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How can one intuitively think about quaternions? Quaternions came up while I was interning not too long ago and it seemed like no one really know how they worked While eventually certain people were tracked down and were able to help with the is
How to define a quaternion group of order 8 The quaternion group has 2 generators a a and b b, satisfying a4 = 1 a 4 = 1, b2 =a2 b 2 = a 2, and ba =a−1b b a = a 1 b From that, you can decide whether any given group presentation is, in fact, the quaternion gorup, and you can find all the subgroups
What does multiplication of two quaternions give? A nice thing is that multiplication of two normalized quaternions again produces a normalized quaternion Quaternion inversion (or just conjugate for the normalized case) creates the inverse rotation (the same rotation in the opposite direction)
Understanding quaternions - Mathematics Stack Exchange I'm trying to understand quaternions a bit better and get some more intuition, mostly in the context of using them as a way to think about rotations in 3D My approach to how one might want to think
Quaternions and spatial translations - Mathematics Stack Exchange From my understanding, in spatial applications (3D rendering, games and similar applications) quaternions can only be used to describe rotations orientations and not translations (like a transforma
Concise description of why rotation quaternions use half the angle The short answer is that for perpendicular inputs either way works If we take the full angle approach of a single quaternion with no conjugate, it will rotate by the full angle But it won't leave parallel inputs unaltered Only the half-angle approach with the conjugate works for both, so that is the correct formulation Read on for the long