%% $Id: pst-node-doc.tex 304 2010-04-22 08:23:39Z herbert $ \documentclass[11pt,english,BCOR10mm,DIV12,bibliography=totoc,parskip=false,smallheadings headexclude,footexclude,oneside]{pst-doc} \listfiles \usepackage[utf8]{inputenc} \usepackage{pst-plot} \usepackage{pst-node} \let\pstFV\fileversion \let\belowcaptionskip\abovecaptionskip % \newcommand\xstrut{\vphantom{\tabular{c}Üg\\Üg\endtabular}} \newcommand\psBox[3][white]{\rput(#2){\rnode{#2}{% \psframebox[fillcolor=#1]{\xstrut\makebox[3.2cm]{\tabular{c}#3\endtabular}}}}} \def\bgImage{% \psscalebox{0.85}{% \begin{pspicture}(-1,-1)(21,7) \psset{framearc=0.2,shadow=true,fillstyle=solid,shadowcolor=black!55} \psBox[blue!30]{7,6}{politische\\Kommunikation} \psBox[red!30]{3,4}{interpersonale\\Kommunikation} \psBox[red!30]{13,4}{massenmediale\\Kommunikation} \psBox[green!30]{1,2}{starke\\Beziehung} \psBox[green!30]{5,2}{schwache\\Beziehung} \psBox[green!30]{9,2}{Fernsehen} \psBox[green!30]{17,2}{Zeitungen} \psBox[cyan!30]{7,0}{öffentlich-rechtl.\\Fernsehen} \psBox[cyan!30]{11,0}{privates\\Fernsehen} \psBox[cyan!30]{15,0}{Boulevard-\\Zeitungen} \psBox[cyan!30]{19,0}{Abonnement-\\Zeitungen} \end{pspicture} \psset{shadow=false,angleA=-90,angleB=90,linewidth=2pt} \ncangles{7,6}{3,4}\ncangles{7,6}{13,4} \ncangles{3,4}{1,2}\ncangles{3,4}{5,2} \ncangles{13,4}{9,2}\ncangles{13,4}{17,2} \ncangles{9,2}{7,0}\ncangles{9,2}{11,0} \ncangles{17,2}{15,0}\ncangles{17,2}{19,0}} } \lstset{explpreset={pos=l,width=-99pt,overhang=0pt,hsep=\columnsep,vsep=\bigskipamount,rframe={}}} \begin{document} \title{\texttt{pst-node}\\Nodes and node connections% \\\small v.\pstFV} %\docauthor{Michael Sharpe\\Herbert Vo\ss} \author{Timothy Van Zandt\\Michael Sharpe\\Herbert Vo\ss} \date{\today} \maketitle \begin{abstract} This version of \LPack{pst-node} uses the extended keyval handling of pst-xkey and has a lot of the macros which were recently in the package \LPack{pstricks-add}. This documentation describes in the first part the basic node commands and connection from the old PSTricks documentation. The second part describes only the new and changed stuff. . \vfill \noindent Thanks to: Marco Daniel; Denis Girou; Rolf Niepraschk; Sebastian Rahtz; \end{abstract} \clearpage \tableofcontents \clearpage \part{Basic commands, connections and labels} The following pages are from the original documentation of \PST. This documentation file \LFile{pst-docfull} should be part of any \TeX\ distribution and was inserted here with the following command: \verb+\includepdf[pages=6-32]{pst-docfull}+ \clearpage \setcounter{page}{33} \part{New commands} %-------------------------------------------------------------------------------------- \section{Relative nodes with \nxLcs{psGetNodeCenter}} %-------------------------------------------------------------------------------------- \begin{BDef} \Lcs{psGetNodeCenter}\Largb{node name}\\ %\Lcs{psGetNodeEdgeA}\Largb{node type}\Largb{node name} \end{BDef} This command makes sense only at the PostScript level. It defines the two variables \Larg{node.x} and \Larg{node.y} which can be used to define relative nodes. The following example defines the node \verb+MyNode+ and a second one relative to the first one, with 4 units left and 4 units up. \Larg{node} must be an existing node name. \begin{LTXexample}[width=5cm] \begin{pspicture}[showgrid=true,arrowscale=2](5,5) \pnode(4.5,0.5){MyNode} \psdot(MyNode) \pnode(! \psGetNodeCenter{MyNode} MyNode.x 4 sub MyNode.y 4 add){MySecondNode} \psdot(MySecondNode) \ncline[linecolor=red]{<->}{MyNode}{MySecondNode} \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=5cm] \begin{pspicture}[showgrid=true](5,5) \rput(1.5,0.5){\trinode{CN}{NodeA}} \rput(3.5,2.5){\trinode{EN}{NodeB}} \pnode(! \psGetNodeCenter{CN} CN.x 2 add CN.y 1 add ){MyCNode} \ncline[linecolor=red]{<->}{MyCNode}{EN} \ncline[linecolor=blue]{<->}{CN}{EN} \end{pspicture} \end{LTXexample} %-------------------------------------------------------------------------------------- \section{\nxLcs{ncdiag} and \nxLcs{pcdiag}} %-------------------------------------------------------------------------------------- With