Multidimensional curve fitting to unorganized data points by nonlinear minimization

Many papers have addressed the problem of fitting curves to data points. However, most of the approaches are subject to a restriction that the data points must be ordered. The paper presents a method for generating a piecewise continuous parametric curve from a set of unordered and error-filled data points. The resulting curve not only provides a good fit to the original data but also possesses good fairness. Excluding the endpoints of the curve, none of the connectivity information needs to be specified, thus eliminating the necessity of an initial parameterization. The standard regularization method for univariate functions is modified for multidimensional parametric functions and results in a nonlinear minimization problem. Successive quadratic programming is applied to find the optimal solution. A physical model is also supplied to facilitate an intuitive understanding of the mathematical background.