%% $Id: pst-node-doc.tex 876 2014-01-28 15:03:13Z 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}
%\usepackage{pax}
\let\pstFV\fileversion
\let\belowcaptionskip\abovecaptionskip
%
\newcommand\xstrut{\vphantom{\tabular{c}Üg\\Üg\endtabular}}
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\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. .

For some copatibility reason you can use the optional argument \Loption{97}
for the package, it loads the version from 1997, which only makes sense
when also running the main package \LPack{pstricks} with this option.

\vfill
\noindent
Thanks to:  Marco Daniel; Denis Girou; Rolf Niepraschk; Sebastian Rahtz;
\end{abstract}

\clearpage
\tableofcontents

\clearpage
\part{Basic commands, connections and labels}

\leavevmode
\marginpar{%
  \leavevmode\lower 20pt\hbox{%
    \hbox to0pt{\hbox to \linewidth{\hss\rnode{file}{\copy\filebox}\hss}\hss}%
    \raise 10pt\hbox to \linewidth{\hss\large\bfseries\sffamily pst-node\hss}}}%

The node and node connection macros let you connect information and place
labels, without knowing the exact position of what you are connecting or where
the lines should connect. These macros are useful for making graphs and trees,
mathematical diagrams, linguistic syntax diagrams, and connecting ideas of any
kind. They are the trickiest tricks in PSTricks!

There are three components to the node macros:
\begin{description}
  \item[Node definitions] The node definitions let you assign a name and shape
  to an object. See Section \ref{S-nodes}.
  \item[Node connections] The node connections connect two nodes, identified
  by their names. See Section \ref{S-nc}.
  \item[Node labels] The node label commands let you affix labels to the node
  connections. See Section \ref{S-nodelabels}.
\end{description}

You can use these macros just about anywhere. The best way to position them
depends on the application. For greatest flexibility, you can use the nodes in
a \Lenv{pspicture}, positioning and rotating them with \Lcs{rput}. You can also use
them in alignment environments. \LPack{pst-node} contains a special alignment
environment, \Lenv{psmatrix}, which is designed for positioning nodes in a grid,
such as in mathematical diagrams and some graphs. \Lcs{psmatrix} is described in
Section \ref{S-psmatrix}. \LPack{pst-node} also contains high-level macros for
trees. These are described in the documentation of \LPack{pst-tree}.

But don't restrict yourself to these more obvious uses. For example:
\begin{center}
  \rnode{A}{%
    \parbox{12cm}{\raggedright
      I made the file symbol a node. Now I can draw an
      arrow so that you know what I am talking about.}}
  \ncarc[nodesep=8pt]{->}{A}{file}
\end{center}

\begin{lstlisting}
  \rnode{A}{%
    \parbox{4cm}{\raggedright
      I made the file symbol a node. Now I can draw an
      arrow so that you know what I am talking about.}}
  \ncarc[nodesep=8pt]{->}{A}{file}
\end{lstlisting}



\section{Nodes}\label{S-nodes}

Nodes have a name. a boundary and a center.
The center of a node is where node connections point to. The boundary is for
determining where to connect a node connection. The various nodes differ in
how they determine the center and boundary. They also differ in what kind of
visable object they create.


The\XInfoDanger[0]{} name is for refering to the node when making node connections and labels.
You specify the name as an argument to the node commands. The name must
contain only letters and numbers, and must begin with a letter. Bad node names
can cause PostScript errors.


Here are the nodes:

\begin{BDef}
\Lcs{rnode}\OptArg{refpoint}\Largb{name}\Largb{stuff}
\end{BDef}

  \Lcs{rnode} puts \Larg{stuff} in a box. The center of the node is \Larg{refpoint}, which
you can specify the same way as for \Lcs{rput}.

\begin{BDef}
\Lcs{Rnode}\Largb{name}\Largb{stuff}
\end{BDef}

  \Lcs{Rnode} also makes a box, but the center is set differently. If you align
\Lcs{rnode}'s by their baseline, differences in the height and depth of the nodes
can cause connecting lines to be not quite parallel, such as in the following
example:

\begin{LTXexample}[width=0.4\linewidth]
  \Large
  \rnode{A}{sp} \hskip 2cm \rnode{B}{Bit}
  \ncline{A}{B}
\end{LTXexample}

With \Lcs{Rnode}, the center is determined relative to the baseline:

\begin{LTXexample}[width=0.4\linewidth]
  \Large
  \Rnode{A}{sp} \hskip 2cm \Rnode{B}{Bit}
  \ncline{A}{B}
\end{LTXexample}

You can usually get by without fiddling with the center of the node, but to
modify it you set the
  \LKeyword{href=num} or 
  \LKeyword{vref=dim}
parameters. In the horizontal direction, the center is located fraction
\Lkeyword{href} from the center to the edge. E.g, if \LKeyword{href=-1}, the center is on
the left edge of the box. In the vertical direction, the center is located
distance \Lkeyword{vref} from the baseline. The \Lkeyword{vref} parameter is evaluated each
time \Lcs{Rnode} is used, so that you can use \verb|ex| units to have the distance
adjust itself to the size of the current font (but without being sensitive to
differences in the size of letters within the current font).

The command \Lcs{pnode}  creates a zero dimensional node at \Largr{\CAny}.
It 
knows an optional argument for an \CAny\ offset, which
expects the two values for $x$ and $y$ separated by a comma:

\begin{BDef}
\Lcs{pnode}\OptArg*{\Largs{\Larga{offset}}}\Largr{\CAny}\Largb{\Larga{node name}}
\end{BDef}


\begin{LTXexample}[width=6cm]
\begin{pspicture}[showgrid](0,-2)(6,2)
\pnode{A}\psdot(A)\uput[90](A){A} 
\pnode[0,-2]{B}\psdot(B)\uput[90](B){B} 
\pnode(2,0){C}\psdot(C)\uput[90](C){C} 
\pnode[1,-2](2,0){D}\psdot(D)\uput[90](D){D} 
\pnode[2,2](3.5,0){E}\psdot(E)\uput[90](E){E} 
\end{pspicture}
\end{LTXexample}


\begin{BDef}
\Lcs{pnodes}\OptArg*{\Largs{\Larga{offset}}}\Largr{coors}\Largb{name}\Largr{coors}\Largb{name}\ldots\\
\Lcs{pnodes}\Largb{name}\Largr{coors}\Largr{coors}\ldots
\end{BDef}

This command is identical to \Lcs{pnode} if it doesn't start with a node name. In this
case it works in another way. See page~\pageref{pnodes} for more information. Instead of
writing

\begin{verbatim}
\pnode(3,1){A}
\pnode(2,4){B}
\end{verbatim}

one can also define the nodes in a short way:
\begin{verbatim}
\pnodes(3,1){A}(2,4){B}
\end{verbatim}

If an optional argument for the offset is used, then it is passes to all nodes.






The command \Lcs{psnode}  is a combination of using \Lcs{rput} and \Lcs{rnode}.

\begin{BDef}
\Lcs{psnode}\OptArgs\Largr{\CAny}\Largb{\Larga{node name}}\Largb{\Larga{node contents}}
\end{BDef}

\begin{LTXexample}
\begin{pspicture}[showgrid](0,0)(4,4)
\psnode(0.5,3){A}{Foo}
\psnode(3,0){B}{Bar}
\ncdiag[arm=5mm,angleA=-90,
        angleB=90]{->}{A}{B}
\end{pspicture}
\end{LTXexample}


\begin{BDef}
\LcsStar{cnode}\OptArgs\Largr{\CAny}\Largb{radius}\Largb{name}
\end{BDef}

  This draws a circle. Here is an example with \Lcs{pnode} and \Lcs{cnode}:
  
\begin{LTXexample}
\begin{pspicture}[showgrid](3,1.25)
  \cnode(0,1){.25}{A}
  \pnode(3,0){B}
  \ncline{<-}{A}{B}
\end{pspicture}
\end{LTXexample}

\begin{BDef}
\LcsStar{Cnode}\OptArgs\Largr{\CAny}\Largb{name}
\end{BDef}

  This is like \Lcs{cnode}, but the radius is the value of \LKeyword{radius=dim}
This is convenient when you want many circle nodes of the same radius.

\begin{BDef}
\LcsStar{circlenode}\OptArgs\Largb{name}\Largb{stuff}
\end{BDef}

  This is a variant of \Lcs{pscirclebox} that gives the node the shape of the
circle.

\begin{BDef}
 \LcsStar{cnodeput}\OptArgs\Largb{angle}\Largr{\CAny}\Largb{name}\Largb{stuff}\\
 \LcsStar{Cnodeput}\OptArgs\Largb{angle}\Largr{\CAny}\Largb{name}\Largb{stuff}
\end{BDef}

