Relevant bibliographies by topics / Voronoiův diagram

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  2. Dissertations / Theses
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Academic literature on the topic 'Voronoiův diagram'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Voronoiův diagram"

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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 Cauchy hyperbolic Delaunay complexes are Fisher orthogonal to the Cauchy hyperbolic Voronoi diagrams. The dual Voronoi diagrams with respect to the dual flat divergences amount to dual Bregman Voronoi diagrams, and their dual complexes are regular triangulations. The primal Bregman Voronoi diagram is the Euclidean Voronoi diagram and the dual Bregman Voronoi diagram coincides with the Cauchy hyperbolic Voronoi diagram. In addition, we prove that the square root of the Kullback-Leibler divergence between Cauchy distributions yields a metric distance which is Hilbertian for the Cauchy scale families.
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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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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 the interaction of stable forced trigger waves and the other that corresponds to the spontaneous initiation and interaction of waves due to point instabilities in the system. In the case of the chemical systems front initiation, propagation and interaction (annihilation) are the primary mechanisms for Voronoi diagram formation, in the case of the barrier gas-discharge system regions of vanishing electric field define the medial axes of the Voronoi diagram. On the basis of cellular automata models the general concept of the formation of Voronoi diagrams has been explained, and related mechanisms have been simulated. Another intuitive approach towards the understanding of self-organized Voronoi diagrams has been given on the basis of reaction–diffusion models explaining the formation of Voronoi diagrams as a result of the mutual interactions of trigger fronts. The variety of systems exhibiting Voronoi diagrams as stationary states indicates that Voronoi diagrams are a generic and natural pattern formation phenomenon.
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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 way as a convex hull relates to the ordinary Voronoi diagram. The Hausdorff Voronoi diagram finds direct application in the problem of computing the critical area of a VLSI Layout, a measure reflecting the sensitivity of a VLSI design to random manufacturing defects, described in a companion paper.13
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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 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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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 construct a convex hull and compute the farthest hull in O(n log n) or output sensitive O(n log h) time, where n is the number of line-segments and h is the number of faces in the corresponding farthest Voronoi diagram. As a result, the farthest line-segment Voronoi diagram can be constructed in output sensitive O(n log h) time. Our algorithms are given in the Euclidean plane but they hold also in the general Lp metric, 1 ≤ p ≤ ∞.
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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 complexity might become too large based on the number of objects. To reduce this computation time in a kNN search, many researchers have proposed a search method that divides regions using a Voronoi diagram. However, since conventional methods generate Voronoi diagrams for objects in order, the processing time for generating Voronoi diagrams might become too large when the number of objects is increased. In this paper, we propose a generation method of the Voronoi diagram by parallelizing the generation of Voronoi regions using a contact zone. Our proposed method can reduce the processing time of generating the Voronoi diagram by generating Voronoi regions in parallel based on the number of targets. Our evaluation confirmed that the processing time under the proposed method was reduced about 15.9\% more than conventional methods that are not parallelized.
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BOUGLEUX, SÉBASTIEN, MAHMOUD MELKEMI, and ABDERRAHIM ELMOATAZ. "STRUCTURE DETECTION FROM A 3D SET OF POINTS WITH ANISOTROPIC ALPHA-SHAPES." International Journal of Image and Graphics 07, no. 04 (2007): 689–708. http://dx.doi.org/10.1142/s0219467807002866.

