A small Python example showing Arun's method (K. S. Arun, T. S. Huang and S. D. Blostein, "Least-Squares Fitting of Two 3-D Point Sets," in IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. PAMI-9, no. 5, pp. 698-700, Sept. 1987, doi: 10.1109/TPAMI.1987.4767965.).
bun_zipper_res4.ply is from the Stanford 3D scanning repository (https://graphics.stanford.edu/data/3Dscanrep/).