Validation and Storage of Polyhedra through Constrained Delaunay Tetrahedralization

Authors:
Edward Verbree;Hang Si
Affiliations:
Research Institute OTB, Section GIS-technology, Delft University of Technology, Delft, the Netherlands 2628BX;Weierstrass Institute for Applied Analysis and Stochastics, Research Group: Numerical Mathematics and Scientific Computing, Berlin, Germany 10117
Venue:
GIScience '08 Proceedings of the 5th international conference on Geographic Information Science
Year:
2008

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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.