Recently, it has been shown that the resolution in cryo-tomography could be improved by considering the sample motion in tilt-series alignment and reconstruction, where a set of quadratic polynomials were used to model this motion. One requirement of this polynomial method is the optimization of a large number of parameters, which may limit its practical applicability. In this work, we propose an alternative method for modeling the sample motion. Starting from the standard fiducial-based tilt-series alignment, the method uses the alignment residual as local estimates of the sample motion at the 3D fiducial positions. Then, a scattered data interpolation technique characterized by its smoothness and a closed-form solution is applied to model the sample motion. The motion model is then integrated in the tomographic reconstruction. The new method improves the tomogram quality similar to the polynomial one, with the important advantage that the determination of the motion model is greatly simplified, thereby overcoming one of the major limitations of the polynomial model. Therefore, the new method is expected to make the beam-induced motion correction methodology more accessible to the cryoET community.