Boundary torus of a tubular neighborhood of torus knots in $S^3$, under stereographic projection
This program computes and visualizes the complement of a regular neighborhood of knots embedded in S3. Given a (p,q) torus knot lying on a Clifford torus, the program computes an ϵ-neighborhood with respect to the spherical metric, parameterizes the boundary torus of this neighborhood, and renders it under stereographic projection into R3.
You can select different torus knots from a menu, and the visualization updates to show the resulting knot complement boundary. The output reveals the rich geometry of these surfaces as submanifolds of the 3-sphere.
Controls: Click and drag to orbit, scroll to zoom.
