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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>26 Coordinate and Canvas Transformations</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="pgfmanualse27.html" >next</a>] [<a
-href="pgfmanualse25.html" >prev</a>] [<a
-href="pgfmanualse25.html#tailpgfmanualse25.html" >prev-tail</a>] [<a
-href="#tailpgfmanualse26.html">tail</a>] [<a
-href="pgfmanual.html#pgfmanualse26.html" >up</a>] </p></div>
- <h3 class="sectionHead"><span class="titlemark">26 </span> <a
- id="x27-27300026"></a>Coordinate and Canvas Transformations</h3>
-<!--l. 10--><p class="noindent">
- <h4 class="subsectionHead"><span class="titlemark">26.1 </span> <a
- id="x27-27400026.1"></a>Overview</h4>
-<!--l. 12--><p class="noindent"><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 two different ways of scaling, shifting, and rotating (these operations are generally known as
-<span
-class="cmti-10">transformations</span>) graphics: You can apply <span
-class="cmti-10">coordinate transformations </span>to all coordinates and you can apply <span
-class="cmti-10">canvas</span>
-<span
-class="cmti-10">transformations </span>to the canvas on which you draw. (The names &#8220;coordinate&#8221; and &#8220;canvas&#8221; transformations are not
-standard, I introduce them only for the purposes of this manual.)
-<!--l. 20--><p class="indent"> The difference is the following:
- <ul class="itemize1">
- <li class="itemize">As the name &#8220;coordinate transformation&#8221; suggests, coordinate transformations apply only to
- coordinates. For example, when you specify a coordinate like <span class="obeylines-h"><span class="verb"><span
-class="cmtt-10">\pgfpoint{1cm}{2cm}</span></span></span> and you wish
- to &#8220;use&#8221; this coordinate--for example as an argument to a <span class="obeylines-h"><span class="verb"><span
-class="cmtt-10">\pgfpathmoveto</span></span></span> command--then the
- coordinate transformation matrix is applied to the coordinate, resulting in a new coordinate. Continuing
- the example, if the current coordinate transformation is &#8220;scale by a factor of two,&#8221; the coordinate
- <span class="obeylines-h"><span class="verb"><span
-class="cmtt-10">\pgfpoint{1cm}{2cm}</span></span></span> actually designates the point (2cm<span
-class="cmmi-10">,</span>4cm).
- <!--l. 35--><p class="noindent">Note that coordinate transformations apply <span
-class="cmti-10">only </span>to coordinates. They do not apply to, say, line width
- or shadings or text.
- </li>
- <li class="itemize">The effect of a &#8220;canvas transformation&#8221; like &#8220;scale by a factor of two&#8221; can be imagined as follows: You
- first draw your picture on a &#8220;rubber canvas&#8221; normally. Then, once you are done, the whole canvas is
- transformed, in this case stretched by a factor of two. In the resulting image <span
-class="cmti-10">everything </span>will be larger:
- Text, lines, coordinates, and shadings.</li></ul>
-<!--l. 47--><p class="indent"> In many cases, it is preferable that you use coordinate transformations and not canvas transformations. When
-canvas transformations are used, <span
-class="cmcsc-10"><small
-class="small-caps">P</small><small
-class="small-caps">G</small><small
-class="small-caps">F</small></span>&nbsp;looses track of the coordinates of nodes and shapes. Also, canvas
-transformations often cause undesirable effects like changing text size. For these reasons, <span
-class="cmcsc-10"><small
-class="small-caps">P</small><small
-class="small-caps">G</small><small
-class="small-caps">F</small></span>&nbsp;makes it easy to setup
-the coordinate transformation, but a bit harder to change the canvas transformation.
-<!--l. 56--><p class="noindent">
- <h4 class="subsectionHead"><span class="titlemark">26.2 </span> <a
- id="x27-27500026.2"></a>Coordinate Transformations</h4>
-<!--l. 59--><p class="noindent">
- <h5 class="subsubsectionHead"><span class="titlemark">26.2.1 </span> <a
- id="x27-27600026.2.1"></a>How PGF Keeps Track of the Coordinate Transformation Matrix</h5>
-<!--l. 61--><p class="noindent"><span
-class="cmcsc-10"><small
-class="small-caps">P</small><small
-class="small-caps">G</small><small
-class="small-caps">F</small></span>&nbsp;has an internal coordinate transformation matrix. This matrix is applied to coordinates &#8220;in certain situations.&#8221;
-This means that the matrix is not always applied to every coordinate &#8220;no matter what.&#8221; Rather,
-<span
-class="cmcsc-10"><small
-class="small-caps">P</small><small
-class="small-caps">G</small><small
-class="small-caps">F</small></span>&nbsp;tries to be reasonably smart at when and how this matrix should be applied. The most prominent
-examples are the path construction commands, which apply the coordinate transformation matrix to their
-inputs.
-<!--l. 69--><p class="indent"> The coordinate transformation matrix consists of four numbers <span
-class="cmmi-10">a</span>, <span
-class="cmmi-10">b</span>, <span
-class="cmmi-10">c</span>, and <span
-class="cmmi-10">d</span>, and two dimensions <span
-class="cmmi-10">s </span>and <span
-class="cmmi-10">t</span>. When
-the coordinate transformation matrix is applied to a coordinate (<span
-class="cmmi-10">x,y</span>) the new coordinate (<span
-class="cmmi-10">ax </span>+ <span
-class="cmmi-10">by </span>+ <span
-class="cmmi-10">s,cx </span>+ <span
-class="cmmi-10">dy </span>+ <span
-class="cmmi-10">t</span>)
-results. For more details on how transformation matrices work in general, please see, for example, the <span
-class="cmcsc-10"><small
-class="small-caps">P</small><small
-class="small-caps">D</small><small
-class="small-caps">F</small> </span>or
-PostScript reference or a textbook on computer graphics.
-<!--l. 77--><p class="indent"> The coordinate transformation matrix is equal to the identity matrix at the beginning. More precisely, <span
-class="cmmi-10">a </span>= 1,
-<span
-class="cmmi-10">b </span>= 0, <span
-class="cmmi-10">c </span>= 0, <span
-class="cmmi-10">d </span>= 1, <span
-class="cmmi-10">s </span>= 0pt, and <span
-class="cmmi-10">t </span>= 0pt.
-
-
-<!--l. 81--><p class="indent"> The different coordinate transformation commands will modify the matrix by concatenating it with
-another transformation matrix. This way the effect of applying several transformation commands will
-<span
-class="cmti-10">accumulate</span>.
