Translation, rotation, scaling, and shearing are all examples of geometric transformations. Multiple copies of an object can be created by drawing the same object using a series of different transformation matrices.

(image courtesy of Robert Lansdale)

The Graphics Pipeline

Definitions Related to Geometric Transformations

affine transformation

A transformation which preserves the parallelism of lines, but not necessarily angles or lengths.

right-handed and left-handed coordinate systems

homogeneous coordinates

In homogeneous coordinates, each cartesian point (x,y,z) is represented in a redundant manner by 4 coordinates, (hx,hy,hz,h). Setting w=0 can be thought of as a point at infinity or, more simply, a direction.