An accelerated triangulation method for cimputing the skeletons of free-form solid models
Turkiyyah, George M., Duane W. Storti, Mark Ganter, Hao Chen and Munikumar Vimawala
Computer-Aided Design, Elsevier, Vol 29, Num 1, pp.5-19, January 1997
Shape skeletons are powerful geometric abstractions that provide useful intermediate representations for a number of geometric operations on solid models including feature recognition, shape decomposition, finite element mesh generation, and shape design. As a result there has been significant interest in the development of effective methods for skeleton generation of general free-form solids. In this paper we describe a method that combines Delaunay triangulation with local numerical optimization schemes for the generation of accurate skeletons of 3D implicit solid models. The proposed method accelerates the convergence of Voronoi diagrams to the skeleton, which without optimization, would require impractically large sample point sets and resulting meshes to attain acceptable accuracy. The Delaunay triangulation forms the basis for generating the topological structure of the skeleton. The optimization step of the process generates the geometry of the skeleton patches by moving the vertices of Delaunay tetrahedra and relocating their centers to form maximally inscribed spheres. The computational advantage of the optimization scheme is 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 the skeleton approximation. We demonstrate the effectiveness of the method on a number of representative solid models. Copyright (c) 1996 Elsevier Science Ltd.
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