Surfaces Defined on Torus Knots
Surfaces Defined on Torus Knots
A torus knot is a particular type of knot that is defined on the surface of an unknotted torus. It is possible to define a surface whose edges coincide with a knot or link, which can be a non-oriented surface, as presented in this Demonstration, or an orientable surface, in which case it is named a Seifert surface, for Herbert Seifert, who introduced a general method for any knot in 1934.
The method applied here is simply starting with a one-to-one mapping between the interval and and defining lines between those points, giving a ruled surface; afterward, the relaxation method (which takes the mean of the four neighbors for each point, keeping fixed boundaries) is applied for a number of steps to give a smoother surface.
[0,π)
[π,2π)