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Inverse Distance Weighted Interpolation
One of the most commonly used techniques for interpolation of scatter points is inverse distance
weighted (IDW) interpolation. Inverse distance weighted methods are based on the assumption that the
interpolating surface should be influenced most by the nearby points and less by the more distant points.
The interpolating surface is a weighted average of the scatter points and the weight assigned to each
scatter point diminishes as the distance from the interpolation point to the scatter point increases.
Several options are available for inverse distance weighted interpolation. The options are selected using
the Inverse Distance Weighted Interpolation Options dialog. This dialog is accessed through the Options
button next to the Inverse distance weighted item in the 2D Interpolation Options dialog. SMS uses
Shepard's Method for IDW:
Shepard's Method
The simplest form of inverse distance weighted interpolation is sometimes called "Shepard's method"
(Shepard 1968). The equation used is as follows:
where n is the number of scatter points in the set, fi are the prescribed function values at the scatter
points (e.g. the data set values), and wi are the weight functions assigned to each scatter point. The
classical form of the weight function is:
where p is an arbitrary positive real number called the power parameter (typically, p=2) and hi is the
distance from the scatter point to the interpolation point or
where (x,y) are the coordinates of the interpolation point and (xi,yi) are the coordinates of each scatter
point. The weight function varies from a value of unity at the scatter point to a value approaching zero as
the distance from the scatter point increases. The weight functions are normalized so that the weights
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