Multi-weight enveloping: least-squares approximation techniques for skin animation

We present a process called multi-weight enveloping for deforming the skin geometry of the body of a digital creature around its skeleton. It is based on a deformation equation whose coefficients we compute using a statistical fit to an input training exercise. In this input, the skeleton and the skin move together, by arbitrary external means, through a range of motion representative of what the creature is expected to achieve in practice. The input can also come from existing pieces of handcrafted skin animation. Using a modified least-squares fitting technique, we compute the coefficients, or "weights", of the deformation equation. The result is that the equation generalizes the skin movement so that it applies well to other sequences of animation. The multi-weight deformation equation is computationally efficient to evaluate; once the training process is complete, even creatures with high levels of geometric detail can move at interactive frames rates with a look that approximates that of anatomical, physically-based models. We demonstrate the technique in a feature film production environment, on a human model whose input poses are sculpted by hand and an animal model whose input poses come from the output of an anatomically-based dynamic simulation.