The transformations involved in making perspective images do not preserve parallelism of lines. For example, a football field is flat and its yard lines are parallel, but on a television screen it might look like the picture on the right:
On the other hand, members of a band on the field might be standing in two non-parallel lines, but the lines could become parallel on the screen:
The kind of transformations that can handle distortions of this kind, while keeping straight lines straight, are called projective transformations. To describe them, we first need a new system of coordinatizing the plane.