I've done some research in this area with examining user input mechanics. This particular example would be solvable using B-spines [1], as one possible approach

I've done some research in this area with examining user input mechanics. This particular example would be solvable using B-spines [1], as one possible approach. The "path CAPTCHA" even provides some great computational hints, by indicating the starting point as a circle! http://mathworld.wolfram.com/B-Spline.html http://mathworld.wolfram.com/B-Spline.html