Ray-VR offers the possibility of investigating Non-Euclidean spaces using ray tracing. Our research includes new algorithms to trace (possibly curved) rays in these spaces with non-trivial geometry and topology.

Ray Tracing in 3-Manifolds

We developed an image-space ray-tracing algorithm to generate interior views of 3-manifolds, orbifolds, and similar polyhedral complexes.

Fundamental domain of the mirrored hyperbolic dodecahedron.

Paper: “An image-space algorithm for immersive views in 3-manifolds”

The Thurston’s 8 Geometries

We investigate Thurston’s Geometrization conjecture and propose an immersive visualization of manifolds modeled by Thurston geometries using ray tracing.

Classification Tree of Thurston’s Geometries.