Keywords: skeleton, medial axis, chordal axis, Voronoi skeleton, mid-surface, mesh generation.

This paper focuses on the extraction of skeletons of CAD models and its applications in finite element (FE) mesh generation. The term "skeleton of a CAD model" can be visualized as analogous to the "skeleton of a human body". The skeletal representations covered in this paper include medial axis transform (MAT) [1], Voronoi diagram (VD), chordal axis transform (CAT) [2], mid surface [3], digital skeletons, and disconnected skeletons [4]. In the literature, the properties of a skeleton have been utilized in developing various algorithms for extracting skeletons. Three main approaches include: (1) the bisection method where the skeleton exists at equidistant from at least two points on boundary, (2) the grassfire propagation method in which the skeleton exists where the opposing fronts meet, and (3) the duality method where the skeleton is a dual of the object. In the last decade, the author has applied different skeletal representations in all-quad meshing [5], hex meshing, mid-surface meshing, mesh size function generation [6], defeaturing, and decomposition. A brief discussion on the related work from other researchers in the area of tri meshing, tet meshing, and anisotropic meshing is also included. This paper concludes by summarizing the strengths and weaknesses of the skeleton-based approaches in solving various geometry-centered problems in FE mesh generation. The skeletons have proved to be a great shape abstraction tool in analyzing the geometric complexity of CAD models as they are symmetric, simpler (reduced dimension), and provide local thickness information. However, skeletons generally require some cleanup, and stability and sensitivity of the skeletons should be controlled during extraction. Also, selecting a suitable application-specific skeleton and a computationally efficient method of extraction is critical.

1

H. Blum, "A transformation for extracting new descriptors of shape", Models for the Perception of Speech and Visual Form, The MIT Press, Cambridge, MA, 326-380, 1967.

2

L. Prasad, "Morphological analysis of shapes", CNLS Newsletter-Center for Nonlinear Studies, Los Alamos National Laboratory, vol 139, 1997.

3

W. Quadros, "An approach for extracting non-manifold mid-surface of thin-wall solids using chordal axis transform", Engineering with Computers, 24(3), June 2008. doi:10.1007/s00366-008-0094-1

4

W. Quadros, K. Shimada, S. Owen, "3D Discrete Skeleton Generation by Wave Propagation on PR-Octree for Finite Element Mesh Sizing", Proc. of ACM Symposium on Solid Modeling and Applications, Genova, Italy, June 9-11, 2004.

5

W. Quadros, K. Ramaswami, F. Prinz, B. Gurumoorthy, "LayTracks: a new approach to automated quadrilateral mesh generation using MAT", Proc. of 9th International Meshing Roundtable Meshing Conference, New Orleans, LA, USA, October 2000.

6

W. Quadros, K. Shimada, S. Owen, "Skeleton-based computational method for generation of 3D finite element mesh sizing function", Engineering with Computers, 20(3), 249-264, Sept. 2004. doi:10.1007/s00366-004-0292-4

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