A note on iterative process for G2-multi degree reduction of Bézier curves
A note on iterative process for G2-multi degree reduction of Bézier curves
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DOI：
10.1016/j.amc.2011.12.055
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发表时间：
2012-02
期刊：
影响因子：
--
通讯作者：
Lizheng Lu
中科院分区：
文献类型：
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作者：
Lizheng Lu
在[A.Rababah，S.Mann，用于Bézier曲线G2多阶降阶的迭代过程，应用数学与计算217(2011)8126-8133]一文中，Rababah和Mann提出了一种在端点具有C_1和G_2连续的Bézier曲线降阶的迭代方法。在本文中，我们给出了迭代过程第一步唯一解的存在性的理论证明，而他们的证明仅适用于某些特殊情况。此外，我们还给出了迭代方法的完全收敛证明。我们用凸二次优化的方法来解决这个问题。
In the paper [A. Rababah, S. Mann, Iterative process for G2-multi degree reduction of Bézier curves, Applied Mathematics and Computation 217 (2011) 8126–8133], Rababah and Mann proposed an iterative method for multi-degree reduction of Bézier curves with C1and G2-continuity at the endpoints. In this paper, we provide a theoretical proof for the existence of the unique solution in the first step of the iterative process, while the proof in their paper applies only in some special cases. Also, we give a complete convergence proof for the iterative method. We solve the problem by using convex quadratic optimization.