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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>21 Constructing Paths</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)"> 
<meta name="originator" content="TeX4ht (http://www.cis.ohio-state.edu/~gurari/TeX4ht/mn.html)"> 
<!-- html --> 
<meta name="src" content="pgfmanual.tex"> 
<meta name="date" content="2005-11-15 18:41:00"> 
<link rel="stylesheet" type="text/css" href="pgfmanual.css"> 
</head><body 
>
   <div class="crosslinks"><p class="noindent">[<a 
href="pgfmanualse22.html" >next</a>] [<a 
href="pgfmanualse20.html" >prev</a>] [<a 
href="pgfmanualse20.html#tailpgfmanualse20.html" >prev-tail</a>] [<a 
href="#tailpgfmanualse21.html">tail</a>] [<a 
href="pgfmanual.html#pgfmanualse21.html" >up</a>] </p></div>
   <h3 class="sectionHead"><span class="titlemark">21   </span> <a 
 id="x22-21500021"></a>Constructing Paths</h3>
<!--l. 10--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">21.1   </span> <a 
 id="x22-21600021.1"></a>Overview</h4>
<!--l. 12--><p class="noindent">The &#8220;basic entity of drawing&#8221; in <span 
class="cmcsc-10"><small 
class="small-caps">P</small><small 
class="small-caps">G</small><small 
class="small-caps">F</small></span>&nbsp;is the <span 
class="cmti-10">path</span>. A path consists of several parts, each of which is either a closed or
open curve. An open curve has a starting point and an end point and, in between, consists of several <span 
class="cmti-10">segments</span>, each
of which is either a straight line or a B&eacute;zier curve. Here is an example of a path (in red) consisting of two parts, one
open, one closed:
<!--l. 19--><p class="noindent"><div class="obeylines-v"></div><object data="pgfmanual-511.svg" width="336.77493 " height="173.6204 " type="image/svg+xml"><p>SVG-Viewer needed.</p></object><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-434-" ><colgroup id="TBL-434-1g"><col 
id="TBL-434-1"></colgroup><tr  
 valign="baseline" id="TBL-434-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-434-1-1"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}[scale=2]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[thick,red]</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;(0,0)</span><span 
class="cmtt-8">&nbsp;coordinate</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;coordinate</span><span 
class="cmtt-8">&nbsp;(ab)</span><span 
class="cmtt-8">&nbsp;(1,.5)</span><span 
class="cmtt-8">&nbsp;coordinate</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><span 
class="cmtt-8">&nbsp;coordinate</span><span 
class="cmtt-8">&nbsp;(bc)</span><span 
class="cmtt-8">&nbsp;controls</span><span 
class="cmtt-8">&nbsp;+(up:1cm)</span><span 
class="cmtt-8">&nbsp;and</span><span 
class="cmtt-8">&nbsp;+(left:1cm)</span><span 
class="cmtt-8">&nbsp;..</span><span 
class="cmtt-8">&nbsp;(3,1)</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;coordinate</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;(0,1)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(2,1)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;coordinate</span><span 
class="cmtt-8">&nbsp;(x)</span><span 
class="cmtt-8">&nbsp;(1,2)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;cycle;</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;node[below]</span><span 
class="cmtt-8">&nbsp;{start</span><span 
class="cmtt-8">&nbsp;part</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;(ab)</span><span 
class="cmtt-8">&nbsp;node[below</span><span 
class="cmtt-8">&nbsp;right]</span><span 
class="cmtt-8">&nbsp;{straight</span><span 
class="cmtt-8">&nbsp;segment}</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;(b)</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;node[right]</span><span 
class="cmtt-8">&nbsp;{end</span><span 
class="cmtt-8">&nbsp;first</span><span 
class="cmtt-8">&nbsp;segment}</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;(c)</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;node[right]</span><span 
class="cmtt-8">&nbsp;{end</span><span 
class="cmtt-8">&nbsp;part</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;(x)</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;node[above</span><span 
class="cmtt-8">&nbsp;right]</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;{part</span><span 
class="cmtt-8">&nbsp;2</span><span 
class="cmtt-8">&nbsp;(closed)};</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table>
</div>
<!--l. 35--><p class="indent">   A path, by itself, has no &#8220;effect,&#8221; that is, it does not leave any marks on the page. It is just a set of
points on the plane. However, you can <span 
class="cmti-10">use </span>a path in different ways. The most natural actions are
<span 
class="cmti-10">stroking </span>(also known as <span 
class="cmti-10">drawing</span>) and <span 
class="cmti-10">filling</span>. Stroking can be imagined as picking up a pen of a certain
diameter and &#8220;moving it along the path.&#8221; Filling means that everything &#8220;inside&#8221; the path is filled
with a uniform color. Naturally, the open parts of a path must first be closed before a path can be
filled.
<!--l. 45--><p class="indent">   In <span 
class="cmcsc-10"><small 
class="small-caps">P</small><small 
class="small-caps">G</small><small 
class="small-caps">F</small></span>, there are numerous commands for constructing paths, all of which start with <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\pgfpath</span></span></span>. There are also
commands for <span 
class="cmti-10">using </span>paths, though most operations can be performed by calling <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\pgfusepath</span></span></span> with an appropriate
parameter.
<!--l. 50--><p class="indent">   As a side-effect, the path construction commands keep track of two bounding boxes. One is the bounding box for
the current path, the other is a bounding box for all paths in the current picture. See Section&nbsp;<a 
href="#x22-22800021.13">21.13<!--tex4ht:ref: section-bb --></a> for more
details.
<!--l. 55--><p class="indent">   Each path construction command extends the current path in some way. The &#8220;current path&#8221; is a global entity
that persists across <span class="TEX">T<span 
class="E">E</span>X</span>&nbsp;groups. Thus, between calls to the path construction commands you can
perform arbitrary computations and even open and closed <span class="TEX">T<span 
class="E">E</span>X</span>&nbsp;groups. The current path only gets
&#8220;flushed&#8221; when the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\pgfusepath</span></span></span> command is called (or when the soft-path subsystem is used directly, see
Section&nbsp;<a 
href="pgfmanualse34.html#x35-32300034">34<!--tex4ht:ref: section-soft-paths --></a>).
<!--l. 63--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">21.2   </span> <a 
 id="x22-21700021.2"></a>The Move-To Path Operation</h4>
<!--l. 65--><p class="noindent">The most basic operation is the move-to operation. It must be given at the beginning of paths, though some path
construction command (like <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\pgfpathrectangle</span></span></span>) generate move-tos implicitly. A move-to operation can also be
used to start a new part of a path.
