Parallel Delaunay Refinement with Off-Centers

Off-centers were recently introduced as an alternative type of Steiner points to circum-centers for computing size-optimal quality guaranteed Delaunay triangulations. In this paper, we study the depth of the off-center insertion hierarchy. We prove that Delaunay refinement with off-centers takes only O(log (L/h)) parallel iterations, where L is the diameter of the domain, and h is the smallest edge in the initial triangulation. This is an improvement over the previously best known algorithm that runs in O(log2(L/h)) iterations.

[1]  Herbert Edelsbrunner,et al.  Sink-insertion for mesh improvement , 2001, SCG '01.

[2]  Alper Üngör.  O.-Centers: A New Type of Steiner Points for Computing Size-Optimal Quality-Guaranteed Delaunay Triangulations , 2004, LATIN.

[3]  L. Paul Chew,et al.  Guaranteed-Quality Triangular Meshes , 1989 .

[4]  Herbert Edelsbrunner,et al.  Geometry and Topology for Mesh Generation , 2001, Cambridge monographs on applied and computational mathematics.

[5]  David Eppstein,et al.  Parallel Construction of Quadtrees and Quality Triangulations , 1993, Int. J. Comput. Geom. Appl..

[6]  Jim Ruppert,et al.  A new and simple algorithm for quality 2-dimensional mesh generation , 1993, SODA '93.

[7]  Martín Farach-Colton.  LATIN 2004: Theoretical Informatics , 2004, Lecture Notes in Computer Science.

[8]  Herbert Edelsbrunner,et al.  Geometry and Topology for Mesh Generation , 2001, Cambridge monographs on applied and computational mathematics.

[9]  John H. Reif,et al.  Parallel Computational Geometry: An Approach using Randomization , 2000, Handbook of Computational Geometry.

[10]  J. Shewchuk,et al.  Delaunay refinement mesh generation , 1997 .

[11]  Herbert Edelsbrunner,et al.  Sliver exudation , 1999, SCG '99.

[12]  W. Frey.  Selective refinement: A new strategy for automatic node placement in graded triangular meshes , 1987 .

[13]  Bharat K. Soni,et al.  Mesh Generation , 2020, Handbook of Computational Geometry.

[14]  Gary L. Miller,et al.  A time efficient Delaunay refinement algorithm , 2004, SODA '04.

[15]  David Eppstein,et al.  Provably Good Mesh Generation , 1994, J. Comput. Syst. Sci..

[16]  Scott A. Mitchell,et al.  Quality mesh generation in three dimensions , 1992, SCG '92.