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<html><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><title>Chapter 15. Different types of linear (cartesian) graph types</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="pt04.html" title="Part IV. Creating linear and non-linear graphs"></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">Chapter 15. Different types of linear (cartesian) graph types</th></tr><tr><td width="20%" align="left"> </td><th width="60%" align="center">Part IV. Creating linear and non-linear graphs</th><td width="20%" align="right"> </td></tr></table><hr></div><div class="chapter" title="Chapter 15. Different types of linear (cartesian) graph types"><div class="titlepage"><div><div><h2 class="title"><a name="id2554010"></a>Chapter 15. Different types of linear (cartesian) graph types</h2></div></div></div><div class="toc"><p><b>Table of Contents</b></p><dl><dt><span class="sect1"><a href="ch15.html#id2553962">15.1. Basic Line and area graphs</a></span></dt><dd><dl><dt><span class="sect2"><a href="ch15.html#sec2.creating-line-graph">15.1.1. Creating a line graph</a></span></dt><dt><span class="sect2"><a href="ch15.html#id2554907">15.1.2. Automatic interpolation of unknown data</a></span></dt><dt><span class="sect2"><a href="ch15.html#sec.adding-marks">15.1.3. Adding marks to the plot (a.k.a. plot marks)</a></span></dt><dt><span class="sect2"><a href="ch15.html#id2555079">15.1.4. Displaying the values at the data points</a></span></dt><dt><span class="sect2"><a href="ch15.html#id2555706">15.1.5. Adding several data series to the same graph</a></span></dt><dt><span class="sect2"><a href="ch15.html#id2555784">15.1.6. Adding a second Y-axis</a></span></dt><dt><span class="sect2"><a href="ch15.html#id2555973">15.1.7. Adding a legend box to the graph</a></span></dt><dt><span class="sect2"><a href="ch15.html#id2556231">15.1.8. Changing the style of the line plot - using the step-style</a></span></dt><dt><span class="sect2"><a href="ch15.html#id2556258">15.1.9. Optimizing line plot using "fast drawing"</a></span></dt><dt><span class="sect2"><a href="ch15.html#sec2.creating-area-graph">15.1.10. Creating a filled line graphs (a.k.a. area plots)</a></span></dt><dt><span class="sect2"><a href="ch15.html#id2557119">15.1.11. Partially filled area graphs</a></span></dt><dt><span class="sect2"><a href="ch15.html#id2557375">15.1.12. Filled lines with NULL values</a></span></dt><dt><span class="sect2"><a href="ch15.html#id2557421">15.1.13. Accumulated line graphs</a></span></dt><dt><span class="sect2"><a href="ch15.html#id2557468">15.1.14. Accumulated line graphs with given X-labels</a></span></dt><dt><span class="sect2"><a href="ch15.html#sec2.creating-cubic-splines">15.1.15. Constructing smooth line plots with Cubic Splines</a></span></dt></dl></dd><dt><span class="sect1"><a href="ch15s02.html">15.2. Bar graphs</a></span></dt><dd><dl><dt><span class="sect2"><a href="ch15s02.html#id2558886">15.2.1. Accumulated bar plots</a></span></dt><dt><span class="sect2"><a href="ch15s02.html#id2559176">15.2.2. Grouped bar plots</a></span></dt><dt><span class="sect2"><a href="ch15s02.html#id2559365">15.2.3. Grouped accumulated bar graphs</a></span></dt><dt><span class="sect2"><a href="ch15s02.html#id2559425">15.2.4. Horizontal bar graphs</a></span></dt><dt><span class="sect2"><a href="ch15s02.html#id2559503">15.2.5. Adjusting the appearance of bar graphs</a></span></dt></dl></dd><dt><span class="sect1"><a href="ch15s03.html">15.3. Error plot graphs</a></span></dt><dd><dl><dt><span class="sect2"><a href="ch15s03.html#id2560625">15.3.1. Line error plots</a></span></dt></dl></dd><dt><span class="sect1"><a href="ch15s04.html">15.4. Stock graphs</a></span></dt><dd><dl><dt><span class="sect2"><a href="ch15s04.html#id2561152">15.4.1. Stock plot variant: Boxplot</a></span></dt><dt><span class="sect2"><a href="ch15s04.html#id2561251">15.4.2.  Image maps for Box and Stock charts</a></span></dt></dl></dd><dt><span class="sect1"><a href="ch15s05.html">15.5. Scatter graphs</a></span></dt><dd><dl><dt><span class="sect2"><a href="ch15s05.html#id2561472">15.5.1. Combining marks with a line</a></span></dt><dt><span class="sect2"><a href="ch15s05.html#id2561573">15.5.2. Creating impulse (or stem) - plots</a></span></dt><dt><span class="sect2"><a href="ch15s05.html#sec1.creating-field-graphs">15.5.3. Field plots</a></span></dt><dt><span class="sect2"><a href="ch15s05.html#sec1.creating-balloon-graphs">15.5.4. Balloon plots</a></span></dt><dt><span class="sect2"><a href="ch15s05.html#sec1.creating-geo-maps">15.5.5. Creating Geo-maps</a></span></dt></dl></dd><dt><span class="sect1"><a href="ch15s06.html">15.6. Contour graphs </a></span></dt><dd><dl><dt><span class="sect2"><a href="ch15s06.html#id2562600">15.6.1. Input data for contour graphs</a></span></dt><dt><span class="sect2"><a href="ch15s06.html#sec.creating-contour-graph">15.6.2. Creating a contour graph</a></span></dt><dt><span class="sect2"><a href="ch15s06.html#id2562850">15.6.3. Adjusting the color and number of isobar lines</a></span></dt><dt><span class="sect2"><a href="ch15s06.html#sec.grid-interpolating">15.6.4. Understanding mesh interpolation</a></span></dt></dl></dd><dt><span class="sect1"><a href="ch15s07.html">15.7. Combining several different plot types in the same graph</a></span></dt><dt><span class="sect1"><a href="ch15s08.html">15.8. Creating several graphs in the same image</a></span></dt><dd><dl><dt><span class="sect2"><a href="ch15s08.html#id2563975">15.8.1. Creating a combined graph</a></span></dt><dt><span class="sect2"><a href="ch15s08.html#id2564308">15.8.2. Adding background images </a></span></dt><dt><span class="sect2"><a href="ch15s08.html#id2564429">15.8.3. Creating rotated combined graphs</a></span></dt><dt><span class="sect2"><a href="ch15s08.html#id2564532">15.8.4. Some caveats when using MGraph</a></span></dt></dl></dd></dl></div>
        
        <p>
            </p><div class="figure"><a name="id2554057"></a><p class="title"><b>Figure 15.1. Supported linear graph types in the library</b></p><div class="figure-contents">
                
                <div class="informaltable">
                    <table border="0"><colgroup><col class="c1"><col class="c2"><col class="c3"></colgroup><tbody><tr><td align="center">
                                    <p><span class="inlinemediaobject"><img src="images/ploticon_line.png" alt="Supported linear graph types in the library"></span></p>
                                    <p>a) Line plot</p>
                                    <p>(See <a class="xref" href="ch15.html#sec2.creating-line-graph" title="Creating a line graph">Creating a line graph</a>)</p>
                                </td><td align="center">
                                    <p><span class="inlinemediaobject"><img src="images/ploticon_area.png" alt="Supported linear graph types in the library"></span></p>
                                    <p>b) Area plot</p>
                                    <p>(See <a class="xref" href="ch15.html#sec2.creating-area-graph" title="Creating a filled line graphs (a.k.a. area plots)">Creating a filled line graphs (a.k.a. area plots)</a>)</p>
                                </td><td align="center">
                                    <p><span class="inlinemediaobject"><img src="images/ploticon_bar.png" alt="Supported linear graph types in the library"></span></p>
                                    <p>c) Bar plot</p>
                                    <p>(See <a class="xref" href="ch15s02.html" title="Bar graphs">Bar graphs</a>)</p>
                                </td></tr><tr><td align="center">
                                    <p><span class="inlinemediaobject"><img src="images/ploticon_field.png" alt="Supported linear graph types in the library"></span></p>
                                    <p>a) Field plot</p>
                                    <p>(See <a class="xref" href="ch15s05.html#sec1.creating-field-graphs" title="Field plots">Field plots</a>)</p>
                                </td><td align="center">
                                    <p><span class="inlinemediaobject"><img src="images/ploticon_error.png" alt="Supported linear graph types in the library"></span></p>
                                    <p>b) Error plot</p>
                                    <p>(See <a class="xref" href="ch15s03.html" title="Error plot graphs">Error plot graphs</a>)</p>
                                </td><td align="center">
                                    <p><span class="inlinemediaobject"><img src="images/ploticon_stock.png" alt="Supported linear graph types in the library"></span></p>
                                    <p>c) Stock plot</p>
                                    <p>(See <a class="xref" href="ch15s04.html" title="Stock graphs">Stock graphs</a>)</p>
                                </td></tr><tr><td align="center">
                                    <p><span class="inlinemediaobject"><img src="images/ploticon_geomap.jpg" alt="Supported linear graph types in the library"></span></p>
                                    <p>a) Geo-map plot</p>
                                    <p>(See <a class="xref" href="ch15s05.html#sec1.creating-geo-maps" title="Creating Geo-maps">Creating Geo-maps</a>)</p>
                                </td><td align="center">
                                    <p><span class="inlinemediaobject"><img src="images/ploticon_impuls.png" alt="Supported linear graph types in the library"></span></p>
                                    <p>b) Impuls (stem) plot</p>
                                    <p>(See <a class="xref" href="ch15s05.html" title="Scatter graphs">Scatter graphs</a>)</p>
                                </td><td align="center">
                                    <p><span class="inlinemediaobject"><img src="images/ploticon_spline.png" alt="Supported linear graph types in the library"></span></p>
                                    <p>c) Spline plot</p>
                                    <p>(See <a class="xref" href="ch15.html#sec2.creating-cubic-splines" title="Constructing smooth line plots with Cubic Splines">Constructing smooth line plots with Cubic Splines</a>)</p>
                                </td></tr><tr><td align="center">
                                    <p><span class="inlinemediaobject"><img src="images/ploticon_balloon.png" alt="Supported linear graph types in the library"></span></p>
                                    <p>a) Balloon plot</p>
                                    <p>(See <a class="xref" href="ch15s05.html#sec1.creating-balloon-graphs" title="Balloon plots">Balloon plots</a>)</p>
                                </td><td align="center">
                                    <p><span class="inlinemediaobject"><img src="images/ploticon_scatter.png" alt="Supported linear graph types in the library"></span></p>
                                    <p>b) Scatter plot</p>
                                    <p>(See <a class="xref" href="ch15s05.html" title="Scatter graphs">Scatter graphs</a>)</p>
                                </td><td align="center">
                                    <p><span class="inlinemediaobject"><img src="images/ploticon_contour.png" alt="Supported linear graph types in the library"></span></p>
                                    <p>c) Contour plot</p>
                                    <p>(See <a class="xref" href="ch15s06.html" title="Contour graphs">Contour graphs </a>)</p>
                                </td></tr></tbody></table>
                </div>
            </div></div><p><br class="figure-break">
        </p>
        <div class="sect1" title="Basic Line and area graphs"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a name="id2553962"></a>Basic Line and area graphs</h2></div></div></div>
            
            <p>Line graphs (we will use the term line graph to refer to an entire graph and the
                term line plot to refer to a single data series in a line graph) is together with
                bar graphs the simplest and perhaps the most commonly used graph type. In <a class="xref" href="ch04s02.html" title="Graphing the number of sun spots during the 19th Century">Graphing the number of sun spots during the 19th Century</a> we have already shown an example of a
                line graph without explaining to much of the details. The remainder of the section
                will go into some more details on the options available when creating a line
                graph.</p>
            <div class="sect2" title="Creating a line graph"><div class="titlepage"><div><div><h3 class="title"><a name="sec2.creating-line-graph"></a>Creating a line graph</h3></div></div></div>
                
                <p>A line graph always make use of one or several instances of the <code class="code">class
                        LinePlot</code> which represent one plotted data series in the graph. In all
                    our example we follow the naming convention to always name the instance of the
                    LinePlot class as "<code class="code">$lineplot</code>"</p>
                <p>The absolutely simplest line graph that is possible to create is shown in
                        <a class="xref" href="ch15.html#fig.example0-0" title="Figure 15.2. The most simple line graph (example0-0.php)">Figure 15.2. The most simple line graph <code class="uri"><a class="uri" href="example_src/example0-0.html" target="_top">(<code class="filename">example0-0.php</code>)</a></code> </a></p>
                <p>
                    </p><div class="example"><a name="example.example0-0"></a><p class="title"><b>Example 15.1. The most simple line graph (<code class="filename">example0-0.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">&lt;?php</span><span class="hl-code"> </span><span class="hl-comment">//</span><span class="hl-comment"> content=&quot;text/plain; charset=utf-8&quot;</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_line.php</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"> Some (random) data</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$ydata</span><span class="hl-code"> = </span><span class="hl-reserved">array</span><span class="hl-brackets">(</span><span class="hl-number">11</span><span class="hl-code">,</span><span class="hl-number">3</span><span class="hl-code">,</span><span class="hl-number">8</span><span class="hl-code">,</span><span class="hl-number">12</span><span class="hl-code">,</span><span class="hl-number">5</span><span class="hl-code">,</span><span class="hl-number">1</span><span class="hl-code">,</span><span class="hl-number">9</span><span class="hl-code">,</span><span class="hl-number">13</span><span class="hl-code">,</span><span class="hl-number">5</span><span class="hl-code">,</span><span class="hl-number">7</span><span class="hl-brackets">)</span><span class="hl-code">;
 
</span><span class="hl-comment">//</span><span class="hl-comment"> Size of the overall graph</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$width</span><span class="hl-code">=</span><span class="hl-number">350</span><span class="hl-code">;
</span><span class="hl-var">$height</span><span class="hl-code">=</span><span class="hl-number">250</span><span class="hl-code">;
 
</span><span class="hl-comment">//</span><span class="hl-comment"> Create the graph and set a scale.</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-comment">//</span><span class="hl-comment"> These two calls are always required</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$graph</span><span class="hl-code"> = </span><span class="hl-reserved">new</span><span class="hl-code"> </span><span class="hl-identifier">Graph</span><span class="hl-brackets">(</span><span class="hl-var">$width</span><span class="hl-code">,</span><span class="hl-var">$height</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetScale</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">intlin</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"> Create the linear plot</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$lineplot</span><span class="hl-code">=</span><span class="hl-reserved">new</span><span class="hl-code"> </span><span class="hl-identifier">LinePlot</span><span class="hl-brackets">(</span><span class="hl-var">$ydata</span><span class="hl-brackets">)</span><span class="hl-code">;
 
</span><span class="hl-comment">//</span><span class="hl-comment"> Add the plot to the graph</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">Add</span><span class="hl-brackets">(</span><span class="hl-var">$lineplot</span><span class="hl-brackets">)</span><span class="hl-code">;
 
</span><span class="hl-comment">//</span><span class="hl-comment"> Display the graph</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</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">?&gt;</span></pre></td></tr></table></div></div></div><p><br class="example-break">  </p><div class="figure"><a name="fig.example0-0"></a><p class="title"><b>Figure 15.2. The most simple line graph <code class="uri"><a class="uri" href="example_src/example0-0.html" target="_top">(<code class="filename">example0-0.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/example0-0.png" alt="The most simple line graph (example0-0.php)"></span> </div></div><p><br class="figure-break">
                </p>
                <p>There are a number of things to point out here</p>
                <p>
                    </p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
                            <p>Both the X and Y axis have been automatically scaled and since we
                                didn't provide any x-scale the data point have been numbered
                                automatically starting at 0</p>
                        </li><li class="listitem">
                            <p>By default the Y-grid is enabled and displayed in a "soft"
                                color</p>
                        </li><li class="listitem">
                            <p>By default the overall graph has a black bordered and a light gray
                                margin</p>
                        </li><li class="listitem">
                            <p>By default the size of the margin around the plot area is
                                automatically calculated</p>
                        </li></ul></div><p>
                </p>
                <p>While the above example is a perfectly fine graph it looks a bit poor and we
                    could probably make use of a graph title as well as titles on the axis to
                    explain the units we are working with. So lets change the simple graph in <a class="xref" href="ch15.html#fig.example0-0" title="Figure 15.2. The most simple line graph (example0-0.php)">Figure 15.2. The most simple line graph <code class="uri"><a class="uri" href="example_src/example0-0.html" target="_top">(<code class="filename">example0-0.php</code>)</a></code> </a> by adding a few lines to set some titles and
                    get the modified graph shown in <a class="xref" href="ch15.html#fig.example2" title="Figure 15.3. Adding some titles (example2.php)">Figure 15.3. Adding some titles <code class="uri"><a class="uri" href="example_src/example2.html" target="_top">(<code class="filename">example2.php</code>)</a></code> </a></p>
                <p>
                    </p><div class="example"><a name="example.example2"></a><p class="title"><b>Example 15.2. Adding some titles (<code class="filename">example2.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">&lt;?php</span><span class="hl-code"> </span><span class="hl-comment">//</span><span class="hl-comment"> content=&quot;text/plain; charset=utf-8&quot;</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_line.php</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"> Some (random) data</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$ydata</span><span class="hl-code"> = </span><span class="hl-reserved">array</span><span class="hl-brackets">(</span><span class="hl-number">11</span><span class="hl-code">,</span><span class="hl-number">3</span><span class="hl-code">,</span><span class="hl-number">8</span><span class="hl-code">,</span><span class="hl-number">12</span><span class="hl-code">,</span><span class="hl-number">5</span><span class="hl-code">,</span><span class="hl-number">1</span><span class="hl-code">,</span><span class="hl-number">9</span><span class="hl-code">,</span><span class="hl-number">13</span><span class="hl-code">,</span><span class="hl-number">5</span><span class="hl-code">,</span><span class="hl-number">7</span><span class="hl-brackets">)</span><span class="hl-code">;
 
