ch15s06.html
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<html><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><title>Contour graphs</title><link rel="stylesheet" type="text/css" href="manual.css"><meta name="generator" content="DocBook XSL Stylesheets V1.76.0"><link rel="home" href="index.html" title="JpGraph Manual"><link rel="up" href="ch15.html" title="Chapter 15. Different types of linear (cartesian) graph types"></head><body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Contour graphs </th></tr><tr><td width="20%" align="left"> </td><th width="60%" align="center">Chapter 15. Different types of linear (cartesian) graph types</th><td width="20%" align="right"> </td></tr></table><hr></div><div class="sect1" title="Contour graphs"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a name="sec.contour-graphs"></a>Contour graphs </h2></div></div></div>
<p>In order to create Radar graphs the module
"<code class="filename">jpgraph_contour.php</code>" must first be included.</p>
<p>
</p><div class="note" title="Note" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Note</h3>
<p> The Pro-version (>= v3.1) also includes a module
"<code class="filename">jpgraph_contourf.php</code>" which is also supports
filled contour plots as well as labelling in the plots of the isobar lines.
The pro-version also uses a more advanced adaptive-mesh algorithm that give
better resolution without manual interpolation of the original data. Both
triangular and rectangular interpolation meshes are supported. The filled
contour is described in <a class="xref" href="ch23.html" title="Chapter 23. Filled contour graphs">Chapter 23. <i>Filled contour graphs</i></a>
</p>
</div><p>
</p>
<p>Contour plots are used to plot the isobar lines (height curves) of a three
dimensional (3D) graph. The contour plot itself is only a two-dimensional plot and
looks like an ordinary topographic map. An example of a contour graph is shown in
<a class="xref" href="ch15s06.html#fig.basic_contourex01" title="Figure 15.75. A basic contour graph (basic_contourex01.php)">Figure 15.75. A basic contour graph <code class="uri"><a class="uri" href="example_src/basic_contourex01.html" target="_top">(<code class="filename">basic_contourex01.php</code>)</a></code> </a></p>
<p>
</p><div class="figure"><a name="fig.basic_contourex01"></a><p class="title"><b>Figure 15.75. A basic contour graph <code class="uri"><a class="uri" href="example_src/basic_contourex01.html" target="_top">(<code class="filename">basic_contourex01.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/basic_contourex01.png" alt="A basic contour graph (basic_contourex01.php)"></span> </div></div><p><br class="figure-break">
</p>
<p>A contour graph is both similar and different from other types x-y graphs.</p>
<p>
</p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
<p>A contour graph uses the standard x-y <code class="code">class Graph</code> as
basic graph canvas</p>
</li><li class="listitem">
<p>A contour graph has all the standard graph formatting options</p>
</li><li class="listitem">
<p>The legend is automatically generated</p>
</li><li class="listitem">
<p>The input data is a matrix and not an array</p>
</li></ul></div><p>
</p>
<p>There are primarily four main parameters that can be used to control the apparency
of the contour plots</p>
<p>
</p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem">
<p><span class="bold"><strong>the number of isobar lines</strong></span>, by
default 10 isobar lines are used</p>
</li><li class="listitem">
<p><span class="bold"><strong>the level of data grid interpolating,</strong></span>
i.e. to give the appearance of smoother isobar lines it is possible to
tell the library to create a number of intermediate points between the
given points in the input data matrix. It is important to note that this
does not create any further real information it only creates smoother
lines under the assumption that it is valid to assume linear
interpolation between the original data points. </p>
<p>The level of interpolation is specified as an integer in the practical
range 1 to 5. A level of 1 corresponds to just keeping the original
data, a level of 2 corresponds to subdividing the original data points
in two, i.e. one extra interpolated points is created in both x- and
y-direction and so on. A level of 3 corresponds to further sub-divding
the level 2 matrix one more time. </p>
<p>Even though it is theoretically possible to use an arbitrary
interpolation factor the library does not allow an interpolation factor
larger than 5. The reason is purely computational since the total number
of data points increases very quickly.</p>
<p>For example if the original grid has size 10x10 (=100 data points)
interpolating this grid with a factor of 5 will generate a new matrix of
size 145x145 (=21025 data points).</p>
</li><li class="listitem">
<p><span class="bold"><strong>flip around the Y-axis</strong></span>. By default
