Optimality of the Delaunay triangulation in \(\mathbb{R}^ d\)
The author defines a power function for a triangulation of a finite point set in \(\mathbb{R}^ d\) and shows that it is minimized by the Delaunay triangulation. From this he obtains a number of new optimality results for Delaunay triangulations and generalizes some results previously known for the plane to \(\mathbb{R}^ d\). E.g. it is shown that a triangulation in \(\mathbb{R}^ d\) is the Delaunay triangulation iff each simplex is self- centered, i.e. contains the center of its circumsphere.
scientific article; zbMATH DE number 644706
scientific article