Laser scanning provides an efficient solution to digital twin construction in civil engineering. The complexity and redundancy of large-scale point clouds substantially prolong the labor-intensive model reconstruction process. This paper presents an automated and high-precision geometric reconstruction approach for cable-net structures with a complete workflow from raw points to the extraction of cable shapes and forces. The strategy involves the extraction of coordinates of key cable regions through the characterization of cable geometry and local registration methods, followed by the computation of cable forces and shapes using segmented catenary theory and nonlinear optimization. The approach is validated with a single-curvature cable-net structure, with the accuracy of cable shapes within ±5 mm and errors in cable forces <5%. The method contributes to health monitoring and rapid reconstruction of cable-net structures. The precise geometry and forces will facilitate the creation of the mechanical models reflecting the physical authenticity of structures.