the first row in the input matrix corresponds to y=0, however this also
means that the plotted contour will be flipped compared with the input
matrix since y=0 is at the bottom of the graph. If for visual appearance
reason one wants the input data matrix to have the same orientation as
the resulting graph it is possible to have the library interpret the
last row in the input data matrix as y=0 instead</p>
</li><li class="listitem">
<p><span class="bold"><strong>the color of the isobar lines</strong></span>. By
default they will be assigned from the natural color spectra with pure
dark blue corresponding to the lowest point in the plot and pure red
corresponding to the highest isobar.</p>
</li></ol></div><p>
</p>
<p>The remaining possibilities to adjust the appearance of the contour plot
corresponds to the standard ways of changing the layout of the graph, for example
adding titles, adjusting colors and changing the type of axis to be
displayed.</p>
<p>The scale of the contour plot is by default the natural scale, i.e. the points are
assumed to be numbered (0..n) where n is the number of points in the corresponding
direction and also corresponds to each entry in the input data matrix.</p>
<div class="sect2" title="Input data for contour graphs"><div class="titlepage"><div><div><h3 class="title"><a name="id2562600"></a>Input data for contour graphs</h3></div></div></div>
<p>The input data to a contour graph is a matrix. The value at each entry in the
matrix represents the heights at the specified (row,col) in the matrix. In all
of our example we will use the following data matrix</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"><?php</span><span class="hl-code">
</span><span class="hl-var">$data</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-code"> </span><span class="hl-brackets">(</span><span class="hl-number">0</span><span class="hl-number">.5</span><span class="hl-code">,</span><span class="hl-number">1</span><span class="hl-number">.1</span><span class="hl-code">,</span><span class="hl-number">1</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">2</span><span class="hl-number">.0</span><span class="hl-code">,</span><span class="hl-number">3</span><span class="hl-code">,</span><span class="hl-number">3</span><span class="hl-code">,</span><span class="hl-number">2</span><span class="hl-code">,</span><span class="hl-number">1</span><span class="hl-code">,</span><span class="hl-number">0</span><span class="hl-number">.1</span><span class="hl-brackets">)</span><span class="hl-code">,
</span><span class="hl-reserved">array</span><span class="hl-code"> </span><span class="hl-brackets">(</span><span class="hl-number">1</span><span class="hl-number">.0</span><span class="hl-code">,</span><span class="hl-number">1</span><span class="hl-number">.5</span><span class="hl-code">,</span><span class="hl-number">3</span><span class="hl-number">.0</span><span class="hl-code">,</span><span class="hl-number">5</span><span class="hl-code">,</span><span class="hl-number">6</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">1</span><span class="hl-code">,</span><span class="hl-number">1</span><span class="hl-number">.2</span><span class="hl-code">,</span><span class="hl-number">1</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-reserved">array</span><span class="hl-code"> </span><span class="hl-brackets">(</span><span class="hl-number">0</span><span class="hl-number">.9</span><span class="hl-code">,</span><span class="hl-number">2</span><span class="hl-number">.0</span><span class="hl-code">,</span><span class="hl-number">2</span><span class="hl-number">.1</span><span class="hl-code">,</span><span class="hl-number">3</span><span class="hl-code">,</span><span class="hl-number">6</span><span class="hl-number">.0</span><span class="hl-code">,</span><span class="hl-number">7</span><span class="hl-code">,</span><span class="hl-number">3</span><span class="hl-code">,</span><span class="hl-number">2</span><span class="hl-code">,</span><span class="hl-number">1</span><span class="hl-code">,</span><span class="hl-number">1</span><span class="hl-number">.4</span><span class="hl-brackets">)</span><span class="hl-code">,
</span><span class="hl-reserved">array</span><span class="hl-code"> </span><span class="hl-brackets">(</span><span class="hl-number">1</span><span class="hl-number">.0</span><span class="hl-code">,</span><span class="hl-number">1</span><span class="hl-number">.5</span><span class="hl-code">,</span><span class="hl-number">3</span><span class="hl-number">.0</span><span class="hl-code">,</span><span class="hl-number">4</span><span class="hl-code">,</span><span class="hl-number">6</span><span class="hl-number">.0</span><span class="hl-code">,</span><span class="hl-number">5</span><span class="hl-code">,</span><span class="hl-number">2</span><span class="hl-code">,</span><span class="hl-number">1</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">2</span><span class="hl-brackets">)</span><span class="hl-code">,
