# 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:

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

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

Where:

- \(\phi_E\) 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.