Real-time rendering in curved spaces

A hypersphere surface provides a finite 3D world in which the user can fly freely without encountering boundaries, while hyperbolic space provides a spacious environment. The algorithm for rendering a scene in a hypersphere is identical to the standard algorithm for rendering a scene in ordinary flat 3D space. Indeed, the computations are so similar that off-the-shelf 3D graphics cards, when fed the correct matrices, will do real-time animations in a hypersphere just as easily and as quickly as they do in flat space.