\\ \Lkeyword{RotSet} & set|concat|keep & set & \pageref{exa:RotSet}\\ \Lkeyword{eulerRotation} & true|false & false & \pageref{eulerRotation}\\ \Lkeyword{IIIDOffset} & \{\} & \{0,0,0\} & \pageref{exa:IIIDOffset}\\ \Lkeyword{zlabelFactor} & & \verb=\relax= & \pageref{exa:zlabelFactor}\\ \Lkeyword{comma} & false|true & false & \pageref{exa:comma}\\ \end{longtable} } \xLcs{pstThreeDCoor} \lstset{wide=false} \begin{LTXexample}[width=4.25cm] \begin{pspicture}(-3,-2.5)(3,4.25) \pstThreeDCoor \end{pspicture} \end{LTXexample} There are no restrictions for the angles and the max and min values for the axes; all \verb|pstricks| options are possible as well. The following example changes the color and the width of the axes. \medskip \noindent\fbox{\parbox{\columnwidth-2\fboxsep}{The angles \verbI{Alpha} and \verbI{Beta} are important to all macros and should always be set with \verbI{psset} to make them global to all other macros. Otherwise they are only local inside the macro to which they are passed.}} \medskip \Lkeyword{Alpha} ist the horizontal and \Lkeyword{Beta} the vertical rotation angle of the Cartesian coordinate system. \label{exa:xMax}\label{exa:yMax}\label{exa:zMax}\label{exa:Alpha}\label{exa:Beta} \begin{LTXexample}[width=4.25cm] \begin{pspicture}(-2,-1.25)(1,2.25) \pstThreeDCoor[linewidth=1.5pt,linecolor=blue, xMax=2,yMax=2,zMax=2, Alpha=-60,Beta=30] \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=4.25cm] \begin{pspicture}(-2,-2)(2,2) \pstThreeDCoor[xMax=2,yMax=2,zMax=2] \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=4.25cm] \begin{pspicture}(-2,-2)(2,2) \pstThreeDCoor[xMax=2,yMax=2,zMax=2, Alpha=30,Beta=60] \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=4.25cm] \begin{pspicture}(-2,-2)(2,2) \pstThreeDCoor[xMax=2,yMax=2,zMax=2, Alpha=30,Beta=-60] \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=4.25cm] \begin{pspicture}(-2,-2)(2,2) \pstThreeDCoor[ xMax=2,yMax=2,zMax=2, Alpha=90,Beta=60] \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=4.25cm] \begin{pspicture}(-2,-2)(2,2) \pstThreeDCoor[linewidth=1.5pt, xMax=2,yMax=2,zMax=2, Alpha=40,Beta=0] \end{pspicture} \end{LTXexample} \lstset{wide=true} \subsection{Ticks, comma and labels} With the option \Lkeyword{IIIDticks} the axes get ticks and with \Lkeyword{IIIDlabels} labels. Without ticks also labels are not possible. The optional argument \Lkeyword{comma}, which is defined in the package \LPack{pst-plot} allows to use a comma instead of a dot for real values. There are several options to place the labels in right plane to get an optimal view. The view of the ticklabels can be changed by redefining the macro \begin{verbatim} \def\psxyzlabel#1{\bgroup\footnotesize\textsf{#1}\egroup} \end{verbatim} \label{exa:IIIDticksize} \xLcs{pstThreeDPut} \psset{unit=1.25,gridlabels=0pt} \begin{LTXexample}[width=7.25cm] \begin{pspicture}(-3,-2.5)(3,4) \pstThreeDCoor[IIIDticks,IIIDticksize=0.05]% \pstThreeDPut(3,0,3){\Huge default} \end{pspicture} \end{LTXexample} \label{exa:IIIDticks}\label{exa:IIIDlabels}\label{exa:xMin}\label{exa:yMin}\label{exa:zMin} \begin{LTXexample}[width=7.25cm] \begin{pspicture}(-3,-2.5)(3,4) \pstThreeDCoor[linecolor=black, IIIDticks,IIIDlabels, xMin=-2,yMin=-2,zMin=-2] \end{pspicture} \end{LTXexample} \label{exa:comma}\label{exa:IIIDzTicksPlane}\label{exa:IIIDyTicksPlane}\label{exa:IIIDxTicksPlane} \label{exa:IIIDxticksep}\label{exa:IIIDyticksep}\label{exa:IIIDzticksep} \label{exa:Dx}\label{exa:Dy}\label{exa:Dz} \begin{LTXexample}[width=7.25cm] \begin{pspicture}(-3,-2.5)(3,4) \pstThreeDCoor[linecolor=black, IIIDticks,IIIDzTicksPlane=yz, IIIDzticksep=-0.2,IIIDlabels, IIIDxTicksPlane=yz,,IIIDxticksep=-0.2, IIIDyTicksPlane=xy,,IIIDyticksep=0.2, comma,Dx=1.25,Dy=1.5,Dz=0.25] \end{pspicture} \end{LTXexample} The following example shows a wrong placing of the labels, the planes should be changed. \begin{LTXexample}[width=7.25cm] \psset{Alpha=-60,Beta=60} \begin{pspicture}(-4,-2.25)(1,3) \pstThreeDCoor[linecolor=black,% IIIDticks,Dx=2,Dy=1,Dz=0.25]% \end{pspicture} \end{LTXexample} \label{exa:planecorr} \begin{LTXexample}[width=7.25cm] \psset{Alpha=-60,Beta=60} \begin{pspicture}(-4,-2.25)(1,3) \pstThreeDCoor[linecolor=black,% IIIDticks,IIIDlabels, planecorr=normal, Dx=2,Dy=1,Dz=0.25]% \end{pspicture} \end{LTXexample} \xLkeyval{xyrot} \begin{LTXexample}[width=7.25cm] \psset{Alpha=-60,Beta=60} \begin{pspicture}(-4,-2.25)(1,3) \pstThreeDCoor[linecolor=black,% IIIDticks,IIIDlabels, planecorr=xyrot, Dx=2,Dy=1,Dz=0.25]% \end{pspicture} \end{LTXexample} For the z axis it is possible to define a factor for the values, e.g. \setIIIDplotDefaults\label{exa:zlabelFactor}\xLkeyword{zlabelFactor} \xLkeyword{zlabelFactor} %\define@key[psset]{pst-3dplot}{zlabelFactor}[\relax]{\def\psk@zlabelFactor{#1}} \begin{LTXexample}[width=7.25cm] \begin{pspicture}(-4,-2.25)(1,4) \pstThreeDCoor[IIIDticks,IIIDlabels, zlabelFactor=$\cdot10^3$] \end{pspicture} \end{LTXexample} \subsection{Offset} The optional argument \Lkeyword{IIIDOffset} allows to set the intermediate point of all axes to another point as the default of \verb+(0,0,0)+. The values have to be put into braces: %\define@key[psset]{pst-3dplot}{zlabelFactor}[\relax]{\def\psk@zlabelFactor{#1}} \label{exa:IIIDOffset}\xLkeyword{IIIDOffset} \begin{LTXexample}[width=7.25cm] \begin{pspicture}(-4,-1.25)(1,4) \pstThreeDCoor[IIIDticks,IIIDlabels, yMin=-3,IIIDOffset={(1,-2,1)}] \end{pspicture} \end{LTXexample} \subsection{Experimental features} All features are as long as they are not really tested called experimental. With the optional argument \Lkeyword{coorType}, which is by default 0, one can change the the viewing of the axes and all other three dimensional objects. With \Lkeyword{coorType}=1 the y--z-axes are orthogonal and the angle between x- and y-axis is \Lkeyword{Alpha}. The angle \Lkeyword{Beta} is not valid. \label{exa:coorType}\xLkeyword{coorType} \begin{LTXexample}[width=9.75cm] \psset{coorType=1,Alpha=135} \begin{pspicture}(-2,-3)(3,3.5) \pstThreeDCoor[IIIDticks,zMax=3]% \end{pspicture} \end{LTXexample} With \Lkeyword{coorType}=2 the y--z-axes are orthogonal and the angle between x- and y-axis is always 135 degrees and the x-axis is shortened by a factor of $1/\sqrt{2}$. The angle \Lkeyword{Alpha} is only valid for placing the ticks, if any. The angle \Lkeyword{Beta} is not valid. \xLkeyval{yz} \begin{LTXexample}[width=9.75cm] \psset{coorType=2,Alpha=90, IIIDxTicksPlane=yz} \begin{pspicture}(-2,-2)(3,3.5) \pstThreeDCoor[IIIDticks,zMax=3]% \end{pspicture} \end{LTXexample} With \Lkeyword{coorType}=3 the y--z-axes are orthogonal and the angle between x- and y-axis is always 45 degrees and the x-axis is shortened by a factor of $1/\sqrt{2}$. The angle \Lkeyword{Alpha} is only valid for placing the ticks, if any. The angle \Lkeyword{Beta} is not valid. \begin{LTXexample}[width=9.75cm] \psset{coorType=3,Alpha=90, IIIDxTicksPlane=yz} \begin{pspicture}(-2,-2)(3,3.5) \pstThreeDCoor[IIIDticks,zMax=3]% \end{pspicture} \end{LTXexample} \Lkeyword{coorType}=4 