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We present a method to extract polyhedral structures from a three-dimensional set of points, even if these structures are embedded in a perturbed background. The method is based on a family of affine diagrams which is an extension of the Voronoi diagram. These diagrams, namely anisotropic diagrams, are defined by using a parameterized distance whose unit ball is an ellipsoidal one. The parameters, upon which this distance depends, control the elongation and the orientation of the associated ellipsoidal ball. The triangulations, dual to the anisotropic diagrams, have the property to connect points that are not neighbors in the Voronoi diagram. Based on these triangulations, we define a family of three-dimensional anisotropic α-shapes. Unlike Euclidean α-shapes, anisotropic ones allow us to detect linear and planar structures in a given direction. The detection of more general polyhedral structures is obtained by merging several anisotropic α-shapes computed for different orientations.
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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 parallel. Thus an increase in the complexity of the data input does not utilise additional computational resource. Additional benefits of these chemical reactions are that a permanent record of the Voronoi diagram calculation (in the form of precipitate free bisectors) is achieved, so there is no requirement for further processing to extract the calculation results. Previously it was assumed that the permanence of the results was also a potential drawback which limited reusability. This paper presents new data which shows that sequential Voronoi diagram calculations can be performed on the same chemical substrate. This is dependent on the reactivity of the original reagent and the cross reactivity of the secondary reagent with the primary product. The authors present the results from a number of binary combinations of metal salts on both potassium ferricyanide and potassium ferrocyanide substrates. The authors observe three distinct mechanisms whereby secondary sequential Voronoi diagrams can be calculated. In most cases the result was two interpenetrating permanent Voronoi diagrams. This is interesting from the perspective of mapping the capability of unconventional computing substrates. But also in the study of natural pattern formation per se.
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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 dimension, we describe a general algorithm that approximates their Voronoi diagram with arbitrary precision. The only primitive operation that is required is the computation of the distance from a point to a site. The method is illustrated by its application to motion planning using retraction. To justify our claims on practical applicability, we provide experimental results obtained with implementations of the method in two and three dimensions.
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Dissertations / Theses on the topic "Voronoiův diagram"

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Žižka, Pavel. "Stereoskopické řízení robota." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2011. http://www.nusl.cz/ntk/nusl-235523.

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This work describes 3D reconstruction using stereo vision. It presents methods for automatic localization of corresponding points in both images and their reprojection into 3D space. Application created can be used for navigation of a robot and object avoidance. Second part of the document describes chosen components of the robot. Path finding algorithms are also discussed, particulary Voronoi's diagram.
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Vosylius, Audrius. "Voronoi diagramų braižymas ląsteliniu automatu." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2005. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2005~D_20050606_192058-10796.

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In this work Voronoi diagrams which are drawn by the cellular automaton are discussed. The square and hexagon cellular automata were created and used for drawing Voronoi diagrams. As a result of using the created programs Voronoi diagrams, which are obtained in case of two and more dots, are observed. The following results of the research were achieved: § Voronoi diagram can be obtained by the cellular automaton. § Voronoi diagrams, which were obtained, are not precise due to different speed of movement in different directions. § In square - cell case the obtained diagrams depend on the chosen situation of the neighbors. § In hexagon - cell case the obtained Voronoi diagrams are more but not completely precise. The mathematic calculations are not being made while creating Voronoi diagrams by the cellular automaton.. The diagrams are obtained in short period of time. It is possible to watch the process of the diagram creation. A lot of computer's operation time is lost not during the calculation but for re-drawing the obtained image. This is the reason why it is necessary to optimize the image creating algorithm.
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Lee, King-for Foris, and 李敬科. "Clustering uncertain data using Voronoi diagram." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2009. http://hub.hku.hk/bib/B43224131.

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Lee, King-for Foris. "Clustering uncertain data using Voronoi diagram." Click to view the E-thesis via HKUTO, 2009. http://sunzi.lib.hku.hk/hkuto/record/B43224131.

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Žvikaitė, Laura. "Voronojaus diagramos ir jų taikymai." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2005. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2005~D_20050603_092713-98814.

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In these theses are pepresented the Voronoi diagram and Network Voronoi diagram. The shortest path Dijkstra’s algorithm was modified in this way that calculates shortest paths from several Voronoi generators at the same time. The first result - partition of the nodes of the network. The seond result - arcs of the network are attributed to the generators, considering especially their direction and asymmetric costs. Applications allow compare Network Voronoi diagrams to Voronoi diagrams. For this puspose we modified Fortune algorithm. We made particular product for Taxi depot. The user can make his own implementation.
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Santana, Juliana Exel 1986. "Representação da área de responsabilidade de jogadores de futebol através do Diagrama de Voronoi." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/274723.

