Particle-based meta-model for continuous breakpoint optimization in smooth local-support curve fitting

•We compute a smooth meta-model of a given set of data points based on local-support free-form parametric curves.•Our method applies a particle-based metaheuristic approach to determine optimal values of unknowns of the fitting curve.•The method does not assume any knowledge about the underlying function of data beyond the data points.•Our approach performs well and in a fully automatic way even for underlying functions exhibiting challenging features.•Our experiments show that our approach outperforms previous approaches in terms of generality and fitting error accuracy.

This paper concerns the process of computing the underlying function of a given set of data points. In many cases, it is not possible to obtain an analytical solution for this problem so the goal is transformed into that of computing a meta-model instead. In this paper we seek to compute a smooth meta-model of such points based on local-support free-form parametric curves. Given an initial parameterization, our method applies a particle-based metaheuristic approach to determine optimal values for the breakpoints and poles of the fitting curve, which is well-known to be a continuous nonlinear optimization problem. The performance of our approach is evaluated by its application to two illustrative examples: a synthetic academic shape and a real-world shape. Our experimental results show that the proposed scheme performs very well, even for shapes with underlying functions exhibiting challenging features, such as self-intersections and sharp changes of curvature. Comparative results show that our approach outperforms previous approaches in terms of generality and fitting error accuracy.