Aha! I always thought parametric curves had a great future in entertainment. There is also a usage for live projections during concerts (HeavyM-style). This one is closed to Zelda: Skyward Sword’s key rotation shadow matching puzzle. Except you also got to match the line’s thickness (which I guess is the cyclic time parameter?)
There was one puzzle where I almost got it right but unfortunately I was stuck at the edge of the parameter range. Going to the other side didn’t seem to cycle the parameter and therefore didn’t allow me to go slightly beyond the limit. I tried to get the symmetrical shape just in case, but it didn’t work either. I solved it surprisingly while move from the symmetrical shape to the original shape I had, so I’m unsure on which position I actually solved the problem (maybe highlighting the last position for a moment would help players moving the cursor a bit too fast).
Alternatively you could require the player to hold the position for a moment, maybe highlighting the shape when correct for more than 0.5s. That would also potentially fix the cheat of sweeping the parameter range with the cursor until you find the solution (mentioned in another comment); or at least make it much slower.
And of course there’s the boosted challenge of 3D parameter search, which makes sweeping very long! … Good thing PANORAMICAL doesn’t require you to find an exact solution, with its 9 parameters you would get crazy!