the new option \Lkeyword{lineAngle} the lines drawn by the \Lcs{ncdiag} macro can now have a specified gradient. Without this option one has to define the two arms (which maybe zero) and PSTricks draws the connection between them. Now there is only a static \Lkeyword{armA}, the second one \Lkeyword{armB} is calculated when an angle \Lkeyword{lineAngle} is defined. This angle is the gradient of the intermediate line between the two arms. The syntax of \Lcs{ncdiag} is \begin{BDef} \Lcs{ncdiag}\OptArgs\Largb{node A}\Largb{node B}\\ \Lcs{pcdiag}\OptArgs\Largs{node A}\Largs{node B} \end{BDef} \begin{tabularx}{\linewidth}{l|X} name & meaning\\\hline \Lkeyword{lineAngle} & angle of the intermediate line segment. Default is 0, which is the same than using \Lcs{ncdiag} without the \Lkeyword{lineAngle} option.\tabularnewline \end{tabularx} \begin{LTXexample}[width=5.5cm] \begin{pspicture}(5,6) \circlenode{A}{A}\quad\circlenode{C}{C}% \quad\circlenode{E}{E} \rput(0,4){\circlenode{B}{B}} \rput(1,5){\circlenode{D}{D}} \rput(2,6){\circlenode{F}{F}} \psset{arrowscale=2,linearc=0.2,% linecolor=red,armA=0.5, angleA=90,angleB=-90} \ncdiag[lineAngle=20]{->}{A}{B} \ncput*[nrot=:U]{line I} \ncdiag[lineAngle=20]{->}{C}{D} \ncput*[nrot=:U]{line II} \ncdiag[lineAngle=20]{->}{E}{F} \ncput*[nrot=:U]{line III} \end{pspicture} \end{LTXexample} The \Lcs{ncdiag} macro sets the \Lkeyword{armB} dynamically to the calculated value. Any user setting of \Lkeyword{armB} is overwritten by the macro. The \Lkeyword{armA} could be set to a zero length: \begin{LTXexample}[width=4.5cm] \begin{pspicture}(4,3) \rput(0.5,0.5){\circlenode{A}{A}} \rput(3.5,3){\circlenode{B}{B}} {\psset{linecolor=red,arrows=<-,arrowscale=2} \ncdiag[lineAngle=60,% armA=0,angleA=0,angleB=180]{A}{B} \ncdiag[lineAngle=60,% armA=0,angleA=90,angleB=180]{A}{B}} \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=4.5cm] \begin{pspicture}(4,3) \rput(1,0.5){\circlenode{A}{A}} \rput(4,3){\circlenode{B}{B}} {\psset{linecolor=red,arrows=<-,arrowscale=2} \ncdiag[lineAngle=60, armA=0.5,angleA=0,angleB=180]{A}{B} \ncdiag[lineAngle=60, armA=0,angleA=70,angleB=180]{A}{B} \ncdiag[lineAngle=60, armA=0.5,angleA=180,angleB=180]{A}{B}} \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=4.5cm] \begin{pspicture}(4,5.5) \cnode*(0,0){2pt}{A} \cnode*(0.25,0){2pt}{C} \cnode*(0.5,0){2pt}{E}\cnode*(0.75,0){2pt}{G} \cnode*(2,4){2pt}{B} \cnode*(2.5,4.5){2pt}{D} \cnode*(3,5){2pt}{F} \cnode*(3.5,5.5){2pt}{H} {\psset{arrowscale=2,linearc=0.2, linecolor=red,armA=0.5, angleA=90,angleB=-90} \pcdiag[lineAngle=20]{->}(A)(B) \pcdiag[lineAngle=20]{->}(C)(D) \pcdiag[lineAngle=20]{->}(E)(F) \pcdiag[lineAngle=20]{->}(G)(H)} \end{pspicture} \end{LTXexample} %-------------------------------------------------------------------------------------- \section{\nxLcs{ncdiagg} and \nxLcs{pcdiagg}} %-------------------------------------------------------------------------------------- This is nearly the same as \Lcs{ncdiag} except that \Lkeyword{armB}=0 and the \Lkeyword{angleB} value is computed by the macro, so that the line ends at the node with an angle like a \Lcs{pcdiagg} line. The syntax of \Lcs{ncdiagg}/\Lcs{pcdiagg} is \begin{BDef} \Lcs{ncdiag}\OptArgs\Largb{node A}\Largb{node B}\\ \Lcs{pcdiag}\OptArgs\Largs{node A}\Largs{node B} \end{BDef} \begin{LTXexample}[width=5cm] \begin{pspicture}(4,6) \psset{linecolor=black} \circlenode{A}{A}\quad\circlenode{C}{C}\quad% \circlenode{E}{E} \rput(0,4){\circlenode{B}{B}} \rput(1,5){\circlenode{D}{D}} \rput(2,6){\circlenode{F}{F}} {\psset{arrowscale=2,linearc=0.2, linecolor=red,armA=0.5, angleA=90} \ncdiagg[lineAngle=-160]{->}{A}{B} \ncput*[nrot=:U]{line I} \ncdiagg[lineAngle=-160]{->}{C}{D} \ncput*[nrot=:U]{line II} \ncdiagg[lineAngle=-160]{->}{E}{F} \ncput*[nrot=:U]{line III}} \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=5cm] \begin{pspicture}(4,6) \psset{linecolor=black} \cnode*(0,0){2pt}{A} \cnode*(0.25,0){2pt}{C} \cnode*(0.5,0){2pt}{E}\cnode*(0.75,0){2pt}{G} \cnode*(2,4){2pt}{B} \cnode*(2.5,4.5){2pt}{D} \cnode*(3,5){2pt}{F} \cnode*(3.5,5.5){2pt}{H} {\psset{arrowscale=2,linearc=0.2, linecolor=red,armA=0.5, angleA=90} \pcdiagg[lineAngle=20]{->}(A)(B) \pcdiagg[lineAngle=20]{->}(C)(D) \pcdiagg[lineAngle=20]{->}(E)(F) \pcdiagg[lineAngle=20]{->}(G)(H)} \end{pspicture} \end{LTXexample} The only catch for \Lcs{ncdiagg} is that you need the right value for \Lkeyword{lineAngle}. If the node connection is on the wrong side of the second node, then choose the corresponding angle, e.