Voronoi Cells of Discrete Point Sets

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dc.contributor.authorVoigt, Ina K.
dc.date.accessioned2008-11-17T12:31:38Z
dc.date.available2008-11-17T12:31:38Z
dc.date.issued2008-11-17T12:31:38Z
dc.description.abstractIt is well known that all cells of the Voronoi diagram of a Delaunay set are polytopes. For a finite point set, all these cells are still polyhedra. So the question arises, if this observation holds for all discrete point sets: Are always all Voronoi cells of an arbitrary, infinite discrete point set polyhedral? In this paper, an answer to this question will be given. It will be shown that all Voronoi cells of a discrete point set are polytopes if and only if every point of the point set is an inner point. Furthermore, the term of a locally finitely generated discrete point set will be introduced and it will be shown that exactly these sets have the property of possessing only polyhedral Voronoi cells.en
dc.identifier.urihttp://hdl.handle.net/2003/25841
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-5086
dc.language.isoende
dc.relation.ispartofseriesPreprints der Fakultät für Mathematik;2008-23de
dc.subject.ddc610
dc.titleVoronoi Cells of Discrete Point Setsen
dc.typeTextde
dc.type.publicationtypepreprintde
dcterms.accessRightsopen access

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