Linear Algebra – Real World Uses of Quaternions

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I've recently started reading about Quaternions, and I keep reading that for example they're used in computer graphics and mechanics calculations to calculate movement and rotation, but without real explanations of the benefits of using them.

I'm wondering what exactly can be done with Quaternions that can't be done as easily (or easier) using more tradition approaches, such as with Vectors?

Best Answer

I believe they are used in quantum physics as well, because rotation with quaternions models Spinors extremely well (due to the lovely property that you need to rotate a point in quaternionic space around 2 full revolutions to get back to your 'original', which is exactly what happens with spin-1/2 particles).

They are also, as you said, used in computer graphics a lot for several reasons:

  1. they are much more space efficient to store than rotation matrices (4 floats rather than 16)
  2. They are much easier to interpolate than euler angle rotations (spherical interpolation or normalised liner interpolation)
  3. They avoid gimbal lock
  4. It's much cooler to say that your rotation is described as 'a great circle on the surface of a unit 4 dimensional hypersphere' :)

I think there are other uses, but a lot of them have been superseded by more general Vectors.

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