-<!--l. 86--><p class="indent"> The coordinate transformation matrix is local to the current <span class="TEX">T<span
-class="E">E</span>X</span>&nbsp;group (unlike the canvas transformation
-matrix, which is local to the current <span class="obeylines-h"><span class="verb"><span
-class="cmtt-10">{pgfscope}</span></span></span>). Thus, the effect of adding a coordinate transformation to the
-coordinate transformation matrix will last only till the end of the current <span class="TEX">T<span
-class="E">E</span>X</span>&nbsp;group.
-<!--l. 95--><p class="noindent">
- <h5 class="subsubsectionHead"><span class="titlemark">26.2.2 </span> <a
- id="x27-27700026.2.2"></a>Commands for Relative Coordinate Transformations</h5>
-<!--l. 97--><p class="noindent">The following commands add a basic coordinate transformation to the current coordinate transformation matrix.
-For all commands, the transformation is applied <span
-class="cmti-10">in addition </span>to any previous coordinate transformations.
-<!--l. 102--><p class="indent">
- <dl class="description"><dt class="description">
-<span
-class="colorbox" id="colorbox321"><span
-class="cmtt-10">\pgftransformshift</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="dx27-277001"></a>
- <!--l. 103--><p class="noindent">Shifts coordinates by <span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">point</span><span
-class="cmsy-10">&gt;</span>.
- <!--l. 104--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular"
-cellspacing="0" cellpadding="0"
-frame="void" id="TBL-519-" ><colgroup id="TBL-519-1g"><col
-id="TBL-519-1"><col
-id="TBL-519-2"></colgroup><tr
- valign="baseline" id="TBL-519-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-519-1-1"
-class="td11"> &nbsp;<object data="pgfmanual-598.svg" width="115.34386 " 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-519-1-2"
-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;\draw</span><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;</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;--</span><span
-class="cmtt-8">&nbsp;(2,1)</span><span
-class="cmtt-8">&nbsp;--</span><span
-class="cmtt-8">&nbsp;(1,0);</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgftransformshift{\pgfpoint{1cm}{1cm}}</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\draw[red]</span><span
-class="cmtt-8">&nbsp;(0,0)</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;(1,0);</span>
-<br><span
-class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td>
-</tr></table></div>
- </dd></dl>
-<!--l. 114--><p class="indent">
- <dl class="description"><dt class="description">
-<span
-class="colorbox" id="colorbox322"><span
-class="cmtt-10">\pgftransformxshift</span><span
-class="cmtt-10">{</span><span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">dimensions</span><span
-class="cmsy-10">&gt;</span><span
-class="cmtt-10">}</span></span> </dt><dd
-class="description">
-<a
- id="dx27-277002"></a>
- <!--l. 115--><p class="noindent">Shifts coordinates by <span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">dimension</span><span
-class="cmsy-10">&gt; </span>along the <span
-class="cmmi-10">x</span>-axis.
- <!--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-520-" ><colgroup id="TBL-520-1g"><col
-id="TBL-520-1"><col
-id="TBL-520-2"></colgroup><tr
- valign="baseline" id="TBL-520-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-520-1-1"
-class="td11"> &nbsp;<object data="pgfmanual-599.svg" width="115.21051 " 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-520-1-2"
-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;\draw</span><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;</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;--</span><span
-class="cmtt-8">&nbsp;(2,1)</span><span
-class="cmtt-8">&nbsp;--</span><span
-class="cmtt-8">&nbsp;(1,0);</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgftransformxshift{.5cm}</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\draw[red]</span><span
-class="cmtt-8">&nbsp;(0,0)</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;(1,0);</span>
-<br><span
-class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td>
-</tr></table></div>
- </dd></dl>
-<!--l. 126--><p class="indent">
- <dl class="description"><dt class="description">
-<span
-class="colorbox" id="colorbox323"><span
-class="cmtt-10">\pgftransformyshift</span><span
-class="cmtt-10">{</span><span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">dimensions</span><span
-class="cmsy-10">&gt;</span><span
-class="cmtt-10">}</span></span> </dt><dd
-class="description">
-<a
- id="dx27-277003"></a>
- <!--l. 127--><p class="noindent">Like <span class="obeylines-h"><span class="verb"><span
-class="cmtt-10">\pgftransformxshift</span></span></span>, only for the <span
-class="cmmi-10">y</span>-axis. </dd></dl>
-<!--l. 130--><p class="indent">
-
-
- <dl class="description"><dt class="description">
-<span
-class="colorbox" id="colorbox324"><span
-class="cmtt-10">\pgftransformscale</span><span
-class="cmtt-10">{</span><span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">factor</span><span
-class="cmsy-10">&gt;</span><span
-class="cmtt-10">}</span></span> </dt><dd
-class="description">
-<a
- id="dx27-277004"></a>
- <!--l. 131--><p class="noindent">Scales coordinates by <span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">factor</span><span
-class="cmsy-10">&gt;</span>.
- <!--l. 132--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular"
-cellspacing="0" cellpadding="0"
-frame="void" id="TBL-521-" ><colgroup id="TBL-521-1g"><col
-id="TBL-521-1"><col
-id="TBL-521-2"></colgroup><tr
- valign="baseline" id="TBL-521-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-521-1-1"
-class="td11"> &nbsp;<object data="pgfmanual-600.svg" width="115.21051 " 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-521-1-2"
-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;\draw</span><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;</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;--</span><span
-class="cmtt-8">&nbsp;(2,1)</span><span
-class="cmtt-8">&nbsp;--</span><span
-class="cmtt-8">&nbsp;(1,0);</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgftransformscale{.75}</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\draw[red]</span><span
-class="cmtt-8">&nbsp;(0,0)</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;(1,0);</span>
-<br><span
-class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td>
-</tr></table></div>
- </dd></dl>
-<!--l. 142--><p class="indent">
- <dl class="description"><dt class="description">
-<span
-class="colorbox" id="colorbox325"><span
-class="cmtt-10">\pgftransformxscale</span><span
-class="cmtt-10">{</span><span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">factor</span><span
-class="cmsy-10">&gt;</span><span
-class="cmtt-10">}</span></span> </dt><dd
-class="description">
-<a
- id="dx27-277005"></a>
- <!--l. 143--><p class="noindent">Scales coordinates by <span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">factor</span><span
-class="cmsy-10">&gt; </span>in the <span
-class="cmmi-10">x</span>-direction.
