Interactive elastic motion editing through space-time position constraints

We present an intuitive and interactive approach for motion editing through spacetime constraints on positions. Given an input motion of an elastic body, our approach enables the user to interactively edit node positions in order to alter and fine-tune the motion. We formulate our motion editing as an optimization problem with dynamics constraints to enforce a physically-plausible result. Through linearization of the editing around the input trajectory, we simplify this constrained optimal control problem into an unconstrained quadratic optimization. The optimal motion thus becomes the solution of a dense linear system, which we solve efficiently by applying the adjoint method in each iteration of a conjugate gradient solver. We demonstrate the efficiency and quality of our motion editing technique on a series of examples.