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Voronoi Diagrams and Convex Hulls of Random Moving Points
2000
Discrete & Computational Geometry
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This report considers the expected combinatorial complexity of the Euclidean Voronoi diagram and the convex hull of sets of n independent random points moving in unit time between two positions drawn independently ...
for the convex hull. ...
Voronoi Diagrams and Convex Hulls of Random Moving Points 345
Voronoi Diagrams and Convex Hulls of Random Moving Points 351
364 R. A. ...
doi:10.1007/pl00009505
fatcat:dbuxuqav3ve7rnjwbpdwyyle2m
Intersections with random geometric objects
1998
Computational geometry
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tree, a Gabriel graph, a relative neighborhood graph, a Hamiltonian circuit, a furthest point Voronoi diagram, a convex hull, a k-dimensional tree, and a rectangular grid. ¢ 1998 Elsevier Science B.V. ...
We first study the expected size of the intersection between a random Voronoi diagram and a generic geometric object that consists of a finite collection of line segments in the plane. ...
It remains unchanged if we remove all points that are not on the convex hull. Consider n points that gives rise to both the Voronoi diagram V and the furthest-point Voronoi diagram G. ...
doi:10.1016/s0925-7721(98)00004-2
fatcat:fpbk62ycsbbd7ahj6hebtsfscm
Optimal Compression of a Polyline with Segments and Arcs
[article]
2017
arXiv
pre-print
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The approach described in this paper finds a compressed polyline with a minimum number of segments and arcs. ...
This paper describes an efficient approach to constructing a resultant polyline with a minimum number of segments and arcs. ...
The closest Voronoi diagram for each point has a cell; however, that is not the case for the farthest Voronoi diagram. Only points of the convex hull have cells. ...
arXiv:1604.07476v5
fatcat:43y4b3ulyvgnbmtjaunzoynbou
Computing Voronoi Treemaps: Faster, Simpler, and Resolution-independent
2012
Computer graphics forum (Print)
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J.: Convex hulls of finite
[BDL05] BALZER M., D EUSSEN O., L EWERENTZ C.: Voronoi sets of points in two and three dimensions. ...
moved to the average of all sample points
chical partition, subdivide this region by a Voronoi diagram closest to them. ...
doi:10.1111/j.1467-8659.2012.03078.x
fatcat:mc33x44dxzfsngifrufaci5awq
Distributed k-Coverage Decision Scheme for System Deployment in Mobile Sensor Networks
2013
International Journal of Distributed Sensor Networks
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In our schemes, the th order Voronoi diagram is used to discover the regions that do not meet the -coverage requirement. ...
This is because an efficient topology structure significantly affects the quality of service and lifetime of WSNs. ...
In particular, the point set contains one point; the convex hull of the set , ( ) = { 1 , 2 , . . . , } and sort the points in anti-clock order; (2) Divide the convex hull with sides into − 2 triangles ...
doi:10.1155/2013/485250
fatcat:d66fmuqokzc5da5wbzteqymlfm
Voronoi Diagrams and Delaunay Triangulations
[chapter]
2004
Handbook of Discrete and Computational Geometry, Second Edition
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6 Further reading Survey papers by Aurenhammer 5 a n d F ortune 15 cover many aspects of Delaunay triangulations and Voronoi diagrams. ...
The book by O k abe, Boots, and Sugihara 24 i s entirely devoted to Voronoi diagrams, and has an extensive discussion of applications. Basic reference for geometric algorithms are 13, 2 5 . ...
of the convex hull of T . ...
doi:10.1201/9781420035315.ch23
fatcat:n7e7x75e4rahta6fzawznhw3pe
VORONOI DIAGRAMS and DELAUNAY TRIANGULATIONS
[chapter]
1992
Lecture Notes Series on Computing
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6 Further reading Survey papers by Aurenhammer 5 a n d F ortune 15 cover many aspects of Delaunay triangulations and Voronoi diagrams. ...
The book by O k abe, Boots, and Sugihara 24 i s entirely devoted to Voronoi diagrams, and has an extensive discussion of applications. Basic reference for geometric algorithms are 13, 2 5 . ...
of the convex hull of T . ...
doi:10.1142/9789814355858_0006
fatcat:l6z2qh3jlbdp7ld27tvxq35hbu
VORONOI DIAGRAMS and DELAUNAY TRIANGULATIONS
[chapter]
1995
Lecture Notes Series on Computing
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6 Further reading Survey papers by Aurenhammer 5 a n d F ortune 15 cover many aspects of Delaunay triangulations and Voronoi diagrams. ...