- <!--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-522-" ><colgroup id="TBL-522-1g"><col
-id="TBL-522-1"><col
-id="TBL-522-2"></colgroup><tr
- valign="baseline" id="TBL-522-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-522-1-1"
-class="td11"> &nbsp;<object data="pgfmanual-601.svg" width="115.21051 " 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-522-1-2"
-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;\draw</span><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;</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;--</span><span
-class="cmtt-8">&nbsp;(2,1)</span><span
-class="cmtt-8">&nbsp;--</span><span
-class="cmtt-8">&nbsp;(1,0);</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgftransformxscale{.75}</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\draw[red]</span><span
-class="cmtt-8">&nbsp;(0,0)</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;(1,0);</span>
-<br><span
-class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td>
-</tr></table></div>
- </dd></dl>
-<!--l. 155--><p class="indent">
- <dl class="description"><dt class="description">
-<span
-class="colorbox" id="colorbox326"><span
-class="cmtt-10">\pgftransformyscale</span><span
-class="cmtt-10">{</span><span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">factor</span><span
-class="cmsy-10">&gt;</span><span
-class="cmtt-10">}</span></span> </dt><dd
-class="description">
-<a
- id="dx27-277006"></a>
- <!--l. 156--><p class="noindent">Like <span class="obeylines-h"><span class="verb"><span
-class="cmtt-10">\pgftransformxscale</span></span></span>, only for the <span
-class="cmmi-10">y</span>-axis. </dd></dl>
-<!--l. 160--><p class="indent">
- <dl class="description"><dt class="description">
-<span
-class="colorbox" id="colorbox327"><span
-class="cmtt-10">\pgftransformxslant</span><span
-class="cmtt-10">{</span><span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">factor</span><span
-class="cmsy-10">&gt;</span><span
-class="cmtt-10">}</span></span> </dt><dd
-class="description">
-<a
- id="dx27-277007"></a>
- <!--l. 161--><p class="noindent">Slants coordinates by <span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">factor</span><span
-class="cmsy-10">&gt; </span>in the <span
-class="cmmi-10">x</span>-direction. Here, a factor of <span class="obeylines-h"><span class="verb"><span
-class="cmtt-10">1</span></span></span> means 45<sup ><span
-class="cmsy-7"><span class="htf-cmbx">o</span></span></sup>.
- <!--l. 163--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular"
-cellspacing="0" cellpadding="0"
-frame="void" id="TBL-523-" ><colgroup id="TBL-523-1g"><col
-id="TBL-523-1"><col
-id="TBL-523-2"></colgroup><tr
- valign="baseline" id="TBL-523-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-523-1-1"
-class="td11"> &nbsp;<object data="pgfmanual-602.svg" width="115.21051 " 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-523-1-2"
-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;\draw</span><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;</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;--</span><span
-class="cmtt-8">&nbsp;(2,1)</span><span
-class="cmtt-8">&nbsp;--</span><span
-class="cmtt-8">&nbsp;(1,0);</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgftransformxslant{.5}</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\draw[red]</span><span
-class="cmtt-8">&nbsp;(0,0)</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;(1,0);</span>
-<br><span
-class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td>
-</tr></table></div>
-
-
- </dd></dl>
-<!--l. 174--><p class="indent">
- <dl class="description"><dt class="description">
-<span
-class="colorbox" id="colorbox328"><span
-class="cmtt-10">\pgftransformyslant</span><span
-class="cmtt-10">{</span><span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">factor</span><span
-class="cmsy-10">&gt;</span><span
-class="cmtt-10">}</span></span> </dt><dd
-class="description">
-<a
- id="dx27-277008"></a>
- <!--l. 175--><p class="noindent">Slants coordinates by <span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">factor</span><span
-class="cmsy-10">&gt; </span>in the <span
-class="cmmi-10">y</span>-direction.
- <!--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-524-" ><colgroup id="TBL-524-1g"><col
-id="TBL-524-1"><col
-id="TBL-524-2"></colgroup><tr
- valign="baseline" id="TBL-524-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-524-1-1"
-class="td11"> &nbsp;<object data="pgfmanual-603.svg" width="115.21051 " height="115.21051 " type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp; </td><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-524-1-2"
-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;\draw</span><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;</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;--</span><span
-class="cmtt-8">&nbsp;(2,1)</span><span
-class="cmtt-8">&nbsp;--</span><span
-class="cmtt-8">&nbsp;(1,0);</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgftransformyslant{-1}</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\draw[red]</span><span
-class="cmtt-8">&nbsp;(0,0)</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;(1,0);</span>
-<br><span
-class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td>
-</tr></table></div>
- </dd></dl>
-<!--l. 188--><p class="indent">
- <dl class="description"><dt class="description">
-<span
-class="colorbox" id="colorbox329"><span
-class="cmtt-10">\pgftransformrotate</span><span
-class="cmtt-10">{</span><span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">degrees</span><span
-class="cmsy-10">&gt;</span><span
-class="cmtt-10">}</span></span> </dt><dd
-class="description">
-<a
- id="dx27-277009"></a>
- <!--l. 189--><p class="noindent">Rotates coordinates counterclockwise by <span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">degrees</span><span
-class="cmsy-10">&gt;</span>.
- <!--l. 190--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular"
-cellspacing="0" cellpadding="0"
-frame="void" id="TBL-525-" ><colgroup id="TBL-525-1g"><col
-id="TBL-525-1"><col
-id="TBL-525-2"></colgroup><tr
- valign="baseline" id="TBL-525-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-525-1-1"
-class="td11"> &nbsp;<object data="pgfmanual-604.svg" width="115.21051 " 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-525-1-2"
-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;\draw</span><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;</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;--</span><span
-class="cmtt-8">&nbsp;(2,1)</span><span
-class="cmtt-8">&nbsp;--</span><span
-class="cmtt-8">&nbsp;(1,0);</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;\draw[red]</span><span
-class="cmtt-8">&nbsp;(0,0)</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;(1,0);</span>
-<br><span
-class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td>
-</tr></table></div>
- </dd></dl>
-<!--l. 201--><p class="indent">
- <dl class="description"><dt class="description">
-<span
-class="colorbox" id="colorbox330"><span
-class="cmtt-10">\pgftransformcm</span><span
-class="cmtt-10">{</span><span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">a</span><span
-class="cmsy-10">&gt;</span><span
-class="cmtt-10">}{</span><span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">b</span><span
-class="cmsy-10">&gt;</span><span
-class="cmtt-10">}{</span><span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">c</span><span
-class="cmsy-10">&gt;</span><span
-class="cmtt-10">}{</span><span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">d</span><span
-class="cmsy-10">&gt;</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="dx27-277010"></a>
- <!--l. 202--><p class="noindent">Applies the transformation matrix given by <span
-class="cmmi-10">a</span>, <span
-class="cmmi-10">b</span>, <span
-class="cmmi-10">c</span>, and <span
-class="cmmi-10">d </span>and the shift <span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">point</span><span
-class="cmsy-10">&gt; </span>to coordinates (in addition to
- any previous transformations already in force).
