This work comes from ideas I originally had in the late 90s, but was only recently able to carry out based on advances in mesh parameterization. In Pattern-based texturing revisited (Neyret and Cani, SIGGRAPH 1999), the authors create a subdivision of a mesh surface into coarse triangles, and map triangular texture swatches into each of the triangles to produce an overall non-repeating texturing. Many subsequent papers explored the use of coarse mesh parameterization to support non-repeating texturing. For some reason, nobody ever demonstrated the opposite extreme, covering a mesh with a highly repetitive pattern.
This work shows that given a planar pattern belonging to one of five common symmetry groups, it is possible to cover a suitably-parameterized mesh surface with an analogous pattern. The re-interpreted pattern isn't exactly the same -- some concession must be made at the vertices of the coarse parameterization to account for varying curvature. But it's clearly a close relative.
I use the triangles from Globally smooth parameterization for groups p6 and p6m, and the squares from Spectral surface quadrangulation for groups p4, p4g and p4m. Given meshes parameterized using these methods, there's really no work left to do; the rest is just texture mapping.
|Craig S. Kaplan||Last updated:|