Abstract: The normal estimation algorithms based on segmentation usually construct affinity matrix by the difference of initial normal. The results for thin sharp features and some smooth surfaces are not very well due to the absence of distance between points. This paper combines the difference of normal and the position information of points by the geodesic path. Firstly, for the neighborhoods of some points, we find the geodesic paths between the neighborhood points, and the similarity between two points is calculated by accumulating the difference of points’ initial normal on the path connecting them. Then, the spectral segmentation is used to segment each neighborhood, and one subneighborhood is selected to estimate the normal. Finally, in order to reduce the computational cost of the algorithm, a normal constrained subspace structure propagation algorithm is proposed, and the segmentation results of the remaining neighborhoods are inferred from the existing segmentation results. Experimental results on simulation and real scan data show that the proposed algorithm is capable of overcoming noise and anisotropic samplings, while preserving sharp features within the original point data.