Effect of Various Edge Configurations on the Accuracy of the Modelling Shape of Shell Structures Using Spline Functions

Abstract

Spline functions are a useful tool for modelling the shape of shell structures. They have curvature continuity that allows good approximation accuracy for various objects, including hyperboloid cooling towers, spherical domes, paraboloid bowls of radio telescopes, or many other types of smooth free surfaces. Spline models can be used to determine the displacement of structures based on point clouds from laser scanning or photogrammetry. The curvature continuity of splines may, however, cause local distortions in models that have edges. Edges may appear in point clouds where surface patches are joined, on surfaces equipped with additional technical infrastructure or with cracks and shifts in the structure. Taking the properties of spline functions into account, several characteristic types of edge configurations can be distinguished, which may, to a different extent, affect the values of modelling errors. The research conducted below was aimed at identifying such configurations based on theoretical considerations and then assessing their effect on the accuracy of modelling shell structures measured by laser scanning. It turned out to be possible to distinguish between edge configurations, based on the deviation values.