is also called the trimetrie-view. One angle of the axis is 5 and the other 15 degrees. The angles \Lkeyword{Alpha} and \Lkeyword{Beta} are not valid. \begin{LTXexample}[width=9.75cm] \psset{coorType=4,IIIDxTicksPlane=yz} \begin{pspicture}(-2,-2)(3,3.5) \pstThreeDCoor[IIIDticks,zMax=3]% \end{pspicture} \end{LTXexample} With \Lkeyword{coorType}=5 the $y$-$z$-axes are orthogonal and the angle between x- and y-axis is variable but should be 30 or 45 degrees and the x-axis is shortened by a factor of $0.5$. The angle \Lkeyword{Beta} is not valid. \xLkeyval{yz}\xLkeyword{coorType} \begin{LTXexample}[width=9.75cm] \psset{coorType=5,Alpha=30, IIIDxTicksPlane=yz} \begin{pspicture}(-2,-2)(3,4) \pstThreeDCoor[IIIDticks,zMax=3]% \end{pspicture} \end{LTXexample} For \Lkeyword{coorType}=6 the $x$-axis us shortend by 0.559. %\setIIIDplotDefaults \psset{unit=1cm} \xLkeyword{coorType} \begin{LTXexample}[width=9cm] \psset{coorType=6} \begin{pspicture}(-3,-2)(6,6) \psset{IIIDxTicksPlane=xz,IIIDyTicksPlane=yz} \pstThreeDCoor[xMin=0,xMax=5,yMin=0,yMax=5, zMin=0,zMax=5,IIIDticks,spotX=180, IIIDlabels=false,linecolor=red]% \multido{\iA=1+1}{4}{\footnotesize% \pstThreeDPut(\iA,-0.3,0.1){\iA}% \pstThreeDPut(-0.3,\iA,0.1){\iA}% \pstThreeDPut(0,-0.3,\iA){\iA}} \end{pspicture} \end{LTXexample} For \Lkeyword{coorType}=7 the $x$-axis us shortend by 0.5. %\setIIIDplotDefaults \psset{unit=1cm} \xLkeyword{coorType} \begin{LTXexample}[width=9cm] \psset{coorType=7} \begin{pspicture}(-3,-2)(6,6) \psset{IIIDxTicksPlane=xz,IIIDyTicksPlane=yz} \pstThreeDCoor[xMin=0,xMax=5,yMin=0,yMax=5, zMin=0,zMax=5,IIIDticks,spotX=180, IIIDlabels=false,linecolor=red]% \multido{\iA=1+1}{4}{\footnotesize% \pstThreeDPut(\iA,-0.3,0.1){\iA}% \pstThreeDPut(-0.3,\iA,0.1){\iA}% \pstThreeDPut(0,-0.3,\iA){\iA}} \end{pspicture} \end{LTXexample} \clearpage \section{Rotation} The coordinate system can be rotated independent from the given Alpha and Beta values. This makes it possible to place the axes in any direction and any order. There are the three options \Lkeyword{RotX}, \Lkeyword{RotY}, \Lkeyword{RotZ} and an additional one for the rotating sequence (\Lkeyword{rotSequence}), which can be any combination of the three letters \verb+xyz+. \label{exa:RotZ} \begin{LTXexample}[pos=t] \begin{pspicture}(-6,-3)(6,3) \multido{\iA=0+10}{18}{% \pstThreeDCoor[RotZ=\iA,xMin=0,xMax=5,yMin=0,yMax=5,zMin=-1,zMax=3]% } \end{pspicture} \end{LTXexample} \label{exa:RotX}\label{exa:RotY}\label{exa:RotSequence} \begin{LTXexample}[pos=t] \psset{unit=2,linewidth=1.5pt,drawCoor=false} \begin{pspicture}(-2,-1.5)(2,2.5)% \pstThreeDCoor[xMin=0,xMax=2,yMin=0,yMax=2,zMin=0,zMax=2]% \pstThreeDBox[RotX=90,RotY=90,RotZ=90,% linecolor=red](0,0,0)(.5,0,0)(0,1,0)(0,0,1.5) \pstThreeDBox[RotSequence=xzy,RotX=90,RotY=90,RotZ=90,% linecolor=yellow](0,0,0)(.5,0,0)(0,1,0)(0,0,1.5) \pstThreeDBox[RotSequence=zyx,RotX=90,RotY=90,RotZ=90,% linecolor=green](0,0,0)(.5,0,0)(0,1,0)(0,0,1.5) \pstThreeDBox[RotSequence=zxy,RotX=90,RotY=90,RotZ=90,% linecolor=blue](0,0,0)(.5,0,0)(0,1,0)(0,0,1.5) \pstThreeDBox[RotSequence=yxz,RotX=90,RotY=90,RotZ=90,% linecolor=cyan](0,0,0)(.5,0,0)(0,1,0)(0,0,1.5) \pstThreeDBox[RotSequence=yzx,RotX=90,RotY=90,RotZ=90,% linecolor=magenta](0,0,0)(.5,0,0)(0,1,0)(0,0,1.5) \pstThreeDBox[fillstyle=gradient,RotX=0](0,0,0)(.5,0,0)(0,1,0)(0,0,1.5) \pstThreeDCoor[xMin=0,xMax=2,yMin=0,yMax=2,zMin=0,zMax=2]% \end{pspicture}% \end{LTXexample} \begin{LTXexample}[pos=t] \begin{pspicture}(-2,-1.5)(2,2.5)% \pstThreeDCoor[xMin=0,xMax=2,yMin=0,yMax=2,zMin=0,zMax=2]% \pstThreeDBox(0,0,0)(.5,0,0)(0,1,0)(0,0,1.5) \pstThreeDBox[RotX=90,linecolor=red](0,0,0)(.5,0,0)(0,1,0)(0,0,1.5) \pstThreeDBox[RotX=90,RotY=90,linecolor=green](0,0,0)(.5,0,0)(0,1,0)(0,0,1.5) \pstThreeDBox[RotX=90,RotY=90,RotZ=90,linecolor=blue](0,0,0)(.5,0,0)(0,1,0)(0,0,1.5) \end{pspicture}% \end{LTXexample} It is sometimes more convenient to rotate the coordinate system by specifying a \emph{single} angle of rotation \Lkeyword{RotAngle} (in degrees) about a vector whose coordinates are \Lkeyword{xRotVec}, \Lkeyword{yRotVec}, and \Lkeyword{zRotVec} using the \Lkeyval{quaternion} option for \Lkeyword{RotSequence}. \label{exa:RotAngle}\label{exa:xRotVec}\label{exa:yRotVec}\label{exa:zRotVec} \begin{LTXexample}[pos=t] \begin{pspicture}(-3,-1.8)(3,3) \multido{\iA=0+10}{18}{% \pstThreeDCoor[linecolor=red, RotSequence=quaternion, RotAngle=\iA, xRotVec=3,yRotVec=0,zRotVec=3, xMin=0,xMax=3, yMin=0,yMax=3, zMin=0,zMax=3]} \pstThreeDCoor[linecolor=blue, RotSequence=quaternion, RotAngle=0, xRotVec=0, yRotVec=0, zRotVec=1, xMin=0,xMax=3, yMin=0,yMax=3, zMin=0,zMax=3] \pstThreeDLine[linecolor=blue, linewidth=2pt, arrows=->](0,0,0)(3,0,3) \uput[0](-2.28,1.2){$\vec{R}_\Phi$} \end{pspicture} \end{LTXexample} Rotations of the coordinate system may be ``accumulated'' by applying successive rotation sequences using the \Lkeyword{RotSet} variable, which is set either as a \LPack{pst-3dplot} object's optional argument, or with a \verb+\psset[pst-3dplot]{RotSet=value}+ command. The usual \TeX{} scoping rules for the value of \Lkeyval{RotSet} hold. The following are valid values of \Lkeyword{RotSet}: \begin{itemize} \item \Lkeyval{set}: Sets the rotation matrix using the rotation parameters. This is the default value for \Lkeyword{RotSet} and is what is used if \verb+RotSet+ is not set as an option for the \verb+pst-3dplot+ object, or if not previously set within the object's scope by a \verb+\psset[pst-3dplot]{RotSet=val}+ command. \item \Lkeyval{concat}: Concatenates the current rotation matrix with a the new rotation that is defined by the rotation parameters. This option is most useful when multiple \Lcs{pstThreeDCoor} calls are made, with or without actual plotting of the axes, to accumulate rotations. A previous value of \Lkeyset{RotSet=set} must have been made! \item \Lkeyval{keep}: Keeps the current rotation matrix, ignoring the rotation parameters. Mostly used internally to eliminate redundant calculations. \end{itemize} \label{exa:RotSet} \begin{LTXexample}[pos=t] \begin{pspicture}(-3,-3)(3.6,3) \pstThreeDCoor[linecolor=blue, RotSequence=quaternion, RotAngle=0, RotSet=set, xRotVec=0,yRotVec=0,zRotVec=1, xMin=0,xMax=3, yMin=0,yMax=3, zMin=0,zMax=3] \pstThreeDCoor[linecolor=green, RotSequence=quaternion, RotSet=concat, RotAngle=22.5, xRotVec=0,yRotVec=0,zRotVec=1, xMin=0,xMax=3, yMin=0,yMax=3, zMin=-0.6,zMax=3] \pstThreeDCoor[linecolor=yellow, RotSequence=quaternion, RotSet=concat, RotAngle=30, xRotVec=0,yRotVec=1,zRotVec=0, xMin=0,xMax=3,yMin=-0.6,yMax=3, zMin=0,zMax=3] \pstThreeDCoor[linecolor=red, RotSequence=quaternion, RotSet=concat, RotAngle=60, xRotVec=1,yRotVec=0,zRotVec=0, xMin=-0.6,xMax=3, yMin=0,yMax=3, zMin=0,zMax=3]% \end{pspicture} \end{LTXexample} \label{eulerRotation} By default, the rotations defined by \verb+RotX+, \verb+RotY+, and \verb+RotZ+ are rotations about the \emph{original} coordinate