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A-priori Delaunay-conformity

Pebay, Philippe P. and Pascal J. Frey

Proceedings, 7th International Meshing Roundtable, Sandia National Lab, pp.321-333, October 1998

INTERNATIONAL
MESHING
ROUNTABLE

7th International Meshing Roundtable
October 26-28, 1998
Dearborn, Michigan, USA

INRIA, Gamma Project, Rocquencourt
BP 105, 78153 Le Chesnay Gedex, France
INSA, L2MCS, Bat. 401 - Avenue A. Einstein
69621 Villeurbanne Cedex, France
E-mail : Philippe.Pebay@inria.fr

Abstract
This communication presents a method for redefining a priori a field of constraints represented in two dimensions by a set of edges, in three dimensions by a surface triangulation. The aim is to provide a resulting constraint, strongly Delaunay-conforming, (i.e., that will be bulit by any Delaunay triangulation of the convex hull of the associated set of vertices). We show that the two-dimensional problem can be easily solved, and hence, we give a classification of edges leading to a convergent algorithm. Although the classification extends to faces, an essential property vanishes in three dimensions, excluding a simple extrapolation of the method. Nevertheless, a heuristic algorithm, based on face subdivisions, governed by a geometric estimate and by means of edge swapping is given in three dimensions. Several examples emphasize the proposed method in two and three dimensions.

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