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Closest-Point Queries for Complex Objects [chapter]

Eugene Greene, Asish Mukhopadhyay
2014 Lecture Notes in Computer Science  
In this paper we report on the implementation of a heuristic for computing the closest of a set of n given points in the plane to a complex query object, to wit a triangle, a circle, a rectangle etc.  ...  Our results indicate that the heuristic is effective for query objects with small perimeter relative to the given point set, and large values of n. * greene6@uwindsor.ca; Supported by an NSERC USRA † asishm  ...  The solution is reduced to two triangle range queries and to two point-locations in a k-th order Voronoi diagram and involves some complicated data structures.  ... 
doi:10.1007/978-3-319-09129-7_28 fatcat:r6bfwzqpird5nnsyitl5oa2tb4

On 2-Site Voronoi Diagrams under Geometric Distance Functions

Gill Barequet, Matthew T. Dickerson, David Eppstein, David Hodorkovsky, Kira Vyatkina
2011 2011 Eighth International Symposium on Voronoi Diagrams in Science and Engineering  
In addition, we bring to notice that 2-point site Voronoi diagrams can be alternatively interpreted as 1-site Voronoi diagrams of segments, and thus, our results also enhance the knowledge on the latter  ...  We consider a few more such distance functions, based on geometric primitives, namely, circles and triangles, and analyze the structure and complexity of the nearest-and furthest-neighbor 2-site Voronoi  ...  Work on this paper by Gill Barequet was performed while he was affiliated with Tufts University in Medford, MA. Gill Barequet et al.: 2-Site Voronoi Diagrams  ... 
doi:10.1109/isvd.2011.13 dblp:conf/isvd/BarequetDEHV11 fatcat:mvrsplp6s5e5jbnwhhc2ckqrda

On 2-Site Voronoi Diagrams Under Geometric Distance Functions

Gill Barequet, Matthew Dickerson, David Eppstein, David Hodorkovsky, Kira Vyatkina
2013 Journal of Computer Science and Technology  
We consider a few more such distance functions, based on geometric primitives, and analyze the structure and complexity of the nearest- and furthest-neighbor Voronoi diagrams of a point set with respect  ...  We revisit a new type of a Voronoi diagram, in which distance is measured from a point to a pair of points.  ...  Work on this paper by Gill Barequet was performed while he was affiliated with Tufts University in Medford, MA. Gill Barequet et al.: 2-Site Voronoi Diagrams  ... 
doi:10.1007/s11390-013-1328-2 fatcat:6o456u3ipnbavdtxvrozed6d2e

Model of Arrangement of Final Material Depots for Concave Construction Sites in CSLP

Attila Pém, Levente Mályusz PhD
2015 Procedia Engineering  
The model solves the problem by using the known Voronoi diagram.  ...  In this paper, we introduce a model and define an algorithm for the Facilities Location Problem with focus on optimizing the arrangement of final material depots at a construction site that is represented  ...  In this study, we present an algorithm based on Voronoi diagram and used the continuous model of LAP that results optimal arrangement of the final material depots for one type of material.  ... 
doi:10.1016/j.proeng.2015.10.057 fatcat:pqhhalnlcnaqlh2ykj3w2tba5q

Constructing Intrinsic Delaunay Triangulations from the Dual of Geodesic Voronoi Diagrams [article]

Yong-Jin Liu and Chun-Xu Xu and Dian Fan and Ying He
2015 arXiv   pre-print
In this paper, we propose a new method for constructing IDT on manifold triangle meshes. Based on the duality of geodesic Voronoi diagrams, our method can guarantee the resultant IDTs are regular.  ...  Moreover, the edge-flipping algorithm may produce non-regular triangulations, which contain self-loops and/or faces with only two edges.  ...  We measure the quality of a triangle t by its anisotropy σ = ph 2 √ 3S , where p is the half-perimeter, h is the length of its longest edge and S is the triangle area.  ... 
arXiv:1505.05590v1 fatcat:bx6alm34ebhydacj4f4nwti32y

ON COMPUTING VORONOI DIAGRAMS FOR SORTED POINT SETS

HRISTO N. DJIDJEV, ANDRZEJ LINGAS
1995 International journal of computational geometry and applications  
We show that the Voronoi diagram of a nite sequence of points in the plane which gives sorted order of the points with respect to two perpendicular directions can be computed in linear time.  ...  In contrast, we observe that the problem of computing the Voronoi diagram of a nite sequence of points in the plane which gives the sorted order of the points with respect to a single direction requires  ...  Finally, it is enough to cut the extended Voronoi diagram along the perimeter of P to to obtain the bounded Voronoi diagram of P.  ... 
doi:10.1142/s0218195995000192 fatcat:q3lr6nyp3fcgdgap2eteh5hb4m

Redundancy and coverage detection in sensor networks

Bogdan Cărbunar, Ananth Grama, Jan Vitek, Octavian Cărbunar
2006 ACM transactions on sensor networks  
We reduce both problems to the computation of Voronoi diagrams, prove and achieve lower bounds on the solution of these problems, and present efficient distributed algorithms for computing and maintaining  ...  We also examine the impact of redundancy elimination on the related problem of coverage-boundary detection.  ...  ACKNOWLEDGMENTS The authors would like to thank the anonymous reviewers for their helpful comments in revising the article.  ... 
doi:10.1145/1138127.1138131 fatcat:os2fumvdnngqhd23isp7kl3ozq

