Relevant bibliographies by topics / Discrete Voronoi Diagram

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  2. Dissertations / Theses
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Academic literature on the topic 'Discrete Voronoi Diagram'

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Published: 6 September 2023

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Journal articles on the topic "Discrete Voronoi Diagram"

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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 potential value in practice.
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Kang, Shun. "A Generic Statistics-Based Tessellation Method of Voronoi Diagram." Journal of Systems Science and Information 3, no. 6 (December 25, 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 Gaussian distribution on spatial data, the validation and soundness of this method are proofed by empirical results.
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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 adjust each cell, and reconstruct the diagram based on the adjustment. We adopt the proposed method to the practical case study of Chiang Mai University’s allocated land for a mixed-use complex. For this case study, compared to other Voronoi diagram-based method, we decrease the land allocation error by 62.557 %. Although our computation time is larger than the previous Voronoi-diagram-based method, it is still suitable for interactive design.
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Chen, Jie, Gang Yang, and Meng Yang. "Computation of Compact Distributions of Discrete Elements." Algorithms 12, no. 2 (February 18, 2019): 41. http://dx.doi.org/10.3390/a12020041.

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In our daily lives, many plane patterns can actually be regarded as a compact distribution of a number of elements with certain shapes, like the classic pattern mosaic. In order to synthesize this kind of pattern, the basic problem is, with given graphics elements with certain shapes, to distribute a large number of these elements within a plane region in a possibly random and compact way. It is not easy to achieve this because it not only involves complicated adjacency calculations, but also is closely related to the shape of the elements. This paper attempts to propose an approach that can effectively and quickly synthesize compact distributions of elements of a variety of shapes. The primary idea is that with the seed points and distribution region given as premise, the generation of the Centroidal Voronoi Tesselation (CVT) of this region by iterative relaxation and the CVT will partition the distribution area into small regions of Voronoi, with each region representing the space of an element, to achieve a compact distribution of all the elements. In the generation process of Voronoi diagram, we adopt various distance metrics to control the shape of the generated Voronoi regions, and finally achieve the compact element distributions of different shapes. Additionally, approaches are introduced to control the sizes and directions of the Voronoi regions to generate element distributions with size and direction variations during the Voronoi diagram generation process to enrich the effect of compact element distributions. Moreover, to increase the synthesis efficiency, the time-consuming Voronoi diagram generation process was converted into a graphical rendering process, thus increasing the speed of the synthesis process. This paper is an exploration of elements compact distribution and also carries application value in the fields like mosaic pattern synthesis.
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Oku, Toshinobu. "Characteristics of Discrete Voronoi Diagram with Ambiguous Boundaries." Journal of the City Planning Institute of Japan 42.3 (2007): 463–68. http://dx.doi.org/10.11361/journalcpij.42.3.463.

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OKU, TOSHINOBU. "Characteristics of Discrete Voronoi Diagram with Ambiguous Boundaries." Journal of the City Planning Institute of Japan 42 (2007): 78. http://dx.doi.org/10.11361/cpij1.42.0.78.0.

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Vozáb, Jan, and Jan Vorel. "Generation of LDPM structure formed by Voronoi cells." Acta Polytechnica CTU Proceedings 40 (July 24, 2023): 111–16. http://dx.doi.org/10.14311/app.2023.40.0111.

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A preliminary study of an approach to internal structure generation used in lattice discrete particle models (LDPMs) [1]. The presented method used for particle generation and placement is intended to help realistically capture the internal structure of materials. First, a method for structure generation using LDPM is presented. Then, the method of particle generation using a Voronoi diagram [2] is described. The last part is the optimizations on the algorithm that use Apollonius circles to calculate the specific points of the Voronoi diagram.
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BEREG, SERGEY, KEVIN BUCHIN, MAIKE BUCHIN, MARINA GAVRILOVA, and BINHAI ZHU. "VORONOI DIAGRAM OF POLYGONAL CHAINS UNDER THE DISCRETE FRÉCHET DISTANCE." International Journal of Computational Geometry & Applications 20, no. 04 (August 2010): 471–84. http://dx.doi.org/10.1142/s0218195910003396.

