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Song, Xinghua; Aigner, Martin; Chen, Falai; Jüttler, Bert

Circular spline fitting using an evolution process. (English) Zbl 1185.65031

J. Comput. Appl. Math. 231, No. 1, 423-433 (2009).
A circular spline curve consists of circular arcs and line segments which are joined with \(G^1\) continuity. The authors propose an evolution method for approximating a given sequence of points in three-dimensional space by a circular spline curve, which allows simple and explicit closest point computation. The method uses an independent set of shape parameters and extends previous work on planar curves. It is proved that the evolution process based on least-squares approximation is equivalent to a Gauss-Newton-type method. The numerical performance of the algorithm is also demonstrated.
Reviewer: Aurelian Bejancu (Safat)

Cited in 4 Documents

MSC:

65D17 Computer-aided design (modeling of curves and surfaces)
65D10 Numerical smoothing, curve fitting
65D07 Numerical computation using splines
65Y20 Complexity and performance of numerical algorithms

Keywords:

circular spline; biarc; organized points; spatial curve fitting; evolution method; least-squares approximation; Gauss-Newton-type method; performance; algorithm
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References:

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