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            "License :: OSI Approved :: MIT License",
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            "Programming Language :: Python",
            "Programming Language :: Python :: 2.7",
            "Programming Language :: Python :: 3.4",
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        "description": "Register 3-D point clouds using rotation, translation, and scale transformations.\n\n##  Usage\n\n```\ndef Superpose3D(X,    # <-- Nx3 array of coords for the \"frozen\" point cloud\n                x,    # <-- Nx3 array of coords for the \"mobile\" point cloud\n                # ---- optional arguments: ----\n                w = None,        # optional weights for the calculation of RMSD\n                allow_rescale=False,   # attempt to rescale mobile point cloud?\n                report_quaternion=False)      # report rotation angle and axis?\n```\n\nSuperpose3D() takes two ordered lists (or numpy arrays) of xyz coordinates\n(*of the same length*, **N**) representing points in a point cloud\n(**X** and **x**). Treating them as rigid objects,\n\"Superpose3D()\" attempts to superimpose them using **rotations**,\n**translations**, and (optionally) **scale** transformations in order\nto minimize the root-mean-squared-distance (RMSD) between corresponding\npoints from either point cloud, where RMSD is defined as:\n```\n   RMSD = sqrt( (\u03a3_n w[n] * \u03a3_i |X[n][i] - (\u03a3_j c*R[i][j]*x[n][j] + T[i])|^2) / (\u03a3_n w[n]) )\n```\nIf *w=None*, equal weights are used.  In that case:\n```\n   RMSD = sqrt( (\u03a3_n \u03a3_i |X[n][i] - (\u03a3_j c*R[i][j]*x[n][j] + T[i])|^2) / N )\n```\n...where:\n```\n    R = a rotation matrix    (a 3x3 numpy array representing the rotation. |R|=1)\n    T = a translation vector (a 1-D numpy array containing x,y,z displacements)\n    c = a scalar             (a number, 1 by default)\n```\nThis function returns a 4-tuple containing the optimal values of:\n```\n   (RMSD, R, T, c)\n```\n*Note:* This function does not attempt to determine *which* pairs of points\nfrom either cloud correspond.  Instead, it infers them from the order of the\narrays.  (It assumes that the *i'th* point from *X* corresponds to the *i'th*\npoint from *x*.)\n\nIf the rotation angle and axis are needed, then set the *report_quaternion*\nargument to *True*. In that case, the function will return this 4-tuple instead:\n```\n   (RMSD, q, T, c)\n```\n  ...where *q* is the\n[quaternion corresponding to rotation *R*](https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation),\nfrom which the rotation angle and rotation axis can be easily determined.\n\nThis function implements a more general variant of the method from this paper:\nR. Diamond, (1988)\n\"A Note on the Rotational Superposition Problem\",\n Acta Cryst. A44, pp. 211-216.\n\nThis version has been augmented slightly to support scale transformations.  (I.E. multiplication by scalars.  This can be useful for the registration of two different annotated volumetric 3-D images of the same object taken at different magnifications.)\n\nNote that if you enable scale transformations (i.e. if *allow_rescale=True*), you should be wary if the function returns a negative **c** value.  Negative **c** values correspond to inversions (reflections).  For this reason, if you are using this function to compare the conformations of molecules, you should probably set *allow_rescale=False*.  This will prevent matching a molecule with its stereoisomer.\n\nNote: A C++ version of this repository is available at\nhttps://github.com/jewettaij/superpose3d_cpp\n\n\n",
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