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+\catcode`\_=8 \catcode`\<=13
+\def\CurrentPackages{spqr,pstcol}
+\newcounter{myN}
+\setlongtables
+\author[Sebastian Rahtz]{Sebastian Rahtz\\Elsevier Science Ltd\\
+Email: \texttt{s.rahtz@elsevier.co.uk}}
+\title{An introduction to PSTricks, part 3}
+\begin{Article}
+%\section{Introduction}
+%%\begin{multicols}{2}
+\section{Tree diagrams}
+\PST\ has an extremely rich environment for drawing trees, which
+allows for very complex structures and presentation. The available
+commands are listed in Table~\ref{PSTtree} and the graphical
+parameters which apply especially to these are listed in
+Table~\ref{PSTtreeparms}. As one might expect, most other commands and
+parameters  are also available, from both the generalized drawing, and
+the node connectors and labels. Each of the node types described
+earlier is turned into a `tree' node, and named by prefixing it with a
+`T' and removing the `node' suffix.
+
+%\end{multicols}
+
+\begin{small}
+\begin{longtable}{lH{.5\textwidth}}
+\caption{\protect\PST\ tree drawing commands\label{PSTtree}}\\
+\hline
+\endfirsthead
+\multicolumn{2}{l}{\protect\PST\ tree drawing commands \emph{cont.}}\\
+\hline
+\endhead
+\PSTCom \pstree{node}{subtrees}
+& draws a node and subtrees connected to it\\
+\PSTCom \psTree{rootnode} subtrees
+%\endpsTree
+& an `environment' form of \Lcs{psTree}\\
+\PSTCom \Tn
+& null tree node \\
+\PSTCom \tspace{dim}
+& leave gap of \emph{dim} before next level\\
+\PSTComOpt \TC
+& tree node like \Lcs{Cnode} node\\
+\PSTComOpt \TR{something}
+& tree node like \Lcs{Rnode} node\\
+\PSTComOpt \Tcircle{something}
+& tree node like \Lcs{circlenode} node\\
+\PSTComOpt \Tc{dim}
+& tree node like \Lcs{cnode} node\\
+\PSTComOpt \Tdia{something}
+& tree node like \Lcs{dianode} node\\
+\PSTComOpt \Tdot
+& tree node like \Lcs{dotnode} node\\
+\PSTComOpt \Tf
+& tree node like \Lcs{fnode} node\\
+\PSTComOpt \Tfan
+& draws a triangle with a top corner of the predecessor node\\
+\PSTComOpt \Toval{something}
+& tree node like \Lcs{ovalnode} node\\
+\PSTComOpt \Tp
+& tree node like \Lcs{pnode} node\\
+\PSTComOpt \Tr{something}
+& tree node like \Lcs{rnode} node\\
+\PSTComOpt \Ttri{something}
+& tree node like \Lcs{trinode} node\\
+\PSTComOpt \skiplevel {nodes or subtrees}
+& miss out entire levels in a particular subtree\\
+\PSTComOpt \skiplevels{n} {nodes or subtrees}
+& skip \emph{n} levels\\
+\end{longtable}
+\end{small}
+
+\begin{small}
+\begin{longtable}{llH{10cm}}
+\caption{\protect\PST\ Graphical parameters for trees}
+\label{PSTtreeparms}\\[1mm]
+\emph{Parameter} & \emph{Default} & \emph{Explanation}\\
+\hline
+\endfirsthead
+\protect\PST\ Graphical parameters for trees \emph{cont.}\\[1mm]
+\emph{Parameter} & \emph{Default} & \emph{Explanation}\\
+\hline
+\endhead
+\mbox{}\\
+\endfoot
+\Par{bbd=dim} ()
+& set lower bounding box to \emph{dim}\\
+\Par{bbh=dim} ()
+& set upper bounding box to \emph{dim}\\
+\Par{bbl=dim} ()
+& set left bounding box to \emph{dim}\\
