Visualization of Nil, Sol, and SL2 Geometries

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 SL2, 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.