Abstract In this work, we propose a novel ray tracing model for immersive visualization of Riemannian manifolds. To do this we introduce Riemannian ray tracing, a generalization of the classic Computer Graphics concept. Specifically, our model is capable of interactive real-time VR visualizations of Nil, Sol, and S L 2 ( R ) ˜ , Thurston’s most nontrivial geometries. These experiences have the potential to allow insights with impact in physics/cosmology research, education, special effects, and games, among other aspects. The Riemannian ray tracing is implemented using the ray-tracing capabilities of the NVidia RTX platform. We discuss the general algorithm in CPU and show how to map the computations to the RTX pipeline.

中文翻译：

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Nil、Sol 和 SL2(R)~ 几何的可视化

摘要 在这项工作中，我们提出了一种新颖的光线追踪模型，用于黎曼流形的沉浸式可视化。为此，我们引入了黎曼光线追踪，这是经典计算机图形学概念的概括。具体来说，我们的模型能够对 Nil、Sol 和 SL 2 ( R ) ˜ 进行交互式实时 VR 可视化，这是 Thurston 最重要的几何图形。这些经验有可能在物理/宇宙学研究、教育、特效和游戏等方面产生影响。黎曼光线追踪是使用 NVidia RTX 平台的光线追踪功能实现的。我们讨论了 CPU 中的通用算法，并展示了如何将计算映射到 RTX 管道。