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<html><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><title>Chapter 23. Filled 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="pt05.html" title="Part V. Additional graph types available in the professional version"></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 23. Filled contour graphs</th></tr><tr><td width="20%" align="left"> </td><th width="60%" align="center">Part V. Additional graph types available in the professional version</th><td width="20%" align="right"> </td></tr></table><hr></div><div class="chapter" title="Chapter 23. Filled contour graphs"><div class="titlepage"><div><div><h2 class="title"><a name="chapter.filled-contour-graphs"></a>Chapter 23. Filled contour graphs</h2></div></div></div><div class="toc"><p><b>Table of Contents</b></p><dl><dt><span class="sect1"><a href="ch23.html#id2594434">23.1. Filled Contour graphs</a></span></dt><dd><dl><dt><span class="sect2"><a href="ch23.html#id2594607">23.1.1. Creating a filled contour graph</a></span></dt><dt><span class="sect2"><a href="ch23.html#id2594628">23.1.2. Enabling and disabling contour lines</a></span></dt><dt><span class="sect2"><a href="ch23.html#id2594656">23.1.3. Specifying a filled contour</a></span></dt><dt><span class="sect2"><a href="ch23.html#id2594673">23.1.4. Adjusting the labels in the contour</a></span></dt><dt><span class="sect2"><a href="ch23.html#id2595002">23.1.5. Selecting the adaptive method to use</a></span></dt></dl></dd></dl></div>
<div class="sect1" title="Filled Contour graphs"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a name="id2594434"></a>Filled Contour graphs</h2></div></div></div>
<p>
</p><div class="note" title="Note" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Note</h3>
<p>This section describes additional functionality available in the pro-version
v3.1p and above.</p>
</div><p>
</p>
<p>The use of filled ContourPlots requires the inclusion of the module
"<code class="filename">jpgraph_contourf.php</code>". The filled version of contour graphs
supports the following additional features compared to the regular contour graphs</p>
<div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
<p>Filled contour plots</p>
</li><li class="listitem">
<p>Labelling of isobar lines in the contour plots</p>
</li><li class="listitem">
<p>Two user selectable adaptive algorithms to determine the contours, one
rectangular and one triangular based adaptive mesh algorithm.</p>
</li></ul></div><p>The enhanced contour plot is contained in the new plot <code class="code">class
FilledContourPlot</code>.</p>
<p>As a quick introduction the two examples below shows two contour graphs which makes
use of these additional features</p>
<p>
<table xmlns="" frame="void" id="id2594508">
<tbody xmlns="">
<tr>
<td>
<div class="figure"><a name="fig.contour2_ex1"></a><p class="title"><b>Figure 23.1. Filled contour with labels <code class="uri"><a class="uri" href="example_src/contour2_ex1.html" target="_top">(<code class="filename">contour2_ex1.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/contour2_ex1.png" alt="Filled contour with labels (contour2_ex1.php)"></span> </div></div><br class="figure-break">
</td>
<td>
<div class="figure"><a name="fig.contour2_ex2"></a><p class="title"><b>Figure 23.2. Filled contour with no isobar lines <code class="uri"><a class="uri" href="example_src/contour2_ex2.html" target="_top">(<code class="filename">contour2_ex2.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/contour2_ex2.png" alt="Filled contour with no isobar lines (contour2_ex2.php)"></span> </div></div><br class="figure-break">
</td>
</tr>
</tbody>
</table>
</p>
<p>All basic formatting, such as specifying colors and number/location of the isobar
lines are handled in exactly the same way as described in the previous section for basic
contours.</p>
<div class="sect2" title="Creating a filled contour graph"><div class="titlepage"><div><div><h3 class="title"><a name="id2594607"></a>Creating a filled contour graph</h3></div></div></div>
<p>The filled contour graph follows the exact same principles as for the non filled
graph described above. The core difference is that a filled graph is created as an
instance of <code class="code">class FilledContourPlot</code>, i.e.</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
</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">$filledContour</span><span class="hl-code"> = </span><span class="hl-reserved">new</span><span class="hl-code"> </span><span class="hl-identifier">FilledContourPlot</span><span class="hl-brackets">(</span><span class="hl-var">$data</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-inlinetags">?&gt;</span></pre></td></tr></table></div><p>
</p>
</div>
<div class="sect2" title="Enabling and disabling contour lines"><div class="titlepage"><div><div><h3 class="title"><a name="id2594628"></a>Enabling and disabling contour lines</h3></div></div></div>
<p>Contour lines are controlled with the method</p>
<p>
</p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
<p><code class="code">FilledContourPlot::ShowLines($aFlg,$aColorWithFilled='black')</code></p>
<p>The <code class="code">$aFlg</code> is a boolean that determines if contour lines
should be shown or not. by default they are enabled. The second argument