  This is a variant of \Lcs{cput} (or \Lcs{Cput}) that gives the node the shape of the
circle. That is, it is like
\begin{lstlisting}
  \rput{<angle>}(<x>,<y>){\circlenode{<name>}{<stuff>}}
  \rput[radius=...]{<angle>}(<x>,<y>){\Circlenode{<name>}{<stuff>}}
\end{lstlisting}


\begin{BDef}
\LcsStar{ovalnode}\OptArgs\Largb{name}\Largb{stuff}
\end{BDef}

  This is a variant of \Lcs{psovalbox} that gives the node the shape of an
ellipse. Here is an example with \Lcs{circlenode} and \Lcs{ovalnode}:

\begin{LTXexample}[width=0.3\textwidth]
\circlenode{A}{Circle} and \ovalnode{B}{Oval}
\ncbar[angle=90]{A}{B}
\end{LTXexample}


\begin{BDef}
\LcsStar{dianode}\OptArgs\Largb{name}\Largb{stuff}
\end{BDef}

  This is like \Lcs{diabox}.


\begin{BDef}
\LcsStar{trinode}\OptArgs\Largb{name}\Largb{stuff}
\end{BDef}

  This is like \Lcs{tribox}.

\begin{LTXexample}[width=5cm]
\begin{pspicture}(4,3)
  \rput[tl](0,3){\dianode{A}{Diamond}}
  \rput[br](4,0){\trinode[trimode=L]{B}{Triangle}}
  \nccurve[angleA=-135,angleB=90]{A}{B}
\end{pspicture}
\end{LTXexample}

\begin{BDef}
\LcsStar{dotnode}\OptArgs\Largr{\CAny}\Largb{name}\\
\LcsStar{dotnodes}\OptArgs\Largr{\CAny}\Largb{name}\Largr{\CAny}\Largb{name}\ldots
\end{BDef}

This is a variant of \Lcs{psdot}. For example:
\begin{LTXexample}
\begin{pspicture}(3,2)
  \dotnode[dotstyle=triangle*,dotscale=2 1](0,0){A}
  \dotnode[dotstyle=+](3,2){B}
  \ncline[nodesep=3pt]{A}{B}
\end{pspicture}
\end{LTXexample}


\begin{BDef}
\LcsStar{fnode}\OptArgs\Largr{\CAny}\Largb{name}
\end{BDef}

  The ``f'' stands for ``frame''. This is like, but easier than, putting a
\Lcs{psframe} in an \Lcs{rnode}.

\begin{LTXexample}
\begin{pspicture}(3,2)
  \fnode{A}
  \fnode*[framesize=1 5pt](2,2){B}
  \ncline[nodesep=3pt]{A}{B}
\end{pspicture}
\end{LTXexample}

There are two differences between \Lcs{fnode} and \Lcs{psframe}:
\begin{itemize}
  \item There is a single (optional) coordinate argument, that gives the
  \emph{center} of the frame.
  \item The width and height of the frame are set by the
  \LKeyword{framesize=dim1 `dim2'} parameter. If you omit <dim2>, you get a square frame.
\end{itemize}


\section{Node connections}\label{S-nc}

All the node connection commands begin with \nxLcs{nc}, and they all have the same
syntax:\footnote{%
The node connections can be used with \Lcs{pscustom}. The beginning of the node
connection is attached to the current point by a straight line, as with
\Lcs{psarc}.}$^,$\footnote{%
See page  \pageref{S-SpecialCoor} if you want to use the nodes as
coordinates in other PSTricks macros.}

\begin{BDef}
  \nxLcs{<nodeconnection>*}\OptArgs\Largb{<arrows>}\Largb{<nodeA>}\Largb{<nodeB>}
\end{BDef}

A line of some sort is drawn from <nodeA> to <nodeB>. Some of the node
connection commands are a little confusing, but with a little experimentation
you will figure them out, and you will be amazed at the things you can do.
When we refer to the \verb|A| and \verb|B| nodes below, we are referring only to the
order in which the names are given as arguments to the node connection
macros.\footnote{%
When a node name cannot be found on the same page as the node connection
command, you get either no node connection or a nonsense node connection.
However, \TeX{} will not report any errors.}

The node connections use many of the usual graphics parameters, plus a few
special ones. Let's start with one that applies to all the node connections:
  \LKeyword{nodesep=dim}

\Lkeyword{nodesep} is the border around the nodes that is added for the purpose of
determining where to connect the lines.

For this and other node connection parameters, you can set different values
for the two ends of the node connection. Set the parameter \Lkeyword{nodesepA} for
the first node, and set \Lkeyword{nodesepB} for the second node.

The first two node connections draw a line or arc directly between the two
nodes:

\begin{BDef}
\LcsStar{ncline}\OptArgs\OptArg*{\Largb{arrows}}\Largb{nodeA}\Largb{nodeB}
\end{BDef}

This draws a straight line between the nodes. For example:
\begin{LTXexample}
\begin{pspicture}(4,3)
  \rput[bl](0,0){\rnode{A}{Idea 1}}
  \rput[tr](4,3){\rnode{B}{Idea 2}}
  \ncline[nodesep=3pt]{<->}{A}{B}
\end{pspicture}
\end{LTXexample}

\begin{BDef}
\LcsStar{ncarc}\OptArgs\OptArg*{\Largb{arrows}}\Largb{nodeA}\Largb{nodeB}
\end{BDef}

This connects the two nodes with an arc.
\begin{LTXexample}
\begin{pspicture}[shift=*](3.5,2.5)
  \cnodeput(0,0){A}{X}
  \cnodeput(3,2){B}{Y}
  \psset{nodesep=3pt}
  \ncarc{->}{A}{B}
  \ncarc{->}{B}{A}
\end{pspicture}
\end{LTXexample}

The angle between the arc and the line between the two nodes is\footnote{%
Rather than using a true arc, \Lcs{ncarc} actually draws a bezier curve. When
connecting two circular nodes using the default parameter values, the curve
will be indistinguishable from a true arc. However, \Lcs{ncarc} is more
flexible than an arc, and works right connecting nodes of different shapes and
sizes. You can set \Lkeyword{arcangleA} and \Lkeyword{arcangleB} separately, and you can
control the curvature with the \Lkeyword{ncurv} parameter, which is described on page
\pageref{p+ncurv}.} \LKeyword{arcangle=angle}


\Lcs{ncline} and \Lcs{ncarc} both determine the angle at which the node
connections join by the relative position of the two nodes. With the next
group of node connections, you specify one or both of the angles in absolute
terms, by setting the
  \LKeyword{angle=angle}
(and \Lkeyword{angleA} and \Lkeyword{angleB}) parameter.

You also specify the length of the line segment where the node connection
joins at one or both of the ends (the ``arms'') by setting the
  \LKeyword{arm=dim}
(and \Lkeyword{armA} and \Lkeyword{armB}) parameter.

These node connections all consist of several line segments, including the
arms. The value of \Lkeyword{linearc} is used for rounding the corners.

Here they are, starting with the simplest one:

\begin{BDef}
\LcsStar{ncdiag}\OptArgs\OptArg*{\Largb{arrows}}\Largb{nodeA}\Largb{nodeB}
\end{BDef}


An arm is drawn at each node, joining at angle \Lkeyword{angleA} or \Lkeyword{angleB},
and with a length of \Lkeyword{armA} or \Lkeyword{armB}. Then the two arms are connected
by a straight line, so that the whole line has three line segments.
For example:

\begin{LTXexample}[width=0.4\textwidth]
\begin{pspicture}(4,3)
  \rput[tl](0,3){\rnode{A}{\psframebox{Node A}}}
  \rput[br](4,0){\ovalnode{B}{Node B}}
  \ncdiag[angleA=-90, angleB=90, arm=.5, linearc=.2]{A}{B}
\end{pspicture}
\end{LTXexample}

You can also set one or both of the arms to zero length. For example, if you
set \LKeyword{arm=0}, the nodes are connected by a straight line, but you get to
determine where the line connects (whereas the connection point is determined
automatically by \Lcs{ncline}. Compare this use of \Lcs{ncdiag} with \Lcs{ncline}
in the following example:

\begin{LTXexample}[width=0.4\textwidth]
\begin{pspicture}[shift=*](4,2.5)
  \rput[r](4,1){\ovalnode{R}{Root}}
  \cnodeput(1,2){A}{XX}
  \cnodeput(1,0){B}{YY}
  \ncdiag[angleB=180, arm=0]{<-}{A}{R}
  \ncline{<-}{B}{R}
\end{pspicture}
\end{LTXexample}

(Note that in this example, the default value \LKeyword{angleA=0} is used.)

\begin{BDef}
\LcsStar{ncdiagg}\OptArgs\OptArg*{\Largb{arrows}}\Largb{nodeA}\Largb{nodeB}
\end{BDef}

\Lcs{ncdiagg} is similar to \Lcs{ncdiag}, but only the arm for node A is drawn.
The end of this arm is then connected directly to node B. Compare
\Lcs{ncdiagg} with \Lcs{ncdiag} when \LKeyword{armB=0}:

\begin{LTXexample}[width=0.4\textwidth]
\begin{pspicture}[shift=*](3.5,1)
\cnode(0,0){12pt}{a}
\rput[l](3,1){\rnode{b}{H}}
\rput[l](3,-1){\rnode{c}{T}}
\ncdiagg[angleA=180,armA=1.5,nodesepA=3pt]{b}{a}
\nbput[npos=1.2]{\texttt{\string\ncdiagg}}
\ncdiag[angleA=180,armA=1.5,armB=0,
        nodesepA=3pt]{c}{a}
\naput[npos=1.2]{\texttt{\string\ncdiag}}
\end{pspicture}
\end{LTXexample}

