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
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.
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