Light and Color

• I am mixing Angel, fifth edition with the RedBook
  • Angel has more theory
• For computer graphics, we would like to simulate the light in the real world.
• However, this is probably too complex for simple computation.
• So we use a simplified model.
• In general we will compute three values for light at each pixel
  • R,G,B
  • This is based on
    • surface properties
    • properties of the lights in the scene
    • The relative positions of the eye, light and surface.
• Light is composed of three components for each color (RGB)
  • The ambient light is the background light.
  • The diffuse light is light reflected from each light without regard to the direction to the viewer.
    • Based on the surface normal and the angle to the light source
    • The light gradually fades as the surface "turns away" from the light.
  • The secular light is light that is reflected from each light with respect to the angle of the surface to the viewer and the light
    • Based on the surface normal, the angle to the light source and the angle to the viewer.
    • Really tight shiny reflections.
• Ambient light
  • I_a = (I_r, I_g< I_b)
  • This is one of the big cheats, there is no ambient light.
  • It is constant throughout the scene.
  • Too much and it will wash out everything.
  • Too little and many details are hidden.
  • This could be a preset constant.
  • Or it could be derived based on each light source.
  • Or a combination.
  • But it should be a low
  • In the book they call this
  • Generally specified between 0 and 1.
• Two shaders that accomplish this

  #version 120
  
  attribute vec4 vColor;
  attribute float vSize;
  attribute vec4 vPosition;
  
  uniform mat4 projectionM = mat4(1.0);
  uniform mat4 cameraM = mat4(1.0);
  uniform mat4 worldM = mat4(1.0);
  uniform mat4 modelM = mat4(1.0);
  uniform mat4 objectM = mat4(1.0);
  
  varying vec4   color;
  
  uniform float time = 1;
  
  void main() {
  
      gl_Position = projectionM * cameraM * worldM
                         * modelM * objectM *  vPosition;
      color = vec4(vColor.rgb, 1.0);
  
      return;
  }
  
  
  #version 120
  
  varying vec4 color;
  
  uniform float Ambient;
  
  
  void main()  {
  
      gl_FragColor = min(color, vec4(1.0));
  }
      

• I modified my code

  •     ShaderInfo shaders [] = {
            { GL_VERTEX_SHADER, "vertex.glsl"},
            { GL_FRAGMENT_SHADER, "fragment.glsl"},
            { GL_NONE, NULL}
        };
    
        switch (shaderScheme_G) {
           case 1:
               shaders[0].filename = "vertexA.glsl";
               shaders[1].filename = "fragmentA.glsl";
               break;
        }
    	 

  • shaderScheme_G is based on argv[1] and is set in main.
  • 'b' and 'B' change the value of ambient.
  • OffObject now calls glPolygonMode(GL_FRONT_AND_BACK, GL_FILL);
• The RedBook uses a vec4 for ambient, with r,g and b components.
• About lights
  • We classify lights as a point light source.
  • They normally have a set of standard properties
    • A location, usually in world coordinates, but this will need to be transformed to viewing coordinates for our computations.
    • A red, green and blue component L_i = (L_r, L_g, L_b)
    • Or even L_{{r,g,b}{a,d,s}}
    • Or even L_a for short.
  • Light fades or attenuates with distance.
    • The light at a point should be modified
    • Let d = distance between the point and the light source.
    • L' = L/d²
    • L' = L/ (a + bd + cd²)
      • L is the original intensity
      • d is a distance computation.
      • a, b, and c are constants associated with each light.
      • They allow better control of the light.
  • Lights might be a spotlight
    • Non-spotlight lights are called directional
    • This is modeled by a vector (direction of light source)
    • And a angle, θ
    • 
    • If t = 180, the light is a point light source.
    • We can calculate the angle between the surface normal (later) and the spotlight to see if it is less than θ. If so, this light contributes.
    • You can also add a fade factor for the spotlight.
    • cos^{e(φ) where φ is the angle between the source and the object.}
    • We will use this later.
    • By the way, the angle between two vectors is the dot product (as long as the vectors are normalized).
    • In any case, the constant e, as well as the angle θ and the vector I are additional components of a spot light.
• Surfaces
  • Surfaces can eventually have properties that define how they interact (or reflect) the different light components.
  • k_{{r,g,b}{a,d,s}}
  • Simplified to k_a for example.
• Phong lighting.
  • This model is based on
    • A point p
    • l, a vector pointing from the point to a light source.
    • A normal to the plane (at the point) n
    • v, a vector from the point to the viewer.
    • r, a perfectly reflected vector from the light.
    • 
  • Intensity (I) at a point
    • If R_x is the reflective coefficient for a material at the point.
    • from a single light source is I = L_aR_a+L_dR_d+L_sR_s
    • And from all light sources
    • I = Σ_i L_iaR_a+L_idR_d+L_isR_s
• We are finally ready for Diffuse Reflections
  • A diffuse reflector scatters light in all directions.
    • If it is smooth, R_d =1
    • If it is rough, R_d is very small.
  • This is modeled by Lambert's cosine law.
    • The amount of light is directly proportional to the cosine of the angle between the light and the surface normal.
    • R_d ≈ cos(θ)
    • Remember, l is a vector to the light and n is the surface normal
    • cos(θ) = l · n
  • So I_d = k_d(l· n)L_d
  • If the angle between l and n is greater than +/- 90, then the result will be negative, so it is common to add
  • I_d = max(0, k_d(l· n)L_d)
  • Or adding the distance attenuation
  • I= max(0,k_d/(a+bd+cd²)(l· n)L_d) + k_aL_a
• Secular reflection
  • Specular highlights are computed as a combination of the the viewer, the surface, and the light source.
  • Angel interprets this as light reflected from smooth surfaces.
  • Phong proposed a model much like that used for spotlights.
  • I_s = k_sL_scos^α φ
    • Where φ is the angle between the reflection vector and the viewer.
    • This make sense as the further from the angle of reflection, the less direct reflection we will see.
    • α is a surface constant
      • This is called shininess
      • And higher values mean a "smaller" specular reflection.
      • Metal is 100 ≤ α ≤ 500
    • 
  • φ = r · v
  • I_s = k_sL_smax((r·v)^α,0)
  • But computing r is somewhat expensive.
  • Blinn modified Phong's model by using a halfway vector
    • let h = (l+v)/|l+v|
    • This is the vector halfway between l and v.
    • 
    • Note, in this diagram ψ is the angle between the normal and the half vector.
    • Angel notes that when v is in the same plane as l, n and r, 2ψ = φ
    • In any case, ψ is about 1/2 of φ
    • So α is adjusted.
  • The final computation is
    • I = k_aL_a + 1/(a + bd+cd²) [ k_dL_dmax(0, l·n) + k_sL_smax((n·h)^α, 0)]