CSC418 - Notes
Topic 7: Illumination

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Key concepts & Readings

OpenGL

The following call enables/disables lighting:

  glEnable(GL_LIGHTING);
  glDisable(GL_LIGHTING);

OpenGL allows for atleast eight light sources in a scene (and possibly more depending upon the implementation). The lights are: GL_LIGHT0,...,GL_LIGHT7. The following call enables/disables a light in OpenGL:

  glEnable(GL_LIGHT0);
  glDisable(GL_LIGHT0);

OpenGL supports point lights, spot lights, and directional lights.

  /* point light */
  GLfloat light_position[] = { 1.0, 1.0, 1.0, 1.0 };
  glLightfv(GL_LIGHT0, GL_POSITION, light_position); /* GL_LIGHT0 is a point light */
  
  /* directional light. w parameter of light_position is 0, 
     so light_position represents a direction */
  GLfloat light_position[] = { 1.0, 1.0, 1.0, 0.0 }; 
  glLightfv(GL_LIGHT0, GL_POSITION, light_position); /* GL_LIGHT0 is a directional light */

  /* spot light */
  GLfloat light_position[] = { 1.0, 1.0, 1.0, 1.0 }; 
  glLightfv(GL_LIGHT0, GL_POSITION, light_position); /* set the position of GL_LIGHT0 */
  GLfloat spot_direction[] = { -1.0, -1.0, 0.0 }; /* direction is specified in homogenous coordinates */
  glLightfv(GL_LIGHT0, GL_SPOT_DIRECTION, spot_direction); /* set the direction of GL_LIGHT0 */
  glLightf(GL_LIGHT0, GL_SPOT_CUTOFF, 45.0); /* set the cutoff angle */

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 );
  glLightf(GL_LIGHT0, GL_CONSTANT_ATTENUATION, 2.0);
  glLightf(GL_LIGHT0, GL_LINEAR_ATTENUATION, 1.0);
  glLightf(GL_LIGHT0, GL_QUADRATIC_ATTENUATION, 0.5);
  glLightf(GL_LIGHT1, GL_SPOT_EXPONENT, 2.0);

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 );

The position and directions of light are affected by the modelview matrix and stored in eye coordinates.

OpenGL supports smooth and gouraud shading model:

  glShadeModel (GL_FLAT); /* flat shading */
  glShadeModel (GL_SMOOTH); /* gouraud shading */    

Notes

Light Sources

Point Light

Direction Light

Spot Light


Spot Light

Area Light

(to be written)

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 ad-hoc 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: 

I_s = I_i k_spec cos^n(alpha)
    = I_i 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:

I_s = I_i k_spec cos^n(alpha)
     = I_i 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 = I_a k_a + I_i k_diff (N.L) + I_i k_spec (R.V)^n

where each of k_a, 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 = I_a_r k_a_r + I_i_r k_diff_r (N.L) + I_i_r k_spec_r (R.V)^n

 I = I_a_g k_a_g + I_i_g k_diff_g (N.L) + I_i_g k_spec_g (R.V)^n

 I = I_a_b k_a_b + I_i_b k_diff_b (N.L) + I_i_b k_spec_b (R.V)^n

Some other problems and their adhoc solutions:

What should be done if I > 1?
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

Physics-based Illumination Models

Shadows

Global Illumination


Definitions

flux
energy per unit time (W)
radiosity, B
exiting flux density (W/m^2)
E
exiting flux density for lightt sources
reflectivity, R
fraction of incoming light which is reflected (unitless)
form factor, Fij
fraction of energy leaving Ai and arriving at Aj,
determined by geometry of polygons i and j

Energy balance

Matrix form of radiosity system

Problems

Partial Solutions

Exercises

Exercise 1

For the following scene, sketch the graphs of the ambient, diffuse, specular, and total illumination seen by the eye. Your graphs should sketch I as a function of x. Use the Phong illumination model, given by:

I = K_a I_a + K_d (N.L) + K_s I_s (R.V)^n

and the following parameter values:

I_a = 0.2, I_d = 1.0, I_s = 1.0, K_a = 0.3, K_d = 0.6, K_s = 0.5, and n = 100.

Exercise 2

Light a triangle using the Phong Illumination model

What’s the intensity at the centroid of the triangle, P = (0.333,1,1)' assuming a white object (r,g,b)=(1,1,1).

Exercise 3

Briefly describe the limitations of the Blinn and Phong illumination models.