Discrete Combinatorial Surfaces

✍ Scribed by J. Francon

• Book ID: 102966589
• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 534 KB
• Volume: 57
• Category: Article
• ISSN: 1077-3169
• DOI: 10.1006/gmip.1995.1003

✦ Synopsis

A new approach to the concept of discrete surfaces is proposed. It is a combinatorial approach. A surface is defined by vertices, edges, and faces satisfying the conditions of two-dimensional combinatorial manifolds. A set of voxels (points with integer coordinates) is a surface iff these points are the vertices of a two-dimensional combinatorial manifold. This approach allows introduction of several notions of discrete surfaces: The first, called a quadrangulated surface, is a combinatorial manifold whose faces are squares; the second, called a triangulated surface, is a combinatorial manifold whose faces are triangles. The last is associated with a neighborhood relation; thus, there are as many concepts of triangulated surfaces as there are neighborhood relations. As a consequence the same concepts, algorithms, and methods can be used in computer imagery and in the field of topology-based geometric modeling (so called "boundary representation"). o 1995 Academic Press, Inc.