Parametrization of spline functions to describe the shape of shell structures.

Abstract

Description of the shape of shell structure surfaces by means of spline functions is a competitive method of approximation to the approximation with a surface of the second degree. They al- low us to present local deformations of the structure. However, they demonstrate sensitivity to a variety of factors, among which the most important is related to the shape of the structure, de- termining the appropriate choice of spline function arguments. Determining of the arguments is carried out in the so-called pa- rametrization process, which is crucial for the accuracy of the obtained approximations. This paper focuses on the application and comparison of several popular parametrization methods for approximating the shape of the surface of shell structures. The main task of the conducted test study was to select the parametrization method bringing the most accurate results for the description of the struc­tures measured with a not too high density of points (every tens of centimeters - meters) for example, using popular reflectorless total stations. For this purpose, two test models were analyzed, with one- and multi-directional variable curvature, from which sets of points distributed alternately were considered, used to construct spline surfaces and to determine the deviations of the surfaces from the test models. The study involved three most common types of parametri­zation [2-4]: with a fixed distance, with the distance between the points and with its root. The conducted analysis of the results allowed us to identify the most accurate parametrization method to describe the shape of the shell structure surface.