[Angel p267-290; Foley p721-741, 760-766]

Illumination Models

local illumination
defines single-light, single-surface interaction

global illumination
models interchange of lights between all surfaces

Local Illumination Models

Traditional graphics LIMs are:

Most such adhoc illumination models have three components: 

 I = ambient + diffuse + specular

The ambient term allows for some global control of brightness in a scene. Typically, 

 I = Ia ka

where Ia is an ambient illumination constant defined once for the entire scene, and ka is an ambient reflection coefficient, usually restricted to lie in [0,1].

Diffuse Reflection 

 


Id = Ii k_diff cos(th), th in [-pi/2, pi/2]
    = Ii k_diff (N.L),   N.L  0 and assuming N and L are          normalized

Ii: intensity of light source i
k_diff: surface reflection coefficient
th: angle between N and L

Phong Specular Reflection

The last component of the commonly-used local illumination model is one that takes into account specular reflections. The following figure illustrates the situation:

The Phong illumination model is one often-used method of calculating the specular component: 

  Is = Ii k_spec cos^n(alpha)
     = Ii K_spec (R.V)^n

where k_spec is a specular reflection coefficient and alpha is the angle between the reflection and viewing vector. The surface parameter 'n' can be thought of as describing the surface roughness, where an ideal mirror would have n=¥ , and a rough surface might have n=1.

How can R be computed?

The function cos^n(alpha) looks as follows:

The Blinn Specular Model

Blinn reformulated the specular reflection model so that it agreed better with experimental results. It makes use of a halfway vector, H, as follows:

Is = Ii k_spec cos^n(alpha)
     = Ii K_spec (N.H)^n

The advantages of this model include:

The Complete Model

Combining the various models and assuming the Phong illumination model gives: 

I = Ia ka + Ii k_diff (N.L) + Ii k_spec (R.V)^n

where each of ka, k_diff, and k_spec are parameters which are associated with specific surfaces and take on values between 0 and 1. To deal with colour, three equations of the above form are typically used: 

I_r = Ia_r ka_r + Ii_r k_diff_r (N.L) + Ii_r k_spec_r (R.V)^n
I_g = Ia_g ka_g + Ii_g k_diff_g (N.L) + Ii_g k_spec_g (R.V)^n
I_b = Ia_b ka_b + Ii_b k_diff_b (N.L) + Ii_b k_spec_b (R.V)^n

Some other problems and their adhoc solutions:

What should be done if I1?
Clamp the value of I to one.
What should be done if N.L < 0?
Clamp the value of I to zero or flip the normal.
How can we handle multiple light sources?
Sum the intensity of the individual contributions.

Shading Algorithms

flat shading
Invoke illumination model (IM) once for the polygon, use this as a colour for the whole polygon
Gouraud shading
Compute IM at the vertices, interpolate these colours across the polygon
Phong shading
Interpolate normals during scan conversion, apply IM at every pixel. (note: renormalization problem)

Problems with shading algorithms

Lighting models in OpenGL

The following are calls which set the parameters of a light: 

  glLightfv(GL_LIGHT0, GL_AMBIENT, amb_light_rgba );
  glLightfv(GL_LIGHT0, GL_DIFFUSE, dif_light_rgba );
  glLightfv(GL_LIGHT0, GL_SPECULAR, spec_light_rgba );
  glLightfv(GL_LIGHT0, GL_POSITION, position);
  glEnable(GL_LIGHT0);

The following calls define the surface properties to be used for all subsequently drawn objects. 

  glMaterialfv( GL_FRONT, GL_AMBIENT, ambient_rgba );
  glMaterialfv( GL_FRONT, GL_DIFFUSE, diffuse_rgba );
  glMaterialfv( GL_FRONT, GL_SPECULAR, specular_rgba );
  glMaterialfv( GL_FRONT, GL_SHININESS, n );

Physics-based Illumination Models

Shadows