DELAUNAY STABILITY VIA PERTURBATIONS

Delaunay stability via perturbations

We present an algorithm that takes as input a finite point set in R, and performs a perturbation that guarantees that the Delaunay triangulation of the resulting perturbed point set has quantifiable stability with respect to the metric and the point positions. There is also a guarantee on the quality of the simplices: they cannot be too flat. The algorithm provides an alternative tool to the we...

Perturbations for Delaunay and weighted Delaunay 3D triangulations

The Delaunay triangulation and the weighted Delaunay triangulation are not uniquely defined when the input set is degenerate. We present a new symbolic perturbation that allows to always define these triangulations in a unique way, as soon as the points are not all coplanar. No flat tetrahedron exists in the defined triangulation. The perturbation scheme is easy to code; It is implemented in cg...

The Stability of Delaunay Triangulations

We introduce a parametrized notion of genericity for Delaunay triangulations which, in particular, implies that the Delaunay simplices of δ-generic point sets are thick. Equipped with this notion, we study the stability of Delaunay triangulations under perturbations of the metric and of the vertex positions. We quantify the magnitude of the perturbations under which the Delaunay triangulation r...

Inscribable polytopes via Delaunay triangulations

Structure alignment via Delaunay tetrahedralization.

A novel protein structure alignment technique has been developed reducing much of the secondary and tertiary structure to a sequential representation greatly accelerating many structural computations, including alignment. Constructed from incidence relations in the Delaunay tetrahedralization, alignments of the sequential representation describe structural similarities that cannot be expressed ...