Applications of Quaternions to Dynamical Simulation, Computer Graphics and Biomechanics (Toepassingen van Quaternionen op Dynamische Simulatie, Computer Graphics en Biomechanika)

摘要

At the heart of this thesis is the ARTIBODIES system for computer-aided modelling and visualization of spatial articulated bodies. Spatial rotations and orientations are in the ARTIBODIES system represented by quaternions. General spatial displacements are represented as a rotation followed by a translation. Chapter 2 contains a group-theoretic treatment of the concepts of location, position and orientation. Chapters 3 - 6 contain a construction of the theory of quaternions aimed at the representation of spatial rotations by quaternions. Some applications of the ARTIBODIES system to orthopedics, dance and ballet and sign languages for the deaf are treated in Chapter 10. The application to dynamical simulation, in particular to the simulation of the rotation of a rigid body about a fixed point, is treated extensively in Chapter 11. An application of quaternions to computer graphics, viz. to the problem of the generation of a smooth spatial rotational motion passing through prescribed orientations at prescribed times, the rotation animation problem, is the subject of Chapter 7. In Chapter 8 a kinematical interpretation of one of the geometrical aspects of Chapter 7 is presented.