基于L-BFGS的B样条曲线快速拟合
Fast B-spline Curve Fitting by L-BFGS
摘要：
提出了一种新的平面B样条曲线到散乱数据点的拟合方法。在传统方法中，控制点和足点的优化在每次迭代中以两个非常耗时的步骤执行：1）通过建立和求解线性方程组来更新控制点;以及2）通过将每个数据点投影到B样条曲线上来计算足点。我们的方法使用L-BFGS优化方法来优化控制点和足点同时进行，因此它不需要在每次迭代中执行矩阵计算或足点投影。因此，我们的方法比现有的方法快得多。
英文摘要：
We propose a novel method for fitting planar B-spline curves to unorganized data points. In traditional methods, optimization of control points and foot points are performed in two very time-consuming steps in each iteration: 1) control points are updated by setting up and solving a linear system of equations; and 2) foot points are computed by projecting each data point onto a B-spline curve. Our method uses the L-BFGS optimization method to optimize control points and foot points simultaneously and therefore it does not need to perform either matrix computation or foot point projection in every iteration. As a result, our method is much faster than existing methods.
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