Diamond's 1988 rotational superposition algorithm (+scale tranforms)
Project description
Register 3-D point clouds using rotation, translation, and scale transformations.
Usage
def Superpose3D(X_i, # <-- Nx3 array of coords for the "frozen" point cloud
x_i, # <-- Nx3 array of coords for the "mobile" point cloud
w_i=None, #<- optional weights for the calculation of RMSD
# (default w_i = 1 for all i)
allow_rescale=False) #<--attempt to rescale mobile point cloud?
Superpose3D() takes two ordered lists (or numpy arrays) of xyz coordinates (of the same length, N) representing points in a point cloud (X_i and x_i). Treating them as rigid objects, "Superpose3D()" attempts to superimpose them using rotations, translations, and (optionally) scale transformations in order to minimize the root-mean-squared-distance (RMSD) between corresponding points from either point cloud, where RMSD is defined as:
RMSD = sqrt((Sum_i w_i * |X_i - Sum_j(c*R_ij*x_j + T_i))|^2) / (Sum_j w_j))
For the specific case of equal weights:
RMSD = sqrt(( Sum_i |X_i - Sum_j(c*R_ij*x_j + T_i) )|^2 ) / N)
...where:
T_j = a translation vector (a 1-D numpy array containing x,y,z displacements),
R_ij = a rotation matrix (a 3x3 numpy array whose determinant = 1),
c = a scalar (a number)
This function returns a 4-tuple containing the optimal values of:
(RMSD, T, R, c)
This function implements a more general variant of the method from this paper: R. Diamond, (1988) "A Note on the Rotational Superposition Problem", Acta Cryst. A44, pp. 211-216.
This 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.)
Note 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.
Project details
Release history Release notifications | RSS feed
Download files
Download the file for your platform. If you're not sure which to choose, learn more about installing packages.
Source Distribution
Built Distribution
Hashes for superpose3d-0.2.3-py3-none-any.whl
Algorithm | Hash digest | |
---|---|---|
SHA256 | 1d58a3bec34cf233244b1304e57a604b5193ae2d1365b80272c3c8ec8387c3fe |
|
MD5 | dcb4547d634b25848e14a9e3aeb42a2a |
|
BLAKE2b-256 | 512d4210ff4ef9e33fff760edaf44719b8268f21cda71a23256ecbcdd1adfcdb |