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). 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. 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. 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.