Data are reported in .dat files, organized in columns. Comments describe the content of .dat files. Figures can be generated running the .p files which are Gnuplot scripts that read the .dat files. In the Oblate-to-toroidal-MEP directory, the folder "Fields" contains the phase-field of each string image in the r-z plane, together with the r- and z-component of the forces. Energies are made dimensionless by dividing by the bending energy of a sphere (8 pi k), while lenghts are scaled with the diffuse interface width parameter 6epsilon = 5 nm.