2-Point site Voronoi diagrams

Gill Barequet, Matthew T. Dickerson, Robert L. Scot Drysdale
2002 Discrete Applied Mathematics  
We focus on a few such distance functions, analyze the structure and complexity of the corresponding nearest-and furthest-neighbor Voronoi diagrams (in which every region is deÿned by a pair of point sites  ...  ), and show how to compute the diagrams e ciently. ?  ...  Acknowledgements We thank Micha Sharir for commenting on the use of lower envelopes for computing the diagrams discussed in this paper.  ... 
doi:10.1016/s0166-218x(01)00320-1 fatcat:mydix3khvved7f6ynumxj4mkoa

Voronoi diagrams---a survey of a fundamental geometric data structure

Franz Aurenhammer
1991 ACM Computing Surveys  
Miles [1970] made a thorough study of Voronoi diagrams induced by a planar homogeneous site process. Expectations of the edge number, edge length, perimeter, and area of the regions are given.  ...  The distance of two clusters is defined as the minimum distance between any two sites, one from each cluster.  ... 
doi:10.1145/116873.116880 fatcat:a6vg5x4mj5fnnckqcrksfwlh2i

A linear-time algorithm for computing the voronoi diagram of a convex polygon

Alok Aggarwal, Leonidas J. Guibas, James Saxe, Peter W. Shor
1989 Discrete & Computational Geometry  
Our techniques can also be used to obtain linear-time algorithms for computing the furthest-site Voronoi diagram and the medial axis of a convex polygon and for deleting a site from a general planar Voronoi  ...  Using this algorithm, we show that the Voronoi diagram of n sites in the plane can be computed in O(n) time when these sites form the vertices of a convex polygon in, say, counterclockwise order.  ...  Acknowledgments The authors would like to thank William Thurston, Jorge Stolfi, and Steve Fortune for helpful discussions; and the referees for several helpful suggestions. 604 A. Aggarwal, L. J.  ... 
doi:10.1007/bf02187749 fatcat:imdybpi2lfh65izvvqu5woeneu

Stylized rendering for multiresolution image representation

Mark Grundland, Chris Gibbs, Neil A. Dodgson, Bernice E. Rogowitz, Thrasyvoulos N. Pappas, Scott J. Daly
2005 Human Vision and Electronic Imaging X  
Keeping track of the spatial influence of each sample on the rendition, a progressively generated discrete Voronoi diagram forms the common foundation for our sampling and rendering framework.  ...  It supports a wide variety of artistic rendering styles based on geometric subdivision or parametric procedural textures.  ...  The images are taken from FreeFoto.com and the Waterloo Brag Zone.  ... 
doi:10.1117/12.596817 dblp:conf/hvei/GrundlandGD05 fatcat:2uzdc6xw3bharmo6y4mrufczwm

Round-Trip Voronoi Diagrams and Doubling Density in Geographic Networks [article]

Matthew T. Dickerson, Michael T. Goodrich, Thomas D. Dickerson
2010 arXiv   pre-print
bound on the number of non-empty Voronoi regions.  ...  In this paper, we prove several new properties of two-site and two-color round-trip Voronoi diagrams in a geographic network, including a relationship between the "doubling density" of sites and an upper  ...  (For C = 2, and for point sites on the Euclidean plane, this distance was referred to in [4] as the "perimeter" distance, in reference to the perimeter of a triangle, since shortest paths are straight  ... 
arXiv:1005.1053v1 fatcat:7kgmdsg2b5biresnmp6ahvev5a

General framework for testing Poisson-Voronoi assumption for real microstructures [article]

Martina Vittorietti, Piet J.J. Kok, Jilt Sietsma, Wei Li, Geurt Jongbloed
2019 arXiv   pre-print
The most basic model for steel microstructure is the Poisson-Voronoi diagram.  ...  The first two are based on the coefficient of variation and the cumulative distribution function of the cells area.  ...  Acknowledgements This research was carried out under project number S41.5.14547b in the framework of the Partnership Program of the Materials innovation institute M2i (www.m2i.nl) and (partly) financed  ... 
arXiv:1902.10981v1 fatcat:2gdalxm2wreqdoe2raq5jazgbm

Stylized multiresolution image representation

Mark Grundland
2008 Journal of Electronic Imaging (JEI)  
A progressively generated discrete Voronoi diagram forms the common foundation for our sampling and rendering framework.  ...  It supports a wide variety of artistic rendering styles based on geometric subdivision or parametric procedural textures.  ...  et les Technologies, the Celanese Canada Internationalist Fellowship, the British Council, the Overseas Research Student Award Scheme, the Cambridge Commonwealth Trust, the Royal Academy of Engineering  ... 
doi:10.1117/1.2898894 fatcat:ofi5u3qmq5dzhgvnrgfb4irssi

General framework for testing Poisson‐Voronoi assumption for real microstructures

Martina Vittorietti, Piet J. J. Kok, Jilt Sietsma, Wei Li, Geurt Jongbloed
2020 Applied Stochastic Models in Business and Industry  
The most basic model for steel microstructure is the Poisson-Voronoi diagram.  ...  Therefore, a general framework for testing the Poisson-Voronoi assumption based on images of two-dimension sections of real metals is set out.  ...  ACKNOWLEDGEMENTS This research was carried out under project number S41.5.14547b in the framework of the Partnership Program of the Materials innovation institute M2i (www.m2i.nl) and (partly) financed  ... 
doi:10.1002/asmb.2517 fatcat:my4w4immavblhpptvqh7bqmyiu
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