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Journal articles on the topic 'Voronoi diagram'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Nielsen, Frank. "On Voronoi Diagrams on the Information-Geometric Cauchy Manifolds." Entropy 22, no. 7 (2020): 713. http://dx.doi.org/10.3390/e22070713.

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We study the Voronoi diagrams of a finite set of Cauchy distributions and their dual complexes from the viewpoint of information geometry by considering the Fisher-Rao distance, the Kullback-Leibler divergence, the chi square divergence, and a flat divergence derived from Tsallis entropy related to the conformal flattening of the Fisher-Rao geometry. We prove that the Voronoi diagrams of the Fisher-Rao distance, the chi square divergence, and the Kullback-Leibler divergences all coincide with a hyperbolic Voronoi diagram on the corresponding Cauchy location-scale parameters, and that the dual

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PAPADOPOULOU, EVANTHIA, and D. T. LEE. "THE HAUSDORFF VORONOI DIAGRAM OF POLYGONAL OBJECTS: A DIVIDE AND CONQUER APPROACH." International Journal of Computational Geometry & Applications 14, no. 06 (2004): 421–52. http://dx.doi.org/10.1142/s0218195904001536.

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We study the Hausdorff Voronoi diagram of a set S of polygonal objects in the plane, a generalization of Voronoi diagrams based on the maximum distance of a point from a polygon, and show that it is equivalent to the Voronoi diagram of S under the Hausdorff distance function. We investigate the structural and combinatorial properties of the Hausdorff Voronoi diagram and give a divide and conquer algorithm for the construction of this diagram that improves upon previous results. As a byproduct we introduce the Hausdorff hull, a structure that relates to the Hausdorff Voronoi diagram in the same

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3

Liu, Qingping, Xuesheng Zhao, Yuanzheng Duan, Mengmeng Qin, Wenlan Xie, and Wenbin Sun. "Dynamic Construction of Spherical Raster Voronoi Diagrams Based on Ordered Dilation." ISPRS International Journal of Geo-Information 13, no. 6 (2024): 202. http://dx.doi.org/10.3390/ijgi13060202.

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The Voronoi diagram on the Earth’s surface is a significant data model, characterized by natural proximity and dynamic stability, which has emerged as one of the most promising solutions for global spatial dynamic management and analysis. However, traditional algorithms for generating spherical raster Voronoi diagrams find it challenging to dynamically adjust the Voronoi diagram while maintaining precision and efficiency. The efficient and accurate construction of the spherical Voronoi diagram has become one of the bottleneck issues limiting its further large-scale application. To this end, th

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MEHLHORN, KURT, STEFAN MEISER, and RONALD RASCH. "FURTHEST SITE ABSTRACT VORONOI DIAGRAMS." International Journal of Computational Geometry & Applications 11, no. 06 (2001): 583–616. http://dx.doi.org/10.1142/s0218195901000663.

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Voronoi diagrams were introduced by R. Klein as a unifying approach to Voronoi diagrams. In this paper we study furthest site abstract Voronoi diagrams and give a unified mathematical and algorithmic treatment for them. In particular, we show that furthest site abstract Voronoi diagrams are trees, have linear size, and that, given a set of n sites, the furthest site abstract Voronoi diagram can be computed by a randomized algorithm in expected time O(n log n).

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Zhou, Meng, Jianyu Li, Chang Wang, Jing Wang, and Li Wang. "Applications of Voronoi Diagrams in Multi-Robot Coverage: A Review." Journal of Marine Science and Engineering 12, no. 6 (2024): 1022. http://dx.doi.org/10.3390/jmse12061022.

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In recent decades, multi-robot region coverage has played an important role in the fields of environmental sensing, target searching, etc., and it has received widespread attention worldwide. Due to the effectiveness in segmenting nearest regions, Voronoi diagrams have been extensively used in recent years for multi-robot region coverage. This paper presents a survey of recent research works on region coverage methods within the framework of the Voronoi diagram, to offer a perspective for researchers in the multi-robot cooperation domain. First, some basic knowledge of the Voronoi diagram is i

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Kim, Jae-Kwan, Youngsong Cho, Donguk Kim, and Deok-Soo Kim. "Voronoi diagrams, quasi-triangulations, and beta-complexes for disks in R2: the theory and implementation in BetaConcept." Journal of Computational Design and Engineering 1, no. 2 (2014): 79–87. http://dx.doi.org/10.7315/jcde.2014.008.

