Ray-Marching Thurston Geometries

We describe algorithms that produce accurate real-time interactive in-space views of the eight Thurston geometries using ray-marching. give a theoretical framework for our algorithms, independent geometry involved. In addition to scenes within X, we also consider quotient manifolds and orbifolds X/Γ. adapt Phong lighting model non-euclidean geometries. The most difficult part this is calculation light intensity, which relates area density geodesic spheres. extensive practical details each geometry.