Possible bug in get_orientations_from_stereographic_triangle()

[EirikOpheim]

I am not sure if this is really a bug or if I am not using the function correctly. I have interpreted the function as giving a list of orientations that span the Euler space for a given crystal structure.

What I have done to test this function is generate a grid of all Euler angles from (-90,-90,0) to (90,90,0) at 5 degree intervals, and simulate diffraction patterns of gold (cubic fcc) for each orientation.
I experience that for my simulated data, if I use a set of orientations from get_orientation_from_stereographic_triangle() in my template library, using a resolution of 1/2 degree, the match is a good fit only in the region characterized by having as corners euler angles (0,-55,0) (-45,-55,0)(-45,55,0)(0,55,0)[I think first angle is along y axis.] And a similar region on top in the image. Outside this range templates do not fit the simulated diffraction maps.

To see if I could find the minimum set of orientations necessary for the template to do the job I have made a template library with the angles in the grid. I find that if I use angles from (-45,-90,0) to (45,90,0) I get a unique match for each pixel, except along the lines (mod(x,90) = 0, : ,0), where I have double matches. See figure

Steps to reproduce the behavior:

1. Generate a simulated set of diffraction patterns for known angles at a regular grid in the range (-90,-90,0) to (90,90,0).
2. Use the same set of angles as a template, but include only angles from (-45,-90,0) to (45,90,0)
3. Perform template matching. Plot orientation map. Use this this as a "perfect match".
4. Generate angles from get_orientations_from_stereographic_triangle() at high resolution.
5. Perform template matching and plot orientation map. See problem.

I would expect that the orientation map obtained using get_orientations_from_stereographic_triangle() would be similar to the "perfect match" all over, with some errors, but in general a smooth result. It seems to me like the Euler space is not covered in get_orientations_from_stereographic_triangle().

Possible solutions:

1. Maybe I have to choose the in-plane rotations in a specific way?
2. Span orientation angles over a the rectangle I have been using

Note: The reason why I choose a smooth orientation map as a quality metric is that if there are multiple correct templates, it seems like the template will somewhat randomly be choosen, as seen in the lines in figure 2. Also, for a distance metric such as the one generating the orientation map the triangle inequality D(a,b) <= D(a,c)+D(c,b) should ensure a smooth orientation map, if the orientation map is correct. If the distance between two neighbouring pixels is more than 5 i suppose one of them must be wrong, as their relative tilt is 5 degrees.

pyxem 0.10.0.

[pc494]

@EirikOpheim, I think you're probably correct that this is a bug. Streographic triangles were always meant to be a gap fill, and I'm currently building a correct solution for orix.

This is likely to be public functionality January time, but I can send you (and anyone else interested, do reach out) a notebook (maybe finished, maybe a couple of geometric bits "left as an exercise for the reader") from early next week? Would that help?

UPD: Another good issue, thank you, this will help the code base move forward a lot.

[EirikOpheim]

If you could send me a notebook next week it would be very helpful. Thank you!

[pc494]

This is being closed by #47 as the functionality will be removed.

[pc494]

A whole range of changes (including #60 and #61) deprecate this issue.