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> Quaternions? Well that's about 4D Quaternions are about 3D. You need 4 numbers for it, but the space that they operate on is 3D.
by aap_ 2y ago
> Quaternions? Well that's about 4D
Quaternions are about 3D. You need 4 numbers for it, but the space that they operate on is 3D.
- raincole 2y agoHe's talking from a mathematical perspective, not a compute graphics one. (Unit) quaternions happens to work as rotations in 3D space. But quaternions' algebraic structure is indeed 4D, just like imaginary numbers' is 2D.
- deleted 2y ago[deleted]
- ducttapecrown 2y agoSince you can multiply a quaternion by a quaternion, the quaternions act on themselves, so they indeed act on a 4D space. They can also act on a couple 3D spaces: the unit sphere in 4D, called the three sphere, or the imaginary quaternions. In math, this is called a representation of a Lie group, and there are representations in all dimensions.