This project studies probabilistic aspects of computational geometry. Particular emphasis is being placed on: -extending known results on the expected running times of algorithms for constructing convex hulls and Voronoi diagrams of random point sets in higher dimensions, -implementing and animating algorithms for Voronoi diagrams, minimum spanning trees, and other geometric problems, and carrying out empirical studies of their performance and their output, -investigating running times of other geometric algorithms on random point sets, -applying methods of integral geometry to define realistic and analyzable distributions of more complex geometric inputs such as sets of line segments and polygon, and -investigating connections to problems in the theory of random graphs and in the theory of data structures.
