Design and visualization of Riemannian metrics

Local and global illumination were recently defined in Riemannian manifolds to visualize classical Non-Euclidean spaces. This work focuses on Riemannian metric construction in ${\mathbb{R}}^3$ to explore special effects like warping, mirages, and deformations. We investigate the possibility of using graphs of functions and diffeomorphism to produce such effects. For these, their Riemannian metrics and geodesics derivations are provided, and ways of accumulating such metrics. We visualize, in “real-time”, the resulting Riemannian manifolds using a ray tracing implemented on top of Nvidia RTX GPUs.