PhD Thesis: Limits of Voronoi diagrams

The abstract:
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.


Chapter by chapter:
Utrecht University Library

Full text:

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.

Original description of the project:

PhD Supervisors:
Dirk Siersma, Wilberd van der Kallen.

Thesis defense:
, ,

Mathematica/LiveGraphics3D demo:
Interactive version of Figure 5.7

Java applets and Mathematica notebooks on Voronoi diagrams.

Roderik Lindenbergh
June 2003