exist to predict the distribution of microfacets. Most assume that the microfacet normals are distributed evenly around the normal; these models are called isotropic. If microfacets are distributed with a preference for a certain direction along the surface, the distribution is anisotropic. NOTE: In most equations, when it says it means Phong distribution In the Phong reflection model, the intensity of the specular highlight is calculated as: Where R is the mirror reflection of the light vector off the surface, and V is the viewpoint vector. In the Blinn–Phong shading model, the intensity of a specular highlight is calculated as: Where N is the smooth surface normal and H is the half-angle direction (the direction vector midway between L, the vector to the light, and V, the viewpoint vector). The number n is called the Phong exponent, and is a user-chosen value that controls the apparent smoothness of the surface. These equations imply that the distribution of microfacet normals is an approximately Gaussian distribution (for large ), or approximately Pearson type II distribution, of the corresponding angle. While this is a useful heuristic and produces believable results, it is not a physically based model. Another similar formula, but only calculated differently: where R is an eye reflection vector, E is an eye vector (view vector), N is surface normal vector. All vectors are normalized (). L is a light vector. For example, then: Approximate formula is this: If vector H is normalized then Gaussian distribution A slightly better model of microfacet distribution can be created using a Gaussian distribution. The usual function calculates specular highlight intensity as: where m is a constant between 0 and 1 that controls the apparent smoothness of the surface. Beckmann distribution A physically based model of microfacet distribution is the Beckmann distribution: where m is the rms slope of the surface microfacets (the roughness of the material). Compared to the empirical models above, this function "gives the absolute magnitude of the reflectance without introducing arbitrary constants; the disadvantage is that it requires more computation". However, this model can be simplified since . Also note that the product of and a surface distribution function is normalized over the half-sphere which is obeyed by this function. Heidrich–Seidel anisotropic distribution The Heidrich–Seidel. distribution is a simple anisotropic distribution, based on the Phong model. It can be used to model surfaces that have small parallel grooves or fibers, such