system's, $x$, $y$, or $z$ axes, respectively. More traditionally, however, these rotation angles are defined as rotations about the rotated coordinate system's \emph{current}, $x$, $y$, or $z$ axis. The \verb+pst-3dplot+ variable option \verb+eulerRotation+ can be set to \verb+true+ to activate Euler angle definitions; i.e., \Lkeyword{eulerRotation}=\true. The default is \verb+eulerRotation=false+. \begin{LTXexample}[pos=t] \begin{pspicture}(-4,-5)(6,5) \pstThreeDCoor[linecolor=red, RotSequence=zyx, RotZ=90,RotY=90,RotX=0, xMin=0,xMax=5, yMin=0,yMax=5, zMin=0,zMax=5] \pstThreeDCoor[linecolor=blue, RotSequence=zyx, RotZ=0,RotY=0,RotX=0, xMin=0,xMax=2.5, yMin=0,yMax=2.5, zMin=0,zMax=2.5] \end{pspicture} \end{LTXexample} \begin{LTXexample}[pos=t] \begin{pspicture}(-3,-5)(7,5) \pstThreeDCoor[eulerRotation=true, linecolor=red, RotSequence=zyx, RotZ=90, RotY=90, RotX=0, xMin=0,xMax=5, yMin=0,yMax=5, zMin=0,zMax=5] \pstThreeDCoor[linecolor=blue, RotSequence=zyx, RotZ=0,RotY=0,RotX=0, xMin=0,xMax=2.5, yMin=0,yMax=2.5, zMin=0,zMax=2.5] \end{pspicture} \end{LTXexample} \clearpage \psset{unit=1cm,gridlabels=7pt} \section{Plane Grids} \begin{BDef} \Lcs{pstThreeDPlaneGrid}\OptArgs(xMin,yMin)(xMax,yMax) \end{BDef} There are three additional options \noindent \begin{tabularx}{\linewidth}{@{}>{\bfseries\ttfamily}lX@{}} planeGrid & can be one of the following values: \Lkeyval{xy}, \Lkeyval{xz}, \Lkeyval{yz}. Default is \Lkeyval{xy}.\\ subticks & Number of ticks. Default is \verb+10+.\footnotemark \\ planeGridOffset & a length for the shift of the grid. Default is \verb+0+. \end{tabularx} \footnotetext{This options is also defined in the package \nxLPack{pstricks-add}, so it is nessecary to to set this option locally or with the family option of \nxLPack{pst-xkey}, eg \Lcs{psset}\texttt{[pst-3dplot]\{subticks=...\}}}. This macro is a special one for the coordinate system to show the units, but can be used in any way. \Lkeyword{subticks} defines the number of ticklines for both axes and \Lkeyword{xsubticks} and \Lkeyword{ysubticks} for each one. \iffalse \newpsstyle{xyPlane}{fillstyle=solid,fillcolor=black!20} \newpsstyle{xzPlane}{fillstyle=solid,fillcolor=black!35,planeGrid=xz} \newpsstyle{yzPlane}{fillstyle=solid,fillcolor=black!50,planeGrid=yz} \fi \noindent \begin{minipage}{0.49\linewidth} \begin{LTXexample}[pos=t,wide=false] \begin{pspicture}(-4,-3.5)(5,4) \pstThreeDCoor[xMin=0,yMin=0,zMin=0,linewidth=2pt] \psset{linewidth=0.1pt,linecolor=lightgray} \pstThreeDPlaneGrid(0,0)(4,4) \pstThreeDPlaneGrid[planeGrid=xz](0,0)(4,4) \pstThreeDPlaneGrid[planeGrid=yz](0,0)(4,4) \end{pspicture} \end{LTXexample} \end{minipage}\hfill \begin{minipage}{0.49\linewidth} \begin{LTXexample}[pos=t,wide=false] \begin{pspicture}(-3,-3.5)(5,4) \psset{coorType=2}% set it globally! \pstThreeDCoor[xMin=0,yMin=0,zMin=0,linewidth=2pt] \psset{linewidth=0.1pt,linecolor=lightgray} \pstThreeDPlaneGrid(0,0)(4,4) \pstThreeDPlaneGrid[planeGrid=xz](0,0)(4,4) \pstThreeDPlaneGrid[planeGrid=yz](0,0)(4,4) \end{pspicture} \end{LTXexample} \end{minipage} \begin{LTXexample}[pos=t] \begin{pspicture}(-1,-2)(10,10) \psset{Beta=20,Alpha=160,subticks=7} \pstThreeDCoor[xMin=0,yMin=0,zMin=0,xMax=7,yMax=7,zMax=7,linewidth=1pt] \psset{linewidth=0.1pt,linecolor=gray} \pstThreeDPlaneGrid(0,0)(7,7) \pstThreeDPlaneGrid[planeGrid=xz,planeGridOffset=7](0,0)(7,7) \pstThreeDPlaneGrid[planeGrid=yz](0,0)(7,7) \pscustom[linewidth=0.1pt,fillstyle=gradient,gradbegin=gray,gradmidpoint=0.5,plotstyle=curve]{% \psset{xPlotpoints=200,yPlotpoints=1} \psplotThreeD(0,7)(0,0){ x dup mul y dup mul 2 mul add x 6 mul sub y 4 mul sub 3 add 10 div } \psset{xPlotpoints=1,yPlotpoints=200,drawStyle=yLines} \psplotThreeD(7,7)(0,7){ x dup mul y dup mul 2 mul add x 6 mul sub y 4 mul sub 3 add 10 div } \psset{xPlotpoints=200,yPlotpoints=1,drawStyle=xLines} \psplotThreeD(7,0)(7,7){ x dup mul y dup mul 2 mul add x 6 mul sub y 4 mul sub 3 add 10 div } \psset{xPlotpoints=1,yPlotpoints=200,drawStyle=yLines} \psplotThreeD(0,0)(7,0){ x dup mul y dup mul 2 mul add x 6 mul sub y 4 mul sub 3 add 10 div }} \pstThreeDPlaneGrid[planeGrid=yz,planeGridOffset=7](0,0)(7,7) \end{pspicture} \end{LTXexample} \begin{LTXexample}[pos=t] \begin{pspicture}(-6,-2)(4,7) \psset{Beta=10,Alpha=30,subticks=7} \pstThreeDCoor[xMin=0,yMin=0,zMin=0,xMax=7,yMax=7,zMax=7,linewidth=1.5pt] \psset{linewidth=0.1pt,linecolor=gray} \pstThreeDPlaneGrid(0,0)(7,7) \pstThreeDPlaneGrid[planeGrid=xz](0,0)(7,7) \pstThreeDPlaneGrid[planeGrid=yz](0,0)(7,7) \pscustom[linewidth=0.1pt,fillstyle=gradient,gradbegin=gray,gradend=white,gradmidpoint=0.5, plotstyle=curve]{% \psset{xPlotpoints=200,yPlotpoints=1} \psplotThreeD(0,7)(0,0){ x dup mul y dup mul 2 mul add x 6 mul sub y 4 mul sub 3 add 10 div } \psset{xPlotpoints=1,yPlotpoints=200,drawStyle=yLines} \psplotThreeD(7,7)(0,7){ x dup mul y dup mul 2 mul add x 6 mul sub y 4 mul sub 3 add 10 div } \psset{xPlotpoints=200,yPlotpoints=1,drawStyle=xLines} \psplotThreeD(7,0)(7,7){ x dup mul y dup mul 2 mul add x 6 mul sub y 4 mul sub 3 add 10 div } \psset{xPlotpoints=1,yPlotpoints=200,drawStyle=yLines} \psplotThreeD(0,0)(7,0){ x dup mul y dup mul 2 mul add x 6 mul sub y 4 mul sub 3 add 10 div }} \pstThreeDPlaneGrid[planeGrid=xz,planeGridOffset=7](0,0)(7,7) \pstThreeDPlaneGrid[planeGrid=yz,planeGridOffset=7](0,0)(7,7) \end{pspicture} \end{LTXexample} \medskip The equation for the examples is \[ f(x,y)=\frac{x^2+2y^2-6x-4y+3}{10} \] \section{Put} There exists a special option for the put macros: \xLkeyword{pOrigin} \begin{verbatim} pOrigin=lt|lB|lb|t|c|B|b|rt|rB|rb \end{verbatim} for the placing of the text or other objects. \fboxsep0pt \newcommand\Gobble[1]{} \newsavebox{\FrBox} \savebox{\FrBox}{\Huge\fbox{Rotating}} \unitlength1pt \begin{center} \newcommand{\Hoehe}{\ht\FrBox\Gobble} \newcommand{\Breite}{\wd\FrBox\Gobble} \newcommand{\Tiefe}{\dp\FrBox\Gobble} \newlength{\totalHeight} \setlength{\totalHeight}{\ht\FrBox} \addtolength{\totalHeight}{\dp\FrBox} \newcommand{\tHoehe}{\totalHeight\Gobble} \begin{picture}(1.7\Breite,\Hoehe) \put(,\Hoehe){\textcolor{red}{\circle*{3}}} % \put(0.5\Breite ,\Hoehe){\textcolor{red}{\circle*{3}}} \put(\Breite,\Hoehe){\textcolor{red}{\circle*{3}}} % center % \put(0,0.5\Hoehe){\textcolor{red}{\circle*{3}}}% \put(0.5\Breite,0.5\Hoehe){\textcolor{red}{\circle*{3}}}% % \put(\Breite,0.5\Hoehe){\textcolor{red}{\circle*{3}}}% % Baseline \put(0,0){\textcolor{red}{\circle*{3}}}% % \put(0.5\Breite,0){\textcolor{red}{\circle*{3}}}% \put(\Breite,0){\textcolor{red}{\circle*{3}}}% % bottom \put(0,-\Tiefe){\textcolor{red}{\circle*{3}}}% % \put(0.5\Breite,-\Tiefe){\textcolor{red}{\circle*{3}}}% \put(\Breite,-\Tiefe){\textcolor{red}{\circle*{3}}}% % labels \put(0,1.2\Hoehe){l} \put(0.5\Breite,1.2\Hoehe){c} \put(\Breite,1.2\Hoehe){r} \put(1.05\Breite,0.9\Hoehe){t} \put(1.05\Breite,0.4\Hoehe){c} \put(1.15\Breite,-1){\textbf{B}aseline} \put(1.05\Breite,-1.2\Tiefe){b} \put(0,0){\usebox{\FrBox}}% \end{picture} \end{center} This