Fabricable Multi-Scale Wang Tiles

Abstract

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".