To me a 3d rotation is a linear transformation from a 3d vector space to itself, so the natural way to represent it is as a 3x3 matrix. Mathematically, this is

To me a 3d rotation is a linear transformation from a 3d vector space to itself, so the natural way to represent it is as a 3x3 matrix. Mathematically, this isn't an unusual way to look at it; you can read the Wikipedia page on this way of representing rotations. The nice thing is that it works basically the same as a 2d rotation, you just have one more row and column in your matrix. https://en.wikipedia.org/wiki/Rotation_matrix https://en.wikipedia.org/wiki/Rotation_matrix I think this is simpler than any of quaternions, rotors, bivectors, or exponential maps.