Visualization of Surfaces in Four-Dimensional Space

摘要

Researchers discuss some issues of displaying two-dimensional surfaces in four-dimensional (4D) space, including the behavior of surface normals under projection, the silhouette points due to the projection, and methods for object orientation and projection center specification. An interactive 4D display system on z-buffer based graphics workstations has been implemented. Preliminary experiments show that such a 4D display system can give valuable insights into high-dimensional geometry. Some pictures are presented from the examples using high-dimensional geometry, offset curve tracing, and collision detection problems; some of the insights they convey are explained.