\,g.: if $20$ is wrong then take $-160$, which differs by $180$. \begin{LTXexample}[width=4cm] \begin{pspicture}(4,1.5) \circlenode{a}{A} \rput[l](3,1){\rnode{b}{H}} \ncdiagg[lineAngle=60,angleA=180,armA=.5,nodesepA=3pt,linecolor=blue]{b}{a} \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=4cm] \begin{pspicture}(4,1.5) \circlenode{a}{A} \rput[l](3,1){\rnode{b}{H}} \ncdiagg[lineAngle=60,armA=.5,nodesepB=3pt,linecolor=blue]{a}{b} \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=4cm] \begin{pspicture}(4,1.5) \circlenode{a}{A} \rput[l](3,1){\rnode{b}{H}} \ncdiagg[lineAngle=-120,armA=.5,nodesepB=3pt,linecolor=blue]{a}{b} \end{pspicture} \end{LTXexample} %-------------------------------------------------------------------------------------- \section{\nxLcs{ncbarr}} %-------------------------------------------------------------------------------------- This has the same behaviour as \Lcs{ncbar}, but has 5 segments and all are horizontal ones. This is the reason why \Lkeyword{angleA} must be $0$ or alternatively $180$. All other values are set to $0$ by the macro. The intermediate horizontal line is symmetrical to the distance of the two nodes. \begin{BDef} \Lcs{ncbarr}\OptArgs\Largb{node A}\Largb{node B}\\ \end{BDef} \begin{LTXexample}[width=3.5cm] \psset{arrowscale=2}% \circlenode{X}{X}\\[1cm] \circlenode{Y}{Y} \ncbarr[angleA=0,arrows=->,arrowscale=2]{X}{Y} \end{LTXexample} \begin{LTXexample}[width=3.5cm] \psset{arrowscale=2}% \ovalnode{X}{Xxxxx}\\[1cm] \circlenode{Y}{Yyyy} \ncbarr[angleA=180,arrows=->,arrowscale=2,linecolor=red]{X}{Y} \end{LTXexample} \begin{LTXexample}[width=3.5cm] \psset{arrowscale=2}% \ovalnode{X}{Xxxxx}\\[1cm] \circlenode{Y}{Yyyy} \ncbarr[angleA=20,arm=1cm,arrows=->,arrowscale=2]{X}{Y} \end{LTXexample} %-------------------------------------------------------------------------------------- \section{\nxLcs{psLNode} and \nxLcs{psLCNode}} %-------------------------------------------------------------------------------------- \Lcs{psLNode} interpolates the Line $\overline{AB}$ by the given value and sets a node at this point. The syntax is % \begin{BDef} \Lcs{psLNode}\Largs{P1}\Largs{P2}\Largb{value}\Largb{node name}\\ \Lcs{psLCNode}\Largs{P1}\Largb{value 1}\Largs{P2}\Largb{value 2}\Largb{node name} \end{BDef} \begin{LTXexample}[width=5cm] \begin{pspicture}(5,5) \psgrid[subgriddiv=0,griddots=10] \psset{linecolor=red} \psline{o-o}(1,1)(5,5) \psLNode(1,1)(5,5){0.75}{PI} \qdisk(PI){4pt} \psset{linecolor=blue} \psline{o-o}(4,3)(2,5) \psLNode(4,3)(2,5){-0.5}{PII} \qdisk(PII){4pt} \end{pspicture} \end{LTXexample} \bigskip The \Lcs{psLCNode} macro builds the linear combination of the two given vectors and stores the end of the new vector as a node. All vectors start at $(0,0)$, so a \Lcs{rput} maybe appropriate. The syntax is \begin{LTXexample}[width=5cm] \begin{pspicture}[showgrid=true](5,3) \psset{linecolor=black} \psline[linestyle=dashed]{->}(3,1.5) \psline[linestyle=dashed]{->}(0.375,1.5) \psset{linecolor=red} \psline{->}(2,1)\psline{->}(0.5,2) \psLCNode(2,1){1.5}(0.5,2){0.75}{PI} \psline[linewidth=2pt]{->}(PI) \psset{linecolor=black} \psline[linestyle=dashed](3,1.5)(PI) \psline[linestyle=dashed](0.375,1.5)(PI) \end{pspicture} \end{LTXexample} %-------------------------------------------------------------------------------------- \section{\nxLcs{nlput} and \nxLcs{psLDNode}} %-------------------------------------------------------------------------------------- \Lcs{ncput} allows you to set a label relative to the first node of the last node connection. With \Lcs{nlput} this can be done absolute to a given node. The syntax is