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Abstract Voronoi diagrams are powerful for solving spatial problems among particles and have been used in many disciplines of science and engineering. In particular, the Voronoi diagram of three-dimensional spheres, also called the additively-weighted Voronoi diagram, has proven its powerful capabilities for solving the spatial reasoning problems for the arrangement of atoms in both molecular biology and material sciences. In order to solve application problems, the dual structure, called the quasi-triangulation, and its derivative structure, called the beta-complex, are frequently used with t

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PAPADOPOULOU, EVANTHIA, and SANDEEP KUMAR DEY. "ON THE FARTHEST LINE-SEGMENT VORONOI DIAGRAM." International Journal of Computational Geometry & Applications 23, no. 06 (2013): 443–59. http://dx.doi.org/10.1142/s0218195913600121.

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The farthest line-segment Voronoi diagram illustrates properties surprisingly different from its counterpart for points: Voronoi regions may be disconnected and they are not characterized by convex-hull properties. In this paper we introduce the farthest hull and its Gaussian map as a closed polygonal curve that characterizes the regions of the farthest line-segment Voronoi diagram, and derive tighter bounds on the (linear) size of this diagram. With the purpose of unifying construction algorithms for farthest-point and farthest line-segment Voronoi diagrams, we adapt standard techniques to co

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DE LACY COSTELLO, BEN, NORMAN RATCLIFFE, ANDREW ADAMATZKY, ALEXEY L. ZANIN, ANDREAS W. LIEHR, and HANS-GEORG PURWINS. "THE FORMATION OF VORONOI DIAGRAMS IN CHEMICAL AND PHYSICAL SYSTEMS: EXPERIMENTAL FINDINGS AND THEORETICAL MODELS." International Journal of Bifurcation and Chaos 14, no. 07 (2004): 2187–210. http://dx.doi.org/10.1142/s021812740401059x.

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The work discusses the formation of Voronoi diagrams in spatially extended nonlinear systems taking experimental and theoretical results into account. Concerning experimental systems a number of chemical systems used previously as prototype chemical processors and a barrier gas-discharge system are investigated. Although the underlying microscopic processes are very different, both types of systems show self-organized Voronoi diagrams for suitable parameters. Indeed certain chemical systems exhibit Voronoi diagrams as an output state for two distinct sets of parameters one that corresponds to

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Devillers, Olivier, and Pierre-Marie Gandoin. "Rounding Voronoi diagram." Theoretical Computer Science 283, no. 1 (2002): 203–21. http://dx.doi.org/10.1016/s0304-3975(01)00076-7.

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10

Jooyandeh, Mohammadreza, Ali Mohades, and Maryam Mirzakhah. "Uncertain Voronoi diagram." Information Processing Letters 109, no. 13 (2009): 709–12. http://dx.doi.org/10.1016/j.ipl.2009.03.007.

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Okahana, Yuuhi, and Yusuke Gotoh. "A Parallelizing Method for Generation of Voronoi Diagram Using Contact Zone." Journal of Data Intelligence 1, no. 2 (2020): 159–75. http://dx.doi.org/10.26421/jdi1.2-4.

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Due to the recent popularization of the Geographic Information System (GIS), spatial network environments that can display the changes of spatial axes on mobile devices are receiving great attention. In spatial network environments, since a query object that seeks location information selects several candidate target objects based on the search conditions, we often use a k-nearest neighbor (kNN) search, which seeks several target objects near the query object. However, since a kNN search needs to find the kNN by calculating the distance from the query to all the objects, the computational comp

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12

Kang, Shun. "A Generic Statistics-Based Tessellation Method of Voronoi Diagram." Journal of Systems Science and Information 3, no. 6 (2015): 568–76. http://dx.doi.org/10.1515/jssi-2015-0568.

