Find minimum distance from point to complicated curve

Question

I have a complicated curve defined as a set of points in a table like so (the full table is here):

#  x   y
1.0577  12.0914
1.0501  11.9946
1.0465  11.9338
.         


        

Answer 1

The curve is by nature parametric, i.e. for each x there isn't necessary a unique y and vice versa. So you shouldn't interpolate a function of the form y(x) or x(y). Instead, you should do two interpolations, x(t) and y(t) where t is, say, the index of the corresponding point.

Then you use scipy.optimize.fminbound to find the optimal t such that (x(t) - x0)^2 + (y(t) - y0)^2 is the smallest, where (x0, y0) are the red dots in your first figure. For fminsearch, you could specify the min/max bound for t to be 1 and len(x_data)