ENERGETICALLY CORRECT REFLECTANCE MODEL BASED ON THE CALCULATION OF THE ANGLE BETWEEN VECTORS

Abstract

Computer graphics allows to significantly increase the bandwidth of the information channel, through which two-way communication between the user and the computer is created, and therefore the value of graphical presentation of calculation results in industry and research practice is increasing. While creating the three-dimensional graphic images, a great attention is paid to realism, which makes it possible to adequately display objects and processes. During the formation of such images it is important to realistically reproduce colors, the gradation of which creates the effect of volume. During the reproduction the specular component of color the bidirectional reflectance distribution function is used, which shows how much light is reflected from the surface to the observer. The most common are the Blinn and Fong models. Unfortunately, these models do not comply with the law of conservation of energy, which certainly affects the realism of the formation of graphic scenes. The work provides a detailed analysis of the most widespread reflectance models. As a base for the modification, the distribution function is chosen, which uses an angle between the median vector and the normal vector. The article describes the search of the normalized coefficient formula for the reflectance model based on the calculation of the angle between the vectors that approximates the Blinn-Fong model. The features of the approximated model are analyzed. The initial data for finding the normalizing coefficient formula on the selected intervals were calculated. Using the Python gplearn library, a program for selecting the normalizing coefficient formula has been developed. The parameters of the genetic algorithm for selecting formulas have been adjusted. The approximation accuracy of the training set is calculated. A table of absolute errors of the hemispherical integral reflectivity is given. The resulting surface reflectance model can be used in highly realistic computer graphics systems to create three-dimensional scenes.