</span><span class="hl-reserved">array</span><span class="hl-code"> </span><span class="hl-brackets">(</span><span class="hl-number">0</span><span class="hl-number">.8</span><span class="hl-code">,</span><span class="hl-number">2</span><span class="hl-number">.0</span><span class="hl-code">,</span><span class="hl-number">3</span><span class="hl-number">.0</span><span class="hl-code">,</span><span class="hl-number">3</span><span class="hl-code">,</span><span class="hl-number">4</span><span class="hl-number">.0</span><span class="hl-code">,</span><span class="hl-number">4</span><span class="hl-code">,</span><span class="hl-number">3</span><span class="hl-code">,</span><span class="hl-number">2</span><span class="hl-number">.4</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-brackets">)</span><span class="hl-code">,
</span><span class="hl-reserved">array</span><span class="hl-code"> </span><span class="hl-brackets">(</span><span class="hl-number">0</span><span class="hl-number">.6</span><span class="hl-code">,</span><span class="hl-number">1</span><span class="hl-number">.1</span><span class="hl-code">,</span><span class="hl-number">1</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">4</span><span class="hl-number">.0</span><span class="hl-code">,</span><span class="hl-number">3</span><span class="hl-number">.5</span><span class="hl-code">,</span><span class="hl-number">3</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">4</span><span class="hl-brackets">)</span><span class="hl-code">,
</span><span class="hl-reserved">array</span><span class="hl-code"> </span><span class="hl-brackets">(</span><span class="hl-number">1</span><span class="hl-number">.0</span><span class="hl-code">,</span><span class="hl-number">1</span><span class="hl-number">.5</span><span class="hl-code">,</span><span class="hl-number">3</span><span class="hl-number">.0</span><span class="hl-code">,</span><span class="hl-number">5</span><span class="hl-code">,</span><span class="hl-number">6</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">1</span><span class="hl-code">,</span><span class="hl-number">1</span><span class="hl-number">.2</span><span class="hl-code">,</span><span class="hl-number">2</span><span class="hl-number">.7</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-reserved">array</span><span class="hl-code"> </span><span class="hl-brackets">(</span><span class="hl-number">0</span><span class="hl-number">.8</span><span class="hl-code">,</span><span class="hl-number">2</span><span class="hl-number">.0</span><span class="hl-code">,</span><span class="hl-number">3</span><span class="hl-number">.0</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-number">.5</span><span class="hl-code">,</span><span class="hl-number">6</span><span class="hl-code">,</span><span class="hl-number">3</span><span class="hl-code">,</span><span class="hl-number">2</span><span class="hl-code">,</span><span class="hl-number">1</span><span class="hl-code">,</span><span class="hl-number">1</span><span class="hl-number">.4</span><span class="hl-brackets">)</span><span class="hl-code">,
</span><span class="hl-reserved">array</span><span class="hl-code"> </span><span class="hl-brackets">(</span><span class="hl-number">1</span><span class="hl-number">.0</span><span class="hl-code">,</span><span class="hl-number">1</span><span class="hl-number">.5</span><span class="hl-code">,</span><span class="hl-number">3</span><span class="hl-number">.0</span><span class="hl-code">,</span><span class="hl-number">4</span><span class="hl-code">,</span><span class="hl-number">6</span><span class="hl-number">.0</span><span class="hl-code">,</span><span class="hl-number">5</span><span class="hl-code">,</span><span class="hl-number">2</span><span class="hl-code">,</span><span class="hl-number">1</span><span class="hl-code">,</span><span class="hl-number">0</span><span class="hl-number">.5</span><span class="hl-code">,</span><span class="hl-number">0</span><span class="hl-number">.2</span><span class="hl-brackets">)</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-inlinetags">?></span></pre></td></tr></table></div><p>
</p>
<p>By default the entry (0,0), i.e. row=0, col=0 will be positioned at graph
position (0,0), i.e. the lower left corner. Since this will represent an
inverted image compare to the data matrix. In order to have the graph oriented
in the same way as the data matrix, i.e. entry (0,0) positioned in the top left
corner the method</p>
<p>
</p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
<p><code class="code">ContourPlot::SetInvert($aFlg=true)</code></p>
</li></ul></div><p>
</p>
<p>In order to get a smooth contour plot it is necessary to have adequate number
of data points. What consists "adequate" number depends on the overall graph
size. The larger graph the more points are needed. To help crate smooth contour
plot the library offers automatic linear interpolation to specified depth. It is
