On shape Delaunay tessellations

Parallel algorithms for planar and spherical Delaunay construction with an application to centroidal Voronoi tessellations

A new algorithm, featuring overlapping domain decompositions, for the parallel construction of Delaunay and Voronoi tessellations is developed. Overlapping allows for the seamless stitching of the partial pieces of the global Delaunay tessellations constructed by individual processors. The algorithm is then modified, by the addition of stereographic projections, to handle the parallel construct...

A systematic review of algorithms with linear-time behaviour to generate Delaunay and Voronoi tessellations

Triangulations and tetrahedrizations are important geometrical discretization procedures applied to several areas, such as the reconstruction of surfaces and data visualization. Delaunay and Voronoi tessellations are discretization structures of domains with desirable geometrical properties. In this work, a systematic review of algorithms with linear-time behaviour to generate 2D/3D Delaunay an...

Large Cells in Poisson-Delaunay Tessellations

It is proved that the shape of the typical cell of a Delaunay tessellation, derived from a stationary Poisson point process in d-dimensional Euclidean space, tends to the shape of a regular simplex, given that the volume of the typical cell tends to infinity. This follows from an estimate for the probability that the typical cell deviates by a given amount from regularity, given that its volume...

Study on Delaunay tessellations of 1-irregular cuboids for 3D mixed element meshes

Mixed elements meshes based on the modified octree approach contain several co-spherical point configurations. While generating Delaunay tessellations to be used together with the finite volume method, it is not necessary to partition them into tetrahedra; co-spherical elements can be used as final elements. This paper presents a study of all co-spherical elements that appear while tessellating...

Gibbs Delaunay tessellations with geometric hardcore conditions