+\Par{bbr=dim} ()
+& set right bounding box to \emph{dim}\\
+\Par{edge=command} (\ncline)
+& the node connector used to join tree nodes\\
+\Par{fansize=dim}   (1cm)
+&size of base for \Lcs{Tfan} tree node\\
+\Par{levelsep=*dim} (2cm)
+& the distance between successive levels in a tree; the * makes the
+dimension be \emph{in addition} to the size of the nodes (levels are
+normally a fixed distance apart)\\
+\Par{showbbox=true/false} (false)
+& draw a dotted frame showing the enclosing rectangle of trees\\
+\Par{thislevelsep=*dim} ()
+& like \emph{levelsep} but applies only to the current tree\\
+\Par{thistreefit=tight/loose} ()
+& like \emph{treefit} but applies only to the current tree\\
+\Par{thistreenodesize=dim} ()
+& like \emph{treenodesize} but applies only to the current tree\\
+\Par{thistreesep=dim} ()
+& like \emph{treesep} but applies only to the current tree\\
+\Par{tndepth=dim} ()
+& the minimum depth of tree node labels\\
+\Par{tnheight=dim} ()
+& the minimum height of tree node labels\\
+\Par{tnpos=l/r/a/b} (b)
+& the position of tree node labels relative to the node (left, right,
+above, below) \\
+\Par{tnsep=dim} ()
+& the gap between tree node labels and the node (by default the same as
+\emph{labelsep} \\
+\Par{treefit=tight/loose} (tight)
+& if tight, \emph{treesep} is the minimum distance between nodes on any level; i
+f loose, \emph{treesep} is the distance between the enclosing
+bounding boxes of subtrees\\
+\Par{treeflip=true/false} (false)
+& does a mirror image of the free, flipping the nodes\\
+\Par{treemode=R/L/U/D} (D)
+& the direction of tree growth (right, left, up and down)\\
+\Par{treenodes=dim} ($-$1pt)
+& if positive, this sets a fixed size for tree nodes, regardless of content\\
+\Par{treesep=dim} (0.75cm)
+& the distance between successive nodes in a tree\\
+\Par{xbbd=dim} ()
+& increase lower bounding box by \emph{dim}\\
+\Par{xbbh=dim} ()
+& increase upper bounding box by \emph{dim}\\
+\Par{xbbl=dim} ()
+& increase left bounding box by \emph{dim}\\
+\Par{xbbr=dim} ()
+& increase right bounding box by \emph{dim}\\
+\end{longtable}
+\end{small}
+
+%\begin{multicols}{2}
+The fundamental concept in \PST\ trees is the \emph{nesting} of trees;
+a simple tree  consists of a root, and one or more nodes:
+\begin{example*}
+\pstree{\TC}{\TC\TC}
+\end{example*}
+\noindent but each node can itself be a tree:
+\begin{example*}
+\pstree{\TC}{\pstree{\TC}{\TC \TC}
+ \pstree{\TC}{\TC \TC}}
+\end{example*}
+This simple construct allows very complicated structures to be
+erected, as the examples below show.
+
+The following tree is a version of that shown in the \emph{\LaTeX\ Companion},
+section 10.5.2, which was drawn using the \Lpack{ecltree} package; the
+ease of notation is roughly similar. As often in \LaTeX, the
+readability depends a great deal on how the code is laid out.  The
+only change to the defaults is to lessen the vertical space between
+trees, and add some extra space around nodes.