                                                                                         
                                                                                         
<!--l. 70--><p class="indent">
     <dl class="description"><dt class="description">
<span 
class="colorbox" id="colorbox217"><span 
class="cmtt-10">\pgfpathmoveto</span><span 
class="cmtt-10">{</span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">coordinate</span><span 
class="cmsy-10">&gt;</span><span 
class="cmtt-10">}</span></span> </dt><dd 
class="description">
<a 
 id="dx22-217001"></a>
     <!--l. 71--><p class="noindent">This command expects a <span 
class="cmcsc-10"><small 
class="small-caps">P</small><small 
class="small-caps">G</small><small 
class="small-caps">F</small></span>-coordinate like <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\pgfpointorigin</span></span></span> as its parameter. When the current
     path is empty, this operation will start the path at the given <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">coordinate</span><span 
class="cmsy-10">&gt;</span>. If a path has already
     been partly constructed, this command will end the current part of the path and start a new
     one.
     <!--l. 76--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-435-" ><colgroup id="TBL-435-1g"><col 
id="TBL-435-1"><col 
id="TBL-435-2"></colgroup><tr  
 valign="baseline" id="TBL-435-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-435-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-512.svg" width="115.3439 " height="39.47017 " type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-435-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{pgfpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathmoveto{\pgfpointorigin}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathlineto{\pgfpoint{1cm}{1cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathlineto{\pgfpoint{2cm}{1cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathlineto{\pgfpoint{3cm}{0.5cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathlineto{\pgfpoint{3cm}{0cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfsetfillcolor{examplefill}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfusepath{fill,stroke}</span>
<br><span 
class="cmtt-8">\end{pgfpicture}</span></div>                                                                                              </td></tr></table> </td>
</tr></table></div>
     <!--l. 87--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-436-" ><colgroup id="TBL-436-1g"><col 
id="TBL-436-1"><col 
id="TBL-436-2"></colgroup><tr  
 valign="baseline" id="TBL-436-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-436-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-513.svg" width="115.3439 " height="39.47017 " type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-436-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{pgfpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathmoveto{\pgfpointorigin}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathlineto{\pgfpoint{1cm}{1cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathlineto{\pgfpoint{2cm}{1cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathmoveto{\pgfpoint{2cm}{1cm}}</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmsltt-10x-x-80">%</span><span 
class="cmsltt-10x-x-80">&nbsp;New</span><span 
class="cmsltt-10x-x-80">&nbsp;part</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathlineto{\pgfpoint{3cm}{0.5cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathlineto{\pgfpoint{3cm}{0cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfsetfillcolor{examplefill}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfusepath{fill,stroke}</span>
<br><span 
class="cmtt-8">\end{pgfpicture}</span></div>                                                                                              </td></tr></table> </td>
</tr></table></div>
     <!--l. 99--><p class="noindent">The command will apply the current coordinate transformation matrix to <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">coordinate</span><span 
class="cmsy-10">&gt; </span>before using
     it.
     <!--l. 102--><p class="noindent">The command will update the bounding box of the current path and picture, if necessary. </dd></dl>
<!--l. 107--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">21.3   </span> <a 
 id="x22-21800021.3"></a>The Line-To Path Operation</h4>
<!--l. 109--><p class="noindent">
     <dl class="description"><dt class="description">
<span 
class="colorbox" id="colorbox218"><span 
class="cmtt-10">\pgfpathlineto</span><span 
class="cmtt-10">{</span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">coordinate</span><span 
class="cmsy-10">&gt;</span><span 
class="cmtt-10">}</span></span> </dt><dd 
class="description">
<a 
 id="dx22-218001"></a>
     <!--l. 110--><p class="noindent">This command extends the current path in a straight line to the given <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">coordinate</span><span 
class="cmsy-10">&gt;</span>. If this command is given
     at the beginning of path without any other path construction command given before (in particular without a
     move-to operation), the <span class="TEX">T<span 
class="E">E</span>X</span>&nbsp;file may compile without an error message, but a viewer application may display
     an error message when trying to render the picture.
     <!--l. 116--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-437-" ><colgroup id="TBL-437-1g"><col 
id="TBL-437-1"><col 
id="TBL-437-2"></colgroup><tr  
 valign="baseline" id="TBL-437-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-437-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-514.svg" width="77.40703 " height="39.47017 " type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-437-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{pgfpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathmoveto{\pgfpointorigin}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathlineto{\pgfpoint{1cm}{1cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathlineto{\pgfpoint{2cm}{1cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfsetfillcolor{examplefill}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfusepath{fill,stroke}</span>
<br><span 
class="cmtt-8">\end{pgfpicture}</span></div>                                                                                              </td></tr></table> </td>
</tr></table></div>
                                                                                         
                                                                                         
     <!--l. 125--><p class="noindent">The command will apply the current coordinate transformation matrix to <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">coordinate</span><span 
class="cmsy-10">&gt; </span>before using
     it.
     <!--l. 128--><p class="noindent">The command will update the bounding box of the current path and picture, if necessary. </dd></dl>
<!--l. 133--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">21.4   </span> <a 
 id="x22-21900021.4"></a>The Curve-To Path Operation</h4>
<!--l. 135--><p class="noindent">
     <dl class="description"><dt class="description">
<span 
class="colorbox" id="colorbox219"><span 
class="cmtt-10">\pgfpathcurveto</span><span 
class="cmtt-10">{</span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">support 1</span><span 
class="cmsy-10">&gt;</span><span 
class="cmtt-10">}{</span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">support 2</span><span 
class="cmsy-10">&gt;</span><span 
class="cmtt-10">}{</span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">coordinate</span><span 
class="cmsy-10">&gt;</span><span 
class="cmtt-10">}</span></span> </dt><dd 
class="description">
<a 
 id="dx22-219001"></a>
     <!--l. 136--><p class="noindent">This  command  extends  the  current  path  with  a  B&eacute;zier  curve  from  the  last  point  of  the  path  to
     <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">coordinate</span><span 
class="cmsy-10">&gt;</span>. The <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">support 1</span><span 
class="cmsy-10">&gt; </span>and <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">support 2</span><span 
class="cmsy-10">&gt; </span>are the first and second support point of the B&eacute;zier
     curve. For more information on B&eacute;zier curve, please consult a standard textbook on computer graphics.
     <!--l. 142--><p class="noindent">Like the line-to command, this command may not be the first path construction command in a
     path.
     <!--l. 144--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-438-" ><colgroup id="TBL-438-1g"><col 
id="TBL-438-1"><col 
id="TBL-438-2"></colgroup><tr  
 valign="baseline" id="TBL-438-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-438-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-515.svg" width="115.3439 " height="39.47017 " type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-438-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{pgfpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathmoveto{\pgfpointorigin}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathcurveto</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;{\pgfpoint{1cm}{1cm}}{\pgfpoint{2cm}{1cm}}{\pgfpoint{3cm}{0cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfsetfillcolor{examplefill}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfusepath{fill,stroke}</span>
<br><span 
class="cmtt-8">\end{pgfpicture}</span></div>                                                                                              </td></tr></table> </td>
</tr></table></div>
     <!--l. 153--><p class="noindent">The command will apply the current coordinate transformation matrix to <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">coordinate</span><span 
class="cmsy-10">&gt; </span>before using
     it.
