Analytical representation of 3D magnetic surfaces

The mathematical description of 3D magnetic surfaces is of paramount importance in several applications, but the solution can be hard in terms of the computing effort or unsatisfactory in terms of accuracy. The paper proposes an effective methodology based on the tracking of a limited portion of the magnetic field line and on the fitting of the line onto a 3D surface described in a suitable set of 3D shape functions. In this way, the field line plays the role of a non-uniform sampling of the magnetic surface and the minimization of a suitable error allows the determination of the expansion coefficients. The computational cost of the line tracking can be limited according to the actual precision needs. The proposed approach allows the introduction of a number of indexes suited to estimate the accuracy and, if the case, to indicate how to upgrade the fitting parameters to meet the actual requirements.