A direct method to solve optimal knots of B-spline curves: An application for non-uniform B-spline curves fitting.
A direct method to solve optimal knots of B-spline curves: An application for non-uniform B-spline curves fitting.
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DOI：
10.1371/journal.pone.0173857
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发表时间：
2017
期刊：
影响因子：
3.7
通讯作者：
Tjahjowidodo T
中科院分区：
文献类型：
--
作者：
Dung VT;Tjahjowidodo T
B样条函数广泛应用于许多工业应用中，例如计算机图形表示，计算机辅助设计，计算机辅助制造，计算机数控等。最近，存在一些需求，例如在逆向工程（RE）领域，采用B样条曲线的非平凡情况下，包括曲线与不连续点，尖点或转折点从采样数据。在这些情况下，最具挑战性的任务是在最有效的计算成本在非均匀空间中的节点的数量和它们各自的位置的识别。本文提出了一种用B样条函数局部拟合任意形状曲线的新方法。提出了一种新的快速节点计算的两步法。在第一步中，使用具有预定允许误差的二分方法对数据进行分割，以获得粗结。其次，节点优化，为位置和连续性水平，采用非线性最小二乘法。因此，B样条函数是通过求解普通的最小二乘问题得到的。所提出的方法的性能进行了验证，通过使用各种数值实验数据，有和没有模拟噪声，这是由一个B样条函数和确定性参数函数产生的。本文还讨论了所提出的方法对现有的方法在文献中的基准。所提出的方法被证明是能够重建B样条函数从采样数据在可接受的公差。它也表明，该方法可以适用于拟合任何类型的曲线，从光滑的不连续的。此外，该方法不需要过多的计算成本，这使得它可以用于自动逆向工程应用。
B-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.