works only well for the \Lcs{pstThreeDPut} macro. The default is \Lkeyval{c} and for the \Lcs{pstPlanePut} the left baseline \Lkeyval{lB}. \subsection{\nxLcs{pstThreeDPut}} The syntax is similiar to the \Lcs{rput} macro: \begin{BDef} \Lcs{pstThreeDPut}\OptArgs\Largr{x,y,z}\Largb{any stuff} \end{BDef} \begin{LTXexample}[width=3.25cm] \begin{pspicture}(-2,-1.25)(1,2.25) \psset{Alpha=-60,Beta=30} \pstThreeDCoor[linecolor=blue,% xMin=-1,xMax=2,yMin=-1,yMax=2,zMin=-1,zMax=2] \pstThreeDPut(1,0.5,1.25){pst-3dplot} \pstThreeDDot[drawCoor=true](1,0.5,1.25) \end{pspicture} \end{LTXexample} \medskip Internally the \Lcs{pstThreeDPut} macro defines the two dimensional node \verb|temp@pstNode| and then uses the default \Lcs{rput} macro from \LPack{pstricks}. In fact of the perspective view od the coordinate system, the 3D dot must not be seen as the center of the printed stuff. \subsection[\texttt{pstPlanePut}]{\texttt{pstPlanePut}\protect\footnote{Thanks to Torsten Suhling}} The syntax of the \Lcs{pstPlanePut} is \begin{BDef} \Lcs{pstPlanePut}\OptArgs\Largr{x,y,z}\Largb{Object} \end{BDef} We have two special parameters, \Lkeyword{plane} and \Lkeyword{planecorr}; both are optional. Let's start with the first parameter, \Lkeyword{plane}. Possible values for the two dimensional plane are \Lkeyval{xy}, \Lkeyval{xz}, and \Lkeyval{yz}. If this parameter is missing then \Lkeyset{plane=xy} is set. The first letter marks the positive direction for the width and the second for the height. The object can be of any type, in most cases it will be some kind of text. The reference point for the object is the left side and vertically centered, often abbreviated as \verb|lB|. The following examples show for all three planes the same textbox. \begin{LTXexample}[width=7.25cm] \begin{pspicture}(-4,-4)(3,4) \psset{Alpha=30} \pstThreeDCoor[xMin=-4,yMin=-4,zMin=-4] \pstPlanePut[plane=xy](0,0,-3){\fbox{\Huge\red xy plane}} \pstPlanePut[plane=xy](0,0,0){\fbox{\Huge\red xy plane}} \pstPlanePut[plane=xy](0,0,3){\fbox{\Huge\red xy plane}} \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=7.25cm] \begin{pspicture}(-5,-3)(2,3) \pstThreeDCoor[xMin=2,yMin=-4,zMin=-3,zMax=2] \pstPlanePut[plane=xz](0,-3,0){\fbox{\Huge\green\textbf{xz plane}}} \pstPlanePut[plane=xz](0,0,0){\fbox{\Huge\green\textbf{xz plane}}} \pstPlanePut[plane=xz](0,3,0){\fbox{\Huge\green\textbf{xz plane}}} \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=7.25cm] \begin{pspicture}(-2,-4)(6,2) \pstThreeDCoor[xMin=-4,yMin=-4,zMin=-4,xMax=2,zMax=2] \pstPlanePut[plane=yz](-3,0,0){\fbox{\Huge\blue\textbf{yz plane}}} \pstPlanePut[plane=yz](0,0,0){\fbox{\Huge\blue\textbf{yz plane}}} \pstPlanePut[plane=yz](3,0,0){\fbox{\Huge\blue\textbf{yz plane}}} \end{pspicture} \end{LTXexample} \bigskip The following examples use the \Lkeyword{pOrigin} option to show that there are still some problems with the xy-plane. The second parameter is \Lkeyword{planecorr}. As first the values: \begin{description} \item[\Lkeyval{off}]~Former and default behaviour; nothing will be changed. This value is set, when parameter is missing. \item[\Lkeyval{normal}]~Default correction, planes will be rotated to be readable. \item[\Lkeyval{xyrot}]~Additionaly correction for $xy$ plane; bottom line of letters will be set parallel to the $y$-axis. \end{description} What kind off correction is ment? In the plots above labels for the $xy$ plane and the $xz$ plane are mirrored. This is not a bug, it's \dots mathematics. \Lcs{pstPlanePut} puts the labels on the plane of it's value. That means, \Lkeyset{plane=xy} puts the label on the $xy$ plane, so that the $x$ marks the positive direction for the width, the $y$ for the height and the label {\small{XY plane}} on the top side of plane. If you see the label mirrored, you just look from the bottom side of plane \dots{} If you want to keep the labels readable for every view, i.\,e.\ for every value of \Lkeyword{Alpha} and \Lkeyword{Beta}, you should set the value of the parameter \Lkeyword{planecorr} to \Lkeyval{normal}; just like in next example: \medskip \begin{LTXexample}[width=6cm] \begin{pspicture}(-3,-2)(3,4) \psset{pOrigin=lb} \pstThreeDCoor[xMax=3.2,yMax=3.2,zMax=4] \pstThreeDDot[drawCoor=true,linecolor=red](1,-1,2) \pstPlanePut[plane=xy,planecorr=normal](1,-1,2) {\fbox{\Huge\red\textbf{XY}}} \pstThreeDDot[drawCoor=true,linecolor=green](1,3,1) \pstPlanePut[plane=xz,planecorr=normal](1,3,1) {\fbox{\Huge\green\textbf{XZ}}} \pstThreeDDot[drawCoor=true,linecolor=blue](-1.5,0.5,3) \pstPlanePut[plane=yz,planecorr=normal](-1.5,0.5,3) {\fbox{\Huge\blue\textbf{YZ}}} \end{pspicture} \end{LTXexample} \medskip But, why we have a third value \Lkeyval{xyrot} of \Lkeyword{planecorr}? If there isn't an symmetrical view, -- just like in this example -- it could be usefull to rotate the label for $xy$-plane, so that body line of letters is parallel to the $y$ axis. It's done by setting \Lkeyset{planecorr=xyrot}\,: \medskip \begin{LTXexample}[width=6cm] \begin{pspicture}(-2,-2)(4,4) \psset{pOrigin=lb} \psset{Alpha=69.3,Beta=19.43} \pstThreeDCoor[xMax=4,yMax=4,zMax=4] \pstThreeDDot[drawCoor=true,linecolor=red](1,-1,2) \pstPlanePut[plane=xy,planecorr=xyrot](1,-1,2) {\fbox{\Huge\red\textbf{XY}}} \pstThreeDDot[drawCoor=true,linecolor=green](1,3.5,1) \pstPlanePut[plane=xz,planecorr=xyrot](1,3.5,1) {\fbox{\Huge\green\textbf{XZ}}} \pstThreeDDot[drawCoor=true,linecolor=blue](-2,1,3) \pstPlanePut[plane=yz,planecorr=xyrot](-2,1,3) {\fbox{\Huge\blue\textbf{YZ}}} \end{pspicture} \end{LTXexample} % --- ende ------------------------------------------------------------ \psset{Alpha=45,xunit=1cm,yunit=1cm,xMin=-1,yMin=-1,zMin=-1} \section{Nodes} The syntax is \begin{BDef} \Lcs{pstThreeDNode}\Largr{x,y,z}\Largb{node name} \end{BDef} This node is internally a two dimensional node, so it cannot be used as a replacement for the parameters \verb|(x,y,z)| of a 3D dot, which is possible with the \Lcs{psline} macro from \LPack{pst-plot}: \verb|\psline{A}{B}|, where \verb|A| and \verb|B| are two nodes. It is still on the to do list, that it may also be possible with \LPack{pst-3dplot}. On the other hand it is no problem to define two 3D nodes \verb|C| and \verb|D| and then drawing a two dimensional line from \verb|C| to \verb|D|. \section{Dots} The syntax for a dot is \begin{BDef} \Lcs{pstThreeDDot}\OptArgs\Largr{x,y,z} \end{BDef} Dots can be drawn with dashed lines for the three coordinates, when the option \Lkeyword{drawCoor} is set to \verb|true|. It is also possible to draw an unseen dot with the option \Lkeyset{dotstyle=none}. In this case the macro draws only the \Index{coordinates} when the \Lkeyword{drawCoor} option is set to true. \begin{LTXexample}[width=4.25cm] \begin{pspicture}(-2,-2)(2,2) \pstThreeDCoor[xMin=-2,xMax=2,yMin=-2,yMax=2,zMin=-2,zMax=2] \psset{dotstyle=*,dotscale=2,linecolor=red,drawCoor=true} \pstThreeDDot(-1,1,1) \pstThreeDDot(1.5,-1,-1) \end{pspicture} \end{LTXexample} In the following figure the coordinates of the dots are $(a,a,a)$ where a is $-2,-1,0,1,2$. \begin{LTXexample}[width=5.25cm] \begin{pspicture}(-3,-3.25)(2,3.25) \psset{Alpha=30,Beta=60,dotstyle=square*,dotsize=3pt,% linecolor=blue,drawCoor=true} \pstThreeDCoor[xMin=-3,xMax=3,yMin=-3,yMax=3,zMin=-3,zMax=3] \multido{\n=-2+1}{5}{\pstThreeDDot(\n,\n,\n)} \end{pspicture} \end{LTXexample} \section{Lines} The syntax for a three dimensional line is just like the same from \verb+\psline+ \begin{BDef} \Lcs{pstThreeDLine}\OptArgs\OptArg{\Larg{}}\Largr{x1,y1,z1}\Largr{...