We describe methods for displaying complex, texturemapped environments with four or more spatial dimensions that allow for real-time interaction. At any one moment in time, a three-dimensional 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 3-D cross section. A variety of interfaces can be used to control position and orientation in 4-D, including a mouse “freelook” interface for use with a computer monitor display, and an interface that uses a head-tracking system with three degrees of freedom 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 2-D or 3-D texture mapping. A computer graphic engine that displays 4-D virtual environments interactively uses these methods, as does a level editor and modeling program that can be used to create 4-D environments.