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<html><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><title>Scatter graphs</title><link rel="stylesheet" type="text/css" href="manual.css"><meta name="generator" content="DocBook XSL Stylesheets V1.76.0"><link rel="home" href="index.html" title="JpGraph Manual"><link rel="up" href="ch15.html" title="Chapter 15. Different types of linear (cartesian) graph types"></head><body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Scatter graphs</th></tr><tr><td width="20%" align="left"> </td><th width="60%" align="center">Chapter 15. Different types of linear (cartesian) graph types</th><td width="20%" align="right"> </td></tr></table><hr></div><div class="sect1" title="Scatter graphs"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a name="sec1.creating-scatter-graphs"></a>Scatter graphs</h2></div></div></div>
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<p>Scatter plots are used to display a number of data points given by there x- and
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y-coordinate. The difference from a line plot is that the x-coordinate must always
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be specified. Each point is stroked on the image with a mark as with line plots. The
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stroked marks can also be connected with an optional line.</p>
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<p>To use a scatter plot the module "<code class="filename">jpgraph_scatter.php</code>" must
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first be included in the script.</p>
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<p>
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</p><div class="note" title="Note" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Note</h3>
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<p>Carefully reviewing the constructor for line plots shows that it also can
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accept both a x- and y-array with coordinates. This means that a line plot
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can also be used to create a scatter plot. However scatter plots have some
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formatting options not available for line plots.</p>
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</div><p>
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</p>
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<p>Even though the normal use of scatter plots is to supply both x- and y-coordinates
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it is still perfectly possible to use a text- or int-scale for the x-coordinates to
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just enumerate the points (the points will be placed along an imaginary integer
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scale). This is especially useful when using the "Impulse" type of scatter plot as
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shown below.</p>
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<p>If no x-coordinates are specified each value will be placed at consecutive
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x-coordinates [<code class="code">1,2,3,..</code>] </p>
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<p>A scatter plot is constructed by creating an instance of the <code class="code">class
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ScatterPlot</code> supplied with the proper arguments, i.e.</p>
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<p>
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</p><div class="hl-main"><table class="hl-table" width="100%"><tr><td class="hl-gutter" align="right" valign="top"><pre>1
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</pre></td><td class="hl-main" valign="top"><pre><span class="hl-code">$scatterplot = new ScatterPlot($ydata, $xdata);</span></pre></td></tr></table></div><p>
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</p>
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<p>The following example shows a very basic scatter plot</p>
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<p>
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</p><div class="example"><a name="example.scatterex1"></a><p class="title"><b>Example 15.3. A basic scatter plot (<code class="filename">scatterex1.php</code>) </b></p><div class="example-contents"> <div class="hl-main"><table class="hl-table" width="100%"><tr><td class="hl-gutter" align="right" valign="top"><pre>1
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</pre></td><td class="hl-main" valign="top"><pre><span class="hl-inlinetags"><?php</span><span class="hl-code"> </span><span class="hl-comment">//</span><span class="hl-comment"> content="text/plain; charset=utf-8"</span><span class="hl-comment"></span><span class="hl-code">
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</span><span class="hl-reserved">require_once</span><span class="hl-code"> </span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">jpgraph/jpgraph.php</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
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</span><span class="hl-reserved">require_once</span><span class="hl-code"> </span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">jpgraph/jpgraph_scatter.php</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
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</span><span class="hl-var">$datax</span><span class="hl-code"> = </span><span class="hl-reserved">array</span><span class="hl-brackets">(</span><span class="hl-number">3</span><span class="hl-number">.5</span><span class="hl-code">,</span><span class="hl-number">3</span><span class="hl-number">.7</span><span class="hl-code">,</span><span class="hl-number">3</span><span class="hl-code">,</span><span class="hl-number">4</span><span class="hl-code">,</span><span class="hl-number">6</span><span class="hl-number">.2</span><span class="hl-code">,</span><span class="hl-number">6</span><span class="hl-code">,</span><span class="hl-number">3</span><span class="hl-number">.5</span><span class="hl-code">,</span><span class="hl-number">8</span><span class="hl-code">,</span><span class="hl-number">14</span><span class="hl-code">,</span><span class="hl-number">8</span><span class="hl-code">,</span><span class="hl-number">11</span><span class="hl-number">.1</span><span class="hl-code">,</span><span class="hl-number">13</span><span class="hl-number">.7</span><span class="hl-brackets">)</span><span class="hl-code">;
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</span><span class="hl-var">$datay</span><span class="hl-code"> = </span><span class="hl-reserved">array</span><span class="hl-brackets">(</span><span class="hl-number">20</span><span class="hl-code">,</span><span class="hl-number">22</span><span class="hl-code">,</span><span class="hl-number">12</span><span class="hl-code">,</span><span class="hl-number">13</span><span class="hl-code">,</span><span class="hl-number">17</span><span class="hl-code">,</span><span class="hl-number">20</span><span class="hl-code">,</span><span class="hl-number">16</span><span class="hl-code">,</span><span class="hl-number">19</span><span class="hl-code">,</span><span class="hl-number">30</span><span class="hl-code">,</span><span class="hl-number">31</span><span class="hl-code">,</span><span class="hl-number">40</span><span class="hl-code">,</span><span class="hl-number">43</span><span class="hl-brackets">)</span><span class="hl-code">;
