Г I ∆ and B I ∆ correspondingly along horizontal and vertical scanlines are constant values and this eliminates necessity of their computing for every rasterization line. Let’s find out interconnection between growth of color intensities along horizontal and vertical rasterization lines. It’s proved that growth of intensities H I ∆ , V I ∆ and D I ∆ in horizontal, vertical and diagonal directions correspondingly are constants and are equal.

On devices without battery consuming and specialized hardware for rendering, it is important to improve the speed and quality so that these methods are suitable for real-time rendering. Furthermore such algorithms are needed on the coming multicore architectures. We show how the methods by Gouraud and Phong, the commonly most used methods for shading, can be improved and made faster for both software rendering as well as simple low energy consuming hardware implementations. Moreover, this paper summarizes the authors' achievements in increasing shading speed and performance and a Bidirectional Reflectance Distribution Function is simplified for faster computing and hardware implementation.

The purpose of this article is approximation of BRDF with functions of argument cos(x). The described approach proposes usage of two functions for BRDF approximation. One of them is a cubic polynomial (with argument cos(x)) and the second one is the function, that assures monotonous falling of the function. Usage of this approach leads to considerable reduce of the approximation error and increases accuracy of the object's highlights representation.