Restricted delaunay triangulations and normal cycle

We address the problem of curvature estimation from sampled smooth surfaces. Building upon the theory of normal cycles, we derive a definition of the curvature tensor for polyhedral surfaces. This definition consists in a very simple and new formula. When applied to a polyhedral approximation of a smooth surface, it yields an efficient and reliable curvature estimation algorithm. Moreover, we bound the difference between the estimated curvature and the one of the smooth surface in the case of restricted Delaunay triangulations. Categories and Subject Descriptors F.2.2 [Analysis of algorithms and problem complexity]: [Geometrical problems and computations, Computations on discrete structures]; G.2.3 [Discrete Mathematics]: Applications General Terms Algorithms, Theory Keywords curvature, geometric measure theory, mesh

• Type: Conference
• Year: 2003
• Where: COMPGEOM
• Authors: David Cohen-Steiner, Jean-Marie Morvan
• Keywords: COMPGEOM 2003, Curvature Estimation, Reliable Curvature Estimation, Smooth Surface