1. Philip Willis Projective Alpha Colour Media Technology Research Centre, University of Bath

2. 1.Digital compositing and alpha 2.Projective geometry 3.How they come together Overview of Talk Media Technology Research Centre, University of Bath

3. Porter and Duff 1984 Opacity, alpha: (r, g, b,  ), 0.0   1.0 Digital Compositing Media Technology Research Centre, University of Bath

4. Porter and Duff 1984 A over B C=  = Digital Compositing Media Technology Research Centre, University of Bath

5. 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

6. 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

7. 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

8. 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

9. Homogeneous Coordinates Media Technology Research Centre, University of Bath Unify rotation, translation, scaling. Why? 4 by 4 matrices.

10. Projective Transformations Media Technology Research Centre, University of Bath

11. 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.

12. 1D Projective Geometry (x,w) Media Technology Research Centre, University of Bath

13. 1D Projective Geometry (x,w) Media Technology Research Centre, University of Bath

14. 2D Projective Geometry (x,y,w) Media Technology Research Centre, University of Bath

15. 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

16. 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]

17. 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]

18. Projective Colour Space Media Technology Research Centre, University of Bath

19. Projective Colour Space Media Technology Research Centre, University of Bath

20. Projective Colour Space Media Technology Research Centre, University of Bath

21. Projective Colour Space Media Technology Research Centre, University of Bath

22. Projective Colour Space Media Technology Research Centre, University of Bath

23. Pre-multiplied colours? Media Technology Research Centre, University of Bath Non pre-multiplied colours?

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

25. 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

26. Colour Transformations Media Technology Research Centre, University of Bath

27. Fluorescence Translation: colour offset Colour rotation Scaling: change area of material Colour vanishing points. Colour Transformations Media Technology Research Centre, University of Bath

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

29. 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

30. Spectral rendering with one alpha value Volume rendering Unbounded energy and alpha Any colour calculations Some Benefits Media Technology Research Centre, University of Bath

31. Example: Filtering/Illumination Media Technology Research Centre, University of Bath

32. Example: Filtering/Illumination Media Technology Research Centre, University of Bath

33. Philip Willis The End Projective Alpha Colour Media Technology Research Centre, University of Bath