Therefore, the rotation equations are Let us verify the above with rotating about the y -axis 90 degree. Affine Transformations Euclidean transformations preserve length and angle measure. Moreover, the shape of a geometric object will not change. That is, lines transform to lines, planes transform to planes, circles transform to circles, and ellipsoids transform to ellipsoid. Only the position and orientation of the object will change.
Affine transformations are generalizations of Euclidean transformations.
Length and angle are not preserved. In this section, we shall discuss scaling, shear and general affine transformations. Scaling Scaling transformations stretch or shrink a given coordinate system and as a result change lengths and angles. So, scaling is not an Euclidean transformation. The meaning of scaling is making the new scale of a coordinate direction p times larger.