</span><span class="hl-comment">//</span><span class="hl-comment"> Size of the overall graph</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$width</span><span class="hl-code">=</span><span class="hl-number">350</span><span class="hl-code">;
</span><span class="hl-var">$height</span><span class="hl-code">=</span><span class="hl-number">250</span><span class="hl-code">;
 
</span><span class="hl-comment">//</span><span class="hl-comment"> Create the graph and set a scale.</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-comment">//</span><span class="hl-comment"> These two calls are always required</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$graph</span><span class="hl-code"> = </span><span class="hl-reserved">new</span><span class="hl-code"> </span><span class="hl-identifier">Graph</span><span class="hl-brackets">(</span><span class="hl-var">$width</span><span class="hl-code">,</span><span class="hl-var">$height</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetScale</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">intlin</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"> Setup margin and titles</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetMargin</span><span class="hl-brackets">(</span><span class="hl-number">40</span><span class="hl-code">,</span><span class="hl-number">20</span><span class="hl-code">,</span><span class="hl-number">20</span><span class="hl-code">,</span><span class="hl-number">40</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">title</span><span class="hl-code">-&gt;</span><span class="hl-identifier">Set</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">Calls per operator</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">subtitle</span><span class="hl-code">-&gt;</span><span class="hl-identifier">Set</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">(March 12, 2008)</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">xaxis</span><span class="hl-code">-&gt;</span><span class="hl-identifier">title</span><span class="hl-code">-&gt;</span><span class="hl-identifier">Set</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">Operator</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">-&gt;</span><span class="hl-identifier">yaxis</span><span class="hl-code">-&gt;</span><span class="hl-identifier">title</span><span class="hl-code">-&gt;</span><span class="hl-identifier">Set</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string"># of calls</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"> Create the linear plot</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$lineplot</span><span class="hl-code">=</span><span class="hl-reserved">new</span><span class="hl-code"> </span><span class="hl-identifier">LinePlot</span><span class="hl-brackets">(</span><span class="hl-var">$ydata</span><span class="hl-brackets">)</span><span class="hl-code">;
 
</span><span class="hl-comment">//</span><span class="hl-comment"> Add the plot to the graph</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">Add</span><span class="hl-brackets">(</span><span class="hl-var">$lineplot</span><span class="hl-brackets">)</span><span class="hl-code">;
 
</span><span class="hl-comment">//</span><span class="hl-comment"> Display the graph</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">Stroke</span><span class="hl-brackets">(</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-inlinetags">?&gt;</span></pre></td></tr></table></div></div></div><p><br class="example-break">  </p><div class="figure"><a name="fig.example2"></a><p class="title"><b>Figure 15.3. Adding some titles <code class="uri"><a class="uri" href="example_src/example2.html" target="_top">(<code class="filename">example2.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/example2.png" alt="Adding some titles (example2.php)"></span> </div></div><p><br class="figure-break">
                </p>
                <p>Worth noting in this example are</p>
                <p>
                    </p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
                            <p>The main graph class instance ($graph) is used as the base to
                                access most properties of the overall graph</p>
                        </li><li class="listitem">
                            <p>The margins have been slightly increased to account for the titles
                                of the axis</p>
                        </li><li class="listitem">
                            <p>The default position for the title of the x-axis is on the far
                                right and for the y-axis it is placed centered in the middle and
                                rotated in a 90 angle (vertical).</p>
                        </li></ul></div><p>
                </p>
                <p>A nice change would now be to have the titles of the axis in a bold font and
                    the line plot a little bit thicker and in blue color. Let's do that by adding
                    the lines</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
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-inlinetags">&lt;?php</span><span class="hl-code">
</span><span class="hl-var">$graph</span><span class="hl-code"> -&gt; </span><span class="hl-identifier">title</span><span class="hl-code"> -&gt; </span><span class="hl-identifier">SetFont</span><span class="hl-code"> </span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-identifier">FF_FONT1</span><span class="hl-code"> , </span><span class="hl-identifier">FS_BOLD</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$graph</span><span class="hl-code"> -&gt; </span><span class="hl-identifier">yaxis</span><span class="hl-code"> -&gt; </span><span class="hl-identifier">title</span><span class="hl-code"> -&gt; </span><span class="hl-identifier">SetFont</span><span class="hl-code"> </span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-identifier">FF_FONT1</span><span class="hl-code"> , </span><span class="hl-identifier">FS_BOLD</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$graph</span><span class="hl-code"> -&gt; </span><span class="hl-identifier">xaxis</span><span class="hl-code"> -&gt; </span><span class="hl-identifier">title</span><span class="hl-code"> -&gt; </span><span class="hl-identifier">SetFont</span><span class="hl-code"> </span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-identifier">FF_FONT1</span><span class="hl-code"> , </span><span class="hl-identifier">FS_BOLD</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$lineplot</span><span class="hl-code"> -&gt; </span><span class="hl-identifier">SetColor</span><span class="hl-code"> </span><span class="hl-brackets">(</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-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$lineplot</span><span class="hl-code"> -&gt; </span><span class="hl-identifier">SetWeight</span><span class="hl-code"> </span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-number">2</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"> Two pixel wide </span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-inlinetags">?&gt;</span></pre></td></tr></table></div><p>
                </p>
                <p>As was explained in <a class="xref" href="ch08.html" title="Chapter 8. Text and font handling">Chapter 8. <i>Text and font handling</i></a> this will adjust
                    the fonts of the titles to make use of a bold variant of the built-in bitmap
                    fonts. Please note the consistent naming conventions used in the library. Most
                    objects support a common set of basic methods to adjust font, size and colors
                    wherever such concepts make sense.</p>
                <p>The result of adding these lines are shown in <a class="xref" href="ch15.html#fig.example3" title="Figure 15.4. Changing fonts of the axis titles and adjusting plot weight (example3.php)">Figure 15.4. Changing fonts of the axis titles and adjusting plot weight <code class="uri"><a class="uri" href="example_src/example3.html" target="_top">(<code class="filename">example3.php</code>)</a></code> </a> (click on the link in the title to see the full source).</p>
                <p>
                    </p><div class="figure"><a name="fig.example3"></a><p class="title"><b>Figure 15.4. Changing fonts of the axis titles and adjusting plot weight <code class="uri"><a class="uri" href="example_src/example3.html" target="_top">(<code class="filename">example3.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/example3.png" alt="Changing fonts of the axis titles and adjusting plot weight (example3.php)"></span> </div></div><p><br class="figure-break">
                </p>
                <p>As a final touch lets make the y-axis have the same color as the data series
                    to stronger show the connection between the data and the scale. At the same time
                    we take the opportunity to add a drop shadow to the overall graph. We do both of
                    these things by adding the following two lines at appropriate places in the
                    script</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
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-inlinetags">&lt;?php</span><span class="hl-code">
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetShadow</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">-&gt;</span><span class="hl-identifier">yaxis</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetColor</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">blue</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-inlinetags">?&gt;</span></pre></td></tr></table></div><p>
                </p>
                <p>The results is shown in <a class="xref" href="ch15.html#fig.example3.0.1" title="Figure 15.5. Adding drop shadow and changing axis color (example3.0.1.php)">Figure 15.5. Adding drop shadow and changing axis color <code class="uri"><a class="uri" href="example_src/example3.0.1.html" target="_top">(<code class="filename">example3.0.1.php</code>)</a></code> </a> below</p>
                <p>
                    </p><div class="figure"><a name="fig.example3.0.1"></a><p class="title"><b>Figure 15.5. Adding drop shadow and changing axis color <code class="uri"><a class="uri" href="example_src/example3.0.1.html" target="_top">(<code class="filename">example3.0.1.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/example3.0.1.png" alt="Adding drop shadow and changing axis color (example3.0.1.php)"></span> </div></div><p><br class="figure-break">
                </p>
                <p>
                    </p><div class="tip" title="Tip" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Tip</h3>
                        <p>Remember that the library has multiple ways to handle null data values
                            as described in <a class="xref" href="ch13s06.html" title="Different types of NULL data handling">Different types of NULL data handling</a></p>
                    </div><p>
                </p>
            </div>
            <div class="sect2" title="Automatic interpolation of unknown data"><div class="titlepage"><div><div><h3 class="title"><a name="id2554907"></a>Automatic interpolation of unknown data</h3></div></div></div>
                
                <p>Line graphs supports automatic linear interpolation of missing data point if
                    the missing data point is replaced by a '-' (hyphen character) for more on
                    handling of NULLs in the input data see <a class="xref" href="ch13s06.html" title="Different types of NULL data handling">Different types of NULL data handling</a>. </p>
                <p>
                    </p><div class="informaltable">
                        <table border="0"><colgroup><col class="c1"><col class="c2"></colgroup><tbody><tr><td>
                                        <div class="figure"><a name="fig.example3.0.3"></a><p class="title"><b>Figure 15.6. Original null values <code class="uri"><a class="uri" href="example_src/example3.0.3.html" target="_top">(<code class="filename">example3.0.3.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/example3.0.3.png" alt="Original null values (example3.0.3.php)"></span> </div></div><br class="figure-break">
                                    </td><td>
                                        <div class="figure"><a name="fig.example3.0.2"></a><p class="title"><b>Figure 15.7. Using '-' to get interpolated lines <code class="uri"><a class="uri" href="example_src/example3.0.2.html" target="_top">(<code class="filename">example3.0.2.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/example3.0.2.png" alt="Using '-' to get interpolated lines (example3.0.2.php)"></span> </div></div><br class="figure-break">
                                    </td></tr></tbody></table>
                    </div><p>
                </p>
                <p>There is one option to control the behavior of the interpolation together with
                    accumulated line plots and that is how to handle the case where the initial or
                    ending data are unknown.</p>
                <p>For accumulated line plots (see below) this is especially critical since each
                    value is plotted with an offset of the "previous" plot and hence all values must
                    be known. By default if the first data value is unknown it will be set to the
                    same value as the first found non-null value. It is also possible, for
                    accumulated line plots, to force the first and last unknown value to be equal to
                    0 (zero). This is controlled by the method</p>
                <p>
                    </p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
                            <p><code class="code">AccLinePlot::SetInterpolateMode($aForceZero)</code></p>
                            <p>A value of true for the for the argument will force any first or
                                last unknown values to be interpreted as 0 for an accumulated line
                                plot.</p>
                        </li></ul></div><p>
                </p>
            </div>
            <div class="sect2" title="Adding marks to the plot (a.k.a. plot marks)"><div class="titlepage"><div><div><h3 class="title"><a name="sec.adding-marks"></a>Adding marks to the plot (a.k.a. plot marks)</h3></div></div></div>
                
                <p>Another common embellishment of plots is to add markers for each data point.
                    The library supports a large number of built-in plot marks as well as the
                    ability to use arbitrary images as plot marks. Plot marks are instantiated as an
                    instance of <code class="code">class PlotMark</code> defined in the module
                        "<code class="filename">jpgraph:plotmark.inc.php</code>"</p>
                <p>There are three types of built-in plot marks</p>
                <p>
                    </p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem">
                            <p><span class="bold"><strong>Line based. </strong></span></p>
                            <p>These marks are drawn directly by the library at the appropriate
                                places in the graph. These marks are simple rectangles, squares,
                                stars etc The size and colors (both edge and fill) are user
                                adjustable.</p>
                        </li><li class="listitem">
                            <p><span class="bold"><strong>Image based symbols. </strong></span></p>
                            <p>These marks look much more "refined" and are actually small
                                built-in images that are scaled and placed (copied) to the
                                appropriate position in the graph. Since these are predefined images
                                they are only available in a certain number of colors and shapes.
                            </p>
                        </li><li class="listitem">
                            <p><span class="bold"><strong>Country flags</strong></span></p>
                            <p>As was previously discussed the library supports (as of Dec 2008)
                                all known countries and it is possible to use the country flags both
                                as background in the graphs as well as plot marks.</p>
                        </li></ol></div><p>
                </p>
                <p>A full list of all available built-in plot marks and there symbolic names are
                    given in <a class="xref" href="ape.html" title="Appendix E. Available plot marks">Appendix E. <i>Available plot marks</i></a>.</p>
                <p>For now lets keep things simple and just add a small triangle at each of the
                    specified data points by adding the lines</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
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-inlinetags">&lt;?php</span><span class="hl-code">
</span><span class="hl-var">$lineplot</span><span class="hl-code">-&gt;</span><span class="hl-identifier">mark</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetType</span><span class="hl-brackets">(</span><span class="hl-identifier">MARK_UTRIANGLE</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$lineplot</span><span class="hl-code">-&gt;</span><span class="hl-identifier">mark</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetColor</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">blue</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$lineplot</span><span class="hl-code">-&gt;</span><span class="hl-identifier">mark</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetFillColor</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">red</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-inlinetags">?&gt;</span></pre></td></tr></table></div><p>
                </p>
                <p>
                    </p><div class="caution" title="Caution" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Caution</h3>
                        <p>The colors of the marks will, if you don't specify them explicitly,
                            follow the line color. Please note that if you want different colors for
                            the marks and the line the call to <code class="code">SetColor()</code> for the marks
                            must be done after the call to the <code class="code">SetColor()</code> for the line
                            since the marks color will always be reset to the lines color when you
                            set the line color.</p>
                    </div><p>
                </p>
                <p>The result after making these modifications are shown in <a class="xref" href="ch15.html#fig.example3.1" title="Figure 15.8. Adding basic plot marks to the plot (example3.1.php)">Figure 15.8. Adding basic plot marks to the plot <code class="uri"><a class="uri" href="example_src/example3.1.html" target="_top">(<code class="filename">example3.1.php</code>)</a></code> </a></p>
                <p>
                    </p><div class="figure"><a name="fig.example3.1"></a><p class="title"><b>Figure 15.8. Adding basic plot marks to the plot <code class="uri"><a class="uri" href="example_src/example3.1.html" target="_top">(<code class="filename">example3.1.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/example3.1.png" alt="Adding basic plot marks to the plot (example3.1.php)"></span> </div></div><p><br class="figure-break">
                </p>
                <p>
                    </p><div class="tip" title="Tip" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Tip</h3>
                        <p>In addition to the built in plot marks it is also possible to use a
                            user specified image as a plot mark. See <a class="xref" href="ch14s02.html#fig.footerex1" title="Figure 14.11. Adding a left,right and center footer (footerex1.php)">Figure 14.11. Adding a left,right and center footer <code class="uri"><a class="uri" href="example_src/footerex1.html" target="_top">(<code class="filename">footerex1.php</code>)</a></code> </a> for an example of how to use this
                            feature. To use this feature the plot mark type is specified as
                                <code class="code">MARK_IMG</code> and the file name of the image is given. For
                            example the following line will us the image file "myimage.jpg" as plot
                            marks and scale the image to 50% of its original size</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">$lineplot-&gt;mark-&gt;SetType(MARK_IMG,'myimage.jpg','0.5');</span></pre></td></tr></table></div><p>
                        </p>
                    </div><p>
                </p>
                <p>As a final example we show an example of using one of the built-in image marks
                    by adding the line</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">$lineplot-&gt;mark-&gt;SetType(MARK_IMG_DIAMOND,'red',0.5);</span></pre></td></tr></table></div><p>
                </p>
                <p>This will add a red diamond mark scaled to 50% of its original size to better
                    fit the overall size of the graph. The result of adding this is shown in <a class="xref" href="ch15.html#fig.example3.1.1" title="Figure 15.9. Using one of the built-in images as plot mark, MARK_IMG_DIAMOND (example3.1.1.php)">Figure 15.9. Using one of the built-in images as plot mark, MARK_IMG_DIAMOND <code class="uri"><a class="uri" href="example_src/example3.1.1.html" target="_top">(<code class="filename">example3.1.1.php</code>)</a></code> </a></p>
                <p>
                    </p><div class="figure"><a name="fig.example3.1.1"></a><p class="title"><b>Figure 15.9. Using one of the built-in images as plot mark, MARK_IMG_DIAMOND <code class="uri"><a class="uri" href="example_src/example3.1.1.html" target="_top">(<code class="filename">example3.1.1.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/example3.1.1.png" alt="Using one of the built-in images as plot mark, MARK_IMG_DIAMOND (example3.1.1.php)"></span> </div></div><p><br class="figure-break">
                </p>
                <p>
                    </p><div class="tip" title="Tip" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Tip</h3>
                        <p>Note that some of the built in images are available in different
                            sizes. The reason is that even though it is possible to n scale them by
                            the third argument there is a visual degradation to scale an image
                            larger than it's original size since some pixels needs to be
                            interpolated. Reducing the size with a scale &lt; 1.0 gives much better
                            visual appearance.</p>
                    </div><p>
                </p>
                <p>In order to use one of the available country flags the type is specified as
                        <code class="code">MARK_FLAG1</code>, <code class="code">MARK_FLAG2</code>, <code class="code">MARK_FLAG3</code> or
                        <code class="code">MARK_FLAG4</code> which represent the native size of the flag (in
                    increasing order). The second argument to <code class="code">SetType()</code> is either the
                    ordinal index number of the country flag or its short name (as listed <a class="xref" href="apf.html" title="Appendix F. List of all country flags">Appendix F. <i>List of all country flags</i></a>). The following example illustrates both
                    these methods of specifying the country flags. The two critical lines are</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
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-inlinetags">&lt;?php</span><span class="hl-code">
</span><span class="hl-var">$p1</span><span class="hl-code">-&gt;</span><span class="hl-identifier">mark</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetType</span><span class="hl-brackets">(</span><span class="hl-identifier">MARK_FLAG1</span><span class="hl-code">,</span><span class="hl-number">197</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$p2</span><span class="hl-code">-&gt;</span><span class="hl-identifier">mark</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetType</span><span class="hl-brackets">(</span><span class="hl-identifier">MARK_FLAG1</span><span class="hl-code">,</span><span class="hl-quotes">'</span><span class="hl-string">united states</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-inlinetags">?&gt;</span></pre></td></tr></table></div><p>
                </p>
                <p>and the result of creating a graph with some data using country flags as data
                    markers are shown in <a class="xref" href="ch15.html#fig.markflagex1" title="Figure 15.10. Using country flags as plot marks (markflagex1.php)">Figure 15.10. Using country flags as plot marks <code class="uri"><a class="uri" href="example_src/markflagex1.html" target="_top">(<code class="filename">markflagex1.php</code>)</a></code> </a></p>
                <p>
                    </p><div class="figure"><a name="fig.markflagex1"></a><p class="title"><b>Figure 15.10. Using country flags as plot marks <code class="uri"><a class="uri" href="example_src/markflagex1.html" target="_top">(<code class="filename">markflagex1.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/markflagex1.png" alt="Using country flags as plot marks (markflagex1.php)"></span> </div></div><p><br class="figure-break">
                </p>
                <p>In addition the plot mark formatting shown above plot marks also supports
                    formating through the use of a callback function. The callback function will be
                    passed the y-value as its only argument and the callback function must return an
                    array consisting of three value, weight, color and fill-color. This could be
                    used to for example alter the colors of the plot marks depending on the actual
                    value. A common use of this feature is to create "balloon" scatter plot where a
                    variable sized filled circle is positioned at specific data points. This is a
                    way t create a 2D plot which conveys three values at each data point, x,y and
                    size. In the section on Scatter plot (see <a class="xref" href="ch15s05.html" title="Scatter graphs">Scatter graphs</a>) we show an example of
                    this.</p>
            </div>
            <div class="sect2" title="Displaying the values at the data points"><div class="titlepage"><div><div><h3 class="title"><a name="id2555079"></a>Displaying the values at the data points</h3></div></div></div>
                
