Four constructions of constant mean curvature (CMC) hypersurfaces in Sn+1 are given, which should be considered analogues of ‘classical’ constructions that are possible for CMC hypersurfaces in Euclidean space. First, Delaunay-like hypersurfaces, consisting roughly of a chain of hyperspheres winding multiple times around an equator, are shown to exist for all the values of the mean curvature. S...

Delaunay tessellation is applied for the first time in the analysis of protein structure. By representing amino acid residues in protein chains by C alpha atoms, the protein is described as a set of points in three-dimensional space. Delaunay tessellation of a protein structure generates an aggregate of space-filling irregular tetrahedra, or Delaunay simplices. The vertices of each simplex defi...

A study is conducted of the influence of microscale geometric and physical randomness on effective moduli of a continuum approximation of disordered microstruetures. A particular class of microstructures investigated is that of planar Delaunay networks made up of linear elastic rods connected by joints. Three types of networks are considered: Delaunay networks with random geometry and random sp...

This paper proposes a routing strategy for wireless sensor networks that is valid even when the sensor nodes are distributed nonuniformly. Energy efficiency is the most important consideration in wireless sensor networks; hence, global communication should be achieved by combinations of local messages. We first propose a new underlying graph called the almost Delaunay planar net, which can be c...

Greedy routing protocols for wireless sensor networks (WSNs) are fast and efficient but in general cannot guarantee message delivery. Hence researchers are interested in the problem of embedding WSNs in low dimensional space (e.g., R) in a way that guarantees message delivery with greedy routing. It is well known that Delaunay triangulations are such embeddings. We present the algorithm FindAng...

Delaunay triangulations have been well-studied and numerous implementations have been proposed and instantiated over the years, but it was not until recently (2008) that a method for computing the Delaunay triangulation has been performed on the GPU. Even still, it was still presented as a hybrid method, utilizing the CPU in conjunction with the GPU. The dual of the Delaunay triangulation, the ...

Minimum spanning tree problem is a very important problem in VLSI CAD. Given n points in a plane, a minimum spanning tree is a set of edges which connects all the points and has a minimum total length. A naive approach enumerates edges on all pairs of points and takes at least (n 2) time. More eecient approaches nd a minimum spanning tree only among edges in the Delaunay triangulation of the po...

For hydrologic applications, terrain models should have few local minima, and drainage lines should coincide with edges. We show that triangulating a set of points with elevations such that the number of local minima of the resulting terrain is minimized is NP-hard for degenerate point sets. The same result applies when there are no degeneracies for higher-order Delaunay triangulations. Two heu...

Facial features determination is essential in many applications such as personal identification, 3D face modeling and model based video coding. Fast and accurate facial feature extraction is still a filed to be explored. In this paper, an automatic extracting algorithm is developed to locate “key points” of facial features. The Delaunay Triangulation/Voronoi Diagram technique well known in comp...

We modify the incremental algorithm for computing Voronoi diagrams in the Euclidean metric proposed by Ohya, Iri and Murota 6] in order to obtain an algorithm for computing Voronoi diagrams (resp. Delaunay triangulations) in Man-hattan and Maximum metric, that is rather simply to implement. We generalize the notions of \Voronoi diagram" and \Delaunay triangulation" in such a way that these stru...