Deformation Detection of the Centroid Axes for Beams with Variable Cross-Sections Based on Point Cloud Data

Accurate extraction of the centroid axes of beams with variable cross-sections is critical for infrastructure health monitoring. While 3D laser scanning provides dense point clouds, existing methods face challenges due to fixed slicing directions, sparse or incomplete boundaries, and inaccurate centroid calculations for concave sections. This study proposes a robust framework to overcome these issues. An improved k-d tree ordering algorithm enhances boundary extraction through starting point constraint strategy and dynamic isolated noise point removal mechanism. A ray casting-based boundary-constrained Delaunay triangulation centroid calculation algorithm accurately computes centroids for arbitrary shapes, including concave profiles. An innovative convex hull centroid-driven adaptive normal iterative slicing method dynamically adjusts orientation using historical centroid data, aligning with the local member axis to minimize errors in variable or deformed regions. Experimental validation shows the method outperforms traditional fixed-direction slicing in effectiveness, parameter sensitivity, and deformation robustness, achieving sub-millimeter accuracy. Applied to monitor ultra-high-performance concrete cantilever beams at the Shanghai Grand Opera House, it produced centroid axis data consistent with total station measurements (differences within ±1.2 mm), supporting phased deformation warnings and safety assessments. This work provides a systematic, high-precision solution for extracting geometric axes from complex structural point clouds.