Multimedia Tools and Applications

, Volume 77, Issue 23, pp 30331–30351 | Cite as

Shape modeling based on specifying the initial B-spline curve and scaled BFGS optimization method

  • A. Ebrahimi
  • G. Barid LoghmaniEmail author


In this paper, we consider the problem of fitting the B-spline curves to a set of ordered points, by finding the control points and the location parameters. The presented method takes two main steps: specifying initial B-spline curve and optimization. The method determines the number and the position of control points such that the initial B-spline curve is very close to the target curve. The proposed method introduces a length parameter in which this allows us to adjust the number of the control points and increases the precision of the initial B-spline curve. Afterwards, the scaled BFGS algorithm is used to optimize the control points and the foot points simultaneously and generates the final curve. Furthermore, we present a new procedure to insert a new control point and repeat the optimization method, if it is necessary to modify the fitting accuracy of the generated B-spline fitting curve. Associated examples are also offered to show that the proposed approach performs accurately for complex shapes with a large number of data points and is able to generate a precise fitting curve with a high degree of approximation.


Geometric modeling Curve fitting Initial B-spline curve Optimization method Scaled BFGS method 



The authors would like to thank anonymous referees for their helpful comments and useful suggestions which improved our paper considerably.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Computer Geometry and Dynamical Systems Laboratory, Faculty of Mathematical SciencesYazd UniversityYazdIran

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