Publication Details
Andrey Chernikov and Nikos Chrisochoides.
Published in SIAM Journal on Scientific Computing, Volume 31, No. 5, pages 3387 -- 3403, 2009
Abstract
Delaunay refinement is a popular mesh generation method which makes it possible to derive mathematical guarantees with respect to the quality of the elements. Traditional Delaunay refinement algorithms insert Steiner points in a small enumerable number (one or two) of specific positions inside circumscribed circles of poor quality triangles and on encroached segments. In this paper we prove that there exist entire two-dimensional and one-dimensional regions that can be used for the insertion of Steiner points (innumerable number of choices) while the guarantees on mesh quality can be preserved. This result opens up the possibility to use multiple point placement strategies, all covered by a single proof. In addition, the parallelization of this generalized algorithm immediately implies the parallelization for each individual point placement method.
