General illumination model

An illumination model gives the intensity of light seen at a surface point. The general model for a surface point includes the local contributions (ambient, diffuse, specular from every light source) and the effects of light from other objects (reflection and transparency).

Local illumination (Phong model with multiple sources and attenuation)

I_local = ka·Ia + Σ_l f(d_l) · IL_l · [ kd (N·L_l) + ks (N·H_l)^n ]

• ka·Ia: ambient term; kd (N·L): diffuse; ks (N·H)^n: specular
• f(d) = min(1/(a0 + a1d + a2d²), 1): distance attenuation
• IL_l: intensity of light source l; n: shininess exponent

Global effects. For shiny and transparent objects, the intensity includes light arriving from the reflected and refracted directions:

I = I_local + kr · I_reflected + kt · I_transmitted

• kr = reflection coefficient, I_reflected = intensity coming from the mirror direction R
• kt = transmission (transparency) coefficient, I_transmitted = intensity coming through the object This is evaluated recursively in ray tracing.

Factors used in the model

1. Light source properties: type, position, intensity, colour, direction (spotlight).
2. Surface properties: colour, reflection coefficients (ka, kd, ks), shininess, transparency, texture.
3. Geometry: normal N, light vector L, view vector V, reflection vector R.
4. Distance of the light source.

 Light --> L      N
        \    |    / R
         \   |   /
          \  |  /   --> V (eye)
  ----------------

The model is used with a surface-rendering method (flat, Gouraud, Phong) to produce the pixel colours. Colour images use the model separately for the R, G and B components.