B-spline surface fitting with knot position optimization
In linear least squares fitting of B-spline surfaces, the choice of knot vector is essentially important to the quality of the approximating surface. In this paper, a heuristic criterion for optimal knot positions in the fitting problem is formulated as an optimization problem according to the geometric feature distribution of the input data. Then, the coordinate descent algorithm is used for the optimal knot computation. Based on knot position optimization, an iterative surface fitting framework is developed, which adaptively introduces more knot isolines passing through the regions with more complex geometry or large fitting errors. Hence, the approximation quality of the reconstructed surface is progressively improved up to a pre-specified threshold. We test several models to demonstrate the efficacy of our method in fitting surface with distinct geometric features. Different from the knot placement technique (NKTP method) proposed in Piegl and Tiller  and the dominant-column-based fitting method (DOM-based method) (Park ) which require input data in semi-grid or grid form, our algorithm takes more general data points as input, i.e., any scattered data sets with parameterization. Comparing to NKTP method and DOM-based method, our method efficiently produces more accurate results by using the same number of knots.
Publication Source (Journal or Book title)
Computers and Graphics (Pergamon)
Zhang, Y., Cao, J., Chen, Z., Li, X., & Zeng, X. (2016). B-spline surface fitting with knot position optimization. Computers and Graphics (Pergamon), 58, 73-83. https://doi.org/10.1016/j.cag.2016.05.010