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AbstractIn terms of distance function and spatial continuity in Voronoi diagram, a generic generating method of Voronoi diagram, named statistical Voronoi diagram, is proposed in this paper based upon statistics with mean vector and covariance matrix. Besides, in order to make good on the discreteness of spatial Voronoi cell, the cross Voronoi cell accomplished the discrete ranges in its continuous domain. In the light of Mahalanobis distance, not only ordinary Voronoi and weighted Voronoi are implemented, but also the theory of Voronoi diagram is improved further. Last but not least, through

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Akhobadze, Merab, Elguja Kurtskhalia, Davit Gegia, and Marika Bregvadze. "Modified Voronoi Diagram and Algorithms for its Application in Practice." Works of Georgian Technical University, no. 3(533) (September 26, 2024): 237–44. http://dx.doi.org/10.36073/1512-0996-2024-3-237-244.

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The scope of application of the Voronoi diagram is quite diverse: artificial intelligence, urban systems, marketing, computer science and others. This is because the so-called spatial relationships are effectively solved using a Voronoi diagram. The classical Voronoi diagram method assumes homogeneity of objects, which, obviously, is far from reality and therefore limits not only the scope of its application, but also its possibilities. When adding potential power about objects, a potential scheme is added to the traditional Voronoi diagram, after which the modified Voronoi method additionally

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Chaidee, S., P. Pakawanwong, V. Suppakitpaisarn, and P. Teerasawat. "INTERACTIVE LAND-USE OPTIMIZATION USING LAGUERRE VORONOI DIAGRAM WITH DYNAMIC GENERATING POINT ALLOCATION." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-2/W7 (September 14, 2017): 1091–98. http://dx.doi.org/10.5194/isprs-archives-xlii-2-w7-1091-2017.

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In this work, we devise an efficient method for the land-use optimization problem based on Laguerre Voronoi diagram. Previous Voronoi diagram-based methods are more efficient and more suitable for interactive design than discrete optimization-based method, but, in many cases, their outputs do not satisfy area constraints. To cope with the problem, we propose a force-directed graph drawing algorithm, which automatically allocates generating points of Voronoi diagram to appropriate positions. Then, we construct a Laguerre Voronoi diagram based on these generating points, use linear programs to a

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SUGIHARA, KOKICHI. "VORONOI DIAGRAMS IN A RIVER." International Journal of Computational Geometry & Applications 02, no. 01 (1992): 29–48. http://dx.doi.org/10.1142/s0218195992000032.

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A new generalized Voronoi diagram is defined on the surface of a river with uniform flow; a point belongs to the territory of a site if and only if a boat starting from the site can reach the point faster than a boat starting from any other site. If the river runs slower than the boat, the Voronoi diagram has the same topological structure as the ordinary Voronoi diagram, and hence can be constructed from the ordinary Voronoi diagram by a certain transformation. If the river runs faster than the boat, on the other hand, the topological structure of the diagram becomes different from the ordina

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16

Tian, Song, and Zheng Wei. "Vector-Based Realization of Area-Weight Proportional Multiplicatively Weighted Voronoi Diagrams With the ArcGIS Engine." Journal of Cases on Information Technology 26, no. 1 (2024): 1–18. http://dx.doi.org/10.4018/jcit.337322.

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In the geographical field, the studies have been on service areas using the Voronoi diagram and its derived models is extensive, but there is a lack of effective methods to achieve a good area-weight proportionality between generators and their exclusive regions. As a famous visualizing method, adaptive multiplicatively weighted Voronoi diagrams are able to achieve it, but are limited to displaying non-spatial data. The approach of the area-weight proportional multiplicatively weighted Voronoi diagram is proposed to solve these problems by allowing for spatial division with a point-fixed itera

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Costello, B. P. J. de Lacy, I. Jahan, and A. Adamatzky. "Sequential Voronoi Diagram Calculations using Simple Chemical Reactions." International Journal of Nanotechnology and Molecular Computation 3, no. 3 (2011): 29–41. http://dx.doi.org/10.4018/ijnmc.2011070103.

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In the authors’ recent paper (de Lacy Costello et al., 2010) the authors described the formation of complex tessellations of the plane arising from the various reactions of metal salts with potassium ferricyanide and ferrocyanide loaded gels. In addition to producing colourful tessellations these reactions are naturally computing generalised Voronoi diagrams of the plane. The reactions reported previously were capable of the calculation of three distinct Voronoi diagrams of the plane. As diffusion coupled with a chemical reaction is responsible for the calculation then this is achieved in para

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18

Xin, Shiqing, Pengfei Wang, Rui Xu, et al. "SurfaceVoronoi." ACM Transactions on Graphics 41, no. 6 (2022): 1–12. http://dx.doi.org/10.1145/3550454.3555453.

