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[low priority] Adding equal-area vector projections. #621

@argerlt

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@argerlt

Low priority, but at some point we should add an equal-area option to the StereographicProjection class. it way less popular than the 'equal angle` one we use now, but it's handy for XRD, and calculating certain statistics, and nicely parallels Homochoric vs Rodriguez in SO(3).

Implementation isn't too difficult. Instead of the current equal-angle:

  • X = vx/(1 + vz),
  • Y = vy/(1 + vz),

The equal-area would be:

  • X = vx * sqrt(2/(1-vz))
  • Y = vy * sqrt(2/(1-vz))

However, the harder part would be updating all the tutorials and examples, and since they are currently being rewritten as part of #618, I think it makes sense to wait.

I'm using "Texture and Anisotropy" (Kocks and Tome) Chapter 2 as the reference for this, but googling "Azimuthal earth projection" gives the same information. Note how in this clipped version of Figure 5 from the same book, the top (equal-angle) projection includes only 90 degree angles between latitude/longitude lines, whereas the bottom (equal-area) has boxes that are all the exact same size.

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