Simulation of Random Set Models for Unions of Discs and the Use of Power Tessellations

Abstract

The power tessellation (or power diagram or Laguerre diagram) turns out to be particularly useful in connection to a flexible class of random set models specified by an underlying process of interacting discs. We discuss how to simulate these models and calculate various geometric characteristics of power tessellations, where new relations for the characteristics are established. The proposed model is fitted to a heather dataset.