important to note that this does not increase the accuracy. It merely creates
artificial point to draw smoother curves. This technique is described in detail
in <a class="xref" href="ch15s06.html#sec.grid-interpolating" title="Understanding mesh interpolation">Understanding mesh interpolation</a></p>
<div class="tip" title="Tip" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Tip</h3>
<p>If the data for the matrix is available in a file a convinient way to get
hold of the dat in the file is to use the utility <code class="code">class
ReadFileData</code> to get hold of the data using the method<code class="code">
ReadFileData::FromMatrix($aFile,$aSeparator=' ')</code> which read the
matrix from a file. Each row of the matrix must be a separate line and each
cell is separated with the character specified as the second argument. By
default a space is used as separator. All values read back are converted to
floating point numbers (double precision). The following short example shows
how easy this is to use</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">$data = ReadFileData::FromMatrix('matrixdata.txt');</span></pre></td></tr></table></div><p>
</p>
</div>
</div>
<div class="sect2" title="Creating a contour graph"><div class="titlepage"><div><div><h3 class="title"><a name="sec.creating-contour-graph"></a>Creating a contour graph</h3></div></div></div>
<p><a class="xref" href="ch15s06.html#fig.basic_contourex01" title="Figure 15.75. A basic contour graph (basic_contourex01.php)">Figure 15.75. A basic contour graph <code class="uri"><a class="uri" href="example_src/basic_contourex01.html" target="_top">(<code class="filename">basic_contourex01.php</code>)</a></code> </a> shows the most basic contour plot.
This is crated by first instantiating a graph and then creating an instance of
<code class="code">class ContourPlot</code> which is added to the graph. </p>
<p>The constructor for <code class="code">class ContourPlot</code> has the following
signature</p>
<p>
</p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
<p><code class="code">ContourPlot::__construct($aDataMatrix, $aIsobar=10,
$aFactor=1, $aInvert=false,
$aIsobarColors=array())</code></p>
<p><code class="code">$aDataMatrix</code>, The input data</p>
<p><code class="code">$aIsobar</code>, The number of isobars if the argument is an
integer or an array specifying the exact locations of each isobar if
the argument is an array</p>
<p><code class="code">$aFactor</code>, Grid interpolation factor</p>
<p><code class="code">$aInvert</code>, Invert the data matrix so the matrix entry
(0,0) corresponds to the top left corner</p>
<p><code class="code">$aIsobarColors</code>, Optional specification of isobar
colors </p>
</li></ul></div><p>
</p>
<p>This means that the common structure to create a basic contour plot will
be</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"><?php</span><span class="hl-code">
</span><span class="hl-var">$data</span><span class="hl-code"> = </span><span class="hl-reserved">array</span><span class="hl-code"> </span><span class="hl-brackets">(</span><span class="hl-code"> </span><span class="hl-reserved">array</span><span class="hl-code"> </span><span class="hl-brackets">(</span><span class="hl-code"> ... </span><span class="hl-brackets">)</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-comment">//</span><span class="hl-comment"> Basic contour graph</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$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-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">$graph</span><span class="hl-code">-></span><span class="hl-identifier">SetScale</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">intint</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-comment">//</span><span class="hl-comment"> Adjust the margins to fit the margin</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$graph</span><span class="hl-code">-></span><span class="hl-identifier">SetMargin</span><span class="hl-brackets">(</span><span class="hl-number">30</span><span class="hl-code">,</span><span class="hl-number">100</span><span class="hl-code">,</span><span class="hl-number">40</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-comment">//</span><span class="hl-comment"> Setup</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$graph</span><span class="hl-code">-></span><span class="hl-identifier">title</span><span class="hl-code">-></span><span class="hl-identifier">Set</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">Basic contour plot</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$graph</span><span class="hl-code">-></span><span class="hl-identifier">title</span><span class="hl-code">-></span><span class="hl-identifier">SetFont</span><span class="hl-brackets">(</span><span class="hl-identifier">FF_ARIAL</span><span class="hl-code">,</span><span class="hl-identifier">FS_BOLD</span><span class="hl-code">,</span><span