Computing Chebyshev knot diagrams
Résumé
A Chebyshev curve $\mathcal{C}(a,b,c,\phi)$ has a parametrization of the form
$ x(t)=T_a(t)$; \ $y(t)=T_b(t)$; $z(t)= T_c(t + \phi)$, where $a,b,c$
are integers, $T_n(t)$ is the Chebyshev polynomial
of degree $n$ and $\phi \in \mathbb{R}$. When $\mathcal{C}(a,b,c,\phi)$ is nonsingular,
it defines a polynomial knot.
We determine all possible knot diagrams when $\phi$ varies.
Let $a,b,c$ be integers, $a$ is odd, $(a,b)=1$, we show that
one can list all possible knots $\mathcal{C}(a,b,c,\phi)$ in
$\tilde{\mathcal{O}}(n^2)$ bit operations, with $n=abc$.
Origine : Fichiers produits par l'(les) auteur(s)
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