Lynwood Dunn(1904-1998)• Visual effects pioneer• Acme-Dunn optical printer

The Over Operator

• How to indicate which parts of front picture are clear and which are opaque

• Use alpha channel to indicate opacity [Smith]

• Over operator [Porter & Duff S’84]• A over B:

CA over B = aA CA + (1 – aA) aB CB

aA over B = aA + (1 – aA) aB

• Note that aA CA used in color eqs,so store aA CA instead of CA

• A over B w/premultiplied alpha

CA over B = CA + (1 – aA) CB

aA over B = aA + (1 – aA) aB

B

A

C = (aR aG aB a)

25% transparent yellow

75% transparent blue

?

CA over B = .75(1,1,0) + .25(.25)(0,0,1)= (.75,.75,0) + (0,0,.125)= (.75,.75,.125)

aA over B = .75 + .25(.25) = .875CABW = .875(.75,.75,.125) +

.125(1)(1,1,1) = (.66,.66,.11)+(.125,…) =(.78,.78,.24)

Academy of Motion Picture Arts & SciencesScientific and Engineering AwardTo Alvy Ray Smith, Tom Duff, Ed Catmull and Thomas Porterfor their Pioneering Inventions in Digital ImageCOMPOSITING.PRESENTED MARCH 2, 1996

Accumulating Opacity• Depends on order of accumulation• Back to front

– Over operator

Cout = a C + (1 – a) Cin

aout = a + (1 – a) ain

– No need to maintain a• Front to back

– Under operator

Cout = ain Cin + (1 – ain) C

aout = ain + (1 – ain) a– Need to maintain a

Cin,ainCout,aout

C,a

Cout,aoutCin,ain

C,a

view

Volume Rendering Methods• Data stored as 3-D array of samples

C – color

a – opacity

N – normal, etc.• Splatting

– “Forward:” voxels to pixels– Overlay planes from volume

• Ray casting– “Backward:” pixels to voxels– Ray marches from voxel to voxel

from SGI’s Volumizer, 1999