Possibility of using local spline functions for estimating displacement values when observing deformations of buildings

This paper discusses the issue of determining the values of displacement points on the walls of buildings and structures during deformations using geodetic measurements of the values of displacements of adjacent points. It is proposed to use spline functions of one or two variables to calculate the offsets of points where no measurements were made, or where observations stopped starting from a certain stage. It is proposed to determine the spline coefficients either by interpolating the results from one observation cycle to arbitrary points, or by interpolating the observation results in previous cycles to points that were not observed in the new observation cycle. A specific example is used to evaluate the accuracy of the interpolation results and provide practical recommendations for using the methods in practical calculations. When considering the two-dimensional case, it is concluded that the approximation of the linear spline of two variables is not accurate enough, and it is proposed to use splines of a higher degree