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One of the most critical problems of realistic visualization of the real-world objects is physically adequate modeling of their reflection of light. Reflection of light by objects occurs both from the surface and the bulk of matter (scattering). Accounting for the light reflection from the surface of objects was solved almost a century ago based on its representation as a Fresnel randomly rough surface. Scattering by a bulk of matter is the subject of radiation transfer theory, which has only recently received its known completion in the form of discrete transfer theory. Strict analytical methods for solving the radiation transport equation (RTE) are often not highly effective for calculating the radiance factor. For a long time, in the absence of effective numerical methods for solving problems and the unavailability of high-speed computers for practical calculations, approximate methods for solving RTE were developed. However, their accuracy and applicability limits were poorly defined. The discrete transfer theory allowed us to evaluate the existing approximate methods for solving the UPI, their accuracy, and the efficiency of application for calculating the radiance factor. It is shown that the most effective method is the method of synthetic iterations. The method is based on the selection of the solution anisotropic part based on a small-angle approximation of the RTE solution. The solution regular part can be calculated by any approximation. Then a simple iteration from the complete solution is performed to refine the angular distribution of the radiance factor.

Methods Calculating the Slab Radiance Factor