Illumination

Illumination Models

Illumination models calculate how light interacts with surfaces. The Phong reflection model is the most widely used local illumination model, consisting of ambient, diffuse, and specular components.

Phong Reflection Model

I = Ia*ka + kd*(L·N)*Id + ks*(R·V)^n * Is

Components:
  Ia*ka           = Ambient light
  kd*(L·N)*Id     = Diffuse reflection
  ks*(R·V)^n * Is = Specular reflection

Variables:
  I  = final intensity
  Ia = ambient light intensity
  ka = ambient reflectance coefficient
  kd = diffuse reflectance coefficient
  L  = light direction (toward light)
  N  = surface normal
  Id = light intensity
  ks = specular reflectance coefficient
  R  = reflection direction
  V  = view direction (toward camera)
  n  = shininess exponent
  Is = specular light intensity

Ambient Light

Simulates indirect illumination by adding a constant base color. This prevents shadowed areas from being completely black.

Ambient = ka * Ia

  ka: material ambient coefficient (0-1)
  Ia: ambient light color/intensity

  Example: dark blue ambient
    ka = 0.2, Ia = (0.1, 0.1, 0.3)
    ambient = 0.2 * (0.1, 0.1, 0.3) = (0.02, 0.02, 0.06)

Diffuse Reflection (Lambertian)

Simulates matte surfaces. Light is scattered equally in all directions. The intensity depends on the angle between the light and surface normal (Lambert's cosine law).

Diffuse = kd * max(0, L·N) * Id

  L = normalize(light_pos - surface_pos)
  N = surface normal
  L·N = cosine of angle between light and normal

  Example:
    L = (0, 1, 0)  (light from above)
    N = (0, 1, 0)  (surface facing up)
    L·N = 1.0      (maximum diffuse)
    
    N = (0.707, 0.707, 0)  (45° tilt)
    L·N = 0.707            (reduced diffuse)

Specular Reflection

Creates bright highlights on shiny surfaces. Depends on the viewing angle and is concentrated around the perfect reflection direction.

Specular = ks * (R·V)^n * Is

  R = 2*(L·N)*N - L  (reflection direction)
  V = normalize(camera - surface)
  n = shininess (higher = tighter highlight)

  n = 10   → broad, dull highlight (plastic)
  n = 100  → sharp, bright highlight (metal)
  n = 500  → very sharp highlight (mirror)

  Blinn-Phong variant (more efficient):
  H = normalize(L + V)  (halfway vector)
  specular = ks * (N·H)^n * Is

Light Sources

Point Light:
  L = normalize(light_pos - surface_pos)
  Intensity falls off with distance:
  I = I0 / (kc + kl*d + kq*d²)

Directional Light:
  L = constant direction (sun)
  No distance attenuation

Spot Light:
  Adds cone angle constraint:
  intensity *= dot(-L, spot_dir) > cutoff ? 1 : 0