Abstract: Enveloping, or the mapping of skeletal controls to the deformations of a surface, is key to driving realistic animated characters. Despite its widespread use, enveloping still relies on slow or inaccurate deformation methods. We propose a method that is both fast, accurate and example-based. Our technique introduces a rotational regression model that captures common skinning deformations such as muscle bulging, twisting, and challenging areas such as the shoulders. Our improved treatment of rotational quantities is made practical by model reduction that ensures real-time solution of least-squares problems, independent of the mesh size. Our method is significantly more accurate than linear blend skinning and almost as fast, suggesting its use as a replacement for linear blend skinning when examples are available.