     <!--l. 156--><p class="noindent">The command will update the bounding box of the current path and picture, if necessary. However, the
     bounding box is simply made large enough such that it encompasses all of the support points and
     the <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">coordinate</span><span 
class="cmsy-10">&gt;</span>. This will guarantee that the curve is completely inside the bounding box, but
     the bounding box will typically be quite a bit too large. It is not clear (to me) how this can be
     avoided without resorting to &#8220;some serious math&#8221; in order to calculate a precise bounding box.
     </dd></dl>
<!--l. 167--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">21.5   </span> <a 
 id="x22-22000021.5"></a>The Close Path Operation</h4>
<!--l. 169--><p class="noindent">
     <dl class="description"><dt class="description">
<span 
class="colorbox" id="colorbox220"><span 
class="cmtt-10">\pgfpathclose</span></span> </dt><dd 
class="description">
<a 
 id="dx22-220001"></a>
     <!--l. 170--><p class="noindent">This command closes the current part of the path by appending a straight line to the start point of the current
     part. Note that there <span 
class="cmti-10">is </span>a difference between closing a path and using the line-to operation to add a straight
     line to the start of the current path. The difference is demonstrated by the upper corners of the triangles in
     the following example:
                                                                                         
                                                                                         
     <!--l. 176--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-439-" ><colgroup id="TBL-439-1g"><col 
id="TBL-439-1"><col 
id="TBL-439-2"></colgroup><tr  
 valign="baseline" id="TBL-439-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-439-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-516.svg" width="118.27718 " height="118.27718 " type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-439-1-2"  
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;\draw[help</span><span 
class="cmtt-8">&nbsp;lines]</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;grid</span><span 
class="cmtt-8">&nbsp;(3,2);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfsetlinewidth{5pt}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathmoveto{\pgfpoint{1cm}{1cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathlineto{\pgfpoint{0cm}{-1cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathlineto{\pgfpoint{1cm}{-1cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathclose</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathmoveto{\pgfpoint{2.5cm}{1cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathlineto{\pgfpoint{1.5cm}{-1cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathlineto{\pgfpoint{2.5cm}{-1cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathlineto{\pgfpoint{2.5cm}{1cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfusepath{stroke}</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
     </dd></dl>
<!--l. 194--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">21.6   </span> <a 
 id="x22-22100021.6"></a>Arc, Ellipse and Circle Path Operations</h4>
<!--l. 196--><p class="noindent">The path construction commands that we have discussed up to now are sufficient to create all paths that can be
created &#8220;at all.&#8221; However, it is useful to have special commands to create certain shapes, like circles, that arise often
in practice.
<!--l. 201--><p class="indent">   In the following, the commands for adding (parts of) (transformed) circles to a path are described.
<!--l. 205--><p class="indent">
     <dl class="description"><dt class="description">
<span 
class="colorbox" id="colorbox221"><span 
class="cmtt-10">\pgfpatharc</span><span 
class="cmtt-10">{</span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">start angle</span><span 
class="cmsy-10">&gt;</span><span 
class="cmtt-10">}{</span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">end angle</span><span 
class="cmsy-10">&gt;</span><span 
class="cmtt-10">}{</span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">radius</span><span 
class="cmsy-10">&gt;</span><span 
class="cmtt-10">}</span></span> </dt><dd 
class="description">
<a 
 id="dx22-221001"></a>
     <!--l. 206--><p class="noindent">This command appends a part of a circle (or an ellipse) to the current path. Imaging the curve between
     <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">start angle</span><span 
class="cmsy-10">&gt; </span>and <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">end angle</span><span 
class="cmsy-10">&gt; </span>on a circle of radius <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">radius</span><span 
class="cmsy-10">&gt; </span>(if <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">start angle</span><span 
class="cmsy-10">&gt; </span><span 
class="cmmi-10">&lt; </span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">end angle</span><span 
class="cmsy-10">&gt;</span>, the curve
     goes around the circle counterclockwise, otherwise clockwise). This curve is now moved such that the
     point where the curve starts is the previous last point of the path. Note that this command will <span 
class="cmti-10">not</span>
     start a new part of the path, which is important for example for filling purposes.
     <!--l. 215--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-440-" ><colgroup id="TBL-440-1g"><col 
id="TBL-440-1"><col 
id="TBL-440-2"></colgroup><tr  
 valign="baseline" id="TBL-440-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-440-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-517.svg" width="133.91231 " height="77.14032 " type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-440-1-2"  
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;\draw[help</span><span 
class="cmtt-8">&nbsp;lines]</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;grid</span><span 
class="cmtt-8">&nbsp;(3,2);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathmoveto{\pgfpointorigin}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathlineto{\pgfpoint{0cm}{1cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpatharc{180}{90}{.5cm}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathlineto{\pgfpoint{3cm}{1.5cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpatharc{90}{-45}{.5cm}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfusepath{fill}</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
     <!--l. 227--><p class="noindent">Saying <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\pgfpatharc{0}{360}{1cm}</span></span></span> &#8220;nearly&#8221; gives you a full circle. The &#8220;nearly&#8221; refers to the fact that the
     circle will not be closed. You can close it using <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\pgfpathclose</span></span></span>.
