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diff --git a/Master/texmf-dist/doc/generic/pgf/version-for-tex4ht/en/pgfmanualse13.html b/Master/texmf-dist/doc/generic/pgf/version-for-tex4ht/en/pgfmanualse13.html new file mode 100644 index 00000000000..26696889f98 --- /dev/null +++ b/Master/texmf-dist/doc/generic/pgf/version-for-tex4ht/en/pgfmanualse13.html @@ -0,0 +1,1385 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" + "http://www.w3.org/TR/html4/loose.dtd"> +<html > +<head><title>13 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="2005-10-23 18:34:00"> +<link rel="stylesheet" type="text/css" href="pgfmanual.css"> +</head><body +> + <div class="crosslinks"><p class="noindent">[<a +href="pgfmanualse12.html" >prev</a>] [<a +href="pgfmanualse12.html#tailpgfmanualse12.html" >prev-tail</a>] [<a +href="#tailpgfmanualse13.html">tail</a>] [<a +href="pgfmanual.html#pgfmanualse13.html" >up</a>] </p></div> + <h3 class="sectionHead"><span class="titlemark">13 </span> <a + id="x14-15400013"></a>Transformations</h3> +<!--l. 10--><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> has a powerful transformation mechanism that is similar to the transformation capabilities of <span +class="cmcsc-10"><small +class="small-caps">M</small><small +class="small-caps">E</small><small +class="small-caps">T</small><small +class="small-caps">A</small><small +class="small-caps">F</small><small +class="small-caps">O</small><small +class="small-caps">N</small><small +class="small-caps">T</small></span>. The +present section explains how you can access it in Ti<span +class="cmti-10">k</span>Z. +<!--l. 15--><p class="noindent"> + <h4 class="subsectionHead"><span class="titlemark">13.1 </span> <a + id="x14-15500013.1"></a>The Different Coordinate Systems</h4> +<!--l. 17--><p class="noindent">It is a long process from a coordinate like, say, (1<span +class="cmmi-10">,</span>2) or (1cm<span +class="cmmi-10">,</span>5<span +class="cmmi-10">mathrm</span><span +class="cmmi-10">pt</span>), to the position a point is finally placed +on the display or paper. In order to find out where the point should go, it is constantly “transformed,” +which means that it is mostly shifted around and possibly rotated, slanted, scaled, and otherwise +mutilated. +<!--l. 24--><p class="indent"> In detail, (at least) the following transformations are applied to a coordinate like (1<span +class="cmmi-10">,</span>2) before a point on the +screen is chosen: + <ol type="1" class="enumerate1" > + <li class="enumerate" value="1" +><a + id="x14-155002x1"></a><span +class="cmcsc-10"><small +class="small-caps">P</small><small +class="small-caps">G</small><small +class="small-caps">F</small></span> interprets a coordinate like (1<span +class="cmmi-10">,</span>2) in its <span +class="cmmi-10">xy</span>-coordinate system as “add the current <span +class="cmmi-10">x</span>-vector once + and the current <span +class="cmmi-10">y</span>-vector twice to obtain the new point.” + </li> + <li class="enumerate" value="2" +><a + id="x14-155004x2"></a><span +class="cmcsc-10"><small +class="small-caps">P</small><small +class="small-caps">G</small><small +class="small-caps">F</small></span> applies its coordinate transformation matrix to the resulting coordinate. This yields the final + position of the point inside the picture. + </li> + <li class="enumerate" value="3" +><a + id="x14-155006x3"></a>The backend driver (like <span class="obeylines-h"><span class="verb"><span +class="cmtt-10">dvips</span></span></span> or <span class="obeylines-h"><span class="verb"><span +class="cmtt-10">pdftex</span></span></span>) adds transformation commands such the coordinate is + shifted to the correct position in <span class="TEX">T<span +class="E">E</span>X</span>’s page coordinate system. + </li> + <li class="enumerate" value="4" +><a + id="x14-155008x4"></a><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) apply the canvas transformation matrix to the point, which can once more change + the position on the page. + </li> + <li class="enumerate" value="5" +><a + id="x14-155010x5"></a>The viewer application or the printer applies the device transformation matrix to transform the + coordinate to its final pixel coordinate on the screen or paper.</li></ol> +<!--l. 49--><p class="indent"> In reality, the process is even more involved, but the above should give the idea: A point is constantly +transformed by changes of the coordinate system. +<!--l. 53--><p class="indent"> In Ti<span +class="cmti-10">k</span>Z, you only have access to the first two coordinate systems: The <span +class="cmmi-10">xy</span>-coordinate system and the coordinate +transformation matrix (these will be explained later). <span +class="cmcsc-10"><small +class="small-caps">P</small><small +class="small-caps">G</small><small +class="small-caps">F</small></span> also allows you to change the canvas transformation +matrix, but you have to use commands of the core layer directly to do so and you “better know what you +are doing” when you do this. The moment you start modifying the canvas matrix, <span +class="cmcsc-10"><small +class="small-caps">P</small><small +class="small-caps">G</small><small +class="small-caps">F</small></span> immediately +looses track of all coordinates and shapes, anchors, and bounding box computations will no longer +work. +<!--l. 64--><p class="noindent"> + <h4 class="subsectionHead"><span class="titlemark">13.2 </span> <a + id="x14-15600013.2"></a>The Xy- and Xyz-Coordinate Systems</h4> +<!