The K-Cell Under Increasing Intensities

In Chap. 8 , we have already studied interactions of a stationary Poisson hyperplane process or the corresponding tessellation with a given convex body. In that chapter, we were interested in what happens inside the convex body. Now we look at the hyperplanes of the process outside the convex body. The intersection of the closed halfspaces bounded by hyperplanes of the process and containing the convex body is a polytope. In this chapter, we deal with the question how well these polytopes approximate the given convex body if the intensity of the hyperplane process increases, and we illuminate the role of the directional distribution of the hyperplane process. The degree of approximation is measured in several different ways.