                <p>Lets continue the previous example by making some minor adjustments to also
                    show the values at each data point. The data label at each data point is
                    represented by the instance variable "$value". This is an instance of the
                        <code class="code">class DisplayValue</code> and all normal text attributes can be
                    adjusted (e.g. color, size, fonts etc). The value is applied to all
                    labels.</p>
                <p>In addition to the usual text formatting it is also possible to adjust how the
                    numeric data labels is formatted. This is done by one of two ways.</p>
                <p>
                    </p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem">
                            <p>by submitting a suitable format string. This format string follows
                                the same syntax as the <code class="code">printf()</code> format string.</p>
                        </li><li class="listitem">
                            <p>by specifying a format callback function. This callback function
                                must take exactly one argument (which is the data value) and return
                                the wanted string that should be displayed.</p>
                        </li></ol></div><p>
                </p>
                <p>In order to display the values the first thing that must happen is to enable
                    the values. This is done by a call to </p>
                <p>
                    </p><div class="hl-main"><table class="hl-table" width="100%"><tr><td class="hl-gutter" align="right" valign="top"><pre>1
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-code">$lineplot-&gt;value-&gt;Show();</span></pre></td></tr></table></div><p>
                </p>
                <p>The result of adding this line is shown in <a class="xref" href="ch15.html#fig.example3.3" title="Figure 15.11.  (example3.3.php)">Figure 15.11.  <code class="uri"><a class="uri" href="example_src/example3.3.html" target="_top">(<code class="filename">example3.3.php</code>)</a></code> </a></p>
                <p>
                    </p><div class="figure"><a name="fig.example3.3"></a><p class="title"><b>Figure 15.11.  <code class="uri"><a class="uri" href="example_src/example3.3.html" target="_top">(<code class="filename">example3.3.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/example3.3.png" alt="(example3.3.php)"></span> </div></div><p><br class="figure-break">
                </p>
                <p>We can now modify the appearance of the labels by changing the font and
                    changing the way the labels are formatted. We do this by adding the following
                    lines to the previous example</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
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-inlinetags">&lt;?php</span><span class="hl-code">
</span><span class="hl-var">$lineplot</span><span class="hl-code">-&gt;</span><span class="hl-identifier">value</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetFont</span><span class="hl-brackets">(</span><span class="hl-identifier">FF_ARIAL</span><span class="hl-code">,</span><span class="hl-identifier">FS_BOLD</span><span class="hl-code">,</span><span class="hl-number">10</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$lineplot</span><span class="hl-code">-&gt;</span><span class="hl-identifier">value</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetColor</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">darkred</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$lineplot</span><span class="hl-code">-&gt;</span><span class="hl-identifier">value</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetFormat</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">(%d)</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-inlinetags">?&gt;</span></pre></td></tr></table></div><p>
                </p>
                <p>The resulting graph can be seen in <a class="xref" href="ch15.html#fig.example3.4" title="Figure 15.12. Changing the appearance of data labels (example3.4.php)">Figure 15.12. Changing the appearance of data labels <code class="uri"><a class="uri" href="example_src/example3.4.html" target="_top">(<code class="filename">example3.4.php</code>)</a></code> </a></p>
                <p>
                    </p><div class="figure"><a name="fig.example3.4"></a><p class="title"><b>Figure 15.12. Changing the appearance of data labels <code class="uri"><a class="uri" href="example_src/example3.4.html" target="_top">(<code class="filename">example3.4.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/example3.4.png" alt="Changing the appearance of data labels (example3.4.php)"></span> </div></div><p><br class="figure-break">
                </p>
                <p>
                    </p><div class="tip" title="Tip" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Tip</h3>
                        <p>To get 1000' separators use the PHP function number_format() as a
                            callback function</p>
                    </div><p>
                </p>
                <p>
                    </p><div class="tip" title="Tip" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Tip</h3>
                        <p>To use method in classes as callback the callback method has to be
                            specified as an array with two string entries. The first entry must be
                            the class and the second entry must be the method name. Note that
                            callback method should be static as no instance context can be
                            created.</p>
                    </div><p>
                </p>
                <p>As a final example we make use of a callback function to format the values as
                        <span class="italic">Roman Numerals</span> . The result of this can
                    be seen in <a class="xref" href="ch15.html#fig.example3.4.1" title="Figure 15.13. Formatting display values as roman numerals (example3.4.1.php)">Figure 15.13. Formatting display values as roman numerals <code class="uri"><a class="uri" href="example_src/example3.4.1.html" target="_top">(<code class="filename">example3.4.1.php</code>)</a></code> </a></p>
                <p>
                    </p><div class="figure"><a name="fig.example3.4.1"></a><p class="title"><b>Figure 15.13. Formatting display values as roman numerals <code class="uri"><a class="uri" href="example_src/example3.4.1.html" target="_top">(<code class="filename">example3.4.1.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/example3.4.1.png" alt="Formatting display values as roman numerals (example3.4.1.php)"></span> </div></div><p><br class="figure-break">
                </p>
            </div>
            <div class="sect2" title="Adding several data series to the same graph"><div class="titlepage"><div><div><h3 class="title"><a name="id2555706"></a>Adding several data series to the same graph</h3></div></div></div>
                
                <p>Up to now all examples we have shown have only had one data series. As was
                    mentioned in the introduction a graph can have an unlimited number of data
                    series (plots) although from a practical consideration (and "viewability") it is
                    probably best to restrict the number of data series in one graph to less than
                    5-6.</p>
                <p>The steps to do this is exactly a repetition of what the examples have shown
                    up to now. The only thing that is needed is to create the second data series, by
                    creating a new instance of a the LinePlot class, set the attributes, and finally
                    add it to the graph.</p>
                <p>The following lines show how to create the new data series/plot and add it to
                    the graph (we only show the new lines - not the full script)</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
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-inlinetags">&lt;?php</span><span class="hl-code">
</span><span class="hl-var">$ydata2</span><span class="hl-code">  = </span><span class="hl-reserved">array</span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-number">1</span><span class="hl-code"> , </span><span class="hl-number">19</span><span class="hl-code"> , </span><span class="hl-number">15</span><span class="hl-code"> , </span><span class="hl-number">7</span><span class="hl-code"> , </span><span class="hl-number">22</span><span class="hl-code"> , </span><span class="hl-number">14</span><span class="hl-code"> , </span><span class="hl-number">5</span><span class="hl-code"> , </span><span class="hl-number">9</span><span class="hl-code"> , </span><span class="hl-number">21</span><span class="hl-code"> , </span><span class="hl-number">13</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"> Create a new data series with a different color</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$lineplot2</span><span class="hl-code"> = </span><span class="hl-reserved">new</span><span class="hl-code">  </span><span class="hl-identifier">LinePlot</span><span class="hl-code"> </span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-var">$ydata2</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$lineplot2</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetWeight</span><span class="hl-code"> </span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-number">2</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"> Also add the new data series to the graph</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">Add</span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-var">$lineplot2</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code">;</span></pre></td></tr></table></div><p>
                </p>
                <p>Making these additions will create the graph in <a class="xref" href="ch15.html#fig.example4" title="Figure 15.14. Adding a second data series (example4.php)">Figure 15.14. Adding a second data series <code class="uri"><a class="uri" href="example_src/example4.html" target="_top">(<code class="filename">example4.php</code>)</a></code> </a></p>
                <p>
                    </p><div class="figure"><a name="fig.example4"></a><p class="title"><b>Figure 15.14. Adding a second data series <code class="uri"><a class="uri" href="example_src/example4.html" target="_top">(<code class="filename">example4.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/example4.png" alt="Adding a second data series (example4.php)"></span> </div></div><p><br class="figure-break">
                </p>
                <p>There are two things to note here</p>
                <p>
                    </p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem">
                            <p>The Y-scale has changed to accommodate the larger range of
                                Y-values for the second graph.</p>
                        </li><li class="listitem">
                            <p>The colors for each successive data series is allocated
                                automatically but of course it is also possible to set the color
                                manually.</p>
                        </li><li class="listitem">
                            <p>If you add several plots to the same graph they should contain the
                                same number of data points. This is not a requirement (the graph
                                will be automatically scaled to accommodate the plot with the
                                largest number of points) but it will not look very good since one
                                of the plot end in the middle of the graph.</p>
                        </li></ol></div><p>
                </p>
                <p>
                    </p><div class="caution" title="Caution" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Caution</h3>
                        <p>Do not mix both manually and automatically assigned colors. When the
                            library assigns colors to a new line plot it will not check if a certain
                            color has been previously manually set and used.</p>
                    </div><p>
                </p>
            </div>
            <div class="sect2" title="Adding a second Y-axis"><div class="titlepage"><div><div><h3 class="title"><a name="id2555784"></a>Adding a second Y-axis</h3></div></div></div>
                
                <p>As was discussed in <a class="xref" href="ch14s06.html" title="Using multiple y-axis">Using multiple y-axis</a> it is possible
                    to add multiple y-axis to a graph. The most common use of this feature is to
                    just use one extra y-axis with a different scale on the right side of the graph.
                    To make this common case as easy as possible to manage the library provides some
                    convenience method to work with one second y-axis (and scale).</p>
                <p>The second y-axis is accessed through the "<code class="code">$y2axis</code>" property of
                    the Graph class and its use is completely analogue to the primary y-axis
                        ("<code class="code">$yaxis</code>").</p>
                <p>As you saw in the preceding example you could add multiple plots to the same
                    graph and Y-axis. However what if the two plots you want to display in the graph
                    has very different ranges? One might for example have Y-values like above but
                    the other might have Y-values in the 100:s. Even though it is perfectly possible
                    to add them as above the graph with the smallest values will have a very low
                    dynamic range since the scale must accommodate for the bigger dynamic range of
                    the second plot. (One other way of solving this particular problem could be to
                    use a logarithmic y-scale).</p>
                <p>The solution to this is to use a second Y-axis with a different scale and add
                    the second plot to this Y-axis instead. Let's take a look at how that is
                    accomplished.</p>
                <p>First we need to create a new data array with large values and secondly we
                    need to specify a scale for the Y2 axis. This is done by adding the lines</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
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-inlinetags">&lt;?php</span><span class="hl-code">
</span><span class="hl-var">$y2data</span><span class="hl-code"> = </span><span class="hl-reserved">array</span><span class="hl-brackets">(</span><span class="hl-number">354</span><span class="hl-code"> , </span><span class="hl-number">200</span><span class="hl-code"> , </span><span class="hl-number">265</span><span class="hl-code"> , </span><span class="hl-number">99</span><span class="hl-code"> , </span><span class="hl-number">111</span><span class="hl-code"> , </span><span class="hl-number">91</span><span class="hl-code"> , </span><span class="hl-number">198</span><span class="hl-code"> , </span><span class="hl-number">225</span><span class="hl-code"> , </span><span class="hl-number">293</span><span class="hl-code"> , </span><span class="hl-number">251</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetY2Scale</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">lin</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-inlinetags">?&gt;</span></pre></td></tr></table></div><p>
                </p>
                <p>To instruct the library to add this data series to the second y-axis we have
                    to make use of the method</p>
                <p>
                    </p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
                            <p><code class="code">Graph::AddY2()</code></p>
                        </li></ul></div><p>
                </p>
                <p>which is used in analogy with the usual Graph::Add()</p>
                <p>To make the graph easier to read we set the color of the second y-axis to be
                    the same as the second data series. The result of this is shown in <a class="xref" href="ch15.html#fig.example5" title="Figure 15.15. Adding a second y-axis to the graph (example5.php)">Figure 15.15. Adding a second y-axis to the graph <code class="uri"><a class="uri" href="example_src/example5.html" target="_top">(<code class="filename">example5.php</code>)</a></code> </a> below.</p>
                <p>
                    </p><div class="figure"><a name="fig.example5"></a><p class="title"><b>Figure 15.15. Adding a second y-axis to the graph <code class="uri"><a class="uri" href="example_src/example5.html" target="_top">(<code class="filename">example5.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/example5.png" alt="Adding a second y-axis to the graph (example5.php)"></span> </div></div><p><br class="figure-break">
                </p>
            </div>
            <div class="sect2" title="Adding a legend box to the graph"><div class="titlepage"><div><div><h3 class="title"><a name="id2555973"></a>Adding a legend box to the graph</h3></div></div></div>
                