  You can use \Lcs{ncdiagg} with \LKeyword{armA=0} if you want a straight line that
joins to node A at the angle you specify, and to node B at an angle that is
determined automatically.

\begin{BDef}
\LcsStar{ncbar}\OptArgs\OptArg*{\Largb{arrows}}\Largb{nodeA}\Largb{nodeB}
\end{BDef}

  This node connection consists of a line with arms dropping ``down'', at
right angles, to meet two nodes at an angle \Lkeyword{angleA}. Each arm is at least
of length \Lkeyword{armA} or \Lkeyword{armB}, but one may be need to be longer.

\begin{LTXexample}[width=0.4\textwidth]
\rnode{A}{Connect} some \rnode{B}{words}!
\ncbar[nodesep=3pt,angle=-90]{<-**}{A}{B}
\ncbar[nodesep=3pt,angle=70]{A}{B}
\end{LTXexample}

 Generally, the whole line has three straight segments.

\begin{BDef}
\LcsStar{ncangle}\OptArgs\OptArg*{\Largb{arrows}}\Largb{nodeA}\Largb{nodeB}
\end{BDef}


  Now we get to a more complicated node connection. \Lcs{ncangle} typically
draws three line segments, like \Lcs{ncdiag}. However, rather than fixing the
length of arm A, we adjust arm A so that the line joining the two arms meets
arm A at a right angle. For example:

\begin{LTXexample}[width=5cm]
\begin{pspicture}(4,3)
  \rput[tl](0,3){\rnode{A}{\psframebox{Node A}}}
  \rput[br](4,0){\ovalnode{B}{Node B}}
  \ncangle[angleA=-90,angleB=90,armB=1cm]{A}{B}
\end{pspicture}
\end{LTXexample}

Now watch what happens when we change \Lkeyword{angleA}:

\begin{LTXexample}[width=5cm]
\begin{pspicture}(4,3)
  \rput[tl](0,3){\rnode{A}{\psframebox{Node A}}}
  \nput[labelsep=0]{-70}{A}{%
     \psarcn(0,0){.4cm}{0}{-70}
     \uput{.4cm}[-35](0,0){\texttt{angleA}}}
  \rput[br](4,0){\ovalnode{B}{Node B}}
  \ncangle[angleA=-70,angleB=90,armB=1cm,linewidth=1.2pt]{A}{B}
  \nput[labelsep=0]{90}{B}{%
    \rput[bl](2pt,1pt){%
      \valign{%
        \vfil#\vfil\cr
        \hbox{\psscaleboxto(.3,.95cm){\}}}\cr%
        \hbox{\kern 1pt{\texttt{armB}}}\cr}}}
  \ncput[nrot=:U,npos=1]{\psframe[dimen=middle](0,0)(.35,.35)}
\end{pspicture}
\end{LTXexample}



\Lcs{ncangle} is also a good way to join nodes by a right angle, with just two
line segments, as in this example:

\begin{LTXexample}[width=5cm]
\begin{pspicture}(4,2)
  \rput[tl](0,2){\rnode{A}{\psframebox{Node A}}}
  \rput[br](4,0){\ovalnode{B}{Node B}}
  \ncangle[angleB=90, armB=0, linearc=.5]{A}{B}
\end{pspicture}
\end{LTXexample}

\begin{BDef}
\LcsStar{ncangles}\OptArgs\OptArg*{\Largb{arrows}}\Largb{nodeA}\Largb{nodeB}
\end{BDef}

 \Lcs{ncangles} is similar to \Lcs{ncangle}, but the length of arm A is fixed by
he \Lkeyword{armA} parameter. Arm A is connected to arm B by two line segments that
eet arm A and each other at right angles. The angle at which they join arm B,
and the length of the connecting segments, depends on the positions of the two
arms. \Lcs{ncangles} generally draws a total of four line segments.\footnote{%
Hence there is one more angle than \Lcs{ncangle}, and hence the \texttt|s| in
\Lcs{ncangles}.}
For example:

\begin{LTXexample}[width=5cm]
\begin{pspicture}(4,4)
  \rput[tl](0,4){\rnode{A}{\psframebox{Node A}}}
  \rput[br](4,0){\ovalnode{B}{Node B}}
  \ncangles[angleA=-90, armA=1cm, armB=.5cm, linearc=.15]{A}{B}
\end{pspicture}
\end{LTXexample}

Let's see what happens to the previous example when we change \Lkeyword{angleB}:

\begin{LTXexample}[width=5cm]
\begin{pspicture}(4,4)
  \rput[tl](0,4){\rnode{A}{\psframebox{Node A}}}
  \rput[br](4,0){\ovalnode{B}{Node B}}
  \ncangles[angleA=-90, angleB=135, armA=1cm, armB=.5cm,
     linearc=.15]{A}{B}
  \nput[labelsep=0]{-90}{A}{%
    \psarcn(0,0){.4cm}{0}{-90}
    \uput{.4cm}[-45](0,0){\texttt{angleA}}
    \rput[tr](-2pt,0){%
      \valign{%
        \vfil#\vfil\cr
        \hbox{\texttt{armA}\kern 1pt}\cr
        \hbox{\psscaleboxto(.28,.95cm){\{}}\cr\cr}}}
  \nput[labelsep=0]{135}{B}{%
    \psarc(0,0){.4cm}{0}{133}
    \uput{.4cm}[50.5](0,0){\texttt{angleB}}}
  \ncput[nrot=:L,npos=2]{\psline(0,-.35)(-.35,-.35)(-.35,0)}
  \ncput[npos=3.5]{%
    \rput[r](-.8,0){\rnode{arm}{\texttt{armB}}}
    \pnode{brak}}%
  \ncline[nodesep=3pt]{->}{arm}{brak}
\end{pspicture}
\end{LTXexample}

\begin{BDef}
\LcsStar{ncloop}\OptArgs\OptArg*{\Largb{arrows}}\Largb{nodeA}\Largb{nodeB}
\end{BDef}

  \Lcs{ncloop} is also in the same family as \Lcs{ncangle} and \Lcs{ncangles}, but
now typically 5 line segments are drawn. Hence, \Lcs{ncloop} can reach around
to opposite sides of the nodes. The lengths of the arms are fixed by \Lkeyword{armA}
and \Lkeyword{armB}. Starting at arm A, \Lcs{ncloop} makes a 90 degree turn to the
left, drawing a segment of length
  \LKeyword{loopsize=dim}
This segment connects to arm B the way arm A connects to arm B with \Lcs{ncline};
that is, two more segments are drawn, which join the first segment and each
other at right angles, and then join arm B. For example:

\begin{LTXexample}[pos=t]
  \vrule width 0pt height 1cm
  \rnode{a}{\psframebox{\Huge A loop}}
  \ncloop[angleB=180,loopsize=1,arm=.5,linearc=.2]{->}{a}{a}
  \ncput[npos=3.5,nrot=:U]{\psline{|<->|}(.5,-.2)(-.5,-.2)}
  \nbput[npos=3.5,nrot=:D,labelsep=.35cm]{{\ttfamily loopsize}}
  \kern .5cm
\end{LTXexample}

In this example, node A and node B are the same node! You can do this with all
the node connections (but it doesn't always make sense).
Here is an example where \Lcs{ncloop} connects two different nodes:

\begin{LTXexample}[pos=t]
  \parbox{3cm}{%
  \rnode{A}{\psframebox{\large\textbf{Begin}}}
  \vspace{1cm}\hspace*{\fill}
  \rnode{B}{\psframebox{\large\textbf{End}}}
  \ncloop[angleA=180,loopsize=.9,arm=.5,linearc=.2]{->}{A}{B}}
  \ncput[npos=1.5,nrot=:U]{\psline{|<->|}(.45,-.2)(-.45,-.2)}
  \nbput[npos=1.5,nrot=:D,labelsep=.35cm]{\texttt{loopsize}}
  \kern .5cm
\end{LTXexample}


The next two node connections are a little different from the rest.

\begin{BDef}
\LcsStar{nccurve}\OptArgs\OptArg*{\Largb{arrows}}\Largb{nodeA}\Largb{nodeB}
\end{BDef}

  \Lcs{nccurve} draws a bezier curve between the nodes.

\begin{LTXexample}[width=5cm]
\begin{pspicture}(4,3)
  \rput[bl](0,0){\rnode{A}{\psframebox{Node A}}}
  \rput[tr](4,3){\ovalnode{B}{Node B}}
  \nccurve[angleB=180]{A}{B}
\end{pspicture}
\end{LTXexample}

You specify the angle at which the curve joins the nodes by setting the
\Lkeyword{angle} (and \Lkeyword{angleA} and \Lkeyword{angleB}) parameter. The distance to the
control points is set with the
  \LKeyword{ncurv=num}
(and \Lkeyword{ncurvA} and \Lkeyword{ncurvB}) parameter. A lower number gives a tighter
curve. (The distance between the beginning of the arc and the first control
point is one-half \Lkeyword{ncurvA} times the distance between the two endpoints.)

\begin{BDef}
\LcsStar{nccircle}\OptArgs\OptArg*{\Largb{arrows}}\Largb{nodeA}\Largb{nodeB}
\end{BDef}

\Lcs{nccircle} draws a circle, or part of a circle, that, if complete, would
pass through the center of the node counterclockwise, at an angle of
\Lkeyword{angleA}.

\begin{LTXexample}
\vrule width 0pt height 1.4cm
\rnode{A}{\textbf{back}}
\nccircle[nodesep=3pt]{->}{A}{.7cm}
\end{LTXexample}

\Lcs{nccircle} can only connect a node to itself; it is the only node
connection with this property. \Lcs{nccircle} is also special because it has an
additional argument, for specifying the radius of the circle.