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In this paper, we propose to compute Voronoi diagrams over mesh surfaces driven by an arbitrary geodesic distance solver, assuming that the input is a triangle mesh as well as a collection of sites P = { Pi } m i =1 on the surface. We propose two key techniques to solve this problem. First, as the partition is determined by minimizing the m distance fields, each of which rooted at a source site, we suggest keeping one or more distance triples, for each triangle, that may help determine the Voronoi bisectors when one uses a mark-and-sweep geodesic algorithm to predict the multi-source distance

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Boonprong, Sornkitja, Nathapat Punturasan, Pariwate Varnakovida, and Wichien Prechathamwong. "Towards Sustainable Urban Mobility: Voronoi-Based Spatial Analysis of EV Charging Stations in Bangkok." Sustainability 16, no. 11 (2024): 4729. http://dx.doi.org/10.3390/su16114729.

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This study leverages the efficacy of Voronoi diagram theory within a mixed-methods approach to thoroughly examine the spatial distribution, service coverage, and optimal locations for expanding electric vehicle (EV) charging infrastructure in Bangkok. Drawing on data from field surveys and public data providers, our analysis unfolds in four key stages. Firstly, we delve into the spatial distribution of charging stations, scrutinizing density, proximity to various road types, and land use through the lens of Voronoi diagrams. Secondly, the application of Voronoi diagrams informs the evaluation

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GAVRILOVA, MARINA L. "AN EXPLICIT SOLUTION FOR COMPUTING THE VERTICES OF THE EUCLIDEAN d-DIMENSIONAL VORONOI DIAGRAM OF SPHERES IN A FLOATING-POINT ARITHMETIC." International Journal of Computational Geometry & Applications 19, no. 05 (2009): 415–24. http://dx.doi.org/10.1142/s0218195909003040.

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The problem of computing a d-dimensional Euclidean Voronoi diagram of spheres is relevant to many areas, including computer simulation, motion planning, CAD, and computer graphics. This paper presents a new algorithm based on the explicit computation of the coordinates and radii of Euclidean Voronoi diagram vertices for a set of spheres. The algorithm is further applied to compute the Voronoi diagram with a specified precision in a fixed length floating-point arithmetic. The algorithm is implemented using the ECLibrary (Exact Computation Library) and tested on the example of a 3-dimensional Vo

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DJIDJEV, HRISTO N., and ANDRZEJ LINGAS. "ON COMPUTING VORONOI DIAGRAMS FOR SORTED POINT SETS." International Journal of Computational Geometry & Applications 05, no. 03 (1995): 327–37. http://dx.doi.org/10.1142/s0218195995000192.

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We show that the Voronoi diagram of a finite 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 finite sequence of points in the plane which gives the sorted order of the points with respect to a single direction requires Ω(n log n) operations in the algebraic decision tree model. As a corollary from the first result, we show that the bounded Voronoi diagrams of simple n-vertex polygons which can be efficiently cut into

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Liu, Liu, Xiao Bo Tang, Cai Hong Zhao, Zhen Ya Sha, and Xin Chen. "The Power Supply Area Divided Based on Improved Voronoi Diagram." Advanced Materials Research 989-994 (July 2014): 1278–81. http://dx.doi.org/10.4028/www.scientific.net/amr.989-994.1278.

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This paper describes the basic principles of dipartition of the power supply area and uses Voronoi diagram on the dipartition of the power supply area. This paper put forward a model of improved Voronoi diagram based on the basic Voronoi diagram. Depending on the existing transformer substation’s capacity and power supply area surrounding the spatial distribution of the load, we determine weights based on the main transformer capacity and the spatial distribution of the load. In the process of generating the power supply area, we adjust the weights depending on different regions ofthe spatial

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PAPADOPOULOU, EVANTHA, and D. T. LEE. "THE L∞ VORONOI DIAGRAM OF SEGMENTS AND VLSI APPLICATIONS." International Journal of Computational Geometry & Applications 11, no. 05 (2001): 503–28. http://dx.doi.org/10.1142/s0218195901000626.