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</span><span class="hl-var">$graph</span><span class="hl-code"> = </span><span class="hl-reserved">new</span><span class="hl-code"> </span><span class="hl-identifier">Graph</span><span class="hl-brackets">(</span><span class="hl-number">300</span><span class="hl-code">,</span><span class="hl-number">200</span><span class="hl-brackets">)</span><span class="hl-code">;
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</span><span class="hl-var">$graph</span><span class="hl-code">-></span><span class="hl-identifier">SetScale</span><span class="hl-brackets">(</span><span class="hl-quotes">"</span><span class="hl-string">linlin</span><span class="hl-quotes">"</span><span class="hl-brackets">)</span><span class="hl-code">;
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</span><span class="hl-var">$graph</span><span class="hl-code">-></span><span class="hl-identifier">img</span><span class="hl-code">-></span><span class="hl-identifier">SetMargin</span><span class="hl-brackets">(</span><span class="hl-number">40</span><span class="hl-code">,</span><span class="hl-number">40</span><span class="hl-code">,</span><span class="hl-number">40</span><span class="hl-code">,</span><span class="hl-number">40</span><span class="hl-brackets">)</span><span class="hl-code">;
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</span><span class="hl-var">$graph</span><span class="hl-code">-></span><span class="hl-identifier">SetShadow</span><span class="hl-brackets">(</span><span class="hl-brackets">)</span><span class="hl-code">;
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</span><span class="hl-var">$graph</span><span class="hl-code">-></span><span class="hl-identifier">title</span><span class="hl-code">-></span><span class="hl-identifier">Set</span><span class="hl-brackets">(</span><span class="hl-quotes">"</span><span class="hl-string">A simple scatter plot</span><span class="hl-quotes">"</span><span class="hl-brackets">)</span><span class="hl-code">;
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</span><span class="hl-var">$graph</span><span class="hl-code">-></span><span class="hl-identifier">title</span><span class="hl-code">-></span><span class="hl-identifier">SetFont</span><span class="hl-brackets">(</span><span class="hl-identifier">FF_FONT1</span><span class="hl-code">,</span><span class="hl-identifier">FS_BOLD</span><span class="hl-brackets">)</span><span class="hl-code">;
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</span><span class="hl-var">$sp1</span><span class="hl-code"> = </span><span class="hl-reserved">new</span><span class="hl-code"> </span><span class="hl-identifier">ScatterPlot</span><span class="hl-brackets">(</span><span class="hl-var">$datay</span><span class="hl-code">,</span><span class="hl-var">$datax</span><span class="hl-brackets">)</span><span class="hl-code">;
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</span><span class="hl-var">$graph</span><span class="hl-code">-></span><span class="hl-identifier">Add</span><span class="hl-brackets">(</span><span class="hl-var">$sp1</span><span class="hl-brackets">)</span><span class="hl-code">;
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</span><span class="hl-var">$graph</span><span class="hl-code">-></span><span class="hl-identifier">Stroke</span><span class="hl-brackets">(</span><span class="hl-brackets">)</span><span class="hl-code">;
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</span><span class="hl-inlinetags">?></span></pre></td></tr></table></div></div></div><p><br class="example-break"> </p><div class="figure"><a name="fig.scatterex1"></a><p class="title"><b>Figure 15.65. A basic scatter plot <code class="uri"><a class="uri" href="example_src/scatterex1.html" target="_top">(<code class="filename">scatterex1.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/scatterex1.png" alt="A basic scatter plot (scatterex1.php)"></span> </div></div><p><br class="figure-break">
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</p>
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<p>In the same way as we adjusted the look and feel for markers for line plot (see
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??) we can do the same here as shown in <a class="xref" href="ch15s05.html#fig.scatterex2" title="Figure 15.66. Adjusting the size and color of the marker (scatterex2.php)">Figure 15.66. Adjusting the size and color of the marker <code class="uri"><a class="uri" href="example_src/scatterex2.html" target="_top">(<code class="filename">scatterex2.php</code>)</a></code> </a></p>
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<p>
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</p><div class="figure"><a name="fig.scatterex2"></a><p class="title"><b>Figure 15.66. Adjusting the size and color of the marker <code class="uri"><a class="uri" href="example_src/scatterex2.html" target="_top">(<code class="filename">scatterex2.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/scatterex2.png" alt="Adjusting the size and color of the marker (scatterex2.php)"></span> </div></div><p><br class="figure-break">
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</p>
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<p>The marks are accessed through the instance variable
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<code class="code">ScatterPlot::mark</code> (in complete analogy with line plots)</p>
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<div class="sect2" title="Combining marks with a line"><div class="titlepage"><div><div><h3 class="title"><a name="id2561472"></a>Combining marks with a line</h3></div></div></div>
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<p>It is possible to combine the individual data points with a line - a link. The
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properties for this link can be accessed by using the instance variable
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<code class="code">ScatterPlot::link</code>.In order to enable the link the method
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<code class="code">ScatterPlot::link::Show()</code> must first be called.</p>
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<p>
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</p><div class="note" title="Note" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Note</h3>
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<p>For historical reasons there is also a utility method
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ScatterPlot::SetLinkPoints() where links can be enabled and adjusted.
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However, this method will be removed in future versions of the
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library.</p>
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</div><p>
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</p>
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<p>The properties that can be adjusted are the normal line properties, i.e.
