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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"  
  "http://www.w3.org/TR/html4/loose.dtd">  
<html > 
<head><title>12 Making Trees Grow</title> 
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> 
<meta name="generator" content="TeX4ht (http://www.cis.ohio-state.edu/~gurari/TeX4ht/mn.html)"> 
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<!-- html --> 
<meta name="src" content="pgfmanual.tex"> 
<meta name="date" content="2005-10-23 18:34:00"> 
<link rel="stylesheet" type="text/css" href="pgfmanual.css"> 
</head><body 
>
   <div class="crosslinks"><p class="noindent">[<a 
href="pgfmanualse13.html" >next</a>] [<a 
href="pgfmanualse11.html" >prev</a>] [<a 
href="pgfmanualse11.html#tailpgfmanualse11.html" >prev-tail</a>] [<a 
href="#tailpgfmanualse12.html">tail</a>] [<a 
href="pgfmanual.html#pgfmanualse12.html" >up</a>] </p></div>
   <h3 class="sectionHead"><span class="titlemark">12   </span> <a 
 id="x13-14700012"></a>Making Trees Grow</h3>
<!--l. 13--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">12.1   </span> <a 
 id="x13-14800012.1"></a>Introduction to the Child Operation</h4>
<!--l. 15--><p class="noindent"><span 
class="cmti-10">Trees </span>are a common way of visualizing hierarchical structures. A simple tree looks like this:
<!--l. 17--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular">
<table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-263-" ><colgroup id="TBL-263-1g"><col 
id="TBL-263-1"><col 
id="TBL-263-2"></colgroup><tr  
 valign="baseline" id="TBL-263-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-263-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-264.svg" width="88.1847pt" height="98.57181pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-263-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\node</span><span 
class="cmtt-8">&nbsp;{root}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{left}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{right}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{child}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{child}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;};</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 28--><p class="indent">   Admittedly, in reality trees are more likely to grow <span 
class="cmti-10">upward </span>and not downward as above. You can tell whether
the author of a paper is a mathematician or a computer scientist by looking at the direction their trees grow. A
computer scientist&#8217;s trees will grow downward while a mathematician&#8217;s tree will grow upward. Naturally, the <span 
class="cmti-10">correct</span>
way is the mathematician&#8217;s way, which can be specify as follows:
<!--l. 35--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular">
<table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-264-" ><colgroup id="TBL-264-1g"><col 
id="TBL-264-1"><col 
id="TBL-264-2"></colgroup><tr  
 valign="baseline" id="TBL-264-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-264-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-265.svg" width="88.1847pt" height="98.57181pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-264-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\node</span><span 
class="cmtt-8">&nbsp;{root}</span><span 
class="cmtt-8">&nbsp;[grow'=up]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{left}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{right}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{child}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{child}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;};</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 46--><p class="indent">   In Ti<span 
class="cmti-10">k</span>Z, trees are specified by adding <span 
class="cmti-10">children </span>to a node on a path using the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">child</span></span></span> operation:
<!--l. 50--><p class="indent">
     <dl class="description"><dt class="description">
<span 
class="colorbox" id="colorbox89"><span id="textcolor90"><span 
class="cmtt-10">\path</span>&nbsp;&nbsp;...</span> <span 
class="cmtt-10">child</span><span 
class="cmtt-10">[</span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">options</span><span 
class="cmsy-10">&gt;</span><span 
class="cmtt-10">]</span><span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">foreach</span></span></span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">variables</span><span 
class="cmsy-10">&gt;</span><span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">in</span></span></span><span 
class="cmtt-10">{</span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">values</span><span 
class="cmsy-10">&gt;</span><span 
class="cmtt-10">}</span><span 
class="cmtt-10">{</span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">child path</span><span 
class="cmsy-10">&gt;</span><span 
class="cmtt-10">}</span>&nbsp;<span id="textcolor91">...<span 
class="cmtt-10">;</span></span></span> </dt><dd 
class="description">
<a 
 id="dx13-148001"></a>
<a 
 id="dx13-148002"></a>
     <!--l. 51--><p class="noindent">This operation should directly follow a completed <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">node</span></span></span> operation or another <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">child</span></span></span> operation, although
     it is permissible that the first <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">child</span></span></span> operation is preceded by options (we will come to that).
                                                                                         