class="hl-number">12</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-comment">//</span><span class="hl-comment"> A simple contour plot with default arguments (e.g. 10 isobar lines)</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$cp</span><span class="hl-code"> = </span><span class="hl-reserved">new</span><span class="hl-code"> </span><span class="hl-identifier">ContourPlot</span><span class="hl-brackets">(</span><span class="hl-var">$data</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-comment">//</span><span class="hl-comment"> Display the legend</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$cp</span><span class="hl-code">-></span><span class="hl-identifier">ShowLegend</span><span class="hl-brackets">(</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$graph</span><span class="hl-code">-></span><span class="hl-identifier">Add</span><span class="hl-brackets">(</span><span class="hl-var">$cp</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-inlinetags">?></span></pre></td></tr></table></div><p>
</p>
<p>Since the most common format for contour graphs is to show axis on all sides
we should add the line</p>
<p>
</p><div class="hl-main"><table class="hl-table" width="100%"><tr><td class="hl-gutter" align="right" valign="top"><pre>1
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-code">$graph->SetAxisStyle(AXSTYLE_BOXOUT);</span></pre></td></tr></table></div><p>
</p>
<p>to our previous example so we get the effect shown in <a class="xref" href="ch15s06.html#fig.basic_contourex02" title="Figure 15.76. Adding axis on all sides (basic_contourex02.php)">Figure 15.76. Adding axis on all sides <code class="uri"><a class="uri" href="example_src/basic_contourex02.html" target="_top">(<code class="filename">basic_contourex02.php</code>)</a></code> </a>. To show the effect of flipping the
data around the center line we have to add the following 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">$cp->SetInvert();</span></pre></td></tr></table></div><p>
</p>
<p>and get the result of adding this line is shown in <a class="xref" href="ch15s06.html#fig.basic_contourex05" title="Figure 15.77. Flipping the data around the center line (basic_contourex05.php)">Figure 15.77. Flipping the data around the center line <code class="uri"><a class="uri" href="example_src/basic_contourex05.html" target="_top">(<code class="filename">basic_contourex05.php</code>)</a></code> </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.basic_contourex02"></a><p class="title"><b>Figure 15.76. Adding axis on all sides <code class="uri"><a class="uri" href="example_src/basic_contourex02.html" target="_top">(<code class="filename">basic_contourex02.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/basic_contourex02.png" alt="Adding axis on all sides (basic_contourex02.php)"></span> </div></div><br class="figure-break">
</td><td>
<div class="figure"><a name="fig.basic_contourex05"></a><p class="title"><b>Figure 15.77. Flipping the data around the center line <code class="uri"><a class="uri" href="example_src/basic_contourex05.html" target="_top">(<code class="filename">basic_contourex05.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/basic_contourex05.png" alt="Flipping the data around the center line (basic_contourex05.php)"></span> </div></div><br class="figure-break">
</td></tr></tbody></table>
</div><p>
</p>
</div>
<div class="sect2" title="Adjusting the color and number of isobar lines"><div class="titlepage"><div><div><h3 class="title"><a name="id2562850"></a>Adjusting the color and number of isobar lines</h3></div></div></div>
<p>As mentioned above the library uses 10 isobar lines by default. The number of
isobar lines can be adjusted by specifying a second integer argument to the
constructor of the contour plot. For example to use only 5 isobar lines the
construction of the contour plot would be changed 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">$contourplot = new ContourPlot($data,5);</span></pre></td></tr></table></div><p>
</p>
<p>The result of changing this in the previous example is shown in <a class="xref" href="ch15s06.html#fig.basic_contourex04" title="Figure 15.78. Using only 5 isobar lines (basic_contourex04.php)">Figure 15.78. Using only 5 isobar lines <code class="uri"><a class="uri" href="example_src/basic_contourex04.html" target="_top">(<code class="filename">basic_contourex04.php</code>)</a></code> </a></p>
<p>
</p><div class="figure"><a name="fig.basic_contourex04"></a><p class="title"><b>Figure 15.78. Using only 5 isobar lines <code class="uri"><a class="uri" href="example_src/basic_contourex04.html" target="_top">(<code class="filename">basic_contourex04.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/basic_contourex04.png" alt="Using only 5 isobar lines (basic_contourex04.php)"></span> </div></div><p><br class="figure-break">
</p>
<p>The values for the isobars are determined by finding the lowest and highest
point in the input data matrix and then spreading the isobars evenly between
