Real-Time Visualization in Anisotropic Geometries

We present novel methods for real-time native geodesic rendering of anisotropic geometries ℍ2×ℝ, S2×ℝ, Solv and similar geometries, Nil, twisted ℍ2×ℝ. We also include partial results for the Berger sphere and explain why such real-time rendering of this geometry is difficult. Current approaches are not applicable for rendering complex shapes in these geometries, such as traditional 3D models, because of the computational complexity of ray-based approaches or significant rendering artifacts in older primitive-based approaches. We use tessellations to represent large shapes without numerical precision issues. Our efficient methods for computing the inverse exponential mapping are applicable not only for visualization but for games, physics simulations, and machine learning purposes as well.