different to the other node connection macros. It uses internally the macro \Lcs{psLDNode} which places a node absolute to two given points, starting from the first one. \begin{BDef} \Lcs{nlput}\OptArgs\Largr{A}\Largr{B}\Largb{distance}\Largb{text}\\ \Lcs{psLDNode}\OptArgs\Largr{A}\Largr{B}\Largb{distance}\Largb{node name} \end{BDef} \begin{LTXexample}[width=5cm] \begin{pspicture}(5,2) \pnode(0,0){A} \pnode(5,2){B} \ncline{A}{B} \psLDNode(A)(B){1.5cm}{KN}\qdisk(KN){2pt} \nlput[nrot=:U](A)(B){1cm}{Test} \nlput[nrot=:D](A)(B){2cm}{Test} \nlput[nrot=:U](A)(B){3cm}{Test} \nlput(A)(B){4cm}{Test} \end{pspicture} \end{LTXexample} \section{Extensions} \subsection{Quick overview} All macros in this section are connected in one way or other with the construction or deployment of one or more nodes of type \Lcs{pnode}, which is to say in effect, named points. For the remainder of this section, node always means \Lcs{pnode}. Nodes are one of the most powerful features of pstricks---the ``trickiest tricks'' in the words of its originator. If used without appropriate caution, they can produce PostScript errors that can be difficult to track down. For example, suppose you have defined a node \texttt{A} by \verb|\pnode(1,1){A}|, and then, a little later, you want to move the node a bit to the right, and you write \verb|\pnode([nodesep=.5cm]A){A}|. On processing the file you will see an error message from ghostscript: \Lps{stackunderflow}\verb| in --exch--|. The lesson is: you may not assign a node name if a node by that name is involved explicitly in its definition. To reassign a node name safely, you have to write instead something like \begin{verbatim} \pnode([nodesep=.5cm]A){Atemp} \pnode(Atemp){A} \end{verbatim} This problem afflicts a number of other node-forming macros based on a \Lcs{pnode} construction, as most are. Nodes are more complicated than they appear. Each node is stored not only with a recipe for finding its coordinates, but also with the coordinate system in effect when it was defined. Part of the retrieval process involves modifying the coordinates if necessary so that they represent the same point on the page even if the coordinate system has changed. This is important, but has some unexpected consequences. Normally, the simplest way to translate an object is with \Lcs{rput}. \begin{verbatim} \pnode(1,1){P}% define P as (1,1) \rput(2,3){\psdot{P}}% places dot at original P=(1,1) \end{verbatim} is different from \begin{verbatim} \rput(2,3){\pnode(1,1){P}\psdot{P}} % places dot at (1,1)+(2,3) \end{verbatim} Effectively, \Lcs{rput} and \Lcs{uput} are not useful for translating previously defined nodes, but they are useful for defining new nodes relative to fixed positions. The new macros in this section are of several kinds: (i) utility macros, some used internally by the package and some of general use; (ii) macros that manipulate one or more nodes to produce other nodes; (iii) constructions intended to be used with nodes and node sequences. By a node sequence is meant one or more nodes having a common root name followed by an index---eg, P0 P1 P2 ... P5 is a node sequence with root name P. It is easy to define such node sequences using the \Lcs{multido} macro, or using one of a number of macros in this section. \subsection{Node expressions} A number of macros in the package (eg, \Lcs{psxline}) permit the use of node expressions, by which is meant an expression like \begin{verbatim} .25(1,3)+.333(2;90)-1.2([nodesep=.5cm]Q) \end{verbatim} which specifies a linear combination of points (the items enclosed in parentheses) specified in any manner acceptable to \Lcs{SpecialCoor}. %The items themselves cannot %themselves be node expressions, as they are not acceptable to \Lcs{SpecialCoor}. Node expressions are handled by \Lcs{nodexn}, which calls the macros \Lcs{hasparen} and \Lcs{parsenodexn} to do the real work. If you write code that needs to be able to handle node expressions, you use \begin{BDef} \Lcs{nodexn}\Largb{expr}\Largb{nodename} \end{BDef} which returns a node \verb|| once \verb|| has been fully