An accelerated triangulation method for computing the skeletons of free-form solid models

Shape skeletons are powerful geometric abstractions that provide useful intermediate representations for a number of geometric operations on solid models includingfeature recognition, shape decomposition, finite element mesh generation, and shape design. As a result there has been significant interest in the development of effectivemethods for skeleton generation of general free-form solids. In this paper we describe a method that combines Delaunay triangulation with local numerical optimizationschemes for the generation of accurate skeletons of 3D implicit solid models. The proposed method accelerates the slow convergence of Voronoi diagrams to theskeleton, which, without optimization, would require impractically large sample point sets and resulting messhes to attain acceptable accuracy. The Delaunaytriangulation forms the basis for generating the topological structure of the skeleton. The optimization step of the process generates the geometry of the skeleton patchesby moving the vertices of Delaunay tetrahedra and relocating their centres to form maximally inscribed spheres. The computational advantage of the optimization schemeis that it involves the solution of one small optimization problem per tetrahedron and its complexity is therefore only linear (O(n)) in the number of points used for theskeleton approximation. We demonstrate the effectiveness of the method on a number of representative solid models