Characteristics of the Cosine Lobe Model

The Lafortune generalized cosine model posseses many characteristics which are desirable in a BRDF.

Lambertian Behavior

First, it contains the Lambertian model of perfectly diffuse reflectance when the Phong exponent is null.

Generalized Diffuse Behavior

[Cx = Cy = 0, Cz = nth_root((n+2)/(2*pi))]

It is capable of representing more generalized diffuse behavior, whose reflectance decreases exponentially according to the azimuthal angle theta.

In the pictures below, the viewpoint is raised along the z-axis to demonstrate the dependence on theta.

The images below illustrate how the diffuse behavior changes as the exponent is decreased.

Phong

[-Cx = -Cy = Cz = nth_root((n+2)/(2*pi))]

The Lafortune model also subsumes the classical cosine lobe model due to Phong. The images below demonstrate how the Phong model behaves as the exponent increases.

The classical Phong model has several difficulties -- among them, the apparent brightness decreases for glancing angles, exactly the opposite of the effect observed in nature. The images below show this effect as the camera is moved in the direction of increasing z.

Specularity at Grazing Angles

[Cx = Cy > Cz]

The Lafortune model can capture increased specularity at glancing angles. In the images below, the camera is moved in the direction of positive z.

Retro-Reflection

[Cx = Cy > 0]

Furthermore, the Lafortune model can capture retroreflective material properties, such as observed in several highway paints. The images below were taken with the viewpoint at the light, and increasing retro-reflection from left to right.

Anisotropy

[Cx != Cy]

The Lafortune model can capture some types of anisotropy. In the images below Cx >> Cy, the camera is looking down the x axis, and we show that increasing the exponent decreases the spread of the reflection of the light.

In the images below, we are looking down the y axis, and we show the effect of increasing the coeficient Cy.

Bill Martin (wmartin@cs.utah.edu)