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weight, color and line style. The following code snippet shows how to add a link
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line with a dotted style drawn in black to scatter plot.</p>
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<p>
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</p><div class="hl-main"><table class="hl-table" width="100%"><tr><td class="hl-gutter" align="right" valign="top"><pre>1
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</pre></td><td class="hl-main" valign="top"><pre><span class="hl-inlinetags"><?php</span><span class="hl-code">
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</span><span class="hl-comment">//</span><span class="hl-comment"> Enable the link lines</span><span class="hl-comment"></span><span class="hl-code">
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</span><span class="hl-var">$scatterplot</span><span class="hl-code">-></span><span class="hl-identifier">link</span><span class="hl-code">-></span><span class="hl-identifier">Show</span><span class="hl-brackets">(</span><span class="hl-brackets">)</span><span class="hl-code">;
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</span><span class="hl-comment">//</span><span class="hl-comment"> Set the properties</span><span class="hl-comment"></span><span class="hl-code">
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</span><span class="hl-var">$scatterplot</span><span class="hl-code">-></span><span class="hl-identifier">link</span><span class="hl-code">-></span><span class="hl-identifier">SetWeigth</span><span class="hl-brackets">(</span><span class="hl-number">1</span><span class="hl-brackets">)</span><span class="hl-code">;
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</span><span class="hl-var">$scatterplot</span><span class="hl-code">-></span><span class="hl-identifier">link</span><span class="hl-code">-></span><span class="hl-identifier">SetColor</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">black</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
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</span><span class="hl-var">$scatterplot</span><span class="hl-code">-></span><span class="hl-identifier">link</span><span class="hl-code">-></span><span class="hl-identifier">SetStyle</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">dotted</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
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</span><span class="hl-inlinetags">?></span></pre></td></tr></table></div><p>
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</p>
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<p>In <a class="xref" href="ch15s05.html#fig.scatterlinkex3" title="Figure 15.67. Combining data points with a dotted line (scatterlinkex3.php)">Figure 15.67. Combining data points with a dotted line <code class="uri"><a class="uri" href="example_src/scatterlinkex3.html" target="_top">(<code class="filename">scatterlinkex3.php</code>)</a></code> </a> and <a class="xref" href="ch15s05.html#fig.scatterlinkex4" title="Figure 15.68. Combining data points with a red line (scatterlinkex4.php)">Figure 15.68. Combining data points with a red line <code class="uri"><a class="uri" href="example_src/scatterlinkex4.html" target="_top">(<code class="filename">scatterlinkex4.php</code>)</a></code> </a> there are two variants of adding a link
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line to a scatter plot. For those figures we have also used two of the
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predefined scientific axis styles (see <a class="xref" href="ch14.html#sec2.predef-axis-setup" title="Predefined scientific axis setups">Predefined scientific axis setups</a>).</p>
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<p>
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</p><div class="informaltable">
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<table border="0"><colgroup><col class="c1"><col class="c2"></colgroup><tbody><tr><td>
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<div class="figure"><a name="fig.scatterlinkex3"></a><p class="title"><b>Figure 15.67. Combining data points with a dotted line <code class="uri"><a class="uri" href="example_src/scatterlinkex3.html" target="_top">(<code class="filename">scatterlinkex3.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/scatterlinkex3.png" alt="Combining data points with a dotted line (scatterlinkex3.php)"></span> </div></div><br class="figure-break">
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</td><td>
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<div class="figure"><a name="fig.scatterlinkex4"></a><p class="title"><b>Figure 15.68. Combining data points with a red line <code class="uri"><a class="uri" href="example_src/scatterlinkex4.html" target="_top">(<code class="filename">scatterlinkex4.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/scatterlinkex4.png" alt="Combining data points with a red line (scatterlinkex4.php)"></span> </div></div><br class="figure-break">
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</td></tr></tbody></table>
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</div><p>
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</p>
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</div>
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<div class="sect2" title="Creating impulse (or stem) - plots"><div class="titlepage"><div><div><h3 class="title"><a name="id2561573"></a>Creating impulse (or stem) - plots</h3></div></div></div>
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<p>A variant of scatter plots often used electrical engineering is the stem plot
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as shown in <a class="xref" href="ch15s02.html#fig.barplot-patterns" title="Figure 15.56. Supported pattern fills for bar plots">Figure 15.56. Supported pattern fills for bar plots</a></p>
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<p>
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</p><div class="figure"><a name="fig.impulsex1"></a><p class="title"><b>Figure 15.69. Stem plot <code class="uri"><a class="uri" href="example_src/impulsex1.html" target="_top">(<code class="filename">impulsex1.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/impulsex1.png" alt="Stem plot (impulsex1.php)"></span> </div></div><p><br class="figure-break">
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</p>
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<p>This variant of the scatter plot is created by calling the method</p>
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<p>
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</p><div class="hl-main"><table class="hl-table" width="100%"><tr><td class="hl-gutter" align="right" valign="top"><pre>1
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</pre></td><td class="hl-main" valign="top"><pre><span class="hl-code">$scatterplot->SetStem();</span></pre></td></tr></table></div><p>
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</p>
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<div class="tip" title="Tip" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Tip</h3>
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<p>It is possible to create a stem graphs without any mark by specifying
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the mark type as (-1) . That way only the impulse lines will be
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drawn.</p>
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</div><p>In order to adjust the look and feel of the stems the following methods
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can be used</p>
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<p>
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</p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
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<p><code class="code">ScatterPlot::SetWeight($aWeight)</code></p>
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</li><li class="listitem">
