自由曲面的高精度匹配技术研究

Study on High Accuracy Matching Technology of Free-form Surface

研究自由曲面的高精度匹配技术。采用两步法即粗匹配和精匹配对曲面匹配进行逐步求精:采用微分进化算法进行粗匹配,获得下一步精匹配迭代过程的初始点,解决了迭代最近点算法(ICP)存在的容易收敛于局部最优点的问题,并克服了遗传算法收敛速度较慢的缺陷;基于最小二乘准则和最小条件原则,分别采用单纯形法和坐标轮换法循环计算进行精匹配,同时对设计变量进行尺度变换,改善了优化设计数学模型的性态。以Visual C++6.0为开发工具,编程实现了自由曲面的高精度匹配。运行实例表明,上述算法是可行和有效的。

The high accuracy matching technology of free-form surface was studied.The two-step surface matching method,i.e. the rough matching step and the accurate matching step,was used to obtain higher accuracy results.In the rough matching step,the differential evolution method,which could avoid the local convergence of iterative closest point （ICP）method and overcome the draw-back of low convergence rate of genetic algorithm,was put forward to obtain initial points,which would be used in the next accurate matching step.Based on the least square criterion and the least condition principle,the simplex method and the coordinate alternation method were presented to obtain the best matching result,respectively.To improve the behavior of the mathematical model,a scale transform was done with the design variables.With the development tool Visual C＋＋6.0,a computer program was implemented to re-alize the high accuracy matching of free-form surface.An experiment was conducted to verify the validity and feasibility of these algo-rithms.