Texture Tiling on Arbitrary Topological Surfaces using Wang Tiles

Abstract

Synthesizing textures on arbitrary surfaces is a time consuming process. We have to analyze the surface geometry and map texture values onto the input surface adaptively. Texture tiling provides an alternative approach by decoupling the texture synthesis process into two steps: surface mapping and tile placement. This paper reformulates the texture tiling mechanism of Wang tiles for arbitrary topological surfaces. Once we created a low distortion conformal map from the input surface to a quad-based geometry, we can generate a tiling graph over the geometric dual graph of the quad-based geometry, and produce a proper tile orientation on all quad faces so that we can layout textured tiles on quads and map texture back to the input surface accordingly. Since tile placement is independent of the input surface geometry, we can perform the tiling process in no time and change texture pattern on the input surface simply by switching a tile set. No additional computation is needed. As a demonstration, we experimented texture tiling of Wang tiles on spheres, polycubes, as well as polycube-mapped models.