Limits of Voronoi Diagrams

Details Limits of Voronoi Diagrams Limits of Voronoi Diagrams

2002-10-22

arxiv.org/abs/math/0210345v1

Mathematics

Metric Geometry

PhD thesis, 132 pages, lots of figures

Scientific paper

In this thesis we study sets of points in the plane and their Voronoi diagrams, in particular when the points coincide. We bring together two ways of studying point sets that have received a lot of attention in recent years: Voronoi diagrams and compactifications of configuration spaces. We study moving and colliding points and this enables us to introduce `limit Voronoi diagrams'. We define several compactifications by considering geometric properties of pairs and triples of points. In this way we are able to define a smooth, real version of the Fulton-MacPherson compactification. We show how to define Voronoi diagrams on elements of these compactifications and describe the connection with the limit Voronoi diagrams.

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