Modified Bézier Curves with Shape-Preserving Characteristics Using Differential Evolution Optimization Algorithm | Zendy

Mohammad Asif Zaman | Zendy; Shuvro Chowdhury | Zendy

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Modified Bézier Curves with Shape-Preserving Characteristics Using Differential Evolution Optimization Algorithm

Author(s) -

Mohammad Asif Zaman,

Shuvro Chowdhury

Publication year - 2013

Publication title -

advances in numerical analysis

Language(s) - English

Resource type - Journals

eISSN - 1687-9570

pISSN - 1687-9562

DOI - 10.1155/2013/858279

Subject(s) - mathematics , parametric equation , bézier curve , curve fitting , parametric statistics , algorithm , differential equation , differential (mechanical device) , least squares function approximation , shape parameter , data point , mathematical optimization , mathematical analysis , geometry , statistics , estimator , engineering , aerospace engineering

A parametric equation for a modified Bézier curve is proposed for curve fitting applications. The proposed equation contains shaping parameters to adjust the shape of the fitted curve. This flexibility of shape control is expected to produce a curve which is capable of following any sets of discrete data points. A Differential Evolution (DE) optimization based technique is proposed to find the optimum value of these shaping parameters. The optimality of the fitted curve is defined in terms of some proposed cost parameters. These parameters are defined based on sum of squares errors. Numerical results are presented highlighting the effectiveness of the proposed curves compared with conventional Bézier curves. From the obtainedresults, it is observed that the proposed method produces a curve that fits the data points more accurately

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