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Polygonal chains are fundamental objects in many applications like pattern recognition and protein structure alignment. A well-known measure to characterize the similarity of two polygonal chains is the (continuous/discrete) Fréchet distance. In this paper, for the first time, we consider the Voronoi diagram of polygonal chains in d-dimension under the discrete Fréchet distance. Given a set [Formula: see text] of n polygonal chains in d-dimension, each with at most k vertices, we prove fundamental properties of such a Voronoi diagram [Formula: see text]. Our main results are summarized as follows. • The combinatorial complexity of [Formula: see text] is at most O(ndk+∊). • The combinatorial complexity of [Formula: see text] is at least Ω(ndk) for dimension d = 1, 2; and Ω(nd(k-1)+2) for dimension d > 2.
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Lu, Xiaomin, Haowen Yan, Wende Li, Xiaojun Li, and Fang Wu. "An Algorithm based on the Weighted Network Voronoi Diagram for Point Cluster Simplification." ISPRS International Journal of Geo-Information 8, no. 3 (February 27, 2019): 105. http://dx.doi.org/10.3390/ijgi8030105.

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Points on maps that stand for geographic objects such as settlements are generally connected by road networks. However, in the existing algorithms for point cluster simplification, points are usually viewed as discrete objects or their distances are considered in Euclidean spaces, and therefore the point cluster generalization results obtained by these algorithms are sometimes unreasonable. To take roads into consideration so that point clusters can be simplified in appropriate ways, the network Voronoi diagram is used and a new algorithm is proposed in this paper. First, the weighted network Voronoi diagram is constructed taking into account the weights of the points and the properties of the related road segments. Second, the network Voronoi polygons are generated and two factors (i.e., the area of the network Voronoi polygon and the total length of the dilated road segments in the polygon) are considered as the basis for point simplification. Last, a Cartesian coordinate system is built based on the two factors and the point clusters are simplified by means of the “concentric quadrants”. Our experiments show that the algorithm can effectively and correctly transmit types of information in the process of point cluster simplification, and the results are more reasonable than that generated by the ordinary Voronoi-based algorithm and the weighted Voronoi-based algorithm.
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Alt, Helmut, Otfried Cheong, and Antoine Vigneron. "The Voronoi Diagram of Curved Objects." Discrete & Computational Geometry 34, no. 3 (August 4, 2005): 439–53. http://dx.doi.org/10.1007/s00454-005-1192-0.

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Dissertations / Theses on the topic "Discrete Voronoi Diagram"

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Sud, Avneesh Manocha Dinesh N. "Efficient computation of discrete Voronoi diagram and homotopy-preserving simplified medial axis of a 3d polyhedron." Chapel Hill, N.C. : University of North Carolina at Chapel Hill, 2006. http://dc.lib.unc.edu/u?/etd,599.

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Thesis (Ph. D.)--University of North Carolina at Chapel Hill, 2006.
Title from electronic title page (viewed Oct. 10, 2007). "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Computer Science." Discipline: Computer Science; Department/School: Computer Science.
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Bougleux, Sébastien. "Reconstruction, Détection et Régularisation de Données Discrètes." Phd thesis, Université de Caen, 2007. http://tel.archives-ouvertes.fr/tel-00203445.

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Cette thèse traite des problématiques de structuration et de traitement de données discrètes organisées ou non. Elle se décompose en deux parties. La première partie concerne la structuration de données représentées par des ensembles de points du plan ou de l'espace Euclidien. Dans ce contexte, nous considérons les problèmes de la reconstruction polygonale de courbes planaires et de la détection de formes géométriques 3D connues. Ces deux problèmes sont traités par des techniques de géométrie algorithmique et combinatoire, basées sur le diagramme de Voronoï et la triangulation de Delaunay. Dans le cadre de la reconstruction de courbes planaires, nous proposons une famille hiérarchique de sous-graphes du graphe de Gabriel, que nous appelons les beta-CRUSTS Locaux. Nous étudions les propriétés de cette famille, qui nous permettent de concevoir un algorithme de reconstruction des courbes simples. Ensuite, nous proposons une méthode de détection de formes géométriques connues à partir d'un ensemble de points 3D (nous nous restreignons au cas des structures linéaires et planaires), plongés dans un milieu bruité ou non. Cette méthode est basée sur une extension des alpha-formes, générées à partir de boules ellipsoïdales. Dans une deuxième partie, nous traitons le problème de la régularisation de données par des méthodes variationnelles discrètes sur graphes pondérés, de topologie quelconque. Pour cela, nous proposons une large famille de fonctionnelles discrètes, basées sur les normes L2 et Lp du gradient. Ceci conduit à des processus de diffusion linéaire ou non-linéaire sur graphes. Ce formalisme étend un certain nombre de modèles variationnels, que nous appliquons à des problèmes de restauration, de lissage, et de simplification d'images et de maillages.
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Masood, Talha Bin. "Geometric and Topological Methods for Biomolecular Visualization." Thesis, 2018. http://etd.iisc.ac.in/handle/2005/4300.

