Evgeny G. Alekseev, Sergey D. Shibaikin
Pages 78–85

The advantages and disadvantages of existing solutions for calculating lighting fixtures (LF) are discussed in the paper. The methods for solving the global illumination problem are demonstrated. The most important illumination models used to calculate LFs have been analyzed. The TorranceSparrow model is used as the primary model of reflective surface. The triangulation method based on approximation of the LF surface by a grid of triangles is used to increase the efficiency of LF design and computation. The optical ray propagation in a 3D optical system was modelled using classical laws of optics and the Monte Carlo method. The structure and the main steps of working with the library for CAD Kompas are described. The approximation of LF surface for different types of light sources and reflector parameters is presented. The implementation of approximations with subsequent ray tracing has demonstrated a good convergence of the problem solution.
More
The results of the study have the potential to be useful for design engineers involved in the design and calculation of LFs, as well as developers of applied software in the field of computer graphics and computeraided design systems. 
1. Ivliev S.N., Mikayeva S.A., Shibaikin S.D. Quality control of the mould on the digital model of the luminous intensity distribution curve // Control. Diagnostics, 2010, #9, pp. 29–33.
More
2. Goral C.M., Torrance K.E., Greenberg D.P., Battaile B. Modelling the Interaction of Light Between Diffuse Surfaces // Computer Graphics, 1984, Vol. 18, # 3, pp. 213–222.
3. Wallace J.R., Cohen M.F., Greenberg D.P. A Twopass Solution to the Rendering Equation: A Synthesis of Ray Tracing and Radiosity Methods // Computer Graphics, 1987, Vol. 21, # 4, pp. 311–320.
4. Budak V., Zheltov V., Notfulin R., Chembaev V. Relation of instant radiosity method with local estimations of Monte Carlo method // Journal of WSCG, 2016, pp. 189–197.
5. Zhdanov D., Ershov S., Shapiro S., Sokolov V., Voloboy A., Galaktionov V., Potemin I. Realistic image synthesis in presence of birefrigent media by backward ray tracing technique // Computational Optics II, 2018, 106940D.
6. Kajiya J. The rendering equation // SIGGRAPH, 1986, Vol. 20, #4, pp. 143–150.
7. Dupuy J., Heitz E., Iehl J., Poulin P., Ostromoukhov V. Extracting Microfacetbased BRDF Parameters from Arbitrary Materials with Power Iterations // Computer Graphics Forum, 2015, Vol. 34, #4, pp. 21–30.
8. Werner S., Velinov Z., Jakob W., Hullin M.B. // Scratch iridescence: Waveoptical rendering of diffractive surface structure. ACM Trans. Graph. (Proc. SIGGRAPH Asia), 2017, Vol. 36, # 6, pp. 220:1–220:11.
9. Shiying L. Estimating Diffuse and Specular Reflectance Parameters from Spectral Images // Doctoral Dissertation / Department of Information Processing Graduate School of Information Science Nara Institute of Science and Technology, 2007, 108p.
10. Torrance K.E., Sparrow E.M. Theory for offspecular reflection from roughened surfaces // Journal of the Optical Society of America, 1967, Vol. 57, #9, pp. 1105–1114.
11. Barla P., Pacanowski R., Vangorp P. A Composite BRDF Model for Hazy Gloss // Computer Graphics Forum, 2018, Vol. 37, #4, pp. 12.
12. Belcour L., Barla P. A Practical Extension to Microfacet Theory for the Modeling of Varying Iridescence // ACM Trans. Graph. (Proc. SIGGRAPH). – 2017. – № 4. – Vol. 36. – p.65:1–65:14.
13. Holzschuch N., Pacanowski R. A twoscale microfacet reflectance model combining reflection and diffraction // ACM Trans. Graph. (Proc. SIGGRAPH), 2017, Vol. 36, #4, pp. 66:1–66:12.
14. Yan L, Hašan M, Marschner S, Ramamoorthi R. Position normal Distributions for Efficient Rendering of Specular Microstructure // ACM Trans. Graph., 2016, Vol. 35, #4, p. 9.
15. Georgoulis S., Vanweddingen V., Proesmans M., Gool L.V. A Gaussian process latent variable model for BRDF inference // IEEE International Conference on Computer Vision (ICCV), 2015, December, pp. 3559–3567.
16. Guarnera D., Guarnera G., Ghosh A., Denk C., Glencross M.: BRDF representation and acquisition // Computer Graphic Forum, 2016, Vol. 35, # 2, pp. 625–650.