Computer Science – Computational Geometry
Scientific paper
2008-02-14
SIAM J. Sci. Comput. 31, 6 (2010) 4497-4523
Computer Science
Computational Geometry
Content has been added to experimental results section. Significant edits in introduction and in summary of current and previo
Scientific paper
10.1137/090748214
Meshes composed of well-centered simplices have nice orthogonal dual meshes (the dual Voronoi diagram). This is useful for certain numerical algorithms that prefer such primal-dual mesh pairs. We prove that well-centered meshes also have optimality properties and relationships to Delaunay and minmax angle triangulations. We present an iterative algorithm that seeks to transform a given triangulation in two or three dimensions into a well-centered one by minimizing a cost function and moving the interior vertices while keeping the mesh connectivity and boundary vertices fixed. The cost function is a direct result of a new characterization of well-centeredness in arbitrary dimensions that we present. Ours is the first optimization-based heuristic for well-centeredness, and the first one that applies in both two and three dimensions. We show the results of applying our algorithm to small and large two-dimensional meshes, some with a complex boundary, and obtain a well-centered tetrahedralization of the cube. We also show numerical evidence that our algorithm preserves gradation and that it improves the maximum and minimum angles of acute triangulations created by the best known previous method.
Guoy Damrong
Hirani Anil N.
Ramos Edgar
VanderZee Evan
No associations
LandOfFree
Well-Centered Triangulation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Well-Centered Triangulation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Well-Centered Triangulation will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-37447