Confusing rand methods with Euler rotaions

[hyrodium]

On current master branch:

• rand(RotX) is same as RotX(2π*rand()).
• rand(RotXY) is same as RotXY(2π*rand(), 2π*rand()).
• rand(RotXYZ) is not same as RotXYZ(2π*rand(), 2π*rand(), 2π*rand()).
• But rand(RotXYZ) is same as RotXYZ(rand(UnitQuaternion)).

This makes confusing, so we have two choices:

• Define rand(RotXYZ) by RotXYZ(2π*rand(), 2π*rand(), 2π*rand()).
• Add more clear documents.

I guess the first choice would be prefered.

cf.

Rotations.jl/src/euler_types.jl

Line 266 in 38b208b

# Not really sure what this distribution is, but it's also not clear what

Not really sure what this distribution is, but it's also not clear what it should be! rand(RotXY) is invariant to pre-rotations by a RotX and post-rotations by a RotY...

[andyferris]

Hmm. I agree with the status-quo for the first and last, because they are the right measure spaces for 2D and 3D rotations respectively, but I'm not sure what space / measure you should use to define RotXY. The current definition doesn't seem like the one it should be, but I have no idea.

As you say, we could just document it (until someone has a better idea of what it should be).

[hyrodium]

Thanks for the comment! Okay, I'll update the document that way.

[hyrodium]

This has been documented in #174, so I will close this issue.
https://juliageometry.github.io/Rotations.jl/dev/functions/#rand-for-RotXY-and-etc.