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In this paper we address the L∞ Voronoi diagram of polygonal objects and present application in VLSI layout and manufacturing. We show that L∞ Voronoi diagram of polygonal objects consists of straight line segments and thus it is much simpler to compute than its Euclidean counterpart; the degree of the computation is significantly lower. Moreover, it has a natural interpretation. In applications where Euclidean precision is not essential the L∞ Voronoi diagram can provide a better alternative. Using the L∞ Voronoi diagram of polygons we address the problem of calculating the critical area for

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DE LACY COSTELLO, B. P. J., and A. I. ADAMATZKY. "ON MULTITASKING IN PARALLEL CHEMICAL PROCESSORS: EXPERIMENTAL FINDINGS." International Journal of Bifurcation and Chaos 13, no. 02 (2003): 521–33. http://dx.doi.org/10.1142/s0218127403006716.

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A parallel chemical processor is a thin-layer of a reagent mixture which reacts to changes in its concentration — data configuration — in a predictable way to form a stationary pattern corresponding to the concentration of the reagent — result configuration. A computation in the chemical processor is implemented via the spreading and interaction of diffusive or phase waves. We design chemical processors that solve a classical problem of computational geometry — computation of a Voronoi diagram. Namely, we study the possibility of designing a multitasking chemical processor that independently a

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DE LACY COSTELLO, B. P. J., I. JAHAN, P. HAMBIDGE, K. LOCKING, D. PATEL, and A. ADAMATZKY. "CHEMICAL TESSELLATIONS — RESULTS OF BINARY AND TERTIARY REACTIONS BETWEEN METAL IONS AND FERRICYANIDE OR FERROCYANIDE LOADED GELS." International Journal of Bifurcation and Chaos 20, no. 07 (2010): 2241–52. http://dx.doi.org/10.1142/s0218127410027064.

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In our recent letter [de Lacy Costello et al., 2009] we described the formation of spontaneous complex tessellations of the plane constructed in simple chemical reactions between drops of metal salts and ferricyanide or ferrocyanide loaded gels. In this paper, we provide more examples of binary tessellations and extend our analysis to tessellations constructed via tertiary mixtures of reactants. We also provide a classification system which describes the tessellation based on the reactivity of the metal salt with the substrate and also the cross-reactivity of the primary products. This results

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Vleugels, Jules, and Mark Overmars. "Approximating Voronoi Diagrams of Convex Sites in Any Dimension." International Journal of Computational Geometry & Applications 08, no. 02 (1998): 201–21. http://dx.doi.org/10.1142/s0218195998000114.

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Generalized Voronoi diagrams of objects are difficult to compute in a robust way, especially in higher dimensions. For a number of applications an approximation of the real diagram within some predetermined precision is sufficient. In this paper we study the computation of such approximate Voronoi diagrams. The emphasis is on practical applicability, therefore we are mainly concerned with fast (in terms of running time) computation, generality, robustness, and easy implementation, rather than optimal combinatorial and computational complexity. Given a set of disjoint convex sites in any dimens

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Syakura, Anisa, and Atika Zahra. "Penentuan Lokasi Strategis ATM pada Bank Sumsel Babel Syariah Menggunakan Diagram Voronoi." JEMST (Journal of Education in Mathematics, Science, and Technology) 7, no. 1 (2025): 10–19. https://doi.org/10.30631/jemst.v7i1.108.

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Penelitian ini bertujuan untuk menentukan lokasi strategis ATM Bank Sumsel Babel Syariah menggunakan diagram Voronoi. ATM merupakan teknologi perbankan yang memberikan kemudahan akses dan efisiensi transaksi bagi nasabah. Pemilihan lokasi ATM sangat penting karena dapat mempengaruhi jumlah nasabah. Dalam penelitian ini, digunakan diagram Voronoi untuk membagi wilayah menjadi sel-sel Voronoi berdasarkan titik-titik ATM yang ada. Analisis dilakukan terhadap titik-titik tersebut untuk mencari lokasi strategis ATM baru. Hasil penelitian ini dapat memberikan solusi dan masukan kepada pihak-pihak ya

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Hao, Zhanjun, Jianwu Dang, Yan Yan, and Xiaojuan Wang. "A node localization algorithm based on Voronoi diagram and support vector machine for wireless sensor networks." International Journal of Distributed Sensor Networks 17, no. 2 (2021): 155014772199341. http://dx.doi.org/10.1177/1550147721993410.

