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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17 Jun 2007
TL;DR: A robust and efficient Lagrangian approach, which is called Delaunay deformable models, for modeling moving surfaces undergoing large deformations and topology changes, and brings a rigorous and efficient alternative to existing topology-adaptive mesh techniques such as T-snakes.
Abstract: In this paper, we propose a robust and efficient Lagrangian approach, which we call Delaunay deformable models, for modeling moving surfaces undergoing large deformations and topology changes. Our work uses the concept of restricted Delaunay triangulation, borrowed from computational geometry. In our approach, the interface is represented by a triangular mesh embedded in the Delaunay tetrahedralization of interface points. The mesh is iteratively updated by computing the restricted Delaunay triangulation of the deformed objects. Our method has many advantages over popular Eulerian techniques such as the level set method and over hybrid Eulerian-Lagrangian techniques such as the particle level set method: localization accuracy, adaptive resolution, ability to track properties associated to the interface, seamless handling of triple junctions. Our work brings a rigorous and efficient alternative to existing topology-adaptive mesh techniques such as T-snakes.
86 citations
Posted Content•
TL;DR: In this paper, the Delaunay triangulation of a set of points in the plane is computed by marching in a triangulating to determine the nearest neighbor of the query at each level, then the march restarts from that neighbor at the level below.
Abstract: We propose a new data structure to compute the Delaunay triangulation of a set of points in the plane. It combines good worst case complexity, fast behavior on real data, and small memory occupation.
The location structure is organized into several levels. The lowest level just consists of the triangulation, then each level contains the triangulation of a small sample of the levels below. Point location is done by marching in a triangulation to determine the nearest neighbor of the query at that level, then the march restarts from that neighbor at the level below. Using a small sample (3%) allows a small memory occupation; the march and the use of the nearest neighbor to change levels quickly locate the query.
86 citations
01 Jan 2008
TL;DR: A Delaunay refinement algorithm has been proposed that can mesh domains as general as piecewise smooth complexes and has a provable guarantee about topology, but certain steps are too expensive to make it practical.
Abstract: Recently a Delaunay refinement algorithm has been proposed that can mesh domains as general as piecewise smooth complexes [7]. This class includes polyhedra, smooth and piecewise smooth surfaces, volumes enclosed by them, and above all non-manifolds. In contrast to previous approaches, the algorithm does not impose any restriction on the input angles. Although this algorithm has a provable guarantee about topology, certain steps are too expensive to make it practical.
86 citations
12 Jul 2006
TL;DR: A centralized sensor deployment method, DT-Score, aims to maximize the coverage of a given sensing area with obstacles and can reach higher coverage than grid-based and random deployment methods with the increasing of deployable sensors.
Abstract: To obtain a satisfied performance of wireless sensor network, an adaptable sensor deployment method for various applications is essential. In this paper, we propose a centralized sensor deployment method, DT-Score, aims to maximize the coverage of a given sensing area with obstacles. The DT-Score consists of two phases. In the first phase, we use a contour-based deployment to eliminate the coverage holes near the boundary of sensing area and obstacles. In the second phase, a deployment method based on the Delaunay triangulation is applied for the uncovered regions. Before deploying a sensor, each candidate position generated from the current sensor configuration is scored by a probabilistic sensor detection model. A new sensor is placed to the position with the most coverage gains. According to the simulation results, DT-Score can reach higher coverage than grid-based and random deployment methods with the increasing of deployable sensors.
86 citations
TL;DR: Through the study of numerous examples of various characteristics, it is found that high-quality triangular element meshes are obtained by the proposed algorithm, and the mesh generation time bears a linear relationship with the number of elements/nodes of the triangulation.
Abstract: This paper investigates the possibility of integrating the two currently most popular mesh generation techniques, namely the method of advancing front and the Delaunay triangulation algorithm. The merits of the resulting scheme are its simplicity, efficiency and versatility. With the introduction of ‘non-Delaunay’ line segments, the concept of using Delaunay triangulation as a means of mesh generation is clarified.
An efficient algorithm is proposed for the construction of Delaunay triangulations over non-convex planar domains. Interior nodes are first generated within the planar domain. These interior nodes and the boundary nodes are then linked up together to produce a valid triangulation. In the mesh generation process, the Delaunay property of each triangle is ensured by selecting a node having the smallest associated circumcircle. In contrast to convex domains, intersection between the proposed triangle and the domain boundary has to be checked; this can be simply done by considering only the ‘non-Delaunay’ segments on the generation front.
Through the study of numerous examples of various characteristics, it is found that high-quality triangular element meshes are obtained by the proposed algorithm, and the mesh generation time bears a linear relationship with the number of elements/nodes of the triangulation.
85 citations