                                                                                         
     <!--l. 56--><p class="noindent">When a <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">node</span></span></span> operation like <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">node</span><span 
class="cmtt-10">&nbsp;{X}</span></span></span> is followed by <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">child</span></span></span>, Ti<span 
class="cmti-10">k</span>Z&nbsp;starts counting the number of child
     nodes that follow the original <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">node</span><span 
class="cmtt-10">&nbsp;{X}</span></span></span>. For this, it scans the input and stores away each <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">child</span></span></span> and
     its arguments until it reaches a path operation that is not a <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">child</span></span></span>. Note that this will fix the character
     codes of all text inside the child arguments, which means, in essence, that you cannot use verbatim
     text inside the nodes inside a <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">child</span></span></span>. Sorry.
     <!--l. 64--><p class="noindent">Once the children have been collected and counted, Ti<span 
class="cmti-10">k</span>Z&nbsp;starts generating the child nodes. For each
     child of a parent node Ti<span 
class="cmti-10">k</span>Z&nbsp;computes an appropriate position where the child is placed. For each child,
     the coordinate system is transformed so that the origin is at this position. Then the <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">child path</span><span 
class="cmsy-10">&gt; </span>is
     drawn. Typically, the child path just consists of a <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">node</span></span></span> specification, which results in a node being
     drawn at the child&#8217;s position. Finally, an edge is drawn from the first node in the <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">child path</span><span 
class="cmsy-10">&gt; </span>to the
     parent node.
     <!--l. 74--><p class="noindent">The optional <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">foreach</span></span></span> part (note that there is no backslash before <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">foreach</span></span></span>) allows you to specify multiple
     children in a single <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">child</span></span></span> command. The idea is the following: A <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\foreach</span></span></span> statement is (internally) used to
     iterate over the list of <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">values</span><span 
class="cmsy-10">&gt;</span>. For each value in this list, a new <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">child</span></span></span> is added to the node. The syntax for
     <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">variables</span><span 
class="cmsy-10">&gt; </span>and for <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">values</span><span 
class="cmsy-10">&gt; </span>is the same as for the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\foreach</span></span></span> statement, see Section&nbsp;<a 
href="pgfmanualse15.html#x16-17900015">15<!--tex4ht:ref: section-foreach --></a>. For example, when you
     say
     <!--l. 82--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-265-" ><colgroup id="TBL-265-1g"><col 
id="TBL-265-1"></colgroup><tr  
 valign="baseline" id="TBL-265-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-265-1-1"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">node</span><span 
class="cmtt-8">&nbsp;{root}</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;[red]</span><span 
class="cmtt-8">&nbsp;foreach</span><span 
class="cmtt-8">&nbsp;\name</span><span 
class="cmtt-8">&nbsp;in</span><span 
class="cmtt-8">&nbsp;{1,2}</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{\name}}</span></div>                                                 </td></tr></table> </td>
</tr></table>
     </div>
     <!--l. 85--><p class="noindent">the effect will be the same as if you had said
     <!--l. 86--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-266-" ><colgroup id="TBL-266-1g"><col 
id="TBL-266-1"></colgroup><tr  
 valign="baseline" id="TBL-266-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-266-1-1"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">node</span><span 
class="cmtt-8">&nbsp;{root}</span><span 
class="cmtt-8">&nbsp;child[red]</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{1}}</span><span 
class="cmtt-8">&nbsp;child[ref]</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{2}}</span></div>                                                       </td></tr></table> </td>
</tr></table>
     </div>
     <!--l. 89--><p class="noindent">When you write
     <!--l. 90--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-267-" ><colgroup id="TBL-267-1g"><col 
id="TBL-267-1"></colgroup><tr  
 valign="baseline" id="TBL-267-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-267-1-1"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">node</span><span 
class="cmtt-8">&nbsp;{root}</span><span 
class="cmtt-8">&nbsp;child[\pos]</span><span 
class="cmtt-8">&nbsp;foreach</span><span 
class="cmtt-8">&nbsp;\name/\pos</span><span 
class="cmtt-8">&nbsp;in</span><span 
class="cmtt-8">&nbsp;{1/left,2/right}</span><span 
class="cmtt-8">&nbsp;{node[\pos]</span><span 
class="cmtt-8">&nbsp;{\name}}</span></div>                           </td></tr></table> </td>
</tr></table>
     </div>
     <!--l. 93--><p class="noindent">the effect will be the same as for
     <!--l. 94--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-268-" ><colgroup id="TBL-268-1g"><col 
id="TBL-268-1"></colgroup><tr  
 valign="baseline" id="TBL-268-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-268-1-1"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">node</span><span 
class="cmtt-8">&nbsp;{root}</span><span 
class="cmtt-8">&nbsp;child[left]</span><span 
class="cmtt-8">&nbsp;{node[left]</span><span 
class="cmtt-8">&nbsp;{1}}</span><span 
class="cmtt-8">&nbsp;child[right]</span><span 
class="cmtt-8">&nbsp;{node[right]</span><span 
class="cmtt-8">&nbsp;{2}}</span></div>                                       </td></tr></table> </td>
</tr></table>
     </div>
     <!--l. 98--><p class="noindent">You can nest things as in the following example:
     <!--l. 99--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-269-" ><colgroup id="TBL-269-1g"><col 
id="TBL-269-1"><col 
id="TBL-269-2"></colgroup><tr  
 valign="baseline" id="TBL-269-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-269-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-266.svg" width="40.23381pt" height="34.54326pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-269-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}[level</span><span 
class="cmtt-8">&nbsp;distance=4mm]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\tikzstyle{level</span><span 
class="cmtt-8">&nbsp;1}=[sibling</span><span 
class="cmtt-8">&nbsp;distance=8mm]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\tikzstyle{level</span><span 
class="cmtt-8">&nbsp;2}=[sibling</span><span 
class="cmtt-8">&nbsp;distance=4mm]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\tikzstyle{level</span><span 
class="cmtt-8">&nbsp;3}=[sibling</span><span 
class="cmtt-8">&nbsp;distance=2mm]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\coordinate</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;foreach</span><span 
class="cmtt-8">&nbsp;\x</span><span 
class="cmtt-8">&nbsp;in</span><span 
class="cmtt-8">&nbsp;{0,1}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;{child</span><span 
class="cmtt-8">&nbsp;foreach</span><span 
class="cmtt-8">&nbsp;\y</span><span 
class="cmtt-8">&nbsp;in</span><span 
class="cmtt-8">&nbsp;{0,1}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;{child</span><span 
class="cmtt-8">&nbsp;foreach</span><span 
class="cmtt-8">&nbsp;\z</span><span 
class="cmtt-8">&nbsp;in</span><span 
class="cmtt-8">&nbsp;{0,1}}};</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
     <!--l. 111--><p class="noindent">The details and options for this operation are described in the rest of this present section. </dd></dl>
<!--l. 117--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">12.2   </span> <a 
 id="x13-14900012.2"></a>Child Paths and the Child Nodes</h4>
<!--l. 119--><p class="noindent">For each <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">child</span></span></span> of a root node, its <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">child path</span><span 
class="cmsy-10">&gt; </span>is inserted at a specific location in the picture (the placement rules
are discussed in Section&nbsp;<a 
href="#x13-15200012.5">12.5<!--tex4ht:ref: section-tree-placement --></a>). The first node in the <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">child path</span><span 
class="cmsy-10">&gt;</span>, if it exists, is special and called the <span 
class="cmti-10">child node</span>. If
there is no first node in the <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">child path</span><span 
class="cmsy-10">&gt;</span>, that is, if the <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">child path</span><span 
class="cmsy-10">&gt; </span>is missing (including the curly braces) or if it
does not start with <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">node</span></span></span> or with <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">coordinate</span></span></span>, then an empty child node of shape <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">coordinate</span></span></span> is automatically
added.
                                                                                         
                                                                                         
<!--l. 128--><p class="indent">   Consider the example <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\node</span><span 
class="cmtt-10">&nbsp;{x}</span><span 
class="cmtt-10">&nbsp;child</span><span 
class="cmtt-10">&nbsp;{node</span><span 
class="cmtt-10">&nbsp;{y}}</span><span 
class="cmtt-10">&nbsp;child;</span></span></span>. For the first child, the <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">child path</span><span 
class="cmsy-10">&gt; </span>has the child
node <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">node</span><span 
class="cmtt-10">&nbsp;{y}</span></span></span>. For the second child, no child node is specified and, thus, it is just <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">coordinate</span></span></span>.
<!--l. 133--><p class="indent">   As for any normal node, you can give the child node a name, shift it around, or use options to influence how it is
rendered.
<!--l. 135--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-270-" ><colgroup id="TBL-270-1g"><col 
id="TBL-270-1"><col 
id="TBL-270-2"></colgroup><tr  
 valign="baseline" id="TBL-270-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-270-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-267.svg" width="74.94632pt" height="61.89008pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-270-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\node[rectangle,draw]</span><span 
class="cmtt-8">&nbsp;{root}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node[circle,draw]</span><span 
class="cmtt-8">&nbsp;(left</span><span 
class="cmtt-8">&nbsp;node)</span><span 
class="cmtt-8">&nbsp;{left}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node[ellipse,draw]</span><span 
class="cmtt-8">&nbsp;(right</span><span 
class="cmtt-8">&nbsp;node)</span><span 
class="cmtt-8">&nbsp;{right}};</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[dashed,-&gt;]</span><span 
class="cmtt-8">&nbsp;(left</span><span 
class="cmtt-8">&nbsp;node)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(right</span><span 
class="cmtt-8">&nbsp;node);</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 144--><p class="indent">   In many cases, the <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">child path</span><span 
class="cmsy-10">&gt; </span>will just consist of a specification of a child node and, possibly, children of this
child node. However, the node specification may be followed by arbitrary other material that will be added to the
picture, transformed to the child&#8217;s coordinate system. For your convenience, a move-to <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">(0,0)</span></span></span> operation is inserted
automatically at the beginning of the path. Here is an example:
<!--l. 152--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-271-" ><colgroup id="TBL-271-1g"><col 
id="TBL-271-1"><col 
id="TBL-271-2"></colgroup><tr  
 valign="baseline" id="TBL-271-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-271-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-268.svg" width="47.07912pt" height="51.28749pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-271-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\node</span><span 
class="cmtt-8">&nbsp;{root}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{[fill]</span><span 
class="cmtt-8">&nbsp;circle</span><span 
class="cmtt-8">&nbsp;(2pt)}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{[fill]</span><span 
class="cmtt-8">&nbsp;circle</span><span 
class="cmtt-8">&nbsp;(2pt)};</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 161--><p class="indent">   At the end of the <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">child path</span><span 
class="cmsy-10">&gt; </span>you may add a special path operation called <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">edge</span><span 
class="cmtt-10">&nbsp;from</span><span 
class="cmtt-10">&nbsp;parent</span></span></span>.
If this operation is not given by yourself somewhere on the path, it will be automatically added at
the end. This option causes a connecting edge from the parent node to the child node to be added
to the path. By giving options to this operation you can influence how the edge is rendered. Also,
nodes following the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">edge</span><span 
class="cmtt-10">&nbsp;from</span><span 
class="cmtt-10">&nbsp;parent</span></span></span> operation will be placed on this edge, see Section&nbsp;<a 
href="#x13-15300012.6">12.6<!--tex4ht:ref: section-edge-from-parent --></a> for
details.
<!--l. 170--><p class="indent">   To sum up:
     <ol type="1" class="enumerate1" >
     <li class="enumerate" value="1" 
><a 
 id="x13-149002x1"></a>The child path starts with a node specification. If it is not there, it is added automatically.
     </li>
     <li class="enumerate" value="2" 
><a 
 id="x13-149004x2"></a>The child path ends with a <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">edge</span><span 
class="cmtt-10">&nbsp;from</span><span 
class="cmtt-10">&nbsp;parent</span></span></span> operation, possibly followed by nodes to be put on this
     edge. If the operation is not given at the end, it is added automatically.</li></ol>
<!--l. 183--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">12.3   </span> <a 
 id="x13-15000012.3"></a>Naming Child Nodes</h4>
<!--l. 185--><p class="noindent">Child nodes can be named like any other node using either the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">name</span></span></span> option or the special syntax in
which the name of the node is placed in round parentheses between the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">node</span></span></span> operation and the node&#8217;s
text.
<!--l. 190--><p class="indent">   If you do not assign a name to a child node, Ti<span 
class="cmti-10">k</span>Z&nbsp;will automatically assign a name as follows: Assume that the
name of the parent node is, say, <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">parent</span></span></span>. (If you did not assign a name to the parent, Ti<span 
class="cmti-10">k</span>Z&nbsp;will do so itself, but that
name will not be user-accessible.) The first child of <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">parent</span></span></span> will be named <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">parent-1</span></span></span>, the second child is named
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">parent-2</span></span></span>, and so on.
<!--l. 198--><p class="indent">   This naming convention works recursively. If the second child <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">parent-2</span></span></span> has children, then the first of these
children will be called <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">parent-2-1</span></span></span> and the second <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">parent-2-2</span></span></span> and so on.
<!--l. 202--><p class="indent">   If you assign a name to a child node yourself, no name is generated automatically (the node does
not have two names). However, &#8220;counting continues,&#8221; which means that the third child of <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">parent</span></span></span> is
called <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">parent-3</span></span></span> independently of whether you have assigned names to the first and/or second child of
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">parent</span></span></span>.
                                                                                         
