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A comment on How Quaternions encode rotations: derivation and sample code. Parent comment
Rotations in 2D are one-dimensional. Complex numbers are two-dimensional but we fix one degree of freedom by fixing the length.
Rotations in 3D are there-dimensional. Quaternions are four-dimensional but we fix the length again.
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Rotations in 2D are one-dimensional. Complex numbers are two-dimensional but we fix one degree of freedom by fixing the length.
Rotations in 3D are there-dimensional. Quaternions are four-dimensional but we fix the length again.