Accurate vegetation-encroachment assessment and risk mitigation require electric utilities to accurately locate and characterize distribution-network assets, including poles and power lines, and distinguish among medium-voltage, low-voltage, neutral, and telecommunication lines. Mobile and aerial Light Detection and Ranging (LiDAR) point clouds provide detailed 3D representations of these assets and their surroundings. However, power-line detection and reconstruction remain challenging because conductor returns are often sparse, incomplete, noisy, or occluded by vegetation. These challenges are especially significant in distribution networks, where lower pole heights and complex line configurations place conductors close to trees. In addition, mobile and aerial LiDAR datasets differ substantially in point density, viewing geometry, spatial coverage, and occlusion patterns. We propose a robust and automated reconstruction method combining scaled density-based clustering, robust polynomial fitting, and iterative fragment merging to recover individual conductors under severe data incompleteness and occlusion. Following semantic classification, the same reconstruction pipeline processes both mobile and aerial LiDAR data without modality-specific code or parameter tuning. The method is evaluated through degradation experiments, benchmarking, parameter sensitivity analysis, and large-scale validation. On the aerial dataset, it achieves 96.87% precision, 96.66% recall, a 96.76% F$_1$-score, and a geometric RMSE of 0.127 m. On the mobile dataset, where conductor-level reference annotations were unavailable, it achieves a point-to-model RMSE of 0.045 m and a reconstruction coverage of 95.27%. Source code, documentation, and evaluation data are publicly available at https://github.com/varen-project.

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