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.Keywordssurfacesdiscrete topologyhomotopysimple points

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.