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Статті в журналах з теми "Tesselations"

Автор: Grafiati

Опубліковано: 4 червня 2021

Оновлено: 1 серпня 2024

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1

Crespo Osório, Filipa, Alexandra Paio, and Sancho Oliveira. "ORIGAMI TESSELATIONS." Boletim da Aproged, no. 34 (December 2018): 73–77. http://dx.doi.org/10.24840/2184-4933_2018-0034_0010.

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Rigid Origami folding surfaces have very interesting qualities for Architecture and Engineering given their geometric, structural and elastic qualities. The ability to turn a flat element, isotropic, without any structural capacity, into a self-supporting element strictly through folds in the material opens the door to a multitude of uses. Besides that, the intrinsic geometry of the crease pattern may allow the surface to assume doubly curved forms while the flat element, before the folding, could never do it without the deformation of the material [01][02]. The main goal of this Ph.D. research is to reach a workflow that allows for the design and implementation of kinetically reconfigurable Origami Surfaces. In this paper, we will address mainly the parameterization of certain folded geometries, illustrating our method, simulating the folding of regular crease patterns through geometric operations on the smallest set of faces (local) that can be reproduced to simulate the whole group (global).

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2

Malina, Roger F., and M. Emmer. "Symmetry and Tesselations." Leonardo 24, no. 1 (1991): 100. http://dx.doi.org/10.2307/1575501.

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3

MEES, ALISTAIR I. "DYNAMICAL SYSTEMS AND TESSELATIONS: DETECTING DETERMINISM IN DATA." International Journal of Bifurcation and Chaos 01, no. 04 (December 1991): 777–94. http://dx.doi.org/10.1142/s0218127491000579.

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Data measurements from a dynamical system may be used to build triangulations and tesselations which can — at least when the system has relatively low-dimensional attractors or invariant manifolds — give topological, geometric and dynamical information about the system. The data may consist of a time series, possibly reconstructed by embedding, or of several such series; transients can be put to good use. The topological information which can be found includes dimension and genus of a manifold containing the state space. Geometric information includes information about folds, branches and other chaos generators. Dynamical information is obtained by using the tesselation to construct a map with stated smoothness properties and having the same dynamics as the data; the resulting dynamical model may be tested in the way that any scientific theory may be tested, by making falsifiable predictions.

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4

Sheilla Puspita, Cama Juli Rianingrum, and Agung Eko Budiwaspada. "MODUL DALAM DESAIN PATTERN MENGGUNAKAN TESSELLATIONS DAN PRINSIP GESTALT." Jurnal Seni dan Reka Rancang: Jurnal Ilmiah Magister Desain 5, no. 2 (May 23, 2023): 205–16. http://dx.doi.org/10.25105/jsrr.v5i2.16815.

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Abstract Pattern Design Module Using Tesselations and Gestalt, will produce faster pattern design. It will also produce the quality of a dinamic pattern design composition. For the quantity as well, it will produce more of new design pattern in a shorter time. The method is using qualitative research of Hawkins Creation Theory. They are problem eksploration through data analysing, improvisation from theory and data data colecction, and the last step is forming, that is about finding a new way to solve the problem through new module treatment. The last is module applicatio. And it’s summary about pattern design module using tesselation and Gestalt, as an optional recommendation to create a design pattern. Abstrak Modul Dalam Desain Pattern Menggunakan Tesselations dan Prinsip Gestalt, menghasilkan suatu cara yang lebih cepat untuk menghasilkan desain pattern. Secara kualitas, akan membuat desain pattern dengan komposisi yang lebih dinamis, dan secara kuantitas dapat menghasilkan desain pattern baru yang cukup banyak dalam waktu yang lebih singkat. Metode yang digunakan dengan pendekatan kualitatif adalah metode penciptaan Hawkins yang terdiri dari eksplorasi permasalahan dan pengumpulan data, improvisasi yang merupakan pengembangan atas temuan yang diolah dari data yang ada, dan forming adalah tahap perumusan modul yang dapat digunakan. Sampai modul tersebut diaplikasikan dan didapatkan kesimpulan sebagai temuan cara baru untuk menciptakan pattern.

