Reliability of extrapolation

In general, extrapolation is not very reliable and the results so obtained are to be viewed with some lack of confidence. In order for extrapolation to be at all reliable, the original data must be very consistent.

How Natgrid does extrapolation

Natgrid does extrapolation by least squares fitting a plane to the original data and using that plane to produce pseudo data values at some distance from the convex hull. These pseudo data points are added to the input data points when natural neighbors are calculated. The result of this is that extrapolated data will asymptote to the least squares fitted plane.

Controlling whether extrapolation is done

Natgrid allows you to turn off extrapolation and set the interpolated functional values to a constant outside of the convex hull. If the control parameter ext is set to 1 (the default), extrapolation is allowed; if ext is set to 0, extrapolation is not allowed.

The parameter nul specifies the value to be assigned to the interpolated function outside of the convex hull when extrapolation is not allowed; by default nul is 0. .


Example 4 uses the same function as Example 3, but expands the output region to allow for extrapolation. As provided, the code for Example 4 allows for extrapolation. For an example that disallows extrapolation, change the setting of ext in the code for Example 4 from 1 to 0. Notice that in the plot that allows extrapolation, the function values tend toward the least squares fitted plane outside of the convex hull. The plot where extrapolation is not allowed uses the same function and illustrates turning extrapolation off and setting the function values to -1.0 outside of the convex hull. The only difference between the code that produced these plots is the setting of the value of the ext parameter.
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