Element Quality: Skew

[claireroche]

1. I think the skew quality over hexahedral element is not computed accurately.

In quality/src/HexQuality.cpp file:
https://github.com/LIHPC-Computational-Geometry/gmds/blob/main/quality/src/HexQuality.cpp
The skew() is not computed on normalized principal axes X1, X2, and X3 as it should according to Sandi'as report on Verdict geometric quality library (https://www.osti.gov/servlets/purl/901967).
I don't know if it is wanted or not. In the current state, the skewness of an element is not necessary between 0 and 1.

2. It Could be useful to add skew computation on quads too, in the QuadQuality class, as described in Sandia's Verdict library.

[claireroche]

Example to add in HexEvalTestSuite.h:
(https://github.com/LIHPC-Computational-Geometry/gmds/blob/main/quality/tst/HexEvalTestSuite.h)

HexQuality hq = HexQuality::build(math::Point(188,28,29), math::Point(191,28,29), math::Point(191,31,26), math::Point(188,31,26), math::Point(188,27,28), math::Point(191,27,28), math::Point(191,29,25), math::Point(188,29,25)); std::cout << "Skew: " << hq.skew() << std::endl;

The returned value is 12, while the hexahedron is shaped as illustrated below.

ROCHE_TIKZ.pdf

[nicolaslg]

Thanks for the report !

• I concur that the implementation is faulty
• we should add the skew for the quads