                                                                                         
<!--l. 208--><p class="indent">   Here is an example:
<!--l. 210--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-272-" ><colgroup id="TBL-272-1g"><col 
id="TBL-272-1"><col 
id="TBL-272-2"></colgroup><tr  
 valign="baseline" id="TBL-272-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-272-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-269.svg" width="101.26805pt" height="99.54404pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-272-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\node</span><span 
class="cmtt-8">&nbsp;(root)</span><span 
class="cmtt-8">&nbsp;{root}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{coordinate</span><span 
class="cmtt-8">&nbsp;(special)}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;};</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\node</span><span 
class="cmtt-8">&nbsp;at</span><span 
class="cmtt-8">&nbsp;(root-1)</span><span 
class="cmtt-8">&nbsp;{root-1};</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\node</span><span 
class="cmtt-8">&nbsp;at</span><span 
class="cmtt-8">&nbsp;(root-2)</span><span 
class="cmtt-8">&nbsp;{root-2};</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\node</span><span 
class="cmtt-8">&nbsp;at</span><span 
class="cmtt-8">&nbsp;(special)</span><span 
class="cmtt-8">&nbsp;{special};</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\node</span><span 
class="cmtt-8">&nbsp;at</span><span 
class="cmtt-8">&nbsp;(root-2-2)</span><span 
class="cmtt-8">&nbsp;{root-2-2};</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 225--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">12.4   </span> <a 
 id="x13-15100012.4"></a>Specifying Options for Trees and Children</h4>
<!--l. 227--><p class="noindent">Each <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">child</span></span></span> may have its own <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">options</span><span 
class="cmsy-10">&gt;</span>, which apply to &#8220;the whole child,&#8221; including all of its grandchildren. Here is
an example:
<!--l. 231--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular">
<table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-273-" ><colgroup id="TBL-273-1g"><col 
id="TBL-273-1"><col 
id="TBL-273-2"></colgroup><tr  
 valign="baseline" id="TBL-273-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-273-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-270.svg" width="71.93185pt" height="86.15823pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-273-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}[thick]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\tikzstyle{level</span><span 
class="cmtt-8">&nbsp;2}=[sibling</span><span 
class="cmtt-8">&nbsp;distance=10mm]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\coordinate</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child[red]</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;{child</span><span 
class="cmtt-8">&nbsp;child}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child[green]</span><span 
class="cmtt-8">&nbsp;{child</span><span 
class="cmtt-8">&nbsp;child[blue]};</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 240--><p class="indent">   The options of the root node have no effect on the children since the options of a node are always &#8220;local&#8221; to that
node. Because of this, the edges in the following tree are black, not red.
<!--l. 244--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-274-" ><colgroup id="TBL-274-1g"><col 
id="TBL-274-1"><col 
id="TBL-274-2"></colgroup><tr  
 valign="baseline" id="TBL-274-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-274-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-271.svg" width="43.47911pt" height="49.48749pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-274-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}[thick]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\node</span><span 
class="cmtt-8">&nbsp;[red]</span><span 
class="cmtt-8">&nbsp;{root}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child;</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 251--><p class="indent">   This raises the problem of how to set options for <span 
class="cmti-10">all </span>children. Naturally, you could always set options for the
whole path as in <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\path</span><span 
class="cmtt-10">&nbsp;[red]</span><span 
class="cmtt-10">&nbsp;node</span><span 
class="cmtt-10">&nbsp;{root}</span><span 
class="cmtt-10">&nbsp;child</span><span 
class="cmtt-10">&nbsp;child;</span></span></span> but this is bothersome in some situations. Instead, it is
easier to give the options <span 
class="cmti-10">before the first child </span>as follows:
                                                                                         
