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

Bezier Interpolation may fit your problem.

This does not address the ordering of the points into a path, however; there are a number of approaches to consider:

• Any "optimal" type of path (e.g. smallest direction change at each point on the path, * Shortest path through all points) will likely boil down the NP complete Travelling Salesman Problem (TSP).
• A "reasonable" path to cluster the nodes and then route between clusters, and within clusters. Of course, the larger the cluster, or the larger the number of clusters the more this smaller problem looks like a large n TSP.
• Ordering the points by one axis. If there are much more than 2 axes, some dimensional reduction strategy may be useful. e.g. Independent Component Analysis.