Second derivative based mesh simplification

One dimensional case

Given a function F one can measure its curvature with |F''|. In discrete case central differences can be used to estimate the value of F''. The points with |F''|<threshold can be removed. This measure, however, is over-sensitive to high frequency variations, what is shown below. The solid line shows the actual F, dotted line shows the aproximation.

Extensions to two dimensions

can be introduced in several ways. We tested two of them:

Both criteria produce the meshes with too much stress on mountains and valleys.
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Last modified: Mon Mar 10 11:19:17 EST 1997