Keyframe Motion Optimization By Relaxing Speed and Timing

While physically based approaches have been shown to be eeective for creating graceful and realistic motions, keyframing systems are still the predominant tool for animation. This is due primarily to the control provided to the animator, as well as to the simple fast computation of in-between frames. In contrast, physical simulation systems automate the creation of realistic motion sequences, but remove most of the control from the animator. Recent work with spacetime constraints and optimal control has focused on balancing control and automation. However, either the algorithmic and computational complexity or the continuing lack of control have made it diicult to integrate these developments into real animation systems. The goal of the research reported here is to avoid disturbing the basic framework of keyframe systems while still ooering many of the advantages of optimization based systems. We present an animation paradigm in which, as in keyframe systems, the user speciies a small number of keyframes for the gure to pass through. As in spacetime constraint systems , the animator may also indicate constraints such as the height of a jump. In constrast to both systems, the time at which the gure reaches the keyframes and the velocity with which it passes each keyframe can be left open and are then determined automatically through an energy minimization. This heavily constrained optimization problem is much smaller than a full spacetime constraints problem and thus converges very quickly. In addition, the familiar keyframe paradigm ooers a high level of control to the animator, while freeing the inexperienced animator from the less intuitive timing and velocity speciications. Including time itself as a variable within the optimization framework is an important change from previously reported systems. Our experiments show that this method is able to create smooth and realistic motions eeciently for complex 3D gures.