--l. 66--><p class="noindent">The first and easiest coordinate systems are <span +class="cmcsc-10"><small +class="small-caps">P</small><small +class="small-caps">G</small><small +class="small-caps">F</small></span>’s <span +class="cmmi-10">xy</span>- and <span +class="cmmi-10">xyz</span>-coordinate systems. The idea is very simple: +Whenever you specify a coordinate like <span class="obeylines-h"><span class="verb"><span +class="cmtt-10">(2,3)</span></span></span> this means 2<span +class="cmmi-10">v</span><sub ><span +class="cmmi-7">x</span></sub> + 3<span +class="cmmi-10">v</span><sub ><span +class="cmmi-7">y</span></sub>, where <span +class="cmmi-10">v</span><sub ><span +class="cmmi-7">x</span></sub> is the current <span +class="cmmi-10">x</span><span +class="cmti-10">-vector </span>and <span +class="cmmi-10">v</span><sub ><span +class="cmmi-7">y</span></sub> is the +current <span +class="cmmi-10">y</span><span +class="cmti-10">-vector</span>. Similarly, the coordinate <span class="obeylines-h"><span class="verb"><span +class="cmtt-10">(1,2,3)</span></span></span> means <span +class="cmmi-10">v</span><sub ><span +class="cmmi-7">x</span></sub> + 2<span +class="cmmi-10">v</span><sub ><span +class="cmmi-7">y</span></sub> + 3<span +class="cmmi-10">v</span><sub ><span +class="cmmi-7">z</span></sub>. +<!--l. 73--><p class="indent"> Unlike other packages, <span +class="cmcsc-10"><small +class="small-caps">P</small><small +class="small-caps">G</small><small +class="small-caps">F</small></span> does not insist that <span +class="cmmi-10">v</span><sub ><span +class="cmmi-7">x</span></sub> actually has a <span +class="cmmi-10">y</span>-component of 0, that is, that it is a +horizontal vector. Instead, the <span +class="cmmi-10">x</span>-vector can point anywhere you want. Naturally, <span +class="cmti-10">normally </span>you will want the +<span +class="cmmi-10">x</span>-vector to point horizontally. + + +<!--l. 79--><p class="indent"> One undesirable effect of this flexibility is that it is not possible to provide mixed coordinates as in (1<span +class="cmmi-10">,</span>2pt). Life +is hard. +<!--l. 82--><p class="indent"> To change the <span +class="cmmi-10">x</span>-, <span +class="cmmi-10">y</span>-, and <span +class="cmmi-10">z</span>-vectors, you can use the following options: + <ul class="itemize1"> + <li class="itemize"><span +class="cmtt-10">x</span><a + id="dx14-156001"></a><a + id="dx14-156002"></a><span class="obeylines-h"><span class="verb"><span +class="cmtt-10">=</span></span></span><span +class="cmsy-10"><</span><span +class="cmti-10">dimension</span><span +class="cmsy-10">> </span>Sets the <span +class="cmmi-10">x</span>-vector of <span +class="cmcsc-10"><small +class="small-caps">P</small><small +class="small-caps">G</small><small +class="small-caps">F</small></span>’s <span +class="cmmi-10">xyz</span>-coordinate system to point <span +class="cmsy-10"><</span><span +class="cmti-10">dimension</span><span +class="cmsy-10">> </span>to the right, + that is, to (<span +class="cmsy-10"><</span><span +class="cmti-10">dimension</span><span +class="cmsy-10">></span><span +class="cmmi-10">,</span>0<span +class="cmmi-10">pt</span>). The default is 1cm. + <!--l. 91--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" +cellspacing="0" cellpadding="0" +frame="void" id="TBL-295-" ><colgroup id="TBL-295-1g"><col +id="TBL-295-1"><col +id="TBL-295-2"></colgroup><tr + valign="baseline" id="TBL-295-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-295-1-1" +class="td11"> <object data="pgfmanual-288.svg" width="57.3055pt" height="3.24544pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object> </td><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-295-1-2" +class="td11"> <table class="minipage"><tr><td><div class="obeylines-v"> +<br><span +class="cmtt-8">\begin{tikzpicture}</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> +(1,0);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[x=2cm,color=red]</span><span +class="cmtt-8"> (0,0.1)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> +(1,0);</span> +<br><span +class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td> +</tr></table></div> + <!--l. 98--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"> +<table class="tabular" +cellspacing="0" cellpadding="0" +frame="void" id="TBL-296-" ><colgroup id="TBL-296-1g"><col +id="TBL-296-1"><col +id="TBL-296-2"></colgroup><tr + valign="baseline" id="TBL-296-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-296-1-1" +class="td11"> <object data="pgfmanual-289.svg" width="85.75824pt" height="57.30548pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object> </td><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-296-1-2" +class="td11"> <table class="minipage"><tr><td><div class="obeylines-v"> +<br><span +class="cmtt-8">\tikz</span><span +class="cmtt-8"> \draw[x=1.5cm]</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> grid</span><span +class="cmtt-8"> (2,2);</span></div> </td></tr></table> </td> +</tr></table></div> + <!--l. 102--><p class="noindent">The last example shows that the size of steppings in grids, just like all other dimensions, are not affected by + the <span +class="cmmi-10">x</span>-vector. After all, the <span +class="cmmi-10">x</span>-vector is only used to determine the coordinate of the upper right corner of the + grid. + </li> + <li class="itemize"><span +class="cmtt-10">x</span><a + id="dx14-156003"></a><a + id="dx14-156004"></a><span class="obeylines-h"><span class="verb"><span +class="cmtt-10">=</span></span></span><span +class="cmsy-10"><</span><span +class="cmti-10">coordinate</span><span +class="cmsy-10">> </span>Sets the <span +class="cmmi-10">x</span>-vector of <span +class="cmcsc-10"><small +class="small-caps">P</small><small +class="small-caps">G</small><small +class="small-caps">F</small></span>’s <span +class="cmmi-10">xyz</span>-coordinate system to the specified <span +class="cmsy-10"><</span><span +class="cmti-10">coordinate</span><span +class="cmsy-10">></span>. If <span +class="cmsy-10"><</span><span +class="cmti-10">coordinate</span><span +class="cmsy-10">></span> + contains a comma, it must be put in braces. + <!