# CS488 - Introduction to Computer Graphics - Lecture 31

## Review

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

### (Un)natural Phenomena at Surfaces

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

• 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