-
-
- <!--l. 205--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular">
-<table class="tabular"
-cellspacing="0" cellpadding="0"
-frame="void" id="TBL-526-" ><colgroup id="TBL-526-1g"><col
-id="TBL-526-1"><col
-id="TBL-526-2"></colgroup><tr
- valign="baseline" id="TBL-526-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-526-1-1"
-class="td11"> &nbsp;<object data="pgfmanual-605.svg" width="115.21051 " height="124.82805 " type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp; </td><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-526-1-2"
-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;\draw</span><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;</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;--</span><span
-class="cmtt-8">&nbsp;(2,1)</span><span
-class="cmtt-8">&nbsp;--</span><span
-class="cmtt-8">&nbsp;(1,0);</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgftransformcm{1}{1}{0}{1}{\pgfpoint{.25cm}{.25cm}}</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\draw[red]</span><span
-class="cmtt-8">&nbsp;(0,0)</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;(1,0);</span>
-<br><span
-class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td>
-</tr></table></div>
- </dd></dl>
-<!--l. 216--><p class="indent">
- <dl class="description"><dt class="description">
-<span
-class="colorbox" id="colorbox331"><span
-class="cmtt-10">\pgftransformarrow</span><span
-class="cmtt-10">{</span><span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">start</span><span
-class="cmsy-10">&gt;</span><span
-class="cmtt-10">}{</span><span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">end</span><span
-class="cmsy-10">&gt;</span><span
-class="cmtt-10">}</span></span> </dt><dd
-class="description">
-<a
- id="dx27-277011"></a>
- <!--l. 217--><p class="noindent">Shift coordinates to the end of the line going from <span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">start</span><span
-class="cmsy-10">&gt; </span>to <span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">end</span><span
-class="cmsy-10">&gt; </span>with the correct rotation.
- <!--l. 219--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular"
-cellspacing="0" cellpadding="0"
-frame="void" id="TBL-527-" ><colgroup id="TBL-527-1g"><col
-id="TBL-527-1"><col
-id="TBL-527-2"></colgroup><tr
- valign="baseline" id="TBL-527-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-527-1-1"
-class="td11"> &nbsp;<object data="pgfmanual-606.svg" width="122.99335 " 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-527-1-2"
-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;\draw</span><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;</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;--</span><span
-class="cmtt-8">&nbsp;(3,1);</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgftransformarrow{\pgfpointorigin}{\pgfpoint{3cm}{1cm}}</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgftext{tip}</span>
-<br><span
-class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td>
-</tr></table></div>
- </dd></dl>
-<!--l. 230--><p class="indent">
- <dl class="description"><dt class="description">
-<span
-class="colorbox" id="colorbox332"><span
-class="cmtt-10">\pgftransformlineattime</span><span
-class="cmtt-10">{</span><span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">time</span><span
-class="cmsy-10">&gt;</span><span
-class="cmtt-10">}{</span><span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">start</span><span
-class="cmsy-10">&gt;</span><span
-class="cmtt-10">}{</span><span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">end</span><span
-class="cmsy-10">&gt;</span><span
-class="cmtt-10">}</span></span> </dt><dd
-class="description">
-<a
- id="dx27-277012"></a>
- <!--l. 231--><p class="noindent">Shifts coordinates by a specific point on a line at a specific time. The point by which the coordinate is
- shifted is calculated by calling <span class="obeylines-h"><span class="verb"><span
-class="cmtt-10">\pgfpointlineattime</span></span></span>, see Section&nbsp;<a
-href="pgfmanualse20.html#x21-21000020.4.2">20.4.2<!--tex4ht:ref: section-pointsattime --></a>.
- <!--l. 236--><p class="noindent">In addition to shifting the coordinate, a rotation <span
-class="cmti-10">may </span>also be applied. Whether this is the case depends on
- whether the <span class="TEX">T<span
-class="E">E</span>X</span>&nbsp;if <span class="obeylines-h"><span class="verb"><span
-class="cmtt-10">\ifpgfslopedattime</span></span></span> is set to true or not.
- <!--l. 239--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular"
-cellspacing="0" cellpadding="0"
-frame="void" id="TBL-528-" ><colgroup id="TBL-528-1g"><col
-id="TBL-528-1"><col
-id="TBL-528-2"></colgroup><tr
- valign="baseline" id="TBL-528-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-528-1-1"
-class="td11"> &nbsp;<object data="pgfmanual-607.svg" width="115.21051 " 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-528-1-2"
-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;\draw</span><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;</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;--</span><span
-class="cmtt-8">&nbsp;(2,1);</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgftransformlineattime{.25}{\pgfpointorigin}{\pgfpoint{2cm}{1cm}}</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgftext{Hi!}</span>
-<br><span
-class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td>
-</tr></table></div>
-
-
- <!--l. 247--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular"
-cellspacing="0" cellpadding="0"
-frame="void" id="TBL-529-" ><colgroup id="TBL-529-1g"><col
-id="TBL-529-1"><col
-id="TBL-529-2"></colgroup><tr
- valign="baseline" id="TBL-529-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-529-1-1"
-class="td11"> &nbsp;<object data="pgfmanual-608.svg" width="115.21051 " 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-529-1-2"
-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;\draw</span><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;</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;--</span><span
-class="cmtt-8">&nbsp;(2,1);</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgfslopedattimetrue</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgftransformlineattime{.25}{\pgfpointorigin}{\pgfpoint{2cm}{1cm}}</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgftext{Hi!}</span>
-<br><span
-class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td>
-</tr></table></div>
- <!--l. 257--><p class="noindent">There is another <span class="TEX">T<span
-class="E">E</span>X</span>&nbsp;if that influences this command. If you set <span class="obeylines-h"><span class="verb"><span
-class="cmtt-10">\ifpgfresetnontranslationattime</span></span></span> to
- true, then, between shifting the coordinate and (possibly) rotating/sloping the coordinate, the
- command <span class="obeylines-h"><span class="verb"><span
-class="cmtt-10">\pgftransformresetnontranslations</span></span></span> is called. See the description of this command for
- details.