}\Largr{xn,yn,zn} \end{BDef} The option and arrow part are both optional and the number of points is only limited to the memory. All options for lines from \verb|pstricks| are possible, there are no special ones for a 3D line. There is no difference in drawing a line or a vector; the first one has an arrow of type "'\verb|-|"` and the second of "'\verb|->|"`. There is no special polygon macro, because you can get nearly the same with \Lcs{pstThreeDLine}. \begin{LTXexample}[width=4.25cm] \begin{pspicture}(-2,-2.25)(2,2.25) \pstThreeDCoor[xMin=-2,xMax=2,yMin=-2,yMax=2,zMin=-2,zMax=2] \psset{dotstyle=*,linecolor=red,drawCoor=true} \pstThreeDDot(-1,1,0.5) \pstThreeDDot(1.5,-1,-1) \pstThreeDLine[linewidth=3pt,linecolor=blue,arrows=->]% (-1,1,0.5)(1.5,-1,-1) \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=4.25cm] \begin{pspicture}(-2,-2.25)(2,2.25) \pstThreeDCoor[xMin=-2,xMax=2,yMin=-2,yMax=2,zMin=-2,zMax=2] \psset{dotstyle=*,linecolor=red,drawCoor=true} \pstThreeDDot(-1,1,1) \pstThreeDDot(1.5,-1,-1) \pstThreeDLine[linewidth=3pt,linecolor=blue](-1,1,1)(1.5,-1,-1) \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=4.25cm] \begin{pspicture}(-2,-2.25)(2,2.25) \psset{Alpha=30,Beta=60,dotstyle=pentagon*,dotsize=5pt,% linecolor=red,drawCoor=true} \pstThreeDCoor[xMin=-2,xMax=2,yMin=-2,yMax=2,zMin=-2,zMax=2] \pstThreeDDot(-1,1,1) \pstThreeDDot(1.5,-1,-1) \pstThreeDLine[linewidth=3pt,linecolor=blue](-1,1,1)(1.5,-1,-1) \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=4.25cm] \begin{pspicture}(-2,-2.25)(2,2.25) \psset{Alpha=30,Beta=-60} \pstThreeDCoor[xMin=-2,xMax=2,yMin=-2,yMax=2,zMin=-2,zMax=2] \pstThreeDDot[dotstyle=square,linecolor=blue,drawCoor=true](-1,1,1) \pstThreeDDot[drawCoor=true](1.5,-1,-1) \pstThreeDLine[linewidth=3pt,linecolor=blue](-1,1,1)(1.5,-1,-1) \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=4.25cm] \begin{pspicture}(-2,-2.25)(2,2.25) \psset{Alpha=30,Beta=-60} \pstThreeDCoor[xMin=-2,xMax=2,yMin=-2,yMax=2,zMin=-2,zMax=2] \pstThreeDDot[dotstyle=square,linecolor=blue,drawCoor=true](-1,1,1) \pstThreeDDot[drawCoor=true](1.5,-1,-1) \pstThreeDLine[linewidth=3pt,arrowscale=1.5,% linecolor=magenta,linearc=0.5]{<->}(-1,1,1)(1.5,2,-1)(1.5,-1,-1) \end{pspicture} \end{LTXexample} \begin{LTXexample}[pos=t] \begin{pspicture}(-3,-2)(4,5)\label{lines} \pstThreeDCoor[xMin=-3,xMax=3,yMin=-1,yMax=4,zMin=-1,zMax=3] \multido{\iA=1+1,\iB=60+-10}{5}{% \ifcase\iA\or\psset{linecolor=red}\or\psset{linecolor=green} \or\psset{linecolor=blue}\or\psset{linecolor=cyan} \or\psset{linecolor=magenta} \fi \pstThreeDLine[SphericalCoor=true,linewidth=3pt]% (\iA,0,\iB)(\iA,30,\iB)(\iA,60,\iB)(\iA,90,\iB)(\iA,120,\iB)(\iA,150,\iB)% (\iA,180,\iB)(\iA,210,\iB)(\iA,240,\iB)(\iA,270,\iB)(\iA,300,\iB)% (\iA,330,\iB)(\iA,360,\iB)% } \multido{\iA=0+30}{12}{% \pstThreeDLine[SphericalCoor=true,linestyle=dashed]% (0,0,0)(1,\iA,60)(2,\iA,50)(3,\iA,40)(4,\iA,30)(5,\iA,20)} \end{pspicture} \end{LTXexample} \section{Triangles} A triangle is given with its three points: \begin{BDef} \Lcs{pstThreeDTriangle}\OptArgs\Largr{P1}\Largr{P2}\Largr{P3} \end{BDef} When the option \Lkeyword{fillstyle} is set to another value than \Lkeyval{none} the triangle is filled with the active color or with the one which is set with the option \Lkeyword{fillcolor}. \begin{LTXexample}[width=6.25cm] \begin{pspicture}(-3,-4.25)(3,3.25) \pstThreeDCoor[xMin=-4,xMax=4,yMin=-3,yMax=5,zMin=-4,zMax=3] \pstThreeDTriangle[drawCoor=true,linecolor=black,% linewidth=2pt](3,1,-2)(1,4,-1)(-2,2,0) \pstThreeDTriangle[fillcolor=yellow,fillstyle=solid,% linecolor=blue,linewidth=1.5pt](5,1,2)(3,4,-1)(-1,-2,2) \end{pspicture} \end{LTXexample} Especially for triangles the option \Lkeyword{linejoin} is important. The default value is $1$, which gives rounded edges. \begin{figure}[htb] \centering \psset{linewidth=0.2} \begin{pspicture}(3,2.25) \psline[linejoin=0](0,0)(1,2)(2,0)(3,2) \end{pspicture}% \hspace{0.4cm}% \begin{pspicture}(4,2.25) \psline[linejoin=1](0,0)(1,2)(2,0)(3,2)(4,0) \end{pspicture}% \hspace{0.4cm}% \begin{pspicture}(3,2.25) \psline[linejoin=2](0,0)(1,2)(2,0)(3,2) \end{pspicture} \caption{The meaning of the option \texttt{linejoin=0|1|2} for drawing lines} \end{figure} \section{Squares} The syntax for a 3D square is: \begin{BDef} \Lcs{pstThreeDSquare}\OptArgs\Largr{vector o}\Largr{vec u}\Largr{vec v} \end{BDef} \begin{LTXexample}[width=5cm] \begin{pspicture}(-1,-1)(4,3) \pstThreeDCoor[xMin=-3,xMax=1,yMin=-1,yMax=2,zMin=-1,zMax=3] \psset{arrows=->,arrowsize=0.2,linecolor=blue,linewidth=1.5pt} \pstThreeDLine[linecolor=green](0,0,0)(-2,2,3)\uput[45](1.5,1){$\vec{o}$} \pstThreeDLine(-2,2,3)(2,2,3)\uput[0](3,2){$\vec{u}$} \pstThreeDLine(-2,2,3)(-2,3,3)\uput[180](1,2){$\vec{v}$} \end{pspicture} \end{LTXexample} \medskip Squares are nothing else than a polygon with the starting point $P_o$ given with the origin \Index{vector} $\vec{o}$ and the two direction vectors $\vec{u}$ and $\vec{v}$, which build the sides of the \Index{square}. \begin{LTXexample}[width=7.25cm] \begin{pspicture}(-3,-2)(4,3) \pstThreeDCoor[xMin=-3,xMax=3,yMin=-1,yMax=4,zMin=-1,zMax=3] {\psset{fillcolor=blue,fillstyle=solid,drawCoor=true,dotstyle=*} \pstThreeDSquare(-2,2,3)(4,0,0)(0,1,0)} \end{pspicture} \end{LTXexample} \section{Boxes} A box is a special case of a square and has the syntax \begin{BDef} \Lcs{pstThreeDBox}\OptArgs\Largr{vector o}\Largr{vec u}\Largr{vec v}\Largr{vec w} \end{BDef} These are the origin vector $\vec{o}$ and three direction vectors $\vec{u}$ ($x$ direction) , $\vec{v}$ ($y$ direction) and $\vec{w}$ ($z$ direction), which are for example shown in the following figure. \begin{LTXexample}[width=5.25cm] \begin{pspicture}(-2,-1.25)(3,4.25) \psset{Alpha=30,Beta=30} \pstThreeDCoor[xMin=-3,xMax=1,yMin=-1,yMax=2,zMin=-1,zMax=4] \pstThreeDDot[drawCoor=true](-1,1,2) \psset{arrows=->,arrowsize=0.2} \pstThreeDLine[linecolor=green](0,0,0)(-1,1,2) \uput[0](0.5,0.5){$\vec{o}$} \uput[0](0.9,2.25){$\vec{u}$} \uput[90](0.5,1.25){$\vec{v}$} \uput[45](2,1.){$\vec{w}$} \pstThreeDLine[linecolor=blue](-1,1,2)(-1,1,4) \pstThreeDLine[linecolor=blue](-1,1,2)(1,1,2) \pstThreeDLine[linecolor=blue](-1,1,2)(-1,2,2) \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=5.25cm] \begin{pspicture}(-2,-1.25)(3,4.25) \psset{Alpha=30,Beta=30} \pstThreeDCoor[xMin=-3,xMax=1,yMin=-1,yMax=2,zMin=-1,zMax=4] \pstThreeDBox[hiddenLine](-1,1,2)(2,0,0)(0,1,0)(0,0,2) \pstThreeDDot[drawCoor=true](-1,1,2) \end{pspicture} \end{LTXexample} Hidden