Validation and storage of polyhedra through constrained delaunay tetrahedralization

Abstract

Closed, watertight, 3D geometries are represented by polyhedra. Current data models define these polyhedra basically as a set of polygons, leaving the test on intersecting polygons or open gaps to external validation rules. If this testing is not performed well, or not at all, non-valid polyhedra could be stored in geo-databases. This paper proposes the utilization of the Constrained Delaunay Tetrahedralization (CDT) for the validation (i.e. check on self-intersecting and closeness) of polyhedra on the one hand, and the efficient storage of valid polyhedra on the other hand. The paper stresses on the decomposition of a polyhedron through a CDT and the possibility to store and compose the polyhedron through the vertices of the CDT, a bitmap that indicates which faces of the Delaunay Tetrahedralization (DT) links to a CDT-face, and a list of non-recovered CDT-faces. © 2008 Springer-Verlag Berlin Heidelberg.