     <!--l. 231--><p class="noindent">The <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">radius</span><span 
class="cmsy-10">&gt; </span>need not always be a single <span class="TEX">T<span 
class="E">E</span>X</span>&nbsp;dimension. Instead, it can also contain a slash,
     in which case it must consist of two dimensions separated by this slash. In this case the first
     dimension is the <span 
class="cmmi-10">x</span>-radius and the second the <span 
class="cmmi-10">y</span>-radius of the ellipse from which the curve is
     taken:
                                                                                         
                                                                                         
     <!--l. 237--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-441-" ><colgroup id="TBL-441-1g"><col 
id="TBL-441-1"><col 
id="TBL-441-2"></colgroup><tr  
 valign="baseline" id="TBL-441-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-441-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-518.svg" width="131.05789 " height="77.27367 " type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-441-1-2"  
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;\draw[help</span><span 
class="cmtt-8">&nbsp;lines]</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;grid</span><span 
class="cmtt-8">&nbsp;(3,2);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathmoveto{\pgfpointorigin}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpatharc{180}{45}{2cm/1cm}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfusepath{draw}</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
     <!--l. 246--><p class="noindent">The axes of the circle or ellipse from which the arc is &#8220;taken&#8221; always point up and right. However, the current
     coordinate transformation matrix will have an effect on the arc. This can be used to, say, rotate an
     arc:
     <!--l. 251--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-442-" ><colgroup id="TBL-442-1g"><col 
id="TBL-442-1"><col 
id="TBL-442-2"></colgroup><tr  
 valign="baseline" id="TBL-442-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-442-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-519.svg" width="125.73721 " height="89.52711 " type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-442-1-2"  
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;\draw[help</span><span 
class="cmtt-8">&nbsp;lines]</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;grid</span><span 
class="cmtt-8">&nbsp;(3,2);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgftransformrotate{30}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathmoveto{\pgfpointorigin}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpatharc{180}{45}{2cm/1cm}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfusepath{draw}</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
     <!--l. 261--><p class="noindent">The command will update the bounding box of the current path and picture, if necessary. Unless rotation or
     shearing transformations are applied, the bounding box will be tight. </dd></dl>
<!--l. 267--><p class="indent">
     <dl class="description"><dt class="description">
<span 
class="colorbox" id="colorbox222"><span 
class="cmtt-10">\pgfpathellipse</span><span 
class="cmtt-10">{</span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">center</span><span 
class="cmsy-10">&gt;</span><span 
class="cmtt-10">}{</span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">first axis</span><span 
class="cmsy-10">&gt;</span><span 
class="cmtt-10">}{</span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">second axis</span><span 
class="cmsy-10">&gt;</span><span 
class="cmtt-10">}</span></span> </dt><dd 
class="description">
<a 
 id="dx22-221002"></a>
     <!--l. 268--><p class="noindent">The effect of this command is to append an ellipse to the current path (if the path is not empty, a
     new part is started). The ellipse&#8217;s center will be <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">center</span><span 
class="cmsy-10">&gt; </span>and <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">first axis</span><span 
class="cmsy-10">&gt; </span>and <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">second axis</span><span 
class="cmsy-10">&gt; </span>are the
     axis <span 
class="cmti-10">vectors</span>. The same effect as this command can also be achieved using an appropriate sequence of
     move-to, arc, and close operations, but this command is easier and faster.
     <!--l. 276--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-443-" ><colgroup id="TBL-443-1g"><col 
id="TBL-443-1"><col 
id="TBL-443-2"></colgroup><tr  
 valign="baseline" id="TBL-443-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-443-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-520.svg" width="134.17896 " height="125.73784 " type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-443-1-2"  
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;\draw[help</span><span 
class="cmtt-8">&nbsp;lines]</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;grid</span><span 
class="cmtt-8">&nbsp;(3,2);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathellipse{\pgfpoint{1cm}{0cm}}</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;{\pgfpoint{1.5cm}{0cm}}</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;{\pgfpoint{0cm}{1cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfusepath{draw}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\color{red}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathellipse{\pgfpoint{1cm}{0cm}}</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;{\pgfpoint{1cm}{1cm}}</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;{\pgfpoint{-0.5cm}{0.5cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfusepath{draw}</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
     <!--l. 291--><p class="noindent">The command will apply coordinate transformations to all coordinates of the ellipse. However, the coordinate
                                                                                         
                                                                                         
     transformations are applied only after the ellipse is &#8220;finished conceptually.&#8221; Thus, a transformation of 1cm to
     the right will simply shift the ellipse one centimeter to the right; it will not add 1cm to the <span 
class="cmmi-10">x</span>-coordinates of
     the two axis vectors.
     <!--l. 298--><p class="noindent">The command will update the bounding box of the current path and picture, if necessary. </dd></dl>
<!--l. 302--><p class="indent">
     <dl class="description"><dt class="description">
<span 
class="colorbox" id="colorbox223"><span 
class="cmtt-10">\pgfpathcirlce</span><span 
class="cmtt-10">{</span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">center</span><span 
class="cmsy-10">&gt;</span><span 
class="cmtt-10">}{</span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">radius</span><span 
class="cmsy-10">&gt;</span><span 
class="cmtt-10">}</span></span> </dt><dd 
class="description">
<a 
 id="dx22-221003"></a>
     <!--l. 303--><p class="noindent">A shorthand for <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\pgfpathellipse</span></span></span> applied to <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">center</span><span 
class="cmsy-10">&gt; </span>and the two axis vectors (<span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">radius</span><span 
class="cmsy-10">&gt;</span><span 
class="cmmi-10">,</span>0) and
     (0<span 
class="cmmi-10">,</span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">radius</span><span 
class="cmsy-10">&gt;</span>). </dd></dl>
<!--l. 308--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">21.7   </span> <a 
 id="x22-22200021.7"></a>Rectangle Path Operations</h4>
<!--l. 310--><p class="noindent">Another shape that arises frequently is the rectangle. Two commands can be used to add a rectangle to the current
path. Both commands will start a new part of the path.
<!--l. 315--><p class="indent">
     <dl class="description"><dt class="description">
<span 
class="colorbox" id="colorbox224"><span 
class="cmtt-10">\pgfpathrectangle</span><span 
class="cmtt-10">{</span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">corner</span><span 
class="cmsy-10">&gt;</span><span 
class="cmtt-10">}{</span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">diagonal vector</span><span 
class="cmsy-10">&gt;</span><span 
class="cmtt-10">}</span></span> </dt><dd 
class="description">
<a 
 id="dx22-222001"></a>
     <!--l. 316--><p class="noindent">Adds a rectangle to the path whose one corner is <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">corner</span><span 
class="cmsy-10">&gt; </span>and whose opposite corner is given by
     <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">corner</span><span 
class="cmsy-10">&gt; </span>+ <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">diagonal vector</span><span 
class="cmsy-10">&gt;</span>.
     <!--l. 320--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-444-" ><colgroup id="TBL-444-1g"><col 
id="TBL-444-1"><col 
id="TBL-444-2"></colgroup><tr  
 valign="baseline" id="TBL-444-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-444-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-521.svg" width="134.17897 " height="77.27367 " type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-444-1-2"  
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;\draw[help</span><span 
class="cmtt-8">&nbsp;lines]</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;grid</span><span 
class="cmtt-8">&nbsp;(3,2);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathrectangle{\pgfpoint{1cm}{0cm}}{\pgfpoint{1.5cm}{1cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathrectangle{\pgfpoint{1.5cm}{0.25cm}}{\pgfpoint{1.5cm}{1cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathrectangle{\pgfpoint{2cm}{0.5cm}}{\pgfpoint{1.5cm}{1cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfusepath{draw}</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
     <!--l. 329--><p class="noindent">The command will apply coordinate transformations and update the bounding boxes tightly.
