In the Euclidean plane, a Delaunay triangulation can be characterized by the requirement that the circumcircle of each triangle be empty of vertices of all other triangles. For triangulating a surface S in R3, the Delaunay paradigm has typically been employed in the form of the restricted Delaunay triangulation, where the empty circumcircle property is defined by using the Euclidean metric in R...

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...

In the pursuit of realistic terrain models, Gudmundsson, Hammar, and van Kreveld introduced higher-order Delaunay triangulations. A usual Delaunay triangulation is a 0order Delaunay triangulation, thus unique for a non-degenerate point set, while order-k Delaunay triangulations can be non-unique when k ≥ 1. In this work, we propose an algorithm to list all order-k Delaunay triangulations of a g...

Voronoi diagram and its geometric dual, the Delaunay triangulation, both are practical geometric constructions which have been applied extensively in spatial analysis. Considering the low efficiency of the algorithm of indirectly building Voronoi diagram, this paper proposes an improved Voronoi diagram generation algorithm based on Delaunay triangulation of randomly distributed points in the Eu...

Comparisons of five data reduction methods associated with dynamic TIN models were conducted. All methods were applied to real world Light Detection and Ranging (LIDAR) topographic data. Data reduction is based on point selection by thresholding in dynamic Delaunay triangulation together with random point selection. The triangulation criteria used include Delaunay and hybrids of Delaunay and da...

This paper present how space of spheres and shelling can be used to delete e ciently a point from d-dimensional triangulation. In 2-dimension, if k is the degree of the deleted vertex, the complexity is O(k log k), but we notice that this number apply only to low cost operations; time consuming computations are done only a linear number of times. This algorithm can be viewed as a variation of H...

An intrinsic discrete Laplace-Beltrami operator on simplicial surfaces S proposed in [2] was established via an intrinsic Delaunay tessellation on S. Up to now, this intrinsic Delaunay tessellations can only be computed by an edge flipping algorithm without any provable complexity analysis. In the paper, we show that the intrinsic Delaunay triangulation can be obtained from a duality of geodesi...

We present an automatic algorithm to construct blocking scheme for multiblock structured meshes in 2D multiphase flow problems. Our solution is based on the concepts of medial axis and Delaunay triangulation. We show that the quality of the blocking scheme strongly depends on the quality of Delaunay triangulation. Therefore, well-known techniques and issues like Delaunay refinement and geometri...