The Disney Research team presented their project focused on the control of interpolations in animation with positional constraints over time as a space-time optimization problem in the tangent space of the curves driving the animation controls.

Usually, the animator starts with combinations of forward and inverse kinematics to pose a character at certain keyframes via controls, and adjusts animation curves driving the controls for fine-tuning. Then, these keyframed controls are interpolated to get the animation. “While forward kinematics leads to intuitive interpolations, it is not possible to impose positional constraints and hence, for example, fix contact points,” noted the team. “Inverse kinematics can be used to fix certain points in space at keyframes, but can lead to inferior interpolations, and does not allow for positional contraints at non-keyframe frames.”

The paper they presented wants to solve these problems by “formulating control interpolation with positional constraints over time as a space-time optimization problem in the tangent space of the animation curves driving the controls.” The team states that

1. It works in the space of artist editable animation curves and hence integrates seamlessly with the current pipelines,
2. Does not add new keyframes
3. Allows for positional trajectories of positions over time, extending inverse kinematics.

You can find the full paper here.