                                                                                         
<!--l. 256--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-275-" ><colgroup id="TBL-275-1g"><col 
id="TBL-275-1"><col 
id="TBL-275-2"></colgroup><tr  
 valign="baseline" id="TBL-275-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-275-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-272.svg" width="43.47911pt" height="49.48749pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-275-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}[thick]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\node</span><span 
class="cmtt-8">&nbsp;[red]</span><span 
class="cmtt-8">&nbsp;{root}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;[green]</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmsltt-10x-x-80">%</span><span 
class="cmsltt-10x-x-80">&nbsp;option</span><span 
class="cmsltt-10x-x-80">&nbsp;applies</span><span 
class="cmsltt-10x-x-80">&nbsp;to</span><span 
class="cmsltt-10x-x-80">&nbsp;all</span><span 
class="cmsltt-10x-x-80">&nbsp;children</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child;</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 265--><p class="indent">   Here is the set of rules:
     <ol type="1" class="enumerate1" >
     <li class="enumerate" value="1" 
><a 
 id="x13-151002x1"></a>Options for the whole tree are given before the root node.
     </li>
     <li class="enumerate" value="2" 
><a 
 id="x13-151004x2"></a>Options for the root node are given directly to the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">node</span></span></span> operation of the root.
     </li>
     <li class="enumerate" value="3" 
><a 
 id="x13-151006x3"></a>Options for all children can be given between the root node and the first child.
     </li>
     <li class="enumerate" value="4" 
><a 
 id="x13-151008x4"></a>Options applying to a specific child path are given as options to the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">child</span></span></span> operation.
     </li>
     <li class="enumerate" value="5" 
><a 
 id="x13-151010x5"></a>Options applying to the node of a child, but not to the whole child path, are given as options to the
     <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">node</span></span></span> command inside the <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">child path</span><span 
class="cmsy-10">&gt;</span>.</li></ol>
<!--l. 284--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-276-" ><colgroup id="TBL-276-1g"><col 
id="TBL-276-1"></colgroup><tr  
 valign="baseline" id="TBL-276-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-276-1-1"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\path</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;[...]</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmsltt-10x-x-80">%</span><span 
class="cmsltt-10x-x-80">&nbsp;Options</span><span 
class="cmsltt-10x-x-80">&nbsp;apply</span><span 
class="cmsltt-10x-x-80">&nbsp;to</span><span 
class="cmsltt-10x-x-80">&nbsp;the</span><span 
class="cmsltt-10x-x-80">&nbsp;whole</span><span 
class="cmsltt-10x-x-80">&nbsp;tree</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;node[...]</span><span 
class="cmtt-8">&nbsp;{root}</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmsltt-10x-x-80">%</span><span 
class="cmsltt-10x-x-80">&nbsp;Options</span><span 
class="cmsltt-10x-x-80">&nbsp;apply</span><span 
class="cmsltt-10x-x-80">&nbsp;to</span><span 
class="cmsltt-10x-x-80">&nbsp;the</span><span 
class="cmsltt-10x-x-80">&nbsp;root</span><span 
class="cmsltt-10x-x-80">&nbsp;node</span><span 
class="cmsltt-10x-x-80">&nbsp;only</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;[...]</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmsltt-10x-x-80">%</span><span 
class="cmsltt-10x-x-80">&nbsp;Options</span><span 
class="cmsltt-10x-x-80">&nbsp;apply</span><span 
class="cmsltt-10x-x-80">&nbsp;to</span><span 
class="cmsltt-10x-x-80">&nbsp;all</span><span 
class="cmsltt-10x-x-80">&nbsp;children</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child[...]</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmsltt-10x-x-80">%</span><span 
class="cmsltt-10x-x-80">&nbsp;Options</span><span 
class="cmsltt-10x-x-80">&nbsp;apply</span><span 
class="cmsltt-10x-x-80">&nbsp;to</span><span 
class="cmsltt-10x-x-80">&nbsp;this</span><span 
class="cmsltt-10x-x-80">&nbsp;child</span><span 
class="cmsltt-10x-x-80">&nbsp;and</span><span 
class="cmsltt-10x-x-80">&nbsp;all</span><span 
class="cmsltt-10x-x-80">&nbsp;its</span><span 
class="cmsltt-10x-x-80">&nbsp;children</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;{</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;node[...]</span><span 
class="cmtt-8">&nbsp;{}</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmsltt-10x-x-80">%</span><span 
class="cmsltt-10x-x-80">&nbsp;Options</span><span 
class="cmsltt-10x-x-80">&nbsp;apply</span><span 
class="cmsltt-10x-x-80">&nbsp;to</span><span 
class="cmsltt-10x-x-80">&nbsp;the</span><span 
class="cmsltt-10x-x-80">&nbsp;child</span><span 
class="cmsltt-10x-x-80">&nbsp;node</span><span 
class="cmsltt-10x-x-80">&nbsp;only</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;...</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child[...]</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmsltt-10x-x-80">%</span><span 
class="cmsltt-10x-x-80">&nbsp;Options</span><span 
class="cmsltt-10x-x-80">&nbsp;apply</span><span 
class="cmsltt-10x-x-80">&nbsp;to</span><span 
class="cmsltt-10x-x-80">&nbsp;this</span><span 
class="cmsltt-10x-x-80">&nbsp;child</span><span 
class="cmsltt-10x-x-80">&nbsp;and</span><span 
class="cmsltt-10x-x-80">&nbsp;all</span><span 
class="cmsltt-10x-x-80">&nbsp;its</span><span 
class="cmsltt-10x-x-80">&nbsp;children</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;;</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 300--><p class="indent">   There are additional styles that influence how children are rendered:
     <ul class="itemize1">
     <li class="itemize"><span 
class="cmtt-10">style=</span><span 
class="cmtt-10">every child</span><a 
 id="dx13-151011"></a><a 
 id="dx13-151012"></a> This style is used at the beginning of each child, as if you had given the options
     to the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">child</span></span></span> operation.
     </li>
     <li class="itemize"><span 
class="cmtt-10">style=</span><span 
class="cmtt-10">every child node</span><a 
 id="dx13-151013"></a><a 
 id="dx13-151014"></a> This style is used at the beginning of each child node in addition to the
     <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">every</span><span 
class="cmtt-10">&nbsp;node</span></span></span> style.
     </li>
     <li class="itemize"><span 
class="cmtt-10">style=</span><span 
class="cmtt-10">level </span><span 
class="cmsy-10">&lt;</span><span 
class="cmitt-10">number</span><span 
class="cmsy-10">&gt;</span><a 
 id="dx13-151015"></a><a 
 id="dx13-151016"></a> This style is used at the beginning of each set of children, where <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">number</span><span 
class="cmsy-10">&gt; </span>is
     the current level in the current tree. For example, when you say <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\node</span><span 
class="cmtt-10">&nbsp;{x}</span><span 
class="cmtt-10">&nbsp;child</span><span 
class="cmtt-10">&nbsp;child;</span></span></span>, then the
     style <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">level</span><span 
class="cmtt-10">&nbsp;1</span></span></span> is used before the first <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">child</span></span></span>. If this first <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">child</span></span></span> has children itself, then <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">level</span><span 
class="cmtt-10">&nbsp;2</span></span></span> would
     be used for them.
                                                                                         
