Global illumination of non-Euclidean spaces. (December 2020) - Novello, Tiago; da Silva, Vincius; Velho, Luiz
Highlights: Introduction of Riemannian global illumination. A path tracer algorithm to approximate the solution of the Riemannian global illumination. A map of the algorithm to the GPU, using the RTX platform. We apply the Non-Euclidean path tracer to render "Photorealistic" inside views of the 3D flat torus, Poincaré sphere, and the hyperbolic mirrored dodecahedron. These are examples of the Euclidean, spherical, and hyperbolic spaces: the Thurston classical geometries. Graphical abstract: Abstract: This paper presents a novel path tracer algorithm for immersive visualization of Riemannian manifolds. To do this, we introduce Riemannian illumination, a generalization of classical Computer Graphics illumination models. In this context, global light transport is expressed by extending the rendering equation to Riemannian manifolds. Using Monte Carlo integration to solve this equation results in the novel path tracer for Non-Euclidean spaces. We discuss its basic principles, as well as the general CPU algorithm. Additionally, we discuss in detail how to implement a GPU version, using the RTX pipeline. Finally, we apply the algorithm to render "photorealistic" inside views of the flat torus, Poincaré sphere, and the hyperbolic mirrored dodecahedron. These are examples of Euclidean, spherical, and hyperbolic spaces: the Thurston classical geometries.