Metadata-Version: 2.1
Name: superpose3d
Version: 0.2.3
Summary: Diamond's 1988 rotational superposition algorithm (+scale tranforms)
Home-page: https://github.com/jewettaij/superpose3d
Author: Andrew Jewett
Author-email: jewett.aij@gmail.com
License: BSD
Download-URL: https://github.com/jewettaij/superpose3d/archive/v0.2.3.zip
Platform: UNKNOWN
Classifier: Development Status :: 3 - Alpha
Classifier: License :: OSI Approved :: BSD License
Classifier: Environment :: Console
Classifier: Operating System :: MacOS :: MacOS X
Classifier: Operating System :: POSIX :: Linux
Classifier: Operating System :: Microsoft :: Windows
Classifier: Programming Language :: Python
Classifier: Topic :: Scientific/Engineering
Description-Content-Type: text/markdown

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.