                                                                                         
     <!--l. 315--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular">
<table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-277-" ><colgroup id="TBL-277-1g"><col 
id="TBL-277-1"><col 
id="TBL-277-2"></colgroup><tr  
 valign="baseline" id="TBL-277-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-277-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-273.svg" width="78.64505pt" height="91.96661pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-277-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\tikzstyle{level</span><span 
class="cmtt-8">&nbsp;1}=[sibling</span><span 
class="cmtt-8">&nbsp;distance=20mm]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\tikzstyle{level</span><span 
class="cmtt-8">&nbsp;2}=[sibling</span><span 
class="cmtt-8">&nbsp;distance=5mm]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\node</span><span 
class="cmtt-8">&nbsp;{root}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;};</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
     </li></ul>
<!--l. 329--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">12.5   </span> <a 
 id="x13-15200012.5"></a>Placing Child Nodes</h4>
<!--l. 333--><p class="noindent">Perhaps the most difficult part in drawing a tree is the correct layout of the children. Typically, the children have
different sizes and it is not easy to arrange them in such a manner that not too much space is wasted, the children
do not overlap, and they are either evenly spaced or their centers are evenly distributed. Calculating good
positions is especially difficult since a good position for the first child may depend on the size of the last
child.
<!--l. 341--><p class="indent">   In Ti<span 
class="cmti-10">k</span>Z, a comparatively simple approach is taken to placing the children. In order to compute a child&#8217;s position,
all that is taken into account is the number of the current child in the list of children and the number of children in
this list. Thus, if a node has five children, then there is a fixed position for the first child, a position for the second
child, and so on. These positions <span 
class="cmti-10">do not depend on the size of the children </span>and, hence, children can easily overlap.
However, since you can use options to shift individual children a bit, this is not as great a problem as it may
seem.
<!--l. 351--><p class="indent">   Although the placement of the children only depends on their number in the list of children and the total
number of children, everything else about the placement is highly configurable. You can change the distance between
children (appropriately called the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">sibling</span><span 
class="cmtt-10">&nbsp;distance</span></span></span>) and the distance between levels of the tree. These distances
may change from level to level. The direction in which the tree grows can be changed globally and for parts of the
tree. You can even specify your own &#8220;growth function&#8221; to arrange children on a circle or along special lines or
curves.
<!--l. 361--><p class="indent">   The default growth function works as follows: Assume that we are given a node and five children. These children
will be placed on a line with their centers (or, more generally, with their anchors) spaced apart by the current
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">sibling</span><span 
class="cmtt-10">&nbsp;distance</span></span></span>. The line is orthogonal to the current <span 
class="cmti-10">direction of growth</span>, which is set with the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">grow</span></span></span> and <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">grow'</span></span></span>
option (the latter option reverses the ordering of the children). The distance from the line to the parent node is
given by the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">level</span><span 
class="cmtt-10">&nbsp;distance</span></span></span>.
                                                                                         
                                                                                         
<!--l. 371--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-278-" ><colgroup id="TBL-278-1g"><col 
id="TBL-278-1"><col 
id="TBL-278-2"></colgroup><tr  
 valign="baseline" id="TBL-278-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-278-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-274.svg" width="71.35466pt" height="148.03824pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-278-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\path</span><span 
class="cmtt-8">&nbsp;[help</span><span 
class="cmtt-8">&nbsp;lines]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;node</span><span 
class="cmtt-8">&nbsp;(root)</span><span 
class="cmtt-8">&nbsp;{root}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;[grow=-10]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{1}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{2}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{3}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{4}};</span>
<br>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[|&lt;-&gt;|,thick]</span><span 
class="cmtt-8">&nbsp;(root-1.center)</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;node[above,sloped]</span><span 
class="cmtt-8">&nbsp;{sibling</span><span 
class="cmtt-8">&nbsp;distance}</span><span 
class="cmtt-8">&nbsp;(root-2.center);</span>
<br>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[|&lt;-&gt;|,thick]</span><span 
class="cmtt-8">&nbsp;(root.center)</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;node[above,sloped]</span><span 
class="cmtt-8">&nbsp;{level</span><span 
class="cmtt-8">&nbsp;distance}</span><span 
class="cmtt-8">&nbsp;+(-10:\tikzleveldistance);</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 390--><p class="indent">   Here is a detailed description of the options:
     <ul class="itemize1">
     <li class="itemize"><span 
class="cmtt-10">level distance</span><a 
 id="dx13-152001"></a><a 
 id="dx13-152002"></a><span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">=</span></span></span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">distance</span><span 
class="cmsy-10">&gt; </span>This option allows you to change the distance between different levels of
     the tree, more precisely, between the parent and the line on which its children are arranged. When
     given to a single child, this will set the distance for this child only.
     <!--l. 398--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-279-" ><colgroup id="TBL-279-1g"><col 
id="TBL-279-1"><col 
id="TBL-279-2"></colgroup><tr  
 valign="baseline" id="TBL-279-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-279-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-275.svg" width="85.75827pt" height="77.74023pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-279-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\node</span><span 
class="cmtt-8">&nbsp;{root}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;[level</span><span 
class="cmtt-8">&nbsp;distance=20mm]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;[level</span><span 
class="cmtt-8">&nbsp;distance=5mm]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child[level</span><span 
class="cmtt-8">&nbsp;distance=10mm];</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
                                                                                         
                                                                                         
     <!--l. 413--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-280-" ><colgroup id="TBL-280-1g"><col 
id="TBL-280-1"><col 
id="TBL-280-2"></colgroup><tr  
 valign="baseline" id="TBL-280-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-280-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-276.svg" width="85.75827pt" height="63.51385pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-280-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\tikzstyle{level</span><span 
class="cmtt-8">&nbsp;1}=[level</span><span 
class="cmtt-8">&nbsp;distance=10mm]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\tikzstyle{level</span><span 
class="cmtt-8">&nbsp;2}=[level</span><span 
class="cmtt-8">&nbsp;distance=5mm]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\node</span><span 
class="cmtt-8">&nbsp;{root}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child[level</span><span 
class="cmtt-8">&nbsp;distance=10mm]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child;</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
     </li>
     <li class="itemize"><span 
class="cmtt-10">sibling distance</span><a 
 id="dx13-152003"></a><a 
 id="dx13-152004"></a><span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">=</span></span></span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">distance</span><span 
class="cmsy-10">&gt; </span>This option specifies the distance between the anchors of the children of a
     parent node.
     <!--l. 432--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-281-" ><colgroup id="TBL-281-1g"><col 
id="TBL-281-1"><col 
id="TBL-281-2"></colgroup><tr  
 valign="baseline" id="TBL-281-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-281-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-277.svg" width="40.23381pt" height="34.54326pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-281-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}[level</span><span 
class="cmtt-8">&nbsp;distance=4mm]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\tikzstyle{level</span><span 
class="cmtt-8">&nbsp;1}=[sibling</span><span 
class="cmtt-8">&nbsp;distance=8mm]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\tikzstyle{level</span><span 
class="cmtt-8">&nbsp;2}=[sibling</span><span 
class="cmtt-8">&nbsp;distance=4mm]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\tikzstyle{level</span><span 
class="cmtt-8">&nbsp;3}=[sibling</span><span 
class="cmtt-8">&nbsp;distance=2mm]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\coordinate</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{child</span><span 
class="cmtt-8">&nbsp;child}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{child</span><span 
class="cmtt-8">&nbsp;child}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{child</span><span 
class="cmtt-8">&nbsp;child}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{child</span><span 
class="cmtt-8">&nbsp;child}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;};</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
                                                                                         