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<p><code class="code">ScatterPlot::SetColor($aColor)</code></p>
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</li></ul></div><p>
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</p>
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<p>Another example of stem plot is shown in <a class="xref" href="ch15s05.html#fig.impulsex3" title="Figure 15.70. Adjusting the overall look and feel for the stem graph (impulsex3.php)">Figure 15.70. Adjusting the overall look and feel for the stem graph <code class="uri"><a class="uri" href="example_src/impulsex3.html" target="_top">(<code class="filename">impulsex3.php</code>)</a></code> </a>
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where we have adjusted both the look and feel of the stem plot as well as the
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position of the x-axis.</p>
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<p>
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</p><div class="figure"><a name="fig.impulsex3"></a><p class="title"><b>Figure 15.70. Adjusting the overall look and feel for the stem graph <code class="uri"><a class="uri" href="example_src/impulsex3.html" target="_top">(<code class="filename">impulsex3.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/impulsex3.png" alt="Adjusting the overall look and feel for the stem graph (impulsex3.php)"></span> </div></div><p><br class="figure-break">
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</p>
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<p>There is also another complex impulse example shown in <a class="xref" href="ch14s08.html#fig.impulsex4" title="Figure 14.58. Adding a static line at y=0 to simulate an extra 0-axis (impulsex4.php)">Figure 14.58. Adding a static line at y=0 to simulate an extra 0-axis <code class="uri"><a class="uri" href="example_src/impulsex4.html" target="_top">(<code class="filename">impulsex4.php</code>)</a></code> </a> where we have used a <code class="code">PlotLine</code> to
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|||
|
create a "virtual" x-axis.</p>
|
|||
|
</div>
|
|||
|
<div class="sect2" title="Field plots"><div class="titlepage"><div><div><h3 class="title"><a name="sec1.creating-field-graphs"></a>Field plots</h3></div></div></div>
|
|||
|
|
|||
|
<p>A variant of scatter plot is the so called Field Plots. </p>
|
|||
|
<p>This is basically a scatter plot where each scatter point is an arrow with a
|
|||
|
direction between 0 to 359 degrees. This effectively allows the visualization of
|
|||
|
3 parameters at each point (x,y and angle). </p>
|
|||
|
<p>A field plot is created as an instance of <code class="code">class FieldPlot</code> with
|
|||
|
three argument</p>
|
|||
|
<p>
|
|||
|
</p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
|
|||
|
<p>an array of y-coordinates</p>
|
|||
|
</li><li class="listitem">
|
|||
|
<p>an array of x-coordinates</p>
|
|||
|
</li><li class="listitem">
|
|||
|
<p>an array of angles</p>
|
|||
|
</li></ul></div><p>
|
|||
|
</p>
|
|||
|
<p>as the following code snippet shows</p>
|
|||
|
<p>
|
|||
|
</p><div class="hl-main"><table class="hl-table" width="100%"><tr><td class="hl-gutter" align="right" valign="top"><pre>1
|
|||
|
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-code">$fieldplot = new FieldPlot($datay, $datax, $angle);</span></pre></td></tr></table></div><p>
|
|||
|
</p>
|
|||
|
<p>The size and color of each arrow in the field plot is controlled by accessing
|
|||
|
the property <code class="code">FieldPlot::arrow</code> and using the two methods</p>
|
|||
|
<p>
|
|||
|
</p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
|
|||
|
<p><code class="code">FieldPlot::arrow->SetSize($aSize,$aArrowSize=2)</code></p>
|
|||
|
<p><code class="code">$aSize</code>, Specifies the length (in pixels) of the
|
|||
|
arrow</p>
|
|||
|
<p><code class="code">$aArrowSize</code>, The arrow size is specified as an
|
|||
|
integer in the range [0,9]. The possible arrow sizes are shown in
|
|||
|
<a class="xref" href="ch15s05.html#fig.field-arrow-sizes" title="Figure 15.71. Possible sizes of arrow heads for field plots">Figure 15.71. Possible sizes of arrow heads for field plots</a>.</p>
|
|||
|
<p>
|
|||
|
</p><div class="figure"><a name="fig.field-arrow-sizes"></a><p class="title"><b>Figure 15.71. Possible sizes of arrow heads for field plots</b></p><div class="figure-contents">
|
|||
|
|
|||
|
<div class="mediaobject"><img src="images/field_arrow_sizes.png" alt="Possible sizes of arrow heads for field plots"></div>
|
|||
|
</div></div><p><br class="figure-break">
|
|||
|
</p>
|
|||
|
</li><li class="listitem">
|
|||
|
<p><code class="code">FieldPlot::arrow->SetColor($aColor)</code></p>
|
|||
|
<p>The color of the arrow</p>
|
|||
|
</li></ul></div><p>
|
|||
|
</p>
|
|||
|
<p>Another way to individually format each arrow is to use a callback method. The
|
|||
|
callback method must have three arguments x- , y-coordinates and angle. The
|
|||
|
callback method must return an array with three elements (color,size,arrow
|
|||
|
size). The callback method is specified by calling</p>
|
|||
|
<p>
|
|||
|
</p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
|
|||
|
<p><code class="code">FieldPlot::SetCallback($aFunc)</code></p>
|
|||
|
</li></ul></div><p>
|
|||
|
</p>
|
|||
|
<p><a class="xref" href="ch15s05.html#fig.fieldscatterex1" title="Figure 15.72. A field plot (fieldscatterex1.php)">Figure 15.72. A field plot <code class="uri"><a class="uri" href="example_src/fieldscatterex1.html" target="_top">(<code class="filename">fieldscatterex1.php</code>)</a></code> </a> shows a field plot with a callback
|
|||
|
function.</p>
|
|||
|
<p>
|
|||
|
</p><div class="figure"><a name="fig.fieldscatterex1"></a><p class="title"><b>Figure 15.72. A field plot <code class="uri"><a class="uri" href="example_src/fieldscatterex1.html" target="_top">(<code class="filename">fieldscatterex1.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/fieldscatterex1.png" alt="A field plot (fieldscatterex1.php)"></span> </div></div><p><br class="figure-break">
|
|||
|
</p>
|
|||
|
</div>
|
|||
|
<div class="sect2" title="Balloon plots"><div class="titlepage"><div><div><h3 class="title"><a name="sec1.creating-balloon-graphs"></a>Balloon plots</h3></div></div></div>
|
|||
|
|
|||
|
<p>This is a variant of scatter plot where each data point is a filled circle and
|
|||
|
the size of the circle is dynamically adjusted. This makes it possible to
|
|||
|
display three values at each data point (x,y,"size"). There is no need for a
|
|||
|
specific plot type for this since these types of plots can be constructed with
|
|||
|
an ordinary scatter plot and a mark formatting callback.</p>
|
|||
|
<p>In order to specify a callback for the marks the following method is
|
|||
|
used</p>
|
|||
|
<p>
|
|||
|
</p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
|
|||
|
<p><code class="code">ScatterPlot::mark::SetCallbackYX($aFunction)</code></p>
|
|||
|
<p>The argument for the callback function is y- and x-value for the
|
|||
|
data point. The return value should specify the format of the marker
|
|||
|
as an array of <span class="italic">(width, border_color,
|
|||
|
fill_color, filename, image scale)</span>. All values must
|
|||
|
be included.</p>
|
|||
|
</li></ul></div><p>
|
|||
|
</p>
|
|||
|
<p>We can now create a balloon plot as follows. </p>
|
|||
|
<p>
|
|||
|
</p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem">
|
|||
|
<p>Create a data array that specifies the data including both x- and
|
|||
|
y-coordinate, color and size of the filled circle. For example
|
|||
|
as:</p>
|
|||
|
<p>
|
|||
|
</p><div class="hl-main"><table class="hl-table" width="100%"><tr><td class="hl-gutter" align="right" valign="top"><pre>1
|
|||
|
2
|
|||
|
3
|
|||
|
4
|
|||
|
5
|
|||
|
6
|
|||
|
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-code">$data = array(
|
|||
|
array(1,12,10,'orange'),
|
|||
|
array(3,41,15,'red'),
|
|||
|
array(4,5,19,'lightblue'),
|
|||
|
array(5,70,22,'yellow')
|
|||
|
);</span></pre></td></tr></table></div><p>
|
|||
|
</p>
|
|||
|
</li><li class="listitem">
|
|||
|
<p>We must now convert this to some suitable data for a scatter plot.