     </dd></dl>
<!--l. 334--><p class="indent">
     <dl class="description"><dt class="description">
<span 
class="colorbox" id="colorbox225"><span 
class="cmtt-10">\pgfpathrectanglecorners</span><span 
class="cmtt-10">{</span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">corner</span><span 
class="cmsy-10">&gt;</span><span 
class="cmtt-10">}{</span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">opposite corner</span><span 
class="cmsy-10">&gt;</span><span 
class="cmtt-10">}</span></span> </dt><dd 
class="description">
<a 
 id="dx22-222002"></a>
     <!--l. 335--><p class="noindent">Adds a rectangle to the path whose two opposing corners are <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">corner</span><span 
class="cmsy-10">&gt; </span>and <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">opposite corner</span><span 
class="cmsy-10">&gt;</span>.
     <!--l. 337--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-445-" ><colgroup id="TBL-445-1g"><col 
id="TBL-445-1"><col 
id="TBL-445-2"></colgroup><tr  
 valign="baseline" id="TBL-445-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-445-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-522.svg" width="115.07718 " height="77.27367 " type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-445-1-2"  
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;\draw[help</span><span 
class="cmtt-8">&nbsp;lines]</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;grid</span><span 
class="cmtt-8">&nbsp;(3,2);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathrectanglecorners{\pgfpoint{1cm}{0cm}}{\pgfpoint{1.5cm}{1cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfusepath{draw}</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
     <!--l. 344--><p class="noindent">The command will apply coordinate transformations and update the bounding boxes tightly.
     </dd></dl>
                                                                                         
                                                                                         
<!--l. 350--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">21.8   </span> <a 
 id="x22-22300021.8"></a>The Grid Path Operation</h4>
<!--l. 352--><p class="noindent">
     <dl class="description"><dt class="description">
<span 
class="colorbox" id="colorbox226"><span 
class="cmtt-10">\pgfpathgrid</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="cmsy-10">&lt;</span><span 
class="cmti-10">lower left</span><span 
class="cmsy-10">&gt;</span><span 
class="cmtt-10">}{</span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">upper right</span><span 
class="cmsy-10">&gt;</span><span 
class="cmtt-10">}</span></span> </dt><dd 
class="description">
<a 
 id="dx22-223001"></a>
     <!--l. 353--><p class="noindent">Appends a grid to the current path. That is, a (possibly large) number of parts are added to the path,
     each part consisting of a single horizontal or vertical straight line segment.
     <!--l. 357--><p class="noindent">Conceptually, the origin is part of the grid and the grid is clipped to the rectangle specified by the
     <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">lower left</span><span 
class="cmsy-10">&gt; </span>and the <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">upper right</span><span 
class="cmsy-10">&gt; </span>corner. However, no clipping occurs (this command just adds parts to
     the current path). Rather, the points where the lines enter and leave the &#8220;clipping area&#8221; are computed
     and used to add simple lines to the current path.
     <!--l. 364--><p class="noindent">Allowed <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">options</span><span 
class="cmsy-10">&gt; </span>are:
         <ul class="itemize1">
         <li class="itemize"><span 
class="cmtt-10">stepx</span><a 
 id="dx22-223002"></a><a 
 id="dx22-223003"></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">dimension</span><span 
class="cmsy-10">&gt; </span>Sets the horizontal stepping to <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">dimension</span><span 
class="cmsy-10">&gt;</span>. Default is 1cm.
         </li>
         <li class="itemize"><span 
class="cmtt-10">stepy</span><a 
 id="dx22-223004"></a><a 
 id="dx22-223005"></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">dimension</span><span 
class="cmsy-10">&gt; </span>Sets the vertical stepping to <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">dimension</span><span 
class="cmsy-10">&gt;</span>. Default is 1cm.
         </li>
         <li class="itemize"><span 
class="cmtt-10">step</span><a 
 id="dx22-223006"></a><a 
 id="dx22-223007"></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">vector</span><span 
class="cmsy-10">&gt; </span>Sets the horizontal stepping to the <span 
class="cmmi-10">x</span>-coordinate of <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">vector</span><span 
class="cmsy-10">&gt; </span>and the vertical stepping
         to its <span 
class="cmmi-10">y</span>-coordinate.</li></ul>
     <!--l. 374--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-446-" ><colgroup id="TBL-446-1g"><col 
id="TBL-446-1"><col 
id="TBL-446-2"></colgroup><tr  
 valign="baseline" id="TBL-446-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-446-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-523.svg" width="138.63931 " height="100.70245 " type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-446-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{pgfpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfsetlinewidth{0.8pt}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathgrid[step={\pgfpoint{1cm}{1cm}}]</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;{\pgfpoint{-3mm}{-3mm}}{\pgfpoint{33mm}{23mm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfusepath{stroke}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfsetlinewidth{0.4pt}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathgrid[stepx=1mm,stepy=1mm]</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;{\pgfpoint{-1.5mm}{-1.5mm}}{\pgfpoint{31.5mm}{21.5mm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfusepath{stroke}</span>
<br><span 
class="cmtt-8">\end{pgfpicture}</span></div>                                                                                              </td></tr></table> </td>
</tr></table></div>
     <!--l. 386--><p class="noindent">The command will apply coordinate transformations and update the bounding boxes tightly. As for ellipses,
     the transformations are applied to the &#8220;conceptually finished&#8221; grid.
     <!--l. 389--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular">
<table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-447-" ><colgroup id="TBL-447-1g"><col 
id="TBL-447-1"><col 
id="TBL-447-2"></colgroup><tr  
 valign="baseline" id="TBL-447-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-447-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-524.svg" width="133.37686 " height="133.37686 " type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-447-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{pgfpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgftransformrotate{10}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathgrid[stepx=1mm,stepy=2mm]{\pgfpoint{0mm}{0mm}}{\pgfpoint{30mm}{30mm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfusepath{stroke}</span>
<br><span 
class="cmtt-8">\end{pgfpicture}</span></div>                                                                                              </td></tr></table> </td>
</tr></table></div>
     </dd></dl>
                                                                                         
                                                                                         
<!--l. 399--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">21.9   </span> <a 
 id="x22-22400021.9"></a>The Parabola Path Operation</h4>
<!--l. 401--><p class="noindent">
     <dl class="description"><dt class="description">
<span 
class="colorbox" id="colorbox227"><span 
class="cmtt-10">\pgfpathparabola</span><span 
class="cmtt-10">{</span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">bend vector</span><span 
class="cmsy-10">&gt;</span><span 
class="cmtt-10">}{</span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">end vector</span><span 
class="cmsy-10">&gt;</span><span 
class="cmtt-10">}</span></span> </dt><dd 
class="description">
<a 
 id="dx22-224001"></a>
     <!--l. 402--><p class="noindent">This command appends two half-parabolas to the current path. The first starts at the current point
     and ends at the current point plus <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">bend vector</span><span 
class="cmsy-10">&gt;</span>. At his point, it has its bend. The second half parabola
     starts at that bend point and end at point that is given by the bend plus <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">end vector</span><span 
class="cmsy-10">&gt;</span>.
