Topic
Delaunay triangulation
About: Delaunay triangulation is a research topic. Over the lifetime, 5816 publications have been published within this topic receiving 126615 citations. The topic is also known as: Delone triangulation.
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TL;DR: The results on the influence graph are used to improve the expected randomized complexity of algorithms from O(n log n) to O( n log* n) in some cases.
Abstract: We use here the results on the influence graph to adapt them for particular cases where additional information is available. In some cases, it is possible to improve the expected randomized complexity of algorithms from O(n log n) to O(n log* n). This technique applies in the following applications: triangulation of a simple polygon, skeleton of a simple polygon, Delaunay triangulation of points knowing the EMST (euclidean minimum spanning tree).
54 citations
TL;DR: In this paper, the authors describe a numerical framework for reliably and robustly simulating the different kinematic conditions exhibited by granular materials while spreading -from a stagnant condition, when the material is at rest, to a transition to granular flow, and back to a deposit profile.
54 citations
TL;DR: In this article, the authors describe a method for efficiently computing parallel transport of tangent vectors on curved surfaces, or more generally, any vector-valued data on a curved manifold.
Abstract: This article describes a method for efficiently computing parallel transport of tangent vectors on curved surfaces, or more generally, any vector-valued data on a curved manifold. More precisely, it extends a vector field defined over any region to the rest of the domain via parallel transport along shortest geodesics. This basic operation enables fast, robust algorithms for extrapolating level set velocities, inverting the exponential map, computing geometric medians and Karcher/Frechet means of arbitrary distributions, constructing centroidal Voronoi diagrams, and finding consistently ordered landmarks. Rather than evaluate parallel transport by explicitly tracing geodesics, we show that it can be computed via a short-time heat flow involving the connection Laplacian. As a result, transport can be achieved by solving three prefactored linear systems, each akin to a standard Poisson problem. To implement the method, we need only a discrete connection Laplacian, which we describe for a variety of geometric data structures (point clouds, polygon meshes, etc.). We also study the numerical behavior of our method, showing empirically that it converges under refinement, and augment the construction of intrinsic Delaunay triangulations so that they can be used in the context of tangent vector field processing.
54 citations
TL;DR: Algorithms to implement fully dynamic and kinetic three-dimensional unconstrained Delaunay triangulations, where the time evolution of the triangulation is not only governed by moving vertices but also by a changing number of vertices are described.
54 citations
21 Sep 1992
TL;DR: An encoding structure for a HTIN is presented and an algorithm for its construction is described, which is a method for compression of spatial data and representation of a topographic surface at successively finer levels of detail.
Abstract: This article describes a new hierarchical model for representing a terrain. The model, called a Hierarchical Triangulated Irregular Network (HTIN), is a method for compression of spatial data and representation of a topographic surface at successively finer levels of detail. A HTIN is a hierarchy of triangle-based surface approximations, where each node, except for the root, is a triangulated irregular network refining a triangle face belonging to its parent in the hierarchy. In this paper we present an encoding structure for a HTIN and we describe an algorithm for its construction.
54 citations