There are at least 4 separate implementations of quaternions in Julia. Some of them are <:AbstractVector, some are <:AbstractMatrix (:neutral_face:), some are <:Number, some follow sijk convention, some follow ijks convention, etc. It would be no problem, but I’m constantly switching between them b…

Yes, bivectors (thought it best not to alter the quote). Insight that you have with regard to this developing implementation, apart from the nature of Grassmann.jl (we all understand that is done on your own time and its goals are wider than Quaternions), is likely helpful. As more detail becomes …

[image] JeffreySarnoff: It may be performant to include an isnorm Bool field to flag realizations that have been normalized. Please don’t do this. The most performant Quaternion is going to be realizable via SIMD. 4 scalars. Additionally, it’s often ok to let your quaternions drift a certa…

[image] JeffreySarnoff: struct Quaternion{S<:Number, T<:Number} <: Number s::S # scalar value i::T # imaginary i value j::T # imaginary j value k::T # imaginary k value end I think the idea is to not have a specific struct Quaternion but rather a set of methods. In anycas…

[image] Ronis_BR: Sure! One very good book about reference systems, coordinate transformation, and also attitude dynamics is I’ll second this book recommendation, and also add this paper by Shuster: A Survey of Attitude Representations ( http://www.malcolmdshuster.com/Pub_1993h_J_Repsurv_scan.…

I recently released SimpleQuaternions mostly as an exercise for myself, but thought it might be useful to others. Some thoughts: I see Quaternions as extensions of the Complex numbers. For that reason, they should be fully interoperable with Complex numbers and Quaternions should be a subtype of N…

[image] tuckermcclure: I seem to recall seeing Rotations.jl implement rotation operations by going to matrices and then back to the desired parameterization for the output. (Please let me know if I’m mistaking this with another package.) This loses more accuracy than dedicated operations for ea…

As others have mentioned, lots of varying conventions make this a difficult task. For example, there’s not consensus on whether i*j is +k or -k. I recently came across this paper (Sommer et al) that provides a nice summary.

[image] bhawkins: For example, there’s not consensus on whether i*j is +k or -k. Generally, the convention you want is i*j*k == -1.

I agree strongly with @Orbots re: isnorm. In fact, in my experience, it’s best for numerical applications to ignore the possibility of a normalized quaternion; when normalization is relevant, it’s better to include the act of normalization explicitly. For example, when rotating a vector v by some …

[image] scheinerman: I recently released SimpleQuaternions … Nice! I’ll echo @chakravala in pointing out that the choice of plane when identifying complex numbers as a sub-algebra of the quaternions is arbitrary. Still, it’s entirely reasonable to just go ahead and make such a choice. Curi…

Taking Quaternions Seriously

Specific Domains Numerics

Ronis_BR August 19, 2020, 12:50pm 44

I completely agree. Those are the two reasons why I kept maintaining ReferenceFrameRotations.jl after Rotations.jl.

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Taking Quaternions Seriously

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