Delaunay has shown that the Delaunay complex of a finite set of points P of Euclidean space R triangulates the convex hull of P , provided that P satisfies a mild genericity property. Voronoi diagrams and Delaunay complexes can be defined for arbitrary Riemannian manifolds. However, Delaunay’s genericity assumption no longer guarantees that the Delaunay complex will yield a triangulation; stron...

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...

For n + 1 disjoint flats of dimension k in H, we produce a Delaunay cell which is a generalization of the Delaunay simplex associated to n + 1 points in H. Combinatorially, these Delaunay cells resemble truncated n-dimensional simplices. For certain classes of arrangements of flats in H, we prove that these Delaunay cells can be glued together to form a Delaunay complex, with the result that al...

In this paper, we give the definition for the voronoi diagram and its dual graph – Delaunay triangulation for 3D cuboids. We prove properties of the 3D Delaunay triangulation, and provide algorithms to construct and update the Delaunay triangulation. The Delaunay triangulation data structure is used to perform proximity searches for both static and kinetic cases. We describe experimental result...

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...

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...

Delaunay triangulationhas beenmuch used in such applicationsas volume rendering, shape representation, terrain modeling and so on. The main disadvantage of Delaunay triangulation is large computation time required to obtain the triangulation on an input points set. This time can be reduced by using more than one processor, and several parallel algorithms for Delaunay triangulation have been pro...