Adaptive knot placement in B-spline curve approximation

Li, Weishi; Xu, Shuhong; Zhao, Gang; Goh, Li Ping

doi:10.1016/j.cad.2004.09.008

Cited by 117 publications

(77 citation statements)

References 7 publications

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“…The method in [68] performs an optimal control over the knots, which is generally difficult to achieve. Other methods use curvature information extracted from input data and are, therefore, restricted to smooth data points [10,30,42,46,51,56]. And since noise in the curvature is more severe than noise in data themselves, all these methods are strongly affected by the noise intensity.…”

Section: Previous Workmentioning

confidence: 99%

Elitist clonal selection algorithm for optimal choice of free knots in B-spline data fitting

Gálvez

Iglesias

Avila

et al. 2015

Applied Soft Computing

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Section: Previous Workmentioning

confidence: 99%

Elitist clonal selection algorithm for optimal choice of free knots in B-spline data fitting

Gálvez

Iglesias

Avila

et al. 2015

Applied Soft Computing

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“…2 for details). Among them, the free-form parametric functions (such as Bézier, B-spline and NURBS) are widely applied in many industrial settings due to their great flexibility and the fact that they can represent smooth shapes with only a few parameters (Barnhill 1992;Jing and Sun 2005;Li et al 2005;Park 2004;Park and Lee 2007). Although it is possible to obtain good fitting results for a number of shapes, these families of functions are still limited: since they are based on polynomials, they cannot adequately describe some particular shapes, such as the quadrics (see our discussion in Sect.…”

Section: Motivationmentioning

confidence: 99%

Memetic electromagnetism algorithm for surface reconstruction with rational bivariate Bernstein basis functions

Iglesias

Gálvez

2016

Nat Comput

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Surface reconstruction is a very important issue with outstanding applications in fields such as medical imaging (computer tomography, magnetic resonance), biomedical engineering (customized prosthesis and medical implants), computer-aided design and manufacturing (reverse engineering for the automotive, aerospace and shipbuilding industries), rapid prototyping (scale models of physical parts from CAD data), computer animation and film industry (motion capture, character modeling), archaeology (digital representation and storage of archaeological sites and assets), virtual/augmented reality, and many others. In this paper we address the surface reconstruction problem by using rational Bézier surfaces. This problem is by far more complex than the case for curves we solved in a previous paper. In addition, we deal with data points subjected to measurement noise and irregular sampling, replicating the usual conditions of real-world applications. Our method is based on a memetic approach combining a powerful metaheuristic method for global optimization (the electromagnetism algorithm) with a local search method. This method is applied to a benchmark of five illustrative examples exhibiting challenging features. Our experimental results show that the method performs very well, and it can recover the underlying shape of surfaces with very good accuracy.

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“…On the other hand, when we use non-uniform B-spline fitting, we have to solve a multivariate and multimodal nonlinear optimization problem in order to determine the control points and knot vector. To address this problem, methods for adaptive knot placement have been proposed by using a heuristic rule [12], a genetic algorithm [31], a stochastic algorithm [19], and L 1 optimization [11].…”

Section: Related Workmentioning

confidence: 99%