- <!--l. 262--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular"
-cellspacing="0" cellpadding="0"
-frame="void" id="TBL-530-" ><colgroup id="TBL-530-1g"><col
-id="TBL-530-1"><col
-id="TBL-530-2"></colgroup><tr
- valign="baseline" id="TBL-530-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-530-1-1"
-class="td11"> &nbsp;<object data="pgfmanual-609.svg" width="115.34386 " 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-530-1-2"
-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;\pgftransformscale{1.5}</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\draw</span><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;</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;--</span><span
-class="cmtt-8">&nbsp;(2,1);</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgfslopedattimetrue</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgfresetnontranslationattimefalse</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgftransformlineattime{.25}{\pgfpointorigin}{\pgfpoint{2cm}{1cm}}</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgftext{Hi!}</span>
-<br><span
-class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td>
-</tr></table></div>
- <!--l. 273--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular"
-cellspacing="0" cellpadding="0"
-frame="void" id="TBL-531-" ><colgroup id="TBL-531-1g"><col
-id="TBL-531-1"><col
-id="TBL-531-2"></colgroup><tr
- valign="baseline" id="TBL-531-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-531-1-1"
-class="td11"> &nbsp;<object data="pgfmanual-610.svg" width="115.34386 " 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-531-1-2"
-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;\pgftransformscale{1.5}</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\draw</span><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;</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;--</span><span
-class="cmtt-8">&nbsp;(2,1);</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgfslopedattimetrue</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgfresetnontranslationattimetrue</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgftransformlineattime{.25}{\pgfpointorigin}{\pgfpoint{2cm}{1cm}}</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgftext{Hi!}</span>
-<br><span
-class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td>
-</tr></table></div>
- </dd></dl>
-<!--l. 288--><p class="indent">
- <dl class="description"><dt class="description">
-<span
-class="colorbox" id="colorbox333"><span
-class="cmtt-10">\pgftransformcurveattime</span><span
-class="cmtt-10">{</span><span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">time</span><span
-class="cmsy-10">&gt;</span><span
-class="cmtt-10">}{</span><span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">start</span><span
-class="cmsy-10">&gt;</span><span
-class="cmtt-10">}{</span><span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">first support</span><span
-class="cmsy-10">&gt;</span><span
-class="cmtt-10">}{</span><span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">second support</span><span
-class="cmsy-10">&gt;</span><span
-class="cmtt-10">}{</span><span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">end</span><span
-class="cmsy-10">&gt;</span><span
-class="cmtt-10">}</span></span> </dt><dd
-class="description">
-<a
- id="dx27-277013"></a>
- <!--l. 289--><p class="noindent">Shifts coordinates by a specific point on a curve at a specific time, see Section&nbsp;<a
-href="pgfmanualse20.html#x21-21000020.4.2">20.4.2<!--tex4ht:ref: section-pointsattime --></a> once more.
- <!--l. 292--><p class="noindent">As for the line-at-time transformation command, <span class="obeylines-h"><span class="verb"><span
-class="cmtt-10">\ifpgfslopedattime</span></span></span> decides whether an additional rotation
- should be applied.
-
-
- <!--l. 294--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular"
-cellspacing="0" cellpadding="0"
-frame="void" id="TBL-532-" ><colgroup id="TBL-532-1g"><col
-id="TBL-532-1"><col
-id="TBL-532-2"></colgroup><tr
- valign="baseline" id="TBL-532-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-532-1-1"
-class="td11"> &nbsp;<object data="pgfmanual-611.svg" width="117.12717 " 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-532-1-2"
-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;\draw</span><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;</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;..</span><span
-class="cmtt-8">&nbsp;controls</span><span
-class="cmtt-8">&nbsp;(0,2)</span><span
-class="cmtt-8">&nbsp;and</span><span
-class="cmtt-8">&nbsp;(1,2)</span><span
-class="cmtt-8">&nbsp;..</span><span
-class="cmtt-8">&nbsp;(2,1);</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgftransformcurveattime{.25}{\pgfpointorigin}</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{0cm}{2cm}}{\pgfpoint{1cm}{2cm}}{\pgfpoint{2cm}{1cm}}</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgftext{Hi!}</span>
-<br><span
-class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td>
-</tr></table></div>
- <!--l. 303--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular"
-cellspacing="0" cellpadding="0"
-frame="void" id="TBL-533-" ><colgroup id="TBL-533-1g"><col
-id="TBL-533-1"><col
-id="TBL-533-2"></colgroup><tr
- valign="baseline" id="TBL-533-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-533-1-1"
-class="td11"> &nbsp;<object data="pgfmanual-612.svg" width="116.02284 " 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-533-1-2"
-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;\draw</span><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;</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;..</span><span
-class="cmtt-8">&nbsp;controls</span><span
-class="cmtt-8">&nbsp;(0,2)</span><span
-class="cmtt-8">&nbsp;and</span><span
-class="cmtt-8">&nbsp;(1,2)</span><span
-class="cmtt-8">&nbsp;..</span><span
-class="cmtt-8">&nbsp;(2,1);</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgfslopedattimetrue</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgftransformcurveattime{.25}{\pgfpointorigin}</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{0cm}{2cm}}{\pgfpoint{1cm}{2cm}}{\pgfpoint{2cm}{1cm}}</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgftext{Hi!}</span>
-<br><span
-class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td>
-</tr></table></div>
- <!--l. 313--><p class="noindent">The value of <span class="obeylines-h"><span class="verb"><span
-class="cmtt-10">\ifpgfresetnontranslationsattime</span></span></span> is also taken into account. </dd></dl>
-<!--l. 319--><p class="indent">
- <dl class="description"><dt class="description">
-<span
-class="colorbox" id="colorbox334"><span
-class="cmtt-10">\ifpgfslopedattime</span></span> </dt><dd
-class="description">
-<a
- id="dx27-277014"></a>
- <!--l. 320--><p class="noindent">Decides whether the &#8220;at time&#8221; transformation commands also rotate coordinates or not. </dd></dl>
-<!--l. 326--><p class="indent">
- <dl class="description"><dt class="description">
-<span
-class="colorbox" id="colorbox335"><span
-class="cmtt-10">\ifpgfresetnontranslationsattime</span></span> </dt><dd
-class="description">
-<a
- id="dx27-277015"></a>
- <!--l. 327--><p class="noindent">Decides whether the &#8220;at time&#8221; transformation commands should reset the non-translations between
- shifting and rotating. </dd></dl>
-<!--l. 333--><p class="noindent">
- <h5 class="subsubsectionHead"><span class="titlemark">26.2.3 </span> <a
- id="x27-27800026.2.3"></a>Commands for Absolute Coordinate Transformations</h5>
-<!--l. 335--><p class="noindent">The coordinate transformation commands introduced up to now are always applied in addition to
-any previous transformations. In contrast, the commands presented in the following can be used to
-change the transformation matrix &#8220;absolutely.&#8221; Note that this is, in general, dangerous and will often
-produce unexpected effects. You should use these commands only if you really know what you are
-doing.
