The performance of accelerator cavities is evaluated based on their eigenmodes. Since the classification of their eigenmodes is cumbersome, we investigate automatic mode recognition by deforming the cavity geometry to an analytically well-known shape and tracking the eigenmodes during the deformation along a deformation parameter. We have already compared two different mappings from the elliptical TESLA cavity to the cylindrical pillbox cavity. In the physical mapping, we model the shape morphing by assembling the geometry at intermediate shapes. In contrast, the algebraic mapping is formulated as a convex combination of the system matrices and hence intermediate results do not represent the solution of physical systems. However, both match the same frequency. The purpose of this thesis is to study and implement more mappings to detect the limitations of this algorithm and formulate the underlying assumptions on the mapping.