A New Approach Towards Delaunay-Conformity in 3 Dimensions

Proceedings, 9th International Meshing Roundtable, Sandia National Laboratories, pp.283-292, October 2000

MESHING
RESEARCH
CORNER

Philippe P. Pébay
INRIA-Rocquencourt, Gamma Project
BP 105, 78153 Le Chesnay Cedex, France
MAPLY-INSA, UMR CNRS-5585, Bat. 401
20 av. Einstein, 69621 Villeurbanne Cedex, France
Email: philippe.pebay@insa-lyon.fr
URL: http://vigemale.insa-lyon.fr/~pebay

Abstract
This communication follows [Pébay, 98] and presents a new approach for redefining a priori a three-dimensional field of constraints represented by a a set of edges and triangular faces. It is shown that, surprisingly, two-dimensional a priori Delaunay-conformity results do not extend naturally to segments in three dimensions. Consequently, a new strong Delaunay-conformity theorem is detailed, allowing to decide whether or not a segment will appear in any Delaunay-triangulation of the convex hull of the related set of vertices. This result provides new perspectives for triangular faces redefinition. In particular, a new algorithm is proposed and a representative set of examples emphasizes its reliability and efficiency.

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