Visualizing Quaternions Course Notes forSIGGRAPH 2001 Course Organizer

This tutorial focuses on establishing an intuitive visual understanding of the relationship between ordinary 3D rotations and their quaternion representations. We begin building this intuition by showing how quaternion-like properties appear and can be exploited even in 2D space. Quaternions are then introduced in several alternative representations that do not necessarily require abstract mathematical constructs for their visualization. We then proceed to develop visualizations of quaternion applications such as moving frames and orientation splines. Finally, we briefly discuss the problem of generalizing quaternion concepts to higher dimensions using Clifford algebras. Presenter’s Biography Andrew J. Hanson is a professor of computer science at Indiana University, and has regularly taught courses in computer graphics, computer vision, and scientific visualization. He received a BA in chemistry and physics from Harvard College in 1966 and a PhD in theoretical physics from MIT in 1971. Before coming to Indiana University, he did research in theoretical physics at the Institute for Advanced Study, Stanford, and Berkeley, and then in computer vision at the SRI Artificial Intelligence Center in Menlo Park, CA. He has published in IEEE Computer, CG&A, TVCG, ACM Computing Surveys, and has over a dozen papers in the IEEE Visualization Proceedings. He has also contributed three articles to the Graphics Gems series dealing with user interfaces for rotations and with techniques of N-dimensional geometry. Previous experience with conference tutorials includes a Siggraph ’98 tutorial on N-dimensional graphics, a Visualization ’98 course on Clifford Algebras and Quaternions, and a tutorial on Visualizing Quaternions presented at both Siggraph ’99 and Siggraph 2000. Major research interests include scientific visualization, machine vision, computer graphics, perception, and the design of interactive user interfaces for virtual reality and visualization applications. Particular visualization applications currently being studied include an astrophysical treatment of the local galactic neighborhood of the sun, the exploitation of constrained navigation for visualization environments, and applications of graphics in dimensions greater than three to mathematics and theoretical physics.