An automatic method for determining quaternion field boundaries for ball-and-socket joint limits

To improve the robustness of human motion synthesis and capture algorithms, our goal is to provide an effective framework for imposing joint limits and reducing ambiguities. To this end, we determine these joint limits from measures performed on human subjects and then transpose them to an intuitive joint limits formalism. We focus on the case of ball-and-socket joint limits, applied to the specific case of the shoulder complex. The first step is to measure the joint motion range using optical motion capture. We then convert the recorded values to joint poses using a coherent quaternion field representation of the joint orientation space. Finally, we obtain a closed, continuous implicit surface approximation for the quaternion orientation-space boundary delimiting the complete space of valid shoulder orientations, and allowing us to determine the closest valid posture for any given invalid one.