We present algorithms for computing the squared Weil and Tate pairings on an elliptic curve and the squared Tate pairing for hyperelliptic curves. The squared pairings introduced i...
We prove that the number of distinct weaving patterns produced by n semi-algebraic curves in R3 defined coordinate-wise by polynomials of degrees bounded by some constant d, is b...
Saugata Basu, Raghavan Dhandapani, Richard Pollack
We wish to endow the manifold M of smooth curves in lRn with a Riemannian metric that allows us to treat continuous morphs (homotopies) between two curves c0 and c1 as trajectorie...
Diffusion curves are a powerful vector graphic representation that stores an image as a set of 2D Bezier curves with colors defined on either side. These colors are diffused over...
Scott uses an efficiently computable isomorphism in order to optimize pairing computation on a particular class of curves with embedding degree 2. He points out that pairing implem...