Geometric spanners can be used for efficient routing in wireless ad hoc networks. Computation of existing spanners for ad hoc networks primarily focused on geometric properties without considering network requirements. In this paper we propose a new spanner called Constrained Delaunay Triangulation (CDT) which considers both geometric properties and network requirements. The CDT is formed by in...

Given a set S of line segments in the plane, we introduce a new family of partitions of the convex hull of S called elementary partitions of S. The set of faces of such a partition is a maximal set of disjoint triangles that cut S at, and only at, their vertices. Surprisingly, several properties of point set triangulations extend to elementary partitions. Thus, the number of their faces is an i...

One of most famous theorems in computational geometry is the duality between Voronoi diagram and Delaunay triangulation in Euclidean space. This paper proposes an extension of that theorem to the Voronoi diagram and Delaunay-type triangulation in dually at space. In that space, the Voronoi diagram and the triangulation can be computed e ciently by using potential functions. We also propose high...

We present algorithms to produce Delaunay meshes from arbitrary triangle meshes by edge flipping and geometrypreserving refinement and prove their correctness. In particular we show that edge flipping serves to reduce mesh surface area, and that a poorly sampled input mesh may yield unflippable edges necessitating refinement to ensure a Delaunay mesh output. Multiresolution Delaunay meshes can ...

Voronoi diagram and its geometric dual, the Delaunay triangulation, both are practical geometric constructions which have been applied extensively in spatial analysis. Considering the low efficiency of the algorithm of indirectly building Voronoi diagram, this paper proposes an improved Voronoi diagram generation algorithm based on Delaunay triangulation of randomly distributed points in the Eu...

We present the theory and implementation for a new automatic adaptive h-re nement and -dere nement method for twoand three-dimensional elliptic problems. An exact lower error bound for dere nement is obtained theoretically in terms of the nite element solution, complementing the various known upper error bounds for re nement. These error bounds are used to determine where to insert and/or remov...