Self-Referential Generalized-Cylinder Fitting for Mast Deformation Measurement from UAV Point Clouds

Dimensional control of tall-ship masts is difficult: rigging occludes deck-based surveys, and registration to a design model assumes it matches the as-built structure. We present a deterministic, self-referential method that measures mast bending from an unmanned aerial vehicle (UAV) photogrammetric point cloud without a computer-aided design model. Each mast is modeled as a tapered generalized cylinder: slices are fitted with trimmed circles, flare and rigging-band slices are rejected, and an uncertainty-weighted centerline is split into rake and bending. A five-mast shared-curvature test provides a candidate bound on photogrammetric doming but is inconclusive here. On the Golden Horizon, the method recovers aft rakes of 1.2–1.9° and bends of 36–160 mm at wavelengths above 16 m. On matched synthetic clouds, assumed spatially correlated reconstruction error sets per-mast floors of 20–27 mm (mean) and 29–40 mm (90th percentile), against 7 mm under independent noise; UAV and terrestrial laser scanning (TLS) profiles have root-mean-square differences of 14–33 mm. Tested against straight synthetic masts, two masts bend significantly at the 5% level, but only the Foremast, which TLS could not check, stays significant under all fourteen error models and, under the default model, after a multiple-testing correction; the Mainmast, significant under eleven, agrees with TLS only transversely.