Triangulations in CGAL

Boissonnat, Jean‐Daniel; Devillers, Olivier; Pion, Sylvain; Teillaud, Monique; Yvinec, Mariette

doi:10.1016/s0925-7721(01)00054-2

Cited by 155 publications

(113 citation statements)

References 30 publications

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“…programming language, using external libraries for some functionalities: (1) GDAL 4 , which allows us to read/write from/to a large variety of data formats common in GIS and to handle the attributes of each polygon; and (2) CGAL 5 which has support for many robust spatial data structures and the operations based on them, including polygons and triangulations (Boissonnat et al 2002). …”

Section: Implementation and Experimentsmentioning

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: Implementation and Experimentsmentioning

confidence: 99%

Solving the horizontal conflation problem with a constrained Delaunay triangulation

Ledoux

Ohori

2016

J Geogr Syst

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“…In a full Delaunay triangulation, this boundary is the convex hull, while in an intermediate triangulation such as DT ⊗ q (P ) it may be not convex. To avoid complicated code for all the special cases, a classic approach adds a dummy vertex ∞ and creates for each facet f of the convex hull a tetrahedron between f and ∞ [3]. Thus, adjacencies between convex hull facets are managed as adjacencies between infinite tetrahedra.…”

Section: Managing the Boundariesmentioning

confidence: 99%

Vertex Deletion for 3D Delaunay Triangulations

Buchin¹,

Devillers²,

Mulzer³

et al. 2013

Lecture Notes in Computer Science

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Abstract. We show how to delete a vertex q from a three-dimensional Delaunay triangulation DT(S) in expected O(C ⊗ (P )) time, where P is the set of vertices neighboring q in DT(S) and C ⊗ (P ) is an upper bound on the expected number of tetrahedra whose circumspheres enclose q that are created during the randomized incremental construction of DT(P ). Experiments show that our approach is significantly faster than existing implementations if q has high degree, and competitive if q has low degree.

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“…If there is no virtual point in constrained edge, we can delete constrained point of this edge one by one using IEE algorithm [12] . Else if there is virtual point in the edge, we use a new algorithm IDRVP.…”

Section: Constrained Edge Deletion In Cd-tinmentioning

confidence: 99%

“…Based on these, some researchers studied on the point deletion for D-TIN or regular triangulations (RT) [2,4,7,[9][10][11] . J. D. Boissonnat, et al presented an algorithm for point deletion of CD-TIN called integral ear elimination (IEE) that improved on the EE algorithm [12] . The algorithm IEE can be used for the deletion of constrained point and non-constrained point of CD-TIN.…”

Section: Introductionmentioning

confidence: 99%

Constrained edge dynamic deleting in CD-TIN based on influence domain retriangulation of virtual point

Wang

Wu²,

Shi³

2007

Geo-spatial Information Science

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Constrained Delaunay triangulated irregular network is one kind of dynamic data structures used in geosciences. The research on point and edges insertion in CD-TIN is the basis of its application. Comparing with the algorithms of points and constrained edge insertion, there are very a few researches on constrained edge deletion in CD-TIN. Based on the analysis of the polymorphism of constrained edge, virtual points are used to describe the intersection of constrained edges. A new algorithm is presented, called as influence domain retriangulating for virtual point (IDRVP), to delete constrained edges with virtual points. The algorithm is complete in topology. Finally, the algorithm is tested by some applications cases.

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Triangulations in CGAL

Abstract: This paper presents the main algorithmic and design choices that have been made to implement triangulations in the computational geometry algorithms library Cgal.

Cited by 155 publications

References 30 publications

Solving the horizontal conflation problem with a constrained Delaunay triangulation

Solving the horizontal conflation problem with a constrained Delaunay triangulation

Vertex Deletion for 3D Delaunay Triangulations

Constrained edge dynamic deleting in CD-TIN based on influence domain retriangulation of virtual point

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