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5

Brass, Peter. "On strongly normal tesselations." Pattern Recognition Letters 20, no. 9 (September 1999): 957–60. http://dx.doi.org/10.1016/s0167-8655(99)00063-x.

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6

Kuiper, Nicolaas H. "Hyperbolic 4-manifolds and tesselations." Publications mathématiques de l'IHÉS 68, no. 1 (January 1988): 47–76. http://dx.doi.org/10.1007/bf02698541.

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7

Besterci, M. "Voronoi tesselations generated by cluster fields." Metal Powder Report 53, no. 7-8 (July 1998): 43. http://dx.doi.org/10.1016/s0026-0657(98)85105-9.

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8

Widiawati, Widiawati. "Desain Pembelajaran Menggunakan Tessellation Berbasis Pendekatan Saintifik pada Materi Translasi dan Refleksi." Jurnal Pendidikan Matematika (JUDIKA EDUCATION) 2, no. 2 (December 12, 2019): 80–90. http://dx.doi.org/10.31539/judika.v2i2.858.

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The purpose of this study was to determine the role of tesselation in translational and reflection material in developing students' mathematical communication based on a scientific approach. The research method uses design research type validation study involving 30 students of class VII SMP 9 Palembang. The research process produces learning trajectory which contains a series of learning processes in two activities, namely scientific on translational material and scientific on reflection material. Every scientific activity consists of observing, asking, reasoning, trying, and forming networks. The results of the study showed that by providing learning material through a scientific approach, the role of tesselations could help students to carry out mathematical communication so that they could identify translational and reflection material. Therefore, students can understand the concepts of translation and reflection and solve problems related to the material. In conclusion, learning using tessellation with a scientific approach effectively helps students understand the concepts of translation and reflection. Through activities such as observing, asking, reasoning, trying, and forming networks Keywords: Mathematical Communication, Scientific Approach, Tessellation

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9

Clifford, A., and R. Z. Goldstein. "Tesselations ofS2and equations over torsion-free groups." Proceedings of the Edinburgh Mathematical Society 38, no. 3 (October 1995): 485–93. http://dx.doi.org/10.1017/s0013091500019283.

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LetGbe a torsion free group,Fthe free group generated byt. The equationr(t) = 1 is said to have a solution overGif there is a solution in some group that containsG. In this paper we generalize a result due to Klyachko who established the solution when the exponent sum oftis one.

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10

Capitaine, M., S. Coste, F. Gabriel, P. Maillard, and C. Mailler. "Random matrices and random graphs." ESAIM: Proceedings and Surveys 74 (November 2023): 137–57. http://dx.doi.org/10.1051/proc/202374137.

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We collect recent results on random matrices and random graphs. The topics covered are: fluctuations of the empirical measure of random matrices, finite-size effects of algorithms involving random matrices, characteristic polynomial of sparse matrices and Voronoi tesselations of split trees.

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11

Soares Jr, Waldir S., E. B. Silva, Emerson J. Vizentim, and Franciele P. B. Soares. "Construction of Polygonal Color Codes from Hyperbolic Tesselations." TEMA (São Carlos) 21, no. 1 (March 27, 2020): 43. http://dx.doi.org/10.5540/tema.2020.021.01.43.

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This current work propose a technique to generate polygonal color codes in the hyperbolic geometry environment. The color codes were introduced by Bombin and Martin-Delgado in 2007, and the called triangular color codes have a higher degree of interest because they allow the implementation of the Clifford group, but they encode only one qubit. In 2018 Soares e Silva extended the triangular codes to the polygonal codes, which encode more qubits. Using an approach through hyperbolic tessellations we show that it is possible to generate Hyperbolic Polygonal codes, which encode more than one qubit with the capacity to implement the entire Clifford group and also having a better coding rate than the previously mentioned codes, for the color codes on surfaces with boundary with minimum distance d = 3.

