基于缩减控制顶点数和自适应遗传算法的船体水线NURBS拟合

通过船体水线几何特点分析,研究用尽可能少的NURBS控制顶点对水线进行拟合.利用已有的水线型值数据、平边线边界点信息、首尾圆弧切点及其切线方向,对首尾自由段分别设置平边线起止点控制顶点、切矢控制顶点以及形状控制顶点,并以其权因子和相关坐标分量为设计变量,设置合适的约束条件,计算已知水线上半宽型值与所拟合的曲线上相应的半宽型值之间的误差,以最小化其中的最大相对误差为目标函数,建立优化模型,采用自适应遗传算法求解该优化问题.利用NURBS的特性,构造组合曲线,用单一NURBS函数构造任意一条由圆弧曲线、自由曲线和直线构成的水线.实船船体线型逼近和设计算例表明,应用该方法对水线进行拟合是可行的,并能满足工程设计要求,同时还可以减少船体水线NURBS表达的数据量.

NURBS approximation of hull waterline based on reduced control points number with adaptive genetic algorithm

Based on the analysis of the geometrical properties of the hull waterline, the waterline was approximated with as few NURBS control points as possible. Using the given waterline offset, the end points of its flat side line, tangent points of the fore and aft arc curves and the tangent vector, the start tangent control point, end tangent control point and form control point are set for the aft and fore free curve respectively. The optimization model is constructed with the weights and the coordinates of the control points as the design variables. The appropriate constraints are set. The objective function of this optimization problem is set to minimize the maximum value among the relative errors between the half breadth values of the the fitted waterline. An adaptive genetic And then, a waterline, combined with ar NURBS curve function. The instances of indicate that it is feasible and can satis given waterline and the corresponding ones of algorithm is applied to solving this optimization problem. c curves, free curves and lines, is described with a single the hull form approximation and design for full-scale ship fy the requirements of the engineering design to fit the waterline. Applying this method, the data used for hull waterline representation can be reduced.