arXiv Open Access 2015

Computing Chebyshev knot diagrams

P. -V Koseleff D Pecker Fabrice Rouillier C Tran

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Abstrak

A Chebyshev curve $\mathcal{C}(a,b,c,φ)$ has a parametrization of the form$ x(t)=T\_a(t)$; \ $y(t)=T\_b(t)$; $z(t)= T\_c(t + φ)$, where $a,b,c$are integers, $T\_n(t)$ is the Chebyshev polynomialof degree $n$ and $φ\in \mathbb{R}$. When $\mathcal{C}(a,b,c,φ)$ is nonsingular,it defines a polynomial knot. We determine all possible knot diagrams when $φ$ varies. Let $a,b,c$ be integers, $a$ is odd, $(a,b)=1$, we show that one can list all possible knots $\mathcal{C}(a,b,c,φ)$ in$\tilde{\mathcal{O}}(n^2)$ bit operations, with $n=abc$.

Topik & Kata Kunci

cs.SC

Penulis (4)

P. -V Koseleff

D Pecker

Fabrice Rouillier

C Tran

Format Sitasi

APA MLA BibTeX

Koseleff, P.-., Pecker, D., Rouillier, F., Tran, C. (2015). Computing Chebyshev knot diagrams. https://arxiv.org/abs/1512.07766

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Informasi Jurnal

Tahun Terbit: 2015
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