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12

Martinovich, C., I. Zalduendo, and P. Cobelli. "CLUSTERING OF LAGRANGIAN PARTICLES IN 2D TURBULENCE." Anales AFA 34, no. 4 (December 28, 2023): 103–8. http://dx.doi.org/10.31527/analesafa.2023.34.4.103.

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In this paper we design and construct an experiment to generate and study 2D turbulence. We calculate velocity and vorticity fields, the energy spectrum and Bondarenko’s parameter for the system both in decay and onset; those values result inαD= (−0.400±0.012)s−1andαE= (0.404±0.005)s−1, respectively. Additionally, we study the distribution of particles in the flux through the use of Voronoi tesselations

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13

Møller, Jesper. "Random Johnson-Mehl tessellations." Advances in Applied Probability 24, no. 4 (December 1992): 814–44. http://dx.doi.org/10.2307/1427714.

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A unified exposition of random Johnson–Mehl tessellations in d-dimensional Euclidean space is presented. In particular, Johnson-Mehl tessellations generated by time-inhomogeneous Poisson processes and nucleation-exclusion models are studied. The ‘practical' cases d = 2 and d = 3 are discussed in detail. Several new results are established, including first- and second-order moments of various characteristics for both Johnson–Mehl tesselations and sectional Johnson–Mehl tessellations.

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14

Møller, Jesper. "Random Johnson-Mehl tessellations." Advances in Applied Probability 24, no. 04 (December 1992): 814–44. http://dx.doi.org/10.1017/s0001867800024964.

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A unified exposition of random Johnson–Mehl tessellations in d-dimensional Euclidean space is presented. In particular, Johnson-Mehl tessellations generated by time-inhomogeneous Poisson processes and nucleation-exclusion models are studied. The ‘practical' cases d = 2 and d = 3 are discussed in detail. Several new results are established, including first- and second-order moments of various characteristics for both Johnson–Mehl tesselations and sectional Johnson–Mehl tessellations.

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15

M⊘ller, Jesper, and Sergei Zouev. "Gamma-type results and other related properties of Poisson processes." Advances in Applied Probability 28, no. 2 (June 1996): 340. http://dx.doi.org/10.1017/s0001867800048412.

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Families of Poisson processes defined on general state spaces and with the intensity measure scaled by a positive parameter are investigated. In particular, mean value relations with respect to the scale parameter are established and used to derive various Gamma-type results for certain geometrical characteristics determined by finite subprocesses. In particular, we deduce Miles' complementary theorem. Applications of the results within stochastic geometry and particularly for random tesselations are discussed.

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16

Anderson, David M., H. T. Davis, and L. E. Scriven. "Mean and Gaussian curvatures of randomly decorated Voronoi and cubic tesselations." Journal of Chemical Physics 91, no. 5 (September 1989): 3246–51. http://dx.doi.org/10.1063/1.456899.

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17

Lemaítre, J., A. Gervois, J. P. Troadec, N. Rivier, M. Ammi, L. Oger, and D. Bideau. "Arrangement of cells in Voronoi tesselations of monosize packing of discs." Philosophical Magazine B 67, no. 3 (March 1993): 347–62. http://dx.doi.org/10.1080/13642819308220137.

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18

Heilbronner, Renée. "Analysis of bulk fabrics and microstructure variations using tesselations of autocorrelation functions." Computers & Geosciences 28, no. 4 (May 2002): 447–55. http://dx.doi.org/10.1016/s0098-3004(01)00088-7.

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19

Annic, C., J. P. Troadec, A. Gervois, J. Lemaître, M. Ammi, and L. Oger. "Experimental study of radical tesselations of assemblies of discs with size distribution." Journal de Physique I 4, no. 1 (January 1994): 115–25. http://dx.doi.org/10.1051/jp1:1994124.