parsed. It is safe to reuse a node name, as in \begin{verbatim} \nodexn{(P)+.5(1,2)}{P} \end{verbatim} The following macros amount to special cases of node expressions. \begin{BDef} \Lcs{AtoB}\Largr{A}\Largr{B}\Largb{C} \end{BDef} defines a node by name C essentially as B-A, as vectors. It is safe to use \Lcs{AtoB}\verb|(Q)(P){P}| and \Lcs{AtoB}\verb|(Q)(P){Q}|. \begin{BDef} \Lcs{AplusB}\Largr{A}\Largr{B}\Largb{C} \end{BDef} defines node by name C essentially as A+B, as vectors. It is safe to use \Lcs{AplusB}\verb|(Q)(P){P}| and \Lcs{AplusB}\verb|(Q)(P){Q}|. \begin{BDef} \Lcs{midAB}\Largr{A}\Largr{B}\Largb{C} \end{BDef} defines node by name C essentially as $(A+B)/2$, as vectors. It is safe to use \Lcs{midAB}\verb|(Q)(P){P}| and \Lcs{midAB}\verb|(Q)(P){Q}|. \begin{LTXexample}[width=.35\textwidth] \begin{pspicture}[showgrid=true](-.5,-.5)(2.5,2.5) \psset{arrows=->,arrowscale=1.5} \pnode(2,1){P}\pnode(.5,1){Q} \AtoB(Q)(P){QP} \AplusB(Q)(P){R} \psline(0,0)(P)\uput[-45](P){P} \psline(0,0)(Q)\uput[135](Q){Q} \psline(0,0)(QP)\uput[-70](QP){QP} \psline(0,0)(R)\uput[160](R){R} \psline[linestyle=dashed](Q)(P) \psline[linestyle=dashed](Q)(R) \psline[linestyle=dashed](P)(R) \end{pspicture} \end{LTXexample} \subsection{The main macros} \begin{BDef} \Lcs{normalvec}\Largr{coords}\Largb{nodename} \end{BDef} For example, \begin{verbatim} \normalvec(P){P}\normalvec(2;30){Q} \end{verbatim} first redefines the node {\tt P} as a node whose vector interpretation is of the same length as the original {\tt P}, but rotated 90 degrees. The second instance has the same effect as \Lcs{pnode}\verb|(2;120){Q}|. \begin{BDef} \Lcs{curvepnode}\Largb{tval}\Largb{expression in t}\Largb{nodename} \end{BDef} For example, \begin{verbatim} \curvepnode{1}{cos(t) | sin(t)}{P} \end{verbatim} sets a node named {\tt P} at \verb|(cos(1), sin(1))| and a node named {\tt Ptang} which represents a unit vector in the tangent direction to the curve at {\tt P}. The expression in {\tt t} in this case is algebraic, which is detected automatically by the macro. \begin{LTXexample}[width=.35\textwidth] \begin{pspicture}[showgrid=true](-.5,-.5)(2.5,2) \def\exn{cos(t) | sin(t)} \psparametricplot[algebraic]{0}{2}{\exn} \curvepnode{1}{\exn}{P} \psdot(P)\uput[45](P){P} \end{pspicture} \end{LTXexample} \vspace{2pc} \begin{BDef} \Lcs{psparnode}\Largb{t}\Largb{expression in t}\Largb{} \end{BDef} is called by the command \Lcs{curvename} if the expression is PostScript, not algebraic. \begin{BDef} \Lcs{algparnode}\Largb{t}\Largb{expression in t}\Largb{nodename} \end{BDef} is called by the command \Lcs{curvename} if the expression is algebraic, not PostScript. \begin{BDef} \Lcs{curvepnodes}\Largb{tmin}\Largb{tmax}\Largb{expr. in t}\Largb{nodeRoot} \end{BDef} Uses current setting of plotpoints (default 50) to define a node sequence of points along the curve. Eg, \begin{verbatim} \curvepnodes[plotpoints=100]{0}{1}{t+t^2 | Ex(-t)}{P} \end{verbatim} sets nodes {\tt P0 .. P99} at equally spaced {\tt t} values along the curve, and assigns the macro \Lcs{Pnodecount} to 99, the highest index. The expression in {\tt t} may be either algebraic or PostScript, and is handled automatically. The values \verb|, | may be expressed using PostScript---eg, \verb|{Pi neg}{PiDiv2}|. \begin{LTXexample}[width=.35\textwidth] \begin{pspicture}[showgrid=true](-.5,-.5)(2.5,3) \def\exn{t+t^2 | 2*Ex(-t)} \psset{plotpoints=100} \psparametricplot[algebraic]{0}{1}{\exn} \curvepnodes{0}{1}{\exn}{P} \psdot(P50)\uput[75](P50){P50} \psdot(P99)\uput[75](P99){P99} \end{pspicture} \end{LTXexample} \begin{BDef} \Lcs{fnpnode}\Largb{xval}\Largb{expression in x}\Largb{nodename} \end{BDef} sets a single node on the graph. Eg, \begin{verbatim} \fnpnode{.5}{x x 1 add mul 2 div}{P} \end{verbatim} declares the node P at the point x=0.5 on the graph. It has the same effect as \begin{verbatim} \pnode(!