Wang Tiles for Image and Texture Generation

This paper discusses the use of Wang Tiles for image and texture generation as originally presented in Cohen et al., 2003. Creating large expanses of nonperiodic texture, point distributions or geometry can be efficiently done at runtime by constructing a tiling of the plane using a small set of Wang tiles. Wang Tiles are squares whose edges are each assigned a color. The method involves filling a small set of Wang Tiles with texture, Poisson point distributions or geometry and non-periodically tiling the plane to stochastically create a continuous representation. For a tiling to be valid, all shared edges between tiles need to have matching colors. An algorithm for runtime generation of such valid tilings is presented. Creating the tiles so that tiles with matching edge colors have textures that fit together is also discussed, as well as usage of an extended notion of Wang Tiles with colored corners that allows discrete objects to overlap tile corners and the creation of inhomogeneous textures. The Wang Tiles technique is also put into perspective through a short introduction to previous methods for texture synthesis and the modeling of complex 3D scenes. The main differences between using Wang Tiles and other techniques are also discussed.