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Academic literature on the topic 'Additively Weighted Voronoi Diagram'

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Published: 6 September 2023

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Journal articles on the topic "Additively Weighted Voronoi Diagram"

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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 (April 1, 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 the Voronoi diagram itself. However, the Voronoi diagram, the quasi-triangulation, and the beta-complexes are sometimes regarded as somewhat difficult for ordinary users to understand. This paper presents the twodimensional counterparts of their definitions and introduce the BetaConcept program which implements the theory so that users can easily learn the powerful concept and capabilities of these constructs in a plane. The BetaConcept program was implemented in the standard C++ language with MFC and OpenGL and freely available at Voronoi Diagram Research Center (http://voronoi.hanyang.ac.kr).
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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 (July 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 in balanced tessellations where both reactants have equal reactivity or unbalanced tessellations where one reactant has a lower reactivity with the gel. The products can also be partially or fully cross reactive which gives a highly complex tessellation. The tessellations are made up of colored cells (corresponding to different metal ferricyanides or ferrocyanides) separated by bisectors of low precipitate concentration. The tessellations constructed by these reactions constitute generalized Voronoi diagrams. In the case of certain binary or tertiary combinations of reactants where the diffusion/reaction rates differ, then multiplicatively weighted crystal growth Voronoi diagrams are constructed. Where one reactant has limited or no reactivity with the gel (or the products are cross reactive) then the fronts originating from the reactive metal ions cross the fronts originating from the partially reactive metal ions. The fronts can annihilate in the formation of a second Voronoi diagram relating to the relative positions of the reactive drops. Therefore, two or more generalised or weighted Voronoi diagrams can be calculated in parallel by these simple chemical systems. However when these reactions were used to calculate an additively weighted Voronoi diagram (the reaction was initiated at different time intervals) the diagram constructed did not correspond to the theoretical calculation. We use the failure of these reactions to construct an additively weighted Voronoi diagram to prove a mechanism of substrate competition for bisector formation. These tessellations are an important class of pattern forming reactions and are useful in modeling natural pattern forming phenomena in addition to being a great resource for scientific demonstrations.
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Manak, M. "Exploration of Empty Space among Spherical Obstacles via Additively Weighted Voronoi Diagram." Computer Graphics Forum 35, no. 5 (August 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 (March 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 products) these processors are also capable of calculating Voronoi diagrams sequentially from distinct chemical inputs. The chemical processors are capable of calculating a range of generalised Voronoi diagrams (either from circular drops of chemical or other geometric shapes made from adsorbent substrates soaked in reagent) , skeletonisation of planar shapes and weighted Voronoi diagrams (e.g., additively weighted Voronoi diagrams, Multiplicitavely weighted Crystal growth Voronoi diagrams). The paper will also discuss some limitations of these processors. These chemical processors constitute a class of pattern forming reactions which have parallels with those observed in natural systems. It is possible that specialised chemical processors of this general type could be useful for synthesising functional structured materials.
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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 (September 1, 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 appropriate gradient ascent-based control scheme is derived so that it guarantees monotonic increase of a coverage objective and is extended with collision avoidance properties. Additionally, a computationally efficient simplified control scheme is offered that is able to achieve comparable performance. Several simulation studies are offered to evaluate the performance of the two control schemes. Finally, two experiments using small differential drive-like robots and an ultra-wideband positioning system were conducted, highlighting the performance of the proposed control scheme in a real world scenario.
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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 (October 2012): 1811–29. http://dx.doi.org/10.1080/13658816.2012.655742.

