Take an infinitely long rope of diameter 1, ideally flexible and ideally slippery. Tie a trefoil knot into it and pull it tight. Describe the resulting rope shape analytically.

The problem is unsolved for every non-trivial open knot. (And also for every closed non-trivial knot.) Solving it seems extremely hard.

The above question was closed; this is an attempt to change this:

Is there at least a practical analytical approximation for the shape of the tight open trefoil? Maybe one whose shape is known to be at most within a certain suitably defined distance from the exact solution?