swMATH ID: 34624
Software Authors: Derouet-Jourdan, Alexandre; Kaji, Shizuo; Mizoguchi, Yoshihiro
Description: LinearWang - An implementation of the algorithm discussed in the paper: A linear algorithm for brick Wang tiling. The Wang tiling is a classical problem in combinatorics. A major theoretical question is to find a (small) set of tiles which tiles the plane only aperiodically. In this case, resulting tilings are rather restrictive. On the other hand, Wang tiles are used as a tool to generate textures and patterns in computer graphics. In these applications, a set of tiles is normally chosen so that it tiles the plane or its sub-regions easily in many different ways. With computer graphics applications in mind, we introduce a class of such tileset, which we call sequentially permissive tilesets, and consider tiling problems with constrained boundary. We apply our methodology to a special set of Wang tiles, called Brick Wang tiles, introduced by extit{A. Derouet-Jourdan} et al. [Math. Ind. (Tokyo) 24, 71–81 (2016; Zbl 1401.68348)] to model wall patterns. We generalise their result by providing a linear algorithm to decide and solve the tiling problem for arbitrary planar regions with holes.
Homepage: https://arxiv.org/abs/1603.04292
Source Code:  https://github.com/KyushuUniversityMathematics/LinearWang
Keywords: Wang tile; texture generation; graphical model; satisfiability problem
Related Software: GitHub; Coq
Cited in: 1 Publication

Citations by Year