Semiregular patterns on surfaces

Inspired by recent advances in high-quality mesh parameterization, I present a technique for decorating surfaces with seamless ornamental patterns. The patterns are transferred from planar drawings with wallpaper symmetry. I show that when the original drawing belongs to one of a few specific symmetry groups, then it can easily be rendered with low distortion on a suitably parameterized mesh. The result is not symmetric, but retains most of the structure of the original drawing.