Doesn't this assume that the object is being rotated about the same point both times for this to be commutative? If the point about which the object was being rotated changes between the two rotations, then wouldn't the object be at a different point in space (same theta but different x and y)?
rgrao
@small_potato_ yes, but remember that the properties of rotation include one which says "keeping the origin fixed". So if we change the point about which rotation happens, that is the same as doing a translation of the origin and then rotating, meaning it is not the same as doing a pure rotation. In 2D, pure rotations will commute, but as we know, translation is an affine operation, so doing rotation and then translation v/s translation and then rotation will not give the same results.
penguin
Is rotation generally counterclockwise direction?
peanut
^^ as the above comment, I will think rotation direction to be default clockwise, but this picture doesn't agree clearly.
xiaol3
I guess its because when you add the angle to the orginal angle, it would rotate counterclockwise
Doesn't this assume that the object is being rotated about the same point both times for this to be commutative? If the point about which the object was being rotated changes between the two rotations, then wouldn't the object be at a different point in space (same theta but different x and y)?
@small_potato_ yes, but remember that the properties of rotation include one which says "keeping the origin fixed". So if we change the point about which rotation happens, that is the same as doing a translation of the origin and then rotating, meaning it is not the same as doing a pure rotation. In 2D, pure rotations will commute, but as we know, translation is an affine operation, so doing rotation and then translation v/s translation and then rotation will not give the same results.
Is rotation generally counterclockwise direction?
^^ as the above comment, I will think rotation direction to be default clockwise, but this picture doesn't agree clearly.
I guess its because when you add the angle to the orginal angle, it would rotate counterclockwise