This thesis presents a new approach to curve reconstruction from over constrained gradients. This type of problem arises when measuring deformation of structures using inclinometers. The new methods investigated are based on discrete orthonormal polynomials and a method of synthesizing constrained basis functions, whereby the constrained basis functions span the complete space of all possible solutions. Furthermore, they are ordered in increasing mode number, which supports a simple solution for spectral regularization. Two new methods are derived for the reconstruction of curves from gradients. The first reconstruction method uses admissible functions for regularization, the second method is of variational nature. Monte Carlo simulations are presented which verify the principle of the numerical approach. Additionally a real inclinometer measurement system for the measurement of a deflected beam was implemented and an independent optical system was constructed for measurement validation. The real measurements confirmed the correctness of the new approach. Furthermore, they revealed issues which are relevant for future research, i.e., placing constraints on the interpolating functions and not on the reconstructed points.