Show pageBacklinksBack to top This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong. ~~NOTOC~~ ====== Bidirectional Reflectance Distribution Function ====== The **bidirectional reflectance distribution function (BRDF)** is a function that defines how <color #fff200>light</color> from a source is reflected off an opaque surface. ==== Notation ==== Let <color #ff7f27>$\displaystyle f_r(\omega_i,\omega_r)$</color> be the BRDF where: <color #00a2e8>$\omega$</color> is direction <color #00a2e8>$(\theta,\phi)$</color> <color #00a2e8>$i$</color> is irradiance <color #00a2e8>$r$</color> is radiance <color #ff7f27>$\displaystyle f_r(\omega_i,\omega_r) = \frac{\mathrm{d}L(\omega_r)}{\mathrm{d}E(\omega_i)}$</color> ==== Properties of physically based BRDFs ==== __Positivity__ <color #ffc90e>$f_r(\omega_i,\omega_r) \geq 0$</color> __Helmholtz reciprocity__ <color #ffc90e>$f_r(\omega_i,\omega_r) = f_r(\omega_r,\omega_i)$</color> __Energy conservation__ <color #ffc90e>$\displaystyle \forall \omega_i, \int_{\Omega} f_r(\omega_i,\omega_r) \cos \theta_r \mathrm{d} \omega_r \leq 1$</color> ==== See also ==== * [[article:computer_graphics|Computer graphics]] * [[article:pbr|Physically based rendering]]