Papers by Tom Duff


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Deep Compositing Using Lie Algebras

Tom Duff
July 2017

Deep compositing is an important practical tool in creating digital imagery, but there has been little theoretical analysis of the underlying mathematical operators. Motivated by finding a simple formulation of the merging operation on OpenEXR-style deep images, we show that the Porter-Duff over function is the operator of a Lie group. In its corresponding ... more

Paper (PDF)

To appear in ACM Transactions on Graphics


Building an Orthonormal Basis, Revisited

Tom Duff, James Burgess, Per Christensen, Christophe Hery, Andrew Kensler, Max Liani, Ryusuke Villemin
March 2017

Frisvad [2012b] describes a widely-used computational method for augmenting a given single unit vector with two other vectors to produce an orthonormal frame in three dimensions, a useful operation for any physically based renderer. The implementation has a precision problem: as the z component of the input vector approaches -1, floating point cancellation causes ... more

Paper (PDF)


Compositing Digital Images

Thomas Porter, Tom Duff
July 1984

Most computer graphics pictures have been computed all at once, so that the rendering program takes care of all computations relating to the overlap of objects. There are several applications, however, where elements must be rendered separately, relying on compositing techniques for the anti-aliased accumulation of the full image. This ... more

Paper (PDF)

Available in the Proceedings of SIGGRAPH 1984.