Animating deformable objects using sparse spacetime constraints

We propose a scheme for animating deformable objects based on spacetime optimization. The main feature is that it robustly and within a few seconds generates interesting motion from a sparse set of spacetime constraints. Providing only partial (as opposed to full) keyframes for positions and velocities is sufficient. The computed motion satisfies the constraints and the remaining degrees of freedom are determined by physical principles using elasticity and the spacetime constraints paradigm. Our modeling of the spacetime optimization problem combines dimensional reduction, modal coordinates, wiggly splines, and rotation strain warping. Our solver is based on a theorem that characterizes the solutions of the optimization problem and allows us to restrict the optimization to low-dimensional search spaces. This treatment of the optimization problem avoids a time discretization and the resulting method can robustly deal with sparse input and wiggly motion.