The paper presents a new dry-dock method for assessing the deformation of submarine hulls using TLS point cloud data and the point cloud spatial expansion method (PCSE). The advantage of the proposed approach is the high-resolution deformation analysis that can be conducted in the case of both the availability and a lack of technical documentation on the submarine hull. The geometry assessment involves two-plane hull symmetry in longitudinal sections of a tested Kobben-class submarine located in Gdynia, Poland. The features of PCSE introduce additional geometrical parameters that are not available in the original point cloud method. The procedure for local fitting of a plane into the expansion eliminates the problem of varying densities of the hull point cloud. Accuracies of several millimetres are achieved and are applicable to multi-temporal monitoring of the deformations of submarine hulls. The assessment of similar deformations is not possible in the original point cloud method, due to the unknown parameters of the orientation and curvature of the convex cylindrical hull surface. The PCSE-based parameterisation presented here enables the creation of alternative quasi-planar point cloud projections to extract new spatial information on the object. The results of this study were verified using theoretical values derived from design data on the Kobben-class submarine, and demonstrated the effectiveness of our method in terms of detecting deformations even without design references. The proposed methodology is uniform, and can be adapted to other symmetrical structures.

Church towers are key cultural heritage. In theory, towers are vertical, while facade elements are symmetrically positioned around the tower axis. However, during service of a structure, building and lifetime conditions cause deviations, with associated risks. Laser scanning point clouds can be used to assess the structural state but a universal approach was missing. The proposed algorithm first estimates the tower inclination, and tests which multi-axis representation best represents the course of the tower. Next, point cloud spatial expansion recovers relative distances and deviations of facade elements. The resulting procedure was applied to assess two Dutch medieval towers including the Old Church in Delft and the St. Bavo Church in Haarlem, respectively. As results of analysis, significant asymmetry was found with a 1.4° deviation of the multi-modal axis of the St. Bavo Church tower together with variations of 0.1%–1.5% for facade slopes, while 0.1°–3.1° radial deviations were found in the position of the turrets of the Old Church tower.