Keyframe animation is a common technique to generate animations
of deformable characters and other soft bodies. With spline interpolation,
however, it can be difficult to achieve secondary motion
effects such as plausible dynamics when there are thousands of degrees
of freedom to animate. Physical methods can provide more
realism with less user effort, but it is challenging to apply them
to quickly create specific animations that closely follow prescribed
animator goals. We present a fast space-time optimization method
to author physically based deformable object simulations that conform
to animator-specified keyframes. We demonstrate our method
with FEM deformable objects and mass-spring systems.
Our method minimizes an objective function that penalizes the sum
of keyframe deviations plus the deviation of the trajectory from
physics. With existing methods, such minimizations operate in
high dimensions, are slow, memory consuming, and prone to local
minima. We demonstrate that significant computational speedups
and robustness improvements can be achieved if the optimization
problem is properly solved in a low-dimensional space. Selecting
a low-dimensional space so that the intent of the animator is accommodated, and that at the same time space-time optimization is
convergent and fast, is difficult. We present a method that generates
a quality low-dimensional space using the given keyframes. It is
then possible to find quality solutions to difficult space-time optimization problems robustly and in a manner of minutes.