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For wireless sensor network, the localization algorithm based on Voronoi diagram has been applied. However, the location accuracy node position in wireless sensor network needs to be optimized by the analysis of the literature, a node location algorithm based on Voronoi diagram and support vector machine is proposed in this article. The basic idea of the algorithm is to first divide the region into several parts using Voronoi diagram and anchor node in the localization region. The range of the initial position of the target node is obtained by locating the target node in each region and then t

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Wu, Xiao Yong, Yi Fan Zhu, and Tao Jing. "The Algorithm of Points Set Extracting from 2D Voronoi Diagram Based on Crystal Growth." Applied Mechanics and Materials 130-134 (October 2011): 2249–52. http://dx.doi.org/10.4028/www.scientific.net/amm.130-134.2249.

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The outputs of constructing voronoi diagram with crystal growth algorithm are pixel points set. A whole methodology of extraction of pixel points set is introduced and magnifier scanning algorithm (MSA) which is used to identifying voronoi vertexes and edges is explained in detail. Experiments show that the methodology and MSA is clear and accurate to weighted voronoi diagram.

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Rupšys, Petras. "Voronoi diagramų tyrimas ir taikymas." Lietuvos matematikos rinkinys 43 (December 22, 2003): 597–601. http://dx.doi.org/10.15388/lmr.2003.32535.

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In this paper an algorithm for constructing Voronoi diagram is given. Efficiency of the algorithm is investigated by the Monte Carlo simulation method. The Voronoi diagram is applied in the field of forestry.

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Adamatzky, Andrew, Ben De Lacy Costello, Julian Holley, Jerzy Gorecki, and Larry Bull. "Vesicle computers: Approximating a Voronoi diagram using Voronoi automata." Chaos, Solitons & Fractals 44, no. 7 (2011): 480–89. http://dx.doi.org/10.1016/j.chaos.2011.01.016.

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Zeinab, Hassani, and Eskandari Marzieh. "On the facility location problem: One-round weighted Voronoi game." Mathematical Researches 6, no. 1 (2020): 47–56. https://doi.org/10.5281/zenodo.4825416.

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The Voronoi game is a simple geometric model for competitive facility location problem which is played by two players, White and Black, in a continuous space (one-dimensional or two-dimensional). In the one-round game, White places all his n points. After that, Black places the same number of points on the game space. The players Cannot change or reuse a point that was placed before. At the end of the game, the Voronoi diagram of all 2n points is constructed and a player who obtains the larger total area is the winner. Ahn et al. considered the Voronoi game on a unit circle and a line. They pr

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NamAnh, Dao, and Nguyen Huu Quynh. "Saliency Detection with VORONOI Diagram." International Journal of Computer Applications 118, no. 12 (2015): 27–34. http://dx.doi.org/10.5120/20798-3468.

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Hanahara, Kazuyuki. "On Generalization of Voronoi Diagram." Transactions of the Institute of Systems, Control and Information Engineers 34, no. 6 (2021): 173–80. http://dx.doi.org/10.5687/iscie.34.173.

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Liu, Jingna, and Ye Zhao. "Spatial Density Network Voronoi Diagram." Open Cybernetics & Systemics Journal 8, no. 1 (2014): 1052–57. http://dx.doi.org/10.2174/1874110x014080101052.

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Aurenhammer, F., and G. Stöckl. "On the Peeper's Voronoi diagram." ACM SIGACT News 22, no. 4 (1991): 50–59. http://dx.doi.org/10.1145/126546.126548.

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Yang, KwangSoo, Apurv Hirsh Shekhar, Dev Oliver, and Shashi Shekhar. "Capacity-Constrained Network-Voronoi Diagram." IEEE Transactions on Knowledge and Data Engineering 27, no. 11 (2015): 2919–32. http://dx.doi.org/10.1109/tkde.2015.2445756.

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Fan, Chenglin, Jun Luo, Wencheng Wang, and Binhai Zhu. "Voronoi diagram with visual restriction." Theoretical Computer Science 532 (May 2014): 31–39. http://dx.doi.org/10.1016/j.tcs.2013.08.008.