-<!--l. 342--><p class="indent">
- <dl class="description"><dt class="description">
-<span
-class="colorbox" id="colorbox336"><span
-class="cmtt-10">\pgftransformreset</span></span> </dt><dd
-class="description">
-<a
- id="dx27-278001"></a>
- <!--l. 343--><p class="noindent">Resets the coordinate transformation matrix to the identity matrix. Thus, once this command is given no
- transformations are applied till the end of the scope.
-
-
- <!--l. 346--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular"
-cellspacing="0" cellpadding="0"
-frame="void" id="TBL-534-" ><colgroup id="TBL-534-1g"><col
-id="TBL-534-1"><col
-id="TBL-534-2"></colgroup><tr
- valign="baseline" id="TBL-534-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-534-1-1"
-class="td11"> &nbsp;<object data="pgfmanual-613.svg" width="115.21051 " 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-534-1-2"
-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;\draw</span><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;</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;--</span><span
-class="cmtt-8">&nbsp;(2,1)</span><span
-class="cmtt-8">&nbsp;--</span><span
-class="cmtt-8">&nbsp;(1,0);</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgftransformreset</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\draw[red]</span><span
-class="cmtt-8">&nbsp;(0,0)</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;(1,0);</span>
-<br><span
-class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td>
-</tr></table></div>
- </dd></dl>
-<!--l. 358--><p class="indent">
- <dl class="description"><dt class="description">
-<span
-class="colorbox" id="colorbox337"><span
-class="cmtt-10">\pgftransformresetnontranslations</span></span> </dt><dd
-class="description">
-<a
- id="dx27-278002"></a>
- <!--l. 359--><p class="noindent">This command sets the <span
-class="cmmi-10">a</span>, <span
-class="cmmi-10">b</span>, <span
-class="cmmi-10">c</span>, and <span
-class="cmmi-10">d </span>part of the coordinate transformation matrix to <span
-class="cmmi-10">a </span>= 1, <span
-class="cmmi-10">b </span>= 0,
- <span
-class="cmmi-10">c </span>= 0, and <span
-class="cmmi-10">d </span>= 1. However, the current shifting of the matrix is not modified.
- <!--l. 363--><p class="noindent">The effect of this command is that any rotation/scaling/slanting is undone in the current <span class="TEX">T<span
-class="E">E</span>X</span>&nbsp;group,
- but the origin is not &#8220;moved back.&#8221;
- <!--l. 367--><p class="noindent">This command is mostly useful directly before a <span class="obeylines-h"><span class="verb"><span
-class="cmtt-10">\pgftext</span></span></span> command to ensure that the text is not scaled or
- rotated.
- <!--l. 369--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular"
-cellspacing="0" cellpadding="0"
-frame="void" id="TBL-535-" ><colgroup id="TBL-535-1g"><col
-id="TBL-535-1"><col
-id="TBL-535-2"></colgroup><tr
- valign="baseline" id="TBL-535-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-535-1-1"
-class="td11"> &nbsp;<object data="pgfmanual-614.svg" width="115.07718 " 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-535-1-2"
-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;\pgftransformscale{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;\pgftransformxshift{1cm}</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;{\color{red}\pgftext{rotated}}</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgftransformresetnontranslations</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgftext{shifted</span><span
-class="cmtt-8">&nbsp;only}</span>
-<br><span
-class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td>
-</tr></table></div>
- </dd></dl>
-<!--l. 383--><p class="indent">
- <dl class="description"><dt class="description">
-<span
-class="colorbox" id="colorbox338"><span
-class="cmtt-10">\pgftransforminvert</span></span> </dt><dd
-class="description">
-<a
- id="dx27-278003"></a>
- <!--l. 384--><p class="noindent">Replaces the coordinate transformation matrix by a coordinate transformation matrix that &#8220;exactly
- undoes the original transformation.&#8221; For example, if the original transformation was &#8220;scale by 2 and
- then shift right by 1cm&#8221; the new one is &#8220;shift left by 1cm and then scale by 1<span
-class="cmmi-10">/</span>2.&#8221;
- <!--l. 390--><p class="noindent">This command will produce an error if the determinant of the matrix is too small, that is, if the matrix is
- near-singular.
-
-
- <!--l. 392--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular"
-cellspacing="0" cellpadding="0"
-frame="void" id="TBL-536-" ><colgroup id="TBL-536-1g"><col
-id="TBL-536-1"><col
-id="TBL-536-2"></colgroup><tr
- valign="baseline" id="TBL-536-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-536-1-1"
-class="td11"> &nbsp;<object data="pgfmanual-615.svg" width="115.21051 " height="96.24208 " type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp; </td><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-536-1-2"
-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;\draw</span><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;</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;--</span><span
-class="cmtt-8">&nbsp;(2,1)</span><span
-class="cmtt-8">&nbsp;--</span><span
-class="cmtt-8">&nbsp;(1,0);</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgftransforminvert</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\draw[red]</span><span
-class="cmtt-8">&nbsp;(0,0)</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;(1,0);</span>
-<br><span
-class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td>
-</tr></table></div>
- </dd></dl>
-<!--l. 404--><p class="noindent">
- <h5 class="subsubsectionHead"><span class="titlemark">26.2.4 </span> <a
- id="x27-27900026.2.4"></a>Saving and Restoring the Coordinate Transformation Matrix</h5>
-<!--l. 406--><p class="noindent">There are two commands for saving and restoring coordinate transformation matrices.
