Computer Graphics beyond the Third Dimension: Geometry, Orientation Control, and Rendering for Graphics in Dimensions Greater than Three Course Notes for SIGGRAPH ’98 Course Organizer

This tutorial provides an intuitive connection between many standard 3D geometric concepts used in computer graphics and their higher-dimensional counterparts. We begin by answering frequently asked geometric questions whose resolution, though obvious in hindsight, may be obscure to those who have never ventured beyond the third dimension. We then develop methods for describing, transforming, interacting with, and displaying geometry in arbitrary dimensions. We discuss several examples directly relevant to ordinary 3D graphics, including the treatment of quaternion frames as 4D geometric objects, and the application of generalized lighting models to 4D representations of 3D volumetric density data. 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, programming languages, 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. He has published a variety of technical articles on machine vision, computer graphics, and visualization methods. He has also contributed three articles to the Graphics Gems series dealing with user interfaces for rotations and with techniques of N-dimensional geometry. His current research interests include scientific visualization (with applications in mathematics and physics), machine vision, computer graphics, perception, and the design of interactive user interfaces for virtual reality and visualization applications.