Why are quaternions used for rotations?

Question

I\'m a physicist, and have been learning some programming, and have come across a lot of people using quaternions for rotations instead of writing things in matrix/vector fo

Answer 1

Opinion: Quaternions are nice.

Rotation matrix: Minor disadvantage: Multiplication of matrices is ~2 times slower than quaternions. Minor Advantage: Matrix-vector multiplication is ~2 times faster, and large. Huge disadvantage: Normalization! Ghram-Shmit is asymmetrical, which does not give a higher order accurate answer when doing differential equations. More sophisticated methods are very complex and expensive.

Axis (angle = length of axis) Minor advantage: Small. Moderate disadvantage: Multiplication and applying to a vector is slow with trig. Moderate disadvantage: North-pole singularity at length = 2*pi, since all axis directions do nothing. More code (and debugging) to automatically rescale it when it gets near 2pi.