Spider: A robust curvature estimator for noisy, irregular meshes

Surface curvature properties are often as important as surface position in understanding shape. Curvature properties are typically computed at mesh vertices by operating on an associated ring neighbourhood of faces. Such approaches are not well suited to noisy, non-uniformly sampled meshes with irregular tessellations. In this paper, we present a principled approach to curvature estimation that can be computed at any point on the unprocessed mesh surface and is robust to noisy and irregular surface sampling and tessellation. The approach achieves user controlled smoothing of the curvature field thus also making it robust to noisy sampling. The nature of the smoothing, in contrast to current approaches, is determined by intuitive user-specified parameters and becomes naturally anisotropic in the vicinity of feature edges. We show this approach to provide better visual results than ring neighbourhood approaches on noisy, non-uniformly sampled meshes with irregular tessellations. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling— [G.2.3]: Discrete Mathematics— Applications