The last two node connections are also special. Rather than connecting the
nodes with an open curve, they enclose the nodes in a box or curved box. You
can think of them as variants of \Lcs{ncline} and \Lcs{ncarc}. In both cases, the
half the width of the box is
  \LKeyword{boxsize=dim}
You have to set this yourself to the right size, so that the nodes fit inside
the box. The \Lkeyword{boxsize} parameter actually sets the \Lkeyword{boxheight} and
\Lkeyword{boxdepth} parameters. The ends of the boxes extend beyond the nodes by
\Lkeyword{nodesepA} and \Lkeyword{nodesepB}.


\begin{BDef}
\LcsStar{ncbox}\OptArgs\Largb{nodeA}\Largb{nodeB}
\end{BDef}

  \Lcs{ncbox} encloses the nodes in a box with straight sides. For example:

\begin{LTXexample}[width=5cm]
\begin{pspicture}[shift=*](4,2.5)
  \rput[bl](.5,0){\rnode{A}{Idea 1}}
  \rput[tr](3.5,2){\rnode{B}{Idea 2}}
  \ncbox[nodesep=.5cm,boxsize=.6,linearc=.2,
    linestyle=dashed]{A}{B}
\end{pspicture}
\end{LTXexample}

\begin{BDef}
\LcsStar{ncarcbox}\OptArgs\Largb{nodeA}\Largb{nodeB}
\end{BDef}

  \Lcs{ncarcbox} encloses the nodes in a curved box that is \Lkeyword{arcangleA} away
from the line connecting the two nodes.

\begin{LTXexample}[width=5cm]
\begin{pspicture}[shift=*](4,2.5)
  \rput[bl](.5,0){\rnode{A}{1}}
  \rput[tr](3.5,2){\rnode{B}{2}}
  \ncarcbox[nodesep=.2cm,boxsize=.4,linearc=.4,
    arcangle=50]{<->}{A}{B}
\end{pspicture}
\end{LTXexample}

The arc is drawn counterclockwise from node A to node B.


There is one other node connection parameter that applies to all the node
connections, except \Lcs{ncarcbox}:
  \LKeyword{offset=dim}
(You can also set \Lkeyword{offsetA} and \Lkeyword{offsetB} independently.) This shifts the
point where the connection joins up by <dim> (given the convention that
connections go from left to right).

There are two main uses for this parameter. First, it lets you make two
parallel lines with \Lcs{ncline}, as in the following example:

\begin{LTXexample}[width=5cm]
\begin{pspicture}[shift=*](3.5,2.5)
  \cnodeput(0,0){A}{X}
  \cnodeput(3,2){B}{Y}
  \psset{nodesep=3pt,offset=4pt,arrows=->}
  \ncline{A}{B}
  \ncline{B}{A}
\end{pspicture}
\end{LTXexample}

Second, it lets you join a node connection to a rectangular node at a right
angle, without limiting yourself to positions that lie directly above, below,
or to either side of the center of the node. This is useful, for example, if
you are making several connections to the same node, as in the following
example:

\begin{LTXexample}
  \rnode{A}{Word1} and \rnode{B}{Word2} and \rnode{C}{Word3}
  \ncbar[offsetB=4pt,angleA=-90,nodesep=3pt]{->}{A}{B}
  \ncbar[offsetA=4pt,angleA=-90,nodesep=3pt]{->}{B}{C}
\end{LTXexample}

Sometimes you might be aligning several nodes, such as in a tree, and you want
to ends or the arms of the node connections to line up. This won't happen
naturally if the nodes are of different size, as you can see in this example:

\begin{LTXexample}[width=5cm]
\begin{pspicture}[shift=*](3.5,3)
  \psset{unit=.9}
  \Huge
  \cnode(1,3){4pt}{a}
  \rput[B](0,0){\Rnode{b}{H}}
  \rput[B](2,0){\Rnode{c}{a}}
  \psset{angleA=90,armA=1,nodesepA=3pt}
  \ncdiagg{b}{a}
  \ncdiagg{c}{a}
\end{pspicture}
\end{LTXexample}

%%??? FIXME
If you set the \Lkeyword{nodesep} or \Lkeyword{arm} parameter to a negative value, PSTricks
will measure the distance to the beginning of the node connection or to the
end of the arm relative to the center of the node, rather than relative to the
boundary of the node or the beginning of the arm. Here is how we fix the
previous example:

\begin{LTXexample}[width=5cm]
\begin{pspicture}[shift=*](3.5,3)
  \psset{unit=.9}
  \Huge
  \cnode(1,3){4pt}{a}
  \rput[B](0,0){\Rnode{b}{H}}
  \rput[B](2,0){\Rnode{c}{a}}
  \psset{angleA=90,armA=1,YnodesepA=12pt}
  \ncdiagg{b}{a}
  \ncdiagg{c}{a}
\end{pspicture}
\end{LTXexample}

Note also the use of \Lcs{Rnode}.

One more parameter trick: By using the \Lkeyword{border} parameter, you can create
the impression that one node connection passes over another.

The node connection commands make interesting drawing tools as well, as an
alternative to \Lcs{psline} for connecting two points. There are variants of
the node connection commands for this purpose. Each begins with \verb|pc| (for
``point connection'') rather than \verb|nc|. E.g.,
  \verb|\pcarc{<->}(3,4)(6,9)|
gives the same result as

\begin{lstlisting}
  \pnode(3,4){A}
  \pnode(6,9){B}
  \pcarc{<->}{A}{B}
\end{lstlisting}

Only \Lcs{nccircle} does not have a \nxLcs{pc} variant:




\begin{center}
\addtolength{\tabcolsep}{8pt}
\def\c#1{\Largb{node#1}}
\begin{tabular}{ll}\bottomrule
  \emph{Command} & \emph{Corresponds to:}\\\midrule

  \Lcs{pcline}\OptArg*{\Largb{arrows}}\c1\c2    & \Lcs{ncline}\\

  \Lcs{pccurve}\OptArg*{\Largb{arrows}}\c1\c2    & \Lcs{nccurve}\\

  \Lcs{pcarc}\OptArg*{\Largb{arrows}}\c1\c2    & \Lcs{ncarc}\\

  \Lcs{pcbar}\OptArg*{\Largb{arrows}}\c1\c2    & \Lcs{ncbar}\\

  \Lcs{pcdiag}\OptArg*{\Largb{arrows}}\c1\c2    & \Lcs{ncdiag}\\

  \Lcs{pcdiagg}\OptArg*{\Largb{arrows}}\c1\c2    & \Lcs{ncdiagg}\\

  \Lcs{pcangle}\OptArg*{\Largb{arrows}}\c1\c2    & \Lcs{ncangle}\\

  \Lcs{pcangles}\OptArg*{\Largb{arrows}}\c1\c2    & \Lcs{ncangles}\\

  \Lcs{pcloop}\OptArg*{\Largb{arrows}}\c1\c2    & \Lcs{ncloop}\\

  \Lcs{pcbox}\c1\c2    & \Lcs{ncbox}\\

  \Lcs{pcarcbox}\c1\c2
    & \Lcs{ncarcbox}
\end{tabular}
\end{center}




\section{Node connections labels: I}\label{S-nodelabels}

Now we come to the commands for attaching labels to the node connections. The
label command must come right after the node connection to which the label is
to be attached. You can attach more than one label to a node connection, and a
label can include more nodes.

The node label commands must end up on the same \TeX{} page as the node
connection to which the label corresponds.

There are two groups of connection labels, which differ in how they select the
point on the node connection. In this section we describe the first group:

\begin{BDef}
  \LcsStar{ncput}\OptArgs\Largb{stuff}\\
  \LcsStar{naput}\OptArgs\Largb{stuff}\\
  \LcsStar{nbput}\OptArgs\Largb{stuff}
\end{BDef}


These three command differ in where the labels end up with respect to the line:

\begin{tabular}{@{}ll}
  \Lcs{ncput} & \emph{on} the line\\
  \Lcs{naput} & \emph{above} the line\\
  \Lcs{nbput} & \emph{below} the line
\end{tabular}

(using the convention that node connections go from left to right).

