Optimal smoothing and interpolating splines with constraints
Optimal smoothing and interpolating splines with constraints
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DOI：
10.1016/j.amc.2011.06.067
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发表时间：
2007-12
期刊：
影响因子：
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通讯作者：
H. Kano;H. Fujioka;C. Martin
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文献类型：
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作者：
H. Kano;H. Fujioka;C. Martin
本文考虑了设计具有等式和/或不等式约束的最优平滑和插值样条的问题。样条是通过采用归一化均匀B样条作为基函数，即k次移位B样条的加权和而构成的。那么一个中心问题是确定所谓控制点的最佳向量。通过采用这种方法，表明各种类型的约束被表示为控制点的线性函数，并且问题简化为二次规划问题。我们通过数值例子证明了其有效性和实用性，包括概率密度函数的近似、不连续函数的近似和轨迹规划。
This paper considers the problem for designing optimal smoothing and interpolating splines with equality and/or inequality constraints. The splines are constituted by employing normalized uniform B-splines as the basis functions, namely as weighted sum of shifted B-splines of degree k. Then a central issue is to determine an optimal vector of the so-called control points. By employing such an approach, it is shown that various types of constraints are formulated as linear function of the control points, and the problems reduce to quadratic programming problems. We demonstrate the effectiveness and usefulness by numerical examples including approximation of probability density functions, approximation of discontinuous functions, and trajectory planning.