+\begin{example*}
+\pstree[nodesep=2pt,
+  levelsep=20pt]{\TR{grandfather}}
+{
+ \pstree{\TR{uncle}}{\TR{cousin}}
+ \pstree{\TR{father}}
+   {
+   \pstree{\TR{brother}}{\TR{nephew}}
+   \pstree{\TR{Me}}
+     {
+      \pstree{\TR{son}}{\TR{grandson}}
+     }
+   }
+}
+\end{example*}
+
+If we now consider another tree drawing package described in
+the \emph{\LaTeX\ Companion}, Vanroose's \Lpack{trees}, the example in section
+10.2.3 is a little harder to reproduce. The skeleton is trivial:
+\begin{example*}
+\pstree{\Tdot}
+{
+\Tdot
+\pstree{\Tdot}
+ {
+ \pstree{\Tdot}
+  {
+   \Tdot
+   \Tdot
+   \Tdot
+  }
+  \Tdot
+ }
+}
+\end{example*}
+
+\noindent but when  we come to add in all the node and connector labels, and
+change a few parameters to make the result nicer, the markup becomes a
+little complex, though the quantity is roughly similar to that of Vanroose:
+
+\begin{example*}
+\psset{labelsep=2pt,tnpos=a,radius=2pt}
+\pstree[treemode=R]{\TC*~{25}}
+{
+\TC*~{5}~[tnpos=r]{$L_a$}
+\taput{$a$}
+\pstree{\TC*~{20}\tbput{$b$}}
+ {
+ \pstree{\TC*~{15}\taput{$a$}}
+  {
+   \TC*~{7}~[tnpos=r]{$L_{baa}$}\taput{$a$}
+   \TC*~{5}~[tnpos=r]{$L_{bab}$}\taput{$b$}
+   \TC*~{3}~[tnpos=r]{$L_{bac}$}\tbput{$c$}
+  }
+  \TC*~{5}~[tnpos=r]{$L_{bb}$}
+  \tbput{$b$}
+ }
+}
+\end{example*}
+
+The node connectors in a tree are created by running
+the macro \Lcs{psedge} with the two nodes; the definition of
+\Lcs{psedge} can be overridden explicitly by a redefinition, or by
+using the \emph{edge} parameter. Here we redefine \Lcs{psedge} to be a
+curve, arrange the angles (bearing in mind that the tree is to grow
+upwards), and obtain a pleasing result. Note also the explicit links
+between named nodes, as well as the regular connections.
+%\end{multicols}
+
+\noindent\hrule
+
+\begin{example*}
+\footnotesize
+\def\psedge{\nccurve}
+\newcommand{\Female}[2][]{\TR[#1]{\emph{#2}}}
+\newcommand{\Male}[2][]{\TR[#1]{#2}}
+\psset{nodesep=2pt,angleA=90,angleB=-90,unit=.6cm}
+\pstree[treemode=U]{\Female{{\bfseries Matilde}}}{
+ \pstree{\Male{Sebastian}}{
+  \pstree{\Male[name=P]{Philip}}{\Male{Frederick}\Female{Ethel}}
+  \pstree{\Female[name=W]{Mary}}{\Male{Lionel}\Female{Agnes}}}
+ \pstree{\Female{Leonor}}{
+  \pstree{\Male[name=R]{Ra\'ul}}{\Male{Joaquim}\Female{J\'ulia}}
+  \pstree{\Female[name=A]{Am\'elia}}{\Male{Melo}\Female{Augusta}}}
+}
+\psset{doubleline=true,linestyle=dotted}
+\ncline{P}{W}\nbput{1940}
+\ncline{R}{A}\nbput{1950}
+\end{example*}
+%\begin{multicols}{2}
+We said earlier that \PST\ does not always work out the extent of
+objects correctly, and this is illustrated by the connectors in the
+following example. Turning on \emph{showbbox}, we can see that without
+the use of \emph{xbbl} etc in the second incarnation, the bounding box
+is not correct:
+\begin{example*}
+\psset{angleB=-90,arrows=->,nrot=:U}
+\def\molesworth#1{%
+ \pstree[#1]{\Tdia{ }}
+ {
+  \Tp[arrows=->,edge={\ncbar[angleA=180]}]
+  \nbput{Gabbitas}
+  {\psset{linestyle=dashed,arrows=-} \Tp }
+  \Tp[arrows=->,edge={\ncbar}]
+  \naput{Thring}
+ }
+}
+\psset{showbbox=true}
+\begin{tabular}{l}
+\molesworth{}\\[10pt]
+\molesworth{xbbl=1cm,xbbr=1cm}
+\end{tabular}
+\end{example*}
+
+The technique  of redefining edges is also necessary if we want
+right-angled joins, rather than straight lines. Again, we need to take
+care of the \emph{angleA} and \emph{angleB}, and ensure that in this
+left-right tree the nodes all line up on their left edges, using the
+\emph{ref} parameter. If this is not done, the \Lcs{ncangle} edges
+produce strange results.
