LinearWang
swMATH ID:  34624 
Software Authors:  DerouetJourdan, 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 subregions 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. DerouetJourdan} 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 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

A linear algorithm for brick Wang tiling. Zbl 1428.05050 DerouetJourdan, Alexandre; Kaji, Shizuo; Mizoguchi, Yoshihiro 
2019

Cited by 3 Authors
1  DerouetJourdan, Alexandre 
1  Kaji, Shizuo 
1  Mizoguchi, Yoshihiro 
Cited in 1 Serial
1  Japan Journal of Industrial and Applied Mathematics 
Cited in 3 Fields
1  Combinatorics (05XX) 
1  Convex and discrete geometry (52XX) 
1  Computer science (68XX) 