Previous | Next --- Slide 56 of 59
Back to Lecture Thumbnails

If we rotate without translating first, the rotation will be done about the origin, which produces a wrong result.


One property about rotations is that it must be kept at the origin to remain a linear transformation. If the rotation is performed at point x, we will experience issues with the additivity [f(u+v)=u+v+x while f(u)+f(v)=u+v+2x] and homogeneity property [f(au)=au +x while af(u)=au+ax]. Hence, the rotation won't be performed correctly if translation does not occur.