                <p>Once we have multiple data series there is a need to separate them and that is
                    usually done by adding a legend box with suitable titles. As was shown in <a class="xref" href="ch14s04.html" title="Adjusting the position and layout of the legend">Adjusting the position and layout of the legend</a> it is possible to both add a
                    legend box and adjusts its position. Lets now continue the previous example by
                    adding a suitable legend box to separate the two data series.</p>
                <p>Each plot type has a '<code class="code">SetLegend()</code>' method which is used to name
                    that plot in the legend. So to name the two plots in the previous example we
                    have been working with so far we need to add the two lines</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
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-inlinetags">&lt;?php</span><span class="hl-code">
</span><span class="hl-var">$lineplot</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetLegend</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">Plot 1</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$lineplot2</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetLegend</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">Plot 2</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-inlinetags">?&gt;</span></pre></td></tr></table></div><p>
                </p>
                <p>As you can see the legend gets automatically sized depending on how many plots
                    there are that have legend texts to display. By default it is placed with it's
                    top right corner close to the upper right edge of the graph. Depending on the
                    image you might want to adjust this or you might want to add a larger margin
                    which is big enough to accompany the legend. Let's do both.</p>
                <p>First we increase the right margin and then we place the legend so that it is
                    roughly centered in the right margin area. We will also enlarge the overall
                    image so the plot area doesn't get too squeezed.</p>
                <p>The legend properties is accessed through the '<code class="code">$legend</code>' property
                    of the graph. So in order to adjust the position (as was described in <a class="xref" href="ch14s04.html" title="Adjusting the position and layout of the legend">Adjusting the position and layout of the legend</a> ) we add the line</p>
                <p>
                    </p><div class="hl-main"><table class="hl-table" width="100%"><tr><td class="hl-gutter" align="right" valign="top"><pre>1
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-code">$graph-&gt;legend-&gt;SetPos(0.05, 0.5, 'right', 'center');</span></pre></td></tr></table></div><p>
                </p>
                <p>This will then give the graph shown in <a class="xref" href="ch15.html#fig.example6" title="Figure 15.16. Adding and adjusting the position of the legend box (example6.php)">Figure 15.16. Adding and adjusting the position of the legend box <code class="uri"><a class="uri" href="example_src/example6.html" target="_top">(<code class="filename">example6.php</code>)</a></code> </a></p>
                <p>
                    </p><div class="figure"><a name="fig.example6"></a><p class="title"><b>Figure 15.16. Adding and adjusting the position of the legend box <code class="uri"><a class="uri" href="example_src/example6.html" target="_top">(<code class="filename">example6.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/example6.png" alt="Adding and adjusting the position of the legend box (example6.php)"></span> </div></div><p><br class="figure-break">
                </p>
                <p>As a reminder we briefly discuss the working of the <code class="code">SetPos()</code>
                    method.</p>
                <p>The position is specified as a fraction of the overall width and height of the
                    entire graph. This makes it possible for to resize the graph without disturbing
                    the relative position of the legend. The second two arguments specifies the
                    anchor point in the legend box that should be aligned with the specified
                    position.</p>
                <p>As can be seen in <a class="xref" href="ch15.html#fig.example6" title="Figure 15.16. Adding and adjusting the position of the legend box (example6.php)">Figure 15.16. Adding and adjusting the position of the legend box <code class="uri"><a class="uri" href="example_src/example6.html" target="_top">(<code class="filename">example6.php</code>)</a></code> </a> the legends are by
                    default placed in a column. It is also possible to adjust this by calling either
                    the <code class="code">Legend::SetLayout()</code> method or specifically set the number of
                    columns to use by calling <code class="code">Legend::SetColumns()</code> . Lets change the
                    layout so the legend texts are set in one row and place the legend box at the
                    bottom of the graph. If we do this we get the result shown in <a class="xref" href="ch15.html#fig.example6.1" title="Figure 15.17. Adjusting the layout of the texts in the legend box (example6.1.php)">Figure 15.17. Adjusting the layout of the texts in the legend box <code class="uri"><a class="uri" href="example_src/example6.1.html" target="_top">(<code class="filename">example6.1.php</code>)</a></code> </a></p>
                <p>
                    </p><div class="figure"><a name="fig.example6.1"></a><p class="title"><b>Figure 15.17. Adjusting the layout of the texts in the legend box <code class="uri"><a class="uri" href="example_src/example6.1.html" target="_top">(<code class="filename">example6.1.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/example6.1.png" alt="Adjusting the layout of the texts in the legend box (example6.1.php)"></span> </div></div><p><br class="figure-break">
                </p>
                <p>As a final example lets combine what we have learnt up to now, i.e. adding
                    plot marks, adding multiple data series to the same graph and adding a legend
                    box into one example. In <a class="xref" href="ch15.html#fig.builtinplotmarksex1" title="Figure 15.18. Using plot marks with several data series and a legend (builtinplotmarksex1.php)">Figure 15.18. Using plot marks with several data series and a legend <code class="uri"><a class="uri" href="example_src/builtinplotmarksex1.html" target="_top">(<code class="filename">builtinplotmarksex1.php</code>)</a></code> </a> we have
                    in addition used the feature with "tabbed" titles which is an alternative way to
                    put titles on graph (as discussed in <a class="xref" href="ch14s02.html#sec2.fomratting-graph-titles" title="Formatting and specifying the titles of the graph">Formatting and specifying the titles of the graph</a>).</p>
                <p>
                    </p><div class="figure"><a name="fig.builtinplotmarksex1"></a><p class="title"><b>Figure 15.18. Using plot marks with several data series and a legend <code class="uri"><a class="uri" href="example_src/builtinplotmarksex1.html" target="_top">(<code class="filename">builtinplotmarksex1.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/builtinplotmarksex1.png" alt="Using plot marks with several data series and a legend (builtinplotmarksex1.php)"></span> </div></div><p><br class="figure-break">
                </p>
            </div>
            <div class="sect2" title="Changing the style of the line plot - using the step-style"><div class="titlepage"><div><div><h3 class="title"><a name="id2556231"></a>Changing the style of the line plot - using the step-style</h3></div></div></div>
                
                <p>Step style refers to an alternate way of rendering line plots by not drawing a
                    direct line between two adjacent points but rather draw two segments. The first
                    segment being a horizontal line to the next X-value and then a vertical line
                    from that point to the correct Y-value at that instance. This is also known as
                    "zero-order hold" (as compared with the first-order hold which is an alternative
                    name for combining each data point with a straight line). Enabling step stylöe
                    is done by calling the method</p>
                <p>
                    </p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
                            <p><code class="code">LinePlot::SetStepStyle($aFlg=true)</code><a class="xref" href="ch15.html#fig.filledlineex01.1" title="Figure 15.21. Having the grid line on top of a filled line plot (filledlineex01.1.php)">Figure 15.21. Having the grid line on top of a filled line plot <code class="uri"><a class="uri" href="example_src/filledlineex01.1.html" target="_top">(<code class="filename">filledlineex01.1.php</code>)</a></code> </a></p>
                        </li></ul></div><p>
                </p>
                <p>In <a class="xref" href="ch15.html#fig.example6.2" title='Figure 15.19. Using the "Step style" for line plots (example6.2.php)'>Figure 15.19. Using the "Step style" for line plots <code class="uri"><a class="uri" href="example_src/example6.2.html" target="_top">(<code class="filename">example6.2.php</code>)</a></code> </a> we have enabled the step style for a
                    basic line graphs to illustrate this concept.</p>
                <p>
                    </p><div class="figure"><a name="fig.example6.2"></a><p class="title"><b>Figure 15.19. Using the "Step style" for line plots <code class="uri"><a class="uri" href="example_src/example6.2.html" target="_top">(<code class="filename">example6.2.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/example6.2.png" alt='Using the "Step style" for line plots (example6.2.php)'></span> </div></div><p><br class="figure-break">
                </p>
            </div>
            <div class="sect2" title='Optimizing line plot using "fast drawing"'><div class="titlepage"><div><div><h3 class="title"><a name="id2556258"></a>Optimizing line plot using "fast drawing"</h3></div></div></div>
                
                <p>For line plots with a large amount of data point that is drawn with a solid
                    line it is possible to speed up the construction of the graph by calling the method:</p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
                            <p><code class="code">LinePlot::SetFastStroke($aFlg=true)</code></p>
                        </li></ul></div>
                <p>This will avoid some of the overhead associated with drawing lines of
                    arbitrary style. The limitations with this optimization is</p>
                <p>
                    </p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem">
                            <p>Only solid lines, no styles on the lines are allowed (including no
                                step-style)</p>
                        </li><li class="listitem">
                            <p>No plot marks</p>
                        </li><li class="listitem">
                            <p>No value labels</p>
                        </li><li class="listitem">
                            <p>No area plot , i.e. no filled line graphs and no filled partial
                                areas</p>
                        </li></ol></div><p>
                </p>
                <p>For line plots with a large amount of data point the savings can be quite
                    substantially and in the order of 40-50% speedup.</p>
            </div>
            <div class="sect2" title="Creating a filled line graphs (a.k.a. area plots)"><div class="titlepage"><div><div><h3 class="title"><a name="sec2.creating-area-graph"></a>Creating a filled line graphs (a.k.a. area plots)</h3></div></div></div>
                
                <p>A filled line plot (also known as an area plot) can be created in two ways
                    depending on whether automatic color handling is sufficient or there is a need
                    to manually specify the color.</p>
                <div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem">
                            <p><span class="bold"><strong>Case 1: Using automatic fill
                                    color</strong></span></p>
                            <p>In this case there is only need to tell that we want t filled line
                                graph by calling the method</p>
                            <p>
                                </p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
                                        <p><code class="code">LinePlot::SetFilled($aFlg=true)</code></p>
                                    </li></ul></div><p>
                            </p>
                            <p>The color assigned to the filled area will be set
                                automatically</p>
                        </li><li class="listitem">
                            <p><span class="bold"><strong>Case 2: Setting a manual fill
                                    color</strong></span></p>
                            <p>In this case the method called to set the fill color will make an
                                implicit call to <code class="code">SetFilled()</code>. Setting the fill color is
                                done by the method</p>
                            <p>
                                </p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
                                        <p><code class="code">LinePlot::SetFillColor($aColor)</code></p>
                                    </li></ul></div><p>
                            </p>
                        </li></ol></div><p>In <a class="xref" href="ch15.html#fig.filledlineex01" title="Figure 15.20. A basic filled line graph (filledlineex01.php)">Figure 15.20. A basic filled line graph <code class="uri"><a class="uri" href="example_src/filledlineex01.html" target="_top">(<code class="filename">filledlineex01.php</code>)</a></code> </a> a basic filled line
                    graph is shown which also have plot marks and an adjusted color so that the line
                    and the fill have different colors.</p>
                <p>
                    </p><div class="figure"><a name="fig.filledlineex01"></a><p class="title"><b>Figure 15.20. A basic filled line graph <code class="uri"><a class="uri" href="example_src/filledlineex01.html" target="_top">(<code class="filename">filledlineex01.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/filledlineex01.png" alt="A basic filled line graph (filledlineex01.php)"></span> </div></div><p><br class="figure-break">
                </p>
                <p>There are a couple of thing worth noting</p>
                <p>
                    </p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
                            <p>If you add multiple filled line plots to one graph make sure you
                                add the one with the highest Y-values first since it will otherwise
                                overwrite the other plots and they will not be visible. Plots are
                                stroked in the order they are added to the graph, so the graph you
                                want front-most must be added last.</p>
                        </li><li class="listitem">
                            <p>When using legends with filled line plot the legend will show the
                                fill color and not the bounding line color.</p>
                        </li><li class="listitem">
                            <p>The area filled is the area between the x-axis at y=0 and the data
                                value</p>
                        </li><li class="listitem">
                            <p>By default the line color will be the same as the fill color. This
                                means that if a different line color is needed then the call to
                                    <code class="code">LinePlot::SetColor()</code> must be <span class="bold"><strong>after</strong></span> the call to
                                    <code class="code">LinePlot::SetFillColor()</code></p>
                        </li><li class="listitem">
                            <p>Grid lines are by default drawn behind the plot (or rather the
                                plot is drawn on top of the plot area). However, this can be
                                adjusted so that the grid lines will always be on top of the line
                                plots. This is done by calling the method</p>
                            <p>
                                </p><div class="itemizedlist"><ul class="itemizedlist" type="circle"><li class="listitem">
                                        <p><code class="code">Graph::SetGridDepth($aDepth)</code> where
                                                <code class="code">$aDepth</code> is either
                                                <code class="code">DEPTH_BACK</code> or <code class="code">DEPTH_FRONT</code>
                                            symbolic defines</p>
                                    </li></ul></div><p>
                            </p>
                            <p>An alternative way of handling this is to make the fill color
                                semi-transparent by setting the alpha-blending for the fill color.
                                See <a class="xref" href="ch07s04.html#sec2.alpha-channel" title="Specifying the alpha channel (color transparency)">Specifying the alpha channel (color transparency)</a> and <a class="xref" href="ch15.html#fig.builtinplotmarksex1" title="Figure 15.18. Using plot marks with several data series and a legend (builtinplotmarksex1.php)">Figure 15.18. Using plot marks with several data series and a legend <code class="uri"><a class="uri" href="example_src/builtinplotmarksex1.html" target="_top">(<code class="filename">builtinplotmarksex1.php</code>)</a></code> </a> above for a real
                                example. Just making this grid depth adjustments will give the
                                result shown in <a class="xref" href="ch15.html#fig.filledlineex01.1" title="Figure 15.21. Having the grid line on top of a filled line plot (filledlineex01.1.php)">Figure 15.21. Having the grid line on top of a filled line plot <code class="uri"><a class="uri" href="example_src/filledlineex01.1.html" target="_top">(<code class="filename">filledlineex01.1.php</code>)</a></code> </a></p>
                            <p>
                                </p><div class="figure"><a name="fig.filledlineex01.1"></a><p class="title"><b>Figure 15.21. Having the grid line on top of a filled line plot <code class="uri"><a class="uri" href="example_src/filledlineex01.1.html" target="_top">(<code class="filename">filledlineex01.1.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/filledlineex01.1.png" alt="Having the grid line on top of a filled line plot (filledlineex01.1.php)"></span> </div></div><p><br class="figure-break">
                            </p>
                        </li></ul></div><p>
                </p>
                <div class="tip" title="Tip" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Tip</h3>
                    <p>By default the fill is only done between y=0 and the line plot. In some
                        cases it might be useful to have the fill go all the way down to whatever
                        the minimum y-value is (for example if the x-axis is always positioned at
                        the minimum y-value). This can be accomplished by calling the method</p>
                    <p>
                        </p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
                                <p><code class="code">LinePlot::SetFillFromYMin($aFlg=true)</code></p>
                            </li></ul></div><p>
                    </p>
                </div>
                <div class="sect3" title="Filling from the top"><div class="titlepage"><div><div><h4 class="title"><a name="id2556711"></a>Filling from the top</h4></div></div></div>
                    
                    <p>As was mentioned in the previous paragraph the fill normally goes from the
                        bottom and up to the line specified by the data series. Another variant is
                        to have the fill go from the top of the plot area down to the line. </p>
                    <p>There is primary one use for this type of fill and that is to create a
                        "mask" for a background image to make the illusion that the area below the
                        line is filled with the image while the area above the line is the normal
                        plot background.</p>
                    <p>This is done by first telling the library the fill shall be from the top
                        with a call to the method</p>
                    <p>
                        </p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
                                <p><code class="code">LinePlot::SetFillFromYMax($aFlg=true)</code></p>
                            </li></ul></div><p>
                    </p>
                    <p>then we create the data series as usual but specify the fill color as the
                        wanted background color and also add the image we want as a background
                        image.</p>
                    <p>Since we only want to use the first plot as a mask we can also specify the
                        line weight to 0 (to avoid the edge lines of the plot going from the first
                        and last point to the top. To have a nice line we can just add a second line
                        plot which is not filled and is just used to draw the line in our specified
                        color and weight. </p>
                    <p>An example of how this can look is shown in <a class="xref" href="ch15.html#fig.lineimagefillex1" title="Figure 15.22. Creating the effect of an area fill with an image (lineimagefillex1.php)">Figure 15.22. Creating the effect of an area fill with an image <code class="uri"><a class="uri" href="example_src/lineimagefillex1.html" target="_top">(<code class="filename">lineimagefillex1.php</code>)</a></code> </a> below which shows a fictive growth
                        in education which is illustrated with an old class room photography.</p>
                    <p>
                        </p><div class="figure"><a name="fig.lineimagefillex1"></a><p class="title"><b>Figure 15.22. Creating the effect of an area fill with an image <code class="uri"><a class="uri" href="example_src/lineimagefillex1.html" target="_top">(<code class="filename">lineimagefillex1.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/lineimagefillex1.png" alt="Creating the effect of an area fill with an image (lineimagefillex1.php)"></span> </div></div><p><br class="figure-break">
                    </p>
                    <p>
                        </p><div class="tip" title="Tip" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Tip</h3>
                            <p>To have the grid lines on top of the area plot (so they are
                                visible since they are vy default drawn at the bottom) the depth of
                                the grid lines can be set with a call to the method</p>
                            <p>
                                </p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
                                        <p><code class="code">Graph::SetGridDepth($aDepth)</code></p>
                                    </li></ul></div><p>
                            </p>
                            <p>For example as in</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">$graph-&gt;SetGridDepth(DEPTH_FRONT);</span></pre></td></tr></table></div><p>
                            </p>
                        </div><p>
                    </p>
                </div>
                <div class="sect3" title="Filling from 0 or from bottom"><div class="titlepage"><div><div><h4 class="title"><a name="id2556721"></a>Filling from 0 or from bottom</h4></div></div></div>
                    
