Virtual Environments with Four or More Spatial Dimensions

We describe methods for displaying complex, texture-mapped environments with four or more spatial dimensions that allow for realtime interaction. At any one moment in time, a threedimensional (3D) cross-section of the high-dimensional environment is rendered using techniques that have been implemented in OpenGL. The position and orientation of the user within the environment determine the 3D cross-section. A variety of interfaces can be used to control position and orientation in 4D, including a mouse freelook interface for use with a computer monitor display, and an interface which uses a three degree-of-freedom head-tracking system and pinch gloves in combination with a head-mounted display. The methods avoid the use of projections that require depth buffering in greater than three dimensions and can be used in conjunction with either 2D or 3D texture mapping. A computer graphic engine that displays 4D virtual environments interactively uses these methods, as does a level editor and modeling program that can be used to create 4D environments. D’Zmura, Colantoni and Seyranian 3