Constrained Delaunay triangulations

Chew, L. Paul

doi:10.1145/41958.41981

Cited by 232 publications

(154 citation statements)

References 8 publications

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“…Observe that while a generic constrained triangulation was sufficient to perform validation and repair in our original work (Arroyo Ohori et al 2012), here a constrained Delaunay triangulations (CDT) is required. A CDT is a triangulation for which the triangles are as equilateral as possible (Chew 1987). We use the edges of the triangles (and their lengths), and having well-shaped triangles is an advantage.…”

Section: Subdividing Gap Regionsmentioning

confidence: 99%

Solving the horizontal conflation problem with a constrained Delaunay triangulation

Ledoux

Ohori

2016

J Geogr Syst

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Datasets produced by different countries or organisations are seldom properly aligned and contain several discrepancies (e.g., gaps and overlaps). This problem has been so far almost exclusively tackled by snapping vertices based on a user-defined threshold. However, as we argue in this paper, this leads to invalid geometries, is error-prone, and leaves several discrepancies along the boundaries. We propose a novel algorithm to align the boundaries of adjacent datasets. It is based on a constrained Delaunay triangulation to identify and eliminate the discrepancies, and the alignment is performed without moving vertices with a snapping operator. This allows us to guarantee that the datasets have been properly conflated and that the polygons are geometrically valid. We present our algorithm, our implementation (based on the stable and fast triangulator in CGAL), and we show how it can be used it practice with different experiments with real-world datasets. Our experiments demonstrate that our approach is highly efficient and that it yields better results than snapping-based methods.

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Section: Subdividing Gap Regionsmentioning

confidence: 99%

Solving the horizontal conflation problem with a constrained Delaunay triangulation

Ledoux

Ohori

2016

J Geogr Syst

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“…The Constrained Delaunay Triangulation (CDT) is a variant of the standard Delaunay Triangulation in which a set of pre-specified edges (in our case, the edges of the obstacles) must lie in the triangulation (Chew 1987). A Constrained Delaunay Triangulation is not truly a Delaunay Triangulation.…”

Section: Constrained Delaunay Triangulationmentioning

confidence: 99%

Multi-robot repeated area coverage

2013

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We address the problem of repeated coverage of a target area, of any polygonal shape, by a team of robots having a limited visual range. Three distributed Clusterbased algorithms, and a method called Cyclic Coverage are introduced for the problem. The goal is to evaluate the performance of the repeated coverage algorithms under the effects of the variables: Environment Representation, and the Robots' Visual Range. A comprehensive set of performance metrics are considered, including the distance the robots travel, the frequency of visiting points in the target area, and the degree of balance in workload distribution among the robots. The Cyclic Coverage approach, used as a benchmark to compare the algorithms, produces optimal or near-optimal solutions for the single robot case under some criteria. The results can be used as a framework for choosing an appropriate combination of repeated coverage algorithm, environment representation, and the robots' visual range based on the particular scenario and the metric to be optimized.

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“…Computational methods for generating and refining triangular and tetrahedral finite element meshes in 2 and 3-dimensions can be roughly classified as Delaunay based methods, [6,19,7,17,50,47] and methods based on the partition of triangles and tetrahedra [39,33,34,28].…”

Section: Introductionmentioning

confidence: 99%

Multithread parallelization of Lepp-bisection algorithms

Rivara

Rodríguez

Montenegro

et al. 2012

Applied Numerical Mathematics

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Longest edge (nested) algorithms for triangulation refinement in two dimensions are able to produce hierarchies of quality and nested irregular triangulations as needed both for adaptive finite element methods and for multigrid methods. They can be formulated in terms of the longest edge propagation path (Lepp) and terminal edge concepts, to refine the target triangles and some related neighbors. We discuss a parallel multithread algorithm, where every thread is in charge of refining a triangle t and its associated Lepp neighbors. The thread manages a changing Lepp(t) (ordered set of increasing triangles) both to find a last longest (terminal) edge and to refine the pair of triangles sharing this edge. The process is repeated until triangle t is destroyed. We discuss the algorithm, related synchronization issues, and the properties inherited from the serial algorithm. We present an empirical study that shows that a reasonably efficient parallel method with good scalability was obtained. Multithread parallelization of lepp-bisection algorithms AbstractLongest edge (nested) algorithms for triangulation refinement in two dimensions are able to produce hierarchies of quality and nested irregular triangulations as needed both for adaptive finite element methods and for multigrid methods. They can be formulated in terms of the longest edge propagation path (Lepp) and terminal edge concepts, to refine the target triangles and some related neighbors. We discuss a parallel multithread algorithm, where every thread is in charge of refining a triangle t and its associated Lepp neighbors. The thread manages a changing Lepp(t) (ordered set of increasing triangles) both to find a last longest (terminal) edge and to refine the pair of triangles sharing this edge. The process is repeated until triangle t is destroyed. We discuss the algorithm, related synchronization issues, and the properties inherited from the serial algorithm. We present an empirical study that shows that a reasonably efficient parallel method with good scalability was obtained.

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Constrained Delaunay triangulations

Cited by 232 publications

References 8 publications

Solving the horizontal conflation problem with a constrained Delaunay triangulation

Solving the horizontal conflation problem with a constrained Delaunay triangulation

Multi-robot repeated area coverage

Multithread parallelization of Lepp-bisection algorithms

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