On flip graph connectivity

Abstract

This paper first surveys some combinatoric results as well as algorithms concerning flip graph connectivity of a finite set S in $R^3$. The algorithm we present uses a local transformation procedure to construct a tetrahedrization of a set of n three-dimensional points that is pseudo-locally optimal with respect to the sphere criterion. We also present some combinatorial results on extremum problems about the number of tetrahedra in a terahedrization of n points in general position in $R^3$.