Planar Quadrangle Quality Measures: Is There Really A Choice ?

Proceedings, 11th International Meshing Roundtable, Sandia National Laboratories, pp.53-62, September 15-18 2002

MESHING
RESEARCH
CORNER

11th International Meshing Roundtable
Ithaca, New York, USA
September 15-18, 2002

Philippe P. Pebay Sandia National Laboratories,
MS 9051 PO Box 969, Livermore CA 94550, U.S.A.
pppebay@ca.sandia.gov

Abstract
In this article some new results are presented about planar quadrangle quality measures. On the one hand, a modification of the triangle quality measure based on the Frobenius norm is proposed, in order to comply with the case where the reference element is no longer equilateral, but a right isosceles triangle. Provided this modication, a natural use of the Frobenius norm for quadrangular elements is proposed. On the other hand, generalizations of two triangle quality measures, based on edge to inradius ratios, to planar quadrangles are proposed and justied, and their limitations, depending on user's expectations, are exhibited, justifying the use of a more complex quality measure.

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