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20

Choksi, Rustum, and Xin Yang Lu. "Bounds on the Geometric Complexity of Optimal Centroidal Voronoi Tesselations in 3D." Communications in Mathematical Physics 377, no. 3 (June 12, 2020): 2429–50. http://dx.doi.org/10.1007/s00220-020-03789-y.

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21

Emily, Mathieu, Didier Morel, Raphael Marcelpoil, and Olivier François. "Spatial Correlation of Gene Expression Measures in Tissue Microarray Core Analysis." Journal of Theoretical Medicine 6, no. 1 (2005): 33–39. http://dx.doi.org/10.1080/10273660500035795.

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Tissue microarrays (TMAs) make possible the screening of hundreds of different tumour samples for the expression of a specific protein. Automatic features extraction procedures lead to a series of covariates corresponding to the averaged stained scores. In this article, we model the random geometry of TMA cores using voronoi tesselations. This formalism enables the computation of indices of spatial correlation of stained scores using both classical and novel approaches. The potential of these spatial statistics to correctly discriminate between diseased and non-diseased cases is evaluated through the analysis of a TMA containing samples of breast carcinoma data. The results indicate a significant improvement in the breast cancer prognosis.

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22

Khalatnikov, I. M., and A. Yu Kamenshchik. "Remarks about the effective conductivity of some three-color tesselations in the plane." Journal of Experimental and Theoretical Physics Letters 72, no. 6 (September 2000): 341–44. http://dx.doi.org/10.1134/1.1328452.

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23

Skamarock, William C., Joseph B. Klemp, Michael G. Duda, Laura D. Fowler, Sang-Hun Park, and Todd D. Ringler. "A Multiscale Nonhydrostatic Atmospheric Model Using Centroidal Voronoi Tesselations and C-Grid Staggering." Monthly Weather Review 140, no. 9 (September 1, 2012): 3090–105. http://dx.doi.org/10.1175/mwr-d-11-00215.1.

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Abstract The formulation of a fully compressible nonhydrostatic atmospheric model called the Model for Prediction Across Scales–Atmosphere (MPAS-A) is described. The solver is discretized using centroidal Voronoi meshes and a C-grid staggering of the prognostic variables, and it incorporates a split-explicit time-integration technique used in many existing nonhydrostatic meso- and cloud-scale models. MPAS can be applied to the globe, over limited areas of the globe, and on Cartesian planes. The Voronoi meshes are unstructured grids that permit variable horizontal resolution. These meshes allow for applications beyond uniform-resolution NWP and climate prediction, in particular allowing embedded high-resolution regions to be used for regional NWP and regional climate applications. The rationales for aspects of this formulation are discussed, and results from tests for nonhydrostatic flows on Cartesian planes and for large-scale flow on the sphere are presented. The results indicate that the solver is as accurate as existing nonhydrostatic solvers for nonhydrostatic-scale flows, and has accuracy comparable to existing global models using icosahedral (hexagonal) meshes for large-scale flows in idealized tests. Preliminary full-physics forecast results indicate that the solver formulation is robust and that the variable-resolution-mesh solutions are well resolved and exhibit no obvious problems in the mesh-transition zones.

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24

Barndorff-Nielsen, O. E. "Sorting, texture and structure." Proceedings of the Royal Society of Edinburgh. Section B. Biological Sciences 96 (1989): 167–79. http://dx.doi.org/10.1017/s0269727000010915.

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SynopsisSands are sorted by the actions of air and water. A mathematical–physical model for the ensuing spatial and temporal variations in the size distributions of the sand grains is outlined. A crucial element in aeolian sorting and transport of sand is the process that takes place when a saltating grain impinges on the sand surface. This raises the problem of describing the texture of sand surfaces. Some initial empirical and mathematical findings concerning this problem are discussed. A closely connected question is that of how the grains in a sand deposit are packed and how this relates to the size distribution. Voronoi tesselations in combination with random point processes seem to offer one useful approach to the question.

