Flipping to robustly delete a vertex in a delaunay tetrahedralization

Authors:
Hugo Ledoux;Christopher M. Gold;George Baciu
Affiliations:
GIS Research Centre, School of Computing, University of Glamorgan, Pontypridd, Wales, UK;GIS Research Centre, School of Computing, University of Glamorgan, Pontypridd, Wales, UK;Department of Computing, Hong Kong Polytechnic University, Hong Kong
Venue:
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and its Applications - Volume Part I
Year:
2005

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Abstract

We discuss the deletion of a single vertex in a Delaunay tetrahedralization (DT). While some theoretical solutions exist for this problem, the many degeneracies in three dimensions make them impossible to be implemented without the use of extra mechanisms. In this paper, we present an algorithm that uses a sequence of bistellar flips to delete a vertex in a DT, and we present two different mechanisms to ensure its robustness.