Abstract
In the framework of combinatorial topology a surface is decribed as a set of faces which are linked by adjacency relations. This corresponds to a structural description of surfaces where we have some desirable properties: for example, any point is surrounded by a set of faces which constitute a “cycle”. The notion of combinatorial surface extracts these “structural” properties of surfaces.
In this paper, we introduce a relation for points in Z 3 which is based on the notion of homotopy. This allows to propose a definition of a class of surfaces which are combinatorial surfaces. We then show that the main existing notions of discrete surfaces belong to this class of combinatorial surfaces.
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© 1997 Springer-Verlag Berlin Heidelberg
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Bertrand, G., Couprie, M. (1997). Some structural properties of discrete surfaces. In: Ahronovitz, E., Fiorio, C. (eds) Discrete Geometry for Computer Imagery. DGCI 1997. Lecture Notes in Computer Science, vol 1347. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0024834
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DOI: https://doi.org/10.1007/BFb0024834
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