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Charalampopoulos, Panagiotis, Paweł Gawrychowski, Yaowei Long, Shay Mozes, Seth Pettie, Oren Weimann, and Christian Wulff-Nilsen. "Almost Optimal Exact Distance Oracles for Planar Graphs." Journal of the ACM 70, no. 2 (March 25, 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) space and log 2+ o (1) n query time, n log 2+ o (1) n space and n o (1) query time, n 4/3+ o (1) space and log 1+ o (1) n query time. We reduce a distance query to a variety of point location problems in additively weighted Voronoi diagrams and develop new algorithms for the point location problem itself using several partially persistent dynamic tree data structures.
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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 (September 22, 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 $$O(n^{\varepsilon })$$ O ( n ε ) time for an update and $$O(\log n)$$ O ( log n ) time for a query [SICOMP 1999]. Our data structure has numerous applications. In all of them, it gives faster algorithms, typically reducing an $$O(n^{\varepsilon })$$ O ( n ε ) factor in the previous bounds to polylogarithmic. In addition, we give here two new applications: an efficient construction of a spanner in a disk intersection graph, and a data structure for efficient connectivity queries in a dynamic disk graph. To obtain this data structure, we combine and extend various techniques from the literature. Along the way, we obtain several side results that are of independent interest. Our data structure depends on the existence and an efficient construction of “vertical” shallow cuttings in arrangements of bivariate algebraic functions. We prove that an appropriate level in an arrangement of a random sample of a suitable size provides such a cutting. To compute it efficiently, we develop a randomized incremental construction algorithm for computing the lowest k levels in an arrangement of bivariate algebraic functions (we mostly consider here collections of functions whose lower envelope has linear complexity, as is the case in the dynamic nearest-neighbor context, under both types of norm). To analyze this algorithm, we also improve a longstanding bound on the combinatorial complexity of the vertical decomposition of these levels. Finally, to obtain our structure, we combine our vertical shallow cutting construction with Chan’s algorithm for efficiently maintaining the lower envelope of a dynamic set of planes in $${{\mathbb {R}}}^3$$ R 3 . Along the way, we also revisit Chan’s technique and present a variant that uses a single binary counter, with a simpler analysis and improved amortized deletion time (by a logarithmic factor; the insertion and query costs remain asymptotically the same).
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Aurenhammer, Franz. "The one-dimensional weighted voronoi diagram." Information Processing Letters 22, no. 3 (March 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 (May 31, 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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Dissertations / Theses on the topic "Additively Weighted Voronoi Diagram"

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Su, Chih-Cheng, and 蘇志盛. "Adaptive 3D Remeshing Scheme Using Weighted Centroidal Voronoi Diagram." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/75039786380329590568.

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碩士
國立成功大學
資訊工程學系碩博士班
91
In computer graphics and geometric modeling, surfaces are often represented by triangular meshes. Somehow, the triangular meshes are often irregular and complicate processing such as numerical analysis, texturing, and storage. We present a novel method to decompose an arbitrary 3D model, and then resample vertices in the model by low-distortion parameterization. There are two goals of this decomposition process: automatic and size-equally. We first need to cut a 2-manifold mesh into several disk-like patches. For each patch, we automatically partition it into more triangular patches. With the help of weighted centroidal Voronoi diagram (WCVD), these triangular patches are equally sized. Recursivelly subdividing these triangular patches, we finally get a regular model.
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Tsai, Yi-Chun, and 蔡宜君. "Using Enhanced Weighted Voronoi Diagram for Mobile Service Positioning System." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/85430946644142957213.

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碩士
國立中山大學
資訊工程學系研究所
93
The objective of this thesis is to design a mobile positioning system on the premise that low system complexity and less modification of components of Mobile Communication System to improve the possibility that adopted by service provider. Therefore we propose a Mobile Service Positioning System for Cellular Mobile Communication System. It works based on location information of base station and mutual relations of signal strength of base stations received by mobile phone. We adjust the environment factor upon different path loss caused by different geographical feature. And then we perform EWVD Algorithm to estimate the area where mobile phone locates in. Eventually, we obtain a Mobile Positioning System which has properties: lower building cost, smaller locating area, and faster response time.
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Books on the topic "Additively Weighted Voronoi Diagram"

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Rosenberger, Harald. Order-k Voronoi diagrams of sites with additive weights in the plane. Urbana, Il: Dept. of Computer Science, University of Illinois at Urbana-Champaign, 1988.

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Schreiber, Thomas. A voronoi diagram based adaptive k-means-type clustering algorithm for multidimensional weighted data. Kaiserslautern: Universität Kaiserslautern, 1991.

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Book chapters on the topic "Additively Weighted Voronoi Diagram"

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Liu, Xin, Yili Tan, and Hongmei Yang. "Dynamic Construction of Additively Weighted Network Voronoi Diagram." In Communications in Computer and Information Science, 322–27. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-34041-3_46.

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Boissonnat, Jean-Daniel, and Christophe Delage. "Convex Hull and Voronoi Diagram of Additively Weighted Points." In Algorithms – ESA 2005, 367–78. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11561071_34.

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Cheung, Jacky Kit, Oscar Kin-Chung Au, and Kening Zhu. "Additive Voronoi Cursor: Dynamic Effective Areas Using Additively Weighted Voronoi Diagrams." In Human-Computer Interaction – INTERACT 2019, 273–92. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-29387-1_16.

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Karavelas, Menelaos I., and Mariette Yvinec. "Dynamic Additively Weighted Voronoi Diagrams in 2D." In Algorithms — ESA 2002, 586–98. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-45749-6_52.

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Lee, Mokwon, Kokichi Sugihara, and Deok-Soo Kim. "Robust Construction of the Additively-Weighted Voronoi Diagram via Topology-Oriented Incremental Algorithm." In Mathematical Software – ICMS 2016, 514–21. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-42432-3_66.

