NURBS-based freeform surface reconstruction from sparse and unstructured contact measurement data using iterative control point optimization

High-precision surface reconstruction is crucial for freeform surface measurement, and the Non-Uniform Rational B-Spline (NURBS) surface fitting is widely used in this process. To improve the NURBS surface fitting accuracy based on sparse and unstructured contact measurement data, this paper proposes a freeform surface reconstruction method that integrates NURBS surface fitting with iterative control point coordinate optimization. The proposed method begins by employing cubic spline interpolation to generate uniformly spaced fitting points from measurement data. Then, the fitting point is parameterized by chord length parameterization and the initial NURBS surface parameter is obtained with least squares fitting. Subsequently, an iterative control point coordinate optimization strategy is applied to reconstruct the surface. In this strategy, the distance between measurement points and the fitted NURBS surface is calculated, and then a new index, the sum of local squared distances (SLSD) is introduced. According to the calculated SLSD, the NURBS surface is reconstructed locally and iteratively by optimizing the control point coordinates corresponding to the max SLSD. With the proposed strategy, only one control point is optimized at a time, and the parameterization results of measurement points within the influence region of the control point are optimized simultaneously. Experiment result shows that the reconstruction accuracy of the proposed method is higher than 0.02 mm.