基于遗传算法的NURBS曲线降阶

采用遗传算法实现NURBS曲线直接降多阶。提出并证明了NURBS曲线保端点降阶的必要条件，在此基础上将NURBS曲线的节点序列、控制顶点和权用浮点数编码为基因个体，运用遗传算法，通过循环执行选择、交叉、变异求解得到最优解或者次优解。实例说明了采用该方法实现NURBS曲线降阶有较高的精确度。

Degree Reduction of NURBS Curves Based on Genetic Algorithm

The genetic algorithms is introduced to reduce several degrees in one time on NURBS curves. Before using the method, necessary conditions of NURBS curves' degree reduction with the same end points have been given and proved. The knot series control vertices and weights of NURBS curves are encoded as genes. The selection, crossover and mutation process are executed cyclically to get the global optimum or the sub-optimal by genetic algorithms. The following example proves the NURBS curves can be reduced sever...