dc.contributor.authorDung, Van Than
dc.contributor.authorTjahjowidodo, Tegoeh
dc.contributor.editorWu, Rongling*
dc.identifier.citationDung, V. T., & Tjahjowidodo, T. (2017). A direct method to solve optimal knots of B-spline curves: An application for non-uniform B-spline curves fitting. PLOS ONE, 12(3), e0173857-.en_US
dc.description.abstractB-spline functions are widely used in many industrial applications such as computer graphic representations, computer aided design, computer aided manufacturing, computer numerical control, etc. Recently, there exist some demands, e.g. in reverse engineering (RE) area, to employ B-spline curves for non-trivial cases that include curves with discontinuous points, cusps or turning points from the sampled data. The most challenging task in these cases is in the identification of the number of knots and their respective locations in non-uniform space in the most efficient computational cost. This paper presents a new strategy for fitting any forms of curve by B-spline functions via local algorithm. A new two-step method for fast knot calculation is proposed. In the first step, the data is split using a bisecting method with predetermined allowable error to obtain coarse knots. Secondly, the knots are optimized, for both locations and continuity levels, by employing a non-linear least squares technique. The B-spline function is, therefore, obtained by solving the ordinary least squares problem. The performance of the proposed method is validated by using various numerical experimental data, with and without simulated noise, which were generated by a B-spline function and deterministic parametric functions. This paper also discusses the benchmarking of the proposed method to the existing methods in literature. The proposed method is shown to be able to reconstruct B-spline functions from sampled data within acceptable tolerance. It is also shown that, the proposed method can be applied for fitting any types of curves ranging from smooth ones to discontinuous ones. In addition, the method does not require excessive computational cost, which allows it to be used in automatic reverse engineering applications.en_US
dc.format.extent24 p.en_US
dc.relation.ispartofseriesPLOS ONEen_US
dc.rights© 2017 Dung, Tjahjowidodo. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.en_US
dc.subjectCurve fittingen_US
dc.titleA direct method to solve optimal knots of B-spline curves: An application for non-uniform B-spline curves fittingen_US
dc.typeJournal Article
dc.contributor.schoolSchool of Mechanical and Aerospace Engineeringen_US
dc.description.versionPublished versionen_US

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