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Well-Centered Triangulation

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Title: Well-Centered Triangulation
Author(s): VanderZee, Evan; Hirani, Anil N.; Guoy, Damrong; Ramos, Edgar
Subject(s): algorithms
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.
Issue Date: 2008-02
Genre: Technical Report
Type: Text
Other Identifier(s): UIUCDCS-R-2008-2936
Rights Information: You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) days from the most recent time that you verified that this technical report is still available from the University of Illinois at Urbana-Champaign Computer Science Department under terms that include this permission. All other rights are reserved by the author(s).
Date Available in IDEALS: 2009-04-22

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