Many people confuse Phong shading with Phong illumination. Phong shading simply refers to process of interpolating the normal across a surface for shading on an individual pixel basis. At each pixel, you can do whatever illumination you prefer. Or, you could use Phong illumination at each vertex, and use Gouraud shading across that surface.

Phong illumination was developed by Phong Bui-Tuong in 1975. Phong's model is hard to do in plain text (lack of Greek symbols) so here are the symbols I'll use:

Ix = result color
Lx = light color
Ax = ambient color
Dx = diffuse color
Sx = specular color
Ka = ambient coefficient
Kd = diffuse coefficient
Ks = specular coefficient
Att = attenuation coefficient
n = usually referred to as "shine" or "roughness"
N = surface normal
L = light vector
R = reflection vector
V = view vector

Given those variables, here's the Phong model (modified to account for specular color):

Ix = AxKaDx + AttLx [KdDx(N dot L) + KsSx(R dot V)^n]

And here's what each of the values means:

The first five values are component values. For the RGB model, they represent one component (R, G or B). They are also scalars (0.0 - 1.0). So to solve the equation for RGB, with no simplifications, it would require 3 solutions:

Ir = ArKaDr + AttLr [KdDr(N dot L) + KsSr(R dot V)^n]
Ig = AgKaDg + AttLg [KdDg(N dot L) + KsSg(R dot V)^n]
Ib = AbKaDb + AttLb [KdDb(N dot L) + KsSb(R dot V)^n]

The Ir, Ig, Ib would be your new RGB. If you're dealing with 24-bit RGB, then the resulting RGB would be [(Ir * 255), (Ig * 255), (Ib * 255)]. Lx (Lr, Lg, Lb) refer to the color of the light source. Ax is the color of the ambient light, Dx would be the color of the surface (typically found in the material), and Sx would be the color of the specular highlight (also found in the material.)

The next three values (the coefficients) are also scalars (0.0 - 1.0) and are typically stored in the material as part of the surface material definition. The first, ambient coefficient (Ka), is used to determine how much ambient light affects a surface. The diffuse coefficient (Kd) specifies how much of the diffuse light (incident light from the light source) affects the object. The specular coefficient (Ks) specifies how bright the specular reflection is. To help explain how these values work together, consider the following example. A white sphere with the world ambient color set to 1.0 (full intensity) given a Ka of 0.2, a Kd of 0.0 and a Ks of 1.0 would yield a circle that is very dark gray with a bright white spot for the specular reflection. The sphere would appear to be a circle because it would have no shading (Kd is 0.0) but only ambient (Ka is 0.2).

The attenuation coefficient is used for atmospheric attenuation (depth cueing). Since the Phong model is a lighting model, then this refers to the attenuation of the light to the object. You may apply a secondary attenuation to the result of the Phong equation to account for atmospheric attenuation from the object to the viewer.

The shine (or some refer to it as "roughness") is used to determine the size of the specular reflection (consider a bowling ball vs a billiard ball.) The larger the value, the smaller the specular reflection. This value is usually chosen by experimentation. To get a good idea, try experimenting with 3.0, 200.0 and 10000.0.

The surface normal (N) is just that. For Phong shading, N is interpolated across the surface. Then, at each pixel, it is normalized and used in the Phong illumination equation. The light vector (L) is the vector from the point on the surface to the light. The reflection vector (R) represents the light vector reflected across the surface normal. R is calculated by:

2N (N dot L) - L

The view vector (V) is the vector from the point on the surface to the viewer.

The information from this document can be obtained from:

"Computer Graphics Principles and Practice, 2nd edition" by Foley, van Dam, Feiner, Hughes

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Date this article was posted to GameDev.net: 8/23/1999
(Note that this date does not necessarily correspond to the date the article was written)

See Also:
Lighting and Shading

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