                    <p>As a complement to what was described in the previous section it is also
                        possible to fill from the bottom. By default an area is filled from the
                        0-line to the boundary of the data series as is shown in <a class="xref" href="ch15.html#fig.manualtickex3" title="Figure 15.23. Filling from the 0-line (The default) (manualtickex3.php)">Figure 15.23. Filling from the 0-line (The default) <code class="uri"><a class="uri" href="example_src/manualtickex3.html" target="_top">(<code class="filename">manualtickex3.php</code>)</a></code> </a> below</p>
                    <p>
                        </p><div class="figure"><a name="fig.manualtickex3"></a><p class="title"><b>Figure 15.23. Filling from the 0-line (The default) <code class="uri"><a class="uri" href="example_src/manualtickex3.html" target="_top">(<code class="filename">manualtickex3.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/manualtickex3.png" alt="Filling from the 0-line (The default) (manualtickex3.php)"></span> </div></div><p><br class="figure-break">
                    </p>
                    <p>By making a call to</p>
                    <p>
                        </p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
                                <p><code class="code">LinePlot::SetFillFromYMin($aFlg=true)</code></p>
                            </li></ul></div><p>
                    </p>
                    <p>The area will instead be filled from the bottom as is shown in <a class="xref" href="ch15.html#fig.manualtickex4" title="Figure 15.24. Filling from the bottom (manualtickex4.php)">Figure 15.24. Filling from the bottom <code class="uri"><a class="uri" href="example_src/manualtickex4.html" target="_top">(<code class="filename">manualtickex4.php</code>)</a></code> </a></p>
                    <p>
                        </p><div class="figure"><a name="fig.manualtickex4"></a><p class="title"><b>Figure 15.24. Filling from the bottom <code class="uri"><a class="uri" href="example_src/manualtickex4.html" target="_top">(<code class="filename">manualtickex4.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/manualtickex4.png" alt="Filling from the bottom (manualtickex4.php)"></span> </div></div><p><br class="figure-break">
                    </p>
                    <p>
                        </p><div class="note" title="Note" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Note</h3>
                            <p>In <a class="xref" href="ch15.html#fig.manualtickex3" title="Figure 15.23. Filling from the 0-line (The default) (manualtickex3.php)">Figure 15.23. Filling from the 0-line (The default) <code class="uri"><a class="uri" href="example_src/manualtickex3.html" target="_top">(<code class="filename">manualtickex3.php</code>)</a></code> </a> and <a class="xref" href="ch15.html#fig.manualtickex4" title="Figure 15.24. Filling from the bottom (manualtickex4.php)">Figure 15.24. Filling from the bottom <code class="uri"><a class="uri" href="example_src/manualtickex4.html" target="_top">(<code class="filename">manualtickex4.php</code>)</a></code> </a> we have used gradient fill in
                                both the plot area and the amrgin area. This is a feature that was
                                introduced in free-version3.0.5 and in pro-version 3.1.3p</p>
                        </div><p>
                    </p>
                </div>
                <div class="sect3" title="Using gradient fills"><div class="titlepage"><div><div><h4 class="title"><a name="id2556978"></a>Using gradient fills</h4></div></div></div>
                    
                    <p>In addition to the solid color fill it is also possible to use gradient
                        fills for are graphs. To specify a gradient fill for a line graph the
                        following method in LinePlot class is used</p>
                    <p>
                        </p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
                                <p><code class="code">LinePlot::SetFillGradient($aFromColor,$aToColor,$aNumColors=100,$aFilled=true)</code></p>
                                <p><code class="code">$aFromColor</code>, <code class="code">$aToColor</code>, The starting
                                    and ending color</p>
                                <p><code class="code">$aNumColors=100</code>, The number of colors to use in
                                    the transition between from and to color</p>
                                <p><code class="code">$aFilled=true</code>, Enable/disable gradient
                                    filling</p>
                            </li></ul></div><p>
                    </p>
                    <p>Some examples of typical use of this is shown below</p>
                    <p>
                        </p><div class="figure"><a name="fig.gradlinefillex1"></a><p class="title"><b>Figure 15.25. A basic gradient fill using default values <code class="uri"><a class="uri" href="example_src/gradlinefillex1.html" target="_top">(<code class="filename">gradlinefillex1.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/gradlinefillex1.png" alt="A basic gradient fill using default values (gradlinefillex1.php)"></span> </div></div><p><br class="figure-break">
                    </p>
                    <p>The following two examples shows the effect of changing the number of
                        intermediate colors that are used to get from the "from color" and to the
                        "to color".</p>
                    <p>
                        </p><div class="informaltable">
                            <table border="0"><colgroup><col class="c1"><col class="c2"></colgroup><tbody><tr><td>
                                            <div class="figure"><a name="fig.gradlinefillex2"></a><p class="title"><b>Figure 15.26. Using the default number of intermediate colors <code class="uri"><a class="uri" href="example_src/gradlinefillex2.html" target="_top">(<code class="filename">gradlinefillex2.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/gradlinefillex2.png" alt="Using the default number of intermediate colors (gradlinefillex2.php)"></span> </div></div><br class="figure-break">
                                        </td><td>
                                            <div class="figure"><a name="fig.gradlinefillex3"></a><p class="title"><b>Figure 15.27. Only using 4 colors in total between start and finish color <code class="uri"><a class="uri" href="example_src/gradlinefillex3.html" target="_top">(<code class="filename">gradlinefillex3.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/gradlinefillex3.png" alt="Only using 4 colors in total between start and finish color (gradlinefillex3.php)"></span> </div></div><br class="figure-break">
                                        </td></tr></tbody></table>
                        </div><p>
                    </p>
                </div>
            </div>
            <div class="sect2" title="Partially filled area graphs"><div class="titlepage"><div><div><h3 class="title"><a name="id2557119"></a>Partially filled area graphs</h3></div></div></div>
                
                <p>In addition to filling the entire area between the line plot and the x-axis
                    (at y=0) the library also offers the possibility to add areas limited by the
                    line and a specified interval on the x-axis. Several such areas can be added and
                    each area having a different color. In ?? a basic example of how this can look
                    is shown.</p>
                <p>
                    </p><div class="figure"><a name="fig.partiallyfilledlineex1"></a><p class="title"><b>Figure 15.28. Adding two partially filled areas to a line plot <code class="uri"><a class="uri" href="example_src/partiallyfilledlineex1.html" target="_top">(<code class="filename">partiallyfilledlineex1.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/partiallyfilledlineex1.png" alt="Adding two partially filled areas to a line plot (partiallyfilledlineex1.php)"></span> </div></div><p><br class="figure-break">
                </p>
                <p>The areas (one or more) are created by calling the method</p>
                <p>
                    </p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
                            <p><code class="code">LinePlot::AddArea($aMin=0,$aMax=0,$aFilled=LP_AREA_NOT_FILLED,$aColor="gray9",$aBorder=LP_AREA_BORDER)</code></p>
                            <p>The extension of the area along the x-axis is given by the
                                    <code class="code">$aMin</code> and <code class="code">$aMax</code> values. </p>
                            <p>The third argument specifies whether the area should be filled or
                                not. This argument can have the values</p>
                            <p>
                                </p><div class="itemizedlist"><ul class="itemizedlist" type="circle"><li class="listitem">
                                        <p><code class="code">LP_AREA_FILLED</code></p>
                                    </li><li class="listitem">
                                        <p><code class="code">LP_AREA_NOT_FILLED</code></p>
                                    </li></ul></div><p>
                            </p>
                            <p>The fourth argument specifies the fill color and the fifth
                                argument specifies if the area should have a border (edge) or not.
                                If the area has a border it will be the same color as the line. The
                                values for the fourth argument can be</p>
                            <p>
                                </p><div class="itemizedlist"><ul class="itemizedlist" type="circle"><li class="listitem">
                                        <p><code class="code">LP_AREA_BORDER</code></p>
                                    </li><li class="listitem">
                                        <p><code class="code">LP_AREA_NO_BORDER</code></p>
                                    </li></ul></div><p>
                            </p>
                        </li></ul></div><p>
                </p>
            </div>
            <div class="sect2" title="Filled lines with NULL values"><div class="titlepage"><div><div><h3 class="title"><a name="id2557375"></a>Filled lines with NULL values</h3></div></div></div>
                
                <p>The NULL value handling follows the same principle as was described for line
                    plots. If the NULL value is specified as '-' the line will be interpretated but
                    if it is specified as 'x' it will be broken up as is shown in <a class="xref" href="ch15.html#fig.filledlineex03" title="Figure 15.29. Area plot with 'x' NULL values (filledlineex03.php)">Figure 15.29. Area plot with 'x' NULL values <code class="uri"><a class="uri" href="example_src/filledlineex03.html" target="_top">(<code class="filename">filledlineex03.php</code>)</a></code> </a></p>
                <p>
                    </p><div class="figure"><a name="fig.filledlineex03"></a><p class="title"><b>Figure 15.29. Area plot with 'x' NULL values <code class="uri"><a class="uri" href="example_src/filledlineex03.html" target="_top">(<code class="filename">filledlineex03.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/filledlineex03.png" alt="Area plot with 'x' NULL values (filledlineex03.php)"></span> </div></div><p><br class="figure-break">
                </p>
            </div>
            <div class="sect2" title="Accumulated line graphs"><div class="titlepage"><div><div><h3 class="title"><a name="id2557421"></a>Accumulated line graphs</h3></div></div></div>
                
                <p>Accumulated line graphs are line graphs that are "stacked" on top of each
                    other. That is, the values in the supplied data for the Y-axis is not the
                    absolute value but rather the relative value from graph below. For example if
                    you have two line graphs with three points each, say [3,7,5] and [6,9,7]. The
                    first graph will be plotted on the absolute Y-values [3,7,5] the second plot
                    will be plotted at [3+6, 7+9, 5+7], hence the values of the previous graphs will
                    be used as offsets.</p>
                <p>An accumulated graph plot is represented by <code class="code">class AccLinePlot</code>
                    which is a container class for line plots. This means that the
                        <code class="code">AccLinePlot</code> needs to be "fed" a number of ordinary instances of
                        <code class="code">LinePlot</code>.</p>
                <p>Any number of ordinary line graphs may be added together (up to the limit of
                    readability of the plot).</p>
                <p>For example, to add three line plots in an accumulated line plot graph the
                    following code is needed</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
11
12
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-inlinetags">&lt;?php</span><span class="hl-code">
</span><span class="hl-comment">//</span><span class="hl-comment"> First create the individual plots</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$p1</span><span class="hl-code"> = </span><span class="hl-reserved">new</span><span class="hl-code"> </span><span class="hl-identifier">LinePlot</span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-var">$datay_1</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$p2</span><span class="hl-code"> = </span><span class="hl-reserved">new</span><span class="hl-code"> </span><span class="hl-identifier">LinePlot</span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-var">$datay_2</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$p3</span><span class="hl-code"> = </span><span class="hl-reserved">new</span><span class="hl-code"> </span><span class="hl-identifier">LinePlot</span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-var">$datay_3</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"> Then add them together to form a accumulated plot</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$ap</span><span class="hl-code">  = </span><span class="hl-reserved">new</span><span class="hl-code">  </span><span class="hl-identifier">AccLinePlot</span><span class="hl-brackets">(</span><span class="hl-reserved">array</span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-var">$p1</span><span class="hl-code"> , </span><span class="hl-var">$p2</span><span class="hl-code"> , </span><span class="hl-var">$p3</span><span class="hl-code"> </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"> Add the accumulated line plot to the graph</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">Add</span><span class="hl-code"> </span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-var">$ap</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code">; 
</span><span class="hl-inlinetags">?&gt;</span></pre></td></tr></table></div><p>
                </p>
                <p>Using some random data for the areas can produce the result shown in <a class="xref" href="ch15.html#fig.example17" title="Figure 15.30. A basic accumulated area plot (example17.php)">Figure 15.30. A basic accumulated area plot <code class="uri"><a class="uri" href="example_src/example17.html" target="_top">(<code class="filename">example17.php</code>)</a></code> </a></p>
                <p>
                    </p><div class="figure"><a name="fig.example17"></a><p class="title"><b>Figure 15.30. A basic accumulated area plot <code class="uri"><a class="uri" href="example_src/example17.html" target="_top">(<code class="filename">example17.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/example17.png" alt="A basic accumulated area plot (example17.php)"></span> </div></div><p><br class="figure-break">
                </p>
            </div>
            <div class="sect2" title="Accumulated line graphs with given X-labels"><div class="titlepage"><div><div><h3 class="title"><a name="id2557468"></a>Accumulated line graphs with given X-labels</h3></div></div></div>
                
                <p>Creating an accumulated line plot, (or a filled accumulated area plot), with
                    multiple data sets at given x-coordinates poses some specific problems when the
                    coordinates for the different data sets are not given at the same x-coordinates.
                    This is a generic problem and has nothing to do with library in particular. This
                    section wil deal with one possible way of handling this by making sure that
                    missing data points are created if they are "missing".</p>
                <p>To understand the problem we will make one simplifications (that is of no real
                    consequence for the end result) that can be stated as </p>
                <p>
                    </p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem">
                            <p>the X-coordinates for all data tuples are whole positive number.
                            </p>
                        </li><li class="listitem">
                            <p>the X-coordinates are in sorted order (non-descending) </p>
                        </li></ol></div><p>
                </p>
                <p>The core issue can be illustrate as follows. Lets assume that we want to make
                    an accumulated graph showing the two data sets </p>
                <p>
                    </p><pre class="screen">data set 1 == (0,5), (2,10), (3,10), (5,20)
data set 2 == (0,7), (1,12), (2,5),  (5,10)
</pre><p>
                </p>
                <p>In the above notation the tuple (0,5) means a data point with X-coordinate = 0
                    and Y-coordinate = 5. </p>
                <p>What the library now needs to do is to first plot data set 1. No problem. When
                    it then becomes time to plot the second data set we face an issue. The only
                    points where we now the Y-value of data set 1 is at the given discrete points
                    (0,2,3,5). </p>
                <p>Plotting the first tuple for data set 2 shown above gives an absolute starting
                    point at </p>
                <p>
                    </p><pre class="screen">(0,5+7) == (0,12)
</pre><p>
                </p>
                <p>The next data point we know for data set 2 is (1,12) so we need to plot this.
                    But now we can see that we do not know the value for data set 1 at X-coordinate
                    = 1. We only know the values at coordinates 0 and 2. This gives us a problem. We
                    need to know at what offset we should plot this data point in data set 2 and we
                    have no direct way of calculating this. </p>
                <p>Now, one might argue that we could just interpolate between the data points
                    (0,5) and (2,10) the Y-value at X=1 (doing a linear interpolation this would
                    give the data point (1,7.5)) so why doesn't the library simply do this? It
                    surely could be done. </p>
                <p>
                    </p><div class="note" title="Note" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Note</h3>
                        <p>In real life using this approach would be much more complex. First of
                            all we need to create a linear succession of all X-values used in all
                            data sets to create an ordered set and then fill in the blanks so that
                            all data sets have values at all given X-coordinates. Those of you
                            familiar with signal processing will recognize this as an (almost)
                            up-sampling of the original data sets followed by a low pass filter.
                        </p>
                    </div><p>
                </p>
                <p>However, by design the library doesn't do this. The crucial observation here
                    is that it can not be a graphic libraries responsibility to "create" missing
                    data points by making assumption that a particular polynomial interpolation is
                    valid (in this case a first degree approximation). What if a linear
                    interpolation is not representative for the data set given? Perhaps a second
                    degree approximation would be more accurate. </p>
                <p>So, this kind of data preparation must be done in the domain of the given data
                    set where knowledge of the underlying data will allow an accurate preparation of
                    the input to a graphing script if we insist of plotting an accumulated graph.
                    One could argue that accumulated data plots can only be done for data series
                    with the same X-coordinates. </p>
                <div class="sect3" title="Preparing the input data"><div class="titlepage"><div><div><h4 class="title"><a name="id2557648"></a>Preparing the input data</h4></div></div></div>
                    
