The Lighting Model

• The intensity (or color) of a pixel is given by I
  • I = <I_r, I_g, I_b>
  • We will frequently deal with I as a scalar.
  • Just remember if we do I=F(x) it is really I = < F(x_r, x_g, x_b >
• Ambient light
  • We can't perfectly model light
  • So we cheat
  • Ambient light is the light that is "in the room".
  • I_a is a vector of ambient light at a point.
  • We can provide a different amount of ambient light from each light source. (L_a)
  • Or we can just have an ambient light contribution in the scene.
  • Each surface can be given an ambient light reflective property (k_a.
    • This is a vector, <k_ar, k_ag, k_ab>
  • I_a = k_aL_a
  • Or for many lights
  • I_a = Σ_lightsk_aL_a
• Diffuse Component
  • Diffuse light is modeled by Lambert's law of cosines
    • The diffuse light is proportional to the incident light and the surface normal.
    • R_d ~ cos(θ)
    • So for a incoming ray of light l
    • And the surface normal n
    • R_d ~ l·n = |l||n|cos(θ);
  • This is modified by
    • The diffuse component of the light source (L_d)
    • The diffuse property of the surface (k_d
  • I_d = k_d(l·n)L_d
    • But since this can be negative, we clamp it to be positive.
    • I_d = max(k_d(l·n)L_d,0) in c++
    • I_d = clamp(k_d(l·n)L_d,0,1) in glsl.
  • Or sum this across all light sources.
  • There are times we want to involve the distance from the light.
    • Normally we would expect it to fall off in proportion to the distance from the light source (d)
    • or 1/d
    • Or even 1/d²
    • But this has been found to be problematic
    • So the formula used in classical lighting is
    • 1/(a+bd+cd²)
      • Where d is the distance to the light source.
      • And a,b and c are constants

  • 	                max(kd(l·n)Ld,0)
    	 Id = Σlights  -----------
    	              a + bd +cd2
    	 

• I = I_a + I_d