Some techniques for visualizing surfaces in four-dimensional space

Abstract The issues of visualizing two-dimensional surfaces in four-dimensional space are discussed, including methods to specify the orientation of objects and of projection centres, to determine silhouette points of a 2-surface with respect to projections and to calculate the normal of a projected 2-surface from its normal plane in 4-space. We have implemented an interactive 4D display system on a z-buffer graphics workstation. Preliminary experiments show that such a 4D display system can give valuable insights into high-dimensional geometry. Some examples are presented illustrating nonuniform material property display, offset curve geometry and collision detection.