--l. 111--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" +cellspacing="0" cellpadding="0" +frame="void" id="TBL-297-" ><colgroup id="TBL-297-1g"><col +id="TBL-297-1"><col +id="TBL-297-2"></colgroup><tr + valign="baseline" id="TBL-297-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-297-1-1" +class="td11"> <object data="pgfmanual-290.svg" width="57.3055pt" height="14.62636pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object> </td><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-297-1-2" +class="td11"> <table class="minipage"><tr><td><div class="obeylines-v"> +<br><span +class="cmtt-8">\begin{tikzpicture}</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,0);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[x={(2cm,0.5cm)},color=red]</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,0);</span> +<br><span +class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td> +</tr></table></div> + <!--l. 118--><p class="noindent">You can use this, for example, to exchange the meaning of the <span +class="cmmi-10">x</span>- and <span +class="cmmi-10">y</span>-coordinate. + <!--l. 121--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"> +<table class="tabular" +cellspacing="0" cellpadding="0" +frame="void" id="TBL-298-" ><colgroup id="TBL-298-1g"><col +id="TBL-298-1"><col +id="TBL-298-2"></colgroup><tr + valign="baseline" id="TBL-298-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-298-1-1" +class="td11"> <object data="pgfmanual-291.svg" width="91.67986pt" height="91.67986pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object> </td><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-298-1-2" +class="td11"> <table class="minipage"><tr><td><div class="obeylines-v"> +<br><span +class="cmtt-8">\begin{tikzpicture}[smooth]</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw</span><span +class="cmtt-8"> plot</span><span +class="cmtt-8"> coordinates{(1,0)</span><span +class="cmtt-8"> (2,0.5)</span><span +class="cmtt-8"> (3,0)</span><span +class="cmtt-8"> (3,1)};</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[x={(0cm,1cm)},y={(1cm,0cm)},color=red]</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> plot</span><span +class="cmtt-8"> coordinates{(1,0)</span><span +class="cmtt-8"> (2,0.5)</span><span +class="cmtt-8"> (3,0)</span><span +class="cmtt-8"> (3,1)};</span> +<br><span +class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td> +</tr></table></div> + </li> + <li class="itemize"><span +class="cmtt-10">y</span><a + id="dx14-156005"></a><a + id="dx14-156006"></a><span class="obeylines-h"><span class="verb"><span +class="cmtt-10">=</span></span></span><span +class="cmsy-10"><</span><span +class="cmti-10">value</span><span +class="cmsy-10">> </span>Works like the <span class="obeylines-h"><span class="verb"><span +class="cmtt-10">x=</span></span></span> option, only if <span +class="cmsy-10"><</span><span +class="cmti-10">value</span><span +class="cmsy-10">> </span>is a dimension, the resulting vector points to + (0<span +class="cmmi-10">,</span><span +class="cmsy-10"><</span><span +class="cmti-10">value</span><span +class="cmsy-10">></span>). + </li> + <li class="itemize"><span +class="cmtt-10">z</span><a + id="dx14-156007"></a><a + id="dx14-156008"></a><span class="obeylines-h"><span class="verb"><span +class="cmtt-10">=</span></span></span><span +class="cmsy-10"><</span><span +class="cmti-10">value</span><span +class="cmsy-10">> </span>Works like the <span class="obeylines-h"><span class="verb"><span +class="cmtt-10">z=</span></span></span> option, but now a dimension is means the point (<span +class="cmsy-10"><</span><span +class="cmti-10">value</span><span +class="cmsy-10">></span><span +class="cmmi-10">,</span><span +class="cmsy-10"><</span><span +class="cmti-10">value</span><span +class="cmsy-10">></span>). + + + <!--l. 136--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" +cellspacing="0" cellpadding="0" +frame="void" id="TBL-299-" ><colgroup id="TBL-299-1g"><col +id="TBL-299-1"><col +id="TBL-299-2"></colgroup><tr + valign="baseline" id="TBL-299-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-299-1-1" +class="td11"> <object data="pgfmanual-292.svg" width="57.70547pt" height="57.70547pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object> </td><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-299-1-2" +class="td11"> <table class="minipage"><tr><td><div class="obeylines-v"> +<br><span +class="cmtt-8">\begin{tikzpicture}[z=-1cm,->,thick]</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[color=red]</span><span +class="cmtt-8"> (0,0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,0,0);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[color=blue]</span><span +class="cmtt-8"> (0,0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (0,1,0);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[color=orange]</span><span +class="cmtt-8"> (0,0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (0,0,1);</span> +<br><span +class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td> +</tr></table></div> + </li></ul> +<!