Bravo, lovely use of a parametric curve. Inspirational creativity.
Question, do you plan to finish the closing of the curtain? Some continued vector of the movement of the touch?
It would probably be too cute, but could you draw a 'holding hand' instead of a circle? See the lower hand in the attached pic.
If you like math you could create your own with a series of Bezier curves. Or a path of a rough trace.