Energy Conservation

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.