Philip Willis

Projective Alpha Colour

Media Technology Research Centre, University of Bath

1. Digital compositing and alpha

2. Projective geometry

3. How they come together

Overview of Talk

Media Technology Research Centre, University of Bath

Porter and Duff 1984

Opacity, alpha:

(r, g, b, ), 0.0 1.0

Digital Compositing

Media Technology Research Centre, University of Bath

Porter and Duff 1984

A over B

C=

=

Digital Compositing

Media Technology Research Centre, University of Bath

Porter and Duff 1984

A over B

C= ACA + (1 – A) BCB

= A + (1 – A) B

Digital Compositing

Media Technology Research Centre, University of Bath

BCB

Porter and Duff 1984

A over B

C= ACA + (1 – A) BCB

= A + (1 – A) B

Digital Compositing

Media Technology Research Centre, University of Bath

CB BCA

A

Porter and Duff 1984

A over B

C= ACA + (1 – A) BCB

= A + (1 – A) B

Digital Compositing

Media Technology Research Centre, University of Bath

CA

A

CB B

1 - A

Porter and Duff 1984

Pre-multiplied colours

C= ACA + (1 – A) BCB

= cA + (1 – A) cB

Digital Compositing

Media Technology Research Centre, University of Bath

Homogeneous Coordinates

Media Technology Research Centre, University of Bath

Unify rotation, translation, scaling.

Why?

4 by 4 matrices.

Projective Transformations

Media Technology Research Centre, University of Bath

s , t, t,t

v,r,r,r

v,r,r,r

vr ,r,r

w)z, y, (x,

zyx

33,33,23,1

22,32,22,1

11,3,1,21,1

Projective Geometry

Media Technology Research Centre, University of Bath

Projective (wx, wy, wz, w)

… normalises to give Euclidean:

(x, y, z, 1)

The “w” coordinate is the scale of the projective space.

1D Projective Geometry (x,w)

Media Technology Research Centre, University of Bath

1D Projective Geometry (x,w)

Media Technology Research Centre, University of Bath

2D Projective Geometry (x,y,w)

Media Technology Research Centre, University of Bath

Projective Geometry and Colour

Media Technology Research Centre, University of Bath

1. (wx, wy, wz, w) … projective

(x, y, z, 1) … normalised

2. (r, g, b, ) … premultiplied

(r, g, b, 1) … normalised

Projective Alpha Colour

Media Technology Research Centre, University of Bath

(r, g, b, )

r, g, b are measures of energy.

They are unbounded

i.e. not just in [0.0, 1.0]

Projective Alpha Colour

Media Technology Research Centre, University of Bath

(r, g, b, )

is a measure of scale: area.

It is unbounded

i.e. not just in [0.0, 1.0]

Projective Colour Space

Media Technology Research Centre, University of Bath

Projective Colour Space

Media Technology Research Centre, University of Bath

Projective Colour Space

Media Technology Research Centre, University of Bath

Projective Colour Space

Media Technology Research Centre, University of Bath

Projective Colour Space

Media Technology Research Centre, University of Bath

Pre-multiplied colours?

Media Technology Research Centre, University of Bath

Non pre-multiplied colours?

• Colours as (r, g, b, ) vectors

• Materials as 4 by 4 projective transformations

• Materials transform colours

Colour Transformations

Media Technology Research Centre, University of Bath

• Blend materials by “blending” matrices:

matrix multiplication or matrix addition

• Colour mixing, illumination, filtering etc.

Colour Transformations

Media Technology Research Centre, University of Bath

• Fluorescence

• Translation: colour offset

• Colour rotation

• Scaling: change area of material

• Colour vanishing points.

Colour Transformations

Media Technology Research Centre, University of Bath

• Correct colour filtering

• Correct illumination effects

• Back-illumination too.

• Subtractive colour (C,M,Y)

• Correct perspective shading

Some Benefits

Media Technology Research Centre, University of Bath

• Spectral rendering with one alpha value

• Volume rendering

• Unbounded energy and alpha

• Any colour calculations

Some Benefits

Media Technology Research Centre, University of Bath

Example: Filtering/Illumination

Media Technology Research Centre, University of Bath

Example: Filtering/Illumination

Media Technology Research Centre, University of Bath

Philip Willis

Thank you!

Projective Alpha Colour

Media Technology Research Centre, University of Bath