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

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

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Porter and Duff 1984 Opacity, alpha: (r, g, b, ), Digital Compositing Media Technology Research Centre, University of Bath

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

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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 CBCB

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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 CACA A

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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 CBCB B 1 - A

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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

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

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Projective Transformations Media Technology Research Centre, University of Bath

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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.

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

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

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

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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

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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]

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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]

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Projective Colour Space Media Technology Research Centre, University of Bath

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Projective Colour Space Media Technology Research Centre, University of Bath

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Projective Colour Space Media Technology Research Centre, University of Bath

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Projective Colour Space Media Technology Research Centre, University of Bath

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Projective Colour Space Media Technology Research Centre, University of Bath

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

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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

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

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

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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

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

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

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

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

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