The bidirectional reflectance distribution function (BRDF; f r ( ω i , ω r ) {\displaystyle f_{\text{r}}(\omega _{\text{i}},\,\omega _{\text{r}})} ) is a function of four real variables that defines how light is reflected at an opaque surface. It is employed in the optics of real-world light, in computer graphics algorithms, and in computer vision algorithms. The function takes an incoming light direction, ω i {\displaystyle \omega _{\text{i}}} , and outgoing direction, ω r {\displaystyle \omega _{\text{r}}} (taken in a coordinate system where the surface normal n {\displaystyle \mathbf {n} } lies along the z-axis), and returns the ratio of reflected radiance exiting along ω r {\displaystyle \omega _{\text{r}}} to the irradiance incident on the surface from direction ω i {\displaystyle \omega _{\text{i}}} . Each direction ω {\displaystyle \omega } is itself parameterized by azimuth angle ϕ {\displaystyle \phi } and zenith angle reference
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