Fabricable Multi-scale Wang Tiles

Presented on SGP 2022

Xiaokang Liu1    Chenran Li1    Lin Lu*1    Oliver Deussen2    Changhe Tu1

1Shandong University   2University of Konstanz  

Design fabricable multi-scale Wang tiles and use them to tile an image, obtaining a physical half-toning result efficiently.



Wang tiles, also known as Wang dominoes, are a jigsaw puzzle system with matching edges. Due to their compactness and expressiveness in representing variations, they have become a popular tool in the procedural synthesis of textures, height fields, 3D printing and representing other large and non-repetitive data. Multi-scale tiles created from low-level tiles allow for a higher tiling efficiency, although they face the problem of combinatorial explosion. In this paper, we propose a generation method for multi-scale Wang tiles that aims at minimizing the amount of needed tiles while still resembling a tiling appearance similar to low-level tiles. Based on a set of representative multi-scale Wang tiles, we use a dynamic generation algorithm for this purpose. Our method can be used for rapid texture synthesis and image halftoning. Respecting physical constraints, our tiles are connected, lightweight, independent of the fabrication scale, able to tile larger areas with image contents and contribute to "mass customization".

Halftoning Tiling Results

Results generated by constraining the types of tile, the density error and the total number of tiles respectively.

Results generated by setting different threshold ψ.


Fabricated and assembled results

A video recording the assembly process of earring girl.

Physical result of cat made up of around one thousand seven hundred pieces with a size of 3 meters by 3 meters.





We thank all the anonymous reviewers for their constructive suggestions. This work is supported by the grant from NSFC (61972232), Oliver Deussen was funded by the German Research Foundation (DFG) - Project-ID 251654672 - TRR 161