                    <p>So what if we are still required to do an accumulated plot even when we
                        don't have all the data sets at the same X-coordinates? Going back to our
                        original two data sets, hereafter referrered to as DS1 and DS2 there are 2
                        manual steps (as described above) that needs to happen. </p>
                    <p>
                        </p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem">
                                <p>Identify all X-data points that needs to exist </p>
                            </li><li class="listitem">
                                <p>Create values for all data sets at those points </p>
                            </li></ol></div><p>
                    </p>
                    <p>So, in DS1 and DS2 the union of the two data sets X-coordinates are </p>
                    <p>
                        </p><pre class="screen">X_coordinates == union(DS1_x, DS2_x) == 0,1,2,3,5
</pre><p>
                    </p>
                    <p>This will force us to augment the two data sets as </p>
                    <p>
                        </p><pre class="screen">data set 1 == (0,5), (1,??), (2,10), (3,10), (5,20)
data set 2 == (0,7), (1,12), (2, 5), (3,??), (5,10)
</pre><p>
                    </p>
                    <p>Where I have added '??' to indicate values that needs to be computed in
                        order to draw an accumulated line/area plot at specific values. Now assume
                        that we are able to find the missing data for these points by some method to
                        be </p>
                    <p>
                        </p><pre class="screen">data set 1 == (0,5), (1, 8), (2,10), (3,10), (5,20)
data set 2 == (0,7), (1,12), (2, 5), (3, 2), (5,10)
</pre><p>
                    </p>
                    <p>Are we now ready to plot these data sets? Unfortunately not quite. The
                        remaining problem is that since the library only handles accumulated plots
                        without a given X-coordinate (using an X-coordinate for the individual line
                        plots will have no affect - and it's behaviour is undefined). This means
                        that the data points are assumed to be equ-distance apart - and this is
                        almost true for the data sets above. There is 1 unit between theme apart
                        from the two last tuples which in fact have a distance of 2 units. In fact
                        the library only plots data sets with a given Y-coordinate and then assumes
                        that the x-coordinate is a linear ordering of (0,1,2, ..) </p>
                    <p>So in order to create a linear equ-distance ordered set we need to further
                        augment the two data sets as </p>
                    <p>
                        </p><pre class="screen">data set 1 == (0,5), (1, 8), (2,10), (3,10), (4,??), (5,20)
data set 2 == (0,7), (1,12), (2, 5), (3, 2), (4,??), (5,10)
</pre><p>
                    </p>
                    <p>So this means that we need to manually calculate another interpolated
                        value. If we know we can make a linear interpolation (or perhaps find the
                        data at this point) it will give us </p>
                    <p>
                        </p><pre class="screen">data set 1 == (0,5), (1, 8), (2,10), (3,10), (4,15), (5,20)
data set 2 == (0,7), (1,12), (2, 5), (3, 2), (4, 6), (5,10)
</pre><p>
                    </p>
                    <p>This final data set is now ready to be sent to the
                            <code class="code">AccLinePlot</code> class. It is left as a (non-trivial) exercise
                        to the reader to define and implement a function that performs the steps
                        outlined above to create proper data sets before reading on.</p>
                </div>
                <div class="sect3" title="Creating plots with non-trivial X-coordinates"><div class="titlepage"><div><div><h4 class="title"><a name="id2557650"></a>Creating plots with non-trivial X-coordinates</h4></div></div></div>
                    
                    <p>With non-trivial X-coordinates we mean for example timestamps or perhaps
                        real numbers. For timestamps it is not so difficult. What we need to do is
                        to identify the proper interval (in the original timestamp domain) and then
                        create a mapping between that domain and the natural numbers (0,1,2,3,...). </p>
                    <p>The reason for this is that the library only accepts Y-coordinates as
                        argument to the accumulated data series and will make the implicit
                        assumption that when it plots the data it will plot the data points at
                        consecutive values as if the X-coordinates had been given as (0,1,2,3,..).
                        Hence we need to manually prepare the data to match this format. </p>
                    <p>As the final step we manually set the labels for the X-axis according to
                        our interpretation. An example (with some code snippets) will make this
                        approach clear. </p>
                    <p><span class="bold"><strong>Example - using timestamps</strong></span></p>
                    <p>Assume we have the two data sets with timestamps </p>
                    <p>
                        </p><pre class="screen">DS1 == (1212199200,12), (1212210000,20), (1212213600,30)
DS1 == (1212199200,12), (1212206400, 8)
</pre><p>
                    </p>
                    <p>and we now that the sampling interval between the data points are 7200s
                        (=2 min). Following the same principle as above we need to find the
                        additional values</p>
                    <p>
                        </p><pre class="screen">DS1 == (1212199200,12), (1212206400,??), (1212210000,20), (1212213600,30)
DS1 == (1212199200,12), (1212206400, 8), (1212210000,??), (1212213600,??)
</pre><p>
                    </p>
                    <p>further assuming that we (by some method) can find these value we can then
                        interpret this data as </p>
                    <p>
                        </p><pre class="screen">DS1 == (1212199200,12), (1212206400,16), (1212210000,20), (1212213600,30)
DS1 == (1212199200,12), (1212206400, 8), (1212210000, 0), (1212213600, 0)
</pre><p>
                    </p>
                    <p>In the above we have made the explicit assumption that unknown data points
                        at the end can be interpretated as 0 in this particular application. </p>
                    <p>We now have an ordered sequence of these tuples and we can imagine a
                        mapping that will allow us to write these sequences as </p>
                    <p>
                        </p><pre class="screen">DS1 == (0,12), (1,16), (2,20), (3,30)
DS1 == (0,12), (1, 8), (2, 0), (3, 0)
</pre><p>
                    </p>
                    <p>The mapping for this is <code class="code">xi=1212199200 + 7200*i, i=0..3</code> which
                        we use when we put the final labels in the graph. </p>
                    <p>The only steps that remain to handle timestamps is to manually replace the
                        X-scale (which in this case would be 0,1,2,3) with the calculated values
                        according to the mapping given above. </p>
                    <p>We do this by creating an array of the timestamps we need to plot and then
                        replace them - in situ - with an application of the standard PHP function
                            <code class="code">array_walk()</code> which applies a user defined function to each
                        value in an array and replaces that value with the return value of the user
                        function. In this case we create a user function that implements the mapping
                        stated above with the additional twist that given an argument as a time
                        stamp it returns a suitable human format for that time stamp. </p>
                    <p>The following code fragments shows how this could be done </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
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-code">// Some userdefined human readable version of the timestamp
function formatDate(&amp;$aVal) {
    $aVal = date('Y-m-d H:i',$aVal);
}
 
$timeStamps = array(212199200,1212206400,1212210000,1212213600);
 
array_walk($time,'formatDate');</span></pre></td></tr></table></div><p>
                    </p>
                    <p>when we now have the labels in a nice human readable format we can put
                        them on the scale labels with </p>
                    <p>
                        </p><div class="hl-main"><table class="hl-table" width="100%"><tr><td class="hl-gutter" align="right" valign="top"><pre>1
2
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-code">$graph-&gt;xaxis-&gt;SetTickLabels($timeStamps);
$graph-&gt;xaxis-&gt;SetLabelAngle(90);</span></pre></td></tr></table></div><p>
                    </p>
                    <p>though strictly not necessary we have also tilted the labels 90 degrees in
                        order to minimize the risk the labels overwrite each other. </p>
                    <p>If we still think that the labels are too close together ea we can chose
                        to only label every second tick mark. We do this with a call to </p>
                    <p>
                        </p><div class="hl-main"><table class="hl-table" width="100%"><tr><td class="hl-gutter" align="right" valign="top"><pre>1
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-code">$graph-&gt;xaxis-&gt;SetTextLabelInterval(2);</span></pre></td></tr></table></div><p>
                    </p>
                    <p><span class="bold"><strong>Example using real (i.e. floating point)
                            x-coordinates</strong></span></p>
                    <p>In principle this is handled in the same way as what we shown above for
                        timestamps. The additional complexity here spells rounding errors. When we
                        establish the equidistant interval between each data point it will be a real
                        number, potentially an irrational number, which means that we cannot
                        represent it exactly and adding the interval repeated times might cause
                        rounding errors if we are not careful. </p>
                    <p>Secondly we need to find a mapping between the ordered sequence of the
                        real numbers we have as X-coordinates and the natural numbers which are the
                        implicit X-coordinates assumed by the library. </p>
                </div>
                <div class="sect3" title="A full example"><div class="titlepage"><div><div><h4 class="title"><a name="id2557943"></a>A full example</h4></div></div></div>
                    
                    <p>In the example below we artifically create some data sets where all the
                        sets have values at all specified timestamps with the following code </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
11
12
13
14
15
16
17
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-inlinetags">&lt;?php</span><span class="hl-code">
</span><span class="hl-comment">//</span><span class="hl-comment">Create some test data</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$xdata</span><span class="hl-code"> = </span><span class="hl-reserved">array</span><span class="hl-brackets">(</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$ydata</span><span class="hl-code"> = </span><span class="hl-reserved">array</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"> Timestamps - 2h (=7200s) apart starting </span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$sampling</span><span class="hl-code"> = </span><span class="hl-number">7200</span><span class="hl-code">;
</span><span class="hl-var">$n</span><span class="hl-code"> = </span><span class="hl-number">50</span><span class="hl-code">; </span><span class="hl-comment">//</span><span class="hl-comment"> data points</span><span class="hl-comment"></span><span class="hl-code">
 
</span><span class="hl-comment">//</span><span class="hl-comment"> Setup the data arrays with some random data</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-reserved">for</span><span class="hl-brackets">(</span><span class="hl-var">$i</span><span class="hl-code">=</span><span class="hl-number">0</span><span class="hl-code">; </span><span class="hl-var">$i</span><span class="hl-code"> &lt; </span><span class="hl-var">$n</span><span class="hl-code">; ++</span><span class="hl-var">$i</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code"> </span><span class="hl-brackets">{</span><span class="hl-code">
    </span><span class="hl-var">$xdata</span><span class="hl-brackets">[</span><span class="hl-var">$i</span><span class="hl-brackets">]</span><span class="hl-code"> = </span><span class="hl-identifier">time</span><span class="hl-brackets">(</span><span class="hl-brackets">)</span><span class="hl-code"> + </span><span class="hl-var">$i</span><span class="hl-code"> * </span><span class="hl-var">$sampling</span><span class="hl-code">;
    </span><span class="hl-var">$ydata</span><span class="hl-brackets">[</span><span class="hl-number">0</span><span class="hl-brackets">]</span><span class="hl-brackets">[</span><span class="hl-var">$i</span><span class="hl-brackets">]</span><span class="hl-code"> = </span><span class="hl-identifier">rand</span><span class="hl-brackets">(</span><span class="hl-number">12</span><span class="hl-code">,</span><span class="hl-number">15</span><span class="hl-brackets">)</span><span class="hl-code">;
    </span><span class="hl-var">$ydata</span><span class="hl-brackets">[</span><span class="hl-number">1</span><span class="hl-brackets">]</span><span class="hl-brackets">[</span><span class="hl-var">$i</span><span class="hl-brackets">]</span><span class="hl-code"> = </span><span class="hl-identifier">rand</span><span class="hl-brackets">(</span><span class="hl-number">100</span><span class="hl-code">,</span><span class="hl-number">155</span><span class="hl-brackets">)</span><span class="hl-code">;
    </span><span class="hl-var">$ydata</span><span class="hl-brackets">[</span><span class="hl-number">2</span><span class="hl-brackets">]</span><span class="hl-brackets">[</span><span class="hl-var">$i</span><span class="hl-brackets">]</span><span class="hl-code"> = </span><span class="hl-identifier">rand</span><span class="hl-brackets">(</span><span class="hl-number">20</span><span class="hl-code">,</span><span class="hl-number">30</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-brackets">}</span><span class="hl-code">
</span><span class="hl-inlinetags">?&gt;</span></pre></td></tr></table></div><p>
                    </p>
                    <p>Since the xdata array is given as timestamps we need to make this more
                        human readable by converting the timestamp using the <code class="code">date()</code>
                        function. To do this we create an axillary helper function and then use the
                            <code class="code">array_walk() </code>standard array function to apply this
                        formatting to all existing values in the timestamp array as follows. </p>
                    <p>
                        </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">// Formatting function to translate the timestamps into human readable labels
function formatDate(&amp;$aVal) {
    $aVal = date('Y-m-d H:i',$aVal);
}
 
// Apply this format to all time values in the data to prepare it to be display
array_walk($time,'formatDate');</span></pre></td></tr></table></div><p>
                    </p>
                    <p>The core of the script can now be written. For a change we make some
                        adjustment from the default values of colors and tick mark positioning as a
                        reminder that there is a lot of flexibility in creating the graphs. </p>
                    <p>
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</pre></td><td class="hl-main" valign="top"><pre><span class="hl-inlinetags">&lt;?php</span><span class="hl-code">
</span><span class="hl-comment">//</span><span class="hl-comment"> Create the graph. </span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$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">700</span><span class="hl-code">, </span><span class="hl-number">400</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">title</span><span class="hl-code">-&gt;</span><span class="hl-identifier">Set</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">Accumulated values with specified X-axis scale</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetScale</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">datlin</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"> Setup margin color</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetMarginColor</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">green@0.95</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"> Adjust the margin to make room for the X-labels</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</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">30</span><span class="hl-code">,</span><span class="hl-number">40</span><span class="hl-code">,</span><span class="hl-number">120</span><span class="hl-brackets">)</span><span class="hl-code">;
 
</span><span class="hl-comment">//</span><span class="hl-comment"> Turn the tick marks out from the plot area</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">xaxis</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetTickSide</span><span class="hl-brackets">(</span><span class="hl-identifier">SIDE_BOTTOM</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">yaxis</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetTickSide</span><span class="hl-brackets">(</span><span class="hl-identifier">SIDE_LEFT</span><span class="hl-brackets">)</span><span class="hl-code">;
 
</span><span class="hl-var">$p0</span><span class="hl-code"> =</span><span class="hl-reserved">new</span><span class="hl-code"> </span><span class="hl-identifier">LinePlot</span><span class="hl-brackets">(</span><span class="hl-var">$a</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$p0</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetFillColor</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">sandybrown</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$p1</span><span class="hl-code"> =</span><span class="hl-reserved">new</span><span class="hl-code"> </span><span class="hl-identifier">LinePlot</span><span class="hl-brackets">(</span><span class="hl-var">$b</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$p1</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetFillColor</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">lightblue</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$p2</span><span class="hl-code"> =</span><span class="hl-reserved">new</span><span class="hl-code"> </span><span class="hl-identifier">LinePlot</span><span class="hl-brackets">(</span><span class="hl-var">$c</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$p2</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetFillColor</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">red</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$ap</span><span class="hl-code"> = </span><span class="hl-reserved">new</span><span class="hl-code"> </span><span class="hl-identifier">AccLinePlot</span><span class="hl-brackets">(</span><span class="hl-reserved">array</span><span class="hl-brackets">(</span><span class="hl-var">$p0</span><span class="hl-code">,</span><span class="hl-var">$p1</span><span class="hl-code">,</span><span class="hl-var">$p2</span><span class="hl-brackets">)</span><span class="hl-brackets">)</span><span class="hl-code">;
 
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">xaxis</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetTickLabels</span><span class="hl-brackets">(</span><span class="hl-var">$time</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">xaxis</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetTextLabelInterval</span><span class="hl-brackets">(</span><span class="hl-number">4</span><span class="hl-brackets">)</span><span class="hl-code">;
 
</span><span class="hl-comment">//</span><span class="hl-comment"> Add the plot to the graph</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">Add</span><span class="hl-brackets">(</span><span class="hl-var">$ap</span><span class="hl-brackets">)</span><span class="hl-code">;
 
</span><span class="hl-comment">//</span><span class="hl-comment"> Set the angle for the labels to 90 degrees</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</span><span class="hl-identifier">xaxis</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetLabelAngle</span><span class="hl-brackets">(</span><span class="hl-number">90</span><span class="hl-brackets">)</span><span class="hl-code">;
 
