Pyramid coordinates for deformation with collision handling

We present an efficient implementation of the reconstruction of pyramid coordinates which are used for the deformation of animated characters. By reformulating the pyramid coordinates as an optimization problem with one-ring neighborhood constraints, we can solve the problem using an efficient projective solver. This greatly improves the overall performance, and makes it easier to incorporate other geometric constraints. Collisions between the deformed and kinematic geometries are handled using a two-pass methodology. By resolving collisions before applying pyramid coordinate constraints, we obtain a consistent result after the constraint projection. Dynamic simulation is also possible by modeling proper constraints and projection operators under the same framework.