Download - Projective Alpha Colour
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