Here is an example:

\begin{LTXexample}[width=5cm]
\begin{pspicture}(3.5,1.5)
  \cnode(0,0){.5cm}{root}
  \cnode*(3,1.5){4pt}{A}
  \cnode*(3,0){4pt}{B}
  \cnode*(3,-1.5){4pt}{C}
  \psset{nodesep=3pt}
  \ncline{root}{A}
  \naput{above}
  \ncline{root}{B}
  \ncput*{on}
  \ncline{root}{C}
  \nbput{below}
\end{pspicture}
\end{LTXexample}

\Lcs{naput} and \Lcs{nbput} use the same algorithm as \Lcs{uput} for displacing
the labels, and the distance beteen the line and labels is \Lkeyword{labelsep} (at
least if the lines are straight).

\Lcs{ncput} uses the same system as \Lcs{rput} for setting the reference
point. You change the reference point by setting the
  \LKeyword{ref=ref}
parameter.

Rotation is also controlled by a graphics parameter:
  \LKeyword{nrot=rot}
<rot> can be in any of the forms suitable for \Lcs{rput}, and you can also use
the form
\verb|{:<angle>}|

The angle is then measured with respect to the node connection. E.g., if the
angle is \verb|{:U}|, then the label runs parallel to the node connection. Since
the label can include other put commands, you really have a lot of control
over the label position.

The next example illustrates the use \verb|{:<angle>}|, the \Lkeyword{offset} parameter,
and \Lcs{pcline}:

\begin{LTXexample}[width=5cm]
\begin{pspicture}(4,2.3)
  \pspolygon(0,0)(4,2)(4,0)
  \pcline[offset=12pt]{|-|}(0,0)(4,2)
  \ncput*[nrot=:U]{Length}
\end{pspicture}
\end{LTXexample}

Here is a repeat of an earlier example, now using \verb|{:<angle>}|:

\begin{LTXexample}[width=5cm]
\begin{pspicture}(3.5,1.5)
  \cnode(0,0){.5cm}{root}
  \cnode*(3,1.5){4pt}{A}
  \cnode*(3,0){4pt}{B}
  \cnode*(3,-1.5){4pt}{C}
  \psset{nodesep=3pt,nrot=:U}
  \ncline{root}{A}
  \naput{above}
  \ncline{root}{B}
  \ncput*{on}
  \ncline{root}{C}
  \nbput{below}
\end{pspicture}
\end{LTXexample}

The position on the node connection is set by the
  \LKeyword{npos=num}
parameter, roughly according to the following scheme: Each node connection has
potentially one or more segments, including the arms and connecting lines.
A number \Lkeyword{npos} between 0 and 1 picks a point on the first segment from node
\verb|A| to \verb|B| (fraction \Lkeyword{npos} from the beginning to the end of the segment),
a number between 1 and 2 picks a number on the second segment, and so on.

Each node connection has its own default value of \Lkeyword{npos}. If you leave the
\Lkeyword{npos} parameter value empty (e.g., \verb|[npos=]|), then the default is
substituted. This is the default mode.

Here are the details for each node connection:
\begin{center}
%  \catcode`\@=11\setbox\@tempboxa=\hbox{1.5}%
%  \edef\t#1{\noexpand\hbox to \the\wd\@tempboxa{\noexpand\tt\noexpand\hss#1}}
  \begin{tabular}{lccc}
    \emph{Connection} & \emph{Segments} & \emph{Range} & \emph{Default}\\[2pt]
    \Lcs{ncline}         & 1               & $0\leq pos\leq 1$ & 0.5\\
    \Lcs{nccurve}        & 1               & $0\leq pos\leq 1$ & 0.5\\
    \Lcs{ncarc}          & 1               & $0\leq pos\leq 1$ & 0.5\\
    \Lcs{ncbar}          & 3               & $0\leq pos\leq 3$ & 1.5\\
    \Lcs{ncdiag}         & 3               & $0\leq pos\leq 3$ & 1.5\\
    \Lcs{ncdiagg}        & 2               & $0\leq pos\leq 2$ & 0.5\\
    \Lcs{ncangle}        & 3               & $0\leq pos\leq 3$ & 1.5\\
    \Lcs{ncangles}       & 4               & $0\leq pos\leq 4$ &1.5\\
    \Lcs{ncloop}         & 5               & $0\leq pos\leq 5$ & 2.5\\
    \Lcs{nccircle}       & 1               & $0\leq pos\leq 1$ & 0.5\\
    \Lcs{ncbox}          & 4               & $0\leq pos\leq 4$ & 0.5\\
    \Lcs{ncarcbox}       & 4               & $0\leq pos\leq 4$ & 0.5
  \end{tabular}
\end{center}




Here is an example:

\begin{LTXexample}[width=5cm]
\begin{pspicture}(4,3)
\rput[tl](0,3){\rnode{A}{\psframebox{Node A}}}
\rput[br](3.5,0){\ovalnode{B}{Node B}}
\ncangles[angleA=-90,arm=.4cm,linearc=.15]{A}{B}
\ncput*{d}
\nbput[nrot=:D,npos=2.5]{par}
\end{pspicture}
\end{LTXexample}

With \Lcs{ncbox} and \Lcs{ncarcbox}\, the segments run counterclockwise, starting
with the lower side of the box. Hence, with \Lcs{nbput} the label ends up
outside the box, and with \Lcs{naput} the label ends up inside the box.

\begin{LTXexample}[width=5cm]
\begin{pspicture}[shift=*](4,2.5)
  \rput[bl](.5,0){\rnode{A}{1}}
  \rput[tr](3.5,2){\rnode{B}{2}}
  \ncarcbox[nodesep=.2cm,boxsize=.4,linearc=.4,
    arcangle=50,linestyle=dashed]{<->}{A}{B}
  \nbput[nrot=:U]{set}
  \nbput[npos=2]{II}
\end{pspicture}
\end{LTXexample}

If you set the parameter
  \LKeyword{shortput=none/nab/tablr/tab}
to \Lkeyval{nab}, then immediately following a node connection or another node
connection label you can use \verb|^| instead of \Lcs{naput} and \verb|_| instead of
\Lcs{nbput}.

\begin{LTXexample}[width=5cm]
\begin{pspicture}[shift=*](3.5,1.5)
  \cnode(0,0){.5cm}{root}
  \cnode*(3,1.5){4pt}{A}
  \cnode*(3,-1.5){4pt}{C}
  \psset{nodesep=3pt,shortput=nab}
  \ncline{root}{A}^{$x$}
  \ncline{root}{C}_{$y$}
\end{pspicture}
\end{LTXexample}

You can still have parameter changes with the short \verb|^| and \verb|_| forms. Another
example is given on page~\pageref{nab-example}.

If you have set \Lkeyset{shortput=nab}, and then you want to use a true \verb|^| or \verb|_|
character right after a node connection, you must precede the \verb|^| or \verb|_| by
\verb|{}| so that PSTricks does not convert it to \Lcs{naput} or \Lcs{nbput}.

You can change the characters that you use for the short form with the

\begin{BDef}
\Lcs{MakeShortNab}\Largb{<char1>}\Largb{<char2>}
\end{BDef}

command.\footnote{%
You can also use \Lcs{MakeShortNab} if you want to use \texttt{\textasciicircum} and \texttt{\_} with
non-standard category codes. Just invoke the command after you have made your
\Lcs{catcode} changes.}

The \Lkeyset{shortput=tablr} and \Lkeyset{shortput=tab} options are described on 
pages~\pageref{tablr} and \pageref{tab}, respectively.

\section{Node connection labels: II}

Now the second group of node connections:
\begin{BDef}
\LcsStar{tvput}\OptArgs\Largb{stuff}\\
\LcsStar{tlput}\OptArgs\Largb{stuff}\\
\LcsStar{trput}\OptArgs\Largb{stuff}\\
\LcsStar{thput}\OptArgs\Largb{stuff}\\
\LcsStar{taput}\OptArgs\Largb{stuff}\\
\LcsStar{tbput}\OptArgs\Largb{stuff}
\end{BDef}

The difference between these commands and the \verb|\n*put| commands is that these
find the position as an intermediate point between the centers of the nodes,
either in the horizontal or vertical direction. These are good for trees and
mathematical diagrams, where it can sometimes be nice to have the labels be
horizontally or vertically aligned. The \verb|t| stands for ``tree''.

You specify the position by setting the
  \LKeyword{tpos=num}
parameter.