--l. 147--><p class="noindent"> + <h4 class="subsectionHead"><span class="titlemark">13.3 </span> <a + id="x14-15700013.3"></a>Coordinate Transformations</h4> +<!--l. 149--><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> and Ti<span +class="cmti-10">k</span>Z allow you to specify <span +class="cmti-10">coordinate transformations</span>. Whenever you specify a coordinate as in <span class="obeylines-h"><span class="verb"><span +class="cmtt-10">(1,0)</span></span></span> or +<span class="obeylines-h"><span class="verb"><span +class="cmtt-10">(1cm,1pt)</span></span></span> or <span class="obeylines-h"><span class="verb"><span +class="cmtt-10">(30:2cm)</span></span></span>, this coordinate is first “reduced” to a position of the form “<span +class="cmmi-10">x </span>points to the right and <span +class="cmmi-10">y</span> +points upwards.” For example, <span class="obeylines-h"><span class="verb"><span +class="cmtt-10">(1in,5pt)</span></span></span> is reduced to “72<img +src="pgfmanual22x.gif" alt="-72 +100" class="frac" align="middle"> points to the right and 5 points upwards” and +<span class="obeylines-h"><span class="verb"><span +class="cmtt-10">(90:100pt)</span></span></span> means “0pt to the right and 100 points upwards.” +<!--l. 157--><p class="indent"> The next step is to apply the current <span +class="cmti-10">coordinate transformation matrix </span>to the coordinate. For example, the +coordinate transformation matrix might currently be set such that it adds a certain constant to the <span +class="cmmi-10">x </span>value. Also, it +might be setup such that it, say, exchanges the <span +class="cmmi-10">x </span>and <span +class="cmmi-10">y </span>value. In general, any “standard” transformation like +translation, rotation, slanting, or scaling or any combination thereof is possible. (Internally, <span +class="cmcsc-10"><small +class="small-caps">P</small><small +class="small-caps">G</small><small +class="small-caps">F</small></span> keeps +track of a coordinate transformation matrix very much like the concatenation matrix used by <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.) +<!--l. 167--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" +cellspacing="0" cellpadding="0" +frame="void" id="TBL-300-" ><colgroup id="TBL-300-1g"><col +id="TBL-300-1"><col +id="TBL-300-2"></colgroup><tr + valign="baseline" id="TBL-300-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-300-1-1" +class="td11"> <object data="pgfmanual-293.svg" width="85.65822pt" height="57.20547pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object> </td><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-300-1-2" +class="td11"> <table class="minipage"><tr><td><div class="obeylines-v"> +<br><span +class="cmtt-8">\begin{tikzpicture}</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[style=help</span><span +class="cmtt-8"> lines]</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> grid</span><span +class="cmtt-8"> (3,2);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> rectangle</span><span +class="cmtt-8"> (1,0.5);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \begin{scope}[xshift=1cm]</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> [red]</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> rectangle</span><span +class="cmtt-8"> (1,0.5);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[yshift=1cm]</span><span +class="cmtt-8"> [blue]</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> rectangle</span><span +class="cmtt-8"> (1,0.5);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[rotate=30]</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> [orange]</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> rectangle</span><span +class="cmtt-8"> (1,0.5);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \end{scope}</span> +<br><span +class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td> +</tr></table></div> +<!--l. 179--><p class="indent"> The most important aspect of the coordinate transformation matrix is <span +class="cmti-10">that it applies to coordinates</span> +<span +class="cmti-10">only! </span>In particular, the coordinate transformation has no effect on things like the line width or the +dash pattern or the shading angle. In certain cases, it is not immediately clear whether the coordinate +transformation matrix <span +class="cmti-10">should </span>apply to a certain dimension. For example, should the coordinate transformation +matrix apply to grids? (It does.) And what about the size of arced corners? (It does not.) The general +rule is “If there is no ‘coordinate’ involved, even ‘indirectly,’ the matrix is not applied.” However, +sometimes, you simply have to try or look it up in the documentation whether the matrix will be +applied. +<!--l. 191--><p class="indent"> Setting the matrix cannot be done directly. Rather, all you can do is to “add” another transformation to the +current matrix. However, all transformations are local to the current <span class="TEX">T<span +class="E">E</span>X</span>-group. All transformations are added +using graphic options, which are described below. +<!--l. 197--><p class="indent"> Transformations apply immediately when they are encountered “in the middle of a path” and they apply only to +the coordinates on the path following the transformation option. +<!