Efficient solver for spacetime control of smoke

We present a novel algorithm to control the physically-based animation of smoke. Given a set of keyframe smoke shapes, we compute a dense sequence of control force fields that can drive the smoke shape to match several keyframes at certain time instances. Our approach formulates this control problem as a spacetime optimization constrained by partial differential equations. In order to compute the locally optimal control forces, we alternatively optimize the velocity fields and density fields using an alternating direction method of multiplier (ADMM) optimizer. In order to reduce the high complexity of multiple passes of fluid resimulation during velocity field optimization, we utilize the coherence between consecutive fluid simulation passes. We demonstrate the benefits of our approach by computing accurate solutions on 2D and 3D benchmarks. In practice, we observe up to an order of magnitude improvement over prior optimal control methods.