Spheric images (Quantification of directional dependence of ordering)

[qzhu2017]

I decided to put our discussion here. If you go to misc/ and run run.py
You expect to see the following images.

The idea is the following
1, convert each hkl to a spherical coordinates (theta, phi)
2, generate 10000 mesh grids to evenly sample the sphere
3, for each hkl, we place a Gaussian on the unit sphere according to the intensity and a sigma value
4, use plotly to show the interctive image
5, use Matplotlib to show the static image (here I used the spherical harmonic expansion)

[qzhu2017]

Our ultimate goal is to generate the following plot to show the directional dependence of XRD intensity. We may change it to some other values later on.

[qzhu2017]

• For a given structure
• Search all hkl within a truncation https://github.com/qzhu2017/PyXtal/blob/aac12c486f023847e157f8aa61d0b4b1059e9191/pyxtal/XRD.py#L117
• For each hkl, calculate the pariwise distance, make the histogram, fit the Gaussian Width for the 1st peak, sigma
• Now we get {h, k, l, sigma}
• make 3D plot.