--l. 201--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" +cellspacing="0" cellpadding="0" +frame="void" id="TBL-301-" ><colgroup id="TBL-301-1g"><col +id="TBL-301-1"><col +id="TBL-301-2"></colgroup><tr + valign="baseline" id="TBL-301-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-301-1-1" +class="td11"> <object data="pgfmanual-294.svg" width="85.75824pt" height="14.62636pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object> </td><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-301-1-2" +class="td11"> <table class="minipage"><tr><td><div class="obeylines-v"> +<br><span +class="cmtt-8">\tikz</span><span +class="cmtt-8"> \draw</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> rectangle</span><span +class="cmtt-8"> (1,0.5)</span><span +class="cmtt-8"> [xshift=2cm]</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> rectangle</span><span +class="cmtt-8"> (1,0.5);</span></div> </td></tr></table> </td> +</tr></table></div> +<!--l. 205--><p class="indent"> A final word of warning: You should refrain from using “aggressive” transformations like a scaling of a factor of +10000. The reason is that all transformations are done using <span class="TEX">T<span +class="E">E</span>X</span>, which has a fairly low accuracy. Furthermore, in +certain situations it is necessary that Ti<span +class="cmti-10">k</span>Z <span +class="cmti-10">inverts </span>the current transformation matrix and this will fail if the +transformation matrix is badly conditioned or even singular (if you do not know what singular matrices are, you are + + +blessed). + <ul class="itemize1"> + <li class="itemize"><span +class="cmtt-10">shift</span><a + id="dx14-157001"></a><a + id="dx14-157002"></a><span class="obeylines-h"><span class="verb"><span +class="cmtt-10">={</span></span></span><span +class="cmsy-10"><</span><span +class="cmti-10">coordinate</span><span +class="cmsy-10">></span><span class="obeylines-h"><span class="verb"><span +class="cmtt-10">}</span></span></span> adds the <span +class="cmsy-10"><</span><span +class="cmti-10">coordinate</span><span +class="cmsy-10">> </span>to all coordinates. + <!--l. 216--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" +cellspacing="0" cellpadding="0" +frame="void" id="TBL-302-" ><colgroup id="TBL-302-1g"><col +id="TBL-302-1"><col +id="TBL-302-2"></colgroup><tr + valign="baseline" id="TBL-302-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-302-1-1" +class="td11"> <object data="pgfmanual-295.svg" width="85.65822pt" height="57.30548pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object> </td><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-302-1-2" +class="td11"> <table class="minipage"><tr><td><div class="obeylines-v"> +<br><span +class="cmtt-8">\begin{tikzpicture}</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[style=help</span><span +class="cmtt-8"> lines]</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> grid</span><span +class="cmtt-8"> (3,2);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,1)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,0);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[shift={(1,1)},blue]</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,1)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,0);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[shift={(30:1cm)},red]</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,1)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,0);</span> +<br><span +class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td> +</tr></table></div> + </li> + <li class="itemize"><span +class="cmtt-10">xshift</span><a + id="dx14-157003"></a><a + id="dx14-157004"></a><span class="obeylines-h"><span class="verb"><span +class="cmtt-10">=</span></span></span><span +class="cmsy-10"><</span><span +class="cmti-10">dimension</span><span +class="cmsy-10">> </span>adds <span +class="cmsy-10"><</span><span +class="cmti-10">dimension</span><span +class="cmsy-10">> </span>to the <span +class="cmmi-10">x </span>value of all coordinates. + <!--l. 227--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" +cellspacing="0" cellpadding="0" +frame="void" id="TBL-303-" ><colgroup id="TBL-303-1g"><col +id="TBL-303-1"><col +id="TBL-303-2"></colgroup><tr + valign="baseline" id="TBL-303-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-303-1-1" +class="td11"> <object data="pgfmanual-296.svg" width="95.75824pt" height="57.20547pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object> </td><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-303-1-2" +class="td11"> <table class="minipage"><tr><td><div class="obeylines-v"> +<br><span +class="cmtt-8">\begin{tikzpicture}</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[style=help</span><span +class="cmtt-8"> lines]</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> grid</span><span +class="cmtt-8"> (3,2);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,1)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,0);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[xshift=2cm,blue]</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,1)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,0);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[xshift=-10pt,red]</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,1)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,0);</span> +<br><span +class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td> +</tr></table></div> + </li> + <li class="itemize"><span +class="cmtt-10">yshift</span><a + id="dx14-157005"></a><a + id="dx14-157006"></a><span class="obeylines-h"><span class="verb"><span +class="cmtt-10">=</span></span></span><span +class="cmsy-10"><</span><span +class="cmti-10">dimension</span><span +class="cmsy-10">> </span>adds <span +class="cmsy-10"><</span><span +class="cmti-10">dimension</span><span +class="cmsy-10">> </span>to the <span +class="cmmi-10">y </span>value of all coordinates. + </li> + <li class="itemize"><span +class="cmtt-10">scale</span><a + id="dx14-157007"></a><a + id="dx14-157008"></a><span class="obeylines-h"><span class="verb"><span +class="cmtt-10">=</span></span></span><span +class="cmsy-10"><</span><span +class="cmti-10">factor</span><span +class="cmsy-10">> </span>multiplies all coordinates by the given <span +class="cmsy-10"><</span><span +class="cmti-10">factor</span><span +class="cmsy-10">></span>. The <span +class="cmsy-10"><</span><span +class="cmti-10">factor</span><span +class="cmsy-10">> </span>should not be excessively large in + absolute terms or very near to zero. + <!