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25

Alabdali, Osama, and Allal Guessab. "Sharp multidimensional numerical integration for strongly convex functions on convex polytopes." Filomat 34, no. 2 (2020): 601–7. http://dx.doi.org/10.2298/fil2002601a.

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This paper introduces and studies a new class of multidimensional numerical integration, which we call ?strongly positive definite cubature formulas?. We establish, among others, a characterization theorem providing necessary and sufficient conditions for the approximation error (based on such cubature formulas) to be bounded by the approximation error of the quadratic function. This result is derived as a consequence of two characterization results, which are of independent interest, for linear functionals obtained in a more general seeting. Thus, this paper extends some result previously reported in [2, 3] when convexity in the classical sense is only assumed. We also show that the centroidal Voronoi Tesselations provide an efficient way for constructing a class of optimal of cubature formulas. Numerical results for the two-dimensional test functions are given to illustrate the efficiency of our resulting cubature formulas.

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26

Nagel, Werner, and Viola Weiss. "CORRIGENDUM: MEAN VALUES FOR HOMOGENEOUS STIT TESSELATIONS IN 3D (2008 IMAGE ANAL STEREOL 27:29-37)." Image Analysis & Stereology 34, no. 2 (June 28, 2015): 145. http://dx.doi.org/10.5566/ias.1359.

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27

Pourmoghaddam, Navid, Michael A. Kraus, Jens Schneider, and Geralt Siebert. "The geometrical properties of random 2D Voronoi tesselations for the prediction of the tempered glass fracture pattern." ce/papers 2, no. 5-6 (October 2018): 325–39. http://dx.doi.org/10.1002/cepa.934.

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28

DARE, V. R., K. G. SUBRAMANIAN, D. G. THOMAS, R. SIROMONEY, and B. LE SAEC. "INFINITE ARRAYS AND RECOGNIZABILITY." International Journal of Pattern Recognition and Artificial Intelligence 14, no. 04 (June 2000): 525–36. http://dx.doi.org/10.1142/s0218001400000337.

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In this paper, the concept of local languages is extended to infinite arrays and ωω-local languages are defined. ωω-recognizable languages of infinite arrays accepted by online tesselation automata are considered. Properties of these languages are studied. The notion of Muller recognizability is extended to infinite arrays. This is related to acceptance of infinite arrays by online tesselation automata.

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29

Settgast, Volker, Kerstin Müller, Christoph Fünfzig, and Dieter Fellner. "Adaptive tesselation of subdivision surfaces." Computers & Graphics 28, no. 1 (February 2004): 73–78. http://dx.doi.org/10.1016/j.cag.2003.10.006.

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30

Riedinger, R., M. Habar, P. Oelhafen, and H. J. Güntherodt. "About the Delaunay-Voronoi tesselation." Journal of Computational Physics 74, no. 1 (January 1988): 61–72. http://dx.doi.org/10.1016/0021-9991(88)90068-x.

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31

Morse, Peter K., and Eric I. Corwin. "Geometric order parameters derived from the Voronoi tessellation show signatures of the jamming transition." Soft Matter 12, no. 4 (2016): 1248–55. http://dx.doi.org/10.1039/c5sm02575c.

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32

Boaventura, Eduardo, Fernando Ducha, and A. P. F. Atman. "Jamming transition evinced by Voronoi Tesselation." EPJ Web of Conferences 140 (2017): 16002. http://dx.doi.org/10.1051/epjconf/201714016002.

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33

Chan, S. L., and E. O. Purisima. "A new tetrahedral tesselation scheme for isosurface generation." Computers & Graphics 22, no. 1 (February 1998): 83–90. http://dx.doi.org/10.1016/s0097-8493(97)00085-x.

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34

Hough, Robert. "Tesselation of a triangle by repeated barycentric subdivision." Electronic Communications in Probability 14 (2009): 270–77. http://dx.doi.org/10.1214/ecp.v14-1471.

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35

Cohn, Harvey. "Iterated ring class fields and the 168-tesselation." Mathematische Annalen 270, no. 1 (March 1985): 69–77. http://dx.doi.org/10.1007/bf01455529.