</span><span class="hl-comment">//</span><span class="hl-comment"> Send the graph back to the browser</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$graph</span><span class="hl-code">-&gt;</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">?&gt;</span></pre></td></tr></table></div><p>
                    </p>
                    <p>The resulting image will now look something like what is shown in
                        ??</p>
                    <p>
                        </p><div class="figure"><a name="fig.prepaccdata_example"></a><p class="title"><b>Figure 15.31. Area plot with specified x coordinates <code class="uri"><a class="uri" href="example_src/prepaccdata_example.html" target="_top">(<code class="filename">prepaccdata_example.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/prepaccdata_example.png" alt="Area plot with specified x coordinates (prepaccdata_example.php)"></span> </div></div><p><br class="figure-break">
                    </p>
                </div>
                <div class="sect3" title="Helper function to create interpolated data"><div class="titlepage"><div><div><h4 class="title"><a name="id2558063"></a>Helper function to create interpolated data</h4></div></div></div>
                    
                    <p>The function <code class="code">InterpolateData()</code> below takes two array of
                        arrays and one integer as arguments. The first array of arrays contains the
                        X-coordinates for each data set and the second array of arrays contains the
                        Y-coordinates for all the data sets. The final integer argument is the
                        distance (or sample rate) that should be assumed between each X-coordinate. </p>
                    <p>The function will return a tuple. The first element in the returned tuple
                        is a single array with all the X-values that should be used and the second
                        element is an array of arrays with all the Y-data sets with all data
                        specified for each X-coordinate. Any missing Y values are interpolated using
                        a linear interpolation schema. </p>
                    <p>So using our first example above as demonstration this would be handled 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
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</pre></td><td class="hl-main" valign="top"><pre><span class="hl-inlinetags">&lt;?php</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-code"> 
    </span><span class="hl-reserved">array</span><span class="hl-brackets">(</span><span class="hl-number">0</span><span class="hl-code">,</span><span class="hl-number">2</span><span class="hl-code">,</span><span class="hl-number">3</span><span class="hl-code">,</span><span class="hl-number">5</span><span class="hl-brackets">)</span><span class="hl-code">,
    </span><span class="hl-reserved">array</span><span class="hl-brackets">(</span><span class="hl-number">0</span><span class="hl-code">,</span><span class="hl-number">1</span><span class="hl-code">,</span><span class="hl-number">2</span><span class="hl-code">,</span><span class="hl-number">5</span><span class="hl-brackets">)</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-code">
    </span><span class="hl-reserved">array</span><span class="hl-brackets">(</span><span class="hl-number">5</span><span class="hl-code">,</span><span class="hl-number">10</span><span class="hl-code">,</span><span class="hl-number">10</span><span class="hl-code">,</span><span class="hl-number">20</span><span class="hl-brackets">)</span><span class="hl-code">,
    </span><span class="hl-reserved">array</span><span class="hl-brackets">(</span><span class="hl-number">7</span><span class="hl-code">,</span><span class="hl-number">12</span><span class="hl-code">,</span><span class="hl-number">5</span><span class="hl-code">,</span><span class="hl-number">10</span><span class="hl-brackets">)</span><span class="hl-brackets">)</span><span class="hl-code">;
 
</span><span class="hl-reserved">list</span><span class="hl-brackets">(</span><span class="hl-var">$datax</span><span class="hl-code">, </span><span class="hl-var">$datay</span><span class="hl-brackets">)</span><span class="hl-code"> = </span><span class="hl-identifier">InterpolateData</span><span class="hl-brackets">(</span><span class="hl-var">$datax</span><span class="hl-code">, </span><span class="hl-var">$datay</span><span class="hl-brackets">)</span><span class="hl-code">;
 
</span><span class="hl-comment">//</span><span class="hl-comment"> $datax = array(0,1,2,3,4,5)</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-comment">//</span><span class="hl-comment"> $datay = array( array(5, 8,10,10,15,20),</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-comment">//</span><span class="hl-comment">                 array(7,12, 5, 2, 6,10));</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-inlinetags">?&gt;</span></pre></td></tr></table></div><p>
                    </p>
                    <p>One possible implementation of this function is given below. It has
                        primarily been written for clarity and not necessary high performance. To
                        interpolate the "missing" Y-values a linear approximation is assumed. </p>
                    <p>
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</pre></td><td class="hl-main" valign="top"><pre><span class="hl-inlinetags">&lt;?php</span><span class="hl-code">
</span><span class="hl-reserved">function</span><span class="hl-code"> </span><span class="hl-identifier">InterpolateData</span><span class="hl-brackets">(</span><span class="hl-var">$aXData</span><span class="hl-code">,</span><span class="hl-var">$aYData</span><span class="hl-code">,</span><span class="hl-var">$aSampleInterval</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-brackets">{</span><span class="hl-code">
 
    </span><span class="hl-comment">//</span><span class="hl-comment"> First do some sanity checks on the input data</span><span class="hl-comment"></span><span class="hl-code">
    </span><span class="hl-var">$nx</span><span class="hl-code"> = </span><span class="hl-identifier">count</span><span class="hl-brackets">(</span><span class="hl-var">$aXData</span><span class="hl-brackets">)</span><span class="hl-code">;
    </span><span class="hl-var">$ny</span><span class="hl-code"> = </span><span class="hl-identifier">count</span><span class="hl-brackets">(</span><span class="hl-var">$aYData</span><span class="hl-brackets">)</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">$nx</span><span class="hl-code"> != </span><span class="hl-var">$ny</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-number">1</span><span class="hl-brackets">)</span><span class="hl-code">;
        
    </span><span class="hl-reserved">for</span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-var">$i</span><span class="hl-code">=</span><span class="hl-number">0</span><span class="hl-code">; </span><span class="hl-var">$i</span><span class="hl-code"> &lt; </span><span class="hl-var">$nx</span><span class="hl-code">; ++</span><span class="hl-var">$i</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code"> </span><span class="hl-brackets">{</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-identifier">count</span><span class="hl-brackets">(</span><span class="hl-var">$aXData</span><span class="hl-brackets">[</span><span class="hl-var">$i</span><span class="hl-brackets">]</span><span class="hl-brackets">)</span><span class="hl-code"> != </span><span class="hl-identifier">count</span><span class="hl-brackets">(</span><span class="hl-var">$aYData</span><span class="hl-brackets">[</span><span class="hl-var">$i</span><span class="hl-brackets">]</span><span class="hl-brackets">)</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-number">2</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"> Create the sorted union of all X-coordinates</span><span class="hl-comment"></span><span class="hl-code">
    </span><span class="hl-var">$unionx</span><span class="hl-code"> = </span><span class="hl-identifier">array_union</span><span class="hl-brackets">(</span><span class="hl-var">$aXData</span><span class="hl-brackets">)</span><span class="hl-code">;
    </span><span class="hl-var">$length</span><span class="hl-code"> = </span><span class="hl-identifier">count</span><span class="hl-brackets">(</span><span class="hl-var">$unionx</span><span class="hl-brackets">)</span><span class="hl-code">;
 
    </span><span class="hl-comment">//</span><span class="hl-comment"> We now have to make sure that the distance between all</span><span class="hl-comment"></span><span class="hl-code">
    </span><span class="hl-comment">//</span><span class="hl-comment"> X-coordinates is 1 unit of the sample interval. If not</span><span class="hl-comment"></span><span class="hl-code">
    </span><span class="hl-comment">//</span><span class="hl-comment"> we will have to insert suitable X-value</span><span class="hl-comment"></span><span class="hl-code">
    </span><span class="hl-var">$i</span><span class="hl-code">=</span><span class="hl-number">1</span><span class="hl-code">;
    </span><span class="hl-reserved">while</span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-var">$i</span><span class="hl-code"> &lt; </span><span class="hl-var">$length</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code"> </span><span class="hl-brackets">{</span><span class="hl-code">
            </span><span class="hl-var">$missing</span><span class="hl-code"> = </span><span class="hl-number">0</span><span class="hl-code">;
            </span><span class="hl-var">$diff</span><span class="hl-code"> = </span><span class="hl-var">$unionx</span><span class="hl-brackets">[</span><span class="hl-var">$i</span><span class="hl-brackets">]</span><span class="hl-code"> - </span><span class="hl-var">$unionx</span><span class="hl-brackets">[</span><span class="hl-var">$i</span><span class="hl-code">-</span><span class="hl-number">1</span><span class="hl-brackets">]</span><span class="hl-code">;
            </span><span class="hl-reserved">if</span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-var">$diff</span><span class="hl-code"> != </span><span class="hl-var">$aSampleInterval</span><span class="hl-code"> </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"> Sanity check to make sure sample interval is an even multiple</span><span class="hl-comment"></span><span class="hl-code">
            </span><span class="hl-comment">//</span><span class="hl-comment"> of the distance between the gven X-coordinates</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">$diff</span><span class="hl-code"> % </span><span class="hl-var">$aSampleInterval</span><span class="hl-code"> !== </span><span class="hl-number">0</span><span class="hl-code"> </span><span class="hl-brackets">)</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-number">4</span><span class="hl-brackets">)</span><span class="hl-code">;
            </span><span class="hl-brackets">}</span><span class="hl-code">
 
                </span><span class="hl-var">$missing</span><span class="hl-code"> = </span><span class="hl-var">$diff</span><span class="hl-code"> / </span><span class="hl-var">$aSampleInterval</span><span class="hl-code"> - </span><span class="hl-number">1</span><span class="hl-code">;
                </span><span class="hl-var">$fill</span><span class="hl-code"> = </span><span class="hl-reserved">array</span><span class="hl-brackets">(</span><span class="hl-brackets">)</span><span class="hl-code">;
                </span><span class="hl-reserved">for</span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-var">$j</span><span class="hl-code">=</span><span class="hl-number">0</span><span class="hl-code">; </span><span class="hl-var">$j</span><span class="hl-code"> &lt; </span><span class="hl-var">$missing</span><span class="hl-code">; ++</span><span class="hl-var">$j</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code"> </span><span class="hl-brackets">{</span><span class="hl-code">
                        </span><span class="hl-var">$fill</span><span class="hl-brackets">[</span><span class="hl-var">$j</span><span class="hl-brackets">]</span><span class="hl-code"> = </span><span class="hl-var">$aSampleInterval</span><span class="hl-code">*</span><span class="hl-brackets">(</span><span class="hl-var">$j</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">$unionx</span><span class="hl-brackets">[</span><span class="hl-var">$i</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-brackets">}</span><span class="hl-code">
                </span><span class="hl-var">$unionx</span><span class="hl-code"> = </span><span class="hl-identifier">array_merge</span><span class="hl-brackets">(</span><span class="hl-code">
                        </span><span class="hl-identifier">array_slice</span><span class="hl-brackets">(</span><span class="hl-var">$unionx</span><span class="hl-code">,</span><span class="hl-number">0</span><span class="hl-code">,</span><span class="hl-var">$i</span><span class="hl-brackets">)</span><span class="hl-code">,</span><span class="hl-var">$fill</span><span class="hl-code">,</span><span class="hl-identifier">array_slice</span><span class="hl-brackets">(</span><span class="hl-var">$unionx</span><span class="hl-code">,</span><span class="hl-var">$i</span><span class="hl-brackets">)</span><span class="hl-brackets">)</span><span class="hl-code">;
             </span><span class="hl-brackets">}</span><span class="hl-code">
             </span><span class="hl-var">$i</span><span class="hl-code"> += </span><span class="hl-var">$missing</span><span class="hl-code">+</span><span class="hl-number">1</span><span class="hl-code">;
             </span><span class="hl-var">$length</span><span class="hl-code"> += </span><span class="hl-var">$missing</span><span class="hl-code">;
    </span><span class="hl-brackets">}</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">$length</span><span class="hl-code"> != </span><span class="hl-identifier">count</span><span class="hl-brackets">(</span><span class="hl-var">$unionx</span><span class="hl-brackets">)</span><span class="hl-code"> </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"> Internal error check</span><span class="hl-comment"></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-number">3</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"> Now loop through all the individual data sets and find out </span><span class="hl-comment"></span><span class="hl-code">
    </span><span class="hl-comment">//</span><span class="hl-comment"> which x-data is missing and hence needs to be interpolated</span><span class="hl-comment"></span><span class="hl-code">
    </span><span class="hl-var">$n</span><span class="hl-code"> = </span><span class="hl-identifier">count</span><span class="hl-brackets">(</span><span class="hl-var">$aXData</span><span class="hl-brackets">)</span><span class="hl-code">;
 
    </span><span class="hl-reserved">for</span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-var">$i</span><span class="hl-code">=</span><span class="hl-number">0</span><span class="hl-code">; </span><span class="hl-var">$i</span><span class="hl-code"> &lt; </span><span class="hl-var">$n</span><span class="hl-code">; ++</span><span class="hl-var">$i</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code"> </span><span class="hl-brackets">{</span><span class="hl-code">
            </span><span class="hl-var">$missing_values</span><span class="hl-code"> = </span><span class="hl-identifier">array_diff</span><span class="hl-brackets">(</span><span class="hl-var">$unionx</span><span class="hl-code">, </span><span class="hl-var">$aXData</span><span class="hl-brackets">[</span><span class="hl-var">$i</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"> Now find the position of each missing X-coordinate</span><span class="hl-comment"></span><span class="hl-code">
            </span><span class="hl-comment">//</span><span class="hl-comment"> and use that position in the corresponding Y array</span><span class="hl-comment"></span><span class="hl-code">
            </span><span class="hl-comment">//</span><span class="hl-comment"> to insert an interpolated value</span><span class="hl-comment"></span><span class="hl-code">
            </span><span class="hl-var">$m</span><span class="hl-code"> = </span><span class="hl-identifier">count</span><span class="hl-brackets">(</span><span class="hl-var">$missing_values</span><span class="hl-brackets">)</span><span class="hl-code">;
            </span><span class="hl-reserved">foreach</span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-var">$missing_values</span><span class="hl-code"> </span><span class="hl-reserved">as</span><span class="hl-code"> </span><span class="hl-var">$key</span><span class="hl-code"> =&gt; </span><span class="hl-var">$val</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code"> </span><span class="hl-brackets">{</span><span class="hl-code">
                </span><span class="hl-var">$idx</span><span class="hl-code"> = </span><span class="hl-identifier">array_search</span><span class="hl-brackets">(</span><span class="hl-var">$val</span><span class="hl-code">,</span><span class="hl-var">$unionx</span><span class="hl-brackets">)</span><span class="hl-code">;
 
                </span><span class="hl-comment">//</span><span class="hl-comment"> Now split the Y-array at that position and insert</span><span class="hl-comment"></span><span class="hl-code">
                </span><span class="hl-comment">//</span><span class="hl-comment"> a new sentinel value</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">$idx</span><span class="hl-code"> &gt;= </span><span class="hl-number">0</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code"> </span><span class="hl-brackets">{</span><span class="hl-code">
                        </span><span class="hl-var">$aYData</span><span class="hl-brackets">[</span><span class="hl-var">$i</span><span class="hl-brackets">]</span><span class="hl-code"> = </span><span class="hl-identifier">array_merge</span><span class="hl-brackets">(</span><span class="hl-code">
                            </span><span class="hl-identifier">array_slice</span><span class="hl-brackets">(</span><span class="hl-var">$aYData</span><span class="hl-brackets">[</span><span class="hl-var">$i</span><span class="hl-brackets">]</span><span class="hl-code">,</span><span class="hl-number">0</span><span class="hl-code">,</span><span class="hl-var">$idx</span><span class="hl-brackets">)</span><span class="hl-code">,
                            </span><span class="hl-reserved">array</span><span class="hl-brackets">(</span><span class="hl-reserved">NULL</span><span class="hl-brackets">)</span><span class="hl-code">,
                            </span><span class="hl-identifier">array_slice</span><span class="hl-brackets">(</span><span class="hl-var">$aYData</span><span class="hl-brackets">[</span><span class="hl-var">$i</span><span class="hl-brackets">]</span><span class="hl-code">,</span><span class="hl-var">$idx</span><span class="hl-brackets">)</span><span class="hl-brackets">)</span><span class="hl-code">;
                </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"> The next step is to actually calculate an interpolated value</span><span class="hl-comment"></span><span class="hl-code">
            </span><span class="hl-comment">//</span><span class="hl-comment"> for the Y-coordinates we don't have. As a special case any</span><span class="hl-comment"></span><span class="hl-code">
            </span><span class="hl-comment">//</span><span class="hl-comment"> beginning or ending non-defined coordinates are set to 0</span><span class="hl-comment"></span><span class="hl-code">
    
