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