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Giavazzi, F., R. Cerbino, S. Mazzoni, M. Giglio, and A. Vailati. "Optical generation of Voronoi diagram." Optics Express 16, no. 7 (2008): 4819. http://dx.doi.org/10.1364/oe.16.004819.

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Laraqui, A., A. Baataoui, A. Saaidi, A. Jarrar, Med Masrar, and K. Satori. "Image mosaicing using voronoi diagram." Multimedia Tools and Applications 76, no. 6 (2016): 8803–29. http://dx.doi.org/10.1007/s11042-016-3478-z.

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Xu, Yong, Xiao Hong Fan, Ke Gao Liu, et al. "Applying and Practicing of MATLAB Programing for Voronoi Tessellation." Advanced Materials Research 706-708 (June 2013): 391–94. http://dx.doi.org/10.4028/www.scientific.net/amr.706-708.391.

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Three-dimensional (3D) Voronoi tessellation diagrams are generated by compiling program in MATLAB software. According to these 3D Voronoi cells, crystal structure, even the disorder structure, can be geometrically described and tessellated into the regular object, reflecting the atomic structural parameters, such as the coordination numbers (CN) and the atomic separation. Studying the characteristic of these tessellations, we can find the rule of atomic packing in real space. This Voronoi diagram is also useful in materials structure teaching curriculum and it is the significant basis to reali

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Azimi, S., M. R. Delavar, and A. Rajabifard. "MULTI-AGENT SIMULATION OF ALLOCATING AND ROUTING AMBULANCES UNDER CONDITION OF STREET BLOCKAGE AFTER NATURAL DISASTER." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-4/W4 (September 27, 2017): 325–32. http://dx.doi.org/10.5194/isprs-archives-xlii-4-w4-325-2017.

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In response to natural disasters, efficient planning for optimum allocation of the medical assistance to wounded as fast as possible and wayfinding of first responders immediately to minimize the risk of natural disasters are of prime importance. This paper aims to propose a multi-agent based modeling for optimum allocation of space to emergency centers according to the population, street network and number of ambulances in emergency centers by constraint network Voronoi diagrams, wayfinding of ambulances from emergency centers to the wounded locations and return based on the minimum ambulance

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BOHLER, CECILIA, and ROLF KLEIN. "ABSTRACT VORONOI DIAGRAMS WITH DISCONNECTED REGIONS." International Journal of Computational Geometry & Applications 24, no. 04 (2014): 347–72. http://dx.doi.org/10.1142/s0218195914600115.

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Abstract Voronoi diagrams, AVDs for short, are based on bisecting curves enjoying simple combinatorial properties, rather than on the geometric notions of sites and distance. They serve as a unifying concept. Once the bisector system of any concrete type of Voronoi diagram is shown to fulfill the AVD axioms, structural results and efficient algorithms become available without further effort; for example, the first optimal algorithms for constructing nearest Voronoi diagrams of disjoint convex objects, or of line segments under the Hausdorff metric, have been obtained this way. One of these axi

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NISHIDA, TETSUSHI, and KOKICHI SUGIHARA. "BOAT-SAIL VORONOI DIAGRAM AND ITS APPLICATION." International Journal of Computational Geometry & Applications 19, no. 05 (2009): 425–40. http://dx.doi.org/10.1142/s0218195909003052.

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A new generalized Voronoi diagram, called a boat-sail Voronoi diagram, is defined on the basis of the time necessary for a boat to reach on water surface with flow. A new concept called a boat-sail distance is introduced on the surface of water with flow, and it is used to define a generalized Voronoi diagram, in such a way that the water surface is partitioned into regions belonging to the nearest harbors with respect to this distance. The problem of computing this Voronoi diagram is reduced to a boundary value problem of a partial differential equation, and a numerical method for solving thi

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LU, YUE, CHUNYUN XIAO, and CHEW LIM TAN. "CONSTRUCTING AREA VORONOI DIAGRAM BASED ON DIRECT CALCULATION OF THE FREEMAN CODE OF EXPANDED CONTOURS." International Journal of Pattern Recognition and Artificial Intelligence 21, no. 05 (2007): 947–60. http://dx.doi.org/10.1142/s0218001407005764.