     <!--l. 408--><p class="noindent">If you set <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">end vector</span><span 
class="cmsy-10">&gt; </span>to the null vector, you append only a half parabola that goes from the current
     point to the bend; by setting <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">bend vector</span><span 
class="cmsy-10">&gt; </span>to the null vector, you append only a half parabola that
     goes to current point plus <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">end vector</span><span 
class="cmsy-10">&gt; </span>and has its bend at the current point.
     <!--l. 414--><p class="noindent">It is not possible to use this command to draw a part of a parabola that does not contain the bend.
     <!--l. 417--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-448-" ><colgroup id="TBL-448-1g"><col 
id="TBL-448-1"><col 
id="TBL-448-2"></colgroup><tr  
 valign="baseline" id="TBL-448-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-448-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-525.svg" width="153.28075 " height="191.21764 " type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-448-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{pgfpicture}</span>
<br><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;Half-parabola</span><span 
class="cmsltt-10x-x-80">&nbsp;going</span><span 
class="cmsltt-10x-x-80">&nbsp;``up</span><span 
class="cmsltt-10x-x-80">&nbsp;and</span><span 
class="cmsltt-10x-x-80">&nbsp;right''</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathmoveto{\pgfpointorigin}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathparabola{\pgfpointorigin}{\pgfpoint{2cm}{4cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\color{red}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfusepath{stroke}</span>
<br>
<br><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;Half-parabola</span><span 
class="cmsltt-10x-x-80">&nbsp;going</span><span 
class="cmsltt-10x-x-80">&nbsp;``down</span><span 
class="cmsltt-10x-x-80">&nbsp;and</span><span 
class="cmsltt-10x-x-80">&nbsp;right''</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathmoveto{\pgfpointorigin}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathparabola{\pgfpoint{-2cm}{4cm}}{\pgfpointorigin}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\color{blue}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfusepath{stroke}</span>
<br>
<br><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;Full</span><span 
class="cmsltt-10x-x-80">&nbsp;parabola</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathmoveto{\pgfpoint{-2cm}{2cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathparabola{\pgfpoint{1cm}{-1cm}}{\pgfpoint{2cm}{4cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\color{orange}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfusepath{stroke}</span>
<br><span 
class="cmtt-8">\end{pgfpicture}</span></div>                                                                                              </td></tr></table> </td>
</tr></table></div>
     <!--l. 438--><p class="noindent">The command will apply coordinate transformations and update the bounding boxes. </dd></dl>
<!--l. 443--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">21.10   </span> <a 
 id="x22-22500021.10"></a>Sine and Cosine Path Operations</h4>
<!--l. 445--><p class="noindent">Sine and cosine curves often need to be drawn and the following commands may help with this. However, they only
allow you to append sine and cosine curves in intervals that are multiples of <span 
class="cmmi-10"><img 
src="cmmi10-19.png" alt="p" class="10x-x-19" />/</span>2.
<!--l. 449--><p class="indent">
     <dl class="description"><dt class="description">
<span 
class="colorbox" id="colorbox228"><span 
class="cmtt-10">\pgfpathsine</span><span 
class="cmtt-10">{</span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">vector</span><span 
class="cmsy-10">&gt;</span><span 
class="cmtt-10">}</span></span> </dt><dd 
class="description">
<a 
 id="dx22-225001"></a>
     <!--l. 450--><p class="noindent">This command appends a sine curve in the interval [0<span 
class="cmmi-10">,<img 
src="cmmi10-19.png" alt="p" class="10x-x-19" />/</span>2] to the current path. The sine curve is squeezed or
     stretched such that the curve starts at the current point and ends at the current point plus
     <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">vector</span><span 
class="cmsy-10">&gt;</span>.
                                                                                         
                                                                                         
     <!--l. 454--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-449-" ><colgroup id="TBL-449-1g"><col 
id="TBL-449-1"><col 
id="TBL-449-2"></colgroup><tr  
 valign="baseline" id="TBL-449-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-449-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-526.svg" width="153.14738 " height="115.34387 " type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-449-1-2"  
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;\draw[help</span><span 
class="cmtt-8">&nbsp;lines]</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;grid</span><span 
class="cmtt-8">&nbsp;(3,1);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathmoveto{\pgfpoint{1cm}{0cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathsine{\pgfpoint{1cm}{1cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfusepath{stroke}</span>
<br>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\color{red}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathmoveto{\pgfpoint{1cm}{0cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathsine{\pgfpoint{-2cm}{-2cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfusepath{stroke}</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
     <!--l. 467--><p class="noindent">The command will apply coordinate transformations and update the bounding boxes. </dd></dl>
<!--l. 471--><p class="indent">
     <dl class="description"><dt class="description">
<span 
class="colorbox" id="colorbox229"><span 
class="cmtt-10">\pgfpathcosine</span><span 
class="cmtt-10">{</span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">vector</span><span 
class="cmsy-10">&gt;</span><span 
class="cmtt-10">}</span></span> </dt><dd 
class="description">
<a 
 id="dx22-225002"></a>
     <!--l. 472--><p class="noindent">This command appends a cosine curve in the interval [0<span 
class="cmmi-10">,<img 
src="cmmi10-19.png" alt="p" class="10x-x-19" />/</span>2] to the current path. The curve is squeezed or
     stretched such that the curve starts at the current point and ends at the current point plus <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">vector</span><span 
class="cmsy-10">&gt;</span>. Using
     several sine and cosine operations in sequence allows you to produce a complete sine or cosine
     curve
     <!--l. 477--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-450-" ><colgroup id="TBL-450-1g"><col 
id="TBL-450-1"><col 
id="TBL-450-2"></colgroup><tr  
 valign="baseline" id="TBL-450-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-450-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-527.svg" width="153.2807 " height="77.40701 " type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-450-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{pgfpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathmoveto{\pgfpoint{0cm}{0cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathsine{\pgfpoint{1cm}{1cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathcosine{\pgfpoint{1cm}{-1cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathsine{\pgfpoint{1cm}{-1cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathcosine{\pgfpoint{1cm}{1cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfsetfillcolor{examplefill}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfusepath{fill,stroke}</span>
<br><span 
class="cmtt-8">\end{pgfpicture}</span></div>                                                                                              </td></tr></table> </td>
</tr></table></div>
     <!--l. 488--><p class="noindent">The command will apply coordinate transformations and update the bounding boxes. </dd></dl>
<!--l. 493--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">21.11   </span> <a 
 id="x22-22600021.11"></a>Plot Path Operations</h4>
<!--l. 495--><p class="noindent">There exist several commands for appending plots to a path. These commands are available through the package
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">pgfbaseplot</span></span></span>. They are documented in Section&nbsp;<a 
href="pgfmanualse29.html#x30-29000029">29<!--tex4ht:ref: section-plots --></a>.
