An accurate and robust algorithm for the in-sphere criterion for automated Delaunay-based tetrahe-dral grid generation

Numerical Grid Generation in Computational Field Simulations, Ed. M. Cross., B. K. Soni, J. F. Thompson, J. Hauser, P. R. Eiseman, Proceedings of the 6th International Conference, held at the University of Greenwich, pp.497-506, July 1998

MESHING
RESEARCH
CORNER

National Aerospace Laboratory NLR,
Anthony Fokkerweg 2,
1059 CM Amsterdam, Netherlands.

Abstract
In Delaunay-based grid generation algorithms the in-sphere criterion plays a central role. A accurate and robust algorithm for employing the in-sphere criterion is proposed. In the derivation of the circumcentre and radius of the circumscribing sphere of a tetrahedral element needed for the in- sphere criterion round-off errors and propagation errors are introduced. The new algorithm is designed such that these errors are minimized. Furthermore, it is shown that the in-sphere criterion can be made invariant for scaling tranformations.