# CS781 - Colour for Computer Graphics - Winter 2009

# Lecture 8

# Visual Response to Light

## Colour Matching Functions

## Metamerism

#### Light Metamerism

Many to one transformation

Evolution says:

- Colour differences that matter are likely to be discriminable
- This is a statement about surfaces
- The colour of an object is the colour of its surface
- Note the difference between transparence/translucence and
whiteness/opacity

#### Illuminant Metamerism

Hold the surface constant

#### Surface Matemerism

Hold the illuminant constant

# Geometric Representations of Colour

## Special Properties of the Spectral Colours

Colours in the rainbow/spectrum = Colours of monochromatic lights

- call them spectral colours

Mix a spectral colour and white

- Move along a straight line in colour space
- As white decreases we get to a point where we can't go any farther

Mix the same spectral colour with any other colour

Remove a little of the spectral colour

- Do the same.
- Arrive at a point joining the first point to the origin

Choose another spectral colour

- In fact, just use the spectral colours to do this for all spectral
colours
- The result is a curve that delimits a cone

## Convex Hull of the Spectral Colours

This is the set of physically realisable colours

## Chromaticity Coordinates

The two meanings of `colour' when we say, `the same colour.'

- Unique hue, saturation and brightness
- Note ambiguity of `bright'
- Intensity might be better than brightness

- Unique hue and saturation

Remember (?) projective geometry

- If we treat all points on a line through the origin as a single point,
- on a sphere for example
- we get a projective space of one lower dimension

- Attractive because straight lines go to straight lines

Consider the projection

- x = X / (X + Y + Z)
y = Y / (X + Y + Z)

z = Z / (X + Y + Z)

- Then x + y + z = 1
- We are projecting onto the (1,1,1) plane.

- Plot (x,y)
- We are projecting the (1,1,1) plane to the (1,1,0) plane by
dropping the z-coordinate

The resulting planar representation of colour is called `chromaticity
coordinates'

- The chromaticity of a colour is its hue and saturation with brightness
ignored
- Because additive mixture of two colours in colour space is convex
combination
- additive mixture of two colours in chromaticity coordinates is
convex combination

It is pretty well impossible to make a true colour picture of the
chromaticity diagram

### Concepts from chromaticity coordinates

#### The white point

#### The purple line

#### Dominant hue

- also dominant wavelength
- relative to
**a** white point

#### Excitation purity

- also relative to a white point

#### Colour Temperature

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