\Lcs{tvput}, \Lcs{tlput} and \Lcs{trput} find the position that lies fraction
<tpos> in the \emph{vertical} direction from the upper node to the lower
node. \Lcs{thput}, \Lcs{taput} and \Lcs{tbput} find the position that lies fraction
<tpos> in the \emph{horizontal} direction from the left node to the right
node.
Then the commands put the label on or next to the line, as follows:
\begin{center}
\begin{tabular}{lll}\toprule
  \emph{Command} & \emph{Direction} & \emph{Placement}\\\midrule
  \Lcs{tvput}       & vertical         & middle\\
  \Lcs{tlput}       & vertical         & left\\
  \Lcs{trput}       & vertical         & right\\
  \Lcs{thput}       & horizontal       & middle\\
  \Lcs{taput}       & horizontal       & above\\
  \Lcs{tbput}       & horizontal       & below\\\bottomrule
\end{tabular}
\end{center}

Here is an example:
\begin{LTXexample}[pos=t]
  \[
    \setlength{\arraycolsep}{1.1cm}
    \begin{array}{cc}
      \Rnode{a}{(X-A)} & \Rnode{b}{A} \\[1.5cm]
      \Rnode{c}{x} & \Rnode{d}{\tilde{X}}
    \end{array}
    \psset{nodesep=5pt,arrows=->} \everypsbox{\scriptstyle}
    \ncline{a}{c}\tlput{r} \ncline{a}{b}\taput{u}
    \ncline[linestyle=dashed]{c}{d}\tbput{b}
    \ncline{b}{d}\trput{s}
   \everypsbox{}
   \begin{array}{cc}
     \rnode{a}{(X-A)} & \rnode{b}{a} \\[1.5cm]
     \rnode{c}{x} & \rnode{d}{\tilde{X}}
    \end{array}
    \psset{nodesep=5pt,arrows=->}\everypsbox{\scriptstyle}
    \ncline{a}{c}\nbput{r} \ncline{a}{b}\naput{u}
    \ncline[linestyle=dashed]{c}{d}\nbput{b}
    \ncline{b}{d}\naput{s}
  \]
\end{LTXexample}

On the left is the diagram with \Lcs{tlput}, \Lcs{trput}, \Lcs{tbput} and \Lcs{Rnode},
as shown in the code. On the right is the same diagram, but with \Lcs{naput},
\Lcs{nbput} and \Lcs{rnode}.

These do not have a rotation argument or parameter. However, you can rotate
\Larg{<stuff>} in 90 degree increments using box rotations (e.g., \Lcs{rotateleft}).

If you set \Lkeyset{shortput=tablr}, then you can use the following single-character
abbreviations for the \verb|t| put commands:\label{tablr}
\begin{center}
  \begin{tabular}{rl}\toprule
    \emph{Char.}         & \emph{Short for:}\\\midrule
\rule{0pt}{4ex}
    \verb|^|                  & \Lcs{taput} \\
    \verb|_|                  & \Lcs{tbput} \\
    \verb|<|                  & \Lcs{tlput} \\
    \verb|>|                  & \Lcs{trput}\\\bottomrule
  \end{tabular}
\end{center}


You can change the character abbreviations with

\begin{BDef}
\Lcs{MakeShortTablr}\Largb{<char1>}\Largb{<char2>}\Largb{<char3>}\Largb{<char4>}
\end{BDef}

The \verb|t| put commands, including an example of \Lkeyset{shortput=tablr}, will be
shown further when we get to mathematical diagrams and trees.

The\XInfoDanger{~} node macros use \Lcs{pstVerb} and \Lcs{pstverbscale}.

\section{Attaching labels to nodes}

The command

\begin{BDef}
\LcsStar{nput}\OptArgs\Largb{refangle}\Largb{name}\Larg{stuff}
\end{BDef}


affixes \Largb{<stuff>} to node \Largb{<name>}. It is positioned distance \Lkeyword{labelsep} from
the node, in the direction \Largb{<refangle>} from the center of the node. The
algorithm is the same as for \Lcs{uput}. If you want to rotate the node, set the
  \LKeyword{rot=rot}
parameter, where \Larg{<rot>} is a rotation that would be valid for \Lcs{rput}.%
\footnote{Not to be confused with the \Lkeyword{nput} parameter.}
The position of the label also takes into account the \Lkeyword{offsetA}
parameter. If \Lkeyword{labelsep} is negative, then the distance is from the center
of the node rather than from the boundary, as with \Lkeyword{nodesep}.

Here is how I used \Lcs{nput} to mark an angle in a previous example:

\begin{LTXexample}[width=4cm]
\begin{pspicture}(4,3)
\rput[br](4,0){\ovalnode{B}{Node B}}
\rput[tl](0,3){\rnode{A}{\psframebox{Node A}}}
\nput[labelsep=0]{-70}{A}{%
  \psarcn(0,0){.4cm}{0}{-70}
  \uput{.4cm}[-35](0,0){\texttt{angleA}}}
\ncangle[angleA=-70,angleB=90,armB=1cm,linewidth=1.2pt]{A}{B}
\ncput[nrot=:U,npos=1]{\psframe[dimen=middle](0,0)(.35,.35)}
\end{pspicture}
\end{LTXexample}

\section{Mathematical diagrams and graphs}\label{S-psmatrix}




For some applications, such as mathematical diagrams and graphs, it is useful
to arrange nodes on a grid. You can do this with alignment environments, such
as \TeX's  \Lcs{halign} primitive, \LaTeX's \Lenv{tabular} environment, and \AmS-\TeX's
\Lcs{matrix}, but PSTricks contains its own alignment environment that is
especially adapted for this purpose:

\begin{BDef}
\Lcs{psmatrix}\OptArgs \ldots \Lcs{endpsmatrix}
\end{BDef}

Here is an example
\begin{LTXexample}[width=5cm]
  $
  \psmatrix[colsep=1cm,rowsep=1cm]
      & A \\
    B & E & C \\
      & D &
  \endpsmatrix
  $
\end{LTXexample}

As an alignment environment, \Lcs{psmatrix} is similar to \AmS-\TeX's
\Lcs{matrix}. There is no argument for specifying the columns. Instead, you can
just use as many columns as you need. The entries are horizontally centered.
Rows are ended by \verb|\\|. \Lcs{psmatrix} can be used in or out of math mode.

Our first example wasn't very interesting, because we didn't make use of the
nodes. Actually, each entry is a node. The name of the node in row <row> and
column \Largb{<col>} is \verb|{<row>,<col>}|, with no spaces. Let's see some node
connections:

\begin{LTXexample}[width=5cm]
  $
  \psmatrix[colsep=1cm]
      & X \\
    Y & Z
  \endpsmatrix
  \everypsbox{\scriptstyle}%
  \psset{nodesep=3pt,arrows=->}
  \ncline{1,2}{2,1}
  \tlput{f}
  \ncline{1,2}{2,2}
  \trput{g}
  \ncline[linestyle=dotted]{2,1}{2,2}
  \tbput{h}
  $
\end{LTXexample}

You can include the node connections inside the \Lcs{psmatrix}, in the last entry
and right before \Lcs{endpsmatrix}. One advantage to doing this is that
\Lkeyset{shortput=tab} is the default within a \Lcs{psmatrix}.

\begin{LTXexample}
$ \begin{psmatrix}
  U \\
 &  X\times_Z Y & X \\
 &      Y       & Z
 \psset{arrows=->,nodesep=3pt}
 \everypsbox{\scriptstyle}
 \ncline{1,1}{2,2}_{y}
 \ncline[doubleline=true,linestyle=dashed]{-}{1,1}{2,3}^{x}
 \ncline{2,2}{3,2}<{q}
 \ncline{2,2}{2,3}_{p}
 \ncline{2,3}{3,3}>{f}
 \ncline{3,2}{3,3}_{g}
 \end{psmatrix} $
\end{LTXexample}

You can change the kind of nodes that are made by setting the
  \LKeyword{mnode=type}
parameter. Valid types are \Lkeyval{R}, 
\Lkeyval{r}, 
\Lkeyval{C}, 
\Lkeyval{f}, \Lkeyval{p}, \Lkeyval{circle}, \Lkeyval{oval}, \Lkeyval{dia},
\Lkeyval{tri}, \Lkeyval{dot} and \Lkeyval{none}, 
standing for \Lcs{Rnode}, \Lcs{rnode}, \Lcs{Cnode}, \Lcs{fnode},
\Lcs{pnode}, \Lcs{circlenode}, \Lcs{ovalnode}, \Lcs{dotnode} and no node,
respectively. Note that for circles, you use \Lkeyset{mnode=C} and set the radius
with the \Lkeyword{radius} parameter.

For example:\label{nab-example}
\begin{LTXexample}
  \psmatrix[mnode=circle,colsep=1]
      & A \\
    B & E & C \\
      & D &
  \endpsmatrix
  \psset{shortput=nab,arrows=->,labelsep=3pt}
  \small
  \ncline{2,2}{2,3}^[npos=.75]{a}
  \ncline{2,2}{2,1}^{b}
  \ncline{3,2}{2,1}^{c}
  \ncarc[arcangle=-40,border=3pt]{3,2}{1,2}%
    _[npos=.3]{d}^[npos=.7]{e}
  \ncarc[arcangle=12]{1,2}{2,1}^{f}
  \ncarc[arcangle=12]{2,1}{1,2}^{g}
\end{LTXexample}

Note that a node is made only for the non-empty entries. You can also specify
a node for the empty entries by setting the
  \LKeyword{emnode=type}
parameter.



