NEW SURFACE REFLECTANCE MODEL WITH THE COMBINATION OF TWO CUBIC FUNCTIONS USAGE
Oleksandr Romanyuk
rom8591@gmail.comVinnytsia National Technical University (Ukraine)
http://orcid.org/0000-0002-2245-3364
Yevhen Zavalniuk
Vinnytsia National Technical University (Ukraine)
http://orcid.org/0009-0005-1202-4653
Sergii Pavlov
Vinnytsia National Technical University (Ukraine)
http://orcid.org/0000-0002-0051-5560
Roman Chekhmestruk
3D GENERATION UA (Ukraine)
http://orcid.org/0000-0002-5362-8796
Zlata Bondarenko
Vinnytsia National Technical University (Ukraine)
http://orcid.org/0000-0003-3339-0570
Tetiana Koval
Mykhailo Kotsiubynskyi State Pedagogical University (Ukraine)
http://orcid.org/0000-0002-3190-1181
Aliya Kalizhanova
University of Power Engineering and Telecommunications; Institute of Information and Computational Technologies MES CS RK (Kazakhstan)
http://orcid.org/0000-0002-5979-9756
Aigul Iskakova
Kazakh National Research Technical University named after K. I. Satpayev (Kazakhstan)
http://orcid.org/0000-0001-8043-819X
Abstract
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.
Keywords:
bidirectional reflectance distribution function, cubic function, reflectance model, shading, combined functionReferences
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Authors
Oleksandr Romanyukrom8591@gmail.com
Vinnytsia National Technical University Ukraine
http://orcid.org/0000-0002-2245-3364
Authors
Yevhen ZavalniukVinnytsia National Technical University Ukraine
http://orcid.org/0009-0005-1202-4653
Authors
Sergii PavlovVinnytsia National Technical University Ukraine
http://orcid.org/0000-0002-0051-5560
Authors
Zlata BondarenkoVinnytsia National Technical University Ukraine
http://orcid.org/0000-0003-3339-0570
Authors
Tetiana KovalMykhailo Kotsiubynskyi State Pedagogical University Ukraine
http://orcid.org/0000-0002-3190-1181
Authors
Aliya KalizhanovaUniversity of Power Engineering and Telecommunications; Institute of Information and Computational Technologies MES CS RK Kazakhstan
http://orcid.org/0000-0002-5979-9756
Authors
Aigul IskakovaKazakh National Research Technical University named after K. I. Satpayev Kazakhstan
http://orcid.org/0000-0001-8043-819X
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