ABSTRACT
This chapter reviews the mathematical knowledge of Johnson–Mehl tessellations. It explains geometric structure of Voronoi and Johnson–Mehl tessellations and describes Poisson models. K. W. Mahin presents simulated results for planar sections through spatial Poisson-Voronoi tessellations and spatial Johnson–Mehl tessellations generated by a time-homogeneous Poisson birth process. J. Moller shows how typical Poisson-Voronoi cells and Johnson–Mehl crystals in the case of time-inhomogeneous Poisson birth processes can be simulated. L. Heinrich and E. Schule consider simulation procedures for some non-Poissonian cases. K. Hanson argues that the so-called ASTM model, which is frequently used in metallurgy, can be described by a Johnson–Mehl tessellation. A tessellation is roughly speaking a subdivision of the space into sets called cells, crystal and tiles depending on the particular application. Typically, the random mechanism is given by some stochastic process of simple geometrical objects which generate the tessellation in accordance to some rules.
