Controllable Skeleton-Sheets Representation Via Shape Diameter Function

Abstract

The Shape Diameter Function (SDF) is a scalar function defined on the mesh surface expressing a measure of the diameter of the objects volume in the neighborhood of each point on the surface. In our approach we propose to compute internal skeleton, from which every mesh vertex is visible. There are automatic techniques for curve-skeleton extraction, but extracted curve-skeletons does not satisfy this condition. Therefore, we have extended Laplacian smoothing based method via the SDF term that moves skeleton vertices near medial axis. In addition, SDF values can be used to modify parameters as weights and grouping distance during Laplacian-based skeleton extraction to obtain better results with skeleton extraction. Resulting skeleton is reliable, centered in the mesh volume, consist of curves and sheets and is useful for skeleton based parametrization of meshes. Our approach is designed to work on generalized discrete geometry data, particularly point clouds, by estimation of Laplacian from local triangulations.