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:Applying and composing rotations aren't the only operations to consider either. Quaternions are easier to interpolate (again, useful for tangent space calculations on a GPU for example, but also for animation, modeling, etc...).
:"more numerically stable" -- this is un-doubtfuly true. When repeatedly composing rotations (eg in rigid body simulations) rotation matrices will inevitably become non-orthogonal. There are different ways to re-orthogonalize them, trading off precision and performance. In contrast to those, quaternions don't suffer from that issue at all. [[User:Ybungalobill|bungalo]] ([[User talk:Ybungalobill|talk]]) 20:09, 19 May 2020 (UTC)
::"compact, efficient, and numerically stable" better are sourced or reasoned indeed IMO.
::The rotation matrix in the tooltip of the linked words "rotation matrices" in the sentence of above quote alone for example requires only Theta, making it more compact than a quaternion. Here reasoning is missing.
::"efficient" in what respect: efficiency is a kind of output per input; are quaternions less time consuming to use for a high research effort? This would make them inefficient. So the respect is missing.
::"numerically stable": comparing rotation matrices sin and cos range 0...1 being multiplied with each other multiple times with unit quaternions being multiplied with each other multiple times, I don't get an idea of a significant different numerical stableness. Non-othogonal is a semantic issue, stableness is rather a syntactic issue. [[Special:Contributions/2A02:2455:30C:7D00:3931:FDDB:9442:9713|2A02:2455:30C:7D00:3931:FDDB:9442:9713]] ([[User talk:2A02:2455:30C:7D00:3931:FDDB:9442:9713|talk]]) 23:55, 29 August 2025 (UTC)
== Labelling the formulas in the Alternative Convention section ==
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