How to determine path from noisy X, Y data

Question

I have an unsorted list of noisy X, Y points. They do, however, form a path through the world. I would like an algorithm to draw an approximation of this data using line segment

Answer 1

The problem with the Bezier curve is that is doesn't actually go though the points you have sampled and even though the points samples are distorted a little; the bezier curve might actually be miles off.

A better approximation, and a solution that seems to resemble the original image way better is a Catmull-Rom Spline because it does run though all the points in the curve.