|
|||
|
The only thing to keep in mind is that we need to share the data
|
|||
|
with the callback function and for that purpose we store the
|
|||
|
formatting data in an external array indexed by the x,y-value. </p>
|
|||
|
<p>
|
|||
|
</p><div class="hl-main"><table class="hl-table" width="100%"><tr><td class="hl-gutter" align="right" valign="top"><pre>1
|
|||
|
2
|
|||
|
3
|
|||
|
4
|
|||
|
5
|
|||
|
6
|
|||
|
7
|
|||
|
8
|
|||
|
9
|
|||
|
10
|
|||
|
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-code">$n = count($data);
|
|||
|
for( $i=0; $i < $n; ++$i ) {
|
|||
|
|
|||
|
$datax[$i] = $data[$i][0];
|
|||
|
$datay[$i] = $data[$i][1];
|
|||
|
|
|||
|
|
|||
|
$format[ strval($datax[$i]) ][ strval($datay[$i]) ] = array( $data[$i][2], $data[$i][3] );
|
|||
|
|
|||
|
}</span></pre></td></tr></table></div><p>
|
|||
|
</p>
|
|||
|
<p>The callback function can now be specified as</p>
|
|||
|
<p>
|
|||
|
</p><div class="hl-main"><table class="hl-table" width="100%"><tr><td class="hl-gutter" align="right" valign="top"><pre>1
|
|||
|
2
|
|||
|
3
|
|||
|
4
|
|||
|
5
|
|||
|
6
|
|||
|
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-code">function FCallback($aYVal,$aXVal) {
|
|||
|
// We need to access the global format array
|
|||
|
global $format;
|
|||
|
return array($format[ strval($aXVal) ][ strval($aYVal) ][0],'',
|
|||
|
$format[ strval($aXVal) ][ strval($aYVal) ][1],'','');
|
|||
|
}</span></pre></td></tr></table></div><p>
|
|||
|
</p>
|
|||
|
<p>The callback function will now return the format value (size and
|
|||
|
color) we specified originally depending on the x,y - coordinate.
|
|||
|
The callback function can be installed with a call to</p>
|
|||
|
<p>
|
|||
|
</p><div class="hl-main"><table class="hl-table" width="100%"><tr><td class="hl-gutter" align="right" valign="top"><pre>1
|
|||
|
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-code">$sp1->mark->SetCallbackYX('FCallback');</span></pre></td></tr></table></div><p>
|
|||
|
</p>
|
|||
|
</li><li class="listitem">
|
|||
|
<p>The final step is to create an ordinary scatter plot with a marker
|
|||
|
that is specified as a filled circle</p>
|
|||
|
<p>
|
|||
|
</p><div class="hl-main"><table class="hl-table" width="100%"><tr><td class="hl-gutter" align="right" valign="top"><pre>1
|
|||
|
2
|
|||
|
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-code">$sp1 = new ScatterPlot($datay,$datax);
|
|||
|
$sp1->mark->SetType(MARK_FILLEDCIRCLE);</span></pre></td></tr></table></div><p>
|
|||
|
</p>
|
|||
|
</li></ol></div><p>
|
|||
|
</p>
|
|||
|
<p>As an optional additions we can also enable the display of the values at each
|
|||
|
data point by calling</p>
|
|||
|
<p>
|
|||
|
</p><div class="hl-main"><table class="hl-table" width="100%"><tr><td class="hl-gutter" align="right" valign="top"><pre>1
|
|||
|
2
|
|||
|
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-code">$sp1->value->Show();
|
|||
|
$sp1->value->SetFont(FF_FONT1,FS_BOLD);</span></pre></td></tr></table></div><p>
|
|||
|
</p>
|
|||
|
<p>Putting all these together gives the result shown in <a class="xref" href="ch15s05.html#fig.balloonex2" title="Figure 15.73. Using format callback to create a balloon plot (balloonex2.php)">Figure 15.73. Using format callback to create a balloon plot <code class="uri"><a class="uri" href="example_src/balloonex2.html" target="_top">(<code class="filename">balloonex2.php</code>)</a></code> </a></p>
|
|||
|
<p>
|
|||
|
</p><div class="figure"><a name="fig.balloonex2"></a><p class="title"><b>Figure 15.73. Using format callback to create a balloon plot <code class="uri"><a class="uri" href="example_src/balloonex2.html" target="_top">(<code class="filename">balloonex2.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/balloonex2.png" alt="Using format callback to create a balloon plot (balloonex2.php)"></span> </div></div><p><br class="figure-break">
|
|||
|
</p>
|
|||
|
</div>
|
|||
|
<div class="sect2" title="Creating Geo-maps"><div class="titlepage"><div><div><h3 class="title"><a name="sec1.creating-geo-maps"></a>Creating Geo-maps</h3></div></div></div>
|
|||
|
|
|||
|
<p>Geo-maps (a.k.a. Geo-charts, push-pin graphs) is used to illustrate locations
|
|||
|
around the world by putting markers on a flat projection of the earth. A Geo-map
|
|||
|
is done by adding a Worldmap background to a standard scatter graph. The library
|
|||
|
includes a suitable background in the "<code class="filename">Examples/</code>" directory
|
|||
|
"<code class="filename">wordmap1.jpg</code>". This can then be done as the following
|
|||
|
example shows</p>
|
|||
|
<p>
|
|||
|
</p><div class="example"><a name="example.pushpinex1"></a><p class="title"><b>Example 15.4. An example with geo maps (<code class="filename">pushpinex1.php</code>) </b></p><div class="example-contents"> <div class="hl-main"><table class="hl-table" width="100%"><tr><td class="hl-gutter" align="right" valign="top"><pre>1
|
|||
|
2
|
|||
|
3
|
|||
|
4
|
|||
|
5
|
|||
|
6
|
|||
|
7
|
|||
|
8
|
|||
|
9
|
|||
|
10
|
|||
|
11
|
|||
|
12
|
|||
|
13
|
|||
|
14
|
|||
|
15
|
|||
|
16
|
|||
|
17
|
|||
|
18
|
|||
|
19
|
|||
|
20
|
|||
|
21
|
|||
|
22
|
|||
|
23
|
|||
|
24
|
|||
|
25
|
|||
|
26
|
|||
|
27
|
|||
|
28
|
|||
|
29
|
|||
|
30
|
|||
|
31
|
