Blade surface reconstruction is one of the necessary steps in blade adaptive machining system. The majority of the current reconstruction methods are based on point-cloud, which is obtained using noncontact measurements. Correspondingly, these methods are invalid when the points are obtained using contact measurements. In this paper, we studied the method of surface reconstruction for thin features based on measured contact points. Owing to the random order of the measured points, and the fact that when the distance between two measured points is larger than the wall thickness of the blade will lead to interpolation errors, a quad tree-based region division method, and a points sorting algorithm, are proposed for correctly ordering the points. On this basis, inverse interpolation of cross-sectional curves using a cubic NURBS curve is used to fit them and reconstruct surfaces. Surface reconstruction examples are presented herein, and a comparison between the reconstructed and designed surfaces is used to verify the validity of our method.
Two theorems on inverse interpolation