目的 为了解决从曲线库(轮廓线集合)中筛选出与期望曲线相匹配的相似曲线段问题,研究基于Kabsch算法的NURBS(非均匀有理B样条)曲线优化匹配组合方法。方法 首先提出一种基于Kabsch算法的曲线相似性判断方法,针对两条NURBS曲线上相同个数点阵,经最优旋转和平移变换得到其最小均方根偏差,进而依据基于最小均方根偏差和相似度指标判断曲线相似性;在此基础上,提出一种类似二分查找法的曲线优化匹配组合方法,对于给定相似度和最小搜索步长,通过曲线分割和相似性判断得到期望曲线分割段数最少的相似组合曲线。结果 给定一条期望的3D曲线,在相似度为0.025和最小搜索步长为0.05情况下,采用所提方法从包含4条3D曲线的曲线库中依次筛选出10段基元构建相似组合曲线。结论 提出了一种新的NURBS曲线优化匹配组合方法,实验结果表明,对不同期望曲线能高效稳定构建相对应的相似组合曲线,适用于类似碎片拼接重构问题。

Objective Non-uniform rational B-splines (NURBS) refers to a unified mathematical method for the free type of curves and surfaces. This method is invariant under common geometric transformations, such as translation, rotation, parallel, and perspective projections. The B-spline model has wide applications in the field of computer-aided design, such as determining whether two surfaces splice or not. This phenomenon depends on whether there are matching curve segments based on contour lines of the surfaces. Therefore, mosaic fragment reconfiguration can be converted to the optimal matching of the curve combinatorial problems. This paper applies the proposed method to discuss the problem of building a similar combination curve, which filters primitives from a curve library (contour set) by optimizing matching combination for an expectation curve (contour). Method Kabsch algorithm is a method for calculating the optimalrotation matrixand translation vector that minimizes the root mean squareddeviation (RMSD) between two paired sets of points. In this paper, the paired sets of points are respectively extracted from two curves described by the NURBS model. The minimum RMSD of the two curves is obtained via the optimal translation and rotation matrix transformation based on the Kabsch algorithm. If the minimum RMSD is not greater than the index of similarity, the two curves are assumed to be similar and can be superimposited through the abovementioend rotation and translation transformation. Finally, an NURBS curve optimal matching combination method is proposed with the binary search algorithm. In terms of satisfying the matching similarity conditions, the method can minimize the number of expectation curve segments. Result We assumed a 3D curve library exists for NURBS curves, and all the weights of the control points are set to 1. The index of similarity is set to 0.025, and the smallest search step is set to 0.05. According to the proposed optimal matching method, the expectation curve is divided into ten sections that are respectively similar to the corresponding primitives from the curve library. The combined curve containing ten matching primitives is similar to the expectation curve. Conclusion This paper presents a new method of NURBS curve optimization matching combination. Experimental results show that different expectation curves can be obtained based on the matching combination curve. The proposed method can be applied to solve that problem of fragment spliced reconfiguration. If the index of similarity is smaller, this means there are more expectation curve segments that could be possibly divided.According to the actual situation, selecting the appropriate index of similarity is necessary. The effectiveness of the proposed method is verified by the experiment on a 3D curve matching optimization combination.