The book by O k abe, Boots, and Sugihara 24 i s entirely devoted to Voronoi diagrams, and has an extensive discussion of applications. Basic reference for geometric algorithms are 13, 2 5 . ...
of the convex hull of T . ...
doi:10.1142/9789812831699_0007
fatcat:hrohranyebethhmym46wlqumtu
Java Applets for the Dynamic Visualization of Voronoi Diagrams
[chapter]
2003
Lecture Notes in Computer Science
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We discuss the design of Java applets that visualize how the Voronoi diagram of n points continuously changes as individual points are moved across the plane, or as the underlying distance function is ...
Moreover, we report on some experiences made in using these applets in teaching and research. The applets can be found and tried out at http://wwwpi6.fernuni-hagen.de/GeomLab/. ...
Theorem 1 A point site's Voronoi region is unbounded if and only if the point lies on the convex hull of the set of all sites. ...
doi:10.1007/3-540-36477-3_14
fatcat:jxtmkiuhzzeavbmqdsfpijxkua
Recent Developments and Open Problems in Voronoi Diagrams
2006
2006 3rd International Symposium on Voronoi Diagrams in Science and Engineering
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, defines a -simplex if that is the convex hull of . ...
The expected complexity of the Voronoi diagram of random points in the threedimensional cube is [4] . ...
doi:10.1109/isvd.2006.30
dblp:conf/isvd/Bereg06
fatcat:vhn4kobn3zblzj4tcspaq2jcgu
Voronoi diagrams over dynamic scenes
1993
Discrete Applied Mathematics
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Given a finite set S of n points in the Euclidean plane [E', we investigate the change of the Voronoi diagram VD(S) and its dual, the Delaunay triangulation DT(S), under continuous motions of the underlying ...
There are a lot of related problems in computational geometry, as for example the dynamic convex hull and the dynamic nearest neighbor problem, but also applications in motion planning and pattern recognition ...
Acknowledgement The author wishes to thank Professor Hartmut Noltemeier for his support and Gerhard Albers for the nice implementation. ...
doi:10.1016/0166-218x(93)90115-5
fatcat:7ee4cbi6fvgy3iykorky4a676a
The Existence of a Convex Polyhedron with Respect to the Constrained Vertex Norms
2020
Mathematics
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However, we proved that there always exists a convex configuration in the three-dimensional case. In the application, we can imply the existence of the non-empty spherical Laguerre Voronoi diagram. ...
Given a set of constrained vertex norms, we proved the existence of a convex configuration with respect to the set of distinct constrained vertex norms in the two-dimensional case when the constrained ...
Acknowledgments: We would like to thank Masaki Moriguchi and Vorapong Suppakitpaisan for their discussions. ...
doi:10.3390/math8040645
fatcat:65rqvub4qzgfzjfy6g5gobhnuq
An introduction to randomization in computational geometry
1996
Theoretical Computer Science
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This paper is not a complete survey on randomized algorithms in computational geometry, but an introduction to this subject providing intuitions and references. ...
First, some basic ideas are illustrated by the sorting problem, and then a few results on computational geometry are briefly explained. * ...
Voronoi diagrams
Points Voronoi diagrams We recall the definition of the Voronoi diagram in the plane. ...
doi:10.1016/0304-3975(95)00174-3
fatcat:bla4hiwv7rfabnd6bfokzsqole
Average case analysis of dynamic geometric optimization
1996
Computational geometry
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We use as subroutines dynamic algorithms for two other geometric graphs: the farthest neighbor forest and the rotating caliper graph related to an algorithm for static computation of point set widths and ...
We also use the rotating caliper graph to maintain the diameter, width" and minimum enclosing rectangle of a point set in expected time O(log n) per update. ...
Voronoi diagram itself, we keep track of the set of input points within each diagram cell, using a convex hull data structure (Fig. 4) . ...
doi:10.1016/0925-7721(95)00018-6
fatcat:tmaeehsaongfdlnh3zxnsihtsm
An efficient algorithm for the three-dimensional diameter problem
2001
Discrete & Computational Geometry
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We explore a new approach for computing the diameter of n points in R3 that is based on the restriction of the furthest-point Voronoi diagram to the convex hull. ...
We show that the restricted Voronoi diagram has linear complexity. We present a deterministic algorithm with O(n log2 n) running time. ...
By Lemma 6, T'(N) = 0(N log N) + T'(N1) + T'(N2), (1) producing T'(N) =
, CH(A) denotes the convex hull of A, and Vor(A) denotes the furthest-point Voronoi diagram of ig. 1. ...
doi:10.1007/s004540010086
fatcat:yfeaxdqzm5cbdkng3s5rkqbn4q
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