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Higher-Order Triangular-Distance Delaunay Graphs: Graph-Theoretical Properties [PDF]
Computational Geometry: Theory and Applications, 2015 We consider an extension of the triangular-distance Delaunay graphs (TD-Delaunay) on a set $P$ of points in the plane. In TD-Delaunay, the convex distance is defined by a fixed-oriented equilateral triangle $\triangledown$, and there is an edge between two points in $P$ if and only if there is an empty homothet of $\triangledown$ having the two points ...
Anil Maheshwari +2 more
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Delaunay Graph-Based Moving Mesh Method With Damping Functions [PDF]
Chinese Journal of Aeronautics, 2018 The fluid–structure interaction and aerodynamic shape optimization usually involve the moving or deforming boundaries, thus the dynamic mesh techniques are the key techniques to cope with such deformation.
Ning Zhao, Ning Qin
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On locally Delaunay geometric graphs
Proceedings of the twentieth annual symposium on Computational geometry, 2004A geometric graph is a simple graph G=(V,E) with an embedding of the set V in the plane such that the points that represent V are in general position. A geometric graph is said to be k-locally Delaunay (or a Dk-graph) if for each edge (u,v) ∈ E there is a (Euclidean) disc d that contains u and v but no other vertex of G that is within k hops from u or ...
Rom Pinchasi, Shakhar Smorodinsky
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The Description of Delaunay Triangulated Graph
Advanced Science and Technology Letters, 2014The image grid occupies very important position in the graphics. In subdivision method of the image, the triangle mesh subdivision is a commonly used method. In this paper, the concentration of commonly used method of triangular mesh is described, and applied to the flame image grid.
Zhenhua Wei, Xiaoyuan Yan
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A Uniqueness Theorem for Delaunay Graphs
Siberian Mathematical Journal, 2013A graph is called a Delauney graph if its edges are segments whose orthogonal hyperplanes through their midpoints form the faces of a Voronoi domain. The author proves a necessary and sufficient condition for two isomoprphic Delauney graphs to be congruent. The proof uses an inductive argument on the congruence of isomorphic pairs of Delauney polyhedra
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Polytope kernel density estimates on Delaunay graphs
2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2011We present a polytope-kernel density estimation (PKDE) methodology that allows us to perform exact mean-shift updates along the edges of the Delaunay graph of the data. We discuss explicit and implicit constructions of such a PKDE, where in the implicit construction one can exploit a smoother kernel such as the standard isotropic Gaussian.
Erhan Bas, Deniz Erdogmus
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Realistic Indoor Trajectory Generation Based on Delaunay Graph
2021 IEEE International Conference on Big Data and Smart Computing (BigComp), 2021Trajectory analysis can be useful to understand pedestrian behaviour in indoor environments. Collecting real data however can be difficult and time consuming, and many publicly available data sets and trajectory generation methods focus on outdoor scenarios.
Passaniti Davide +2 more
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On spanning properties of various Delaunay graphs
2012 Ninth International Symposium on Voronoi Diagrams in Science and Engineering, 2012A geometric graph G is a graph whose vertices are points in the plane and whose edges are line segments weighted by the Euclidean distance between their endpoints. In this setting, a t-spanner of G is a connected spanning subgraph G' with the property that for every pair of vertices x, y, the shortest path from x to y in G' has weight at most L ≥ 1 ...
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A Self-stabilizing and Local Delaunay Graph Construction
2009This paper 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 go a step further and explore a natural 2-dimensional generalization.
Riko Jacob +3 more
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Kinetic Pie Delaunay Graph and Its Applications
2012We construct a new proximity graph, called the Pie Delaunay graph, on a set of n points which is a super graph of Yaograph and Euclidean minimum spanning tree (EMST). We efficiently maintain the PieDelaunaygraph where the points are moving in the plane.
Mohammad Ali Abam +2 more
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