Abstract: How to determine the shape parameters of cubic β-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.

Key words: genetic algorithm, energy optimization method, β-spline, shape parameters

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。

关键词: 遗传算法, 能量优化法, β样条, 形状参数