lines are only possible if you view the object from the front and not from behind. \iffalse If you are looking from behind, then change the order of the ditection vectors: \begin{LTXexample}[width=5.25cm] \begin{pspicture}(-2,-1.25)(3,4.25) \psset{Alpha=210,Beta=30} \pstThreeDCoor[xMin=-3,xMax=1,yMin=-1,yMax=2,zMin=-1,zMax=4] \pstThreeDBox[hiddenLine,alternative](-1,1,2)(2,0,0)(0,1,0)(0,0,2) \pstThreeDDot[drawCoor=true](-1,1,2) \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=5.25cm] \begin{pspicture}(-2,-1.25)(3,4.25) \psset{Alpha=30,Beta=30} \pstThreeDCoor[xMin=-3,xMax=1,yMin=-1,yMax=2,zMin=-1,zMax=4] \pstThreeDBox[hiddenLine](-1,1,2)(0,0,2)(2,0,0)(0,1,0) \pstThreeDDot[drawCoor=true](-1,1,2) \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=5.25cm] \begin{pspicture}(-2,-1.25)(3,4.25) \psset{Alpha=130,Beta=30} \pstThreeDCoor[xMin=-3,xMax=1,yMin=-1,yMax=2,zMin=-1,zMax=4] \pstThreeDBox[hiddenLine](-1,1,2)(2,0,0)(0,1,0)(0,0,2) \pstThreeDDot[drawCoor=true](-1,1,2) \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=5.25cm] \begin{pspicture}(-2,-1.25)(3,4.25) \psset{Alpha=130,Beta=100} \pstThreeDCoor[xMin=-3,xMax=1,yMin=-1,yMax=2,zMin=-1,zMax=4] \pstThreeDBox[hiddenLine](-1,1,2)(2,0,0)(0,1,0)(0,0,2) \pstThreeDDot[drawCoor=true](-1,1,2) \end{pspicture} \end{LTXexample} \fi \clearpage \begin{BDef} \Lcs{psBox}\OptArgs\Largr{vector o}\Largb{width}\Largb{depth}\Largb{height} \end{BDef} The origin vector $\vec{o}$ determines the left corner of the box. \begin{LTXexample}[width=6.25cm] \begin{pspicture}(-3,-2)(3,5) \psset{Alpha=2,Beta=10} \pstThreeDCoor[zMax=5,yMax=7] \psBox(0,0,0){2}{4}{3} \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=6.25cm] \begin{pspicture}(-3,-3)(3,3) \psset{Beta=50} \pstThreeDCoor[xMax=3,zMax=6,yMax=6] \psBox[showInside=false](0,0,0){2}{5}{3} \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=6.25cm] \begin{pspicture}(-3,-4)(3,2) \psset{Beta=40} \pstThreeDCoor[zMax=3] \psBox[RotY=20,showInside=false](0,0,0){2}{5}{3} \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=6.25cm] \psset{Beta=10,xyzLight=-7 3 4} \begin{pspicture}(-3,-2)(3,4) \pstThreeDCoor[zMax=5] \psBox(0,0,0){2}{5}{3} \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=6.25cm] \psset{Beta=10,xyzLight=-7 3 4} \begin{pspicture}(-3,-2)(3,4) \psset{Alpha=110} \pstThreeDCoor[zMax=5] \psBox(0,0,0){2}{5}{3} \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=6.25cm] \psset{Beta=10,xyzLight=-7 3 4} \begin{pspicture}(-3,-2)(3,3) \psset{Alpha=200} \pstThreeDCoor[zMax=3] \psBox(0,0,0){2}{2}{3} \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=6.25cm] \psset{Beta=10,xyzLight=-7 3 4} \begin{pspicture}(-3,-2)(3,4) \psset{Alpha=290} \pstThreeDCoor[zMax=5] \psBox(0,0,0){2}{5}{3} \end{pspicture} \end{LTXexample} \section{Ellipses and circles} The equation for a two dimensional ellipse (figure \ref{fig:ellipse})is: \begin{equation} e:\frac{\left(x-x_{M}\right)^{2}}{a^{2}}+\frac{\left(y-y_{M}\right)^{2}}{b^{2}}=1 \label{gl.600} \end{equation} \begin{figure}[htb] \centering \begin{pspicture*}(-3,-1.5)(3,1.5) \psset{unit=0.75cm} \psline{->}(-3.5,0)(3.5,0) \rput(3.3,-0.3){x}\psline{->}(0,-2.5)(0,2.5)\rput(-0.3,2.3){y} \pscircle(-2,0){0.1}\pscircle(2,0){0.1} \psline[linestyle=dotted,linewidth=0.5pt](-2,0)(0,2)(2,0) \rput(-1.4,1){a}\rput(1.4,1){a} \psline[linewidth=0.5pt,linearc=.25]% (-3,0)(-3,-0.25)(-1.5,-0.25)% (-1.5,-0.4)(-1.5,-0.25)(0,-0.25)(0,0) \rput(-1.5,-0.7){a} \psline[linewidth=0.5pt,linearc=.25]% (0,2)(0.2,2)(0.2,1)(0.4,1)(0.2,1)(0.2,0)(0,0) \rput(0.7,1){b} \psellipse[linewidth=2pt](3,2) \rput(-.4,-.4){M}\rput(2,-.4){$F_2$} \rput(-2.2,0.4){$F_1$} \rput(1,.2){e}\rput(-1,.2){e} \rput(-1,-1){$r_1$}\rput(1.7,-1){$r_2$} \psline[linestyle=dotted,linewidth=1pt]{->}(-2,0)(1,-1.8) \psline[linestyle=dotted,linewidth=1pt]{<-}(1,-1.8)(2,0) \end{pspicture*} \caption{Definition of an Ellipse}\label{fig:ellipse} \end{figure} $\left(x_m;y_m\right)$ is the center, $a$ and $b$ the semi major and semi minor axes respectively and $e$ the excentricity. For $a=b=1$ in equation~\ref{gl.600} we get the one for the circle, which is nothing else than a special ellipse. The equation written in the parameterform is \begin{equation}\label{gl601} \begin{split} x = a\cdot\cos\alpha\\ y = b\cdot\sin\alpha \end{split} \end{equation} or the same with vectors to get an ellipse in a 3D system: \begin{align}\label{gl.6} e:\vec{x} &=\vec{m}+\cos\alpha\cdot\vec{u}+\sin\alpha\cdot\vec{v}\qquad 0\leq\alpha\leq360 \end{align} where $\vec{m}$ is the center, $\vec{u}$ and $\vec{v}$ the directions vectors which are perpendicular to each other. \subsection{Options} In addition to all possible options from \verb|pst-plot| there are two special options to allow drawing of an arc (with predefined values for a full ellipse/circle): % \begin{verbatim} beginAngle=0 endAngle=360 \end{verbatim} Ellipses and circles are drawn with the in section~\ref{subsec:parametricplotThreeD} described \verb|parametricplotThreeD| macro with a default setting of $50$ points for a full ellipse/circle. \subsection{Ellipse} It is very difficult to see in a 3D coordinate system the difference of an ellipse and a circle. Depending to the view point an ellipse maybe seen as a circle and vice versa. The syntax of the ellipse macro is: \begin{BDef} \Lcs{pstThreeDEllipse}\OptArgs\Largr{cx,cy,cz}\Largr{ux,uy,uz}\Largr{vx,vy,vz} \end{BDef} where \verb|c| is for center and \verb|u| and \verb|v| for the two direction vectors. The order of these two vectors is important for the drawing if it is a left or right turn. It follows the right hand rule: flap the first vector $\vec{u}$ on the shortest way into the second one $\vec{u}$, then you'll get the positive rotating. \begin{LTXexample}[pos=t] \begin{pspicture}(-3,-2)(3,3) \pstThreeDCoor[IIIDticks] \psset{arrowscale=2,arrows=->} \pstThreeDLine(0,0,0)(3,0,0)\pstThreeDLine(0,0,0)(0,3,0)\pstThreeDLine(0,0,0)(0,0,3) \psset{linecolor=blue,linewidth=1.5pt,beginAngle=0,endAngle=90} \pstThreeDEllipse(0,0,0)(3,0,0)(0,3,0) \pstThreeDEllipse(0,0,0)(0,0,3)(3,0,0) \pstThreeDEllipse(0,0,0)(0,3,0)(0,0,3) \end{pspicture}\hspace{2em} \begin{pspicture}(-3,-2)(3,3) \pstThreeDCoor[IIIDticks] \psset{arrowscale=2,arrows=->} \pstThreeDLine(0,0,0)(3,0,0)\pstThreeDLine(0,0,0)(0,3,0)\pstThreeDLine(0,0,0)(0,0,3) \psset{linecolor=blue,linewidth=1.5pt,beginAngle=0,endAngle=90} \pstThreeDEllipse(0,0,0)(0,3,0)(3,0,0) \pstThreeDEllipse(0,0,0)(3,0,0)(0,0,3) \pstThreeDEllipse(0,0,0)(0,0,3)(0,3,0) \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=4.25cm] \begin{pspicture}(-2,-2.25)(2,2.25) \pstThreeDCoor[xMax=2,yMax=2,zMax=2] \pstThreeDDot[linecolor=red,drawCoor=true](1,0.5,0.5) \psset{linecolor=blue, linewidth=1.5pt} \pstThreeDEllipse(1,0.5,0.5)(-0.5,1,0.5)(1,-0.5,-1) \psset{beginAngle=0,endAngle=270,linecolor=green} \pstThreeDEllipse(1,0.5,0.5)(-0.5,0.5,0.5)(0.5,0.5,-1) \pstThreeDEllipse[RotZ=45,linecolor=red](1,0.5,0.5)(-0.5,0.5,0.5)(0.5,0.5,-1) \end{pspicture} \end{LTXexample} \subsection{Circle} The circle is a special case of an ellipse (equ.