Сферично-кутова інтерполяція векторів на основі квадратичних поліномів

Abstract

In the article, it is proposed new quadratic expressions to increase the productivity of calculating intermediate vectors of a rasterization line based on parallel spherical-angular interpolation. The key features of using normal vectors, light incidence, and light reflection vectors to form highly realistic three-dimensional images are analyzed. The need for high-performance vector calculation for faster image formation is substantiated. The shortcomings of existing methods of linear interpolation of vectors, spherical-linear interpolation of vectors, and spherical-angular interpolation of vectors are analyzed. The advantages of the iterative spherical-angular interpolation method of vectors are considered, as well as the prospects for parallel application of this method. The increase in the computational complexity of the coefficients of the expression of parallel spherical-angular interpolation of vectors at each subsequent point is investigated. The feasibility of developing simplified coefficient expressions to increase the productivity of parallel spherical-angular interpolation of vectors is substantiated. Simplified coefficient quadratic polynomials are developed by using polynomial regression. The performance of applying the developed expressions and the original full expressions is compared. Depending on the rasterization line point number, the combined use of these expressions is proposed. Additionally, the performance of the combined use of full and simplified expressions for parallel vector interpolation and traditional non-parallel vector interpolation methods is compared. The performance gain from the use of new expressions is calculated. The deviation of the lengths of vectors calculated on the basis of simplified quadratic coefficients from the unit length is analyzed. Visualized examples of the calculated intermediate vectors of the rasterization line are provided. An image of a test figure is formed in the Idx3d 3D rendering software based on the use of the proposed expressions. The proposed coefficient quadratic expressions provide high-performance formation of realistic images in rendering systems operating in real time.