基于广义延拓逼近法的复杂曲面重构研究

Research on the Complicated Surface Reconstruction Based on Generalized Extended Interpolation Method

针对逆向工程中复杂曲面重构,基于广义延拓逼近法,提出一种逼近算法。该算法一方面能在分片边界点上满足插值条件,使得各分片之间的变化具有一定的协调性;另一方面,利用分片插值区域周围结点(包括内点)的信息,实现分片区域内部的最佳逼近,同时算法又使曲面形状具有局部可控性、变差减少性和凸包性等特性。仿真实例证实,该算法改善了传统逼近算法方法在重构曲面时产生的失真和运算的不稳定现象,并且得到较高的曲面重构精度,具有计算稳定、快速和方便的优点。

For the complicated curved surface reconstruction in reverse engineering-oriented, a approach algorithm for handling 3D scan point cloud data was presents, based on generalized extended interpolation method.On one hand, this algorithm could meet the interpolation conditions on the partitioned boundary points and make the changes between partitions assort with each other. On the other hand, by using junction points, including inner points, which are around the partitioned interpolation area, we achieved the best approach inside partitioned area. Meanwhile, this algorithm makes the curved surface possess the features of partial controllability, error reduction, and convex hull. The simulated sample approved that this algorithm could improve the distortion of curved surface and unstable situation when using typical approach methods. Moreover, it could achieve higher precision of curved surface reconstruction. Finally, this algorithm has the advantages of stable calculation, speediness and convenience.