--l. 243--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"> +<table class="tabular" +cellspacing="0" cellpadding="0" +frame="void" id="TBL-304-" ><colgroup id="TBL-304-1g"><col +id="TBL-304-1"><col +id="TBL-304-2"></colgroup><tr + valign="baseline" id="TBL-304-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-304-1-1" +class="td11"> <object data="pgfmanual-297.svg" width="114.11096pt" height="85.75822pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object> </td><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-304-1-2" +class="td11"> <table class="minipage"><tr><td><div class="obeylines-v"> +<br><span +class="cmtt-8">\begin{tikzpicture}</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[style=help</span><span +class="cmtt-8"> lines]</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> grid</span><span +class="cmtt-8"> (3,2);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,1)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,0);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[scale=2,blue]</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,1)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,0);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[scale=-1,red]</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,1)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,0);</span> +<br><span +class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td> +</tr></table></div> + </li> + <li class="itemize"><span +class="cmtt-10">xscale</span><a + id="dx14-157009"></a><a + id="dx14-157010"></a><span class="obeylines-h"><span class="verb"><span +class="cmtt-10">=</span></span></span><span +class="cmsy-10"><</span><span +class="cmti-10">factor</span><span +class="cmsy-10">> </span>multiplies only the <span +class="cmmi-10">x</span>-value of all coordinates by the given <span +class="cmsy-10"><</span><span +class="cmti-10">factor</span><span +class="cmsy-10">></span>. + + + <!--l. 255--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" +cellspacing="0" cellpadding="0" +frame="void" id="TBL-305-" ><colgroup id="TBL-305-1g"><col +id="TBL-305-1"><col +id="TBL-305-2"></colgroup><tr + valign="baseline" id="TBL-305-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-305-1-1" +class="td11"> <object data="pgfmanual-298.svg" width="114.11096pt" height="57.20547pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object> </td><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-305-1-2" +class="td11"> <table class="minipage"><tr><td><div class="obeylines-v"> +<br><span +class="cmtt-8">\begin{tikzpicture}</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[style=help</span><span +class="cmtt-8"> lines]</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> grid</span><span +class="cmtt-8"> (3,2);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,1)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,0);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[xscale=2,blue]</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,1)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,0);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[xscale=-1,red]</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,1)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,0);</span> +<br><span +class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td> +</tr></table></div> + </li> + <li class="itemize"><span +class="cmtt-10">yscale</span><a + id="dx14-157011"></a><a + id="dx14-157012"></a><span class="obeylines-h"><span class="verb"><span +class="cmtt-10">=</span></span></span><span +class="cmsy-10"><</span><span +class="cmti-10">factor</span><span +class="cmsy-10">> </span>multiplies only the <span +class="cmmi-10">y</span>-value of all coordinates by <span +class="cmsy-10"><</span><span +class="cmti-10">factor</span><span +class="cmsy-10">></span>. + </li> + <li class="itemize"><span +class="cmtt-10">xslant</span><a + id="dx14-157013"></a><a + id="dx14-157014"></a><span class="obeylines-h"><span class="verb"><span +class="cmtt-10">=</span></span></span><span +class="cmsy-10"><</span><span +class="cmti-10">factor</span><span +class="cmsy-10">> </span>slants the coordinate horizontally by the given <span +class="cmsy-10"><</span><span +class="cmti-10">factor</span><span +class="cmsy-10">></span>: + <!