TD-Delaunay graphs, where TD stands for triangular distance, is a variation of the classical Delaunay triangulations obtained from a specific convex distance function [5]. In [2] the authors noticed that every triangulation is the TD-Delaunay graph of a set of points in R, and conversely every TD-Delaunay graph is planar. It seems natural to study the generalization of this property in higher d...

We introduce a novel learning-based, visibility-aware, surface reconstruction method for large-scale, defect-laden point clouds. Our approach can cope with the scale and variety of cloud defects encountered in real-life Multi-View Stereo (MVS) acquisitions. relies on 3D Delaunay tetrahedralization whose cells are classified as inside or outside by graph neural network an energy model solvable c...

The Delaunay tessellation of several sets of real and simplified model protein structures has been used to explore graph theoretic properties of residue contact networks. The system of contacts defined by residues joined by edges in the Delaunay simplices can be thought of as a graph or network and analyzed using techniques from elementary graph theory and the theory of complex networks. Such a...

In this paper we describe a generic C++ adaptor, that adapts a 2-dimensional triangulated Delaunay graph and to the corresponding a Voronoi diagram, represented as a doubly connected edge list (DCEL) data structure. Our adaptor has the ability to automatically eliminate, in a consistent manner, degenerate features of the Voronoi diagram, that are artifacts of the requirement that Delaunay graph...

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...

This article studies the construction of self-stabilizing topologies for distributed systems. While recent research has focused on chain topologies where nodes need to be linearized with respect to their identifiers, we explore a natural and relevant 2-dimensional generalization. In particular, we present a local self-stabilizing algorithm DStab which is based on the concept of ‘‘local Delaunay...

This paper discusses a problem for determining whether a given plane graph is a Delaunay graph, i.e., whether it is topologically equivalent to a Delaunay triangulation. There exists a theorem which characterizes Delaunay graphs and yields a polynomial time algorithm for the problem only by solving a certain linear inequality system. The theorem was proved by Rivin based on arguments of hyperbo...

Consider the Delaunay graph and the Voronoi tessellation constructed with respect to a planar Poisson point process. The sequence of nuclei of the Voronoi cells that are crossed by a line deenes a path on the Delaunay graph. We show that the evolution of this path is governed by a Markov chain. We study the ergodic properties of the chain and nd its stationary distribution. As a corollary we ob...