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Delaunay triangulations approximate anchor hulls
2007
Computational geometry
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We show that, for two-dimensional shapes, the Delaunay triangulation approximates a specific structure which we call anchor hulls. ...
The corresponding question for the dual Delaunay triangulation is not addressed in the literature. ...
We establish that a subset of the Delaunay triangulation approximates the anchor hulls of the shape. ...
doi:10.1016/j.comgeo.2006.01.001
fatcat:y6rd56iayba2xc4reqannqwhba
MESH GENERATION AND OPTIMAL TRIANGULATION
[chapter]
1992
Lecture Notes Series on Computing
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Proof: We use the lifting relation between DTs and convex hulls. ...
Under the mapping that takes (x; y) to (x; y; x 2 + y 2 ), the DT of the input vertices lifts to the lower convex hull, and|due to the input edges|the CDT lifts to a surface above the lower convex hull ...
This material spans a spectrum from purely theoretical results (for example, Chazelle's linear-time triangulation algorithm), through a middle ground (our own work on Steiner triangulations), to practical ...
doi:10.1142/9789814355858_0002
fatcat:zjlfgakee5df7nihosmpeuhco4
MESH GENERATION AND OPTIMAL TRIANGULATION
[chapter]
1995
Lecture Notes Series on Computing
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Proof: We use the lifting relation between DTs and convex hulls. ...
Under the mapping that takes (x; y) to (x; y; x 2 + y 2 ), the DT of the input vertices lifts to the lower convex hull, and|due to the input edges|the CDT lifts to a surface above the lower convex hull ...
This material spans a spectrum from purely theoretical results (for example, Chazelle's linear-time triangulation algorithm), through a middle ground (our own work on Steiner triangulations), to practical ...
doi:10.1142/9789812831699_0003
fatcat:ec6436f5i5bszheuiherz452ae
Meshing skin surfaces with certified topology
2007
Computational geometry
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The complexity of the mesh is linear in the size of the Delaunay triangulation of the balls, which is worst case optimal. ...
With each face of this complex we associate an anchor point, which plays a crucial role in the meshing algorithm. ...
The affine hulls of a Delaunay simplex δ X and its dual Voronoi cell ν X are complementary and orthogonal. ...
doi:10.1016/j.comgeo.2006.01.003
fatcat:2gwxoem54ba6ffe6l3ai5ayw3i
Improvement of volume estimation of stockpile of earthworks using a concave hull- footprint
2015
Micro, Macro & Mezzo Geoinformation
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Several algorithms for creating concave hulls are suggested, in this paper an algorithm based on Delaunay triangulation and linear referencing was used to create the concave hull. ...
A comparison of volume estimations of stockpiles taking into consideration the footprint via convex hull, concave hull and manually delineated outline showed that volumes based on the concave hull are ...
Alpha shapes are considered as a generalization of the convex hull and a sub-graph of the Delaunay triangulation. ...
doaj:41b5cf23fee94e209b7ecfb8e64b8f14
fatcat:u6mzxwagzrhibk6r4u2vwvxhkm
Design and Implementation of a Practical Parallel Delaunay Algorithm
1999
Algorithmica
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We use the well known reduction of 2D Delaunay triangulation to find the 3D convex hull of points on a paraboloid. ...
This paper describes the design and implementation of a practical parallel algorithm for Delaunay triangulation that works well on general distributions. ...
Return DELAUNAY(P L , B L ) ∪ DELAUNAY(P R , B R ) Fig. 3. The projection-based parallel Delaunay triangulation algorithm. Initially B is the convex hull of P. ...
doi:10.1007/pl00008262
fatcat:fz4tkkuicnb75b467cmparbccy
A Short Proof of the Toughness of Delaunay Triangulations
[article]
2019
arXiv
pre-print
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An important implication of this result is that Delaunay triangulations have perfect matchings. ...
Another implication of our result is a proof of the conjecture of Aichholzer et al. (2010) that at least n points are required to block any n-vertex Delaunay triangulation ...
This Delaunay triangulation can be blocked by n points that are placed outside the convex hull: two points are placed very close to p and n − 2 points are placed very close to the n − 2 convex hull edges ...
arXiv:1907.01617v2
fatcat:k5bqub5e5vbhzhdvblruomcrva
The greedy triangulation can be computed from the Delaunay triangulation in linear time
1999
Computational geometry
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In this paper we show that for any planar point set S, if the Delaunay triangulation of S is given, then the greedy triangulation of S can be computed in linear worst-case time (and linear space). ...
