Visualization of Nil, Sol, and SL_2(R) geometries

摘要

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(R))over tilde, 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. (C) 2020 Elsevier Ltd. All rights reserved.