|||
|
32
|
|||
|
33
|
|||
|
34
|
|||
|
35
|
|||
|
36
|
|||
|
37
|
|||
|
38
|
|||
|
39
|
|||
|
40
|
|||
|
41
|
|||
|
42
|
|||
|
43
|
|||
|
44
|
|||
|
45
|
|||
|
46
|
|||
|
47
|
|||
|
48
|
|||
|
49
|
|||
|
50
|
|||
|
51
|
|||
|
52
|
|||
|
53
|
|||
|
54
|
|||
|
55
|
|||
|
56
|
|||
|
57
|
|||
|
58
|
|||
|
59
|
|||
|
60
|
|||
|
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-inlinetags"><?php</span><span class="hl-code"> </span><span class="hl-comment">//</span><span class="hl-comment"> content="text/plain; charset=utf-8"</span><span class="hl-comment"></span><span class="hl-code">
|
|||
|
</span><span class="hl-reserved">require_once</span><span class="hl-code"> </span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">jpgraph/jpgraph.php</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
|
|||
|
</span><span class="hl-reserved">require_once</span><span class="hl-code"> </span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">jpgraph/jpgraph_scatter.php</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
|
|||
|
|
|||
|
</span><span class="hl-reserved">DEFINE</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">WORLDMAP</span><span class="hl-quotes">'</span><span class="hl-code">,</span><span class="hl-quotes">'</span><span class="hl-string">worldmap1.jpg</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
|
|||
|
|
|||
|
</span><span class="hl-reserved">function</span><span class="hl-code"> </span><span class="hl-identifier">markCallback</span><span class="hl-brackets">(</span><span class="hl-var">$y</span><span class="hl-code">,</span><span class="hl-var">$x</span><span class="hl-brackets">)</span><span class="hl-code"> </span><span class="hl-brackets">{</span><span class="hl-code">
|
|||
|
</span><span class="hl-comment">//</span><span class="hl-comment"> Return array width</span><span class="hl-comment"></span><span class="hl-code">
|
|||
|
</span><span class="hl-comment">//</span><span class="hl-comment"> width,color,fill color, marker filename, imgscale</span><span class="hl-comment"></span><span class="hl-code">
|
|||
|
</span><span class="hl-comment">//</span><span class="hl-comment"> any value can be false, in that case the default value will</span><span class="hl-comment"></span><span class="hl-code">
|
|||
|
</span><span class="hl-comment">//</span><span class="hl-comment"> be used.</span><span class="hl-comment"></span><span class="hl-code">
|
|||
|
</span><span class="hl-comment">//</span><span class="hl-comment"> We only make one pushpin another color</span><span class="hl-comment"></span><span class="hl-code">
|
|||
|
</span><span class="hl-reserved">if</span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-var">$x</span><span class="hl-code"> == </span><span class="hl-number">54</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code">
|
|||
|
</span><span class="hl-reserved">return</span><span class="hl-code"> </span><span class="hl-reserved">array</span><span class="hl-brackets">(</span><span class="hl-reserved">false</span><span class="hl-code">,</span><span class="hl-reserved">false</span><span class="hl-code">,</span><span class="hl-reserved">false</span><span class="hl-code">,</span><span class="hl-quotes">'</span><span class="hl-string">red</span><span class="hl-quotes">'</span><span class="hl-code">,</span><span class="hl-number">0</span><span class="hl-number">.8</span><span class="hl-brackets">)</span><span class="hl-code">;
|
|||
|
</span><span class="hl-reserved">else</span><span class="hl-code">
|
|||
|
</span><span class="hl-reserved">return</span><span class="hl-code"> </span><span class="hl-reserved">array</span><span class="hl-brackets">(</span><span class="hl-reserved">false</span><span class="hl-code">,</span><span class="hl-reserved">false</span><span class="hl-code">,</span><span class="hl-reserved">false</span><span class="hl-code">,</span><span class="hl-quotes">'</span><span class="hl-string">green</span><span class="hl-quotes">'</span><span class="hl-code">,</span><span class="hl-number">0</span><span class="hl-number">.8</span><span class="hl-brackets">)</span><span class="hl-code">;
|
|||
|
</span><span class="hl-brackets">}</span><span class="hl-code">
|
|||
|
|
|||
|
</span><span class="hl-comment">//</span><span class="hl-comment"> Data arrays</span><span class="hl-comment"></span><span class="hl-code">
|
|||
|
</span><span class="hl-var">$datax</span><span class="hl-code"> = </span><span class="hl-reserved">array</span><span class="hl-brackets">(</span><span class="hl-number">10</span><span class="hl-code">,</span><span class="hl-number">20</span><span class="hl-code">,</span><span class="hl-number">30</span><span class="hl-code">,</span><span class="hl-number">40</span><span class="hl-code">,</span><span class="hl-number">54</span><span class="hl-code">,</span><span class="hl-number">60</span><span class="hl-code">,</span><span class="hl-number">70</span><span class="hl-code">,</span><span class="hl-number">80</span><span class="hl-brackets">)</span><span class="hl-code">;
|
|||
|