The Delaunay triangulation, which is the straight-line dual of the Voronoi diagram, can be produced in O(n log n) worst-case time, and often even faster, by several practical algorithms. ...
of its convex hull has already been fully triangulated. ...
doi:10.1016/s0925-7721(99)00037-1
fatcat:wuhsbwhrqja73ozv255zvsklhe
Adaptive skin meshes coarsening for biomolecular simulation
2011
Computer Aided Geometric Design
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Firstly, the quality of both the surface triangulations and tetrahedral meshes is guaranteed. Secondly, the interface in the tetrahedral mesh is an accurate approximation of the molecular boundary. ...
Thirdly, our meshes are Delaunay meshes. Finally, the meshes are adaptive to the geometry. ...
We note that the restricted Delaunay triangulation differs from the constrained Delaunay triangulation as follows: the restricted Delaunay triangulation is the subset of the Delaunay triangulation of a ...
doi:10.1016/j.cagd.2011.04.001
pmid:21779137
pmcid:PMC3138625
fatcat:vnf4s6wgo5d57ilcnjcd6juy2i
Updating and constructing constrained delaunay and constrained regular triangulations by flips
2003
Proceedings of the nineteenth conference on Computational geometry - SCG '03
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Constrained Delaunay tetrahedralizations (CDTs) are valuable for generating meshes of nonconvex domains and domains with internal boundaries, but they are difficult to maintain robustly when finite-precision ...
The Delaunay triangulation of V has the same combinatorial structure as the underside of the convex hull of V + . ...
Delaunay triangulations and convex hulls are connected through the wellknown parabolic lifting map of Seidel [13] . Let V be a set of vertices in R 3 for which a Delaunay triangulation is sought. ...
doi:10.1145/777792.777821
dblp:conf/compgeom/Shewchuk03
fatcat:kvstswvk35elzpb7jsmezdig4i
Incrementally Constructing and Updating Constrained Delaunay Tetrahedralizations with Finite Precision Coordinates
[chapter]
2013
Proceedings of the 21st International Meshing Roundtable
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Constrained Delaunay tetrahedralizations (CDTs) are valuable for generating meshes of nonconvex domains and domains with internal boundaries, but they are difficult to maintain robustly when finite-precision ...
The Delaunay triangulation of V has the same combinatorial structure as the underside of the convex hull of V + . ...
Delaunay triangulations and convex hulls are connected through the wellknown parabolic lifting map of Seidel [13] . Let V be a set of vertices in R 3 for which a Delaunay triangulation is sought. ...
doi:10.1007/978-3-642-33573-0_11
dblp:conf/imr/SiS12
fatcat:2uxlroulmfeqflrikys3x47fvy
Experimental results on quadrangulations of sets of fixed points
2002
Computer Aided Geometric Design
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on the dual graph of the triangulations. ...
Therefore we propose and experimentally investigate a heuristic approach to solve this problem by converting "nice" triangulations to the desired quadrangulations with the aid of maximum matchings computed ...
new half-ray anchored at the second point of the spiral chain, and so on until all the points in S are marked. ...
doi:10.1016/s0167-8396(02)00133-4
fatcat:cisaq4vpjzhg5dcocuv6psbs64
Incrementally constructing and updating constrained Delaunay tetrahedralizations with finite-precision coordinates
2013
Engineering with Computers
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The file type is application/pdf.
Constrained Delaunay tetrahedralizations (CDTs) are valuable for generating meshes of nonconvex domains and domains with internal boundaries, but they are difficult to maintain robustly when finite-precision ...
The Delaunay triangulation of V has the same combinatorial structure as the underside of the convex hull of V + . ...
Delaunay triangulations and convex hulls are connected through the wellknown parabolic lifting map of Seidel [13] . Let V be a set of vertices in R 3 for which a Delaunay triangulation is sought. ...
doi:10.1007/s00366-013-0331-0
fatcat:pwtguahmgfcxxmrqbl3n4u364q
Natural neighbor extrapolation using ghost points
2009
Computer-Aided Design
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However, its restriction to the convex hull of the data sites is a limitation that has not yet been satisfyingly overcome. ...
Similar methods addressing the extension of Delaunay triangulations past their convex hull have been discussed in [29] , Section 6.3, where it was concluded that the quality of the resulting triangulation ...
interpolants can be computed directly from the Delaunay triangulation of the data sites, such that the preprocessing amounts to the construction of the Delaunay triangulation and a possible generation ...
doi:10.1016/j.cad.2008.08.007
fatcat:flraoqmz35h7tfesm3okbd2fty
Bounded-degree plane geometric spanners in practice
[article]
2022
arXiv
pre-print
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This was the first algorithm that can construct boundeddegree plane spanners using the classic L 2 -Delaunay triangulation. First, a Delaunay triangulation DT of P is constructed. ...
Eight of the eleven algorithms use L 2 -Delaunay triangulation as the starting point. The remaining three use L ∞ or T D-Delaunay triangulations, as described later in this section. ...
arXiv:2205.03204v1
fatcat:jfklsbxq7vflbj2kpzjuhrfizm
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