/x 0.5 def x x x 1 add mul 2 div}){P} \end{verbatim} If your expression in {\tt t} is algebraic, you must specify the keyword {\tt algebraic}, as in \Lcs{fnpnode}\verb|[algebraic]{0.5}{x*(x+1)/2}{P}|. \begin{LTXexample}[width=.35\textwidth] \begin{pspicture}[showgrid=true](-.5,-.5)(2.5,3) \def\exn{x x 1 add mul 2 div} \psplot{0}{2}{\exn} \fnpnode{0.5}{\exn}{Q} \psdot(Q)\uput[-45](Q){Q} \end{pspicture} \end{LTXexample} \vspace{2pc} \begin{BDef} \Lcs{fnpnodes}\Largb{xmin}\Largb{xmax}\Largb{expression in x}\Largb{nodeRoot} \end{BDef} Is similar to \Lcs{curvenodes}, but for the graph of a function. The keyword \Lkeyword{algebraic} must be specified if your expression is indeed algebraic. \begin{LTXexample}[width=.35\textwidth] \begin{pspicture}[showgrid=true](-.5,-.5)(2.5,3) \def\exn{x x 1 add mul 2 div} \psplot{0}{2}{\exn} \fnpnodes[plotpoints=10]{0}{2}{\exn}{A} \psdot(A4)\uput[-45](A4){A4} \end{pspicture} \end{LTXexample} \vspace{2pc} \begin{BDef} \Lcs{shownode}\Largr{P} \end{BDef} is a debugging tool, which displays in the console window the coordinates of node P. This will not appear until the final stage of processing the PostScript file. You will get a PostScript error if the node you specify is undefined. \begin{BDef} \Lcs{getnodelist}\Largb{node root name}\Largb{next command} \end{BDef} is useful in writing pstricks macros, where there is a list of parenthesized coordinates to be read and turned into a node sequence, following which \verb|| is followed. \begin{BDef} \Lcs{pnodes}\Largb{P}\Largr{1,2}\Largr{2;3}\ldots \end{BDef} is effectively \Lcs{getnodelist}\Largb{P}\Largb{}\verb|(1,2)(2;3)...|, just a quick way to turn a list of coordinates into a node sequence P0 P1 ... \begin{BDef} \Lcs{psnline}\OptArgs\Largb{arrows}\Largr{coors}\Largb{name} \end{BDef} for example, expects that there are nodes named P3..P8, and gives the same result as \begin{verbatim} \psline[linewidth=1pt]{->}(P3)(P4)(P5)(P6)(P7)(P8) \end{verbatim} \begin{LTXexample}[width=.35\textwidth] \begin{pspicture}[showgrid=true](-.5,-.5)(2.5,2) \pnodes{P}(.1,.1)(1;10)(*2 {x^2/4})(0,1.4) %defines P0..P3--now join them \psnline[arrowscale=2]{-D>}(0,3){P} \end{pspicture} \end{LTXexample} \vspace{2pc} \begin{BDef} \Lcs{psLCNodeVar}\Largr{node A}\Largr{node B}\Largr{factorA,factorB}\Largb{node name} \end{BDef} is similar to \Lcs{psLCNode}, and provides a means of forming a linear combination of two nodes, thought of as vectors. Where \begin{verbatim} \psLCNode(A){a}(B){b}{C} \end{verbatim} effectively makes \verb|C=aA+bB|, \begin{verbatim} \psLCNodeVar(A)(B)(a,b){C} \end{verbatim} does the same, but the third argument \verb|(a,b)| may be specified in any form acceptable to \Lcs{SpecialCoor}. (With \Lcs{psLCNode}, each coefficient may be specified in PostScript code.) One other difference is that \Lcs{psLCNodeVar} allows the reuse of a node name in place. For example, it is possible to write \begin{verbatim} \psLCNodeVar(A)(B)(2,3){A}% symbol A reassigned \end{verbatim} where the equivalent in \Lcs{psLCNode} will lead to a PostScript error. Since \Lcs{AtoB} and \Lcs{AplusB} are defined using \Lcs{psLCNodeVar}, they also allow node name reuse: \Lcs{AtoB}\verb|(Q)(P){P}| is legal. \begin{BDef} \Lcs{psRelNodeVar}\Largr{node A}\Largr{node B}\Largr{radius;angle}\Largb{node name} \end{BDef} is similar to \Lcs{psRelNode}, and provides a means of scaling and rotating a line segment AB about A. The effect of \begin{verbatim} \psRelNodeVar(A)(B)(2;30){C} \end{verbatim} is the same as \begin{verbatim} \psRelNode[angle=30](A)(B){2}{C} \end{verbatim} but the third argument (2;30) may be specified in any form acceptable to \Lcs{SpecialCoor}, while specifying the angle argument in \Lcs{psRelNode} using PostScript is not possible. Note that \Lcs{psRelNodeVar}\verb|(0,0)(A)(B){C}| may be interpreted as defining {\tt C} to be the complex product of {\tt A} and {\tt B}. \begin{LTXexample}[width=5cm] \begin{pspicture}[showgrid=true](-.5,-.5)(3.5,3) \pnode(0,.5){P}\pnode(1.5,.75){Q} \psRelNodeVar(P)(Q)(2;20){R} \psline(Q)(P)\uput[-45](P){P} \uput[-70](Q){Q} \psline(P)(R)\uput[-70](R){R} \end{pspicture} \end{LTXexample} \begin{BDef} \Lcs{psRelLineVar}\Largr{node A}\Largr{node B}\Largr{radius;angle}\Largb{node name} \end{BDef} stands to \Lcs{psRelLine} as \Lcs{psRelNodeVar} stands