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Visualization of the Dirichlet-Voronoi cells in S<sup>2</sup>Ă—R space |
Tartalom: | http://real.mtak.hu/66747/ |
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Archívum: | MTA Könyvtár |
Gyűjtemény: |
Status = Published
Type = Article |
Cím: |
Visualization of the Dirichlet-Voronoi cells in S<sup>2</sup>Ă—R space
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Létrehozó: |
Pallagi, János
Szirmai, Jenő
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Kiadó: |
Akadémiai Kiadó
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Dátum: |
2012
info:eu-repo/date/embargoEnd/2032-01-31
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Téma: |
TA Engineering (General). Civil engineering (General) / általános mérnöki tudományok
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Tartalmi leírás: |
The S<sup>2</sup>×R geometry can be derived by the direct product of the spherical plane S<sup>2</sup> and the real line R. In [1] J. Z. Farkas has classified and given the complete list its space groups. In [6] the second author has studied the geodesic balls and their volumes in S<sup>2</sup>×R space, moreover he has introduced the notion of geodesic ball packing and its density and have determined the densest geodesic ball packing for generalized Coxeter space groups of S<sup>2</sup>×R.The aim of this paper to develop a method to study and visualize the Dirichlet-Voronoi cells belonging to a given ball packing. We apply our former results on the equidistant surfaces of the S<sup>2</sup>×R geometry (see [5]) to determine the D-V cells to locally optimal ball packings belonging to S<sup>2</sup>×R space groups generated by glide reflections.E. Molnár has shown in [3], that the homogeneous 3-spaces have a unified interpretation in the real projective 3-sphere, in our work we will use this projective model of S<sup>2</sup>×R geometry. We will use the Wolfram Mathematica software for visualization of the arrangement of a locally optimal geodesic ball packing and its Dirichlet-Voronoi cell of a given glide reflection space group.
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Nyelv: |
magyar
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Típus: |
Article
PeerReviewed
info:eu-repo/semantics/article
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Formátum: |
text
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Azonosító: |
Pallagi, János and Szirmai, Jenő (2012) Visualization of the Dirichlet-Voronoi cells in S<sup>2</sup>×R space. Pollack Periodica, 7 (Supple). pp. 95-104. ISSN 1788-1994
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Kapcsolat: |
https://doi.org/10.1556/Pollack.7.2012.S.9
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Létrehozó: |
info:eu-repo/semantics/embargoedAccess
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