                                                                                         
     <!--l. 449--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-282-" ><colgroup id="TBL-282-1g"><col 
id="TBL-282-1"><col 
id="TBL-282-2"></colgroup><tr  
 valign="baseline" id="TBL-282-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-282-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-278.svg" width="105.2446pt" height="98.13142pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-282-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}[level</span><span 
class="cmtt-8">&nbsp;distance=10mm]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\tikzstyle{every</span><span 
class="cmtt-8">&nbsp;node}=[fill=red!60,circle,inner</span><span 
class="cmtt-8">&nbsp;sep=1pt]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\tikzstyle{level</span><span 
class="cmtt-8">&nbsp;1}=[sibling</span><span 
class="cmtt-8">&nbsp;distance=20mm,</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;set</span><span 
class="cmtt-8">&nbsp;style={{every</span><span 
class="cmtt-8">&nbsp;node}+=[fill=red!45]}]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\tikzstyle{level</span><span 
class="cmtt-8">&nbsp;2}=[sibling</span><span 
class="cmtt-8">&nbsp;distance=10mm,</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;set</span><span 
class="cmtt-8">&nbsp;style={{every</span><span 
class="cmtt-8">&nbsp;node}+=[fill=red!30]}]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\tikzstyle{level</span><span 
class="cmtt-8">&nbsp;3}=[sibling</span><span 
class="cmtt-8">&nbsp;distance=5mm,</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;set</span><span 
class="cmtt-8">&nbsp;style={{every</span><span 
class="cmtt-8">&nbsp;node}+=[fill=red!15]}]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\node</span><span 
class="cmtt-8">&nbsp;{31}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{30}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{20}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{5}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{4}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{10}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{9}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{1}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{20}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{19}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{1}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child[fill=none]</span><span 
class="cmtt-8">&nbsp;{edge</span><span 
class="cmtt-8">&nbsp;from</span><span 
class="cmtt-8">&nbsp;parent[draw=none]}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{18}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;};</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
     </li>
     <li class="itemize"><span 
class="cmtt-10">grow</span><a 
 id="dx13-152005"></a><a 
 id="dx13-152006"></a><span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">=</span></span></span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">direction</span><span 
class="cmsy-10">&gt; </span>This option is used to define the <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">direction</span><span 
class="cmsy-10">&gt; </span>in which the tree will grow. The <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">direction</span><span 
class="cmsy-10">&gt; </span>can
     either be an angle in degrees or one of the following special text strings: <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">down</span></span></span>, <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">up</span></span></span>, <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">left</span></span></span>, <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">right</span></span></span>, <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">north</span></span></span>, <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">south</span></span></span>,
     <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">east</span></span></span>, <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">west</span></span></span>, <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">north</span><span 
class="cmtt-10">&nbsp;east</span></span></span>, <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">north</span><span 
class="cmtt-10">&nbsp;west</span></span></span>, <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">south</span><span 
class="cmtt-10">&nbsp;east</span></span></span>, and <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">south</span><span 
class="cmtt-10">&nbsp;west</span></span></span>. All of these have &#8220;their obvious
     meaning,&#8221; so, say, <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">south</span><span 
class="cmtt-10">&nbsp;west</span></span></span> is the same as the angle <span 
class="cmsy-10">-</span>135<sup ><span 
class="cmsy-7"><span class="htf-cmbx">o</span></span></sup>.
     <!--l. 488--><p class="noindent">As a side effect, this option installs the default growth function.
     <!--l. 490--><p class="noindent">In addition to setting the direction, this option also has a seemingly strange effect: It sets the sibling distance
     for the current level to <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">0pt</span></span></span>, but leaves the sibling distance for later levels unchanged.
     <!--l. 495--><p class="noindent">This somewhat strange behaviour has a highly desirable effect: If you give this option before the list of
     children of a node starts, the &#8220;current level&#8221; is still the parent level. Each child will be on a later level and,
     hence, the sibling distance will be as specified originally. This will cause the children to be neatly aligned in a
     line orthogonal to the given <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">direction</span><span 
class="cmsy-10">&gt;</span>. However, if you give this option locally to a single child,
     then &#8220;current level&#8221; will be the same as the child&#8217;s level. The zero sibling distance will then
     cause the child to be placed exactly at a point at distance <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">level</span><span 
class="cmtt-10">&nbsp;distance</span></span></span> in the direction
     <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">direction</span><span 
class="cmsy-10">&gt;</span>. However, the children of the child will be placed &#8220;normally&#8221; on a line orthogonal to the
     <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">direction</span><span 
class="cmsy-10">&gt;</span>.
     <!--l. 508--><p class="noindent">These placement effects are best demonstrated by some examples:
     <!--l. 509--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular">
<table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-283-" ><colgroup id="TBL-283-1g"><col 
id="TBL-283-1"><col 
id="TBL-283-2"></colgroup><tr  
 valign="baseline" id="TBL-283-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-283-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-279.svg" width="55.25378pt" height="43.07912pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-283-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\tikz</span><span 
class="cmtt-8">&nbsp;\node</span><span 
class="cmtt-8">&nbsp;{root}</span><span 
class="cmtt-8">&nbsp;[grow=right]</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;child;</span></div>                                                                  </td></tr></table> </td>
</tr></table></div>
                                                                                         
                                                                                         
     <!--l. 513--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular">
<table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-284-" ><colgroup id="TBL-284-1g"><col 
id="TBL-284-1"><col 
id="TBL-284-2"></colgroup><tr  
 valign="baseline" id="TBL-284-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-284-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-280.svg" width="57.84273pt" height="51.87648pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-284-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\tikz</span><span 
class="cmtt-8">&nbsp;\node</span><span 
class="cmtt-8">&nbsp;{root}</span><span 
class="cmtt-8">&nbsp;[grow=south</span><span 
class="cmtt-8">&nbsp;west]</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;child;</span></div>                                                             </td></tr></table> </td>
</tr></table></div>
     <!--l. 517--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-285-" ><colgroup id="TBL-285-1g"><col 
id="TBL-285-1"><col 
id="TBL-285-2"></colgroup><tr  
 valign="baseline" id="TBL-285-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-285-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-281.svg" width="71.53181pt" height="43.07913pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-285-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}[level</span><span 
class="cmtt-8">&nbsp;distance=10mm,sibling</span><span 
class="cmtt-8">&nbsp;distance=5mm]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\node</span><span 
class="cmtt-8">&nbsp;{root}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;[grow=down]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child[grow=right]</span><span 
class="cmtt-8">&nbsp;{</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;child</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;};</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
     <!--l. 529--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-286-" ><colgroup id="TBL-286-1g"><col 
id="TBL-286-1"><col 
id="TBL-286-2"></colgroup><tr  
 valign="baseline" id="TBL-286-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-286-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-282.svg" width="74.16605pt" height="76.64778pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-286-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}[level</span><span 
class="cmtt-8">&nbsp;distance=2em]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\node</span><span 
class="cmtt-8">&nbsp;{C}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child[grow=up]</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{H}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child[grow=left]</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{H}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child[grow=down]</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{H}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child[grow=right]</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{C}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child[grow=up]</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{H}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child[grow=right]</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{H}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child[grow=down]</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{H}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;edge</span><span 
class="cmtt-8">&nbsp;from</span><span 
class="cmtt-8">&nbsp;parent[double]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;coordinate</span><span 
class="cmtt-8">&nbsp;(wrong)</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;};</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[&lt;-,red]</span><span 
class="cmtt-8">&nbsp;([yshift=-2mm]wrong)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;+(0,-1)</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;node[below]{This</span><span 
class="cmtt-8">&nbsp;is</span><span 
class="cmtt-8">&nbsp;wrong!};</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
     <!--l. 547--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-287-" ><colgroup id="TBL-287-1g"><col 
id="TBL-287-1"><col 
id="TBL-287-2"></colgroup><tr  
 valign="baseline" id="TBL-287-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-287-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-283.svg" width="94.15204pt" height="77.74896pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object> &nbsp; </td> <td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-287-1-2"  
class="td11"> <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\node[rectangle,draw]</span><span 
class="cmtt-8">&nbsp;(a)</span><span 
class="cmtt-8">&nbsp;at</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;{start</span><span 
class="cmtt-8">&nbsp;node};</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\node[rectangle,draw]</span><span 
class="cmtt-8">&nbsp;(b)</span><span 
class="cmtt-8">&nbsp;at</span><span 
class="cmtt-8">&nbsp;(2,1)</span><span 
class="cmtt-8">&nbsp;{end};</span>
<br>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(a)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(b)</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;node[coordinate,midway]</span><span 
class="cmtt-8">&nbsp;{}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child[grow=100,&lt;-]</span><span 
class="cmtt-8">&nbsp;{node[above]</span><span 
class="cmtt-8">&nbsp;{the</span><span 
class="cmtt-8">&nbsp;middle</span><span 
class="cmtt-8">&nbsp;is</span><span 
class="cmtt-8">&nbsp;here}};</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
     </li>
     <li class="itemize"><span 
class="cmtt-10">grow'</span><a 
 id="dx13-152007"></a><a 
 id="dx13-152008"></a><span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">=</span></span></span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">direction</span><span 
class="cmsy-10">&gt; </span>This option has the same effect as <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">grow</span></span></span>, only the children are arranged in the opposite
     order.
     </li>
     <li class="itemize"><span 
class="cmtt-10">growth function</span><a 
 id="dx13-152009"></a><a 
 id="dx13-152010"></a><span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">=</span></span></span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">macro name</span><span 
class="cmsy-10">&gt; </span>This rather low-level option allows you to set a new growth function. The
                                                                                         
