Well-Centered Triangulation

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

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

Description

Title

Well-Centered Triangulation

Author(s)

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

Issue Date

2008-02

Keyword(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.

Type of Resource

text

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

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