-<!--l. 409--><p class="indent">
- <dl class="description"><dt class="description">
-<span
-class="colorbox" id="colorbox339"><span
-class="cmtt-10">\pgfgettransform</span><span
-class="cmtt-10">{</span><span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">macro</span><span
-class="cmsy-10">&gt;</span><span
-class="cmtt-10">}</span></span> </dt><dd
-class="description">
-<a
- id="dx27-279001"></a>
- <!--l. 410--><p class="noindent">This command will (locally) define <span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">macro</span><span
-class="cmsy-10">&gt; </span>to a representation of the current coordinate transformation
- matrix. This matrix can later on be reinstalled using <span class="obeylines-h"><span class="verb"><span
-class="cmtt-10">\pgfsettransform</span></span></span>. </dd></dl>
-<!--l. 416--><p class="indent">
- <dl class="description"><dt class="description">
-<span
-class="colorbox" id="colorbox340"><span
-class="cmtt-10">\pgfsettransform</span><span
-class="cmtt-10">{</span><span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">macro</span><span
-class="cmsy-10">&gt;</span><span
-class="cmtt-10">}</span></span> </dt><dd
-class="description">
-<a
- id="dx27-279002"></a>
- <!--l. 417--><p class="noindent">Reinstalls a coordinate transformation matrix that was previously saved using <span class="obeylines-h"><span class="verb"><span
-class="cmtt-10">\pgfgettransform</span></span></span>. </dd></dl>
-<!--l. 423--><p class="noindent">
- <h4 class="subsectionHead"><span class="titlemark">26.3 </span> <a
- id="x27-28000026.3"></a>Canvas Transformations</h4>
-<!--l. 425--><p class="noindent">The canvas transformation matrix is not managed by <span
-class="cmcsc-10"><small
-class="small-caps">P</small><small
-class="small-caps">G</small><small
-class="small-caps">F</small></span>, but by the output format like <span
-class="cmcsc-10"><small
-class="small-caps">P</small><small
-class="small-caps">D</small><small
-class="small-caps">F</small></span>&nbsp;or PostScript. All the
-<span
-class="cmcsc-10"><small
-class="small-caps">P</small><small
-class="small-caps">G</small><small
-class="small-caps">F</small></span>&nbsp;does is to call appropriate low-level <span class="obeylines-h"><span class="verb"><span
-class="cmtt-10">\pgfsys@</span></span></span> commands to change the canvas transformation
-matrix.
-<!--l. 430--><p class="indent"> Unlike coordinate transformations, canvas transformations apply to &#8220;everything,&#8221; including images, text,
-shadings, line thickness, and so on. The idea is that a canvas transformation really stretches and deforms the canvas
-after the graphic is finished.
-<!--l. 435--><p class="indent"> Unlike coordinate transformations, canvas transformations are local to the current <span class="obeylines-h"><span class="verb"><span
-class="cmtt-10">{pgfscope}</span></span></span>, not to the
-current <span class="TEX">T<span
-class="E">E</span>X</span>&nbsp;group. This is due to the fact that they are managed by the backend driver, not by <span class="TEX">T<span
-class="E">E</span>X</span>&nbsp;or
-<span
-class="cmcsc-10"><small
-class="small-caps">P</small><small
-class="small-caps">G</small><small
-class="small-caps">F</small></span>.
-<!--l. 440--><p class="indent"> Unlike the coordinate transformation matrix, it is not possible to &#8220;reset&#8221; the canvas transformation matrix. The
-only way to change it is to concatenate it with another canvas transformation matrix or to end the current
-<span class="obeylines-h"><span class="verb"><span
-class="cmtt-10">{pgfscope}</span></span></span>.
-<!--l. 445--><p class="indent"> Unlike coordinate transformations, <span
-class="cmcsc-10"><small
-class="small-caps">P</small><small
-class="small-caps">G</small><small
-class="small-caps">F</small></span>&nbsp;does not &#8220;keep track&#8221; of canvas transformations. In particular, it
-will not be able to correctly save the coordinates of shapes or nodes when a canvas transformation is
-used.
-<!--l. 450--><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;does not offer a whole set of special commands for modifying the canvas transformation matrix. Instead,
-different commands allow you to concatenate the canvas transformation matrix with a coordinate transformation
-matrix (and there are numerous commands for specifying a coordinate transformation, see the previous
-section).
-<!--l. 456--><p class="indent">
-
-
- <dl class="description"><dt class="description">
-<span
-class="colorbox" id="colorbox341"><span
-class="cmtt-10">\pgflowlevelsynccm</span></span> </dt><dd
-class="description">
-<a
- id="dx27-280001"></a>
- <!--l. 457--><p class="noindent">This command concatenates the canvas transformation matrix with the current coordinate
- transformation matrix. Afterward, the coordinate transformation matrix is reset.
- <!--l. 461--><p class="noindent">The effect of this command is to &#8220;synchronize&#8221; the coordinate transformation matrix and the
- canvas transformation matrix. All transformations that were previously applied by the coordinate
- transformations matrix are now applied by the canvas transformation matrix.
- <!--l. 467--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular"
-cellspacing="0" cellpadding="0"
-frame="void" id="TBL-537-" ><colgroup id="TBL-537-1g"><col
-id="TBL-537-1"><col
-id="TBL-537-2"></colgroup><tr
- valign="baseline" id="TBL-537-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-537-1-1"
-class="td11"> &nbsp;<object data="pgfmanual-616.svg" width="115.61052 " height="77.67368 " type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp; </td><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-537-1-2"
-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{1pt}</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgftransformscale{5}</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\draw</span><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;</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;--</span><span
-class="cmtt-8">&nbsp;(0.4,.2);</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgftransformxshift{0.2cm}</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgflowlevelsynccm</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\draw[red]</span><span
-class="cmtt-8">&nbsp;(0,0)</span><span
-class="cmtt-8">&nbsp;--</span><span
-class="cmtt-8">&nbsp;(0.4,.2);</span>
-<br><span
-class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td>
-</tr></table></div>
- </dd></dl>
-<!--l. 481--><p class="indent">
- <dl class="description"><dt class="description">
-<span
-class="colorbox" id="colorbox342"><span
-class="cmtt-10">\pgflowlevel</span><span
-class="cmtt-10">{</span><span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">transformation code</span><span
-class="cmsy-10">&gt;</span><span
-class="cmtt-10">}</span></span> </dt><dd
-class="description">
-<a
- id="dx27-280002"></a>
- <!--l. 482--><p class="noindent">This command concatenates the canvas transformation matrix with the coordinate transformation
- specified by <span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">transformation code</span><span
-class="cmsy-10">&gt;</span>.
