1. Projects

# Surface Reflectances

## Smooth Surfaces

#### Surface reflectance

• For smooth surfaces the surface reflectance is mirror-like.
• Amount reflected versus amount transmitted is a function of the complex index of refraction
• Real part of the index of refraction determines the wavelength of light
• Complex part of the index of refraction determines the surface penetration of light into metallic surfaces.

## Rough Surfaces

#### Random roughness

Surface is well-modelled as a collection of small flat surfaces oriented in random directions

• Statistical regularities exist in the BRDF, but because of self-occlusion they are not simply related to the statistics of the surface
• In a certain model of roughness the surface reflection can even be Lambertian.

#### Structured roughness

Some of the most interesting BRDF effects are the result of structured roughness

• grooves on CD
• scratched plastic

# Body Reflectance

• just like selective absorption
• doesn't come out at the same place: Why doesn't it matter?
• edges of a surface

#### Multiple interaction with pigment

1. Encounters with two identical pigment particles.
2. Encounters with two different pigment particles.

#### Lambertian reflectance

Lambert 1728-1777

Consider a small circular hole in the surface and ask how much light comes through it in different directions

• Assume light direction is completely randomized
• The directional factor is the cosine zenith angle

The luminance of light in any direction is constant.

When the volume immediately below the surface has spatial structure, the direction of light re-emitted through the surface is not necessarily isotropic.

#### The Moon

• What would the full moon look like if its surface were Lambertian?
• What does the full moon actually look like?

# Colour Mixing in Body Reflectance

Paint is the usual example, but there are others

1. Fruit ripening
2. Leaves turning colour in the fall
3. Colour of human skin

#### Kubelka-Munk colour mixing model

1. Infinitesimally thin layers, thickness proportional to the density of the pigment
• One set of layers for each pigment
2. Use reflection/refraction plus Beer's law
3. Solve in equilibrium at the boundaries between layers
• Infinite depth
• White underlayer
• Black underlayer

Engineering model

• We don't use densities, reflection/refraction coefficients, etc calculated from physics.
• We get humans to say whether colours look the same or not, and by how much they differ, and find the best coefficients.

Recall difference between

• blind surgery -- calculate like paint -- and

computer-animated movies -- let the artist play with coefficients