<!--l. 501--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">21.12   </span> <a 
 id="x22-22700021.12"></a>Rounded Corners</h4>
<!--l. 503--><p class="noindent">Normally, when you connect two straight line segments or when you connect two curves that end and start &#8220;at
different angles&#8221; you get &#8220;sharp corners&#8221; between the lines or curves. In some cases it is desirable to produce
&#8220;rounded corners&#8221; instead. Thus, the lines or curves should be shortened a bit and then connected by
arcs.
<!--l. 509--><p class="indent">   <span 
class="cmcsc-10"><small 
class="small-caps">P</small><small 
class="small-caps">G</small><small 
class="small-caps">F</small></span>&nbsp;offers an easy way to achieve this effect, by calling the following two commands.
<!--l. 512--><p class="indent">
                                                                                         
                                                                                         
     <dl class="description"><dt class="description">
<span 
class="colorbox" id="colorbox230"><span 
class="cmtt-10">\pgfsetcornersarced</span><span 
class="cmtt-10">{</span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">point</span><span 
class="cmsy-10">&gt;</span><span 
class="cmtt-10">}</span></span> </dt><dd 
class="description">
<a 
 id="dx22-227001"></a>
     <!--l. 513--><p class="noindent">This command causes all subsequent corners to be replaced by little arcs. The effect of this command
     lasts till the end of the current <span class="TEX">T<span 
class="E">E</span>X</span>&nbsp;scope.
     <!--l. 517--><p class="noindent">The <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">point</span><span 
class="cmsy-10">&gt; </span>dictates how large the corner arc will be. Consider a corner made by two lines <span 
class="cmmi-10">l </span>and&nbsp;<span 
class="cmmi-10">r</span>
     and assume that the line <span 
class="cmmi-10">l </span>comes first on the path. The <span 
class="cmmi-10">x</span>-dimension of the <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">point</span><span 
class="cmsy-10">&gt; </span>decides by how
     much the line&nbsp;<span 
class="cmmi-10">l </span>will be shortened, the <span 
class="cmmi-10">y</span>-dimension of <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">point</span><span 
class="cmsy-10">&gt; </span>decides by how much the line <span 
class="cmmi-10">r </span>will be
     shortened. Then, the shortened lines are connected by an arc.
     <!--l. 524--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-451-" ><colgroup id="TBL-451-1g"><col 
id="TBL-451-1"><col 
id="TBL-451-2"></colgroup><tr  
 valign="baseline" id="TBL-451-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-451-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-528.svg" width="115.3439 " height="77.40703 " type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-451-1-2"  
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;\draw[help</span><span 
class="cmtt-8">&nbsp;lines]</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;grid</span><span 
class="cmtt-8">&nbsp;(3,2);</span>
<br>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfsetcornersarced{\pgfpoint{5mm}{5mm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathrectanglecorners{\pgfpointorigin}{\pgfpoint{3cm}{2cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfusepath{stroke}</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
     <!--l. 534--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-452-" ><colgroup id="TBL-452-1g"><col 
id="TBL-452-1"><col 
id="TBL-452-2"></colgroup><tr  
 valign="baseline" id="TBL-452-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-452-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-529.svg" width="115.3439 " height="77.40703 " type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-452-1-2"  
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;\draw[help</span><span 
class="cmtt-8">&nbsp;lines]</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;grid</span><span 
class="cmtt-8">&nbsp;(3,2);</span>
<br>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfsetcornersarced{\pgfpoint{10mm}{5mm}}</span>
<br><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;10mm</span><span 
class="cmsltt-10x-x-80">&nbsp;entering,</span>
<br><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;5mm</span><span 
class="cmsltt-10x-x-80">&nbsp;leaving.</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathmoveto{\pgfpointorigin}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathlineto{\pgfpoint{0cm}{2cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathlineto{\pgfpoint{3cm}{2cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathcurveto</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;{\pgfpoint{3cm}{0cm}}</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;{\pgfpoint{2cm}{0cm}}</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;{\pgfpoint{1cm}{0cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfusepath{stroke}</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
     <!--l. 552--><p class="noindent">If the <span 
class="cmmi-10">x</span>- and <span 
class="cmmi-10">y</span>-coordinates of <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">point</span><span 
class="cmsy-10">&gt; </span>are the same and the corner is a right angle, you will get a perfect
     quarter circle (well, not quite perfect, but perfect up to six decimals). When the angle is not 90<sup ><span 
class="cmsy-7"><span class="htf-cmbx">o</span></span></sup>, you only get
     a fair approximation.
     <!--l. 557--><p class="noindent">More or less &#8220;all&#8221; corners will be rounded, even the corner generated by a <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\pgfpathclose</span></span></span> command. (The
     author is a bit proud of this feature.)
     <!--l. 561--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-453-" ><colgroup id="TBL-453-1g"><col 
id="TBL-453-1"><col 
id="TBL-453-2"></colgroup><tr  
 valign="baseline" id="TBL-453-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-453-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-530.svg" width="70.16187 " height="73.69295 " type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-453-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{pgfpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfsetcornersarced{\pgfpoint{4pt}{4pt}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathmoveto{\pgfpointpolar{0}{1cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathlineto{\pgfpointpolar{72}{1cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathlineto{\pgfpointpolar{144}{1cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathlineto{\pgfpointpolar{216}{1cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathlineto{\pgfpointpolar{288}{1cm}}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfpathclose</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\pgfusepath{stroke}</span>
<br><span 
class="cmtt-8">\end{pgfpicture}</span></div>                                                                                              </td></tr></table> </td>
</tr></table></div>
                                                                                         
                                                                                         
     <!--l. 574--><p class="noindent">To return to normal (unrounded) corners, use <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\pgfsetcornersarced{\pgfpointorigin}</span></span></span>.
     <!--l. 577--><p class="noindent">Note that the rounding will produce strange and undesirable effects if the lines at the corners are too short. In
     this case the shortening may cause the lines to &#8220;suddenly extend over the other end&#8221; which is rarely desirable.
     </dd></dl>
<!--l. 586--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">21.13   </span> <a 
 id="x22-22800021.13"></a>Internal Tracking of Bounding Boxes for Paths and Pictures</h4>
<!--l. 592--><p class="noindent">The path construction commands keep track of two bounding boxes: One for the current path, which is reset
whenever the path is used and thereby flushed, and a bounding box for the current <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">{pgfpicture}</span></span></span>.
