The generation of high-quality staggered unstructured grids for computational simulation is considered; leading to the development of a new optimisation-based strategy for the construction of weighted ‘RegularPower’ tessellations appropriate for co-volume type numerical techniques. This new framework aims to extend the conventional Delaunay-Voronoi primal-dual structure; seeking to assemble gen...

This paper considers the problem of updating efficiently a Delaunay triangulation when vertices are moving under small perturbations. Its main contribution is a set of algorithms based on the concept of vertex tolerance. Experiment shows that it is able to outperform the naive rebuilding algorithm in certain conditions. For instance, when points, in two dimensions, are relocated by Lloyd’s iter...

The skeletal structures of solid objects play an important role in medical and industrial applications. Given a volumetrically sampled solid object, our method extracts a nice-looking skeletal structure represented as a polygon mesh. The purpose is to achieve a noise-robust extraction of the skeletal mesh from a real-world object obtained using a scanning technology such as the CT scan method. ...

The Delaunay triangulation (DT) is one of the most common and useful triangulations of point sets P in the plane. DT is not unique when P is degenerate, specifically when it contains quadruples of co-circular points. One way to achieve uniqueness is by applying a small (or infinitesimal) perturbation to P . We consider a specific perturbation of such degenerate sets, in which the coordinates of...

A new triangular mesh adaptivity algorithm for elliptic PDEs that combines a posteriori error estimation with centroidal Voronoi/Delaunay tessellations of domains in two dimensions is proposed and tested. The ability of the first ingredient to detect local regions of large error and the ability of the second ingredient to generate superior unstructured grids results in an mesh adaptivity algori...

Delaunay flip is an elegant, simple tool to convert a triangulation of a point set to its Delaunay triangulation. The technique has been researched extensively for full dimensional triangulations of point sets. However, an important case of triangulations which are not full dimensional is surface triangulations in three dimensions. In this paper we address the question of converting a surface t...

For a given lattice, we establish an equivalence involving a closed zone of the corresponding Voronoi polytope, a lamina hyperplane of the corresponding Delaunay partition and a quadratic form of rank 1 being an extreme ray of the corresponding L-type domain. 1991 Mathematics Subject classification: primary 52C07; secondary 11H55 An n-dimensional lattice determines two normal partitions of the ...