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Projective Alpha Colour

Projective Alpha Colour. Philip Willis. Media Technology Research Centre, University of Bath. Overview of Talk. Digital compositing and alpha Projective geometry How they come together. Media Technology Research Centre, University of Bath. Digital Compositing. Porter and Duff 1984

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Projective Alpha Colour

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

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

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

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

  5. Digital Compositing CB aB Porter and Duff 1984 A over B C= aACA + (1 – aA)aBCB a= aA + (1 – aA)aB Media Technology Research Centre, University of Bath

  6. Digital Compositing CA CB aB aA Porter and Duff 1984 A over B C= aACA + (1 – aA)aBCB a= aA + (1 – aA)aB Media Technology Research Centre, University of Bath

  7. Digital Compositing CA CB aB aA 1 - aA Porter and Duff 1984 A over B C= aACA + (1 – aA) aBCB a= aA + (1 – aA) aB Media Technology Research Centre, University of Bath

  8. Digital Compositing Porter and Duff 1984 Pre-multiplied colours C= aACA + (1 – aA) aBCB = cA + (1 – aA) cB Media Technology Research Centre, University of Bath

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

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

  11. Projective Geometry Projective (wx, wy, wz, w) … normalises to give Euclidean: (x, y, z, 1) The “w” coordinate is the scale of the projective space. Media Technology Research Centre, University of Bath

  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 1. (wx, wy, wz, w) … projective (x, y, z, 1) … normalised 2. (ar, ag, ab, a) … premultiplied (r, g, b, 1) … normalised Media Technology Research Centre, University of Bath

  16. Projective Alpha Colour (r, g, b, a) r, g, b are measures of energy. They are unbounded i.e. not just in [0.0, 1.0] Media Technology Research Centre, University of Bath

  17. Projective Alpha Colour (r, g, b, a) a is a measure of scale: area. It is unbounded i.e. not just in [0.0, 1.0] Media Technology Research Centre, University of Bath

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

  24. Colour Transformations Colours as (r, g, b, a) vectors Materials as 4 by 4 projective transformations Materials transform colours Media Technology Research Centre, University of Bath

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

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

  27. Some Benefits Correct colour filtering Correct illumination effects Back-illumination too. Subtractive colour (C,M,Y) Correct perspective shading Media Technology Research Centre, University of Bath

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

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

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

  31. Projective Alpha Colour Philip Willis Thank you! Media Technology Research Centre, University of Bath

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