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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Analysis of triangle quality measures


Authors: Philippe P. Pébay and Timothy J. Baker
Journal: Math. Comp. 72 (2003), 1817-1839
MSC (2000): Primary 32B25, 65M50; Secondary 51N20
Published electronically: January 8, 2003
MathSciNet review: 1986806
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Abstract: Several of the more commonly used triangle quality measures are analyzed and compared. Proofs are provided to verify that they do exhibit the expected extremal properties. The asymptotic behavior of these measures is investigated and a number of useful results are derived. It is shown 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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Additional Information

Philippe P. Pébay
Affiliation: Mechanical and Aerospace Engineering Department, E-Quad, Princeton University, New Jersey 08544
Email: pebay@harrier.princeton.edu Current E-mail address: pppebay@ca.sandia.gov

Timothy J. Baker
Affiliation: Mechanical and Aerospace Engineering Department, E-Quad, Princeton University, New Jersey 08544
Email: baker@tornado.princeton.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-03-01485-6
PII: S 0025-5718(03)01485-6
Keywords: Triangulation, surface triangulation, triangle quality, mesh quality
Received by editor(s): July 9, 2001
Received by editor(s) in revised form: December 21, 2001
Published electronically: January 8, 2003
Additional Notes: The first author was supported in part by CNRS, UMR 5585, France.
Article copyright: © Copyright 2003 American Mathematical Society