Physical Reflection Models

Blinn-Phong is a cheap calculation of lighting but it is not an accurate model of how light physically distributes itself. We need to use electromagnetic theory to get even more realistic.

A bidirectional reflectance distribution function (BRDF) is a function which takes:

  • as input: A direction \(\vec{L}\) to a light source
  • as input: A reflection direction \(\vec{R}\)
  • as output: the amount of incident light from the direction \(\vec{L}\) reflected in the \(\vec{R}\) direction
Flux density

The power emitted by a light source or received by a surface per unit area, measured in watts per square meter, \(\frac{W}{m^2}\).

Radiosity is the flux density emitted by a surface.

Irradiance of a light is the flux density incident on a surface.

The power emitted by the light source differs from teh power received by a surface due to the Lambertian effect, and it is modeled like so:

\[ \phi_I = \frac{P}{A} \ = \phi_E \left( \vec{N} \cdot \vec{L} \right) \]

\[ \phi_E = \phi_I \frac{1}{\left( \vec{N} \cdot \vec{L} \right)} = \frac{P}{A \left( \vec{N} \cdot \vec{L} \right)} \]


  • \(\phi_E\) is the light emitted by a light source
  • \(\phi_I\) is the light incident on a surface
  • \(P\) is the watts of power emitted by the light source.
  • \(A\) is area of the surface receiving the light
  • \(\vec{N}\) is the surface normal
  • \(\vec{L}\) is the unit vector pointing toward the light source.