University of Illinois Urbana-Champaign

Well-Centered Triangulation

VanderZee, Evan; Hirani, Anil N.; Guoy, Damrong; Ramos, Edgar

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Well-Centered Triangulation.pdf

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https://hdl.handle.net/2142/11425

Description

Title
Well-Centered Triangulation
Author(s)
  • VanderZee, Evan
  • Hirani, Anil N.
  • Guoy, Damrong
  • Ramos, Edgar
Issue Date
2008-02
Keyword(s)
algorithms
Date of Ingest
2009-04-22T20:59:37Z
Abstract
Well-centered meshes (meshes composed of well-centered simplices) have the advantage of having nice orthogonal dual meshes (the dual Voronoi diagram), which is useful for certain numerical algorithms that require or prefer such primal-dual mesh pairs. We present a characterization of a well-centered n-simplex and introduce a cost function that quantifies well-centeredness of a simplicial mesh. We investigate some properties of the cost function and describe an iterative algorithm for optimizing the cost function. The algorithm can transform a given triangulation into a well-centered one by moving the interior vertices while keeping the mesh connectivity and boundary vertices fixed. We show the results of applying our algorithm to small, large, and graded two-dimensional meshes as well as one tiny three-dimensional mesh and a small tetrahedralization of the cube. Also, we prove for planar meshes that the optimal triangulation with respect to the cost function is the minmax angle triangulation.
Type of Resource
text
Genre of Resource
Technical Report
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http://hdl.handle.net/2142/11425
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