Array points densification without classical interpolation (non-unique solutions)

Hi!

I would like to 'densify' the points within an array of x and y points. For instance I would like to turn:

size([x y]) = (200,2) 

into a new set of points such that:

size([xi yi]) = (10000,2)

I can't do it with interp1 because the curve doesn't have unique solutions (see below), so it needs to perform as a 'local' interpolation of some sort. I found a workaround with the interpm2 function, but it's slower than I would like to. Any ideas?

Thanks!