Body coherence in curved-space virtual reality games

Virtual-reality simulations of curved space are most effective and most fun when presented as a game (for example, curved-space billiards), so the user not only has something to see in the curved space, but also has something fun to do there. However, such simulations encounter a geometrical problem: they must track the player's hands as well as her head, and in curved space the effects of holonomy would quickly lead to violations of "body coherence". That is, what the player sees with her eyes would disagree with what she feels with her hands. This article presents a solution to the body coherence problem, as well as several other questions that arise in interactive VR simulations in curved space (radians vs. meters, visualization of the projection transformation, native-inhabitant view vs. tourist view, and mental models of curved space).