</span><span class="hl-var">$datay</span><span class="hl-code"> = </span><span class="hl-reserved">array</span><span class="hl-brackets">(</span><span class="hl-number">12</span><span class="hl-code">,</span><span class="hl-number">23</span><span class="hl-code">,</span><span class="hl-number">65</span><span class="hl-code">,</span><span class="hl-number">18</span><span class="hl-code">,</span><span class="hl-number">84</span><span class="hl-code">,</span><span class="hl-number">28</span><span class="hl-code">,</span><span class="hl-number">86</span><span class="hl-code">,</span><span class="hl-number">44</span><span class="hl-brackets">)</span><span class="hl-code">;
|
|||
|
|
|||
|
</span><span class="hl-comment">//</span><span class="hl-comment"> Setup the graph</span><span class="hl-comment"></span><span class="hl-code">
|
|||
|
</span><span class="hl-var">$graph</span><span class="hl-code"> = </span><span class="hl-reserved">new</span><span class="hl-code"> </span><span class="hl-identifier">Graph</span><span class="hl-brackets">(</span><span class="hl-number">400</span><span class="hl-code">,</span><span class="hl-number">270</span><span class="hl-brackets">)</span><span class="hl-code">;
|
|||
|
|
|||
|
</span><span class="hl-comment">//</span><span class="hl-comment"> We add a small 1pixel left,right,bottom margin so the plot area</span><span class="hl-comment"></span><span class="hl-code">
|
|||
|
</span><span class="hl-comment">//</span><span class="hl-comment"> doesn't cover the frame around the graph.</span><span class="hl-comment"></span><span class="hl-code">
|
|||
|
</span><span class="hl-var">$graph</span><span class="hl-code">-></span><span class="hl-identifier">img</span><span class="hl-code">-></span><span class="hl-identifier">SetMargin</span><span class="hl-brackets">(</span><span class="hl-number">1</span><span class="hl-code">,</span><span class="hl-number">1</span><span class="hl-code">,</span><span class="hl-number">1</span><span class="hl-code">,</span><span class="hl-number">1</span><span class="hl-brackets">)</span><span class="hl-code">;
|
|||
|
</span><span class="hl-var">$graph</span><span class="hl-code">-></span><span class="hl-identifier">SetScale</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">linlin</span><span class="hl-quotes">'</span><span class="hl-code">,</span><span class="hl-number">0</span><span class="hl-code">,</span><span class="hl-number">100</span><span class="hl-code">,</span><span class="hl-number">0</span><span class="hl-code">,</span><span class="hl-number">100</span><span class="hl-brackets">)</span><span class="hl-code">;
|
|||
|
|
|||
|
</span><span class="hl-comment">//</span><span class="hl-comment"> We don't want any axis to be shown</span><span class="hl-comment"></span><span class="hl-code">
|
|||
|
</span><span class="hl-var">$graph</span><span class="hl-code">-></span><span class="hl-identifier">xaxis</span><span class="hl-code">-></span><span class="hl-identifier">Hide</span><span class="hl-brackets">(</span><span class="hl-brackets">)</span><span class="hl-code">;
|
|||
|
</span><span class="hl-var">$graph</span><span class="hl-code">-></span><span class="hl-identifier">yaxis</span><span class="hl-code">-></span><span class="hl-identifier">Hide</span><span class="hl-brackets">(</span><span class="hl-brackets">)</span><span class="hl-code">;
|
|||
|
|
|||
|
</span><span class="hl-comment">//</span><span class="hl-comment"> Use a worldmap as the background and let it fill the plot area</span><span class="hl-comment"></span><span class="hl-code">
|
|||
|
</span><span class="hl-var">$graph</span><span class="hl-code">-></span><span class="hl-identifier">SetBackgroundImage</span><span class="hl-brackets">(</span><span class="hl-identifier">WORLDMAP</span><span class="hl-code">,</span><span class="hl-identifier">BGIMG_FILLPLOT</span><span class="hl-brackets">)</span><span class="hl-code">;
|
|||
|
|
|||
|
</span><span class="hl-comment">//</span><span class="hl-comment"> Setup a nice title with a striped bevel background</span><span class="hl-comment"></span><span class="hl-code">
|
|||
|
</span><span class="hl-var">$graph</span><span class="hl-code">-></span><span class="hl-identifier">title</span><span class="hl-code">-></span><span class="hl-identifier">Set</span><span class="hl-brackets">(</span><span class="hl-quotes">"</span><span class="hl-string">Pushpin graph</span><span class="hl-quotes">"</span><span class="hl-brackets">)</span><span class="hl-code">;
|
|||
|
</span><span class="hl-var">$graph</span><span class="hl-code">-></span><span class="hl-identifier">title</span><span class="hl-code">-></span><span class="hl-identifier">SetFont</span><span class="hl-brackets">(</span><span class="hl-identifier">FF_ARIAL</span><span class="hl-code">,</span><span class="hl-identifier">FS_BOLD</span><span class="hl-code">,</span><span class="hl-number">16</span><span class="hl-brackets">)</span><span class="hl-code">;
|
|||
|
</span><span class="hl-var">$graph</span><span class="hl-code">-></span><span class="hl-identifier">title</span><span class="hl-code">-></span><span class="hl-identifier">SetColor</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">white</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
|
|||
|
