NEW SURFACE REFLECTANCE MODEL WITH THE COMBINATIONOF TWO CUBIC FUNCTIONS USAG

Abstract

In the article themodel of light reflection based on the combination of two cubicbidirectional reflectancedistribution functions is developed.The main components of color and the main requirements for reproducing the object`s glaresareanalyzed. The usage characteristicsof Cook-Torrance, Bagher, Oren-Nayar, coupled Shirley reflection models are described. The advantages and disadvantages of the highly productive Blinn-Phong modelare 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 deviationof the function from the reference function in the glare’sattenuation zone. Thecombined 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 equationsfor calculating the coefficients of the second function was created. The formula for the connectionpointof two cubic functions is obtained. A graphof 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’sepicenterzone, 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 modeldepending on the shininessand the angle value is built. Visualization results based on the combined and the original cubic functionsare compared. It is confirmed that the proposed reflection model increases the realismof glare formation in the attenuation zone. The resulting combined reflection model provides a highlyaccurate approximation of the Blinn-Phong model and is highly efficient because the third power function is used