Tangent Space Optimization of Controls for Character Animation

We formulate 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. Our method has the key properties that it (1) allows for the manipulation of positions and orientations over time, extending inverse kinematics, (2) does not add new keyframes, and 3) works in the space of editable animation curves and hence integrates seamlessly with current pipelines.
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