<code class="code">$aColorWithFilled</code> determines what color the contour
lines should have when the contour is filled. If the contour is not
filled then the contour lines will have the color of the isobar.</p>
</li></ul></div><p>
</p>
</div>
<div class="sect2" title="Specifying a filled contour"><div class="titlepage"><div><div><h3 class="title"><a name="id2594656"></a>Specifying a filled contour</h3></div></div></div>
<p>In order to have the contour filled the method</p>
<div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
<p><code class="code">ContourPlot::SetFilled($aFlg)</code> Determines if the contour
should be filled or not.</p>
</li></ul></div>
<p>should be called.</p>
<p>Since there are <span class="italic">n</span> isobar lines and there needs to be <span class="italic">n+1</span> colors to fill the graph there is a choice of what
side should the color for isobar line <span class="italic">n</span> fill. The area above or the area below the isobar. In
this library we use the convention that the color for isobar line <span class="italic">n</span> is used to fill the area up to the next highest
isobar <span class="italic">n+1</span>. </p>
<p>If the colors are specified manually it is important that one more color than the
number of isobar lines are specified. The convention is such that the color
specified in the first position (position = 0 ) in the color array is used to fill
the area below the lowest specified isobar.</p>
<p>An example will make this clear.</p>
<p>The graph below only uses three isobar lines (to keep things simple) which means
that we need four colors. To create such a graph we use the lines</p>
<div class="hl-main"><table class="hl-table" width="100%"><tr><td class="hl-gutter" align="right" valign="top"><pre>1
2
3
4
5
6
7
8
9
10
11
12
</pre></td><td class="hl-main" valign="top"><pre><span class="hl-inlinetags">&lt;?php</span><span class="hl-code">
</span><span class="hl-var">$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-brackets">)</span><span class="hl-code">;
</span><span class="hl-var">$isobar_colors</span><span class="hl-code"> = </span><span class="hl-reserved">array</span><span class="hl-brackets">(</span><span class="hl-quotes">'</span><span class="hl-string">lightgray</span><span class="hl-quotes">'</span><span class="hl-code">,</span><span class="hl-quotes">'</span><span class="hl-string">teal:1.3</span><span class="hl-quotes">'</span><span class="hl-code">,</span><span class="hl-quotes">'</span><span class="hl-string">orange</span><span class="hl-quotes">'</span><span class="hl-code">,</span><span class="hl-quotes">'</span><span class="hl-string">red</span><span class="hl-quotes">'</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-comment">//</span><span class="hl-comment"> Create a new contour graph with three isobar lines</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$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">$data</span><span class="hl-code">,</span><span class="hl-number">3</span><span class="hl-brackets">)</span><span class="hl-code">;
</span><span class="hl-comment">//</span><span class="hl-comment"> Specify the colors manually</span><span class="hl-comment"></span><span class="hl-code">
</span><span class="hl-var">$cp</span><span class="hl-code">-&gt;</span><span class="hl-identifier">SetIsobarColors</span><span class="hl-brackets">(</span><span class="hl-var">$isobar_colors</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 class="figure"><a name="fig.contour2_ex3"></a><p class="title"><b>Figure 23.3. Manual colors for contour <code class="uri"><a class="uri" href="example_src/contour2_ex3.html" target="_top">(<code class="filename">contour2_ex3.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/contour2_ex3.png" alt="Manual colors for contour (contour2_ex3.php)"></span> </div></div><p><br class="figure-break">
</p>
<p>as can be seen from the labels in the graph the algorithm has resulted in three
isobar lines (as specified) at values <span class="italic">6.2</span>, <span class="italic">10.5</span> and <span class="italic">14.8</span>. The first color "gray" is used to fill the area
below the smallest isobar (<span class="italic">6.2</span>).</p>
<p>It should be noted that by specifying <code class="code">SetFilled(false)</code> a non filled
contour graph can be created. However, the visual appearance compared with the
<code class="code">class ContourPlot</code> will be slightly different. The reason is that
the filled contour plot class uses an adaptive algorithm that gives better fidelity
than the simpler non adaptive algorithm used in the standard (non-filled) contour
plot class. The contour corresponds to creating a contour with the plain contour
plot algorithm (class ContourPlot) using an interpolation factor of ~3-4.</p>
</div>
<div class="sect2" title="Adjusting the labels in the contour"><div class="titlepage"><div><div><h3 class="title"><a name="id2594673"></a>Adjusting the labels in the contour</h3></div></div></div>
<p>In order to make it easier to follow the contour labels can be added inside the
contour. The labels are placed using a heuristic algorithm that tries to place
enough labels to make the plot easy to read but not as many labels as to make it
crowded.</p>
<p>There are two main characteristic of the labels that can be controlled.</p>
