Estimating Curvatures and Their Derivatives on Triangle Meshes

Abstract:

The computation of curvature and other differential properties of
surfaces is essential for many techniques in analysis and rendering. We
present a finite-differences approach for estimating curvatures on irregular
triangle meshes that may be thought of as an extension of a common
method for estimating per-vertex normals. The technique is stable and
robust, offers accuracy comparable to or better than existing methods,
and generalizes naturally to computing derivatives of curvature and
higher-order surface differentials.