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Delaunay triangulations approximate anchor hulls

2007
*
Computational geometry
*

We show that, for two-dimensional shapes, the

doi:10.1016/j.comgeo.2006.01.001
fatcat:y6rd56iayba2xc4reqannqwhba
*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. ...##
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MESH GENERATION AND OPTIMAL TRIANGULATION
[chapter]

1992
*
Lecture Notes Series on Computing
*

Proof: We use the lifting relation between DTs and convex

doi:10.1142/9789814355858_0002
fatcat:zjlfgakee5df7nihosmpeuhco4
*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 ...##
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MESH GENERATION AND OPTIMAL TRIANGULATION
[chapter]

1995
*
Lecture Notes Series on Computing
*

Proof: We use the lifting relation between DTs and convex

doi:10.1142/9789812831699_0003
fatcat:ec6436f5i5bszheuiherz452ae
*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 ...##
###
Meshing skin surfaces with certified topology

2007
*
Computational geometry
*

The complexity of the mesh is linear in the size of the

doi:10.1016/j.comgeo.2006.01.003
fatcat:2gwxoem54ba6ffe6l3ai5ayw3i
*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. ...##
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Improvement of volume estimation of stockpile of earthworks using a concave hull- footprint

2015
*
Micro, Macro & Mezzo Geoinformation
*

Several algorithms for creating concave

doaj:41b5cf23fee94e209b7ecfb8e64b8f14
fatcat:u6mzxwagzrhibk6r4u2vwvxhkm
*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*. ...##
###
Design and Implementation of a Practical Parallel Delaunay Algorithm

1999
*
Algorithmica
*

We use the well known reduction of 2D

doi:10.1007/pl00008262
fatcat:fz4tkkuicnb75b467cmparbccy
*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. ...##
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A Short Proof of the Toughness of Delaunay Triangulations
[article]

2019
*
arXiv
*
pre-print

An important implication of this result is that

arXiv:1907.01617v2
fatcat:k5bqub5e5vbhzhdvblruomcrva
*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 ...##
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The greedy triangulation can be computed from the Delaunay triangulation in linear time

1999
*
Computational geometry
*

In this paper we show that for any planar point set S, if the

doi:10.1016/s0925-7721(99)00037-1
fatcat:wuhsbwhrqja73ozv255zvsklhe
*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*. ...##
###
Adaptive skin meshes coarsening for biomolecular simulation

2011
*
Computer Aided Geometric Design
*

Firstly, the quality of both the surface

doi:10.1016/j.cagd.2011.04.001
pmid:21779137
pmcid:PMC3138625
fatcat:vnf4s6wgo5d57ilcnjcd6juy2i
*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 ...##
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Updating and constructing constrained delaunay and constrained regular triangulations by flips

2003
*
Proceedings of the nineteenth conference on Computational geometry - SCG '03
*

Constrained

doi:10.1145/777792.777821
dblp:conf/compgeom/Shewchuk03
fatcat:kvstswvk35elzpb7jsmezdig4i
*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. ...##
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Incrementally Constructing and Updating Constrained Delaunay Tetrahedralizations with Finite Precision Coordinates
[chapter]

2013
*
Proceedings of the 21st International Meshing Roundtable
*

Constrained

doi:10.1007/978-3-642-33573-0_11
dblp:conf/imr/SiS12
fatcat:2uxlroulmfeqflrikys3x47fvy
*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. ...##
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Experimental results on quadrangulations of sets of fixed points

2002
*
Computer Aided Geometric Design
*

on the dual graph of the

doi:10.1016/s0167-8396(02)00133-4
fatcat:cisaq4vpjzhg5dcocuv6psbs64
*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. ...##
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Incrementally constructing and updating constrained Delaunay tetrahedralizations with finite-precision coordinates

2013
*
Engineering with Computers
*

Constrained

doi:10.1007/s00366-013-0331-0
fatcat:pwtguahmgfcxxmrqbl3n4u364q
*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. ...##
###
Natural neighbor extrapolation using ghost points

2009
*
Computer-Aided Design
*

However, its restriction to the convex

doi:10.1016/j.cad.2008.08.007
fatcat:flraoqmz35h7tfesm3okbd2fty
*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 ...##
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Bounded-degree plane geometric spanners in practice
[article]

2022
*
arXiv
*
pre-print

This was the first algorithm that can construct boundeddegree plane spanners using the classic L 2 -

arXiv:2205.03204v1
fatcat:jfklsbxq7vflbj2kpzjuhrfizm
*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. ...
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