NEW SURFACE REFLECTANCE MODEL WITH THE COMBINATION OF TWO CUBIC FUNCTIONS USAGE
NOWY MODEL ODBICIA ŚWIATŁA OD POWIERZCHNI WYKORZYSTUJĄCY KOMBINACJĘ DWÓCH FUNKCJI SZEŚCIENNYCH
Romanyuk O. Zavalniuk Y. Pavlov S. Chekhmestruk R. Bondarenko Z. Koval T. Kalizhanova A. Iskakova A.
2023Politechnika Lubelska
Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Srodowiska
2023#13Issue 3101 - 106 pp.
In the article the model of light reflection based on the combination of two cubic bidirectional reflectance distribution functions is developed. The main components of color and the main requirements for reproducing the object`s glares are analyzed. The usage characteristics of Cook-Torrance, Bagher, Oren-Nayar, coupled Shirley reflection models are described. The advantages and disadvantages of the highly productive Blinn-Phong model are considered. The necessity of approximating the Blinn-Phong model by a function of low degree is justified. The characteristics of the cubic polynomial approximation of the Blinn-Phong model are determined. It was established that the main drawback of this approximation is a significant deviation of the function from the reference function in the glare’s attenuation zone. The combined function that combines two cubic functions is proposed. The first cubic function reproduces the glare’s epicenter, and the second replaces the specified function in the attenuation zone. A system of equations for calculating the coefficients of the second function was created. The formula for the connection point of two cubic functions is obtained. A graph of the developed combined model based on cubic functions is obtained. For the combined and original cubic functions a comparison of the maximum relative errors in the glare’s epicenter zone, the maximum absolute errors, and the relative errors at the inflection point was made. A three-dimensional plot of the absolute error of the combined cubic model from the Blinn-Phong model depending on the shininess and the angle value is built. Visualization results based on the combined and the original cubic functions are compared. It is confirmed that the proposed reflection model increases the realism of glare formation in the attenuation zone. The resulting combined reflection model provides a highly accurate approximation of the Blinn-Phong model and is highly efficient because the third power function is used.
bidirectional reflectance distribution function , combined function , cubic function , reflectance model , shading
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Vinnytsia National Technical University, Vinnytsia, Ukraine
3D GENERATION UA, Vinnytsia, Ukraine
Mykhailo Kotsiubynskyi State Pedagogical University, Vinnytsia, Ukraine
University of Power Engineering and Telecommunications, Institute of Information and Computational Technologies MES CS RK, Almaty, Kazakhstan
Kazakh National Research Technical University named after K. I. Satpayev, Almaty, Kazakhstan
Vinnytsia National Technical University
3D GENERATION UA
Mykhailo Kotsiubynskyi State Pedagogical University
University of Power Engineering and Telecommunications
Kazakh National Research Technical University named after K. I. Satpayev
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026