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A Voronoi diagram of image elements provides an intuitive and appealing definition of proximity, which has been suggested as an effective tool for the description of relations among the neighboring objects in a digital image. In this paper, an implementation algorithm based on direct calculation of the Freeman code of expanded contours is proposed for generating area Voronoi diagram of connected components. A closed convex polygon is utilized to bound each connected component, as an approximate representation, and the contour is represented using Freeman chain coding, from which we can compute

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GÖRKE, ROBERT, CHAN-SU SHIN, and ALEXANDER WOLFF. "CONSTRUCTING THE CITY VORONOI DIAGRAM FASTER." International Journal of Computational Geometry & Applications 18, no. 04 (2008): 275–94. http://dx.doi.org/10.1142/s0218195908002623.

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Given a set P of n point sites in the plane, the city Voronoi diagram subdivides the plane into the Voronoi regions of the sites, with respect to the city metric. This metric is induced by quickest paths according to the Manhattan metric and an accelerating transportation network that consists of c non-intersecting axis-parallel line segments. We describe an algorithm that constructs the city Voronoi diagram (including quickest path information) using O((c+n) polylog (c+n)) time and storage by means of a wavefront expansion. For [Formula: see text] our algorithm is faster than an algorithm by

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Liu, Yilin, Jiale Chen, Shanshan Pan, Daniel Cohen-Or, Hao Zhang, and Hui Huang. "Split-and-Fit: Learning B-Reps via Structure-Aware Voronoi Partitioning." ACM Transactions on Graphics 43, no. 4 (2024): 1–13. http://dx.doi.org/10.1145/3658155.

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We introduce a novel method for acquiring boundary representations (B-Reps) of 3D CAD models which involves a two-step process: it first applies a spatial partitioning , referred to as the "split", followed by a "fit" operation to derive a single primitive within each partition. Specifically, our partitioning aims to produce the classical Voronoi diagram of the set of ground-truth (GT) B-Rep primitives. In contrast to prior B-Rep constructions which were bottom-up, either via direct primitive fitting or point clustering, our Split-and-Fit approach is top-down and structure-aware , since a Voro

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Wang, Hui. "Discrete Construction of Compoundly Weighted Voronoi Diagram." Applied Mechanics and Materials 467 (December 2013): 545–48. http://dx.doi.org/10.4028/www.scientific.net/amm.467.545.

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Compoundly weighted Voronoi diagram is difficult to construct because the bisector is fairly complex. In traditional algorithm, production process is always extremely complex and it is more difficult to graphic display because of the complex definition of mathematic formula. In this paper, discrete algorithms are used to construct compoundly weighted Voronoi diagrams. The algorithm can get over all kinds of shortcomings that we have just mentioned. So it is more useful and effective than the traditional algorithm. The results show that the algorithm is both simple and useful, and it is of high

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SMID, MICHIEL, and RAVI JANARDHAN. "ON THE WIDTH AND ROUNDNESS OF A SET OF POINTS IN THE PLANE." International Journal of Computational Geometry & Applications 09, no. 01 (1999): 97–108. http://dx.doi.org/10.1142/s021819599900008x.

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Let S be a set of points in the plane. The width (resp. roundness) of S is defined as the minimum width of any slab (resp. annulus) that contains all points of S. We give a new characterization of the width of a point set. Also, we give a rigorous proof of the fact that either the roundness of S is equal to the width of S, or the center of the minimum-width annulus is a vertex of the closest-point Voronoi diagram of S, the furthest-point Voronoi diagram of S, or an intersection point of these two diagrams. This proof corrects the characterization of roundness used extensively in the literature

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HERMANTO, MELINDA, TJOKORDA BAGUS OKA, and I. PUTU EKA NILA KENCANA. "PENENTUAN LOKASI SMA NEGERI MENGGUNAKAN DIAGRAM VORONOI BERBOBOT DI KOTA DENPASAR." E-Jurnal Matematika 2, no. 2 (2013): 27. http://dx.doi.org/10.24843/mtk.2013.v02.i02.p034.

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In school development problem, determining location is one of important things to consider. In this research, the purpose is to determine the location of SMAN 9 Denpasar if it will be built. One of algorithms in computational geometry that can be used to find solution of facility location problem is multiplicatively weighted Voronoi diagram in two dimensions. The result of weighted Voronoi diagram shows the influence of each site to the surrounding area. Then, the location of SMAN 9 Denpasar is obtained by determining the center of the largest empty circle of the weighted Voronoi diagram.

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