                                                                                         
     <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">macro name</span><span 
class="cmsy-10">&gt; </span>must be the name of a macro without parameters. This macro will be called for each child of a
     node.
     <!--l. 566--><p class="noindent">The effect of executing the macro should be the following: It should transform the coordinate system in such a
     way that the origin becomes the place where the current child should be anchored. When the macro is called,
     the current coordinate system will be setup such that the anchor of the parent node is in the origin. Thus, in
     each call, the <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">macro name</span><span 
class="cmsy-10">&gt; </span>must essentially do a shift to the child&#8217;s origin. When the macro is called, the
     <span class="TEX">T<span 
class="E">E</span>X</span>&nbsp;counter <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\tikznumberofchildren</span></span></span> will be set to the total number of children of the parent
     node and the counter <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\tikznumberofcurrentchild</span></span></span> will be set to the number of the current
     child.
     <!--l. 577--><p class="noindent">The macro may, in addition to shifting the coordinate system, also transform the coordinate system further.
     For example, it could be rotated or scaled.
     <!--l. 581--><p class="noindent">Additional growth functions are defined in the library, see Section&nbsp;<a 
href="pgfmanualse14.html#x15-17400014.6">14.6<!--tex4ht:ref: section-tree-library --></a>.</li></ul>
<!--l. 587--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">12.6   </span> <a 
 id="x13-15300012.6"></a>Edges From the Parent Node</h4>
<!--l. 591--><p class="noindent">Every child node is connected to its parent node via a special kind of edge called the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">edge</span><span 
class="cmtt-10">&nbsp;from</span><span 
class="cmtt-10">&nbsp;parent</span></span></span>. This edge
is added to the <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">child path</span><span 
class="cmsy-10">&gt; </span>when the following path operation is encountered:
<!--l. 595--><p class="indent">
     <dl class="description"><dt class="description">
<span 
class="colorbox" id="colorbox92"><span id="textcolor93"><span 
class="cmtt-10">\path</span>&nbsp;&nbsp;...</span> <span 
class="cmtt-10">edge from parent</span><span 
class="cmtt-10">[</span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">options</span><span 
class="cmsy-10">&gt;</span><span 
class="cmtt-10">]</span>&nbsp;<span id="textcolor94">...<span 
class="cmtt-10">;</span></span></span> </dt><dd 
class="description">
<a 
 id="dx13-153001"></a>
<a 
 id="dx13-153002"></a>
     <!--l. 596--><p class="noindent">This path operation can only be used inside <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">child paths</span><span 
class="cmsy-10">&gt; </span>and should be given at the end, possibly
     followed by node specifications (we will come to that). If a <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">child path</span><span 
class="cmsy-10">&gt; </span>does not contain this operation,
     it will be added at the end of the <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">child path</span><span 
class="cmsy-10">&gt; </span>automatically.
     <!--l. 602--><p class="noindent">This operation has several effects. The most important is that it inserts the current &#8220;edge from parent path&#8221;
     into the child path. The edge from parent path can be set using the following option:
         <ul class="itemize1">
         <li class="itemize"><span 
class="cmtt-10">edge from parent path</span><a 
 id="dx13-153003"></a><a 
 id="dx13-153004"></a><span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">=</span></span></span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">path</span><span 
class="cmsy-10">&gt; </span>This options allows you to set the edge from parent path to a new path.
         The default for this path is the following:
         <!--l. 610--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-288-" ><colgroup id="TBL-288-1g"><col 
id="TBL-288-1"></colgroup><tr  
 valign="baseline" id="TBL-288-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-288-1-1"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">(\tikzparentnode\tikzparentanchor)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(\tikzchildnode\tikzchildanchor)</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span></div>                                                                                                          </td></tr></table> </td>
</tr></table></div>
         <!--l. 613--><p class="noindent">The <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\tikzparentnode</span></span></span> is a macro that will expand to the name of the parent node. This works even
         when you have not assigned a name to the parent node, in this case an internal name is automatically
         generated. The <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\tikzchildnode</span></span></span> is a macro that expands to the name of the child node. The two
         <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">...anchor</span></span></span> macros are empty by default. So, what is essentially inserted is just the path segment
         <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">(\tikzparentnode)</span><span 
class="cmtt-10">&nbsp;--</span><span 
class="cmtt-10">&nbsp;(\tikzchildnode)</span></span></span>; which is exactly an edge from the parent to the
         child.
         <!--l. 622--><p class="noindent">You can modify this edge from parent path to achieve all sorts of effects. For example, we could replace
         the straight line by a curve as follows:
                                                                                         
