Bidirectional reflectance distribution function

The bidirectional reflectance distribution function (BRDF; ${\displaystyle f_{\text{r}}(\omega _{\text{i}},\,\omega _{\text{r}})}$ ) is a function of four real variables that defines how light is reflected at an opaque surface. It is employed both in the optics of real-world light, in computer graphics algorithms, and in computer vision algorithms. The function takes an incoming light direction, ${\displaystyle \omega _{\text{i}}}$, and outgoing direction, ${\displaystyle \omega _{\text{r}}}$ (taken in a coordinate system where the surface normal ${\displaystyle \mathbf {n} }$ lies along the z-axis), and returns the ratio of reflected radiance exiting along ${\displaystyle \omega _{\text{r}}}$ to the irradiance incident on the surface from direction ${\displaystyle \omega _{\text{i}}}$. Each direction ${\displaystyle \omega }$ is itself parameterized by azimuth angle ${\displaystyle \phi }$ and zenith angle ${\displaystyle \theta }$, therefore the BRDF as a whole is a function of 4 variables. The BRDF has units sr⁻¹, with steradians (sr) being a unit of solid angle.

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