Surface Fitting for Quasi Scattered Data from Coordinate Measuring Systems

Non-uniform rational B-spline (NURBS) surface fitting from data points is wildly used in the fields of computer aided design (CAD), medical imaging, cultural relic representation and object-shape detection. Usually, the measured data acquired from coordinate measuring systems is neither gridded nor completely scattered. The distribution of this kind of data is scattered in physical space, but the data points are stored in a way consistent with the order of measurement, so it is named quasi scattered data in this paper. Therefore they can be organized into rows easily but the number of points in each row is random. In order to overcome the difficulty of surface fitting from this kind of data, a new method based on resampling is proposed. It consists of three major steps: (1) NURBS curve fitting for each row, (2) resampling on the fitted curve and (3) surface fitting from the resampled data. Iterative projection optimization scheme is applied in the first and third step to yield advisable parameterization and reduce the time cost of projection. A resampling approach based on parameters, local peaks and contour curvature is proposed to overcome the problems of nodes redundancy and high time consumption in the fitting of this kind of scattered data. Numerical experiments are conducted with both simulation and practical data, and the results show that the proposed method is fast, effective and robust. What's more, by analyzing the fitting results acquired form data with different degrees of scatterness it can be demonstrated that the error introduced by resampling is negligible and therefore it is feasible.