Cannot take the mean of single or two axis euler rotations

[colinxs]

Note that mean() is fully broken on master. To reproduce this you'll have to checkout the fix/mean branch on my fork (will be merged after I write a test) and do the following.

julia> r=[RotZ(pi/2) for _ in 1:5000];

julia> mean(r)
ERROR: MethodError: RotZ{Float64}(::Quat{Float64}) is ambiguous. Candidates:
  (::Type{RotZ{T}})(theta) where T in Rotations at /home/colinxs/workspace/Rotations.jl/src/euler_types.jl:17
  (::Type{SA})(a::StaticArrays.StaticArray) where SA<:StaticArrays.StaticArray in StaticArrays at /home/colinxs/.julia/packages/StaticArrays/mcf7t/src/convert.jl:5
Possible fix, define
  (::Type{RotZ{T}})(::StaticArrays.StaticArray)
Stacktrace:
 [1] mean(::Array{RotZ{Float64},1}) at /home/colinxs/workspace/Rotations.jl/src/mean.jl:50
 [2] top-level scope at none:0

julia> r2=[RotXY(0,pi/2) for _ in 1:5000];

julia> mean(r2)
ERROR: Cannot construct a two-axis rotation from a matrix
Stacktrace:
 [1] error(::String) at ./error.jl:33
 [2] Type at /home/colinxs/workspace/Rotations.jl/src/euler_types.jl:232 [inlined]
 [3] Type at /home/colinxs/.julia/packages/StaticArrays/mcf7t/src/convert.jl:5 [inlined]
 [4] mean(::Array{RotXY{Float64},1}) at /home/colinxs/workspace/Rotations.jl/src/mean.jl:50
 [5] top-level scope at none:0

julia> r3=[RotXYZ(0,0,pi/2) for _ in 1:5000];

julia> mean(r3)
3×3 RotXYZ{Float64}(3.14159, 0.0, 3.14159):
 -1.0          -1.22465e-16   0.0        
 -1.22465e-16   1.0          -1.22465e-16
  1.49976e-32  -1.22465e-16  -1.0        

[andyferris]

Hmm... this is unfortunate - we should fix this.

I'm also wondering if mean should just do the AbstractArray thing (not return a rotation) and we should have some other function for mean rotations (or closest orthogonal matrix or whatever)?