these extreme points. </p>
<p>In some applications however it is necessary to have better control over where
exactly the isobars are placed and for this reason it is possible to tell the
library exactly at what values the isobars should be. </p>
<p>This is done by providing an array with the values of the isobars instead of a
single number in the creation of the contour plot as the following example
shows</p>
<p>
</p><div class="hl-main"><table class="hl-table" width="100%"><tr><td class="hl-gutter" align="right" valign="top"><pre>1
2
3
4
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-inlinetags"><?php</span><span class="hl-code">
</span><span class="hl-var">$isoBars</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">0</span><span class="hl-number">.1</span><span class="hl-code">, </span><span class="hl-number">0</span><span class="hl-number">.2</span><span class="hl-code">, </span><span class="hl-number">0</span><span class="hl-number">.3</span><span class="hl-code">, </span><span class="hl-number">0</span><span class="hl-number">.4</span><span class="hl-code">, </span><span class="hl-number">0</span><span class="hl-number">.5</span><span class="hl-code">, </span><span class="hl-number">0</span><span class="hl-number">.6</span><span class="hl-code"> </span><span class="hl-brackets">)</span><span class="hl-code">
</span><span class="hl-var">$cp</span><span class="hl-code"> = </span><span class="hl-reserved">new</span><span class="hl-code"> </span><span class="hl-identifier">ContourPlot</span><span class="hl-brackets">(</span><span class="hl-var">$data</span><span class="hl-code">, </span><span class="hl-var">$isoBars</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-inlinetags">?></span></pre></td></tr></table></div><p>
</p>
<p>The isobar colors can be adjusted by specifying a color array that specifies
the color for each isobar.</p>
<p>However, there is some simpler changes that ca be made to change the colors
without having to go through the "trouble" of såspecifying a color array. </p>
<p>There are usually two reasons for changing the default color spectra. </p>
<p>
</p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem">
<p>to use more high contrast colors</p>
</li><li class="listitem">
<p>to use only black and white colors</p>
</li></ol></div><p>
</p>
<p>This can be accomplished with a call to the method </p>
<p>
</p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
<p><code class="code">ContourPlot::UseHighContrastColor($aFlg=true,$aBW=false)
</code></p>
</li></ul></div><p>
</p>
<p>as the following example shows</p>
<p>
</p><div class="hl-main"><table class="hl-table" width="100%"><tr><td class="hl-gutter" align="right" valign="top"><pre>1
2
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-code">$cp = new ContourPlot( $data );
$cp->UseHighContrastColor( true );</span></pre></td></tr></table></div><p>
</p>
<p>The above example will only use a blue to red color scale and avoid the
"low-contrast" greenish middle color spectrum colors.</p>
<p>By also setting the second argument to the high contrast method to true the
colors are restricted to only black and white. This will of course make it
impossible to exactly know the value each isobar represents but could be useful
for gaining some insight in the topography of a graph and would allow better
printing on black and white devices.</p>
<p>Specifying manual colors of the isobar can be done in two ways. </p>
<p>
</p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem">
<p>By specifying the color array as the fifth argument to the
constructor of ContourPlot as shown in <a class="xref" href="ch15s06.html#sec.creating-contour-graph" title="Creating a contour graph">Creating a contour graph</a></p>
</li><li class="listitem">
<p>By using the method
<code class="code">ContourPlot::SetIsobarColors($aColors)</code></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>The number of colors specified must match the number of
isobars.</p>
</div><p>
</p>
</div>
<div class="sect2" title="Understanding mesh interpolation"><div class="titlepage"><div><div><h3 class="title"><a name="sec.grid-interpolating"></a>Understanding mesh interpolation</h3></div></div></div>
<p>As mentioned above it is possible to use mesh interpolation to generate
smoother contour graphs. In order to better understand the effect of specifying
different interpolation factors we will show how what effect this have.</p>
<p>The data we will be using is given by the following data matrix</p>
<p>
</p><div class="hl-main"><table class="hl-table" width="100%"><tr><td class="hl-gutter" align="right" valign="top"><pre>1
2
3
4
5
6
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-code">$data = array(
array ( 12,7,3,15 ),
array ( 18,5,1, 9 ),
array ( 13,9,5,12),
array ( 5,3,8, 9 ),
array ( 1,8,5, 7 ));</span></pre></td></tr></table></div><p>
</p>
