We give sufficient conditions for a discrete set of points in any dimensional real hyperbolic space to have positive anchored expansion. The first condition is an bounded density property, ensuring not too many can accumulate large regions. second vacancy condition, effectively there much left vacant by the over These properties as easy corollary that stationary Poisson–Delaunay graphs expansio...

A wireless sensor network can be represented by a graph. While the network graph is extremely useful, it often exhibits undesired irregularity. Therefore, special treatment of the graph is required by a variety of network algorithms and protocols. In particular, many geometry-oriented algorithms depend on a type of subgraph called Delaunay triangulation. However, when location information is un...

A new O(nlog(n)) algorithm is presented for performing Delaunay triangulation of sets of 2D points. The novel component of the algorithm is a radially propagating sweep-hull (sequentially created from the radially sorted set of 2D points, giving a non-overlapping triangulation), paired with a final triangle flipping step to give the Delaunay triangluation. In empirical tests the algorithm runs ...

We use the generalized Weierstrass representation to analyze the asymptotic behavior of a constant mean curvature surface that locally arises from an ODE with a regular singularity. We show that if system is a perturbation of that of a Delaunay surface, then the corresponding constant mean curvature surface has a properly immersed end that is asymptotically Delaunay. Furthermore, that end is em...

Given a finite set of points in Rn and a radius parameter, we study the Čech, Delaunay–Čech, Delaunay (or alpha), and Wrap complexes in the light of generalized discrete Morse theory. Establishing the Čech and Delaunay complexes as sublevel sets of generalized discrete Morse functions, we prove that the four complexes are simple-homotopy equivalent by a sequence of simplicial collapses, which a...

We present an automatic algorithm to construct blocking scheme for multiblock structured meshes in 2D multiphase flow problems. Our solution is based on the concepts of medial axis and Delaunay triangulation. We show that the quality of the blocking scheme strongly depends on the quality of Delaunay triangulation. Therefore, well-known techniques and issues like Delaunay refinement and geometri...

Given a finite sampling P ⊂ R of an unknown surface S, surface reconstruction is concerned with the calculation of a model of S from P . The model can be represented as a smooth or a triangulated surface, and is expected to match S from a topological and geometric standpoints. In this survey, we focus on the recent developments of Delaunay based surface reconstruction methods, which were the fi...

We present an algorithmic framework for producing Delaunay triangulations of manifolds. The input to the algorithm is a set of sample points together with coordinate patches indexed by those points. The transition functions between nearby coordinate patches are required to be bi-Lipschitz with a constant close to 1. The primary novelty of the framework is that it can accommodate abstract manifo...