<div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
<p>The font and color of the labels which are controlled by the two methods
<code class="code">FilledContourPlot::SetFont()</code> and
<code class="code">FilledContourPlot::SetFontColor()</code></p>
</li><li class="listitem">
<p>Whether or not the label should follow the gradient of the isobar line at
the point where the label is displayed or if it should always be drawn
horizontally.</p>
</li></ul></div>
<p>To enable or disable the display of the labels as well as determining if the label
should follow the gradient or not the method</p>
<p>
</p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
<p><code class="code">FilledContourPlot::ShowLabel($aFlg,$aFollowGradient)</code></p>
</li></ul></div><p>
</p>
<p>is used. The two examples below show two variants of the same contour where the
left graph have labels which follows the gradient and the right graph have labels
that are always oriented horizontally.</p>
<p>
<table xmlns="" frame="void" id="id2594914">
<tbody xmlns="">
<tr>
<td>
<div class="figure"><a name="fig.contour2_ex4"></a><p class="title"><b>Figure 23.4. Labels that follows the gradients <code class="uri"><a class="uri" href="example_src/contour2_ex4.html" target="_top">(<code class="filename">contour2_ex4.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/contour2_ex4.png" alt="Labels that follows the gradients (contour2_ex4.php)"></span> </div></div><br class="figure-break">
</td>
<td>
<div class="figure"><a name="fig.contour2_ex5"></a><p class="title"><b>Figure 23.5. Labels that are always horizontal. In this example we have also shown how to change the colors. <code class="uri"><a class="uri" href="example_src/contour2_ex5.html" target="_top">(<code class="filename">contour2_ex5.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/contour2_ex5.png" alt="Labels that are always horizontal. In this example we have also shown how to change the colors. (contour2_ex5.php)"></span> </div></div><br class="figure-break">
</td>
</tr>
</tbody>
</table>
</p>
</div>
<div class="sect2" title="Selecting the adaptive method to use"><div class="titlepage"><div><div><h3 class="title"><a name="id2595002"></a>Selecting the adaptive method to use</h3></div></div></div>
<p>
</p><div class="note" title="Note" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Note</h3>
<p>This section can be skipped without loss of continuity. The default method
"rectangular" recursive adaptation is good enough for most
circumstances.</p>
</div><p>
</p>
<p>In order to fully understand the effect of selecting which adaptive method to use
it is first necessary to understand some background on how contours are created
algorithmically. </p>
<p>Determining general contours for a function of two independent variables is
equivalent to the problem of finding the equivalence class of all coordinate pairs <span class="italic">(x,y)</span> for which for <span class="italic">C=f(x,y)</span> which in general is a non-linear problem. This
is an example of a problem that is computational very expensive to mathematically
solve correct but quite tractable if we view a sampled version of the function. This
means that we in general do not have access to <span class="italic">f(x,y)</span> instead we only know of its values at a number
of grid points. This is also the cause of visually different contour plots for the
same input data.</p>
<p>The difference lay in the core problem that in order to draw a continues contour
we need to interpolate the unknown values in between the known sample points. This
is therefore a degree of freedom where the actual choice of how we do the
interpolation will cause the contour to be visually different depending on our
choice.</p>
<p>While it would take to far in this manual to describe the full adaptive algorithm
in all details we will show the different principles that underlying the two methods
hat the user can select between.</p>
<p>In order to determine the isobars the given data points are considered to be
vertices in a grid where each vertice is connected with an edge. There are two basic
ways to connect the points with edges; rectangular and triangular. In the first way
four points are connected to form a square and in the second way three point are
connected to form a triangle. The so created square or triangles will be referred to
as a submesh consisting of four and three sides respectively.</p>
<p>To determine the isobars each submesh is recursively divided until each side is
small enough to only have one crossing isobar. The exact position of the crossing is
determined by linear interpolation between the two corresponding vertices.</p>
<p>The figures below shows the sequences for the triangle recursive division. The
recursion continues until each edge has exactly one crossing of an isobar.</p>
<p>
</p><div class="informaltable">
<table border="0"><colgroup><col class="c1"><col class="c2"><col class="c3"></colgroup><tbody><tr><td align="center">
<div class="figure"><a name="id2595141"></a><p class="title"><b>Figure 23.6. Triangulation step 0</b></p><div class="figure-contents">
<div class="mediaobject"><img src="images/tri_step0.png" alt="Triangulation step 0"></div>
</div></div><br class="figure-break">
</td><td align="center">
