Comparison of Quaternion and Euler Angle Methods for Joint Angle Animation of Human Figure Models

摘要

This thesis presents articulated rigid body kinematics models for humans. The main area of research is to investigate models for real-time computer graphics applications in Virtual Environments (VE). Existing models have singularity problems and become too slow once the number of humans in view becomes large. The approach taken is to develop a full body kinematics model with quaternions. Another common method, Euler angles, has singularity and interpolation problems. Both methods are compared for memory, computation and user input considerations. The implementation includes joint angle constraints. The model is then manipulated with user inputs by a mouse. As part of this research, the real-time display of human arm tracking with two inertial sensors, human walking, inverse kinematics, and key frame animation is also demonstrated. The major conclusion of this thesis is that a kinematics model with quaternions can eliminate the singularity problems of existing models. Joint orientation interpolation is also more direct and less convoluted with quaternions. Neither representation exhibits a decisive advantage over the other in terms of computational speed. For memory considerations, the Euler angle method is best. To apply joint constraints, quaternion representations are converted to Euler angles, which causes additional computation for the system.