The Research Of Sampling Plan Of Inspection Points Based On Uniform B-spline Fitting

With the widely application of computers, curves and surfaces defined by mathematical methods have been put into practical applications, which greatly promoted the emergence and development of CAGD. Information of object surface can be acquired from taking sample points from the known CAD model with CMM, which is usually fitted as an substitute surface, and the error between substitute and the original CAD model can be seen as the precision of samples. The issue of measuring samples is important in mechanical manufacturing, because sometimes the accuracy of measurement affect the quality and precision of products. The research of sampling plan of inspection points based on uniform B-spline fitting is mainly discussed in the thesis.To improve the B-spline curve fitting accuracy, two methods are more commonly used, one is to increase the polynomial order, and the other is to increase the number of polynomial segments. In order to avoid the occurrence of a large amount of computing unstable situation by using high-order polynomial to calculate, uniform cubic B-spline curves and surfaces interpolation is focused in this thesis. The B-spline curve/surface fitting accuracy is improved by increasing the number of polynomial segments, which is the origin of the algorithm referred. The specific practice of curve algorithm is:first a series of reasonable data points depending on the size of curvature should be taken, the B-spline fitting curve is built with a few sample points using least squares fitting method, the minimum distances between the fitting curve and remaining data points are calculated to select the next interpolation point, which aimed to increase the number of polynomial segments interpolation, and the curve interpolation continues until meet the accuracy requirements. This algorithm includes an improved constrained Newton iterative method to calculate the minimum distance between the data point and the curve, with the least squares fitting method to get unknown control points. Since surface is an extension of the curve, the surface algorithm is focused on how to construct the whole control grid vertices, and how to surface in the process of iterative search to.determine position at the first step and calculate, effectively improve the fitting efficiency. Because the gap between the interpolation curve or surface and the original model is small, the final interpolation points can be seen as a sampling strategy with CMM. Finally, in order to prove the referred B-spline curve/surface interpolation method has good effect, some simulation models using matlab software are built, including the cubic and quartic b-spline curve/surface fitting model, the curve/surface fitting models with and without fairness. The experiment results confirmed that a large amount of high order polynomial calculation and bad volatile situation can be avoided by the model of cubic B-spline, and the fitting effect is better because of the introduction of the fairness.A new method acquiring the CMM inspection sample points based on the improved B-spline curve/surface fitting method is introduced in the thesis. If the surface model is simple, the ordinary spacing method can meet the measuring requirements, however, once the surface is relatively complicated like the curvature change greatly, this approach is no longer applicable. With a large number of different types of matlab simulation model proofs, this method can meet the different requests of precision for sculptured surface modeling.