三次样条曲线的选点修改法

本文根据样条曲线的力学性质,提出新的光顺准则和选点修改的方法,并推导出修改量和修改方向均较为合理的综合计算公式。通过实船计算表明,本方法能较准确地依次找到引起样条曲线不光顺的最坏的型值点,并逐一进行有效的修改,最后达到曲线上各节点的外力符号分片同号,力的大小过渡均匀,即基本达到所谓精光顺的要求。由于选点准确,同时又是局部修改,所以在对船体进行三向光顺计算时收敛也较快。本计算方法的应用条件是:需要修顺的曲线必须能用点点通过的三次样条曲线进行拟合,然后才能进行选点修顺。

METHOD FOR MODIFYING THE CHOSEN POINT OF CUBIC SPLINE CURVES

A new criterion for fairing, and a rational formula for modifying the chosen point have been achieved by utilizing the mechanical characteristics of spline curves. It has been proved in practice that utilizing this method, effective modification can be performed step by step by accurately judging the worst point which causes unfairing to the spline curve, and that forces acting on joint points within an interval take the same sign and change uniformly so that the requirements for fairing are met. As choice of the point to be modified is accurate and modification can be carried out locally, the exact curve can be converged rapidly by calculation during fairing three-dimensional lines of the hull.