Efficient Adaptive Sampling Methods Based on Deviation Analysis of Piecewise Cubic Spline Interpolation

The on-machine inspection technique requires a certain manufacturing time, so it is important for a sampling approach to achieve high precision for a fixed number of inspection points. This study designs an efficient adaptive sampling method for the non-uniform rational basis spline (NURBS) curves and surfaces based on deviation analysis. For the free-form curves, it is an iterative method that is used to remove points that are less significant to the reconstruction error from the dense points on the curve. That is, the points are ranked by their maximum deviation from the theoretical curves. Different from the existing methods, a closed-form is derived to approximate the maximum deviation by analyzing the curve reconstruction method, i.e., piecewise cubic spline interpolation. The proposed method is compared with recent curve sampling methods, and the comparison results have shown that, under the same number of inspection points, the reconstruction error of the proposed method is reduced by 82%. The proposed curve sampling algorithm is then further extended to surface sampling, where the global characteristics of a surface are extracted as a series of curves on the surface. Thus, surface sampling is simplified to curve sampling in two directions. The proposed surface sampling strategy is compared with classic surface sampling methods using three representative surfaces. The results show that by using the proposed surface sampling strategy, the reconstruction error is reduced significantly. By applying our sampling method to the on-machine inspection system, the inspection accuracy can be greatly improved.