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Construction of continuum from a discrete surface by its iterated subdivisions
- Publication Year :
- 2018
-
Abstract
- Given a trivalent graph in the 3-dimensional Euclidean space, we call it a discrete surface because it has a tangent space at each vertex determined by its neighbor vertices. To abstract a continuum object hidden in the discrete surface, we introduce a subdivision method by applying the Goldberg-Coxeter subdivision and discuss the convergence of a sequence of discrete surfaces defined inductively by the subdivision. We also study the limit set as the continuum geometric object associated with the given discrete surface.<br />Comment: 22 pages, 10 figures and 2 tables
- Subjects :
- Mathematics - Differential Geometry
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1806.03531
- Document Type :
- Working Paper