A plot with the fitted ln curve overlay would be helpful to check goodness of fit. It looks like 30-45 is actually somewhat linear and not ln, and without domain knowledge about what x and y are I find it difficult to propose curve fits about what looks to be a piecewise function
Even in 3D space, the number of vectors in a given angle to another vector are infinite, so which would you pick in an n dimensional space? In general calculating the angle between two vectors is a loss-introducing function (you take two sets of n numbers and condense it down to one). You can narrow it down to a set of N-1 linearly independent vectors that form a base of the given set of vectors in a given angle. Somebody with more linear algebra knowledge feel free to correct me.