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

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.

BibTeX: Download