… 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, …

… Perelman was able to show that this algorithm terminates and each connected component
of the resulting manifold admits one of the Thurston geometries. In other words, Perelman …

… We give more details of Thurston geometries in Section 2.6. Let … on one of the eight Thurston’s
geometries. Remember that a 3-… geometry is the richest among the Thurston geometries. …

… geometry modeled by Thurston geometries. A manifold N has its geometry modeled by a model
geometry M … polygonal approximation given by the above computation (ie, ray marching). …

… This paper presents an expository account of Sol geometry, … of the building blocks
arising in Thurston’s geometrization. It … by adapting the technique of ray-marching to non-euclidean …

… Thurston geometries in Section 1.4. We explain the word construct in Theorem 2. A 3-manifold
is geometrically modeled by one of Thurston geometries … (ie, ray marching). The …

… with the geometry modeled by Thurston geometries. Remember that a manifold N has its
geometry modeled by a model geometry M … given by the above computation (ie, ray marching). …

… recently in the visualization of Thurston geometries [3, 8, 6]. … (R) geometries: the six more
interesting Thurston geometries. … Ray Marching. To launch a ray we need to solve the geodesic …

… geometries, called the Thurston geometries. Our focus is on the patterns of growth typical
to these geometries. As such, our work is not limited to Thurston geometries, and we focus on …

… spaces such as hyperbolic and elliptic geometries, all Euclid’s … presented in Section 3 lies
in ray marching (as shown in Fig. 2-… Given the polytopes, a single step of ray marching is made …