Interactive visualization methods for four dimensions

Making accurate computer graphics representations of surfaces and volumes (2-manifolds and 3-manifolds) embedded in four-dimensional space typically involves complex and time-consuming computations. In order to make simulated worlds that help develop human intuition about the fourth dimensions, we need techniques that permit real-time, interactive manipulation of the most sophisticated depictions available. We propose the following new methods that bring us significantly closer to this goal: an approach to high-speed 4D illuminated surface rendering incorporating 4D shading and occlusion coding; a procedure for rapidly generating 2D screen images of tessellated 3-manifolds illuminated by 4D light. These methods are orders of magnitude faster than previous approaches, enabling the real-time manipulation of high-resolution 4D images on commercial graphics hardware