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Biomolecules like proteins are the basic building blocks of living systems. It has been observed that the structure of a biomolecule plays an important role in defining its function. In this thesis, we describe novel geometric and topological techniques to understand the structure of molecules. In particular, we focus on the problems related to identification and visualization of cavities and channels in proteins. Cavities refer to empty regions within the molecule, while channels are pathways through the cavities. We pursue an integrated geometric and topological approach towards solving the problems in this domain. While topological structures provide efficient data structure representations of molecular space, geometric techniques allow accurate computation of various geometric measures having biological significance. In the first part of the thesis, we describe two methods: one for extraction and visualization of biomolecular channels, and the other for extraction of cavities in uncertain data. We also describe the two software tools based on the proposed methods targeted at the end-user, the biologists. These two web server tools publicly available for use are called ChExVis and Robust Cavities. The first method uses an alpha complex-based framework for extraction and visualization of geometrically feasible channels in biomolecules. We show that our proposed method has several advantages in terms of representation power over existing channel finding algorithms. In addition, we present novel ways of visualizing the amino-acids lining the channels together with their physicochemical properties. The second method addresses the problem of cavity extraction in biomolecules while taking into account uncertainties associated with empirically determined atomic positions and radii. We propose an approach that connects user-specified cavities by computing an optimal conduit within the region occupied by the molecule. The conduit is computed using a topological representation of the occupied and empty regions and is guaranteed to satisfy well defined geometric optimality criteria. We also describe a user interface with multiple linked views for interactive extraction and exploration of stable cavities. We demonstrate the utility of both the proposed methods using multiple case studies. In the second part of the thesis, we describe efficient parallel algorithms for two geometric structures widely used in the study of biomolecules. One of the structures we discuss is discrete Voronoi diagram which finds applications in channel visualization, while the other structure is alpha complex which is extremely useful in studying geometric and topological properties of biomolecules. We introduce a variant of the jump flooding algorithm to compute the discrete Voronoi diagram called Facet-JFA. The algorithm optimizes the number of pixels processed by computing only the faces of the Voronoi tessellation. We observed speed-up of up to 10x over JFA. As an application of the proposed algorithm, we present a GPU based method for extraction of channel centrelines in biomolecules. Secondly, we propose a GPU based parallel algorithm for the computation of the alpha complex, a subcomplex of the Delaunay triangulation that is widely used to represent biomolecules. The algorithm exploits the knowledge of typical distribution and sizes of atoms in biomolecules. Practically, we observed speed-up of up to 22x over the state-of-the-art algorithm using our implementation.
Microsoft Research India, Department of Science and Technology, DST Center for Mathematical Biology
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Masood, Talha Bin. "Geometric and Topological Methods for Biomolecular Visualization." Thesis, 2017. http://etd.iisc.ac.in/handle/2005/4324.

