Point cloud registration plays a central role in various applications, such as 3D scene reconstruction, preservation of cultural heritage and deformation monitoring. The point cloud data are usually huge. Processing such huge data is very time-consuming, so a fast and accurate registration method is crucial. However, the existing registration methods still have high computation complexity or low accuracy. To address this issue, we develop a registration method for terrestrial point clouds. The method projects the point clouds onto the horizontal plane. Therefore, our method processes point cloud data in 2D space, leading to high computation efficiency. Then, the 2D feature lines are extracted from the projected point clouds. We calculate the intersection points of the 2D feature lines, which are treated as the 2D feature points. Due to the high accuracy of the 2D feature lines, the 2D feature points also have high accuracy. Thus, our method can get accurate registration results. Afterward, the feature triangles are constructed by using the 2D feature points, and the geometric constraints are utilized to find the corresponding feature triangles for calculating the 2D transformation. This strategy boosts the process of searching for the corresponding 2D feature points. Subsequently, the Z-axis displacement is computed by the cylindrical neighbourhoods. By combining the Z-axis displacement and 2D transformation, the 3D rigid transformation is obtained. Experimental evaluation conducted on two publicly available datasets well demonstrate that the proposed registration method can achieve good computational efficiency and high accuracy. The code will be available at: https://github.com/taowuyong?tab=repositories after publication.