Outlying points and roughness estimates

Natgrid has facilities for special treatment of points near function values where the function values are not consistent with neighboring values. For each input point an outlier index is calculated if the point is not on the convex hull; for points on the convex hull, a roughness index is calculated. Both of these indices are a normalized measure of the consistency of an input function value with its neighbors. For details on how these indices are defined and calculated, see Dave Watson's book.

The effects of using the outlier and roughness indices are primarily to attenuate the influence of gradient estimates near points with high values for either of the two indices. This means that in the neighborhood of such points, the interpolation tends more toward natural neighbor linear interpolation. This prevents oversmoothing in those areas, and oversmoothing could result in incorrect deductions being made from analysis of the resulting surface. Exaggerated oscillations surrounding outlying points, that are produced by some curve fitting techniques, are also minimized. See Example 7.

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