Talk:Quaternions and spatial rotation: Difference between revisions

Revision as of 15:23, 19 May 2020

Revision as of 20:10, 19 May 2020

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However, quaternion rotation requires 24 add/mul operations but a 3x3 matrix requires only 15 add/mul operations. Also, the "more numerically stable" claim is unjustified and I cannot find a reference. <!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/80.47.47.163|80.47.47.163]] ([[User talk:80.47.47.163#top|talk]]) 15:22, 19 May 2020 (UTC)</small> <!--Autosigned by SineBot-->

:I'm not sure where are those numbers from. As far as the number of operation goes, quaternions require less operations to compose rotations and more operations to apply a rotation to a vector. What ends up being more efficient depends on the application.

:Besides, efficiency is not only the number of mul/adds. Quaternions take less than half the memory and, accordingly, bandwidth. Which is, again, important in some applications (e.g. tangent space calculations on a GPU).

: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)