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Orientador: Sérgio Augusto Cunha<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Educação Física<br>Made available in DSpace on 2018-08-17T12:23:18Z (GMT). No. of bitstreams: 1 Santana_JulianaExel_M.pdf: 6461488 bytes, checksum: 731aaed1e02fe448da4b39f4f7b8fb28 (MD5) Previous issue date: 2011<br>Resumo: O desempenho de jogadores de futebol de elite durante uma partida é diretamente influenciado por fatores físicos, psicológicos, técnicos, táticos e entre outros. Um suporte científico capaz de buscar e aplicar metodologias que quantifiquem esses fatores é uma fonte importante de informações para que técnicos e treinadores tenham melhores condições de efetuar uma boa preparação da sua equipe. Dentro dos estudos cinemáticos no esporte, a videogrametria tem se mostrado uma ferramenta acurada para a obtenção da posição dos jogadores em função do tempo. Dentro dos aspectos táticos de um jogo de futebol, a forma como uma equipe divide o campo em áreas de responsabilidade e como essa distribuição se dá ao longo do jogo pode ser descrita através de técnicas matemáticas. Nesse sentido, o objetivo deste estudo será apresentar uma forma de representação da área de responsabilidade de jogadores de futebol durante partidas oficiais, através do Diagrama de Voronoi. Para tal, foram coletadas as imagens de 4 jogos de futebol. Os processos de segmentação das imagens e de rastreamento dos jogadores para a obtenção dos dados 2D em função do tempo foram realizados através do software DVideo®. Para as análises, foi aplicado a metodologia do Diagrama de Voronoi nas coordenadas 2D de 33 jogadores de uma mesma equipe, a cada instante de tempo, em cada jogo. Dado um conjunto de pontos no plano (que nesse caso, representam as posições dos jogadores em função do tempo), o Diagrama de Voronoi divide o plano em regiões de acordo com as distâncias entre os pontos desse conjunto, chamados Polígonos de Voronoi. As áreas dos polígonos foram calculadas. Essa ferramenta permite, através de uma representação por mapas de superfície, obter um resumo dos locais do campo contidos nos Polígonos de Voronoi associados a cada jogador, durante todo o jogo. As áreas de responsabilidade foram maiores para goleiros, laterais e atacantes, quando comparados aos zagueiros e volantes e meias.Para caracterizar a região de responsabilidade dos jogadores, foi utilizado o contorno topográfico correspondente às áreas do campo contidas nos Polígonos dos jogadores por no mínimo 60% do jogo. Os resultados obtidos para os jogos estudados mostram que o contorno que caracteriza a área de responsabilidade para os jogadores é uma boa ferramenta qualitativa e quantitativa, que representa a forma como os jogadores dividem a área do campo entre si. A utilização do Diagrama de Voronoi se mostrou uma técnica eficiente na determinação das áreas de responsabilidade dos jogadores. Técnicos e treinadores podem dessa maneira obter informações adicionais importantes para a criação de melhores estratégias de posicionamento da sua equipe para uma melhor cobertura do espaço do campo de futebol<br>Abstract: The performance of football elite players is directly influenced by physical, psychological, technical and tactical aspects. A scientific support capable of seek and apply methodologies to quantifying these factors is an important source of information to coaches improve their conditions to well prepare their teams. About football tactical aspects, the manner a team share the pitch in responsibility areas and how this distribution behaviours during the match can be described through mathematical techniques. Thus, the aim of this study is to show players' responsibility area during official matches using Voronoi Diagram (VD). To do so, we collected images of 4 football matches. To extract 2D players' coordinates during the entire match, images segmentation, tracking and 2D reconstruction were performed in DVideo® software. In the analysis, VD method was applied to players' 2D coordinates to all 33 players of a same team, at each instant of time and in the 4 matches. Given a set of points on plan (representing players positions as function of time), VD share the plan in regions according to distances between all points of the set, called Voronoi polygons (VP). Voronoi areas were calculated a determined as players' responsibility areas. This tool permits obtaining a summary of pitchlocations inside Voronoi polygons of each player, during the entire match, using hitmaps. To characterize responsibility areas, the contours of hitmaps corresponding to pitch areas inside VP by, at least, 60% of the match were performed. The results showed contours as an effective tool to qualitatively and quantitatively represent responsibility areas in a match. Besides, mathematical properties related to known geometric structures, as convex polygons, facilitate calculating areas. They showed be higher to goalkeepers, external defenders and forwards when compared to central defenders, defensive and offensive midfielders<br>Mestrado<br>Biodinamica do Movimento Humano<br>Mestre em Educação Física
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Lemaire-Beaucage, Jonathan. "Voronoi Diagrams in Metric Spaces." Thesis, Université d'Ottawa / University of Ottawa, 2012. http://hdl.handle.net/10393/20736.

