DEVELOPMENT OF A MODEL OF REFLECTIVE SURFACE CAPACITY USING CHEBYSHEV POLYNOMES

Abstract

At this stage of computer graphics development, an important task is to ensure high productivity of graphic scenes, sufficient for real-time and interactive mode, when it is assumed that the trajectories of objects are not set in advance, but determined by user actions in interaction with the system. For such modes there are strict requirements for the time of formation of three-dimensional graphic scenes. In the formation of three-dimensional images for the optical properties of the surface is responsible for the two-beam distributive function of reflectivity (DFVZ). It is a model of illumination and determines what proportion of the radiation received at a point from the direction of the light source will be reflected in the direction of the observer. A fundamental requirement for DFVZ is its calculation through the cosine of the angle between the corresponding vectors of normals, which is easy to find through the scalar product of vectors. When developing the model, it is important that the image of the reflection relative to the reference implementation has no visual differences. Simple hardware implementation of the function is possible when using low-degree polynomials, provided that the calculation does not use complex functions and long-term operations that take place for known approaches. When forming glare, it is important to reproduce its epicenter with sufficient accuracy. For peripheral areas, which characterize the attenuation of light intensity to a minimum value, it is necessary to ensure the monotony of color intensity change, which eliminates the appearance of artifacts. The paper develops a new model of surface reflectivity using Chebyshev polynomials, which has a second degree and a simple hardware implementation and satisfies the above requirements. Formulas for calculating the component coefficients are obtained. The developed model reproduces the epicenter of the glare with high accuracy. Estimates of the accuracy of the approximation are obtained. The structural scheme of the device for formation of a two-beam distributive function of reflectivity is developed. The developed model of surface reflectivity can be used in systems of dynamic three-dimensional graphics.