Ray Tracing in Poincaré's ball model of hyperbolic space

used for creating realistic 3D scene images, taking into consideration viewing parameters,
geometrical description of objects, lighting, material parameters | anything
that aects the nal appearance of the scene. Hyperbolic space is a geometrical
structure that often goes against our intuition. In order to create a tool for the
hyperbolic space visualization, we have developed a hyperbolic version of the Ray
Tracing algorithm which, to the best of our knowledge, did not exist before. The
obtained images, adapted at certain stage to Euclidian plane for displaying purposes,
are visualizations of hyperbolic objects. The developed algorithm, methods
for solving problems during development as well as the nal results will be shown
in our presentation. This algorithm and the corresponding library (HMathLib) can
be applied in teaching and popularization of mathematics, exploring hyperbolic
geometry and in digital art.