Phong Reflection Model - Description

Description

Phong reflection is an empirical model of local illumination. It describes the way a surface reflects light as a combination of the diffuse reflection of rough surfaces with the specular reflection of shiny surfaces. It is based on Bui Tuong Phong's informal observation that shiny surfaces have small intense specular highlights, while dull surfaces have large highlights that fall off more gradually. The model also includes an ambient term to account for the small amount of light that is scattered about the entire scene.

For each light source in the scene, components and are defined as the intensities (often as RGB values) of the specular and diffuse components of the light sources respectively. A single term controls the ambient lighting; it is sometimes computed as a sum of contributions from all light sources.

For each material in the scene, the following parameters are defined:

: specular reflection constant, the ratio of reflection of the specular term of incoming light

: diffuse reflection constant, the ratio of reflection of the diffuse term of incoming light (Lambertian reflectance)

: ambient reflection constant, the ratio of reflection of the ambient term present in all points in the scene rendered

: is a shininess constant for this material, which is larger for surfaces that are smoother and more mirror-like. When this constant is large the specular highlight is small.

Furthermore, is defined as the set of all light sources, as the direction vector from the point on the surface toward each light source ( specifies the light source), as the normal at this point on the surface, as the direction that a perfectly reflected ray of light would take from this point on the surface, and as the direction pointing towards the viewer (such as a virtual camera).

Then the Phong reflection model provides an equation for computing the illumination of each surface point :

where the direction vector is calculated as the reflection of on the surface characterized by the surface normal using:

and the hats indicate that the vectors are normalized. The diffuse term is not affected by the viewer direction . The specular term is large only when the viewer direction is aligned with the reflection direction . Their alignment is measured by the power of the cosine of the angle between them. The cosine of the angle between the normalized vectors and is equal to their dot product. When is large, in the case of a nearly mirror-like reflection, the specular highlight will be small, because any viewpoint not aligned with the reflection will have a cosine less than one which rapidly approaches zero when raised to a high power.

Although the above formulation is the common way of presenting the Phong reflection model, each term should only be included if the term's dot product is positive. (Additionally, the specular term should only be included if the dot product of the diffuse term is positive.)

When the color is represented as RGB values, as often is the case in computer graphics, this equation is typically modeled separately for R, G and B intensities, allowing different reflections constants and for the different color channels.