The control parameter exp can be used to specify the power of the distances used in calculating the weights -- by default this value is 3.0. Example 2 illustrates the effect of varying the exponent used for the distances in the weight calculations. When the exponent is 1., cone-like surfaces are formed around the input data values; for values of the exponent greater than 1., flat spots occur around the input data values (the larger the exponent, the larger the flat spot); for values of the exponent smaller than 1., cusps are formed around the input data points.

The control parameter dmx can be used to supply a radius around an interpolation point outside of which input data points will not be used to calculate weights. If no input data points lie within the specified radius for a given interpolation point, the interpolated value is set to a special missing value. This missing value can be set using the control parameter dmv -- the default value is -9999.

You can set any control parameters you want before interpolating at individual points.

For the same number of input and output points, using the Dsgrid entries for interpolation at individual points invokes about a 30% overhead compared to using the Dsgrid entries to interpolate on a grid.

Outside of the convex hull, the interpolated values in Dsgrid tend quickly toward a constant value. This constant is the arithmetic average of the input functional values. Example 5 illustrates this. It presents the function f(x,y) = (x-1/4)**2 + (y-1/2)**2 defined on the unit square and extrapolated to a rectangular region beyond that square.

The idea of the shadowing algorithm is that, given a point where an interpolated value is desired, the weights for the input data values are decreased by a factor that depends on the extent to which one input data point is "behind" another with respect to the point of interpolation. For example, if two input data values lie on a straight line emanating from the interpolation point, then the data value that is farther from the input data point will receive a weighting factor of zero. In general an angle is computed measuring how close a data value is to any other, and the tangent of this angle is used to weight the input data value.

Example 4 illustrates how this works. In that example we have a group of points clustered about the input coordinate (0.7, 0.7). Compare the plot with the shadowing feature turned on to the plot with the shadowing feature turned off. Notice that in the latter plot, the values at the cluster of points dominate the interpolated values in the surrounding area (the large smooth mound).