Previous virtual-reality simulations of curved space, which typically present honeycombs or other periodic structures, have proven effective in letting mathematicians experience curved space directly. By contrast, for students and other non-mathematicians, a game like Non-Euclidean Billiards is more effective because it gives students not just something to see, but also something to do in the curved space. 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. This is, what the player sees with her eyes would disagree with what she feels with her hands. The present article presents a solution to the body coherence problem, as well as several other questions that arise in interactive VR simulations in curved space.

中文翻译：

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弯曲空间的虚拟现实模拟

先前对弯曲空间的虚拟现实模拟（通常呈现蜂窝状或其他周期性结构）已被证明可以有效地让数学家直接体验弯曲空间。相比之下，对于学生和其他非数学家来说，像 Non-Euclidean Billiards 这样的游戏更有效，因为它不仅能让学生看到一些东西，还能让他们在弯曲的空间里做一些事情。然而，这样的模拟遇到了一个几何问题：他们必须跟踪玩家的手和她的头，而在弯曲的空间中，整体性的影响会很快导致身体连贯性的违反。也就是说，玩家用她的眼睛看到的与她用手的感觉不一致。本文提出了解决身体连贯性问题的方法，