  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. We also give extensive practical details for each geometry.