- <!--l. 485--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular"
-cellspacing="0" cellpadding="0"
-frame="void" id="TBL-538-" ><colgroup id="TBL-538-1g"><col
-id="TBL-538-1"><col
-id="TBL-538-2"></colgroup><tr
- valign="baseline" id="TBL-538-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-538-1-1"
-class="td11"> &nbsp;<object data="pgfmanual-617.svg" width="115.07718 " 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-538-1-2"
-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{1pt}</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgflowlevel{\pgftransformscale{5}}</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\draw</span><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;</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;--</span><span
-class="cmtt-8">&nbsp;(0.4,.2);</span>
-<br><span
-class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td>
-</tr></table></div>
- </dd></dl>
-<!--l. 496--><p class="indent">
- <dl class="description"><dt class="description">
-<span
-class="colorbox" id="colorbox343"><span
-class="cmtt-10">\pgflowlevelobj</span><span
-class="cmtt-10">{</span><span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">transformation code</span><span
-class="cmsy-10">&gt;</span><span
-class="cmtt-10">}{</span><span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">code</span><span
-class="cmsy-10">&gt;</span><span
-class="cmtt-10">}</span></span> </dt><dd
-class="description">
-<a
- id="dx27-280003"></a>
- <!--l. 497--><p class="noindent">This command creates a local <span class="obeylines-h"><span class="verb"><span
-class="cmtt-10">{pgfscope}</span></span></span>. Inside this scope, <span class="obeylines-h"><span class="verb"><span
-class="cmtt-10">\pgflowlevel</span></span></span> is first called with the
- argument <span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">transformation code</span><span
-class="cmsy-10">&gt;</span>, then the <span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">code</span><span
-class="cmsy-10">&gt; </span>is inserted.
-
-
- <!--l. 501--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular"
-cellspacing="0" cellpadding="0"
-frame="void" id="TBL-539-" ><colgroup id="TBL-539-1g"><col
-id="TBL-539-1"><col
-id="TBL-539-2"></colgroup><tr
- valign="baseline" id="TBL-539-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-539-1-1"
-class="td11"> &nbsp;<object data="pgfmanual-618.svg" width="115.07718 " 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-539-1-2"
-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{1pt}</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgflowlevelobj{\pgftransformscale{5}}</span><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;{\draw</span><span
-class="cmtt-8">&nbsp;(0,0)</span><span
-class="cmtt-8">&nbsp;--</span><span
-class="cmtt-8">&nbsp;(0.4,.2);}</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\pgflowlevelobj{\pgftransformxshift{-1cm}}{\draw</span><span
-class="cmtt-8">&nbsp;(0,0)</span><span
-class="cmtt-8">&nbsp;--</span><span
-class="cmtt-8">&nbsp;(0.4,.2);}</span>
-<br><span
-class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td>
-</tr></table></div>
- </dd></dl>
-<!--l. 512--><p class="indent">
- <dl class="description"><dt class="description">
-<span
-class="colorbox" id="colorbox344"><span
-class="cmtt-10">\begin{</span><span
-class="cmtt-10">pgflowlevelscope</span><span
-class="cmtt-10">}{</span><span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">transformation code</span><span
-class="cmsy-10">&gt;</span><span
-class="cmtt-10">}</span></span> </dt><dd
-class="description">
- </dd><dt class="description">
-<span
-class="colorbox" id="colorbox345"><span
-class="cmtt-10">&nbsp;</span><span
-class="cmtt-10">&nbsp;</span><span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">environment contents</span><span
-class="cmsy-10">&gt;</span></span> </dt><dd
-class="description">
- </dd><dt class="description">
-<span
-class="colorbox" id="colorbox346"><span
-class="cmtt-10">\end{</span><span
-class="cmtt-10">pgflowlevelscope</span><span
-class="cmtt-10">}</span></span> </dt><dd
-class="description">
-<a
- id="dx27-280004"></a>
-<a
- id="dx27-280005"></a>
- <!--l. 513--><p class="noindent">This environment first surrounds the <span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">environment contents</span><span
-class="cmsy-10">&gt; </span>by a <span class="obeylines-h"><span class="verb"><span
-class="cmtt-10">{pgfscope}</span></span></span>. Then it calls
- <span class="obeylines-h"><span class="verb"><span
-class="cmtt-10">\pgflowlevel</span></span></span> with the argument <span
-class="cmsy-10">&lt;</span><span
-class="cmti-10">transformation code</span><span
-class="cmsy-10">&gt;</span>.
- <!--l. 517--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular"
-cellspacing="0" cellpadding="0"
-frame="void" id="TBL-540-" ><colgroup id="TBL-540-1g"><col
-id="TBL-540-1"><col
-id="TBL-540-2"></colgroup><tr
- valign="baseline" id="TBL-540-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-540-1-1"
-class="td11"> &nbsp;<object data="pgfmanual-619.svg" width="115.07718 " 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-540-1-2"
-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{1pt}</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\begin{pgflowlevelscope}{\pgftransformscale{5}}</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\draw</span><span
-class="cmtt-8">&nbsp;(0,0)</span><span
-class="cmtt-8">&nbsp;--</span><span
-class="cmtt-8">&nbsp;(0.4,.2);</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\end{pgflowlevelscope}</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\begin{pgflowlevelscope}{\pgftransformxshift{-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;\draw</span><span
-class="cmtt-8">&nbsp;(0,0)</span><span
-class="cmtt-8">&nbsp;--</span><span
-class="cmtt-8">&nbsp;(0.4,.2);</span>
-<br><span
-class="cmtt-8">&nbsp;</span><span
-class="cmtt-8">&nbsp;\end{pgflowlevelscope}</span>
-<br><span
-class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td>
-</tr></table></div>
- </dd></dl>
-
-
-
-
-
-
- <div class="crosslinks"><p class="noindent">[<a
-href="pgfmanualse27.html" >next</a>] [<a
-href="pgfmanualse25.html" >prev</a>] [<a
-href="pgfmanualse25.html#tailpgfmanualse25.html" >prev-tail</a>] [<a
-href="pgfmanualse26.html" >front</a>] [<a
-href="pgfmanual.html#pgfmanualse26.html" >up</a>] </p></div>
-<!--l. 8--><p class="indent"> <a
- id="tailpgfmanualse26.html"></a>
-</body></html>