# Rdf for aspherical particles (ellipses).

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### Jenis Thongam

May 18, 2023, 9:14:32 AM5/18/23
to freud-users
Dear all,

I have a system of elliptical particles of aspect ratio 3:1 and I have been using freud to obtain the general radial distribution function of these particles.
But to have more information on the type of structures these elliptical particles form when they aggregate together, I would like to have parallel and perpendicular rdf. Parallel in the sense that rdf function is computed along the major axis and the perpendicular rdf is computed along the minor axis.
Would these computations be possible using freud? If so, could someone please point me to documentation or an example?

Regards,
Jenis.

### Tommy Waltmann

May 18, 2023, 11:06:06 AM5/18/23
to freud-users
Hi Jenis,

Great question! freud doesn't have anything specifically for this use case, however we can modify the problem at bit so freud can still be helpful.

I think the best way to do your calculation is to project your points onto the desired subspaces and then compute the RDF for the projected 2D space. For example, to get the perpendicular RDF, project all points onto a 2D plane P which is perpendicular to the semimajor axis. Then, rotate P such that all points in P are in the XY plane. At this point, freud can compute the RDF for the 2D system.

Give this a try and let me know if its useful!

- Tommy

### Joshua Anderson

May 18, 2023, 11:11:18 AM5/18/23
to Tommy Waltmann, freud-users
Jenis,

PMFTXY (https://freud.readthedocs.io/en/latest/modules/pmft.html#freud.pmft.PMFTXY) can give you a quantity related to g(r) in all directions out from the shape. Read the references linked in the docs for details on the theory behind this calculation. If you need g(r) style normalization, you can take the bin_counts output from PMFTXY and normalize accordingly.
------
Joshua A. Anderson, Ph.D.
Research Area Specialist, Chemical Engineering, University of Michigan

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