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Relevant bibliographies by topics / Additively Weighted Voronoi Diagram

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Academic literature on the topic 'Additively Weighted Voronoi Diagram'

Author: Grafiati

Published: 6 September 2023

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Journal articles on the topic "Additively Weighted Voronoi Diagram"

1

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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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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3

Manak, M. "Exploration of Empty Space among Spherical Obstacles via Additively Weighted Voronoi Diagram." Computer Graphics Forum 35, no. 5 (2016): 249–58. http://dx.doi.org/10.1111/cgf.12980.

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De Lacy Costello, Ben. "Calculating Voronoi Diagrams Using Simple Chemical Reactions." Parallel Processing Letters 25, no. 01 (2015): 1540003. http://dx.doi.org/10.1142/s0129626415400034.

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This paper overviews work on the use of simple chemical reactions to calculate Voronoi diagrams and undertake other related geometric calculations. This work highlights that this type of specialised chemical processor is a model example of a parallel processor. For example increasing the complexity of the input data within a given area does not increase the computation time. These processors are also able to calculate two or more Voronoi diagrams in parallel. Due to the specific chemical reactions involved and the relative strength of reaction with the substrate (and cross-reactivity with the

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Papatheodorou, Sotiris, Anthony Tzes, Konstantinos Giannousakis, and Yiannis Stergiopoulos. "Distributed area coverage control with imprecise robot localization." International Journal of Advanced Robotic Systems 15, no. 5 (2018): 172988141879749. http://dx.doi.org/10.1177/1729881418797494.

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This article examines the static area coverage problem by a network of mobile, sensor-equipped agents with imprecise localization. Each agent has uniform radial sensing ability and is governed by first-order kinodynamics. To partition the region of interest, a novel partitioning scheme, the Additively Weighted Guaranteed Voronoi diagram is introduced which takes into account both the agents’ positioning uncertainty and their heterogeneous sensing performance. Each agent’s region of responsibility corresponds to its Additively Weighted Guaranteed Voronoi cell, bounded by hyperbolic arcs. An app

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Moreno-Regidor, Pilar, Jésus García López de Lacalle, and Miguel-Ángel Manso-Callejo. "Zone design of specific sizes using adaptive additively weighted Voronoi diagrams." International Journal of Geographical Information Science 26, no. 10 (2012): 1811–29. http://dx.doi.org/10.1080/13658816.2012.655742.

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7

Charalampopoulos, Panagiotis, Paweł Gawrychowski, Yaowei Long, et al. "Almost Optimal Exact Distance Oracles for Planar Graphs." Journal of the ACM 70, no. 2 (2023): 1–50. http://dx.doi.org/10.1145/3580474.

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We consider the problem of preprocessing a weighted directed planar graph in order to quickly answer exact distance queries. The main tension in this problem is between space S and query time Q , and since the mid-1990s all results had polynomial time-space tradeoffs, e.g., Q = ~ Θ( n/√ S ) or Q = ~Θ( n 5/2 /S 3/2 ). In this article we show that there is no polynomial tradeoff between time and space and that it is possible to simultaneously achieve almost optimal space n 1+ o (1) and almost optimal query time n o (1) . More precisely, we achieve the following space-time tradeoffs: n 1+ o (1) s

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Kaplan, Haim, Wolfgang Mulzer, Liam Roditty, Paul Seiferth, and Micha Sharir. "Dynamic Planar Voronoi Diagrams for General Distance Functions and Their Algorithmic Applications." Discrete & Computational Geometry 64, no. 3 (2020): 838–904. http://dx.doi.org/10.1007/s00454-020-00243-7.

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Abstract We describe a new data structure for dynamic nearest neighbor queries in the plane with respect to a general family of distance functions. These include $$L_p$$ L p -norms and additively weighted Euclidean distances. Our data structure supports general (convex, pairwise disjoint) sites that have constant description complexity (e.g., points, line segments, disks, etc.). Our structure uses $$O(n \log ^3 n)$$ O ( n log 3 n ) storage, and requires polylogarithmic update and query time, improving an earlier data structure of Agarwal, Efrat, and Sharir which required $$O(n^{\varepsilon })$

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9

Aurenhammer, Franz. "The one-dimensional weighted voronoi diagram." Information Processing Letters 22, no. 3 (1986): 119–23. http://dx.doi.org/10.1016/0020-0190(86)90055-4.

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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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