~\ref{gl.6}) with the vectors $\vec{u}$ and $\vec{v}$ which build the circle plain. They must not be othogonal to each other. The circle macro takes the length of vector $\vec{u}$ into account for the radius. The orthogonal part of vector $\vec{v}$ is calculated internally \begin{BDef} \Lcs{pstThreeDCircle}\OptArgs\Largr{cx,cy,cz}\Largr{ux,uy,uz}\Largr{vx,vy,vz} \end{BDef} \begin{LTXexample}[width=4.25cm] \begin{pspicture}(-2,-1.25)(2,2.25) \pstThreeDCoor[xMax=2,yMax=2,zMax=2,linecolor=black] \pstThreeDCircle[linestyle=dashed](1,1,0)(1,0,0)(3,4,0) \pstThreeDCircle[linecolor=blue](1.6,1.6,1.7)(0.8,0.4,0.8)(0.8,-0.8,-0.4) \pstThreeDDot[drawCoor=true,linecolor=blue](1.6,1.6,1.7) \psset{linecolor=red,linewidth=2pt,plotpoints=20,showpoints=true} \pstThreeDCircle(1.6,0.6,1.7)(0.8,0.4,0.8)(0.8,-0.8,-0.4) \pstThreeDDot[drawCoor=true,linecolor=red](1.6,0.6,1.7) \end{pspicture} \end{LTXexample} \begin{center} \bgroup \makebox[\linewidth]{% \def\radius{4 }\def\PhiI{20 }\def\PhiII{50 } % \def\RadIs{\radius \PhiI sin mul} \def\RadIc{\radius \PhiI cos mul} \def\RadIIs{\radius \PhiII sin mul} \def\RadIIc{\radius \PhiII cos mul} \begin{pspicture}(-4,-4)(4,5) \psset{Alpha=45,Beta=30,linestyle=dashed} \pstThreeDCoor[linestyle=solid,xMin=-5,xMax=5,yMax=5,zMax=5,IIIDticks] \pstThreeDEllipse[linecolor=red](0,0,0)(0,\radius,0)(0,0,\radius) \pstThreeDEllipse(\RadIs,0,0)(0,\RadIc,0)(0,0,\RadIc) \pstThreeDEllipse(\RadIIs,0,0)(0,\RadIIc,0)(0,0,\RadIIc) % \pstThreeDEllipse[linestyle=dotted,SphericalCoor](0,0,0)(\radius,90,\PhiI)(\radius,0,0) \pstThreeDEllipse[SphericalCoor, beginAngle=-90,endAngle=90](0,0,0)(\radius,90,\PhiI)(\radius,0,0) \pstThreeDEllipse[linestyle=dotted,SphericalCoor](0,0,0)(\radius,90,\PhiII)(\radius,0,0) \pstThreeDEllipse[SphericalCoor, beginAngle=-90,endAngle=90](0,0,0)(\radius,90,\PhiII)(\radius,0,0) % \psset{linecolor=blue,arrows=->,arrowscale=2,linewidth=1.5pt,linestyle=solid} \pstThreeDEllipse[SphericalCoor,beginAngle=\PhiI,endAngle=\PhiII]% (0,0,0)(\radius,90,\PhiII)(\radius,0,0) \pstThreeDEllipse[beginAngle=\PhiII,endAngle=\PhiI](\RadIIs,0,0)(0,\RadIIc,0)(0,0,\RadIIc) \pstThreeDEllipse[SphericalCoor,beginAngle=\PhiII,endAngle=\PhiI]% (0,0,0)(\radius,90,\PhiI)(\radius,0,0) \pstThreeDEllipse[beginAngle=\PhiI,endAngle=\PhiII](\RadIs,0,0)(0,\RadIc,0)(0,0,\RadIc) \end{pspicture} \begin{pspicture}(-4,-4)(4,5) \psset{Alpha=45,Beta=30,linestyle=dashed} \pstThreeDCoor[linestyle=solid,xMin=-5,xMax=5,yMax=5,zMax=5,IIIDticks] \pstThreeDEllipse[linecolor=red](0,0,0)(0,\radius,0)(0,0,\radius) \pstThreeDEllipse(\RadIs,0,0)(0,\RadIc,0)(0,0,\RadIc) \pstThreeDEllipse(\RadIIs,0,0)(0,\RadIIc,0)(0,0,\RadIIc) % \pstThreeDEllipse[linestyle=dotted,SphericalCoor](0,0,0)(\radius,90,\PhiI)(\radius,0,0) \pstThreeDEllipse[SphericalCoor, beginAngle=-90,endAngle=90](0,0,0)(\radius,90,\PhiI)(\radius,0,0) \pstThreeDEllipse[linestyle=dotted,SphericalCoor](0,0,0)(\radius,90,\PhiII)(\radius,0,0) \pstThreeDEllipse[SphericalCoor, beginAngle=-90,endAngle=90](0,0,0)(\radius,90,\PhiII)(\radius,0,0) % \pscustom[fillstyle=solid,fillcolor=blue]{ \pstThreeDEllipse[SphericalCoor,beginAngle=\PhiI,endAngle=\PhiII]% (0,0,0)(\radius,90,\PhiII)(\radius,0,0) \pstThreeDEllipse[beginAngle=\PhiII,endAngle=\PhiI](\RadIIs,0,0)(0,\RadIIc,0)(0,0,\RadIIc) \pstThreeDEllipse[SphericalCoor,beginAngle=\PhiII,endAngle=\PhiI]% (0,0,0)(\radius,90,\PhiI)(\radius,0,0) \pstThreeDEllipse[beginAngle=\PhiI,endAngle=\PhiII](\RadIs,0,0)(0,\RadIc,0)(0,0,\RadIc) } \end{pspicture} } \egroup \end{center} \begin{lstlisting} \def\radius{4 }\def\PhiI{20 }\def\PhiII{50 } % \def\RadIs{\radius \PhiI sin mul} \def\RadIc{\radius \PhiI cos mul} \def\RadIIs{\radius \PhiII sin mul} \def\RadIIc{\radius \PhiII cos mul} \begin{pspicture}(-4,-4)(4,5) \psset{Alpha=45,Beta=30,linestyle=dashed} \pstThreeDCoor[linestyle=solid,xMin=-5,xMax=5,yMax=5,zMax=5,IIIDticks] \pstThreeDEllipse[linecolor=red](0,0,0)(0,\radius,0)(0,0,\radius) \pstThreeDEllipse(\RadIs,0,0)(0,\RadIc,0)(0,0,\RadIc) \pstThreeDEllipse(\RadIIs,0,0)(0,\RadIIc,0)(0,0,\RadIIc) % \pstThreeDEllipse[linestyle=dotted,SphericalCoor](0,0,0)(\radius,90,\PhiI)(\radius,0,0) \pstThreeDEllipse[SphericalCoor, beginAngle=-90,endAngle=90](0,0,0)(\radius,90,\PhiI)(\radius,0,0) \pstThreeDEllipse[linestyle=dotted,SphericalCoor](0,0,0)(\radius,90,\PhiII)(\radius,0,0) \pstThreeDEllipse[SphericalCoor, beginAngle=-90,endAngle=90](0,0,0)(\radius,90,\PhiII)(\radius,0,0) % \psset{linecolor=blue,arrows=->,arrowscale=2,linewidth=1.5pt,linestyle=solid} \pstThreeDEllipse[SphericalCoor,beginAngle=\PhiI,endAngle=\PhiII]% (0,0,0)(\radius,90,\PhiII)(\radius,0,0) \pstThreeDEllipse[beginAngle=\PhiII,endAngle=\PhiI](\RadIIs,0,0)(0,\RadIIc,0)(0,0,\RadIIc) \pstThreeDEllipse[SphericalCoor,beginAngle=\PhiII,endAngle=\PhiI]% (0,0,0)(\radius,90,\PhiI)(\radius,0,0) \pstThreeDEllipse[beginAngle=\PhiI,endAngle=\PhiII](\RadIs,0,0)(0,\RadIc,0)(0,0,\RadIc) \end{pspicture} \begin{pspicture}(-4,-4)(4,5) [ ... ] \pstThreeDEllipse[linestyle=dotted,SphericalCoor](0,0,0)(\radius,90,\PhiI)(\radius,0,0) \pstThreeDEllipse[SphericalCoor, beginAngle=-90,endAngle=90](0,0,0)(\radius,90,\PhiI)(\radius,0,0) \pstThreeDEllipse[linestyle=dotted,SphericalCoor](0,0,0)(\radius,90,\PhiII)(\radius,0,0) \pstThreeDEllipse[SphericalCoor, beginAngle=-90,endAngle=90](0,0,0)(\radius,90,\PhiII)(\radius,0,0) % \pscustom[fillstyle=solid,fillcolor=blue]{ \pstThreeDEllipse[SphericalCoor,beginAngle=\PhiI,endAngle=\PhiII]% (0,0,0)(\radius,90,\PhiII)(\radius,0,0) \pstThreeDEllipse[beginAngle=\PhiII,endAngle=\PhiI](\RadIIs,0,0)(0,\RadIIc,0)(0,0,\RadIIc) \pstThreeDEllipse[SphericalCoor,beginAngle=\PhiII,endAngle=\PhiI]% (0,0,0)(\radius,90,\PhiI)(\radius,0,0) \pstThreeDEllipse[beginAngle=\PhiI,endAngle=\PhiII](\RadIs,0,0)(0,\RadIc,0)(0,0,\RadIc) } \end{pspicture} \end{lstlisting} % --------------------------------------------------------------------------------------- \section{\Lcs{pstIIIDCylinder}} % --------------------------------------------------------------------------------------- The syntax is \begin{BDef} \Lcs{pstIIIDCylinder}\OptArgs\Largr{x,y,z}\Largb{radius}\Largb{height} \end{BDef} \verb+(x,y,z)+ defines the center of the lower part of the cylinder. If it is missing, then \verb+(0,0,0)+ are taken into account. \begin{LTXexample}[width=6.5cm] \psframebox{% \begin{pspicture}(-3.5,-2)(3,6) \pstThreeDCoor[zMax=6] \pstIIIDCylinder{2}{5} \end{pspicture} } \end{LTXexample} \begin{LTXexample}[width=6.5cm] \psframebox{% \begin{pspicture}(-3.5,-2)(3,6.75) \pstThreeDCoor[zMax=7] \pstIIIDCylinder[RotY=30,fillstyle=solid, fillcolor=red!20,linecolor=black!60](0,0,0){2}{5} \end{pspicture} } \end{LTXexample} \begin{LTXexample}[width=6.5cm] \psframebox{% \begin{pspicture}(-3.2,-1.75)(3,6.25) \pstThreeDCoor[zMax=7] \pstIIIDCylinder[linecolor=black!20, increment=0.4,fillstyle=solid]{2}{5} \psset{linecolor=red} \pstThreeDLine{->}(0,0,5)(0,0,7) \end{pspicture} } \end{LTXexample} \begin{LTXexample}[width=7.5cm] \psframebox{% \begin{pspicture}(-4.5,-1.5)(3,6.8) \psset{Beta=20} \pstThreeDCoor[zMax=7] \pstIIIDCylinder[fillcolor=blue!20, RotX=45](1,1,0){2}{5} \end{pspicture} } \end{LTXexample} % --------------------------------------------------------------------------------------- \section{\nxLcs{psCylinder}} % --------------------------------------------------------------------------------------- The