Grouping and parameterizing irregularly spaced points for curve fitting

Given a large set of irregularly spaced points in the plane, an algorithm for partitioning the points into subsets and fitting a parametric curve to each subset is described. The points could be measurements from a physical phenomenon, and the objective in this process could be to find patterns among the points and describe the phenomenon analytically. The points could be measurements from a geometric model, and the objective could be to reconstruct the model by a combination of parametric curves. The algorithm proposed here can be used in various applications, especially where given points are dense and noisy. Examples demonstrating the behavior of the algorithm under noise and density of the points are presented and discussed.