Voronoi cells: Difference between revisions
Jump to navigation
Jump to search
Carl McBride (talk | contribs) mNo edit summary |
m (Placed external links at foot of page.) |
||
| Line 13: | Line 13: | ||
#[http://dx.doi.org/10.1016/0021-9991(83)90087-6 Masaharu Tanemura, Tohru Ogawa and Naofumi Ogita "A new algorithm for three-dimensional voronoi tessellation", Journal of Computational Physics '''51''' pp. 191-207 (1983)] | #[http://dx.doi.org/10.1016/0021-9991(83)90087-6 Masaharu Tanemura, Tohru Ogawa and Naofumi Ogita "A new algorithm for three-dimensional voronoi tessellation", Journal of Computational Physics '''51''' pp. 191-207 (1983)] | ||
#[http://dx.doi.org/10.1016/0021-9991(86)90123-3 N. N. Medvedev "The algorithm for three-dimensional voronoi polyhedra", Journal of Computational Physics '''67''' pp. 223-229 (1986)] | #[http://dx.doi.org/10.1016/0021-9991(86)90123-3 N. N. Medvedev "The algorithm for three-dimensional voronoi polyhedra", Journal of Computational Physics '''67''' pp. 223-229 (1986)] | ||
==References== | ==References== | ||
# G. F. Voronoi "Nouvelles applications des paramètres continus à la théorie des formes quadratiques - Deuxième mémoire", Journal für die reine und angewandte Mathematik '''134''' pp. 198-287 (1908) | # G. F. Voronoi "Nouvelles applications des paramètres continus à la théorie des formes quadratiques - Deuxième mémoire", Journal für die reine und angewandte Mathematik '''134''' pp. 198-287 (1908) | ||
| Line 23: | Line 21: | ||
#[http://dx.doi.org/10.1063/1.2011390 V. Senthil Kumar and V. Kumaran "Voronoi cell volume distribution and configurational entropy of hard-spheres", Journal of Chemical Physics '''123''' 114501 (2005)] | #[http://dx.doi.org/10.1063/1.2011390 V. Senthil Kumar and V. Kumaran "Voronoi cell volume distribution and configurational entropy of hard-spheres", Journal of Chemical Physics '''123''' 114501 (2005)] | ||
#[http://dx.doi.org/10.1063/1.2000233 V. Senthil Kumar and V. Kumaran "Voronoi neighbor statistics of hard-disks and hard-spheres", Journal of Chemical Physics '''123''' 074502 (2005)] | #[http://dx.doi.org/10.1063/1.2000233 V. Senthil Kumar and V. Kumaran "Voronoi neighbor statistics of hard-disks and hard-spheres", Journal of Chemical Physics '''123''' 074502 (2005)] | ||
==External links== | |||
*[http://www.cgal.org/Manual/3.3/doc_html/cgal_manual/packages.html#part_IX The CGAL project on computational geometry] | |||
[[category: Computer simulation techniques ]] [[category: Mathematics ]] | [[category: Computer simulation techniques ]] [[category: Mathematics ]] | ||
Revision as of 20:23, 11 December 2008
|
This article is a 'stub' page, it has no, or next to no, content. It is here at the moment to help form part of the structure of SklogWiki. If you add sufficient material to this article then please remove the {{Stub-general}} template from this page. |
A Voronoi cell (also known as: Voronoi polyhedra, Voronoi tessellations, Dirichlet tesselations, Wigner-Seitz cells). is the diagram that results when a cell is defined around each of the points (or nodes, or vertices) of a network with the following criterion: each point in the cell is closer to its node than to any of the others. This very intuitive partition of space results in the Voronoi tessellation. The typical example is to, e.g., assign areas of a country to different fire stations, so that if a fire occurs, the corresponding station is the closest one.
Voronoi cells are dual of Delaunay simplexes.
Algorithms
- Witold Brostow, Jean-Pierre Dussault and Bennett L. Fox "Construction of Voronoi polyhedra", Journal of Computational Physics 29 pp. 81-92 (1978)
- J. L. Finney "A procedure for the construction of Voronoi polyhedra", Journal of Computational Physics 32 pp. 137-143 (1979)
- Masaharu Tanemura, Tohru Ogawa and Naofumi Ogita "A new algorithm for three-dimensional voronoi tessellation", Journal of Computational Physics 51 pp. 191-207 (1983)
- N. N. Medvedev "The algorithm for three-dimensional voronoi polyhedra", Journal of Computational Physics 67 pp. 223-229 (1986)
References
- G. F. Voronoi "Nouvelles applications des paramètres continus à la théorie des formes quadratiques - Deuxième mémoire", Journal für die reine und angewandte Mathematik 134 pp. 198-287 (1908)
- C. S. Hsu and Aneesur Rahman "Interaction potentials and their effect on crystal nucleation and symmetry", Journal of Chemical Physics 71 pp. 4974-4986 (1979)
- J. Neil Cape, John L. Finney and Leslie V. Woodcock "An analysis of crystallization by homogeneous nucleation in a 4000-atom soft-sphere model", Journal of Chemical Physics 75 pp. 2366-2373 (1981)
- Nikolai N. Medvedev, Alfons Geiger and Witold Brostow "Distinguishing liquids from amorphous solids: Percolation analysis on the Voronoi network", Journal of Chemical Physics 93 pp. 8337-8342 (1990)
- J. C. Gil Montoro and J. L. F. Abascal "The Voronoi polyhedra as tools for structure determination in simple disordered systems", Journal of Physical Chemistry 97 pp. 4211 - 4215 (1993)
- V. Senthil Kumar and V. Kumaran "Voronoi cell volume distribution and configurational entropy of hard-spheres", Journal of Chemical Physics 123 114501 (2005)
- V. Senthil Kumar and V. Kumaran "Voronoi neighbor statistics of hard-disks and hard-spheres", Journal of Chemical Physics 123 074502 (2005)