You can change parameters for a single entry by starting this entry with the
parameter changes, enclosed in square brackets. Note that the changes affect
the way the node is made, but not contents of the entry (use \Lcs{psset} for
this purpose). For example:
\begin{LTXexample}
$ \psmatrix[colsep=1cm]
      & [mnode=circle] X \\
    Y & Z
  \endpsmatrix
  \psset{nodesep=3pt,arrows=->}
  \ncline{1,2}{2,1}
  \ncline{1,2}{2,2}
  \ncline[linestyle=dotted]{2,1}{2,2} $
\end{LTXexample}

If you want your entry to begin with a \verb|[| that is not meant to indicate
parameter changes, the precede it by \verb|{}|.

You can assign your own name to a node by setting the
  \LKeyword{name=<name>}
parameter at the beginning of the entry, as described above. You can still
refer to the node by \verb|{<row>,<col>}|, but here are a few reasons for giving
your own name to a node:
\begin{itemize}
  \item The name may be easier to keep track of;
  \item Unlike the  \verb|{<row>,<col>}|  names, the names you give remain valid
  even when you add extra rows or columns to your matrix.
  \item The names remain valid even when you start a new \Lcs{psmatrix} that
  reuses the \verb|{<row>,<col>}| names.
\end{itemize}


Here a few more things you should know:
\begin{itemize}
 \item The baselines of the nodes pass through the centers of the
 nodes. \Lcs{psmatrix} achieves this by setting the
  \LKeyword{nodealign=true/false}
parameter to \verb|true|. You can also set this parameter outside of \Lcs{psmatrix}
when you want this kind of alignment.

 \item You can left or right-justify the nodes by setting the
  \LKeyword{mcol=l/r/c}
parameter. \verb|l|, \verb|r| and \verb|c| stand for \verb|left|, \verb|right| and \verb|center|,
respectively.

 \item The space between rows and columns is set by the
  \LKeyword{rowsep=dim} and 
  \LKeyword{colsep=dim}
parameters.

 \item If you want all the nodes to have a fixed width, set
  \LKeyword{mnodesize=dim}
to a positive value.

 \item If \Lcs{psmatrix} is used in math mode, all the entries are set in math
 mode, but you can switch a single entry out of math mode by starting and
 ending the entry with \verb|$|. %$

 \item The radius of the \verb|c| \Lkeyword{mnode} (corresponding to \Lcs{cnode}) is set by
the \Lkeyword{radius} parameter.

 \item Like in \LaTeX, you can end a row with \verb|\\[<dim>]| to insert an extra
 space <dim> between rows.

 \item The command \Lcs{psrowhookii} is executed, if defined, at the beginning of
 every entry in row \verb|ii| (row 2), and the command \Lcs{pscolhookv} is executed at
 athe beginning of every entry in column \verb|v| (etc.). You can use these hooks,
 for example, to change the spacing between two columns, or to use a special
 \Lkeyword{mnode} for all the entries in a particular row.

 \item An entry can itself be a node. You might do this if you want an entry
 to have two shapes.

 \item If you want an entry to stretch across several (\Largb{<int>}) columns, use the

\begin{BDef}
\Lcs{psspan}\Largb{int}
\end{BDef}

 \emph{at the end of the entry}. This is like Plain \TeX's \Lcs{multispan}, or
 \LaTeX's \Lcs{multicolumn}, but the template for the current column (the first
  column that is spanned) is still used. If you want wipe out the template as
  well, use \Lcs{multispan}\Largb{<int>} \emph{at the beginning of the entry} instead.
  If you just want to wipe out the template, use \Lcs{omit} before the entry.

  \item \Lcs{psmatrix} can be nested, but then all node connections and other
  references to the nodes in the \verb|{<row>,<col>}| form for the nested matrix
  \emph{must go inside} the \Lcs{psmatrix}. This is how  PSTricks decides which
  matrix you are referring to. It is still neatest to put all the node
  connections towards the end; just be sure to put them before \Lcs{endpsmatrix}.
  Be careful also not to refer to a node until it actually appears. The whole
  matrix can itself go inside a node, and node connections can be made as
  usual. This is not the same as connecting nodes from two different
  \Lcs{psmatrix}'s. To do this, you must give the nodes names and refer to them
  by these names.

\end{itemize}

\section{Obsolete put commands}

This is old documentation, but these commands will continue to be supported.

There is also an obsolete command \Lcs{Lput} for putting labels
next to node connections. The syntax is

\begin{BDef}
  \Lcs{Lput}\Largb{<labelsep>}\Largs{<refpoint>}\Largb{<rotation>}\Largr(<pos>)\Largb{<stuff>}
\end{BDef}

It is a combination of \Lcs{Rput} and \Lcs{lput}, equivalent to

\begin{BDef}
  \Lcs{lput}\Largr{<pos>}\Largb{\Lcs{Rput}\Largb{<labelsep>}\Largs{<refpoint>}\Largb{<rotation>}\Largr{0,0}\Largb{<stuff>}}
\end{BDef}

\Lcs{Mput} is a short version of \Lcs{Lput} with no
\verb|{<rotation>}| or \verb|(<pos>)| argument. \Lcs{Lput} and \Lcs{Mput} remain part of
PSTricks only for backwards compatibility.

Here are the node label commands:

\begin{BDef}
\LcsStar{lput}\OptArgs\Largs{refpoint}\Largb{rotation}\Largr{pos}\Largb{stuff}
\end{BDef}

The \verb|l| stands for ``label''. Here is an example illustrating the use of the
optional star and \verb|:<angle>| with \Lcs{lput}, as well as the use of the
\Lkeyword{offset} parameter with \Lcs{pcline}:

\begin{LTXexample}[width=5cm]
\begin{pspicture}(4,2.3)
  \pspolygon(0,0)(4,2)(4,0)
  \pcline[offset=12pt]{|-|}(0,0)(4,2)
  \lput*{:U}{Length}
\end{pspicture}
\end{LTXexample}

(Remember that with the \nxLcs{?put} commands, you can omit the coordinate if you
include the angle of rotation. You are likely to use this feature with the
node label commands.)

With \Lcs{lput} and \Lcs{rput}, you have a lot of control over the position of the
label. E.\,g.,

\begin{LTXexample}[width=5cm]
\begin{pspicture}(4,2)
  \pcline(0,0)(4,2)
  \lput{:U}{\rput[r]{N}(0,.4){label}}
\end{pspicture}
\end{LTXexample}



puts the label upright on the page, with right side located .4 centimeters
``above'' the position 0.5 of the node connection (above if the node
connection points to the right). However, the \Lcs{aput} and \Lcs{bput} commands
described below handle the most common cases without \Lcs{rput}.\footnote{%
There is also an obsolete command \Lcs{Lput} for putting labels
next to node connections. The syntax is

\begin{BDef}
  \LcsStar{Lput}\Largb{<labelsep>}\Largs{<refpoint>}\Largb{<rotation>}\Largr{<pos>}\Largb{<stuff>}
\end{BDef}

It is a combination of \Lcs{Rput} and \Lcs{lput}, equivalent to

\begin{BDef}
  \LcsStar{lput}\Largr{<pos>}\Largb{\Lcs{Rput}\Largb{<labelsep>}\Largs{<refpoint>}\Largb{<rotation>}\Largr{0,0}\Largb{<stuff>}}
\end{BDef}

\Lcs{Mput} is a short version of \Lcs{Lput} with no
\texttt{\{<rotation>\}} or \texttt{(<pos>)} argument. \Lcs{Lput} and \Lcs{Mput} remain part of
PSTricks only for backwards compatibility.}

\begin{BDef}
\LcsStar{aput}\Largs{labelsep}\Largb{angle}\Largr{pos}\Largb{stuff}
\end{BDef}

  \Largb{<stuff>} is positioned distance \Lcs{pslabelsep} \emph{above} the node
connection, given the convention that node connections point to the right.
\Lcs{aput} is a node-connection variant of \Lcs{uput}. For example:

\begin{LTXexample}[width=5cm]
\begin{pspicture}(4,2)
  \pspolygon(0,0)(4,2)(4,0)
  \pcline[linestyle=none](0,0)(4,2)
  \aput{:U}{Hypotenuse}
\end{pspicture}
\end{LTXexample}

\begin{BDef}
\LcsStar{bput}\Largs{labelsep}\Largb{angle}\Largr{pos}\Largb{stuff}
\end{BDef}

  This is like \Lcs{aput}, but \Largb{<stuff>} is positioned \emph{below} the node
connection.