</span><span class="hl-var">$graph</span><span class="hl-code">-></span><span class="hl-identifier">SetTitleBackground</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">darkgreen</span><span class="hl-quotes">'</span><span class="hl-code">,</span><span class="hl-identifier">TITLEBKG_STYLE1</span><span class="hl-code">,</span><span class="hl-identifier">TITLEBKG_FRAME_BEVEL</span><span class="hl-brackets">)</span><span class="hl-code">;
|
|||
|
</span><span class="hl-var">$graph</span><span class="hl-code">-></span><span class="hl-identifier">SetTitleBackgroundFillStyle</span><span class="hl-brackets">(</span><span class="hl-identifier">TITLEBKG_FILLSTYLE_HSTRIPED</span><span class="hl-code">,</span><span class="hl-quotes">'</span><span class="hl-string">blue</span><span class="hl-quotes">'</span><span class="hl-code">,</span><span class="hl-quotes">'</span><span class="hl-string">darkgreen</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
|
|||
|
|
|||
|
</span><span class="hl-comment">//</span><span class="hl-comment"> Finally create the scatterplot</span><span class="hl-comment"></span><span class="hl-code">
|
|||
|
</span><span class="hl-var">$sp</span><span class="hl-code"> = </span><span class="hl-reserved">new</span><span class="hl-code"> </span><span class="hl-identifier">ScatterPlot</span><span class="hl-brackets">(</span><span class="hl-var">$datay</span><span class="hl-code">,</span><span class="hl-var">$datax</span><span class="hl-brackets">)</span><span class="hl-code">;
|
|||
|
|
|||
|
</span><span class="hl-comment">//</span><span class="hl-comment"> We want the markers to be an image</span><span class="hl-comment"></span><span class="hl-code">
|
|||
|
</span><span class="hl-var">$sp</span><span class="hl-code">-></span><span class="hl-identifier">mark</span><span class="hl-code">-></span><span class="hl-identifier">SetType</span><span class="hl-brackets">(</span><span class="hl-identifier">MARK_IMG_PUSHPIN</span><span class="hl-code">,</span><span class="hl-quotes">'</span><span class="hl-string">blue</span><span class="hl-quotes">'</span><span class="hl-code">,</span><span class="hl-number">0</span><span class="hl-number">.6</span><span class="hl-brackets">)</span><span class="hl-code">;
|
|||
|
|
|||
|
</span><span class="hl-comment">//</span><span class="hl-comment"> Install the Y-X callback for the markers</span><span class="hl-comment"></span><span class="hl-code">
|
|||
|
</span><span class="hl-var">$sp</span><span class="hl-code">-></span><span class="hl-identifier">mark</span><span class="hl-code">-></span><span class="hl-identifier">SetCallbackYX</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">markCallback</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
|
|||
|
|
|||
|
</span><span class="hl-comment">//</span><span class="hl-comment"> ... and add it to the graph</span><span class="hl-comment"></span><span class="hl-code">
|
|||
|
</span><span class="hl-var">$graph</span><span class="hl-code">-></span><span class="hl-identifier">Add</span><span class="hl-brackets">(</span><span class="hl-var">$sp</span><span class="hl-brackets">)</span><span class="hl-code">;
|
|||
|
|
|||
|
</span><span class="hl-comment">//</span><span class="hl-comment"> .. and output to browser</span><span class="hl-comment"></span><span class="hl-code">
|
|||
|
</span><span class="hl-var">$graph</span><span class="hl-code">-></span><span class="hl-identifier">Stroke</span><span class="hl-brackets">(</span><span class="hl-brackets">)</span><span class="hl-code">;
|
|||
|
|
|||
|
</span><span class="hl-inlinetags">?></span></pre></td></tr></table></div></div></div><p><br class="example-break"> </p><div class="figure"><a name="fig.pushpinex1"></a><p class="title"><b>Figure 15.74. An example with geo maps <code class="uri"><a class="uri" href="example_src/pushpinex1.html" target="_top">(<code class="filename">pushpinex1.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/pushpinex1.png" alt="An example with geo maps (pushpinex1.php)"></span> </div></div><p><br class="figure-break">
|
|||
|
</p>
|
|||
|
<p>Another example of using worldmaps with Pie graphs is shown in <a class="xref" href="ch16.html#sec.pie-image-background" title="Adding background images to Pie graphs">Adding background images to Pie graphs</a></p>
|
|||
|
<p>
|
|||
|
</p><div class="note" title="Note" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Note</h3>
|
|||
|
<p>The library does not include any conversion utility to/from
|
|||
|
Longitude/Latitude to UTM coordinates that could be used to
|
|||
|
automatically position data marks on the Mercator projection map. The
|
|||
|
options to stretch and scale the worldmap would make it rather
|
|||
|
cumbersome to create a accurate conversion. For a good overview on this
|
|||
|
kind of translation see <code class="uri"><a class="uri" href="http://www.gpsy.com/gpsinfo/geotoutm/" target="_top">Converting
|
|||
|
Latitude/Longitude to Universal Transverse Mercator
|
|||
|
(UTM)</a></code></p>
|
|||
|
</div><p>
|
|||
|
</p>
|
|||
|
</div>
|
|||
|
</div><div class="navfooter"><hr><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"> </td><td width="20%" align="center"><a accesskey="u" href="ch15.html">Up</a></td><td width="40%" align="right"> </td></tr><tr><td width="40%" align="left" valign="top"> </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> </td></tr></table></div></body></html>
|