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.
Configuration Spaces and Limits of Voronoi Diagrams.
Roderik Lindenbergh, Wilberd van der Kallen, Dirk Siersma, in press, (2002).
Survey article, describing the highlights of the thesis.