Before revision: We examine the problem of transforming matching collections of data points into optimal correspondence. The classic RMSD (root-mean-square deviation) method calculates a 3D rotation that minimizes the RMSD of a set of test data points relative to a reference set of corresponding points. Similar literature in aeronautics, photogrammetry, and proteomics employs numerical methods to find the maximal eigenvalue of a particular 4\!\times\! 4 quaternion-based matrix, thus specifying the quaternion eigenvector corresponding to the optimal 3D rotation.
After revision: We review the general problem of finding a global rotation that transforms a given set of points and/or coordinate frames (the "test" data) into the best possible alignment with a corresponding set (the "reference" data). For 3D rotation.