relative to \Lcs{psRelNode}. \Lcs{psRelLine}\verb|Var(A)(B)(a;b){C}| defines the node {\tt C}, and, in addition, draws the line segment {\tt AC}. \begin{BDef} \Lcs{rhombus}\Largb{edge length}\Largr{A}\Largb{B}\Largb{C}\Largb{D} \end{BDef} computes the two remaining vertices C, D given two opposing vertices A, B of a rhombus with specified edge length. It does not draw the rhombus, which could be handled easily by \Lcs{psline}. Internally, \Lcs{rhombus} uses \Lcs{psRelNodeVar}. \begin{BDef} \Lcs{psrline}\Largr{P}\Largr{Q}\ldots \end{BDef} is like \Lcs{psline}, but drawing a line starting at (P), with successive increments (Q)... It has the same options as\Lcs{psline}. \begin{LTXexample}[width=.35\textwidth] \begin{pspicture}[showgrid=true](-.5,-.5)(3.5,3) \pnode(0,.5){P}\pnode(1,1){Q} \psrline{->}(P)(Q)(2;20) \uput[-45](P){P} \end{pspicture} \end{LTXexample} \begin{BDef} \Lcs{psxline}\Largr{basept}\Largb{nodexpr1}\Largb{nodexpr2} \end{BDef} The {\tt x} here stands for expression. The idea is that one builds a line from \verb|+| to \verb|+|. \begin{LTXexample}[width=.35\textwidth] \begin{pspicture}[showgrid=true](-.5,-.5)(3.5,4) \def\pfn{t | t^2/4} \psparametricplot[algebraic]{0}{3.5}{\pfn} \curvepnode{2}{\pfn}{P}% sets P, Ptang \normalvec(Ptang){Q}\uput[-45](P){P} \psxline[linecolor=red]{<->}(P){-(Ptang)}{1.5(Ptang)} \psxline[linecolor=blue]{->}(P){}{.5(Q)}%can use {} for {(0,0)} \end{pspicture} \end{LTXexample} \vspace{2pc} \begin{BDef} \Lcs{polyIntersections}\Largb{Name1}\Largb{Name2}\Largr{A}\Largr{B}\Largb{P}\ldots\\ \Lcs{polyIntersections}\Largb{Name1}\Largb{Name2}\Largr{A}\Largr{B}\Largb{P}\Largb{n}\\ \end{BDef} is the most complicated macro in the collection. It has two forms. \begin{verbatim} \polyIntersections{}{}(A)(B)(1,2)(3;30)(6,5)... \end{verbatim} defines the polyline \verb|L=(1,2)(3;30)(6,5)...|, and computes the two points of intersection closest to {\tt A} in each direction with the directed line starting at A heading toward B. The first intersection point in the positive direction is named \verb||, and the first intersection point in the opposite direction (from A) is named \verb||. If one or other of these intersections is empty, the nodes are set to remote points on the line {\tt AB}. The effect of the line joining the constructed nodes depends on the location of {\tt A} and {\tt B} relative to {\tt L}, with two cases worth noting. \begin{itemize} \item if {\tt L} is closed and if {\tt A, B} are interior to one of its components, the resulting line extends across that component of {\tt L}, and contains {\tt AB}. \item If {\tt L} is simple and closed, one of {\tt A, B} is inside and the other outside, the resulting line segment will contain {\tt A} but not {\tt B}. \end{itemize} \begin{verbatim} \polyIntersections{}{}(A)(B){P}{n} \end{verbatim} has exactly the same effect as \begin{verbatim} \polyIntersections{}{}(A)(B)(P0)(P1)...(Pn) \end{verbatim} assuming \verb|P0...Pn| to be previously defined nodes. \begin{LTXexample}[width=.375\textwidth] \begin{pspicture}[showgrid=true](-.5,-.5)(3.5,3) \pnodes{P}(0,.5)(3,.5)(2.5,2)(.5,2.5)(0,.5) \pnode(1,1.1){A}\pnode(2,1.5){B} \polyIntersections{N1}{N2}(A)(B){P}{4} \psnline(0,4){P} \psdots(A)(B)\psline(N1)(N2) \uput[-60](A){A}\uput[-60](B){B} \uput[0](N1){N1}\uput[-180](N2){N2} \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=.375\textwidth] \begin{pspicture}[showgrid=true](-.5,-.5)(3.5,3) \pnodes{P}(0,.5)(3,.5)(2.5,2)(.5,2.5)(0,.5) \pnode(1,1.1){A}\pnode(2,3){B} \polyIntersections{N1}{N2}(A)(B){P}{4} \psnline(0,4){P} \psdots(A)(B)\psline(N1)(N2) \uput[-60](A){A}\uput[-60](B){B} \uput[90](N1){N1}\uput[-90](N2){N2} \end{pspicture} \end{LTXexample} \begin{LTXexample}[width=.375\textwidth] \begin{pspicture}[showgrid=true](-.5,-.5)(3.5,3) \def\fn{1.5+sin(t)+.4*sin(2*t)% | 1+cos(t)+.2*cos(2*t)+.2*sin(4*t)}% \pnode(1,1.1){A}\pnode(2,1.2){B} \psset{plotpoints=100} \psparametricplot[algebraic]{0}{6.283}{\fn} \curvepnodes{0}{6.283}{\fn}{Z} \polyIntersections{N1}{N2}(A)(B){Z}{99} \psdots(A)(B)\psline(N1)(N2) \uput[-60](A){A}\uput[-60](B){B} \uput[0](N1){N1}\uput[220](N2){N2} \end{pspicture} \end{LTXexample} \vspace{1pc} \begin{LTXexample}[width=.375\textwidth] \begin{pspicture}[showgrid=true](-.5,-.5)(3.5,3) \def\fn{1.5+sin(t)+.4*sin(2*t)% | 