<p>A basic contour graph using the above data is shown in <a class="xref" href="ch15s06.html#fig.basic_contourex03-1" title="Figure 15.79. Interpolation factor=1 (basic_contourex03-1.php)">Figure 15.79. Interpolation factor=1 <code class="uri"><a class="uri" href="example_src/basic_contourex03-1.html" target="_top">(<code class="filename">basic_contourex03-1.php</code>)</a></code> </a></p>
<p>
</p><div class="figure"><a name="fig.basic_contourex03-1"></a><p class="title"><b>Figure 15.79. Interpolation factor=1 <code class="uri"><a class="uri" href="example_src/basic_contourex03-1.html" target="_top">(<code class="filename">basic_contourex03-1.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/basic_contourex03-1.png" alt="Interpolation factor=1 (basic_contourex03-1.php)"></span> </div></div><p><br class="figure-break">
</p>
<p>In order to specify a grid interpolation factor we need to specify this as the
third argument in the constructor for the contour plot. So in order to specify a
interpolation factor of 2 we would add the line</p>
<p>
</p><div class="hl-main"><table class="hl-table" width="100%"><tr><td class="hl-gutter" align="right" valign="top"><pre>1
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-code">$contourplot = new ContourPlot($data,10,3);</span></pre></td></tr></table></div><p>
</p>
<p>To see the difference between different interpolation factor <a class="xref" href="ch15s06.html#fig.basic_contourex03-2" title="Figure 15.80. Interpolation factor=2 (basic_contourex03-2.php)">Figure 15.80. Interpolation factor=2 <code class="uri"><a class="uri" href="example_src/basic_contourex03-2.html" target="_top">(<code class="filename">basic_contourex03-2.php</code>)</a></code> </a> and <a class="xref" href="ch15s06.html#fig.basic_contourex03-3" title="Figure 15.81. Interpolation factor=3 (basic_contourex03-3.php)">Figure 15.81. Interpolation factor=3 <code class="uri"><a class="uri" href="example_src/basic_contourex03-3.html" target="_top">(<code class="filename">basic_contourex03-3.php</code>)</a></code> </a> shows the effect of using both a
grid interpolation factor of 2 and 3 on the example in <a class="xref" href="ch15s06.html#fig.basic_contourex03-1" title="Figure 15.79. Interpolation factor=1 (basic_contourex03-1.php)">Figure 15.79. Interpolation factor=1 <code class="uri"><a class="uri" href="example_src/basic_contourex03-1.html" target="_top">(<code class="filename">basic_contourex03-1.php</code>)</a></code> </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.basic_contourex03-2"></a><p class="title"><b>Figure 15.80. Interpolation factor=2 <code class="uri"><a class="uri" href="example_src/basic_contourex03-2.html" target="_top">(<code class="filename">basic_contourex03-2.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/basic_contourex03-2.png" alt="Interpolation factor=2 (basic_contourex03-2.php)"></span> </div></div><br class="figure-break">
</td><td>
<div class="figure"><a name="fig.basic_contourex03-3"></a><p class="title"><b>Figure 15.81. Interpolation factor=3 <code class="uri"><a class="uri" href="example_src/basic_contourex03-3.html" target="_top">(<code class="filename">basic_contourex03-3.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/basic_contourex03-3.png" alt="Interpolation factor=3 (basic_contourex03-3.php)"></span> </div></div><br class="figure-break">
</td></tr></tbody></table>
</div><p>
</p>
<p>We can now make two observations based on the above two figures</p>
<p>
</p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem">
<p>The lines get smoother the higher interpolation factor we
use</p>
</li><li class="listitem">
<p>The automatic scale has changed. This is not surprising since we
have in effect increase the number of data points each time we
increase the interpolation factor. The scale corresponds to the
matrix size (an entry in matrix at position (r,c) corresponds to the
point (x=c,y=r) in the graph.)</p>
<p>Initially we had a data matrix of size 5x4=20 data points, after
doing one interpolation (factor=2) the data matrix will have a size
of 9x7=63 data points and after doing one more interpolation
(factor=3) the data matrix will have a size of 17x13=221 data
points. </p>
<p>If we would have done one more interpolation we would have a data
matrix of size 33x25=825 data points.</p>
<p>The exponential growth of the total number of data point for a
10x10 matrix is shown in <a class="xref" href="ch15s06.html#fig.interpolation-growth" title="Figure 15.82. The exponential growth of the data size due to grid interpolation factor (interpolation-growth.php)">Figure 15.82. The exponential growth of the data size due to grid interpolation factor <code class="uri"><a class="uri" href="example_src/interpolation-growth.html" target="_top">(<code class="filename">interpolation-growth.php</code>)</a></code> </a>. This also makes a good
example of using a logarithmic y-scale. If the graph is a straight
line when plotted against a logarithmic scale this confirms our
suspicion that this is indeed a exponentially growing function.
