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Specular reflection

Short answer

Specular reflection is the mirror-like highlight from a shiny surface. The Phong model gives I_spec = ks·IL·(R·V)^n, where R = 2(N·L)N−L, n is the shininess exponent. Total intensity: I = ka·Ia + IL[kd(N·L) + ks(R·V)^n].

Define specular reflection and explain the Phong model for specular reflection, with the intensity expression (for a point light source).

Specular reflection is the mirror-like reflection of light from a shiny surface, producing a bright spot (highlight) on the surface. The reflected light is concentrated around the direction of ideal reflection R, so the highlight is seen only when the viewer is near that direction. For a perfect mirror, light is reflected only in the direction R; for real surfaces it spreads in a narrow cone.

Phong specular model. The intensity of the specular reflection is proportional to cos^n φ, where φ is the angle between the direction of reflection R and the viewing direction V.

I_spec = ks · IL · cos^n φ = ks · IL · (R · V)^n

  • ks = specular reflection coefficient (0 to 1, may depend on the incidence angle)
  • IL = intensity of the point light source
  • n = specular reflection exponent (shininess): 1 for very rough surfaces, 100 or more for very shiny metals; larger n gives a smaller, sharper highlight
  • L = unit vector to the light, N = unit surface normal, V = unit vector to the viewer
  • R = reflection vector = 2(N·L)N − L
  N   R
  | /   . 
  |/ phi V
--+---------- surface
   \ L

The Blinn-Phong version uses the halfway vector H = (L + V)/|L + V| and (N·H)^n, which avoids computing R.

Total with ambient and diffuse:

I = ka·Ia + IL [ kd (N·L) + ks (R·V)^n ]

(Specular is taken as zero when N·L < 0 or R·V < 0.)

✓ Answer checked by Claude Opus 5.5 (high effort)

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