<!--l. 596--><p class="indent">   The bounding boxes are not accessible by &#8220;normal&#8221; macros. Rather, two sets of four dimension variables are
used for this, all of which contain the letter&nbsp;<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">@</span></span></span>.
<!--l. 600--><p class="indent">
     <dl class="description"><dt class="description">
<span 
class="colorbox" id="colorbox231"><span 
class="cmtt-10">\pgf@pathminx</span></span> </dt><dd 
class="description">
<a 
 id="dx22-228001"></a>
     <!--l. 601--><p class="noindent">The minimum <span 
class="cmmi-10">x</span>-coordinate &#8220;mentioned&#8221; in the current path. Initially, this is set to 16000pt. </dd></dl>
<!--l. 605--><p class="indent">
     <dl class="description"><dt class="description">
<span 
class="colorbox" id="colorbox232"><span 
class="cmtt-10">\pgf@pathmaxx</span></span> </dt><dd 
class="description">
<a 
 id="dx22-228002"></a>
     <!--l. 606--><p class="noindent">The maximum <span 
class="cmmi-10">x</span>-coordinate &#8220;mentioned&#8221; in the current path. Initially, this is set to <span 
class="cmsy-10">-</span>16000pt. </dd></dl>
<!--l. 610--><p class="indent">
     <dl class="description"><dt class="description">
<span 
class="colorbox" id="colorbox233"><span 
class="cmtt-10">\pgf@pathminy</span></span> </dt><dd 
class="description">
<a 
 id="dx22-228003"></a>
     <!--l. 611--><p class="noindent">The minimum <span 
class="cmmi-10">y</span>-coordinate &#8220;mentioned&#8221; in the current path. Initially, this is set to 16000pt. </dd></dl>
<!--l. 615--><p class="indent">
     <dl class="description"><dt class="description">
<span 
class="colorbox" id="colorbox234"><span 
class="cmtt-10">\pgf@pathmaxy</span></span> </dt><dd 
class="description">
<a 
 id="dx22-228004"></a>
     <!--l. 616--><p class="noindent">The maximum <span 
class="cmmi-10">y</span>-coordinate &#8220;mentioned&#8221; in the current path. Initially, this is set to <span 
class="cmsy-10">-</span>16000pt. </dd></dl>
<!--l. 620--><p class="indent">
     <dl class="description"><dt class="description">
<span 
class="colorbox" id="colorbox235"><span 
class="cmtt-10">\pgf@picminx</span></span> </dt><dd 
class="description">
<a 
 id="dx22-228005"></a>
     <!--l. 621--><p class="noindent">The minimum <span 
class="cmmi-10">x</span>-coordinate &#8220;mentioned&#8221; in the current picture. Initially, this is set to 16000pt. </dd></dl>
<!--l. 625--><p class="indent">
     <dl class="description"><dt class="description">
<span 
class="colorbox" id="colorbox236"><span 
class="cmtt-10">\pgf@picmaxx</span></span> </dt><dd 
class="description">
<a 
 id="dx22-228006"></a>
     <!--l. 626--><p class="noindent">The maximum <span 
class="cmmi-10">x</span>-coordinate &#8220;mentioned&#8221; in the current picture. Initially, this is set to <span 
class="cmsy-10">-</span>16000pt. </dd></dl>
<!--l. 630--><p class="indent">
     <dl class="description"><dt class="description">
<span 
class="colorbox" id="colorbox237"><span 
class="cmtt-10">\pgf@picminy</span></span> </dt><dd 
class="description">
<a 
 id="dx22-228007"></a>
     <!--l. 631--><p class="noindent">The minimum <span 
class="cmmi-10">y</span>-coordinate &#8220;mentioned&#8221; in the current picture. Initially, this is set to 16000pt. </dd></dl>
                                                                                         
                                                                                         
<!--l. 635--><p class="indent">
     <dl class="description"><dt class="description">
<span 
class="colorbox" id="colorbox238"><span 
class="cmtt-10">\pgf@picmaxy</span></span> </dt><dd 
class="description">
<a 
 id="dx22-228008"></a>
     <!--l. 636--><p class="noindent">The maximum <span 
class="cmmi-10">y</span>-coordinate &#8220;mentioned&#8221; in the current picture. Initially, this is set to <span 
class="cmsy-10">-</span>16000pt. </dd></dl>
<!--l. 641--><p class="indent">   Each time a path construction command is called, the above variables are (globally) updated. To facilitate this,
you can use the following command:
<!--l. 645--><p class="indent">
     <dl class="description"><dt class="description">
<span 
class="colorbox" id="colorbox239"><span 
class="cmtt-10">\pgf@protocolsizes</span><span 
class="cmtt-10">{</span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">x-dimension</span><span 
class="cmsy-10">&gt;</span><span 
class="cmtt-10">}{</span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">y-dimension</span><span 
class="cmsy-10">&gt;</span><span 
class="cmtt-10">}</span></span> </dt><dd 
class="description">
<a 
 id="dx22-228009"></a>
     <!--l. 646--><p class="noindent">Updates all of the above dimension in such a way that the point specified by the two arguments
     is  inside  both  bounding  boxes.  For  the  picture&#8217;s  bounding  box  this  updating  occurs  only  if
     <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\ifpgf@relevantforpicturesize</span></span></span> is true, see below. </dd></dl>
<!--l. 652--><p class="indent">   For the bounding box of the picture it is not always desirable that every path construction command affects this
bounding box. For example, if you have just used a clip command, you do not want anything outside the clipping
area to affect the bounding box. For this reason, there exists a special &#8220;<span class="TEX">T<span 
class="E">E</span>X</span>&nbsp;if&#8221; that (locally) decides whether
updating should be applied to the picture&#8217;s bounding box. Clipping will set this if to false, as will certain other
commands.
<!--l. 660--><p class="indent">
     <dl class="description"><dt class="description">
<span 
class="colorbox" id="colorbox240"><span 
class="cmtt-10">\pgf@relevantforpicturesizefalse</span></span> </dt><dd 
class="description">
<a 
 id="dx22-228010"></a>
     <!--l. 661--><p class="noindent">Suppresses updating of the picture&#8217;s bounding box. </dd></dl>
<!--l. 664--><p class="indent">
     <dl class="description"><dt class="description">
<span 
class="colorbox" id="colorbox241"><span 
class="cmtt-10">\pgf@relevantforpicturesizetrue</span></span> </dt><dd 
class="description">
<a 
 id="dx22-228011"></a>
     <!--l. 665--><p class="noindent">Causes updating of the picture&#8217;s bounding box. </dd></dl>
                                                                                         
                                                                                         
                                                                                         
                                                                                         
                                                                                         
                                                                                         
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