Optical system visualization of combined reflectance model based on cubic and quadratic functions

Abstract

In the article the combined reflectance model based on quadratic and cubic polynomials is discussed. The main characteristics of physically accurate Torrance-Sparrow, Löw models and empirical Blinn, Phong, Schlick models are analyzed. The advantages and disadvantages of the cubic and quadratic Blinn-Phong model approximations are explored. The need in the development of new Blinn-Phong model approximation through combining the quadratic and cubic functions is justified. The cubic model is improved in order to improve the accuracy of Blinn-Phong model approximation in the attenuation zone. The formulas of the improved cubic model coefficients are simplified. The precise and approximated formulas for the calculation of connection point between quadratic and cubic functions are obtained. The productivity gain from the replacing the cubic function by the quadratic function in the glare’s epicenter zone is calculated. The absolute and relative errors of Blinn-Phong model approximation by the quadratic, cubic and the proposed model are compared. Through the visualization of the test figures “Teapot” and “Robot” the advantages of the proposed function usage for increasing the realism of glares formation are shown.