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Biomolecules like proteins are the basic building blocks of living systems. It has been observed that the structure of a biomolecule plays an important role in defining its function. In this thesis, we describe novel geometric and topological techniques to understand the structure of molecules. In particular, we focus on the problems related to identification and visualization of cavities and channels in proteins. Cavities refer to empty regions within the molecule, while channels are pathways through the cavities. We pursue an integrated geometric and topological approach towards solving the problems in this domain. While topological structures provide efficient data structure representations of molecular space, geometric techniques allow accurate computation of various geometric measures having biological significance. In the first part of the thesis, we describe two methods: one for extraction and visualization of biomolecular channels, and the other for extraction of cavities in uncertain data. We also describe the two software tools based on the proposed methods targeted at the end-user, the biologists. These two web server tools publicly available for use are called ChExVis and RobustCavities. The first method uses an alpha complex based framework for extraction and visualization of geometrically feasible channels in biomolecules. We show that our proposed method has several advantages in terms of representation power over existing channel finding algorithms. In addition, we present novel ways of visualizing the amino-acids lining the channels together with their physico- chemical properties. The second method addresses the problem of cavity extraction in biomolecules while taking into account uncertainties associated with empirically determined atomic positions and radii. We propose an approach that connects user-specified cavities by computing an optimal conduit within the region occupied by the molecule. The conduit is computed using a topological representation of the occupied and empty regions and is guaranteed to satisfy well defined geometric optimality criteria. We also describe a user interface with multiple linked views for interactive extraction and exploration of stable cavities. We demonstrate the utility of both the proposed methods using multiple case studies. In the second part of the thesis, we describe efficient parallel algorithms for two geometric structures widely used in the study of biomolecules. One of the structures we discuss is discrete Voronoi diagram which finds applications in channel visualization, while the other structure is alpha complex which is extremely useful in studying geometric and topological properties of biomolecules. We introduce a variant of the jump flooding algorithm to compute the discrete Voronoi diagram called Facet-JFA. The algorithm optimizes the number of pixels processed by computing only the faces of the Voronoi tessellation. We observed speed-up of upto 10x over JFA. As an application of the proposed algorithm, we present a GPU based method for extraction of channel centerlines in biomolecules. Secondly, we propose a GPU based parallel algorithm for the computation of the alpha complex, a subcomplex of the Delaunay triangulation that is widely used to represent biomolecules. The algorithm exploits the knowledge of typical distribution and sizes of atoms in biomolecules. Practically, we observed speed-up of upto 22x over the state-of-the-art algorithm using our implementation.
Supported by Microsoft Corporation and Microsoft Research India under the Microsoft Research India Ph.D. Fellowship Award.
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Books on the topic "Discrete Voronoi Diagram"

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Transactions On Computational Science Xiv Special Issue On Voronoi Diagrams And Delaunay Triangulation. Springer, 2012.

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Book chapters on the topic "Discrete Voronoi Diagram"

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Devillers, Olivier, and Pierre-Marie Gandoin. "Rounding Voronoi Diagram." In Discrete Geometry for Computer Imagery, 375–87. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/3-540-49126-0_29.

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Zhao, Ye, Shu-juan Liu, and Yi-li Tan. "Discrete Construction of order-k Voronoi Diagram." In Information Computing and Applications, 79–85. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-16167-4_11.

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Tan, Yili, Ye Zhao, and Yourong Wang. "Discrete Construction of Power Network Voronoi Diagram." In Information Computing and Applications, 290–97. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-25255-6_37.

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Barequet, Gill, and Minati De. "Voronoi Diagram for Convex Polygonal Sites with Convex Polygon-Offset Distance Function." In Algorithms and Discrete Applied Mathematics, 24–36. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-53007-9_3.

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van der Putte, Tom, and Hugo Ledoux. "Modelling Three-Dimensional Geoscientific Datasets with the Discrete Voronoi Diagram." In Lecture Notes in Geoinformation and Cartography, 227–42. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-12670-3_14.

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Schwarzkopf, Otfried. "Parallel computation of discrete Voronoi diagrams." In STACS 89, 193–204. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/bfb0028984.

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Hiyoshi, Hisamoto, and Kokichi Sugihara. "An Interpolant Based on Line Segment Voronoi Diagrams." In Discrete and Computational Geometry, 119–28. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-540-46515-7_10.

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Schmitt, Dominique, and Jean-Claude Spehner. "Order-k Voronoi Diagrams, k-Sections, and k-Sets." In Discrete and Computational Geometry, 290–304. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-540-46515-7_26.

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Oh, Eunjin. "Optimal Algorithm for Geodesic Nearest-point Voronoi Diagrams in Simple Polygons." In Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, 391–409. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2019. http://dx.doi.org/10.1137/1.9781611975482.25.

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Seidel, R. "Exact upper bounds for the number of faces in 𝑑-dimensional Voronoi diagrams." In DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 517–30. Providence, Rhode Island: American Mathematical Society, 1991. http://dx.doi.org/10.1090/dimacs/004/40.

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Conference papers on the topic "Discrete Voronoi Diagram"

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Jianliang, Peng, Zhu Fan, Sun Xiuxia, and Sun Biao. "On Route-Planning of UAV Based on Discrete PSO and Voronoi Diagram." In 2007 Chinese Control Conference. IEEE, 2006. http://dx.doi.org/10.1109/chicc.2006.4347571.

