This work presents computer animations of three-dimensional refold structures and their two-dimensional interference patterns, which visualize the complex geometry of simple kinematic fold superposition models. The animations help to improve the understanding of fold interference in both teaching the geometrical background and classifying the enormous variability of natural examples. Because the interference patterns are not indicative for a relative spatial orientation of superposed folds, the refold structures are distinguished by the angles between the kinematic axes (i.e. fold axis, the pole to the axial plane and the normal to these axes) of the initial and the superposing fold. These orthogonal triplets of directions can be elegantly plotted in a refold-stereoplot, which is simply a stereographic projection where the initial fold axis is oriented W-E and the pole to the axial plane N-S. Six orthogonal, geometrical end-members can be distinguished and used for a classification of all possible superposition geometries, including Type 1-3 after Ramsay (1967). The classical Type 0 end-member refold, which in case of perfect cylindrical fold shapes produces no interference patterns, has to be divided in three different classes Type 01-03. Although these classes are probably difficult to distinguish in the field, Type 01-03 refolds result in markedly different distributions of finite strains.