High-voltage and ultra-high-voltage overhead power lines are important to meet the electricity demand of our daily activities and productions. Due to the overgrowth of trees/vegetation within the corridor area, the distance between the power lines and its surroundings may break through the safety threshold, which could cause potential hazards such as discharge and fire. To ensure the safe and stable operation of the power lines, it is necessary to survey them regularly so that the potential hazards from the surroundings within the power line corridor could be investigated timely. This paper is motivated to quickly and accurately survey the power line corridor with the 3D point clouds. The main contributions of this paper include: (1) the spatial line clustering is proposed to accurately classify and complete the power line points, which can greatly overcome the sparsity and missing of LiDAR points within the complex power line corridor. (2) The contextual relationship between power lines and pylon is well investigated by the grid-based analysis, so that the suspension points of power lines on the pylon are well located. (3) The catenary plane-based simplification of 3D spatial distance calculation between power lines and ground objects facilitates the survey of the power line corridor. Experimental results show that the accuracy of safety distance surveying is 5 cm for power line corridors of all voltage levels. Compared to the ground-truth point-to-point calculation, the speed of surveying is enhanced thousands of times. It is promising to greatly improve both the accuracy and efficiency of surveying the potential hazards of power line corridor.