Shape Description By Medial Surface Construction

The medial surface is a skeletal abstraction of a solid that provides useful shape information, which compliments existing model representation schemes. The medial surface and its associated topological entities are defined, and an algorithm for computing the medial surface of a large class of B-rep solids is then presented. The algorithm is based on the domain Delaunay triangulation of a relatively sparse distribution of points, which are generated on the boundary of the object. This strategy is adaptive in that the boundary point set is refined to guarantee a correct topological representation of the medial surface.

[1]  Ching-Shoei Chiang.  The Euclidean distance transform , 1992 .

[2]  M. Sabin,et al.  Hexahedral mesh generation by medial surface subdivision: Part I. Solids with convex edges , 1995 .

[3]  Nicholas M. Patrikalakis,et al.  Computation of the Medial Axis Transform of 3-D polyhedra , 1995, Symposium on Solid Modeling and Applications.

[4]  Fritz B. Prinz,et al.  Continuous skeletons of discrete objects , 1993, Solid Modeling and Applications.

[5]  Damian J. Sheehy,et al.  Computing the medial surface of a solid from a domain Delaunay triangulation , 1995, Symposium on Solid Modeling and Applications.

[6]  Nickolas S. Sapidis,et al.  Domain Delaunay Tetrahedrization of arbitrarily shaped curved polyhedra defined in a solid modeling system , 1991, SMA '91.

[7]  Ling Chen,et al.  SIMD hypercube algorithm for complete Euclidean distance transform , 1995, Proceedings 1st International Conference on Algorithms and Architectures for Parallel Processing.

[8]  Damian J. Sheehy,et al.  Numerical Computations of Medial Surface Vertices , 1994, IMA Conference on the Mathematics of Surfaces.

[9]  Christoph M. Hoffmann,et al.  How to Construct the Skeleton of CSG Objects , 1990 .

[10]  Debasish Dutta,et al.  On the Skeleton of Simple CSG Objects , 1993 .

[11]  James H. Davenport,et al.  Voronoi diagrams of set-theoretic solid models , 1992, IEEE Computer Graphics and Applications.

[12]  T. Tam,et al.  2D finite element mesh generation by medial axis subdivision , 1991 .

[13]  Nicholas M. Patrikalakis,et al.  An Algorithm for the Medial Axis Transform of 3D Polyhedral Solids , 1996, IEEE Trans. Vis. Comput. Graph..

[14]  George M. Turkiyyah,et al.  Computation of 3D skeletons using a generalized Delaunay triangulation technique , 1995, Comput. Aided Des..

[15]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[16]  Gene H. Golub,et al.  Matrix computations , 1983 .

[17]  John A. Goldak,et al.  Constructing 3-D discrete medial axis , 1991, SMA '91.