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=  A C A + (1 –  A )  B C B  =  A + (1 –  A )  B Digital Compositing Media Technology Research Centre, University of Bath BB CBCB

Porter and Duff 1984 A over B C=  A C A + (1 –  A )  B C B  =  A + (1 –  A )  B Digital Compositing Media Technology Research Centre, University of Bath CBCB BB CACA AA

Porter and Duff 1984 A over B C=  A C A + (1 –  A )  B C B  =  A + (1 –  A )  B Digital Compositing Media Technology Research Centre, University of Bath CACA AA CBCB BB 1 -  A

Porter and Duff 1984 Pre-multiplied colours C=  A C A + (1 –  A )  B C B  = c A + (1 –  A ) c B 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

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?

Subtractive colours in printing: C, M, Y primaries. Media Technology Research Centre, University of Bath Negative alpha and colour?

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

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

Blend materials by “blending” matrices: matrix multiplication or matrix addition Colour mixing, illumination, filtering etc. 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 The End Projective Alpha Colour Media Technology Research Centre, University of Bath