Bidirectional Reflectance Distribution Function

The bidirectional reflectance distribution function (BRDF) is a function that defines how light from a source is reflected off an opaque surface.

Let $\displaystyle f_r(\omega_i,\omega_r)$ be the BRDF where:

$\omega$ is direction $(\theta,\phi)$

$i$ is irradiance

$r$ is radiance

$\displaystyle f_r(\omega_i,\omega_r) = \frac{\mathrm{d}L(\omega_r)}{\mathrm{d}E(\omega_i)}$

Positivity

$f_r(\omega_i,\omega_r) \geq 0$

Helmholtz reciprocity

$f_r(\omega_i,\omega_r) = f_r(\omega_r,\omega_i)$

Energy conservation

$\displaystyle \forall \omega_i, \int_{\Omega} f_r(\omega_i,\omega_r) \cos \theta_r \mathrm{d} \omega_r \leq 1$

• Computer graphics
• Physically based rendering