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.
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© 2012 Springer-Verlag Berlin Heidelberg
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Worboys, M. (2012). The Maptree: A Fine-Grained Formal Representation of Space. In: Xiao, N., Kwan, MP., Goodchild, M.F., Shekhar, S. (eds) Geographic Information Science. GIScience 2012. Lecture Notes in Computer Science, vol 7478. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33024-7_22
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DOI: https://doi.org/10.1007/978-3-642-33024-7_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33023-0
Online ISBN: 978-3-642-33024-7
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