Computing Chebyshev knot diagrams
arXiv:1001.5192
Abstract
A Chebyshev curve C(a,b,c,ϕ) has a parametrization of the form x(t)=Ta(t); y(t)=T_b(t) ; z(t)= Tc(t + ϕ), where a,b,c are integers, Tn(t) is the Chebyshev polynomial of degree n and ϕ\in \RR. When C(a,b,c,ϕ) has no double points, it defines a polynomial knot. We determine all possible knots when a, b and c are given.
8p