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

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<?php
$data = array(
            array (0.5,1.1,1.5,1,2.0,3,3,2,1,0.1),
            array (1.0,1.5,3.0,5,6.0,2,1,1.2,1,4),
            array (0.9,2.0,2.1,3,6.0,7,3,2,1,1.4),
            array (1.0,1.5,3.0,4,6.0,5,2,1.5,1,2),
            array (0.8,2.0,3.0,3,4.0,4,3,2.4,2,3),
            array (0.6,1.1,1.5,1,4.0,3.5,3,2,3,4),
            array (1.0,1.5,3.0,5,6.0,2,1,1.2,2.7,4),
            array (0.8,2.0,3.0,3,5.5,6,3,2,1,1.4),
            array (1.0,1.5,3.0,4,6.0,5,2,1,0.5,0.2));
?>

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

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 Understanding mesh interpolation

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$data = ReadFileData::FromMatrix('matrixdata.txt');

Figure 15.75. A basic contour graph (basic_contourex01.php) shows the most basic contour plot. This is crated by first instantiating a graph and then creating an instance of class ContourPlot which is added to the graph.

The constructor for class ContourPlot has the following signature

This means that the common structure to create a basic contour plot will be

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<?php
$data = array ( array ( ... ) );
 
// Basic contour graph
$graph = new Graph($width,$height);
$graph->SetScale('intint');
 
// Adjust the margins to fit the margin
$graph->SetMargin(30,100,40,30);
 
// Setup
$graph->title->Set('Basic contour plot');
$graph->title->SetFont(FF_ARIAL,FS_BOLD,12);
 
// A simple contour plot with default arguments (e.g. 10 isobar lines)
$cp = new ContourPlot($data);
 
// Display the legend
$cp->ShowLegend();
 
$graph->Add($cp);
?>

Since the most common format for contour graphs is to show axis on all sides we should add the line

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$graph->SetAxisStyle(AXSTYLE_BOXOUT);

to our previous example so we get the effect shown in Figure 15.76. Adding axis on all sides (basic_contourex02.php) . To show the effect of flipping the data around the center line we have to add the following line

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$cp->SetInvert();

and get the result of adding this line is shown in Figure 15.77. Flipping the data around the center line (basic_contourex05.php)

Figure 15.76. Adding axis on all sides (basic_contourex02.php)

Figure 15.77. Flipping the data around the center line (basic_contourex05.php)

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

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$contourplot = new ContourPlot($data,5);

The result of changing this in the previous example is shown in Figure 15.78. Using only 5 isobar lines (basic_contourex04.php)

Figure 15.78. Using only 5 isobar lines (basic_contourex04.php)

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.

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.

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

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<?php
$isoBars = array( 0.1,  0.2,  0.3,  0.4,  0.5,  0.6 )
$cp = new ContourPlot($data, $isoBars); 
?>

The isobar colors can be adjusted by specifying a color array that specifies the color for each isobar.

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.

There are usually two reasons for changing the default color spectra.

This can be accomplished with a call to the method

as the following example shows

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$cp = new  ContourPlot( $data );
$cp->UseHighContrastColor( true );

The above example will only use a blue to red color scale and avoid the "low-contrast" greenish middle color spectrum colors.

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.

Specifying manual colors of the isobar can be done in two ways.

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.

The data we will be using is given by the following data matrix

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$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 ));

A basic contour graph using the above data is shown in Figure 15.79. Interpolation factor=1 (basic_contourex03-1.php)

Figure 15.79. Interpolation factor=1 (basic_contourex03-1.php)

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

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$contourplot = new ContourPlot($data,10,3);

To see the difference between different interpolation factor Figure 15.80. Interpolation factor=2 (basic_contourex03-2.php) and Figure 15.81. Interpolation factor=3 (basic_contourex03-3.php) shows the effect of using both a grid interpolation factor of 2 and 3 on the example in Figure 15.79. Interpolation factor=1 (basic_contourex03-1.php)

Figure 15.80. Interpolation factor=2 (basic_contourex03-2.php)

Figure 15.81. Interpolation factor=3 (basic_contourex03-3.php)

We can now make two observations based on the above two figures

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<?php
$dataMatrix = array( ... );
$factor = ... ;
$grid_interpolate = new Interpolate();
$dataMatrix = $grid_interpolate->Linear($dataMatrix, $factor);
?>

Figure 15.82. The exponential growth of the data size due to grid interpolation factor (interpolation-growth.php)

Figure 15.83. The exponential growth of the data size due to the grid interpolation factor (log scale) (interpolation-growth-log.php)