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

Akemi Gálvez and Andrés Iglesias

Applied Mathematics and Computation, 2016, vol. 275, issue C, 195-212

Abstract: 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.

Keywords: Particle swarm; Meta-model; Breakpoint optimization; Local-support curves; Curve fitting; CAD/CAM (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:275:y:2016:i:c:p:195-212

DOI: 10.1016/j.amc.2015.11.050

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