|We are often required to generate a Delaunay mesh whose element size is within a constant factor of a control spacing function, i.e., well-conformed, in addition to the fact that each mesh element has small aspect ratio, i.e., well-shaped. However, generating wellshaped Delaunay meshes is an open problem for a long time. Observe that slivers have small radius-edge ratio thus the Delaunay trian...

How do errors of measurement a ect a Delaunay triangulation of the measured points? We are given an `exact' and a `measured' set of points P and P 0, respectively, in the plane. The error of measurement is bounded above by ". Obviously, two Delaunay triangulations T of P and T 0 of P 0 may di er in their topologies. However, for certain edges of T we can guarantee that any `measured' triangulat...

In two dimensions, a constrained Delaunay triangulation (CDT) respects a set of segments that constrain the edges of the triangulation, while still maintaining most of the favorable properties of ordinary Delaunay triangulations (such as maximizing the minimum angle). CDTs solve the problem of enforcing boundary conformity—ensuring that triangulation edges cover the boundaries (both interior an...

The technique of Delaunay refinement has been recognized as a versatile tool to generate Delaunay meshes of a variety of geometries. Despite its usefulness, it suffers from one lacuna that limits its application. It does not scale well with the mesh size. As the sample point set grows, the Delaunay triangulation starts stressing the available memory space which ultimately stalls any effective p...

We study rotational surfaces with constant Minkowski Gaussian curvature and mean in a 3-dimensional normed space rotationally symmetric norm. have generalization of the catenoid, pseudo-sphere Delaunay surfaces.

Some of the first routing algorithms for geographically aware wireless networks used the Delaunay triangulation among the network’s nodes as the underlying connectivity graph [4]. These solutions were considered impractical, however, because in general the Delaunay triangulation may contain arbitrarily long edges, and because calculating the Delaunay triangulation generally requires a global vi...

are constant mean curvature (CMC) surfaces of revolution, and they are translationally periodic. By a rigid motion and homothety of R we may place the Delaunay surfaces so that their axis of revolution is the x1-axis and their constant mean curvature is H = 1 (henceforth we assume this). We consider the profile curve in the half-plane {(x1, 0, x3) ∈ R |x3 > 0} that gets rotated about the x1-axi...

Several localized routing protocols [1] guarantee the delivery of the packets when the underlying network topology is the Delaunay triangulation of all wireless nodes. However, it is expensive to construct the Delaunay triangulation in a distributed manner. Given a set of wireless nodes, we more accurately model the network as a unit-disk graph UDG , in which a link in between two nodes exist o...

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...