Parabolic Sphere Tracing of Signed Distance Fields for Old Glass Modelling and Rendering

We present a method for modeling and rendering irregular and heterogeneous glass objects, with a specific emphasis on stained glass windows and window works often encountered in architecture from middle age to 18th century. The artisanal production of sheet glass results in glass panels displaying a vast variety of surface and volume irregularities like bubbles, irregular surface or smoothly varying refractive index, all of which contribute to the specific visual aspect of old glass. We propose to account for all the aforementioned effects in a unified framework based on signed distance functions and an analytic solution of the ray tracing equations on tetrahedral volume elements. We demonstrate how to construct an unbiased estimator for the transmitted lighting produced by such panels by using Fermat's principle and results from seismic ray theory. We use texture coordinates to map arbitrary sections of a complex glass panel onto the individual faces of a mesh, allowing the modeling and rendering of complex 3-dimensional objects composed of colored glass facets such as stained glass windows.