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The Kabsch algorithm, named after Wolfgang Kabsch, is a method for calculating the optimal rotation matrix that minimizes the RMSD (root mean squared deviation) between two paired sets of points. It is useful in graphics, cheminformatics to compare molecular structures, and also bioinformatics for comparing protein structures (in particular, see root-mean-square deviation (bioinformatics)). The algorithm only computes the rotation matrix, but it also requires the computation of a translation vector. When both the translation and rotation are actually performed, the algorithm is sometimes called partial Procrustes superimposition (see also orthogonal Procrustes problem). == Description == The algorithm starts with two sets of paired points, ''P'' and ''Q''. Each set of points can be represented as an ''N''×3 matrix. The first row is the coordinates of the first point, the second row is the coordinates of the second point, the ''N''th row is the coordinates of the ''N''th point. : The algorithm works in three steps: a translation, the computation of a covariance matrix, and the computation of the optimal rotation matrix. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Kabsch algorithm」の詳細全文を読む スポンサード リンク
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