Chew’s second Delaunay refinement algorithm with offcenter Steiner vertices leads to practical improvement over Ruppert’s algorithm for quality mesh generation, but the most thorough theoretical analysis is known only for Ruppert’s algorithm. A detailed analysis of Chew’s second Delaunay refinement algorithm with offcenters is given, improving the guarantee of well-graded output for any minimum...

In this paper we determine the stretch factor of the L1-Delaunay and L∞-Delaunay triangulations, and we show that this stretch is √ 4 + 2 √ 2 ≈ 2.61. Between any two points x, y of such triangulations, we construct a path whose length is no more than

It is shown that it is an NP-complete problem to determine whether a Delaunay trian-gulation or an inscribable polyhedron has a Hamiltonian cycle. It is also shown that there exist nondegenerate Delaunay triangulations and simplicial, inscribable polyhedra without 2-factors. Irvine through an allocation of computer resources.

This paper presents a new combinatorial algorithm for surface reconstruction. It is an interactive and incremental algorithm based on a deenition of the strength of a Delaunay triangle. Local topology of a 2D manifold is enforced while Delaunay triangles are inserted into the partially reconstructed surface in the decreasing order of their strength.

We present a definition of a pointed Delaunay pseudotriangulation of a simple polygon. We discuss why our definition is reasonable. Our approach will be motivated from maximal locally convex functions, and extends the work of Aichholzer et al.[1]. Connections between the polytope of the pointed pseudotriangulations and the Delaunay pseudo-triangulation will be given.