Editing Voronoi cells
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A '''Voronoi cell''' | 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 | 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 | than to any of the others. This very intuitive partition of space results in the Voronoi tessellation. The | ||
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Voronoi cells are [[dual lattice | dual]] of [[Delaunay simplexes]]. | Voronoi cells are [[dual lattice | dual]] of [[Delaunay simplexes]]. | ||
==Algorithms== | ==Algorithms== | ||
#[http://dx.doi.org/10.1016/0021-9991(78)90110-9 Witold Brostow, Jean-Pierre Dussault and Bennett L. Fox "Construction of Voronoi polyhedra", Journal of Computational Physics '''29''' pp. 81-92 (1978)] | |||
#[http://dx.doi.org/10.1016/0021-9991(79)90146-3 J. L. Finney "A procedure for the construction of Voronoi polyhedra", Journal of Computational Physics '''32''' pp. 137-143 (1979)] | |||
#[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)] | |||
==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) | |||
''' | #[http://dx.doi.org/10.1063/1.438311 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)] | ||
#[http://dx.doi.org/10.1063/1.442299 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)] | |||
#[http://dx.doi.org/10.1063/1.459711 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)] | |||
#[http://dx.doi.org/10.1021/j100118a044 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)] | |||
#[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)] | |||
==External links and resources== | ==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)]. | *[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 ]] | ||