A new characterization of simple elements in a tetrahedral mesh

This paper deals with topological analysis of sets of tetrahedra (“tetrahedral meshes” of three-dimensional objects). We introduce a definition of simple elements for any normal tetrahedral representation. Then we prove a local characterization of simple tetrahedra in the case of a scene composed of one object and its background, based on homology groups and on relative homology. This allows us to define homotopic deformations of a tetrahedral representation. Using this characterization, we illustrate the problem of generating three-dimensional finite element meshes from medical voxel datasets.