Anthony Lasenby and Joan Lasenby
Surface Evolution and Representation using Geometric Algebra
In Roberto Cipolla and Ralph Martin eds. The Mathematics of Surfaces IX: Proceedings of the ninth IMA conference on the mathematics of surfaces, p144-168, Springer, London (2001)

Abstract: Recent developments in geometric algebra have shown that by moving from a projective to a conformal representation (5d representation of 3d space), one is able to extend the range of geometrical operations that can be carried out in an efficient and elegant way. For example, while in projective space one is able to intersect lines and planes in a simple fashion, in conformal space one is able to intersect and represent spheres, lines, circles and planes. In addition, all the operations of Euclidean geometry (dilations, translations, rotations and inversions) are smoothly integrated with the projective representation.

The paper will use the conformal representation to look at the problems of surface representation and evolution, and of wavefront propagation from such surfaces.

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