Is order any more important in 3D compared to 2D for linear transformation?
ecohen2
Yes! I think it was mentioned in class that order matters in 3D. I get why this is true when trying to walk through the math, but I was also wondering ... is there a general intuition for this?
Also, what was the intuition behind one dimension being unchanged?
Spantheras
My intuition for this is that in 2D there is only one axis to rotate on (z), so there is not much that could go wrong, while in 3D there are three axes.
(try to do the in-class activity again but you're only allowed to rotate in ONE plane - and imagine that's the XY plane)
Is order any more important in 3D compared to 2D for linear transformation?
Yes! I think it was mentioned in class that order matters in 3D. I get why this is true when trying to walk through the math, but I was also wondering ... is there a general intuition for this?
Also, what was the intuition behind one dimension being unchanged?
My intuition for this is that in 2D there is only one axis to rotate on (z), so there is not much that could go wrong, while in 3D there are three axes.
(try to do the in-class activity again but you're only allowed to rotate in ONE plane - and imagine that's the XY plane)
Longer explanation: https://www.quora.com/Why-is-there-only-one-axis-to-rotate-on-in-2D-but-3-in-3D
Commutativity of rotations in 3D space only holds for infinitesimal angles, when cos x~1 and sin x~x.