用遗传算法确定三次β样条曲线的形状参数

摘要

研究了三次β样条曲线插值中形状参数的选取问题.给出了三次β样条曲线的能量模型,提出了一种用遗传算法确定插值三次β样条曲线形状参数的方法.对于给定的插值点,以曲线的形状参数作为决策变量,以插值曲线的能量最小作为目标,利用遗传算法确定最优形状参数.实验结果表明利用该算法得到的插值曲线具有较好的光顺性.%How to determine the shape parameters of cubicβ-spline curves to interpolate given points is considered. The energy model is introduced for cubic β-spline curves and a new method is proposed for determining the shape parameters of β-spline curves based on genetic algorithm. For given points,the shape parameters are determined by minimizing the energy of the interpolating β-spline curves using genetic algorithm.The experiments show that the interpolating cubic β-spline curves obtained by this algorithm possesses good fairness and smoothness.