Decimation and smoothing of triangular meshes based on curvature from the polyhedral Gauss map

This paper presents an improvement on methods to simplify, de-noise and identify feature regions of a triangular mesh, based on curvature estimations. Computations of curvature are obtained from the polyhedral Gauss Maps of the individual vertices. This allows identification of positive and negative curvature components, thus determining the Total Absolute Curvature (TAC) of a vertex. Using this new measure the curvature computed is more reliable and provides more information on the features of the polyhedral surface. The TAC of a region is obtained by summing the TAC's of the vertices in the region, which also provides identification of regions of similar curvature on a mesh model. In order to use this information for mesh simplification we introduce the weighted total absolute curvature measure, abbreviated as WTAC, which takes into consideration not only the curvature but also the area of the region, normalised in a specific way. We apply then the triangle decimation of a mesh, by removing vertices with the smallest WTAC. The decimation algorithm automatically performs also a smoothing (de-noising) operation by deleting outliers. By setting thresholds on the WTAC one can. obtain various degrees of decimation (smoothness). All operations are linear with respect to the number of vertices in the mesh.