--l. 269--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" +cellspacing="0" cellpadding="0" +frame="void" id="TBL-306-" ><colgroup id="TBL-306-1g"><col +id="TBL-306-1"><col +id="TBL-306-2"></colgroup><tr + valign="baseline" id="TBL-306-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-306-1-1" +class="td11"> <object data="pgfmanual-299.svg" width="85.75822pt" height="57.20547pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object> </td><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-306-1-2" +class="td11"> <table class="minipage"><tr><td><div class="obeylines-v"> +<br><span +class="cmtt-8">\begin{tikzpicture}</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[style=help</span><span +class="cmtt-8"> lines]</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> grid</span><span +class="cmtt-8"> (3,2);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,1)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,0);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[xslant=2,blue]</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,1)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,0);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[xslant=-1,red]</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,1)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,0);</span> +<br><span +class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td> +</tr></table></div> + </li> + <li class="itemize"><span +class="cmtt-10">yslant</span><a + id="dx14-157015"></a><a + id="dx14-157016"></a><span class="obeylines-h"><span class="verb"><span +class="cmtt-10">=</span></span></span><span +class="cmsy-10"><</span><span +class="cmti-10">factor</span><span +class="cmsy-10">> </span>slants the coordinate vertically by the given <span +class="cmsy-10"><</span><span +class="cmti-10">factor</span><span +class="cmsy-10">></span>: + <!--l. 280--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"> +<table class="tabular" +cellspacing="0" cellpadding="0" +frame="void" id="TBL-307-" ><colgroup id="TBL-307-1g"><col +id="TBL-307-1"><col +id="TBL-307-2"></colgroup><tr + valign="baseline" id="TBL-307-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-307-1-1" +class="td11"> <object data="pgfmanual-300.svg" width="85.65822pt" height="114.21097pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object> </td><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-307-1-2" +class="td11"> <table class="minipage"><tr><td><div class="obeylines-v"> +<br><span +class="cmtt-8">\begin{tikzpicture}</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[style=help</span><span +class="cmtt-8"> lines]</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> grid</span><span +class="cmtt-8"> (3,2);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,1)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,0);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[yslant=2,blue]</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,1)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,0);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[yslant=-1,red]</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,1)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,0);</span> +<br><span +class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td> +</tr></table></div> + </li> + <li class="itemize"><span +class="cmtt-10">rotate</span><a + id="dx14-157017"></a><a + id="dx14-157018"></a><span class="obeylines-h"><span class="verb"><span +class="cmtt-10">=</span></span></span><span +class="cmsy-10"><</span><span +class="cmti-10">degree</span><span +class="cmsy-10">> </span>rotates the coordinate system by <span +class="cmsy-10"><</span><span +class="cmti-10">degree</span><span +class="cmsy-10">></span>: + <!--l. 291--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" +cellspacing="0" cellpadding="0" +frame="void" id="TBL-308-" ><colgroup id="TBL-308-1g"><col +id="TBL-308-1"><col +id="TBL-308-2"></colgroup><tr + valign="baseline" id="TBL-308-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-308-1-1" +class="td11"> <object data="pgfmanual-301.svg" width="85.65822pt" height="66.93704pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object> </td><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-308-1-2" +class="td11"> <table class="minipage"><tr><td><div class="obeylines-v"> +<br><span +class="cmtt-8">\begin{tikzpicture}</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[style=help</span><span +class="cmtt-8"> lines]</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> grid</span><span +class="cmtt-8"> (3,2);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,1)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,0);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[rotate=40,blue]</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,1)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,0);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[rotate=-20,red]</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,1)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,0);</span> +<br><span +class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td> +</tr></table></div> + + + </li> + <li class="itemize"><span +class="cmtt-10">rotate around</span><a + id="dx14-157019"></a><a + id="dx14-157020"></a><span class="obeylines-h"><span class="verb"><span +class="cmtt-10">={</span></span></span><span +class="cmsy-10"><</span><span +class="cmti-10">degree</span><span +class="cmsy-10">></span><span class="obeylines-h"><span class="verb"><span +class="cmtt-10">:</span></span></span><span +class="cmsy-10"><</span><span +class="cmti-10">coordinate</span><span +class="cmsy-10">></span><span class="obeylines-h"><span class="verb"><span +class="cmtt-10">}</span></span></span> rotates the coordinate system by <span +class="cmsy-10"><</span><span +class="cmti-10">degree</span><span +class="cmsy-10">> </span>around the point + <span +class="cmsy-10"><</span><span +class="cmti-10">coordinate</span><span +class="cmsy-10">></span>. + <!