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

摘要

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 minimised. Furthermore, it is shown that the in-sphere criterion can be made invariant for scaling tranformations.