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In this thesis, we will present examples of Voronoi diagrams that are not tessellations. Moreover, we will find sufficient conditions on subspaces of E2, S2 and the Poincaré disk and the sets of sites that guarantee that the Voronoi diagrams are pre-triangulations. We will also study g-spaces, which are metric spaces with ‘extendable’ geodesics joining any 2 points and give properties for a set of sites in a g-space that again guarantees that the Voronoi diagram is a pre-triangulation.
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Patel, Nirav B. "Voronoi diagrams robust and efficient implementation /." Diss., Online access via UMI:, 2005.

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Petersson, Filip, and Daniel Windhede. "Procedurell generering av racerbanor genom Voronoi diagram : Procedurellt genererade Formel 1 racerbanor genom modifierade Voronoi diagram och self-avoiding random walk." Thesis, Högskolan i Skövde, Institutionen för informationsteknologi, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:his:diva-19872.

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Arbetet undersökte om det är möjligt att procedurellt generera giltiga och underhållande racerbanor för Formel 1 genom användandet av Voronoi diagram och self-avoiding random walk. En procedurell algoritm skapades och två enkäter konstruerades för att undersöka denna algoritms underhållningsvärde. Dessa enkäter distribuerades till kunniga individer inom racinggenren. Både algoritmen som helhet och dess dynamiska parametrar undersöktes. Det fastställdes att det är möjligt att procedurellt generera Formel 1 racerbanor som är underhållande med detta tillvägagångssätt. Vidare visar resultatet att en stor del av svarspersonerna finner artefaktens procedurella racerbanor underhållande, även i kontrast till riktiga racerbanor. Gynnsamma värden för artefaktens dynamiska parametrar i mån av ökad underhållning har också fastställts. En mer omfattande algoritm kan skapas utifrån detta arbete som tar hänsyn till exempelvis höjdskillnader och camber. Framtida arbeten kan då undersöka dessa delar av en racerbanas underhållningsvärde. Algoritmen kan även jämföras med andra procedurella metoder inom racing och andra spel.<br><p>Det finns övrigt digitalt material (t.ex. film-, bild- eller ljudfiler) eller modeller/artefakter tillhörande examensarbetet som ska skickas till arkivet.</p>
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Cabrera, Vives Guillermo. "Bayesian Image Reconstruction Based on Voronoi Diagrams." Tesis, Universidad de Chile, 2008. http://repositorio.uchile.cl/handle/2250/101966.

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Books on the topic "Voronoiův diagram"

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Aronov, Boris. The furthest-site geodesic Voronoi diagram. Courant Institute of Mathematical Sciences, New York University, 1988.

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Rolf, Klein. Concrete and abstract Voronoi diagrams. Springer-Verlag, 1989.

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Concrete and abstract Voronoi diagrams. Springer-Verlag, 1989.

