Modern computer graphics systems are characterized bythe requirements of highly-realistic and highly-productive image formation. In order to increase image formation productivity, the improvement of existing light reflectance models and the development of new models are constantly carried out. In the article the development of a combined light reflectance model based on the cosine-power functions is described. The main aspects of surface bidirectional reflectance distribution functions calculation and usage are analyzed. The features of simple empirical models and theoretical models that take into account microfacetedsurface representation are described. The disadvantages of existing surface reflectance models are discussed. The cosine-power functions of the fourth and sixteenth degreesare discussed. The necessity of the development ofanew surface reflectance model based on two cosine-power functions is justified. The calculation formula of the developed combined surface reflection functionis proposed. The formula oftheconnection point of two cosine-power functions was obtained. The obtained formula was approximated with a simpler formula using Chebyshev polynomials. The plot of cosine-power functions connection point valueswas built. The plot of productivity gain from combined function calculationrelative to the shininess coefficientis given. The average productivity gain value from combined function calculation was found. The plot of relative and absolute errors between the combinedfunction and the Blinn function relative to the shininess surface coefficient is given. The three-dimensional plot of absolute error between the combined function and the Blinn function was built. Using OpenGL shadinglanguage the developed model was implemented in the software application Bidirectional Reflectance Distribution FunctionsExplorer. The teapot visualization results based on the proposed combined function are given.The developed combined model combines the advantages oftwocosine-power functions and can be used in highly-productive three-dimensional computer graphics systems

A method of visualization of surface and volumetric caustics of reflected and refracted light on mirror surfaces in volume and on functionally specified surfaces consisting of patches of free forms is proposed. Caustics are surfaces near which the intensity of the light field increases sharply. The visualization method tracks the rays of light in the light space when displaying mirror surfaces. Light rays are projected from light sources onto patches of free-form scenes. The limiting volumes of caustic rays are determined, thereby reducing the number of calculations. Only caustic rays are calculated, which make the main contribution to the resulting image.