  It is fairly common to want to use the default position and rotation with
these node connections, but you have to include at least one of these
arguments. Therefore, PSTricks contains some variants:

\begin{BDef}
\Lcs{mput}\Largs{refpoint}\Largb{stuff}\\
\Lcs{Aput}\Largs{labelsep}\Largb{stuff}\\
\Lcs{Bput}\Largs{labelsep}\Largb{stuff}
\end{BDef}

of \Lcs{lput}, \Lcs{aput} and \Lcs{bput}, respectively, that have no angle or
positioning argument. For example:

\begin{LTXexample}[width=5cm]
\begin{pspicture}(4,2)
  \cnode*(0,0){3pt}{A}
  \cnode*(4,2){3pt}{B}
  \ncline[nodesep=3pt]{A}{B}
  \mput*{1}
\end{pspicture}
\end{LTXexample}

Here is another:

\begin{LTXexample}[width=5cm]
\begin{pspicture}(4,2)
  \pcline{<->}(0,0)(4,2)
  \Aput{Label}
\end{pspicture}
\end{LTXexample}

\clearpage
\part{New commands}

\section{Nodes}


\section{Setting bounding box nodes with \nxLcs{psDefBoxNodes}}

\begin{BDef}
\Lcs{psDefBoxNodes}\Largb{node name}\Largb{text}\\
\end{BDef}

Setting nodes for a bounding box of a given text. There will be 12 nodes defined,
with the name that has the suffixes 
\texttt{:tl, :tC, :tr, 
:Cl, :C, :Cr,  
:Bl, :BC, :Br, 
:bl, :bc, :br}. The prefix is always the given node name. The node name shouldn't contain spaces or special
characters, like umlauts or an active \PS\ character, like \texttt{(}.

\lstset{style=code}
\begin{LTXexample}[pos=t,wide,vsep=10mm,preset=\centering,columns=fixed]
\psscalebox{15}{\psDefBoxNodes{Age}{\color{red!50}\sffamily \"Age}}%
\pspolygon[fillstyle=solid,
  fillcolor=blue!30,opacity=0.3](Age:tl)(Age:tr)(Age:br)(Age:bl)%
\psline[linestyle=dashed](Age:Bl)(Age:Br)%
\psdots(Age:tl)(Age:tC)(Age:tr)(Age:Cl)(Age:C)(Age:Cr)%
       (Age:Bl)(Age:BC)(Age:Br)(Age:bl)(Age:bC)(Age:br)%
\pcline[arrows=<->,linecolor=blue,arrowscale=1.25](Age:tC)(Age:Br)
\uput[180](Age:tl){tl}\uput[180](Age:Cl){Cl}\uput[180](Age:Bl){Bl}\uput[180](Age:bl){bl}
\uput[90](Age:tC){tC} \uput[0](Age:C){C}    \uput[0](Age:BC){BC}  \uput[-90](Age:bC){bC}
\uput[0](Age:tr){tr}  \uput[0](Age:Cr){Cr}  \uput[0](Age:Br){Br}  \uput[0](Age:br){br}
\end{LTXexample}




\clearpage

%--------------------------------------------------------------------------------------
\section{Relative nodes with \nxLcs{psGetNodeCenter} or \texttt{N-<name>.x|y}}
%--------------------------------------------------------------------------------------

\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. Nodes are saved in an own
dictionary with the current transformation matrix, which is reset when
using the macro \Lcs{psGetNodeCenter}.

\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}


The coordinates of the nodes can also be saved with \Lkeyset{saveNodeCoors=true} in global defined names
\texttt{N-<name>.x} and \texttt{N-<name>.y}. With the optional argument \Lkeyword{NodeCoorPrefix}, which is
by default empty, the name setting can be changed to \texttt{<NodeCoorPrefix><name>x} and \texttt{<NodeCoorPrefix><name>y}.

The forgoing examples can be simplified if you
do not need the resetting of the transformation matrix:



\begin{LTXexample}[width=5cm]
\begin{pspicture}[showgrid,arrowscale=2,
  saveNodeCoors](5,5)
\pnode(4.5,0.5){MyNode}
\psdot(MyNode)
\pnode(! N-MyNode.x 4 sub N-MyNode.y 4 add){MySecondNode}
\psdot(MySecondNode)
\ncline[linecolor=red]{<->}{MyNode}{MySecondNode}
\end{pspicture}
\end{LTXexample}


\bigskip
In the following example it doesn't work because the relative node setting via \Lcs{rput}
is not taken into account.

\begin{LTXexample}[width=5cm]
\begin{pspicture}[showgrid,saveNodeCoors](5,5)
\rput(1.5,0.5){\trinode{CN}{NodeA}}
\rput(3.5,2.5){\trinode{EN}{NodeB}}
\pnode(! N-CN.x 2 add N-CN.y 1 add ){MyCNode}
\ncline[linecolor=red]{<->}{MyCNode}{EN}
\ncline[linecolor=blue]{<->}{CN}{EN}
\end{pspicture}
\end{LTXexample}




%--------------------------------------------------------------------------------------
\section{Getting node edges with \nxLcs{psGetNodeEdgeA} and \nxLcs{psGetNodeEdgeB}}
%--------------------------------------------------------------------------------------

\begin{BDef}
\Lcs{psGetNodeEdgeA}\Largb{node name}\\
\Lcs{psGetNodeEdgeB}\Largb{node name}\\
\end{BDef}

When two nodes are connected the line often did not use the center of the defined
nodes. Values as \Lkeyword{nodesep} or \Lkeyword{offset} are also taken into account
as a surrounding border of a node. With these new macros one can get the edge coordinates
of two given nodes. The coordinates are saved on \PS side in the values \Larg{node.x}
and \Larg{node.y}.


\begin{LTXexample}[pos=t]
\Huge
\hspace*{4cm}\rnode{B}{Node B}

\vspace{2cm}
\rnode{A}{Node A}
\ncline{A}{B}
\pscircle*[linecolor=blue,opacity=0.4](!\psGetEdgeA{A}{B}){10pt}
\pscircle*[linecolor=blue,opacity=0.4](!\psGetEdgeB{A}{B}){10pt}
\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|<nodename>| once \verb|<expr>| 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 \texttt{P} as a node whose vector interpretation is of the same 
length as the original \texttt{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 \texttt{P} at \verb|(cos(1), sin(1))| and a node named \texttt{Ptang} 
 which represents a unit vector in the tangent direction to the curve at \texttt{P}. 
 The expression in \texttt{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{<nodename>}
\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 \texttt{P0 .. P99} at equally spaced \texttt{t} values along the curve, 
 and assigns the macro \Lcs{Pnodecount} to 99, the highest index. The expression in \texttt{t} 
 may be either algebraic or PostScript, and is handled automatically. The values 
 \verb|<tmin>, <tmax>| 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 \texttt{t} is algebraic, you must specify the keyword \texttt{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|<next command>| is followed.
\label{pnodes}
\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,algebraic](-.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{psncurve}\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}
\pscurve[linewidth=1pt]{->}(P3)(P4)(P5)(P6)(P7)(P8)
\end{verbatim}

\begin{LTXexample}[width=.35\textwidth]
\begin{pspicture}[showgrid=true,algebraic](-.5,-.5)(2.5,2)
\pnodes{P}(.1,.1)(1;10)(*2 {x^2/4})(0,1.4)
%defines P0..P3--now join them
\psncurve[arrowscale=2]{-D>}(0,3){P}
\end{pspicture} 
\end{LTXexample}
\vspace{2pc}

\begin{LTXexample}[width=.35\textwidth]
\begin{pspicture}[showgrid=true,algebraic](-.5,-.5)(2.5,2)
\pnodes{P}(.1,.1)(1;10)(*2 {x^2/4})(0,1.4)
%defines P0..P3--now join them
\psnccurve[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 \texttt{C} to 
 be the complex product of \texttt{A} and \texttt{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 \texttt{C}, and, in addition, draws the line segment \texttt{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 \texttt{x} here stands for expression. The idea is that one builds a 
line from \verb|<basept>+<nodexpr1>| to \verb|<basept>+<nodexpr2>|.

\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{<Name1>}{<Name2>}(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 \texttt{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|<Name1>|, and the first intersection point in the opposite direction (from A) 
is named \verb|<Name2>|. If one or other of these intersections is empty, the nodes are 
set to remote points on the line \texttt{AB}.  The effect of the line joining the constructed 
nodes depends on the location of \texttt{A} and \texttt{B} relative to \texttt{L}, with two cases worth noting.
\begin{itemize}
\item if \texttt{L} is closed and if \texttt{A, B} are interior to one of its components, the 
resulting line extends across that component of \texttt{L}, and contains \texttt{AB}.
\item If \texttt{L} is simple and closed, one of \texttt{A, B} is inside and the other outside, 
the resulting line segment will contain \texttt{A} but not \texttt{B}. 
\end{itemize}

\begin{verbatim}
\polyIntersections{<Name1>}{<Name2>}(A)(B){P}{n}
\end{verbatim}

has exactly the same effect as 

\begin{verbatim}
\polyIntersections{<Name1>}{<Name2>}(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\func{x+sin(2*x)}
\psplot[algebraic]{0}{3.14}{\func}
\fnpnodes[algebraic]{0}{3.14}{\func}{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{<NodeName>}\Largb{<nodeindex>}\Largb{<direction>}\Largb{<Notch>}
\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|<Notch>|. The arrowhead may then be 
drawn with a command like \Lcs{psline}\verb|{->}(N)(P3)|, assuming the tip was to be \texttt{P3} 
and the notch was \texttt{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 \texttt{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 \texttt{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}
