KnotCurve

The sampled points of a knot's embedding in space — only a torus knot has a parameterisation on file, so any other knot declines rather than guessing one from a braid word.

KnotCurve(knot, samples?)the sampled points of $T(p,q)$'s torus embedding

Typed signatures

Type	Package	Applies
(expression<Braid> | expression<FigureEightKnot> | expression<Link> | expression<PretzelKnot> | expression<TorusKnot> | expression<TwistKnot> | string, integer?) -> list<list<real>>	braid	always

Domain: Braids and knots

Examples

Basic #

The trefoil, sampled at 50 points

live ↗

In$\mathrm{Length}(\mathrm{KnotCurve}(\mathrm{TorusKnot}(2, 3), 50))$Out$50$

The curve starts on the outer circle of the torus

live ↗

In$\mathrm{First}(\mathrm{KnotCurve}(\mathrm{TorusKnot}(2, 3), 40))$Out$\bigl\lbrack3, 0, 0\bigr\rbrack$

About

Examples	2

See also: ParametricCurve, TorusKnot