Use `sinc` to fix RotationVec near zero

[timholy]

By converting straight from RotationVec->QuatRotation, and using an implementation that exploits sinc to handle θ ≈ 0, we get continuous & differentiable behavior.

Requires https://github.com/JuliaDiff/ForwardDiff.jl/pull/669 before tests will pass.

What this fixes: currently, near the origin the Hessian is zero (which is wrong), because *(::RotationVec, ::SVector{3}) expands only to linear order. But the fix is aimed at being broader than this specific case (otherwise, we could have just implemented a second-order approximation).

Note: please check whether the relaxation of the adjoint test is reasonable, perhaps exact equality is necessary? If so I'll need to come up with a fix.

[codecov[bot]]

Codecov Report

Merging #272 (6811364) into master (149edac) will increase coverage by 0.08%. Report is 2 commits behind head on master. The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master     #272      +/-   ##
==========================================
+ Coverage   90.42%   90.50%   +0.08%     
==========================================
  Files          17       17              
  Lines        1660     1664       +4     
==========================================
+ Hits         1501     1506       +5     
+ Misses        159      158       -1     

Files	Coverage Δ
src/angleaxis_types.jl	99.00% <100.00%> (+1.07%)	:arrow_up:

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[hyrodium]

A type instability was introduced in this PR.

Before this PR

julia> using Rotations

julia> QuatRotation(RotationVec(0f0, 0f0, 0f0))
3×3 QuatRotation{Float32} with indices SOneTo(3)×SOneTo(3)(QuaternionF32(1.0, 0.0, 0.0, 0.0)):
 1.0  0.0  0.0
 0.0  1.0  0.0
 0.0  0.0  1.0

julia> QuatRotation(RotationVec(0f0, 0f0, 2f0))
3×3 QuatRotation{Float32} with indices SOneTo(3)×SOneTo(3)(QuaternionF32(0.540302, 0.0, 0.0, 0.841471)):
 -0.416147  -0.909297  0.0
  0.909297  -0.416147  0.0
  0.0        0.0       1.0

After this PR

julia> using Rotations

julia> QuatRotation(RotationVec(0f0, 0f0, 0f0))
3×3 QuatRotation{Float64} with indices SOneTo(3)×SOneTo(3)(QuaternionF64(1.0, 0.0, 0.0, 0.0)):
 1.0  0.0  0.0
 0.0  1.0  0.0
 0.0  0.0  1.0

julia> QuatRotation(RotationVec(0f0, 0f0, 2f0))
3×3 QuatRotation{Float32} with indices SOneTo(3)×SOneTo(3)(QuaternionF32(0.540302, 0.0, 0.0, 0.841471)):
 -0.416147  -0.909297  0.0
  0.909297  -0.416147  0.0
  0.0        0.0       1.0