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36

Rożniatowski, Krzysztof, and Marek Kosmulski. "Advanced Analysis of SEM Images of Carbon-Ceramic Composites." Adsorption Science & Technology 25, no. 7 (September 2007): 473–78. http://dx.doi.org/10.1260/0263-6174.25.7.473.

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Carbon deposits obtained by the pyrolysis of cyclohexene and of glucose in the pores of porous monoliths of alumina and Y-modified zirconia consist of randomly distributed insulated islands. This explains their relatively low electric conductance. A tesselation method was applied to quantify the distribution of carbon deposits in the ceramic matrix.

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37

Shenton, D., and Z. Cendes. "Three-Dimensional finite element mesh generation using delaunay tesselation." IEEE Transactions on Magnetics 21, no. 6 (November 1985): 2535–38. http://dx.doi.org/10.1109/tmag.1985.1064165.

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38

Velho, Luiz, Luiz Henrique de Figueiredo, and Jonas Gomes. "A unified approach for hierarchical adaptive tesselation of surfaces." ACM Transactions on Graphics 18, no. 4 (October 1999): 329–60. http://dx.doi.org/10.1145/337680.337717.

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39

Kovalenko, Igor N. "On certain random polygons of large areas." Journal of Applied Mathematics and Stochastic Analysis 11, no. 3 (January 1, 1998): 369–76. http://dx.doi.org/10.1155/s1048953398000306.

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Consider the tesselation of a plane into convex random polygons determined by a unit intensity Poissonian line process. Let M(A) be the ergodic intensity of random polygons with areas exceeding a value A. A two-sided asymptotic bound exp{−2A/π+c0A16}<M(A)<exp{−2A/π+c1A16} is established for large A, where c0>2.096, c1>6.36.

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40

Rocha, André. "Meromorphic extension of the Selberg zeta function for Kleinian groups via thermodynamic formalism." Mathematical Proceedings of the Cambridge Philosophical Society 119, no. 1 (January 1996): 179–90. http://dx.doi.org/10.1017/s0305004100074065.

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AbstractWe prove the existence of a piecewise analytic expanding map associated to certain Kleinian groups without parabolics acting in the 3-dimensional hyperbolic space. These groups have a fundamental domain ℛ with the property that the geodesic planes containing each face are part of the tesselation. We use this map together with the methods of thermodynamic formalism to give another proof that the Selberg zeta function for such groups has a meromorphic extension to ℂ.

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41

Oluwole, O. O., and A. L. Akinkunmi. "Modeling Grain Structures of Some Carbon Steels using Voronoi Tesselation." Journal of Minerals and Materials Characterization and Engineering 10, no. 03 (2011): 309–14. http://dx.doi.org/10.4236/jmmce.2011.103021.

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42

Еfimov, A. S., and E. V. Mosyagin. "ANALYSIS AND IMPROVEMENT OF SEISMIC EXPLORATION METHODS IN EASTERN SIBERIA." Geology and mineral resources of Siberia, no. 1 (2021): 56–73. http://dx.doi.org/10.20403/2078-0575-2021-1-56-73.

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Анотація:

Many enterprises and authors have often addressed the problem of increasing the efficiency of seismic exploration (geological constructions and forecasting) at the prospecting stage in the Siberian Platform (SP) throughout the entire period of oil prospecting in Eastern Siberia. This is confirmed by numerous publications and production reports. Unfortunately, it should be admitted that there is still no cardinal progress in solving this problem. The reasons for the low information content of geophysical materials for the SP conditions in these publications are substantiated and set out in great detail. This is both a sharply dissected relief, and small-block models of the near-surface section, and an energy dissipation in rudaceous pyroclastic rocks of the Triassic, background of reverberation, near-surface waves formed by thin layers of traps in near-surface section, local velocity anomalies in the middle part of the section, background and interference of partially multiple reflections, complex salt tectonics, blocking and tesselation of secondary changes in Riphean rocks, forming tesselation of seismoacoustic properties. These are the main, in authors’ opinion, reasons reducing reliability of the geological section forecast based on seismic data. Some of them are removed using a complex of geophysical data. But tie, backbone on seismic horizons lies also at the heart of integration. Therefore, increasing the information content of seismic survey in regard to fixing the reflecting boundaries based on selection and substantiation, field observation systems and technologies is the most important issue in the problem under discussion.

