Re: [Algorithms] Rotation Matrices

[Ron L. <ro...@do...>]

> The deal is that 2D rotations always happen about the same axis
> (there IS only one after all) - so multiplication of rotation
> matrices is just like adding the angles - and addition is
> commutative.
>
Indeed, when you consider rotations about a common center in the plane, say
the origin, then concatenating rotations is isomorphic to adding angles
modulo 2pi.
Since addition of numbers is commutative you can conclude that concatenation
of plane rotations about a common center is also commutative.

However, it is worth mentioning that when you are considering affine
mappings of the plane, you need to consider the problem of concatenating
rotations about different centers (or, considered as 3D rotations, about
different but parallel axes).
These plane rotations about different centers, of course, do not have to
commute. But of course, you cannot represent them by 2x2 rotation matrices,
either.