I am currently trying to discretise a torus knot onto a square lattice grid.
My method of achieving this has been to first use the Torus knot parametric equation, then define a circle that follows the torus knot path using the normal and binormal, similarly to that done in this prior question.
Using this method, should have yielded me the surface of the knot, which when computed using Sympy, gives the following image of a trefoil surface. So I am assuming I have done this correctly.
However, I now need to discretise the volume enclosed by this surface. My method of choice would be to pick a point and test if it exists within the surface. This previous question suggests using the Stokes-Cartan theorem to perform this, and would at the surface appear to be a good solution.
However, I have vague memories of a lecture I attended that suggested this only applies to "simple" enclosed surfaces that do not overlap.
Hence: Is the Stokes-Carten theorem suitable for knotted manifolds