                                                                                         
         <!--l. 625--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-289-" ><colgroup id="TBL-289-1g"><col 
id="TBL-289-1"><col 
id="TBL-289-2"></colgroup><tr  
 valign="baseline" id="TBL-289-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-289-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-284.svg" width="88.1847pt" height="98.57181pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-289-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}[edge</span><span 
class="cmtt-8">&nbsp;from</span><span 
class="cmtt-8">&nbsp;parent</span><span 
class="cmtt-8">&nbsp;path=</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;{(\tikzparentnode.south)</span><span 
class="cmtt-8">&nbsp;..</span><span 
class="cmtt-8">&nbsp;controls</span><span 
class="cmtt-8">&nbsp;+(0,-1)</span><span 
class="cmtt-8">&nbsp;and</span><span 
class="cmtt-8">&nbsp;+(0,1)</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;..</span><span 
class="cmtt-8">&nbsp;(\tikzchildnode.north)}]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\node</span><span 
class="cmtt-8">&nbsp;{root}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{left}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{right}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{child}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{child}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;};</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
         <!--l. 638--><p class="noindent">Further useful edge from parent paths are defined in the tree library, see Section&nbsp;<a 
href="pgfmanualse14.html#x15-17400014.6">14.6<!--tex4ht:ref: section-tree-library --></a>.
         <!--l. 641--><p class="noindent">As said before, the anchors in the default edge from parent path are empty. However, you can set them
         using the following options:
             <ul class="itemize2">
             <li class="itemize"><span 
class="cmtt-10">child anchor</span><a 
 id="dx13-153005"></a><a 
 id="dx13-153006"></a><span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">=</span></span></span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">anchor</span><span 
class="cmsy-10">&gt; </span>Specifies the anchor where the edge from parent meets the child
             node by setting the macro <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\tikzchildanchor</span></span></span> to <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">.</span></span></span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">anchor</span><span 
class="cmsy-10">&gt;</span>.
             <!--l. 649--><p class="noindent">If you specify <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">border</span></span></span> as the <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">anchor</span><span 
class="cmsy-10">&gt;</span>, then the macro <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\tikzchildanchor</span></span></span> is set to the empty string.
             The effect of this is that the edge from the parent will meet the child on the border at an
             automatically calculated position.
             <!--l. 653--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-290-" ><colgroup id="TBL-290-1g"><col 
id="TBL-290-1"><col 
id="TBL-290-2"></colgroup><tr  
 valign="baseline" id="TBL-290-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-290-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-285.svg" width="88.1847pt" height="98.57181pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-290-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\node</span><span 
class="cmtt-8">&nbsp;{root}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;[child</span><span 
class="cmtt-8">&nbsp;anchor=north]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{left}</span><span 
class="cmtt-8">&nbsp;edge</span><span 
class="cmtt-8">&nbsp;from</span><span 
class="cmtt-8">&nbsp;parent[dashed]}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{right}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{child}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{child}</span><span 
class="cmtt-8">&nbsp;edge</span><span 
class="cmtt-8">&nbsp;from</span><span 
class="cmtt-8">&nbsp;parent[draw=none]}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;};</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
             </li>
             <li class="itemize"><span 
class="cmtt-10">parent anchor</span><a 
 id="dx13-153007"></a><a 
 id="dx13-153008"></a><span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">=</span></span></span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">anchor</span><span 
class="cmsy-10">&gt; </span>This option works the same way as the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">child</span><span 
class="cmtt-10">&nbsp;anchor</span></span></span>, only for the
             parent.</li></ul>
         </li></ul>
     <!--l. 670--><p class="noindent">Besides inserting the edge from parent path, the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">edge</span><span 
class="cmtt-10">&nbsp;from</span><span 
class="cmtt-10">&nbsp;parent</span></span></span> operation has another effect: The
     <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">options</span><span 
class="cmsy-10">&gt; </span>are inserted directly before the edge from parent path and the following style is also installed prior
     to inserting the path:
         <ul class="itemize1">
         <li class="itemize"><span 
class="cmtt-10">style=</span><span 
class="cmtt-10">edge from parent</span><a 
 id="dx13-153009"></a><a 
 id="dx13-153010"></a> This style is inserted right before the edge from parent path and before the
         <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">options</span><span 
class="cmsy-10">&gt; </span>are inserted. By default, it just draws the edge from parent, but you can use it to make the
         edge look different.
                                                                                         
                                                                                         
         <!--l. 680--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-291-" ><colgroup id="TBL-291-1g"><col 
id="TBL-291-1"><col 
id="TBL-291-2"></colgroup><tr  
 valign="baseline" id="TBL-291-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-291-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-286.svg" width="88.1847pt" height="98.57181pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-291-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\tikzstyle{edge</span><span 
class="cmtt-8">&nbsp;from</span><span 
class="cmtt-8">&nbsp;parent}=[draw,red,thick]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\node</span><span 
class="cmtt-8">&nbsp;{root}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{left}</span><span 
class="cmtt-8">&nbsp;edge</span><span 
class="cmtt-8">&nbsp;from</span><span 
class="cmtt-8">&nbsp;parent[dashed]}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{right}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{child}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{child}</span><span 
class="cmtt-8">&nbsp;edge</span><span 
class="cmtt-8">&nbsp;from</span><span 
class="cmtt-8">&nbsp;parent[draw=none]}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;};</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
         </li></ul>
     <!--l. 693--><p class="noindent">Note: The <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">options</span><span 
class="cmsy-10">&gt; </span>inserted before the edge from parent path is added <span 
class="cmti-10">apply to the whole child path</span>. Thus, it
     is not possible to, say, draw a circle in red as part of the child path and then have an edge to parent
     in blue. However, as always, the child node is a node and can be drawn in a totally different
     way.
     <!--l. 699--><p class="noindent">Finally, the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">edge</span><span 
class="cmtt-10">&nbsp;from</span><span 
class="cmtt-10">&nbsp;parent</span></span></span> operation has one more effect: It causes all nodes <span 
class="cmti-10">following </span>the operation to be
     placed on the edge. This is the same effect as if you had added the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">pos</span></span></span> option to all these nodes, see also
     Section&nbsp;<a 
href="pgfmanualse11.html#x12-14300011.6.1">11.6.1<!--tex4ht:ref: section-pos-option --></a>.
     <!--l. 704--><p class="noindent">As an example, consider the following code:
     <!--l. 705--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-292-" ><colgroup id="TBL-292-1g"><col 
id="TBL-292-1"></colgroup><tr  
 valign="baseline" id="TBL-292-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-292-1-1"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\node</span><span 
class="cmtt-8">&nbsp;(root)</span><span 
class="cmtt-8">&nbsp;{}</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;(child)</span><span 
class="cmtt-8">&nbsp;{}</span><span 
class="cmtt-8">&nbsp;edge</span><span 
class="cmtt-8">&nbsp;to</span><span 
class="cmtt-8">&nbsp;parent</span><span 
class="cmtt-8">&nbsp;node</span><span 
class="cmtt-8">&nbsp;{label}};</span></div>                                          </td></tr></table> </td>
</tr></table>
     </div>
     <!--l. 708--><p class="noindent">The <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">edge</span><span 
class="cmtt-10">&nbsp;to</span><span 
class="cmtt-10">&nbsp;parent</span></span></span> operation and the following <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">node</span></span></span> operation will, together, have the same effect as if we
     had said:
     <!--l. 710--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-293-" ><colgroup id="TBL-293-1g"><col 
id="TBL-293-1"></colgroup><tr  
 valign="baseline" id="TBL-293-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-293-1-1"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">(root)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(child)</span><span 
class="cmtt-8">&nbsp;node</span><span 
class="cmtt-8">&nbsp;[pos=0.5]</span><span 
class="cmtt-8">&nbsp;{label}</span></div>                                                                      </td></tr></table> </td>
</tr></table>
     </div>
     <!--l. 714--><p class="noindent">Here is a more complicated example:
                                                                                         
                                                                                         
     <!--l. 715--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-294-" ><colgroup id="TBL-294-1g"><col 
id="TBL-294-1"><col 
id="TBL-294-2"></colgroup><tr  
 valign="baseline" id="TBL-294-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-294-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-287.svg" width="88.1847pt" height="98.57181pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-294-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\node</span><span 
class="cmtt-8">&nbsp;{root}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;node</span><span 
class="cmtt-8">&nbsp;{left}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;edge</span><span 
class="cmtt-8">&nbsp;from</span><span 
class="cmtt-8">&nbsp;parent</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;node[left]</span><span 
class="cmtt-8">&nbsp;{a}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;node[right]</span><span 
class="cmtt-8">&nbsp;{b}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;node</span><span 
class="cmtt-8">&nbsp;{right}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;node</span><span 
class="cmtt-8">&nbsp;{child}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;edge</span><span 
class="cmtt-8">&nbsp;from</span><span 
class="cmtt-8">&nbsp;parent</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;node[left]</span><span 
class="cmtt-8">&nbsp;{c}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;child</span><span 
class="cmtt-8">&nbsp;{node</span><span 
class="cmtt-8">&nbsp;{child}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;edge</span><span 
class="cmtt-8">&nbsp;from</span><span 
class="cmtt-8">&nbsp;parent</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;node[near</span><span 
class="cmtt-8">&nbsp;end]</span><span 
class="cmtt-8">&nbsp;{x}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;};</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
     </dd></dl>
                                                                                         
                                                                                         
                                                                                         
                                                                                         
                                                                                         
                                                                                         
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