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

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  • Gálvez, Akemi
  • Iglesias, Andrés

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.

Suggested Citation

  • Gálvez, Akemi & Iglesias, Andrés, 2016. "Particle-based meta-model for continuous breakpoint optimization in smooth local-support curve fitting," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 195-212.
    • Handle: RePEc:eee:apmaco:v:275:y:2016:i:c:p:195-212
    DOI: 10.1016/j.amc.2015.11.050
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    References listed on IDEAS

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    1. Yuan Yuan & Nan Chen & Shiyu Zhou, 2013. "Adaptive B-spline knot selection using multi-resolution basis set," IISE Transactions, Taylor & Francis Journals, vol. 45(12), pages 1263-1277.
    2. Matthew Martin, 1997. "Introduction," African Development Review, African Development Bank, vol. 9(1), pages 1-19.
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