Energy conservation is a restriction on the reflection model that requires that the total amount of reflected light cannot be more than the incoming light (0).

$$

\int_{\Omega} f(\vec{x}, \phi, \theta) L_i \cos \theta \,\delta\omega\leq L_i

$$

- f – BRDF(any?)

We have to calculate energy conservation for Diffuse and Specular and than combined model need to fit this:

$$ C_d C_s \leq 1 $$

This means that if you want to make material with more specular, you may have to reduce the diffuse.

Left: A sphere with a high diffuse intensity, and low specular intensity. Right: High specular intensity, low diffuse. Middle: Maximum diffuse AND specular intensity. Note how it looks blown out and too bright for the scene (1)

The upper part of the table shows the normalized *reflection density function* (RDF). This is the probability density that a photon from the incoming direction is reflected to the outgoing direction, and is the BRDF times . Here, is the angle between and , which is, for the assumed view position, also the angle between and , resp. and .

The lower part of the table shows the normalized *normal distribution function* (NDF) for a micro-facet model. This is the probability density that the normal of a micro-facet is oriented towards . It is the same expression in spherical coordinates than that for of the Phong RDF, just over a different variable, , the angle between and . The heightfield distribution does it slightly different, it normalizes the projected area of the micro-facets to the area of the ground plane (adding yet another cosine term). (3)

With and without energy conservation /π (4)

Beware to overdo the result with minimal maximum.