Abstract:

Free-form curve reconstruction method was proposed based on an IGA. The IGA employed real coding and generation-alternation model based on the minimal generation gap(MGP) and blend crossover operators (BLX-α). Compared with conventional optimization methods, it has the advantages of simple algorithm and high optimization efficiency. Firstly, free-form curve was expressed by NURBS. The average value of Euclidean distance between the points on reconstructed curve and measured data was regarded as the objective function. Curve parameterization, knot vectors and the weights of control points were optimized by IGA. Then, the coordinates of control points were calculated by the least square method according to the parametric values of data points and the weights of control points optimized by IGA and then the free-form curve was reconstructed. Finally, the experimental results show the proposed method has the advantages of rapid computation speed, high accuracy of reconstructed curve, and has strong robustness and it can reconstruct free-form curve with different degrees and different numbers of control points. 

Key words: free-form curve reconstruction, improved genetic algorithm(IGA), non-uniform rational B-spline(NURBS);blend crossover operator

摘要：

提出一种基于改进遗传算法的自由曲线重建方法,该改进遗传算法基于实数编码,采用基于代沟最小的代选择模型,选用BLX-α混合交叉算子,算法简单、优化效率高;其中用非均匀有理B样条表示自由曲线,以重建曲线上点与测得数据点间的欧式距离的平均值作为目标函数,曲线参数化、节点向量及控制顶点的权值通过改进遗传算法优化确定,再根据已确定的数据参数和控制顶点权值用最小二乘法计算控制顶点坐标,完成自由曲线重建。实例证明,该算法不仅计算速度快,重建曲线精度高,而且算法鲁棒性强,可以方便地实现不同次数和不同控制顶点个数的自由曲线重建。
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关键词: 自由曲线重建, 改进遗传算法, 非均匀有理B样条, 混合交叉算子