CS488 - Introduction to Computer Graphics - Lecture 31

Comments and Questions

Review

1. Partitioned rendering
2. Texture, etc. mapping
3. Final proposal on Friday

(Un)natural Phenomena at Surfaces

Fresnel Reflection (See also.)

How does reflection actually work?

The key concept is the index of refraction

• measure of the speed of light in a substance
• speed of light determines refraction and reflection angles (drawing)
• note that it's the angle to the surface that gives Snell's Law.

Reflected and refracted rays

• How much goes into each of the reflected and refracted rays?
• depends on indices of refraction
  • How?
  • You don't want to know... unless you do!

Discuss two approaches to modelling.

Brewster's Angle

• For `small enough' angles the refracted light is zero
• Small enough depends on the index of refraction

Subsurface Scattering

Think about the Lambertian surface

• Why did the light come out of the surface at the location where it entered?
  • It didn't.
• Why doesn't it matter?
  • Try translating the surface

  Partitioned rendering reminder.

• When translational invariance is missing
  • structure in surface
  • structure in light

  then you have to think about how light moves inside the surface.

A general formulation

• If light of wavelength \lambda enters at x, it emerges at x' with probability R(x', x, \lambda)
• Therefore, light emerging at x' is \sum_x R(x', x, \lambda) L(x, \lambda)
• Critical question
  • How `wide' is R(x', x, \lambda)?
  • This tells you when subsurface scattering will make a difference.

Bidirectional Reflectance Function

BRDF as an example of partitioned rendering

Examples:

1. Human skin
   • skin structure
   • keratin, melanin, blood in different proportions
     • place to place on the body
     • person to person
     • time to time
   • We could let the rays go through the skin and interact with the pigments,

     or we could summarize everything in a parametrized reflectance function

     • R(x, \lambda) = R(k(x), m(x), b(x), \lambda)
   • Obviously the second strategy is better,
     • but only if it works
     • Select a model, work out a reflectance function, check that it agrees with reality

     Note two different definitions of `agrees with reality'.

2. Recently cut grass

Modelling

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