The maptree: A fine-grained formal representation of space

Abstract

This paper introduces a new formal structure, called the maptree, that is shown to uniquely specify, up to homeomorphism, the topological structure of embeddings of graphs in orientable, closed surfaces. A simple modification is made to show that the representation also works for planar embeddings. It is shown that the maptrees are capable of providing a rich representation of the topology of 2D spatial objects and their relationships. The maptree representation is then used to characterize some properties of topological change in these embeddings. © 2012 Springer-Verlag.