Ray Tracing in Poincare's Ball Model of Hyperbolic Space

realistic
3D scene images, taking into consideration viewing parameters, geometrical description of objects,
lighting, material parameters - anything that affects the final appearance of the scene. Hyperbolic
space
is a geometrical structure that often goes against our intuition. In order to create a tool for
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. This algorithm and the
corresponding programming library (HMathLib) can be applied in teaching and popularization of
mathematics, exploring hyperbolic geometry and in digital art.