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Erschienen in:
2018 | OriginalPaper | Buchkapitel
8. Tessellations of the Plane
verfasst von : Marc Barthelemy
Erschienen in: Morphogenesis of Spatial Networks
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Abstract
Another way to think of planar networks is by focusing on their faces and how to generate them. An example is given by tessellations of a plane that are divisions of the plane into polygons. There is a vast literature on tessellations (see [188] and references therein) and in this chapter, we will discuss selected examples only. Many tessellations are constructed from a random set of points and we will first focus in this chapter on the well-known Voronoi tessellation and its dual, the Delaunay graph. We then discuss briefly another class of tessellation obtained by growing lines from points (with the Gilbert model) or obtained by adding random lines (STIT models). Finally, we briefly discuss the case of planar fragmentation, and in the last section how we can use Delaunay graphs for constructing a null model of spatial multilayer networks.