Pattern mapping with quad-pattern-coverable quad-meshes

Abstract

Pattern mapping (i.e. texturing arbitrary surfaces with repetitive patterns [Soler et al. 2002]) is a particularly useful texture mapping technique, since repeating a pattern reduces the memory cost, by mapping the same texture image to all faces. Moreover, pattern mapping does not require painting a texture image for each surface or generating a global texture map on each surface. Pattern mapping can potentially provide natural-looking materials, such as stone, wood, or marble, as well as human-made materials, such as wallpapers or repeating tiles. One of the main challenges arising when mapping patterns to arbitrary polyhedral meshes is to avoid texture discontinuities caused by singularities non-4-valent vertices in the quad-meshes. These discontinuities can appear at seams along the edges, which can be visually distracting. Unfortunately, it is not always possible to avoid non-4-valent vertices, since 4-regular quadmeshes exist only for genus-1 surfaces.