An integer representation for periodic tilings of the plane by regular polygons
Soto Sanchez JE, Weyrich T, Medeiros E Sa A, De Figueiredo LH (2021)
Publication Type: Journal article
Publication year: 2021
Journal
Book Volume: 95
Pages Range: 69-80
DOI: 10.1016/j.cag.2021.01.007
Abstract
We describe a representation for periodic tilings of the plane by regular polygons. Our approach is to represent explicitly a small subset of seed vertices from which we systematically generate all elements of the tiling by translations. We represent a tiling concretely by a (2+n)×4 integer matrix containing lattice coordinates for two translation vectors and n seed vertices. We discuss several properties of this representation and describe how to exploit the representation elegantly and efficiently for reconstruction, rendering, and automatic crystallographic classification by symmetry detection.
Authors with CRIS profile
Involved external institutions
National Institute for Pure and Applied Mathematics / Instituto Nacional de Matemática Pura e Aplicada (IMPA)
Brazil (BR)
University College London (UCL)
United Kingdom (GB)
Fundação Getulio Vargas (FGV)
Brazil (BR)
Brazil (BR)
University College London (UCL)
United Kingdom (GB)
Fundação Getulio Vargas (FGV)
Brazil (BR)
How to cite
APA:
Soto Sanchez, J.E., Weyrich, T., Medeiros E Sa, A., & De Figueiredo, L.H. (2021). An integer representation for periodic tilings of the plane by regular polygons. Computers & Graphics, 95, 69-80. https://doi.org/10.1016/j.cag.2021.01.007
MLA:
Soto Sanchez, Jose Ezequiel, et al. "An integer representation for periodic tilings of the plane by regular polygons." Computers & Graphics 95 (2021): 69-80.
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