1+cos(t)+.2*cos(2*t)+.2*sin(4*t)}% \pnode(.8,.6){A}\pnode(2.5,-.5){B} \psset{plotpoints=100} \psparametricplot[algebraic]{0}{6.283}{\fn} \curvepnodes{0}{6.283}{\fn}{Z} \polyIntersections{N1}{N2}(A)(B){Z}{99} \psdots(A)(B)\psline(N1)(N2) \uput[90](A){A}\uput[-60](B){B} \uput[70](N1){N1}\uput[180](N2){N2} \end{pspicture} \end{LTXexample} \vspace{1pc} \begin{LTXexample}[width=.375\textwidth] \begin{pspicture}[showgrid=true](-.5,-.5)(3.5,3) \pnodes{P}(0,.5)(3,.5)(2.5,2)(.5,2.5)(0,.5) \pnode(1,1.1){A}\pnode(2,1.5){B} \polyIntersections{N1}{N2}(A)(B){P}{3} \psnline(0,3){P} \psdots(A)(B) \psclip{\psframe[linestyle=none](-.5,-.5)(3.5,2.5)} \psline(N1)(N2)\endpsclip \uput[-60](A){A}\uput[-60](B){B} \uput[0](N1){N1}\uput[-180](N2){N2} \end{pspicture} \end{LTXexample} \vspace{1pc} \begin{LTXexample}[width=.375\textwidth] \begin{pspicture}[showgrid=true](-.5,-.5)(3.5,3) \def\fn{x+sin(2*x)} \psplot[algebraic]{0}{3.14}{\fn} \fnpnodes[algebraic]{0}{3.14}{\fn}{P} \pnode(.6,.8){A}\pnode(1.5,1.1){B} \polyIntersections{N1}{N2}(A)(B){P}{49} \psdots(A)(B) \uput[-90](A){A}\uput[-90](B){B} \psline(N1)(N2) \psset{linestyle=dashed} \psline(N1)(N1 | 0,0) \psline(N2)(N2 | 0,0) \uput[70](N1){N1}\uput[170](N2){N2} \end{pspicture} \end{LTXexample} \vspace{1pc} \begin{BDef} \Lcs{ArrowNotch}\Largb{}\Largb{}\Largb{}\Largb{} \end{BDef} takes as inputs the root name of the node sequence, the index at which the arrow tip is to be drawn, and the direction (one of \verb+>,<+) of the arrow. It then constructs the notch as a node with name \verb||. The arrowhead may then be drawn with a command like \Lcs{psline}\verb|{->}(N)(P3)|, assuming the tip was to be {\tt P3} and the notch was {\tt N}. Keep in mind that the macro takes its settings for linewidth, arrowscale, etc from the current values, so it is generally preferable to include them in a \Lcs{psset} before drawing the curve and calling \Lcs{ArrowNotch}. (Alternatively, they may be included as optional settings in \Lcs{ArrowNotch}.) The first example below shows a case where the native arrow direction is not good. The second shows how to make a version using \Lcs{ArrowNotch}. Notice that the minimum and maximum parameter values in the second example had to be modified to keep the curve from protruding near the end arrowheads. \Lcs{ArrowNotch} is a computationally expensive macro (quadratic in {\tt plotpoints}) designed to improve the placement of arrows on curves in those cases (high curvature, large values of linewidth, arrowscale, etc) where the native arrow direction is not optimal. The macro depends on the construction of a node sequence, say {\tt P0..Pn}, of samples of the curve (eg, with \Lcs{curvepnodes}) from which it computes the position of the notch of the arrow so that, when drawn, the arrow notch will be located on the curve in all cases. It operates with only two particular arrow shapes---those arrows specified with either \verb|->| or \verb|-D>|, or their reverses. \begin{LTXexample}[width=.375\textwidth] \def\fn{1.5+1.5*cos(t) | 1+sin(t)} \psset{linewidth=2pt,arrowscale=3} \begin{pspicture}(0,0)(3.5,3) \psparametricplot[algebraic,arrows=<->]{PiDiv2 neg}{Pi}{\fn} \end{pspicture} \end{LTXexample} \vspace{1pc} \begin{LTXexample}[width=.375\textwidth] \def\fn{1.5+1.5*cos(t) | 1+sin(t)} \psset{linewidth=2pt,arrowscale=3} \begin{pspicture}(0,0)(3.5,3) \curvepnodes{PiDiv2 neg}{Pi}\fn{P}%create P0..P49 \ArrowNotch{P}{0}{<}{Q} \ArrowNotch{P}{49}{>}{R} \ArrowNotch[arrowscale=1.5]{P}{27}{>}{S} \psparametricplot[algebraic]{-1.47}{2.95}{\fn} \psline{->}(Q)(P0) \psline{->}(R)(P49) \psline[arrowscale=1.5]{->}(S)(P27) \end{pspicture} \end{LTXexample} \clearpage \section{List of all optional arguments for \texttt{pst-node}} \xkvview{family=pst-node,columns={key,type,default}} \nocite{*} \bgroup \RaggedRight \bibliographystyle{plain} \bibliography{pst-node-doc} \egroup \printindex \end{document}