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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)">
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-<!-- 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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