A Comparison Of Triangle Quality Measures

Proceedings, 10th International Meshing Roundtable, Sandia National Laboratories, pp.327-340, October 7-10 2001

MESHING
RESEARCH
CORNER

10th International Meshing Roundtable
Newport Beach, California, U.S.A.
October 7-10, 2001

Timothy J. Baker
Mechanical and Aerospace Engineering Department
E-Quad, Princeton University
Princeton, NJ 08540, USA
Email: baker@tornado.princeton.edu

Philippe P. Pebay
MAPLY-INSA, UMR CNRS-5585, Leonard de Vinci
20 av. Einstein, 69621 Villeurbanne Cedex, France
Email: philippe.pebay@insa-lyon.fr

Abstract
We investigate several of the more commonly used triangle quality measures, and provide proofs to verify that they do exhibit the expected extremal properties. In particular, we examine the asymptotic behavior of these measures and derive a number of useful results. We also show that some of the quality measures are equivalent, in the sense of displaying the same extremal and asymptotic behavior, and that it is therefore possible to achieve a concise classification of triangle quality measures.

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