Detection of periodic displacements of shell structures with edges using spline surfaces, meshes and point clouds

This research paper tackles the problem of determining displacements of complex-shaped shell structures, measured periodically using laser scanning. Point clouds obtained during different measurement epochs can be compared with each other directly or they can be converted into continuous models in the form of a triangle mesh or smooth patches (spline functions). The accuracy of the direct comparison of point clouds depends on the scanning density, while the accuracy of comparing the point cloud to the model depends on approximation errors that are formed during its creation. Modelling using triangle meshes flattens the local structure of the object compared to the spline model. However, if the shell has edges in its structure, their exact representation by spline models is impossible due to the undulations of functions along them. Edges can also be distorted by the mesh model by their chamfering with transverse triangles. These types of surface modelling errors can lead to the generation of pseudo-deformation of the structure, which is difficult to distinguish from real deformation. In order to assess the possibility of correct determination of deformation using the above-mentioned methods, laser scanning of a complex shell structure in two epochs was performed. Then, modelling and comparison of the results of periodic measurements were carried out. As a result of the research, advantages and disadvantages of each method were identified. It was noticed that none of the methods made it possible to correctly represent all deformations while suppressing pseudo-deformation. However, the combination of their best qualities made it possible to determine the actual deformation of the structure.