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Estimating intrinsic geometric properties of a surface from a polygonal mesh obtained from range data is an important stage of numerous algorithms in computer and robot vision, computer graphics, geometric modeling, industrial and biomedical engineering. This work considers different computational schemes for local estimation of intrinsic curvature geometric properties. Five different algorithms and their modifications were tested on triangular meshes that represent tesselations of synthetic geometric models. The results were compared with the analytically computed values of the Gaussian and mean curvatures of the non uniform rational B-spline (NURBs) surfaces, these meshes originated from. This work manifests the best algorithms suited for total (Gaussian) and mean curvature estimation, and shows that indeed different alogrithms should be employed to compute the Gaussian and mean curvatures.

Results from analyzing the curvature of a surface can be used to improve the implementation, etllciency, and effectiveness of manufacturing and visualization of sculptured surfaces.We develop a robust method using hybrid symbolic and numeric operators ta create trimmed surfaces, each of which is solely convex, concave, or saddle and partitions the original surface. The same method is also used to identify regions whose curvature lies within prespecified bounds.