Validation and Storage of Polyhedra through Constrained Delaunay Tetrahedralization

  • Edward Verbree
  • Hang Si
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5266)


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.


Delaunay Triangulation Steiner Point Polyhedral Surface Polygonal Surface Geographic Markup Language 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Edward Verbree
    • 1
  • Hang Si
    • 2
  1. 1.Research Institute OTB, Section GIS-technologyDelft University of TechnologyDelftthe Netherlands
  2. 2.Weierstrass Institute for Applied Analysis and Stochastics, Research Group: Numerical Mathematics and Scientific ComputingBerlinGermany

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