Voronoizellen diskreter Punktmengen
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Date
2008-11-20T09:58:06Z
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Abstract
In dieser Arbeit wird eine Charakterisierung derjenigen diskreten Punktmengen angegeben, für die gilt, dass alle Voronoizellen Polyeder (bzw. Polytope) sind. Dazu wird der Begriff einer lokal endlich erzeugten diskreten Punktmenge eingeführt. Desweiteren wird der Rand der konvexen Hülle einer diskreten Punktmenge näher untersucht und geometrisch beschrieben.
This thesis gives a characterization of those discrete point sets which exhibit the property that all its Voronoi cells are polyhedra (resp. polytopes). To do this we introduce the term of locally finitely generated discrete point sets. Furthermore we investigate the boundary of the convex hull of a discrete point set and give a geometrical description.
This thesis gives a characterization of those discrete point sets which exhibit the property that all its Voronoi cells are polyhedra (resp. polytopes). To do this we introduce the term of locally finitely generated discrete point sets. Furthermore we investigate the boundary of the convex hull of a discrete point set and give a geometrical description.
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Vornoizellen, Lokal endlich erzeugte Punktmenge, Richtungskegel, Konvexe Hülle, Polyeder, Voronoi cell, Locally finitely generated discrete point set, Direction cone, Convex hull, Polyhedron