A transformation maps a point (x,y,z) to a new
location. There are four elementary transformations that are used
over and over again:
Translation
Translation slides the points a given distance in some direction.
Scaling
Scaling stretches or squashes the object along the direction of the
principal axes. Note that the stretching along an axis is relative to
the zero of that axis, so the object may appear to move as well.
Rotation
Rotation spins the object around the origin in 2D, or around an axis
in higher dimensions. These equations, derived
for two dimensions here, correspond to rotation about the
z axis.
Shear
Shear produces a translational movement in the direction of one axis
whose magnitude increases along another axis.