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Klein, Rolf. Concrete and Abstract Voronoi Diagrams. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/3-540-52055-4.

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N, Boots B., and Sugihara Kōkichi 1948-, eds. Spatial tessellations: Concepts and applications of Voronoi diagrams. Wiley, 1992.

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Gavrilova, Marina L. Generalized Voronoi diagram: A geometry-based approach to computational intelligence. Springer, 2008.

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Gavrilova, Marina L., ed. Generalized Voronoi Diagram: A Geometry-Based Approach to Computational Intelligence. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-85126-4.

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Aronov, Boris. On the geodesic Voronoi diagram of point sites in a simple polygon. Courant Institute of Mathematical Sciences, New York University, 1988.

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Rosenberger, Harald. Order-k Voronoi diagrams of sites with additive weights in the plane. 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. Universität Kaiserslautern, 1991.

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Book chapters on the topic "Voronoiův diagram"

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Kang, James M. "Voronoi Diagram." In Encyclopedia of GIS. Springer US, 2008. http://dx.doi.org/10.1007/978-0-387-35973-1_1461.

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Gass, Saul I., and Carl M. Harris. "Voronoi diagram." In Encyclopedia of Operations Research and Management Science. Springer US, 2001. http://dx.doi.org/10.1007/1-4020-0611-x_1116.

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Kang, James M. "Voronoi Diagram." In Encyclopedia of GIS. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-23519-6_1461-2.

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Kang, James M. "Voronoi Diagram." In Encyclopedia of GIS. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-17885-1_1461.

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Crato, Nuno. "Voronoi Diagrams." In Figuring It Out. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-04833-3_32.

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de Berg, Mark, Marc van Kreveld, Mark Overmars, and Otfried Schwarzkopf. "Voronoi Diagrams." In Computational Geometry. Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-662-03427-9_7.

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Shahabi, Cyrus, and Mehdi Sharifzadeh. "Voronoi Diagrams." In Encyclopedia of Database Systems. Springer New York, 2018. http://dx.doi.org/10.1007/978-1-4614-8265-9_451.

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Shahabi, Cyrus, and Mehdi Sharifzadeh. "Voronoi Diagrams." In Encyclopedia of Database Systems. Springer US, 2009. http://dx.doi.org/10.1007/978-0-387-39940-9_451.

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Joswig, Michael, and Thorsten Theobald. "Voronoi Diagrams." In Universitext. Springer London, 2013. http://dx.doi.org/10.1007/978-1-4471-4817-3_6.

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Grima, Clara I., and Alberto Márquez. "Voronoi Diagrams." In Computational Geometry on Surfaces. Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-015-9809-5_4.

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Conference papers on the topic "Voronoiův diagram"

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Fan, Chenglin, Jianbiao He, Jun Luo, and Binhai Zhu. "Moving Network Voronoi Diagram." In 2010 International Symposium on Voronoi Diagrams in Science and Engineering (ISVD). IEEE, 2010. http://dx.doi.org/10.1109/isvd.2010.21.

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Fan, Chenglin, Jun Luo, Jinfei Liu, and Yinfeng Xu. "Half-Plane Voronoi Diagram." In 2011 Eighth International Symposium on Voronoi Diagrams in Science and Engineering (ISVD). IEEE, 2011. http://dx.doi.org/10.1109/isvd.2011.25.

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Pegna, Joseph, Chi Guo, and Thierry P. Hilaire. "Design of a Nanometric Position Sensor Based on Computational Metrology of the Circle." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0040.