<div class="figure"><a name="id2595170"></a><p class="title"><b>Figure 23.7. Triangulation step 1</b></p><div class="figure-contents">
<div class="mediaobject"><img src="images/tri_step1.png" alt="Triangulation step 1"></div>
</div></div><br class="figure-break">
</td><td align="center">
<div class="figure"><a name="id2595196"></a><p class="title"><b>Figure 23.8. Triangulation step 2</b></p><div class="figure-contents">
<div class="mediaobject"><img src="images/tri_step2.png" alt="Triangulation step 2"></div>
</div></div><br class="figure-break">
</td></tr></tbody></table>
</div><p>
</p>
<p> In the same way the sequence of figures below shows the principle for the
quadratic recursive subdivsion of the mesh for first three steps. </p>
<p>
</p><div class="informaltable">
<table border="0"><colgroup><col class="c1"><col class="c2"><col class="c3"></colgroup><tbody><tr><td align="center">
<div class="figure"><a name="id2595278"></a><p class="title"><b>Figure 23.9. "Rectangularization" step 0</b></p><div class="figure-contents">
<div class="mediaobject"><img src="images/rect_step0.png" alt='"Rectangularization" step 0'></div>
</div></div><br class="figure-break">
</td><td align="center">
<div class="figure"><a name="id2595302"></a><p class="title"><b>Figure 23.10. "Rectangularization" step 1</b></p><div class="figure-contents">
<div class="mediaobject"><img src="images/rect_step1.png" alt='"Rectangularization" step 1'></div>
</div></div><br class="figure-break">
</td><td align="center">
<div class="figure"><a name="id2595327"></a><p class="title"><b>Figure 23.11. "Rectangularization" step 2</b></p><div class="figure-contents">
<div class="mediaobject"><img src="images/rect_step2.png" alt='"Rectangularization" step 2'></div>
</div></div><br class="figure-break">
</td></tr></tbody></table>
</div><p>
</p>
<p> Needless to say these two variants give slightly different visual appearance of
the resulting contour plot and neither of the two method can be considered "the
right method". Triangularization tends to work better (and faster) for high
frequency contour plots and gives a more "edgy" result. The quadratic subdivision
might require more recursive steps for high frequency contours but in general gives
a smoother look of the resulting contour.</p>
<p>By default the library uses a rectangular mesh division and that is the method
that has been used in all the previous examples. As an illustration the effect of
the method have the two figures below shows the same data as we have used in the
previous figures to display a contour plot with 7 isobars. The left figures uses a
rectangular division (the default) and the right figure uses a triangular
division.</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.contour2_ex6"></a><p class="title"><b>Figure 23.12. 7 Isobars, "rect" method <code class="uri"><a class="uri" href="example_src/contour2_ex6.html" target="_top">(<code class="filename">contour2_ex6.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/contour2_ex6.png" alt='7 Isobars, "rect" method (contour2_ex6.php)'></span> </div></div><br class="figure-break">
</td><td>
<div class="figure"><a name="fig.contour2_ex7"></a><p class="title"><b>Figure 23.13. 7 Isobars, "tri" method <code class="uri"><a class="uri" href="example_src/contour2_ex7.html" target="_top">(<code class="filename">contour2_ex7.php</code>)</a></code> </b></p><div class="figure-contents"> <span class="inlinemediaobject"><img src="images/contour2_ex7.png" alt='7 Isobars, "tri" method (contour2_ex7.php)'></span> </div></div><br class="figure-break">
</td></tr></tbody></table>
</div><p>
</p>
<p>As can be seen in this case the triangular method favour elongated contours from
southwest to northeast while the rectangular method favours circular contours. </p>
<p>The way to choose what method to use is by the method</p>
<p>
</p><div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
<p><code class="code">FilledContourPlot::SetMethod($aMethod)</code>
</p>
<p>The possible options for <code class="code">$aMethod</code> are</p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem">
<p>"rect" - Rectangualr algortihm (default)</p>
</li><li class="listitem">
<p>"tri" - Triangular algorithm</p>
</li></ol></div>
</li></ul></div><p>
</p>
<p>
</p><div class="tip" title="Tip" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title">Tip</h3>
<p>It is possible to show the triangulation used by calling the method
<code class="code">FilledContourPlot::ShowTriangulation($aFlg)</code>. In the two
figures below the triangulation for the "rect" and "tri" method in the
previous examples are shown.</p>
<p>
<table xmlns="" frame="void" id="id2595547">
<tbody xmlns="">
<tr>
<td>
<div class="figure"><a name="id2595567"></a><p class="title"><b>Figure 23.14. Rectangular sub-division</b></p><div class="figure-contents">
<div class="mediaobject"><img src="images/contour_rectang.png" alt="Rectangular sub-division"></div>
</div></div><br class="figure-break">
</td>
<td>
<div class="figure"><a name="id2595593"></a><p class="title"><b>Figure 23.15. Triangular sub-division</b></p><div class="figure-contents">
<div class="mediaobject"><img src="images/contour_triangulation.png" alt="Triangular sub-division"></div>
</div></div><br class="figure-break">
</td>
</tr>
</tbody>
</table>
</p>
</div><p>
</p>
</div>
</div>
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