# 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.