I have this idea of using groups to study closed curves and nearby symmetries I.e slight deformations of a curve yielding a bunch of symmetries. The goal is to detect the "nearby" symmetries of a curve and to be able to find the existing symmetries of a curve.
I want to know if it is moot/ if someone has already done it?
I am also thinking of using a tad bit of variational calculus for some extra parts of it. Invariably someone will have done it, I am just hoping someone hasn't.
EDIT:
To clarify the deformations are very exactly chosen to remove symmetry breaking bumps on loops etc, the goal is to, given a closed nice enough loop: To know its symmetries and to detect the symmetries that don't exist but could exist with a deformation excising the symmetry breaking bumps.
I have some additional ideas about representing the loop in polar coords being periodic in angle coords and just excising noisy terms that way although that is something I haven't investigated very much, its more of an adumbrated untouched concept for now.