- Illumination
- Ambient illumination
- Notes terminology
- l - the ray from the light osurce to the surface
- n - the normal to the surface
- v - the direction to the eye
- r - the specular reflection direction
- Lin, Lout

This material is described with diagrams here.

We are only interested in the light leaving the surface in a particular direction. Why?

The light divides into two parts at the surface

- part is reflected: `surface reflectance'
- part enters the surface: `body reflectance'

The simplest model of body reflectance is Lambert's cosine law. Surfaces with body reflectance following Lambert's cosine law are called Lambertian.

What makes a Lambertian surface Lambertian?

- Half-sphere within the body, centred at the bit of surface
- Half-sphere above the body, bottom at the surface
- Draw a little cylinder passing through the centre.
- Whatever goes in the bottom comes out the top
- modified by the angular size of the hole
- cosine factor

What goes into the eye

- Same geometry as illumination, only backward
- cosine factor

- Cosine factors cancel one another

**Important point**

**The ubiquitous cosine terms (l.n, v.n, etc.) occur whenever we translate between areas on a plane and areas on a sphere.**

What colour is the light?

- Each time the incoming light interacts with a pigment particle its
spectral content is multiplied by a particle property, r(\lambda).
- E1(\lambda) = E(\lambda) * r(\lambda)

- It can interact many times
- Assuming only one type of particle,
- En(\lambda) = E(\lambda) * ( r(\lambda) )^n

- When the light re-emerges from the surface fraction fi of the light has
interacted i times
- Light re-emerging has spectral content E(\lambda) * \sum_i fi ( r(\lambda) )^i
- R(\lambda) = \sum_i fi ( r(\lambda) )^i is called the body reflectance.

- In real calculations we discretize wavelength
Using only three samples we get the RGB model

- Illumination (Ir, Ig, Ib)
- Reflectance (Rr, Rg, Rb)
- Outgoing light: (IrRr, IgRg, IbRb)

Part of the light didn't enter the body of the surface, but was reflected

- Called `surface reflection'
- Where does it go to?

Suppose the surface is smooth

- It is reflected, called `spectular'
- which means out = in - 2 * (in.normal) normal
- what is the colour?
- does it enter the eye?

Suppose we roughen the surface just a little

- The light spreads a little, centred on the specular direction.
- Amount entering the eye depends on the angle between the eye ray and the specular direction

And if we roughen the surface a lot

- The light goes out all over the place
- This is called a matte surface

Here is the hack

- Named Phong shading after Phong Bui-Tuong
- Let the specular term be ( r.v )^p
- small p - matte
- large p - highly specular

How is the incoming light divided between ambient, surface and body reflection?

- Depends on the surface
- L(\lambda) = Ia * ka(\lambda) + Id * (l.n) * kd(\lambda) + Is * ( r.v
)^p * ks
- Implicit v.n / v.n in the second term
- Missing 1 / v.n in the third term