Visualization of Surfaces in Four-Dimensional Space *

We discuss some issues of displaying ~wo-dimensional surfaces in four-dimensional (4D) space, including the behavior of surface normals under projedion, the silhouette points due to the projection, and methods Cor object orientation and projection center specification. We have implemented an interactive 4D display system on z-butrer based graphics workstations. Preliminary experiments show that such a 4D display system can give valuable insights into high-dimensional geometry. We present some pictures from the examples using high-dimensional geometry, offset curve tracing and collision detection problems, and explain some of the insights they convey.