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- URL: https://x.com/EricLengyel/status/1482868119399911427
- Author: Eric Lengyel (@EricLengyel)
- Posted: 2022-01-17 00:11:24
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1/ @EricLengyel
@joonturbo
Rotations in 3D space have 3 degrees of freedom. This means they can be unambiguously represented by 3 numbers. Since a quaternion q corresponds to the same rotation as −q, we can always choose one with unit magnitude such that the scalar part (w) is positive. 1/2
2/ @EricLengyel
@joonturbo
Any rotation is then unambiguously represented by only the x, y, and z coordinates of the bivector part because these determine that value of the scalar part as w = sqrt(1 − x² − y² − z²).