The paper reveals a method of highly productive determination of normalized vectors for the surfaces of threedimensional objects. The method is based on the approximated calculation of even vectors of the rasterization line by adding the odd neighboring unit vectors. For the determination of further need in the normalization of obtained vectors, the computation of special threshold metrics is proposed. For the accelerated calculation of the threshold metrics, the developed expressions are given. In case of normalization of even vectors, it is recommended to use the developed polynomial approximate expressions. The plots of relative errors between obtained simplified and reference expressions are given. The possibility of increasing the productivity of the method by calculating the shared vector coordinate increments for each rasterization line is analyzed. The experimental research of productivity gain from the new method usage is carried out. During the study, the six variants of possible method usage are considered. The results of the research analysis are given in the table. The new method is designed for usage in highly effective visualization systems.
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.
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