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Abstract:
Abstract The work presented in this paper derives from the design of a position sensing interferometer, in which circular fringe patterns are automatically analyzed by a computer vision system. Central to this process is a circle fitting problem in the sense of least Linfinity norm, also known as Chebichev or MinMax fit. The problem at hand can be formulated as follows: Given a set of points in the plane, find the pair of concentric circles with minimum radial gap enclosing all the points. The solution to this problem is elegantly given by common computational geometry tools, indeed the center of such a circle is necessarily a vertex of the Nearest Point Voronoi Diagram (NVD), a vertex of the Farthest Point Voronoi Diagram (FVD), or an intersection of edges from both diagrams. An algorithm for determining the Chebichev circular fit is presented and illustrated on the basis of that observation. Applications and potential extensions of this method to soft gauging and image metrology will also be discussed.
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Cheng, Reynold, Xike Xie, Man Lung Yiu, Jinchuan Chen, and Liwen Sun. "UV-diagram: A Voronoi diagram for uncertain data." In 2010 IEEE 26th International Conference on Data Engineering (ICDE 2010). IEEE, 2010. http://dx.doi.org/10.1109/icde.2010.5447917.

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Canny, J., and B. Donald. "Simplified Voronoi diagrams." In the third annual symposium. ACM Press, 1987. http://dx.doi.org/10.1145/41958.41974.

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Tetsuo Asano. "Angular Voronoi Diagram with Applications." In 2006 3rd International Symposium on Voronoi Diagrams in Science and Engineering. IEEE, 2006. http://dx.doi.org/10.1109/isvd.2006.9.

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Muta, Hidetoshi, and Kimikazu Kato. "Degeneracy of Angular Voronoi Diagram." In 4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007). IEEE, 2007. http://dx.doi.org/10.1109/isvd.2007.14.

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Yang, KwangSoo, Apurv Hirsh Shekhar, Dev Oliver, and Shashi Shekhar. "Capacity-Constrained Network-Voronoi Diagram." In 2016 IEEE 32nd International Conference on Data Engineering (ICDE). IEEE, 2016. http://dx.doi.org/10.1109/icde.2016.7498423.

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Qu, Jilin. "Outlier Detection Using Voronoi Diagram." In 2008 International Symposium on Computational Intelligence and Design (ISCID). IEEE, 2008. http://dx.doi.org/10.1109/iscid.2008.88.

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Christianto, Daud Sandy, Kiki Maulana Adhinugraha, Anisa Herdiani, and Sultan Alamri. "Highest order Voronoi diagram optimization." In 2017 5th International Conference on Information and Communication Technology (ICoIC7). IEEE, 2017. http://dx.doi.org/10.1109/icoict.2017.8074644.

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Reports on the topic "Voronoiův diagram"

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Bernal, J. An expected linear 3-dimensional Voronoi diagram algorithm. National Institute of Standards and Technology, 1990. http://dx.doi.org/10.6028/nist.ir.4340.

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Liotta, G., F. P. Preparata, and R. Tamassia. Robust Proximity Queries in Implicit Voronoi Diagrams. Defense Technical Information Center, 1996. http://dx.doi.org/10.21236/ada313538.

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Mount, David M. Voronoi Diagrams on the Surface of a Polyhedron. Defense Technical Information Center, 1985. http://dx.doi.org/10.21236/ada166220.

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Bemal, Javier. On the expected complexity of the 3-dimensional voronoi diagram. National Institute of Standards and Technology, 1989. http://dx.doi.org/10.6028/nist.ir.89-4100.

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Bernal, J. On the expected complexity of the 3-dimensional Voronoi diagram. National Institute of Standards and Technology, 1990. http://dx.doi.org/10.6028/nist.ir.4321.

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Cronin, T. M. The Voronoi Diagram for the Euclidean Traveling Salesman Problem Is Piecemeal Quartic and Hyperbolic. Defense Technical Information Center, 1990. http://dx.doi.org/10.21236/ada256112.

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Bernal, Javier. Expected O(N) and O(N??�) algorithms for constructing Voronoi diagrams in two and three dimensions. National Bureau of Standards, 1987. http://dx.doi.org/10.6028/nbs.ir.87-3679.

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Bibliographic notes on Voronoi diagrams. National Institute of Standards and Technology, 1993. http://dx.doi.org/10.6028/nist.ir.5164.

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