+\begin{example*}
+\def\Item#1{\Tr[ref=l]{%
+ \psframebox[linestyle=none]{#1}}}
+\def\psedge{\ncangle}
+\psset{xbbd=1.5cm,treemode=R,
+  angleB=-180,angleA=0,levelsep=72pt}
+\pstree{\Item{langs}}{%
+  \Item{german}
+  \pstree{\Item{greek}}{%
+    \Item{hamilton-kelly}
+    \pstree{\Item{levy}}{%
+      \Item{doc}
+      \Item{src}
+       }
+    }
+  \Item{italian}
+  \pstree{\Item{portuguese}}{
+    \Item{hyphenation}
+   }
+  \pstree{\Item{turkish}}{%
+    \Item{doc}
+    \Item{hyphen}
+    \Item{inputs}
+    \Item{mf}
+    \Item{misc}
+   }
+\Item{xettex}
+}
+\end{example*}
+
+This allows us to remake the small family again, but this time with
+nicer connectors:
+\begin{example*}
+\def\XX#1{%
+ \Tr{\psframebox{\rule{0pt}{9pt}#1}}%
+}
+\def\psedge{\ncangle}
+\psset{angleB=90,angleA=-90,
+   levelsep=36pt,armB=14pt}
+\pstree{\XX{grandmother}}
+{%
+\pstree{\XX{aunt}}{\XX{cousin}}
+\pstree{\XX{mother}}
+   {
+ \pstree{\XX{sister}}{\XX{niece}}
+ \pstree{\XX{Me}}
+    {
+    \pstree{\XX{daughter}}
+    {\XX{granddaughter}}
+  }
+ }
+}
+\end{example*}
+The node connectors are, of course, standard \PST\ objects, so they
+obey all the normal parameters; here we draw the lower part of the
+tree with dashed lines, and each node content is set in math mode.
+\begin{example*}
+\footnotesize
+\psset{nodesep=2pt}
+\def\XX#1#2{%
+ \TR{\ensuremath{#1_{\mbox{#2}}}}%
+}
+\pstree[xbbr=1.5cm]{\XX{R}{AMSU}}
+ {
+  \XX{S}{RawData}
+  \pstree{\XX{S}{combine}
+          \trput{\ensuremath{\oplus}}
+          \tlput{\ensuremath{\oplus}}}
+   {
+   \psset{linestyle=dashed}
+   \XX{R}{Modes}
+   \XX{R}{Normal}
+   \XX{R}{Vertical}
+   \XX{R}{Latched}
+   \XX{R}{Tripped}
+   }
+  \XX{S}{GenerateData}
+ }
+\end{example*}
+
+If we want to hang distinct-looking trees off one node,
+the \emph{ncangle} connector, with some offsets, produces the right result.
+ \begin{example*}
+\psset{framearc=.2,levelsep=4cm,
+  armB=1cm,angleB=-180}
+\def\psedge{\ncangle}
+\def\TreeBox#1{\Tr{\psframebox{#1}}}
+\pstree[treemode=R]{\TreeBox{Monitor}}
+{
+ \psset{offsetA=4pt}
+ \TreeBox{Attitude Generator}
+ \naput[npos=2.5]{{\small init}}
+ \nbput[npos=2.5]{{\small stop}}
+ \psset{offsetA=-4pt}
+ \TreeBox{Normal Generator}
+}
+\end{example*}
+
+With simple connectors, we do not need to worry about the offsets or
+angles; what this example shows is how nested trees can change direction:
+
+\begin{example*}
+\psset{arrows=->,framearc=.2}
+\def\Treebox#1{%
+ \Tr{\psframebox{#1}}
+}
+\pstree[treemode=R]
+{\Treebox{A$\rightarrow$B}}{
+\pstree{
+   \Treebox{B$\rightarrow$C}
+         }{
+ \Treebox{A$\rightarrow$D}
+\pstree[treemode=L]
+ {\Treebox{B$\rightarrow$E}}
+ {\Tn\TC[arrows=<-]}
+      }
+}
+\end{example*}
+
+Finally, let us not forget the simple empty node:
+\begin{example*}
+\pstree{\Tp}{
+ \Tcircle{A}
+ \Tcircle{B}
+}
+\end{example*}
+%\catcode`\<=12
+\end{Article}