--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-309-" ><colgroup id="TBL-309-1g"><col +id="TBL-309-1"><col +id="TBL-309-2"></colgroup><tr + valign="baseline" id="TBL-309-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-309-1-1" +class="td11"> <object data="pgfmanual-302.svg" width="93.674pt" height="68.83777pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object> </td><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-309-1-2" +class="td11"> <table class="minipage"><tr><td><div class="obeylines-v"> +<br><span +class="cmtt-8">\begin{tikzpicture}</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[style=help</span><span +class="cmtt-8"> lines]</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> grid</span><span +class="cmtt-8"> (3,2);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,1)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,0);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[rotate</span><span +class="cmtt-8"> around={40:(1,1)},blue]</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,1)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,0);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[rotate</span><span +class="cmtt-8"> around={-20:(1,1)},red]</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,1)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,0);</span> +<br><span +class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td> +</tr></table></div> + </li> + <li class="itemize"><span +class="cmtt-10">cm</span><a + id="dx14-157021"></a><a + id="dx14-157022"></a><span class="obeylines-h"><span class="verb"><span +class="cmtt-10">={</span></span></span><span +class="cmsy-10"><</span><span +class="cmmi-10">a</span><span +class="cmsy-10">></span><span class="obeylines-h"><span class="verb"><span +class="cmtt-10">,</span></span></span><span +class="cmsy-10"><</span><span +class="cmmi-10">b</span><span +class="cmsy-10">></span><span class="obeylines-h"><span class="verb"><span +class="cmtt-10">,</span></span></span><span +class="cmsy-10"><</span><span +class="cmmi-10">c</span><span +class="cmsy-10">></span><span class="obeylines-h"><span class="verb"><span +class="cmtt-10">,</span></span></span><span +class="cmsy-10"><</span><span +class="cmmi-10">d</span><span +class="cmsy-10">></span><span class="obeylines-h"><span class="verb"><span +class="cmtt-10">,</span></span></span><span +class="cmsy-10"><</span><span +class="cmti-10">coordinate</span><span +class="cmsy-10">></span><span class="obeylines-h"><span class="verb"><span +class="cmtt-10">}</span></span></span> applies the following transformation to all coordinates: Let (<span +class="cmmi-10">x,y</span>) be the + coordinate to be transformed and let <span +class="cmsy-10"><</span><span +class="cmti-10">coordinate</span><span +class="cmsy-10">> </span>specify the point (<span +class="cmmi-10">t</span><sub ><span +class="cmmi-7">x</span></sub><span +class="cmmi-10">,t</span><sub ><span +class="cmmi-7">y</span></sub>). Then the new coordinate is given + by <img +src="pgfmanual23x.gif" alt="(a b) + c d" class="left" align="middle"><img +src="pgfmanual24x.gif" alt=" x +(y)" class="left" align="middle"> + <img +src="pgfmanual25x.gif" alt="(tx) + ty" class="left" align="middle">. Usually, you do not use this option directly. + <!--l. 321--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" +cellspacing="0" cellpadding="0" +frame="void" id="TBL-310-" ><colgroup id="TBL-310-1g"><col +id="TBL-310-1"><col +id="TBL-310-2"></colgroup><tr + valign="baseline" id="TBL-310-1-"><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-310-1-1" +class="td11"> <object data="pgfmanual-303.svg" width="85.65822pt" height="57.30548pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object> </td><td align="left" style="white-space:nowrap; text-align:left;" id="TBL-310-1-2" +class="td11"> <table class="minipage"><tr><td><div class="obeylines-v"> +<br><span +class="cmtt-8">\begin{tikzpicture}</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[style=help</span><span +class="cmtt-8"> lines]</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> grid</span><span +class="cmtt-8"> (3,2);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,1)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,0);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[cm={1,1,0,1,(0,0)},blue]</span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> </span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,1)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,0);</span> +<br><span +class="cmtt-8"> </span><span +class="cmtt-8"> \draw[cm={0,1,1,0,(1cm,1cm)},red]</span><span +class="cmtt-8"> (0,0)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,1)</span><span +class="cmtt-8"> --</span><span +class="cmtt-8"> (1,0);</span> +<br><span +class="cmtt-8">\end{tikzpicture}</span></div> </td></tr></table> </td> +</tr></table></div> + </li> + <li class="itemize"><span +class="cmtt-10">reset cm</span><a + id="dx14-157023"></a><a + id="dx14-157024"></a> completely resets the coordinate transformation matrix to the identity matrix. This will destroy not + only the transformations applied in the current scope, but also all transformations inherited from surrounding + scopes. Do not use this option.</li></ul> + + + + + <div class="crosslinks"><p class="noindent">[<a +href="pgfmanualse12.html" >prev</a>] [<a +href="pgfmanualse12.html#tailpgfmanualse12.html" >prev-tail</a>] [<a +href="pgfmanualse13.html" >front</a>] [<a +href="pgfmanual.html#pgfmanualse13.html" >up</a>] </p></div> +<!--l. 181--><p class="indent"> <a + id="tailpgfmanualse13.html"></a> +</body></html> |