The construction of anisotropic triangulations is desirable for various applications, such as the numerical solving of partial differential equations and the representation of surfaces in graphics. To solve this notoriously difficult problem in a practical way, we introduce the discrete Riemannian Voronoi diagram, a discrete structure that approximates the Riemannian Voronoi diagram. This struc...

A localized Delaunay triangulation owns the following interesting properties in a wireless ad hoc setting: it can be built with localized information, the communication cost imposed by control information is limited and it supports geographical routing algorithms that offer guaranteed convergence. This paper presents a localized algorithm that builds a graph called planar localized Delaunay tri...

An algorithm based on spatial tessellation and approximation of each triangle patch in the Delaunay triangulation (with smoothness constraints) by a bivariate polynomial is advanced to construct a high resolution (HR) high quality image from a set of low resolution (LR) frames. This algorithm, followed by post filtering, is suitable for real-time image sequence processing because of the fast ex...

Let S be a finite set of points on the unit-sphere S. In 1987, Raghavan suggested that the convex hull of S is a Euclidean t-spanner, for some constant t. We prove that this is the case for t = 3π(π/2 + 1)/2. Our proof consists of generalizing the proof of Dobkin et al. [2] from the Euclidean Delaunay triangulation to the spherical Delaunay triangulation.

Delaunay triangulation exposes highly irregular computation patterns, which imposes challenge on high-level language designers and implementors, in terms of adequate expressiveness of the language and eecient implementation of supported language features. This paper reports an implementation of divide-and-conquer parallel Delaunay triangulation with High Performance Fortran (HPF), a high-level ...

This paper presents a novel algorithm for volumetric reconstruction of objects from planar sections using Delaunay triangulation, which solves the main problems posed to models defined by reconstruction, particularly from the viewpoint of producing meshes that are suitable for interaction and simulation tasks. The requirements for these applications are discussed here and the results of the met...

Consider a weighted graph G where vertices are points in the plane and edges are line segments. The weight of each edge is the Euclidean distance between its two endpoints. A routing algorithm on G has a competitive ratio of c if the length of the path produced by the algorithm from any vertex s to any vertex t is at most c times the length of the shortest path from s to t in G. If the length o...

We consider a Delaunay triangulation defined on n points distributed independently and uniformly on a planar compact convex set of positive volume. Let the stabbing number be the maximal number of intersections between a line and edges of the triangulation. We show that the stabbing number Sn is Θ( √ n) in the mean, and provide tail bounds for P{Sn ≥ t √ n}. Applications to planar point locatio...

Terrains are often modeled by triangulations and one of the criteria is that: triangulation should have “nice shape”. Delaunay triangulation is a good way to formalize nice shape. Another criterion is slope fidelity in terrains. In natural terrains there are no abrupt changes in slope. A triangulation for a terrain should use triangles of nice shape and have slope fidelity. To achieve these cha...

We describe a randomized algorithm that, given a set P of points in the plane, computes the best location to insert a new point p, such that the Delaunay triangulation of P ∪ {p} has the largest possible minimum angle. The expected running time of our algorithm is at most cubic, improving the roughly quartic time of the best previously known algorithm. It slows down to slightly super-cubic if w...