Voronoi cells: Difference between revisions
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A '''Voronoi cell''' (also known as: '''Voronoi polyhedra''', '''Voronoi tessellations''', '''Dirichlet tesselations''', '''Wigner-Seitz cells'''). | 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, | is the diagram that results when a cell is defined around each of the points (or nodes, | ||
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#[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== | ==External links and resources== | ||
*[http://www.cgal.org/Manual/3.3/doc_html/cgal_manual/packages.html#part_IX The CGAL project on computational geometry] | *[http://www.cgal.org/Manual/3.3/doc_html/cgal_manual/packages.html#part_IX The CGAL project on computational geometry] | ||
*[ftp://ftp.dl.ac.uk/ccp5/ALLEN_TILDESLEY/F.35 The Voronoi construction in 2d and 3d] sample FORTRAN computer code from the book [http://www.oup.com/uk/catalogue/?ci=9780198556459 M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", Oxford University Press (1989)]. | |||
[[category: Computer simulation techniques ]] [[category: Mathematics ]] | [[category: Computer simulation techniques ]] [[category: Mathematics ]] | ||
Revision as of 18:37, 8 February 2009
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)
External links and resources
- The CGAL project on computational geometry
- The Voronoi construction in 2d and 3d sample FORTRAN computer code from the book M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", Oxford University Press (1989).