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Rational BRDF
Nov. 2012 (vol. 18 no. 11)
pp. 1824-1835
R. Pacanowski, Inst. d'Opt. Grad. Sch., Univ. de Bordeaux, Talence, France
Oliver Salazar Celis, Dept. of Math. & Comput. Sci., Univ. of Antwerpen, Antwerp, Belgium
C. Schlick, Inst. d'Opt. Grad. Sch., Univ. de Bordeaux, Talence, France
X. Granier, Inst. d'Opt. Grad. Sch., Univ. de Bordeaux, Talence, France
P. Poulin, Dept. I.R.O., Univ. de Montreal, Montreal, QC, Canada
A. Cuyt, Dept. of Math. & Comput. Sci., Univ. of Antwerpen, Antwerp, Belgium
Over the last two decades, much effort has been devoted to accurately measuring Bidirectional Reflectance Distribution Functions (BRDFs) of real-world materials and to use efficiently the resulting data for rendering. Because of their large size, it is difficult to use directly measured BRDFs for real-time applications, and fitting the most sophisticated analytical BRDF models is still a complex task. In this paper, we introduce Rational BRDF, a general-purpose and efficient representation for arbitrary BRDFs, based on Rational Functions (RFs). Using an adapted parametrization, we demonstrate how Rational BRDFs offer 1) a more compact and efficient representation using low-degree RFs, 2) an accurate fitting of measured materials with guaranteed control of the residual error, and 3) efficient importance sampling by applying the same fitting process to determine the inverse of the Cumulative Distribution Function (CDF) generated from the BRDF for use in Monte-Carlo rendering.
Index Terms:
sampling methods,Monte Carlo methods,rendering (computer graphics),adapted parametrization,rational BRDF,bidirectional reflectance distribution functions,rational functions,Monte-Carlo rendering,CDF,cumulative distribution function,fitting process,importance sampling,residual error,low-degree RF,Monte Carlo methods,Materials,Polynomials,Rendering (computer graphics),Quadratic programming,Mathematical model,Monte-Carlo rendering,BRDF,fitting,importance sampling
Citation:
R. Pacanowski, Oliver Salazar Celis, C. Schlick, X. Granier, P. Poulin, A. Cuyt, "Rational BRDF," IEEE Transactions on Visualization and Computer Graphics, vol. 18, no. 11, pp. 1824-1835, Nov. 2012, doi:10.1109/TVCG.2012.73
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