3D power line reconstruction is one motivation for power line patrols using LiDAR systems mounted on helicopters. Two new models for 3D power line reconstruction are proposed. The first model combines a line segment and a catenary, while the second model is a combination of a line segment and a parabola. In both models, the line segment is located in the xy
-plane, and the catenary or the parabola is on a vertical plane through the line segment. The two proposed models are innovative in that a scalar factor was employed as the parameter for the catenary and the parabola. The scalar factor is calculated by projecting a 2D point on the xy
-plane onto a fitted line by the 2D points. Specifically, a 2D point is constructed by projecting a 3D LiDAR point on the xy
-plane. Six experimental data sets and four criterion were used to test the six methods for 3D power line reconstruction. These experiments suggest that he second model has the highest efficiency and reconstruction accuracy. Moreover, three factors, including the selection of the vertical plane, selection of the projected models in the vertical plane, and consideration of the errors, have significant influences on the performance of the methods for 3D power line reconstructions.