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Lin, Chao-Hung, Chung-Ren Yan, Ji-Hsen Hsu, and Tong-Yee Lee. "Multiresolution Remeshing Using Weighted Centroidal Voronoi Diagram." In Computational Science – ICCS 2006, 295–301. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11758525_39.

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Malmir, Mohammadhossein, Shahin Boluki, and Saeed Shiry Ghidary. "Offensive Positioning Based on Maximum Weighted Bipartite Matching and Voronoi Diagram." In RoboCup 2014: Robot World Cup XVIII, 562–70. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-18615-3_46.

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Daescu, Ovidiu, and James Dean Palmer. "Modeling Optimal Beam Treatment with Weighted Regions for Bio-medical Applications." In Generalized Voronoi Diagram: A Geometry-Based Approach to Computational Intelligence, 215–32. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-85126-4_9.

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Will, Hans Martin. "Fast and efficient computation of additively weighted Voronoi cells for applications in molecular biology." In Algorithm Theory — SWAT'98, 310–21. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0054378.

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Dang, Xiaochao, Yili Hei, and Zhanjun Hao. "A Clustering Density Weighted Algorithm of KNN Fingerprint Location Based on Voronoi Diagram." In Communications in Computer and Information Science, 175–90. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-10-8123-1_16.

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Conference papers on the topic "Additively Weighted Voronoi Diagram"

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Nguyen, N. A., S. Olaru, and P. Rodriguez-Ayerbe. "Recognition of additively weighted Voronoi diagrams and weighted Delaunay decompositions." In 2015 European Control Conference (ECC). IEEE, 2015. http://dx.doi.org/10.1109/ecc.2015.7330565.

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Ohyama, Takashi. "Division of a Region into Equal Areas Using Additively Weighted Power Diagrams." In 4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007). IEEE, 2007. http://dx.doi.org/10.1109/isvd.2007.20.

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Sadakane, K., H. Imai, K. Onishi, M. Inaba, F. Takeuchi, and K. Imai. "Voronoi diagrams by divergences with additive weights." In the fourteenth annual symposium. New York, New York, USA: ACM Press, 1998. http://dx.doi.org/10.1145/276884.276929.

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Long, X. Q., Y. B. Zhang, and Y. R. Chen. "The method of network-based weighted Voronoi diagram." In 2013 International Conference of Information Science and Management Engineering. Southampton, UK: WIT Press, 2013. http://dx.doi.org/10.2495/isme131382.

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Zhu, Xiaojun, Wenzuo Tang, Yumin Liu, Hongqin Yang, Wei Cong, and Wuyang Gai. "Distribution substation planning method based on weighted Voronoi diagram." In 2016 IEEE PES Asia-Pacific Power and Energy Engineering Conference (APPEEC). IEEE, 2016. http://dx.doi.org/10.1109/appeec.2016.7779819.

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Albano, Michele, Laura Ricci, and Luca Genovali. "Hierarchical p2p overlays for DVE: An Additively Weighted Voronoi based approach." In Workshops (ICUMT). IEEE, 2009. http://dx.doi.org/10.1109/icumt.2009.5345362.

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Feng, Liang, Shaoyun Ge, and Hong Liu. "Electric Vehicle Charging Station Planning Based on Weighted Voronoi Diagram." In 2012 IEEE PES Asia-Pacific Power and Energy Engineering Conference (APPEEC). IEEE, 2012. http://dx.doi.org/10.1109/appeec.2012.6307218.

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Xiangang Tang, Junyong Liu, Xiaoyin Wang, and Jie Xiong. "Electric vehicle charging station planning based on weighted Voronoi diagram." In 2011 International Conference on Transportation and Mechanical & Electrical Engineering (TMEE). IEEE, 2011. http://dx.doi.org/10.1109/tmee.2011.6199443.

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Fan, Yong-Feng, Wen-Xia Liu, Jian-Hua Zhang, and Xu Yang. "The Dynamic Planning of Urban Substation Based on Weighted Voronoi Diagram." In 2009 Asia-Pacific Power and Energy Engineering Conference. IEEE, 2009. http://dx.doi.org/10.1109/appeec.2009.4918879.

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Feng, Dianjun, Chenhua Shen, Xujiao Wang, Yali Si, and Chaoling Li. "Spatial distribution optimization of rural settlements using the Weighted Voronoi Diagram." In International Conference on Earth Science and Environmental Protection (ICESEP2013). Southampton, UK: WIT Press, 2013. http://dx.doi.org/10.2495/icesep130741.

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