<a class="xref" href="ch15s06.html#fig.interpolation-growth-log" title="Figure 15.83. The exponential growth of the data size due to the grid interpolation factor (log scale) (interpolation-growth-log.php)">Figure 15.83. The exponential growth of the data size due to the grid interpolation factor (log scale) <code class="uri"><a class="uri" href="example_src/interpolation-growth-log.html" target="_top">(<code class="filename">interpolation-growth-log.php</code>)</a></code> </a> shows a
variant with a logarithmic y-scale (which confirms our
suspicion.)</p>
</li></ol></div><p>
</p>
<div class="tip" title="Tip" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Tip</h3>
<p>The helper class to do the actual interpolation can also be used directly
in other context. In order to create a new interpolated data matrix with a
specific interpolation factor the following code snippet can be used.</p>
<p>
</p><div class="hl-main"><table class="hl-table" width="100%"><tr><td class="hl-gutter" align="right" valign="top"><pre>1
2
3
4
5
6
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-inlinetags"><?php</span><span class="hl-code">
</span><span class="hl-var">$dataMatrix</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-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$factor</span><span class="hl-code"> = ... ;
</span><span class="hl-var">$grid_interpolate</span><span class="hl-code"> = </span><span class="hl-reserved">new</span><span class="hl-code"> </span><span class="hl-identifier">Interpolate</span><span class="hl-brackets">(</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$dataMatrix</span><span class="hl-code"> = </span><span class="hl-var">$grid_interpolate</span><span class="hl-code">-></span><span class="hl-identifier">Linear</span><span class="hl-brackets">(</span><span class="hl-var">$dataMatrix</span><span class="hl-code">, </span><span class="hl-var">$factor</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-inlinetags">?></span></pre></td></tr></table></div><p>
</p>
</div>
<p>
</p><div class="tip" title="Tip" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Tip</h3>
<p>There is also a utility function
<code class="code">doMeshInterpolate(&$aData,$aFactor)</code> that can be
sued to interpolate a matrix in place. This creates the necessary class,
interpolates its first argument and then fills the argument with the
interpolated data. By using call by reference some data copying is
avoided.</p>
</div><p>
</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.interpolation-growth"></a><p class="title"><b>Figure 15.82. The exponential growth of the data size due to grid interpolation factor <code class="uri"><a class="uri" href="example_src/interpolation-growth.html" target="_top">(<code class="filename">interpolation-growth.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/interpolation-growth.png" alt="The exponential growth of the data size due to grid interpolation factor (interpolation-growth.php)"></span> </div></div><br class="figure-break">
</td><td>
<div class="figure"><a name="fig.interpolation-growth-log"></a><p class="title"><b>Figure 15.83. The exponential growth of the data size due to the grid interpolation factor (log scale) <code class="uri"><a class="uri" href="example_src/interpolation-growth-log.html" target="_top">(<code class="filename">interpolation-growth-log.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/interpolation-growth-log.png" alt="The exponential growth of the data size due to the grid interpolation factor (log scale) (interpolation-growth-log.php)"></span> </div></div><br class="figure-break">
</td></tr></tbody></table>
</div><p>
</p>
</div>
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