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Dardenne, Julien, Sebastien Valette, Nicolas Siauve, Bassem Khaddour, and Remy Prost. "Exploiting curvature to compute the medial axis with Constrained Centroidal Voronoi Diagram on discrete data." In 2009 16th IEEE International Conference on Image Processing (ICIP 2009). IEEE, 2009. http://dx.doi.org/10.1109/icip.2009.5414401.

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Trefftz, Christian, Byron DeVries, and Benjamin Jenkins. "An Algorithm to solve a Facility Location Problem using a Discrete Approximation to the Voronoi Diagram." In 2021 IEEE International Conference on Electro Information Technology (EIT). IEEE, 2021. http://dx.doi.org/10.1109/eit51626.2021.9491915.

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Kalde, Nassim, Olivier Simonin, and Francois Charpillet. "Asynchronous Computing of a Discrete Voronoi Diagram on a Cellular Automaton Using 1-Norm: Application to Roadmap Extraction." In 2014 IEEE 26th International Conference on Tools with Artificial Intelligence (ICTAI). IEEE, 2014. http://dx.doi.org/10.1109/ictai.2014.130.

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Sequeira, Raul E., and Francoise J. Preteux. "Dynamic algorithm for constructing discrete Voronoi diagrams." In Electronic Imaging: Science & Technology, edited by Edward R. Dougherty, Jaakko T. Astola, and Harold G. Longbotham. SPIE, 1996. http://dx.doi.org/10.1117/12.235832.

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Zhao, Ye, Ya-Jing Zhang, and Qing-Hong Zhang. "Discrete construction of Voronoi diagrams for cross generators." In 2010 International Conference on Machine Learning and Cybernetics (ICMLC). IEEE, 2010. http://dx.doi.org/10.1109/icmlc.2010.5580811.

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Bing Liu. "Discrete construction of voronoi diagrams for intersectant curves." In 2014 IEEE Workshop on Electronics, Computer and Applications (IWECA). IEEE, 2014. http://dx.doi.org/10.1109/iweca.2014.6845579.

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Yamamoto, Yoshihito, Soichiro Okazaki, Hikaru Nakamura, Masuhiro Beppu, and Taiki Shibata. "Crack Propagation and Local Failure Simulation of Reinforced Concrete Subjected to Projectile Impact Using RBSM." In ASME 2016 35th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/omae2016-54969.

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In this paper, numerical simulations of reinforced mortar beams subjected to projectile impact are conducted by using the proposed 3-D Rigid-Body-Spring Model (RBSM) in order to investigate mechanisms of crack propagation and scabbing mode of concrete members under high-velocity impact. The RBSM is one of the discrete-type numerical methods, which represents a continuum material as an assemblage of rigid particle interconnected by springs. The RBSM have advantages in modeling localized and oriented phenomena, such as cracking, its propagation, frictional slip and so on, in concrete structures. The authors have already developed constitutive models for the 3D RBSM with random geometry generated Voronoi diagram in order to quantitatively evaluate the mechanical responses of concrete including softening and localization fractures, and have shown that the model can simulate cracking and various failure modes of reinforced concrete structures. In the target tests, projectile velocity is set 200m/s. The reinforced mortar beams with or without the shear reinforcing steel plates were used to investigate the effects of shear reinforcement on the crack propagation and the local failure modes. By comparing the numerical results with the test results, it is confirmed that the proposed model can reproduce well the crack propagation and the local failure behaviors. In addition, effects of the reinforcing plates on the stress wave and the crack propagation behaviors are discussed from the observation of the numerical simulation results. As a result, it was found that scabbing of reinforced mortar beams subjected to high velocity impact which is in the range of the tests is caused by mainly shear deformation of a beam.
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Liu, Chih-Hung, and D. T. Lee. "Higher-Order Geodesic Voronoi Diagrams in a Polygonal Domain with Holes." In Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2013. http://dx.doi.org/10.1137/1.9781611973105.117.

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Rong, Guodong, and Tiow-Seng Tan. "Variants of Jump Flooding Algorithm for Computing Discrete Voronoi Diagrams." In 4th International Symposium on Voronoi Diagrams in Science and Engineering (ISVD 2007). IEEE, 2007. http://dx.doi.org/10.1109/isvd.2007.41.

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