Tessellations

Abstract

A tessellation is a division of space into small units or cells. The cells are usually polytopes (polygons in IR², polyhedra in IR³), but this is not strictly necessary. Depending on the application considered, a tessellation can be regarded either as a partition of space or as a random function (by assigning each cell a value), or even as a population of cells. Of course, different interpretations lead to different statistical characterizations. A brief description of the possible interpretations is given in the first section of this chapter. Then we turn to the presentation and the (conditional) simulation of two well known tessellation models, namely the Voronoi and the Poisson tessellations.