Local Topological Parameters in a Tetrahedral Representation

Abstract

This paper deals with topological properties of sets of tetrahedra (“tetrahedral representations” of three-dimensional objects). Classes of such representations which we call normal and strongly normal are defined and some of their basic properties are established. Computationally efficient methods of counting the cavities and tunnels in the neighborhood of a tetrahedron are defined. A characterization of a simple tetrahedron is formulated, and an efficient approach is developed to identifying simple tetrahedra and computing measures of the local topological change when a tetrahedron is deleted.