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43

Brumfiel, G., H. Hilden, M. T. Lozano, J. M. Montesinos, E. Ramirez, H. Short, D. Tejada, and M. Toro. "Harmonic manifolds and embedded surfaces arising from a super regular tesselation." Journal of Knot Theory and Its Ramifications 26, no. 09 (August 2017): 1743003. http://dx.doi.org/10.1142/s0218216517430039.

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The main result of this paper is the construction of two Hyperbolic manifolds, [Formula: see text] and [Formula: see text], with several remarkable properties: (1) Every closed orientable [Formula: see text]-manifold is homeomorphic to the quotient space of the action of a group of order [Formula: see text] on some covering space of [Formula: see text] or [Formula: see text]. (2) [Formula: see text] and [Formula: see text] are tesselated by 16 dodecahedra such that the pentagonal faces of the dodecahedra fit together in a certain way. (3) There are 12 closed non-orientable hyperbolic surfaces of Euler characteristic [Formula: see text] each of which is tesselated by regular right angled pentagons and embedded in [Formula: see text] or [Formula: see text]. The union of the pentagonal faces of the tesselating dodecahedra equals the union of the 12 images of the embedded surfaces of Euler characteristic [Formula: see text].

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44

Kayser, K., and H. Stute. "Minimum Spanning Tree - Voronoi's Tesselation - Johnson-Mehl Diagrams - Human Lung Carcinoma." Pathology - Research and Practice 185, no. 5 (December 1989): 729–34. http://dx.doi.org/10.1016/s0344-0338(89)80228-6.

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45

Kanaun, S., and O. Tkachenko. "Mechanical Properties of Open Cell Foams: Simulations by Laguerre Tesselation Procedure." International Journal of Fracture 140, no. 1-4 (July 2006): 305–12. http://dx.doi.org/10.1007/s10704-006-0112-5.

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46

Riedinger, R., M. Habar, P. Oelhafen, and H. J. Güntherodt. "A New Realization of the Global Delaunay-Voronoi Tesselation in Arbitrary Dimension*." Zeitschrift für Physikalische Chemie 157, Part_1 (January 1988): 47–51. http://dx.doi.org/10.1524/zpch.1988.157.part_1.047.

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47

IWAMOTO, Takeshi, and Shinji KUBO. "Computational simulation of deformation behavior of polycrystal TRIP steel by Voronoi tesselation." Proceedings of The Computational Mechanics Conference 2003.16 (2003): 421–22. http://dx.doi.org/10.1299/jsmecmd.2003.16.421.

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Kumar, S., S. K. Kurtz, J. R. Banavar, and M. G. Sharma. "Properties of a three-dimensional poisson-voronoi tesselation: A Monte Carlo study." Journal of Statistical Physics 71, no. 1-2 (April 1993): 349. http://dx.doi.org/10.1007/bf01048105.

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Kumar, Susmit, Stewart K. Kurtz, Jayanth R. Banavar, and M. G. Sharma. "Properties of a three-dimensional Poisson-Voronoi tesselation: A Monte Carlo study." Journal of Statistical Physics 67, no. 3-4 (May 1992): 523–51. http://dx.doi.org/10.1007/bf01049719.

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50

Kumar, Susmit, and Stewart K. Kurtz. "Properties of a two-dimensional Poisson-Voronoi tesselation: A Monte-Carlo study." Materials Characterization 31, no. 1 (July 1993): 55–68. http://dx.doi.org/10.1016/1044-5803(93)90045-w.

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