Traditional digital geometry mainly focuses on local geometric features such as curvature and normal of 3D models. Although the curvature can describe the geometric curvature of the model surface, these local geometric properties cannot describe the global functional structure and associated properties of the 3D model. The purpose of this paper was to study the accurate splicing of cultural relic fragments based on the intrinsic structural features of the 3D model, such as geometry, texture, and function, whose method is the key to realizing the virtual reconstruction of damaged cultural relics. In this paper, a method for analyzing the intrinsic structure of 3D point cloud data is proposed, the feature representation method of 3D discrete curves and surfaces is studied, and a method for identifying geometric features of 3D point clouds based on the similarity measure of the principal curvature is proposed, which realizes the effective extraction of geometric features of the 3D point cloud model of cultural relics. By calculating the visual curvature distribution of the model under multiscale constraints, the effective extraction of the structural primitives of cultural relics with rich surface noise is realized. The experimental results in this paper show that the initial matching time is 1.416 seconds, the final matching time is 1.555 seconds, the average number of iterations is 13, the average stitching error is 1.7233 mm, and the standard deviation is 1.0265 mm. The experimental data show that the algorithm proposed in this chapter has good convergence characteristics and effectively avoids the divergence phenomenon that is easy to occur in the existing stitching algorithms.