Finishing the Basic Lighting Model

• We need to compute the specular component of the lighting model.
• I = I_a + I_d + Is
• Specular is the "tight" reflection.
  • The author says a red ball will have a specular reflection the color of the light.
  • Without specular reflections, everything looks like chalk
  • There are no shiny objects.
• This reflection very much depends on where the viewer is WRT the light.
  • let r be a perfectly reflected ray
  • Let v be a vector to the viewer
  • φ is the angle between the two.
  • cos(φ) = r ·l, if r and v are normalized.
  • There is a surface constant k_s that models the colors of the specular reflection.
  • L_s models the specular light of a light source.
  • α describes the "shininess" of the surface.
    • This is used to control the shape of the cos function
    • The higher α the tighter the spot.

      phi=-pi/2:0.01:pi/2
      plot(phi,(cos(phi)).^1)
      hold on
      plot(phi,(cos(phi)).^2)
      plot(phi,(cos(phi)).^3)
      plot(phi,(cos(phi)).^100)
      	       

  • In theory we want cos^α(φ)
  • or I_s = k_sL_sclamp((r·v)^α,0,1)
  • We could add a distance term to this as well.
• This is the Phong lighting model
  • PhD thesis in 1975
• r is hard to compute.
  • It is a per pixel value.
• So the Phong-Blinn model
  • Uses a vector halfway between the viewer and the light to approximate this.
  • This can be computed once per redo
  • And this reduces the total computation.
  • h = (l+v)/|l+v|
  • And the angle between h and the surface normal is approximately the angle between r and v.
  • See the picture on page 288.
  • So we replace (r·v) with (n·h)