DISCRETE COMBINATORIAL SURFACES

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 mani folds. A set of voxels (points with integer coordinates) is a surface iff these points are the vertices of a two-dimensional combinatorial m anifold. This approach allows introduction of several notions of discr ete surfaces: The first, called a quadrangulated surface, is a combina torial manifold whose faces are squares; the second, called a triangul ated surface, is a combinatorial manifold whose faces are triangles, T he last is associated with a neighborhood relation; thus, there are as many concepts of triangulated surfaces as there are neighborhood rela tions. As a consequence the same concepts, algorithms, and methods can be used in computer imagery and in the field of topology-based geomet ric modeling (so called ''boundary representation''). (C) 1995 Academi c Press, Inc.