            </span><span class="hl-comment">//</span><span class="hl-comment"> Set all beginning NULL to 0</span><span class="hl-comment"></span><span class="hl-code">
            </span><span class="hl-reserved">for</span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-var">$j</span><span class="hl-code">=</span><span class="hl-number">0</span><span class="hl-code">; </span><span class="hl-var">$j</span><span class="hl-code"> &lt; </span><span class="hl-var">$length</span><span class="hl-code">; ++</span><span class="hl-var">$j</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code"> </span><span class="hl-brackets">{</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">$aYData</span><span class="hl-brackets">[</span><span class="hl-var">$i</span><span class="hl-brackets">]</span><span class="hl-brackets">[</span><span class="hl-var">$j</span><span class="hl-brackets">]</span><span class="hl-code"> !== </span><span class="hl-reserved">NULL</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code">
                        </span><span class="hl-reserved">break</span><span class="hl-code">;
                </span><span class="hl-var">$aYData</span><span class="hl-brackets">[</span><span class="hl-var">$i</span><span class="hl-brackets">]</span><span class="hl-brackets">[</span><span class="hl-var">$j</span><span class="hl-brackets">]</span><span class="hl-code"> = </span><span class="hl-number">0</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"> Set all ending NULL to 0</span><span class="hl-comment"></span><span class="hl-code">
            </span><span class="hl-reserved">for</span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-var">$j</span><span class="hl-code">=</span><span class="hl-var">$length</span><span class="hl-code">-</span><span class="hl-number">1</span><span class="hl-code">; </span><span class="hl-var">$j</span><span class="hl-code"> &gt;= </span><span class="hl-number">0</span><span class="hl-code">; --</span><span class="hl-var">$j</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code"> </span><span class="hl-brackets">{</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">$aYData</span><span class="hl-brackets">[</span><span class="hl-var">$i</span><span class="hl-brackets">]</span><span class="hl-brackets">[</span><span class="hl-var">$j</span><span class="hl-brackets">]</span><span class="hl-code"> !== </span><span class="hl-reserved">NULL</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code">
                        </span><span class="hl-reserved">break</span><span class="hl-code">;
                </span><span class="hl-var">$aYData</span><span class="hl-brackets">[</span><span class="hl-var">$i</span><span class="hl-brackets">]</span><span class="hl-brackets">[</span><span class="hl-var">$j</span><span class="hl-brackets">]</span><span class="hl-code"> = </span><span class="hl-number">0</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"> Calculate the remaingin missing values as a linear</span><span class="hl-comment"></span><span class="hl-code">
            </span><span class="hl-comment">//</span><span class="hl-comment"> interpolation and keeping in mind that there might be</span><span class="hl-comment"></span><span class="hl-code">
            </span><span class="hl-comment">//</span><span class="hl-comment"> multiple missing values in a row.</span><span class="hl-comment"></span><span class="hl-code">
            </span><span class="hl-var">$j</span><span class="hl-code"> = </span><span class="hl-number">0</span><span class="hl-code">;
            </span><span class="hl-reserved">while</span><span class="hl-brackets">(</span><span class="hl-var">$j</span><span class="hl-code"> &lt; </span><span class="hl-var">$length</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code"> </span><span class="hl-brackets">{</span><span class="hl-code">
                </span><span class="hl-reserved">if</span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-var">$aYData</span><span class="hl-brackets">[</span><span class="hl-var">$i</span><span class="hl-brackets">]</span><span class="hl-brackets">[</span><span class="hl-var">$j</span><span class="hl-brackets">]</span><span class="hl-code"> === </span><span class="hl-reserved">NULL</span><span class="hl-code"> </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"> How many unknown values in a row?</span><span class="hl-comment"></span><span class="hl-code">
                        </span><span class="hl-var">$cnt</span><span class="hl-code"> = </span><span class="hl-number">1</span><span class="hl-code">;
                        </span><span class="hl-reserved">while</span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-var">$j</span><span class="hl-code">+</span><span class="hl-var">$cnt</span><span class="hl-code"> &lt; </span><span class="hl-var">$length</span><span class="hl-code"> &amp;&amp; </span><span class="hl-var">$aYData</span><span class="hl-brackets">[</span><span class="hl-var">$i</span><span class="hl-brackets">]</span><span class="hl-brackets">[</span><span class="hl-var">$j</span><span class="hl-code">+</span><span class="hl-var">$cnt</span><span class="hl-brackets">]</span><span class="hl-code">===</span><span class="hl-reserved">NULL</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code"> </span><span class="hl-brackets">{</span><span class="hl-code">
                            ++</span><span class="hl-var">$cnt</span><span class="hl-code">;
                        </span><span class="hl-brackets">}</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">$cnt</span><span class="hl-code"> == </span><span class="hl-number">1</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code"> </span><span class="hl-brackets">{</span><span class="hl-code">
                            </span><span class="hl-var">$aYData</span><span class="hl-brackets">[</span><span class="hl-var">$i</span><span class="hl-brackets">]</span><span class="hl-brackets">[</span><span class="hl-var">$j</span><span class="hl-brackets">]</span><span class="hl-code"> = </span><span class="hl-brackets">(</span><span class="hl-var">$aYData</span><span class="hl-brackets">[</span><span class="hl-var">$i</span><span class="hl-brackets">]</span><span class="hl-brackets">[</span><span class="hl-var">$j</span><span class="hl-code">-</span><span class="hl-number">1</span><span class="hl-brackets">]</span><span class="hl-code">+</span><span class="hl-var">$aYData</span><span class="hl-brackets">[</span><span class="hl-var">$i</span><span class="hl-brackets">]</span><span class="hl-brackets">[</span><span class="hl-var">$j</span><span class="hl-code">+</span><span class="hl-number">1</span><span class="hl-brackets">]</span><span class="hl-brackets">)</span><span class="hl-code">/</span><span class="hl-number">2</span><span class="hl-code">;
                        </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-brackets">{</span><span class="hl-code">
                            </span><span class="hl-var">$step</span><span class="hl-code"> = </span><span class="hl-brackets">(</span><span class="hl-var">$aYData</span><span class="hl-brackets">[</span><span class="hl-var">$i</span><span class="hl-brackets">]</span><span class="hl-brackets">[</span><span class="hl-var">$j</span><span class="hl-code">+</span><span class="hl-var">$cnt</span><span class="hl-brackets">]</span><span class="hl-code"> - </span><span class="hl-var">$aYData</span><span class="hl-brackets">[</span><span class="hl-var">$i</span><span class="hl-brackets">]</span><span class="hl-brackets">[</span><span class="hl-var">$j</span><span class="hl-code">-</span><span class="hl-number">1</span><span class="hl-brackets">]</span><span class="hl-brackets">)</span><span class="hl-code">/</span><span class="hl-brackets">(</span><span class="hl-var">$cnt</span><span class="hl-code">+</span><span class="hl-number">1</span><span class="hl-brackets">)</span><span class="hl-code">;
                            </span><span class="hl-reserved">for</span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-var">$k</span><span class="hl-code">=</span><span class="hl-number">1</span><span class="hl-code">; </span><span class="hl-var">$k</span><span class="hl-code"> &lt;= </span><span class="hl-var">$cnt</span><span class="hl-code">; ++</span><span class="hl-var">$k</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code"> </span><span class="hl-brackets">{</span><span class="hl-code">
                                    </span><span class="hl-var">$aYData</span><span class="hl-brackets">[</span><span class="hl-var">$i</span><span class="hl-brackets">]</span><span class="hl-brackets">[</span><span class="hl-var">$j</span><span class="hl-code">+</span><span class="hl-var">$k</span><span class="hl-code">-</span><span class="hl-number">1</span><span class="hl-brackets">]</span><span class="hl-code"> = </span><span class="hl-var">$step</span><span class="hl-code">*</span><span class="hl-var">$k</span><span class="hl-code">+</span><span class="hl-var">$aYData</span><span class="hl-brackets">[</span><span class="hl-var">$i</span><span class="hl-brackets">]</span><span class="hl-brackets">[</span><span class="hl-var">$j</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-brackets">}</span><span class="hl-code">
                        </span><span class="hl-brackets">}</span><span class="hl-code">
                </span><span class="hl-brackets">}</span><span class="hl-code">
                ++</span><span class="hl-var">$j</span><span class="hl-code">;
            </span><span class="hl-brackets">}</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-var">$unionx</span><span class="hl-code">,</span><span class="hl-var">$aYData</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">------------------------------------------------------------------------</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-comment">//</span><span class="hl-comment"> Helper function to create the union of two arrays</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-comment">//</span><span class="hl-comment">------------------------------------------------------------------------</span><span class="hl-comment"></span><span class="hl-code">
 
</span><span class="hl-comment">//</span><span class="hl-comment"> Create the sorted union of all numeric arrays given as argument</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-reserved">function</span><span class="hl-code"> </span><span class="hl-identifier">array_union</span><span class="hl-brackets">(</span><span class="hl-var">$a</span><span class="hl-brackets">)</span><span class="hl-code"> </span><span class="hl-brackets">{</span><span class="hl-code">
 
    </span><span class="hl-var">$n</span><span class="hl-code"> = </span><span class="hl-identifier">count</span><span class="hl-brackets">(</span><span class="hl-var">$a</span><span class="hl-brackets">)</span><span class="hl-code">;
    </span><span class="hl-var">$res</span><span class="hl-code"> = </span><span class="hl-var">$a</span><span class="hl-brackets">[</span><span class="hl-number">0</span><span class="hl-brackets">]</span><span class="hl-code">;
    </span><span class="hl-reserved">for</span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-var">$i</span><span class="hl-code">=</span><span class="hl-number">1</span><span class="hl-code">; </span><span class="hl-var">$i</span><span class="hl-code"> &lt; </span><span class="hl-var">$n</span><span class="hl-code">; ++</span><span class="hl-var">$i</span><span class="hl-brackets">)</span><span class="hl-code"> </span><span class="hl-brackets">{</span><span class="hl-code">
            </span><span class="hl-var">$res</span><span class="hl-code"> = </span><span class="hl-identifier">_array2_union</span><span class="hl-brackets">(</span><span class="hl-var">$res</span><span class="hl-code">,</span><span class="hl-var">$a</span><span class="hl-brackets">[</span><span class="hl-var">$i</span><span class="hl-brackets">]</span><span class="hl-brackets">)</span><span class="hl-code">;
    </span><span class="hl-brackets">}</span><span class="hl-code">
    </span><span class="hl-identifier">sort</span><span class="hl-brackets">(</span><span class="hl-var">$res</span><span class="hl-brackets">)</span><span class="hl-code">;
    </span><span class="hl-reserved">return</span><span class="hl-code"> </span><span class="hl-var">$res</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 the union between two numeric arrays</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-reserved">function</span><span class="hl-code"> </span><span class="hl-identifier">_array2_union</span><span class="hl-brackets">(</span><span class="hl-var">$a</span><span class="hl-code">,</span><span class="hl-var">$b</span><span class="hl-brackets">)</span><span class="hl-code"> </span><span class="hl-brackets">{</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">$a</span><span class="hl-code"> == </span><span class="hl-reserved">NULL</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code"> </span><span class="hl-reserved">return</span><span class="hl-code"> </span><span class="hl-var">$b</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">$b</span><span class="hl-code"> == </span><span class="hl-reserved">NULL</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code"> </span><span class="hl-reserved">return</span><span class="hl-code"> </span><span class="hl-var">$a</span><span class="hl-code">;
 
    </span><span class="hl-comment">//</span><span class="hl-comment"> A standard &quot;trick&quot; to calculate the union of two arrays</span><span class="hl-comment"></span><span class="hl-code">
    </span><span class="hl-reserved">return</span><span class="hl-code"> </span><span class="hl-identifier">array_merge</span><span class="hl-brackets">(</span><span class="hl-code">
            </span><span class="hl-identifier">array_intersect</span><span class="hl-brackets">(</span><span class="hl-var">$a</span><span class="hl-code">,</span><span class="hl-var">$b</span><span class="hl-brackets">)</span><span class="hl-code">,
            </span><span class="hl-identifier">array_diff</span><span class="hl-brackets">(</span><span class="hl-var">$a</span><span class="hl-code">, </span><span class="hl-var">$b</span><span class="hl-brackets">)</span><span class="hl-code">,
            </span><span class="hl-identifier">array_diff</span><span class="hl-brackets">(</span><span class="hl-var">$b</span><span class="hl-code">, </span><span class="hl-var">$a</span><span class="hl-brackets">)</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-brackets">}</span><span class="hl-code">
</span><span class="hl-inlinetags">?&gt;</span></pre></td></tr></table></div><p>
                    </p>
                </div>
            </div>
            <div class="sect2" title="Constructing smooth line plots with Cubic Splines"><div class="titlepage"><div><div><h3 class="title"><a name="sec2.creating-cubic-splines"></a>Constructing smooth line plots with Cubic Splines</h3></div></div></div>
                
                <p>The library support interpolation between data point by the use of cubic
                    splines. This will make the implicit assumption that the underlying phenomenon
                    that is plotted can be represented by a 3:rd degree polynomial between the given
                    data points (also known as a control points).</p>
                <p>Cubic splines have the property that the constructed line will pass through
                    all control points given.</p>
                <p>To construct a spline you both the X and Y coordinates for the known data
                    points are needed since the library can make no assumption on the step size
                    between the data points.</p>
                <p>The cubic spline functionality in the library is encapsulated in the
                        <code class="code">class Spline</code> which is define the module
                        "<code class="filename">jpgraph_regstat.inc.php</code>" which must be added to the
                    included files in the script.</p>
                <p>The first step is to construct new Spline instance. This class is instantiated
                    by calling the constructor with the two known data arrays (X and Y) as
                    follows.</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">$spline = new Spline( $xdata , $ydata );</span></pre></td></tr></table></div><p>
                </p>
                <p>This call initializes the spline with the data points given. These data points
                    are also known as Control points for the spline. This helper class doesn't draw
                    any line itself. Instead it is merely used to get a new (larger) data array
                    which have all the interpolated values. These new value are then used to make
                    the actual line plot. This way gives great flexibility in how to use the
                    interpolated data points.</p>
                <p>To get the y- and x-axis data to be plotted we call the method
                        <code class="code">Spline::Get()</code> to get an interpolated array containing a
                    specified number of points. So for example the line</p>
                <p>
                    </p><div class="hl-main"><table class="hl-table" width="100%"><tr><td class="hl-gutter" align="right" valign="top"><pre>1
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-code">list($sdatax , $sdatay) = $spline-&gt;Get( 50 );</span></pre></td></tr></table></div><p>
                </p>
                <p>will construct the two new data arrays '<code class="code">$sdatax</code>' and
                        '<code class="code">$sdatay</code>' which contains 50 data points. These two arrays are
                    constructed from the control points we specified when we created the
                        '<code class="code">$spline</code>' object. These data arrays are then used to make the
                    actual plot just as for a "standard" plot. In <a class="xref" href="ch15.html#fig.splineex1" title="Figure 15.32. Constructing a smooth spline curve from 8 control points (splineex1.php)">Figure 15.32. Constructing a smooth spline curve from 8 control points <code class="uri"><a class="uri" href="example_src/splineex1.html" target="_top">(<code class="filename">splineex1.php</code>)</a></code> </a> we have used 8 control points to construct a spline.</p>
                <p>
                    </p><div class="figure"><a name="fig.splineex1"></a><p class="title"><b>Figure 15.32. Constructing a smooth spline curve from 8 control points <code class="uri"><a class="uri" href="example_src/splineex1.html" target="_top">(<code class="filename">splineex1.php</code>)</a></code> </b></p><div class="figure-contents">  <span class="inlinemediaobject"><img src="images/splineex1.png" alt="Constructing a smooth spline curve from 8 control points (splineex1.php)"></span> </div></div><p><br class="figure-break">
                </p>
                <p>In order to make the example more interesting we actually used two plots.
                    First a line plot to get the smooth curve and then a standard scatter plot
                    (discussed later in this manual) which is used to illustrate where the control
                    points are situated.</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 also support the construction of <span class="italic">Bezier curves</span> which is built on a similar concept of
                            constructing a smooth line from a number of control points, The biggest
                            difference between cubic splines and Bezier curves is that while a cubic
                            spline is always guaranteed to pass through all control point a Bezier
                            curve will in general not pass through any control points. Instead the
                            Bezier control point are outside the curve and affects the curvature of
                            the curve. Bezier type curves are not in general used together with data
                            visualization but are instead used to create specific curves, usually
                            for CAD and 3D graphic purposes. In the discussion of Canvas graphs, see
                                <a class="xref" href="ch17s03.html" title="Canvas graphs">Canvas graphs</a>, we discuss this
                            further.</p>
                    </div><p>
                </p>
            </div>
        </div>
        
        
        
        
        
        
        
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