采用正交函数优化三维自由曲面

摘要

自由曲面重建时,一般采用增加控制点个数来提高曲面拟合精度,但控制点的增加会引起曲面连续阶数变低.通过分析传统算法在曲面拟合中的不足,提出采用正交函数的曲面拟合方法,该算法避开不规则数据点进行拟合,保证了曲面的光顺性.当采用3×3阶曲面,36个控制点进行曲面拟合时,曲面重构最大误差仅为0.077 0mm,曲面满足G2曲率连续.实验结果表明,所提出的曲面优化算法,实现了曲面控制点数与曲面光顺和重构精度的最佳匹配,提高了曲面拟合的品质.%In free surface fitting,the method of increasing control points to improve surface fitting accuracy is generally utilized.But with the increment of control points,the order of surface continuity decreases.According to the disadvantages of the traditional method of surface reconstruction,the surface fitting algorithm using orthogonal function is proposed.It avoids irregular points to implement surface fitting,which can ensure the smoothness of the surface.3 ×3 order surface and 36 control points are used in surface fitting with the maximum error 0.077 0ram,and the surface patches are G2 curvature continuous.Experimental results show that the proposed method realizes the best matching of surface control points,surface curvature and reconstruction precision.The quality of surface reconstruction is greatly improved.