syntax is \begin{BDef} \Lcs{psCylinder}\OptArgs\Largr{x,y,z}\Largb{radius}\Largb{height} \end{BDef} \verb+(x,y,z)+ defines the center of the lower part of the cylinder. If it is missing, then \verb+(0,0,0)+ are taken into account. With \Lkeyval{increment} for the angle step and \Lkeyword{Hincrement} for the height step, the number of segemnts can be defined. They are preset to 10 and 0.5. \begin{LTXexample}[width=7cm] \begin{pspicture}(-3,-2)(3,7) \psset{Beta=10} \pstThreeDCoor[zMax=7] \psCylinder[increment=5]{2}{5} \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=7cm] \begin{pspicture}(-3,-2)(3,2) \psset{Beta=10} \pstThreeDCoor[zMax=1] \psCylinder[increment=5,Hincrement=0.1]{2}{0.5} \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=7cm] \begin{pspicture}(-3,-2)(3,6) \psset{Beta=60} \pstThreeDCoor[zMax=9] \psCylinder[RotX=10,increment=5]{3}{5} \pstThreeDLine[linecolor=red](0,0,0)(0,0,8.5) \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=7cm] \begin{pspicture}(-3,-2)(3,6) \psset{Beta=60} \pstThreeDCoor[zMax=9] \psCylinder[RotX=10,RotY=45,showInside=false]{2}{5} \pstThreeDLine[linecolor=red](0,0,0)(0,0,8.5) \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=7cm] \begin{pspicture}(-3,-2)(3,6) \psset{Beta=60} \pstThreeDCoor[zMax=9] \psCylinder[RotY=-45](0,1,0){2}{5} \end{pspicture} \end{LTXexample} \clearpage % --------------------------------------------------------------------------------------- \section{\Lcs{pstParaboloid}} % --------------------------------------------------------------------------------------- The syntax is \begin{BDef} \Lcs{pstParaboloid}\OptArgs\Largb{height}\Largb{radius} \end{BDef} \Larg{height} and \Larg{radius} depend to each other, it is the radius of the circle at the height. By default the paraboloid is placed in the origin of coordinate system, but with \Lcs{pstThreeDput} it can be placed anywhere. The possible options are listed in table~\ref{tab:paraboloid}. The segment color must be set as a cmyk color \verb|SegmentColor={[cmyk]{c,m,y,k}}| in parenthesis, otherwise \LPack{xcolor} cannot read the values. A white color is given by \verb|SegmentColor={[cmyk]{0,0,0,0}}|. \begin{table}[htb] \centering \caption{Options for the \Lcs{pstParaboloid} macro}\label{tab:paraboloid} \smallskip \begin{tabular}{l|l} \textbf{Option name} & \textbf{value}\\\hline \verb|SegmentColor| & cmyk color for the segments (0.2,0.6,1,0)\\ \verb|showInside| & show inside (true)\\ \verb|increment| & number for the segments (10) \end{tabular} \end{table} % x=radius/sqrt(h)*V*cos(V) % y=radius/sqrt(h)*V*sin(V) % z=radius/sqrt(h)*V*V \begin{LTXexample}[width=4cm] \begin{pspicture}(-2,-1)(2,5) \pstThreeDCoor[xMax=2,yMax=2,zMin=0,zMax=6,IIIDticks]% \pstParaboloid{5}{1}% Hoehe 5 und Radius 1 \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=.65\linewidth,wide] \begin{pspicture}(-.25\linewidth,-1)% (.25\linewidth,7.5) \pstParaboloid[showInside=false, SegmentColor={[cmyk]{0.8,0.1,.11,0}}]{4}{5}% \pstThreeDCoor[xMax=3,yMax=3, zMax=7.5,IIIDticks] \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=9cm,wide] \begin{pspicture}(0,-3)(7,5) \pstThreeDCoor[xMax=2,yMax=13,zMin=0,zMax=6,IIIDticks]% \multido{\rA=2.0+2.5, \rB=0.15+0.20}{5}{% \pstParaboloid[% SegmentColor={[cmyk]% {\rB,0.1,0.11,0.1}}]% (0,\rA,0){5}{1}}% height 5 and radius 1 \pstThreeDLine[linestyle=dashed]{->}(0,0,5)(0,13,5) \end{pspicture} \end{LTXexample} \clearpage \section{Spheres}\label{sec:spheres} \begin{LTXexample}[width=6.25cm] \begin{pspicture}(-4,-2.25)(2,4.25) \pstThreeDCoor[xMin=-3,yMax=2] \pstThreeDSphere(1,-1,2){2} \pstThreeDDot[dotstyle=x,linecolor=red,drawCoor=true](1,-1,2) \end{pspicture} \end{LTXexample} \begin{BDef} \Lcs{pstThreeDSphere}\OptArgs\Largr{x,y,z}\Largb{Radius} \end{BDef} \Largr{x,y,z} is the center of the sphere and possible options are listed in table~\ref{tab:sphereOptions}. The segment color must be set as a cmyk color \Lkeyword{SegmentColor}\verb|={[cmyk]{c,m,y,k}}| in parenthesis, otherwise \LPack{xcolor} cannot read the values. A white color is given by \Lkeyword{SegmentColor}\verb|={[cmyk]{0,0,0,0}}|. \begin{table}[htb] \centering \caption{Options for the sphere macro}\label{tab:sphereOptions} \smallskip \begin{tabular}{l|l} \textbf{Option name} & \textbf{value}\\\hline \verb|SegmentColor| & cmyk color for the segments (0.2,0.6,1,0)\\ \verb|increment| & number for the segments (10) \end{tabular} \end{table} \begin{LTXexample}[width=6.25cm] \begin{pspicture}(-4,-2.25)(2,4.25) \pstThreeDCoor[xMin=-3,yMax=2] \pstThreeDSphere[SegmentColor={[cmyk]{0,0,0,0}}](1,-1,2){2} \pstThreeDDot[dotstyle=x,linecolor=red,drawCoor=true](1,-1,2) \end{pspicture} \end{LTXexample} \section{Mathematical functions} There are two macros for plotting mathematical functions, which work similiar to the one from \LPack{pst-plot}. \subsection{Function $f(x,y)$} The macro for plotting functions does not have the same syntax as the one from \LPack{pst-plot}~\cite{dtk02.1:voss:mathematischen}, but it is used in the same way: \begin{BDef} \Lcs{psplotThreeD}\OptArgs\Largr{xMin,xMax}\Largr{yMin,yMax}\Largb{the function} \end{BDef} The function has to be written in \PS{} code and the only valid variable names are $x$ and $y$, f.ex: \verb|{x dup mul y dup mul add sqrt}| for the math expression $\sqrt{x^2 + y^2}$. The macro has the same plotstyle options as \Lcs{psplot}, except the \Lkeyword{plotpoints}-option which is split into one for $x$ and one for $y$ (table~\ref{tab:lineOptions}). \begin{table}[htb] \centering \caption{Options for the plot Macros}\label{tab:lineOptions} \smallskip \begin{tabular}{l|l} \textbf{Option name} & \textbf{value}\\\hline \verb|plotstyle| & \verb|dots|\\ & \verb|line|\\ & \verb|polygon|\\ & \verb|curve|\\ & \verb|ecurve|\\ & \verb|ccurve|\\ & \verb|none| (default)\\ \verb|showpoints| & default is false\\ \verb|xPlotpoints| & default is $25$\\ \verb|yPlotpoints| & default is $25$\\ \verb|drawStyle| & default is \verb|xLines|\\ & \verb|yLines|\\ & \verb|xyLines|\\ & \verb|yxLines|\\ \verb|hiddenLine| & default is false\\ \verb|algebraic| & default is false \end{tabular} \end{table} The equation \ref{eq:3dfunc} is plotted with the following parameters and seen in figure \ref{fig:3dfunc}. \begin{align}\label{eq:3dfunc} z&=10\left(x^3+xy^4-\frac{x}{5}\right)e^{-\left(x^2+y^2\right)}+ e^{-\left((x-1.225)^2+y^2\right)} \end{align} The function is calculated within two loops: {\small\begin{verbatim} for (float y=yMin; y