Editing Hard cube model
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[[Image:cube.png|thumb|right]] | [[Image:cube.png|thumb|right]] | ||
The ''' | The '''Hard cube model''' models cube-shaped particles interacting purely through excluded-volume interactions. The phase behavior has been studied extensively | ||
<ref>[http://dx.doi.org/10.1073/pnas.1211784109 F. Smallenburg, L. Filion, M. Marechal, and M. Dijkstra "Vacancy-stabilized crystalline order in hard cubes", Proc. Natl. Acad. Sci. USA '''109''' pp. 17886-17891 (2012)]</ref>. | <ref>[http://dx.doi.org/10.1038/nmat2959 Umang Agarwal and Fernando A. Escobedo "Mesophase behaviour of polyhedral particles", Nature Materials '''10''' pp. 230-235 (2011)]</ref> | ||
The simple cubic crystal phase has been shown to contain a high number of mobile, delocalized vacancies, similar to those seen in [[Parallel hard cubes]]. | <ref>[http://dx.doi.org/10.1073/pnas.1211784109 F. Smallenburg, L. Filion, M. Marechal, and M. Dijkstra "Vacancy-stabilized crystalline order in hard cubes", Proc. Natl. Acad. Sci. USA '''109''' pp. 17886-17891 (2012)]</ref>. The simple cubic crystal phase has been shown to contain a high number of mobile, delocalized vacancies, similar to those seen in [[Parallel hard cubes]]. | ||
==Implementation== | ==Implementation== | ||
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For two cubes, the overlap check therefore corresponds to the projection of both shapes onto 15 axes: the three edge vectors of both particles (6 in total), and the axes given by the 9 possible cross products of an edge vector of one cube with an edge vector of the other cube. The particles overlap if and only if the projections of the two particles on all 15 axes overlap as well. | For two cubes, the overlap check therefore corresponds to the projection of both shapes onto 15 axes: the three edge vectors of both particles (6 in total), and the axes given by the 9 possible cross products of an edge vector of one cube with an edge vector of the other cube. The particles overlap if and only if the projections of the two particles on all 15 axes overlap as well. | ||
==References== | ==References== |