Use sinc to fix RotationVec near zero
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By converting straight from RotationVec->QuatRotation, and using an implementation that exploits `sinc` to handle θ ≈ 0, we get continuous & differentiable behavior.
hyrodium
reviewed
Oct 14, 2023
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## master #272 +/- ##
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+ Coverage 90.42% 90.50% +0.08%
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Files 17 17
Lines 1660 1664 +4
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+ Misses 159 158 -1
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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 1.0After 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 |
hyrodium
requested changes
Oct 24, 2023
hyrodium
approved these changes
Nov 10, 2023
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By converting straight from RotationVec->QuatRotation,
and using an implementation that exploits
sincto handle θ ≈ 0,we get continuous & differentiable behavior.
Requires JuliaDiff/ForwardDiff.jl#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
adjointtest is reasonable, perhaps exact equality is necessary? If so I'll need to come up with a fix.