3D utility functions

[bergey]

Some basic conveniences for working in 3D.

• unit vectors
• a few angle functions
• rotation transforms

I'd like feedback on:

• Is overlapping with 2D names a mistake? I think the parallels are mnemonic, even though we'll need to import parts of Diagrams qualified. But I'm open to persuasion.
• The choice of rotation functions
• For some reason I used unicode θ φ as variable names. Is this a terrible idea, or only a bad idea? I usually assume that people can read unicode but can only type ASCII. Should I fix it?

[bergey]

Having tried to work with this a bit more today, I think I'll add a Direction class, like the Angle class. That will make type signatures more useful Otherwise I think we'll end up with lots of comments saying that this or that R3 will be normalized. So spherical & fromSpherical will go away. Do you want to hold off merging until I have an implementation?

[byorgey]

OK, sounds good.

[byorgey]

Also,

1. I think overlapping with 2D names is fine.
2. Rotation functions look good to me.
3. I fully endorse all uses of non-ASCII characters so long as users do not have to type them to use the library. We are finally living in the Age of Unicode, let's enjoy it.

[bergey]

Yes, I certainly did forget to update the documentation. Thank you!

[bergey]

I added the new Direction type class, which is specific to 3D. Polar is the only instance for now. I also stuck angleRatio in this branch, even though that commit doesn't touch any 3D files. I think this is good to go now.

[byorgey]

Should be aboutZ instead of rotate

[byorgey]

The semantics of Polar are not clear to me. Is it supposed to represent spherical coordinate angles? In that case might Spherical be a better name? Though I guess "spherical coordinates" usually refers to two angles paired with a distance rather than just the bare angles. Or is it supposed to be more general somehow?

[bergey]

I meant spherical coordinates. Renaming it Spherical makes sense to me. I think the Direction instance makes it clear enough that it doesn't include the distance. I'll try to improve the docstring while I'm at it. I took out the old version because it said that the angles were normalized (to [0,2pi), [-pi/2,pi/2]) which isn't true.