Let denote the coordinates of any point, after has been applied.
What would happen if we took all points and directly projected them into the vertical plane by forcing each coordinate to be 0? In other words,
, which is called *orthographic projection*. If we imagine the plane as a virtual display of the models, then there would be several problems:

- A jumble of objects would be superimposed, rather than hiding parts of a model that are in front of another.
- The display would extend infinitely in all directions (except ). If the display is a small rectangle in the plane, then the model parts that are outside of its range can be eliminated.
- Objects that are closer should appear larger than those further away. This happens in the real world. Recall from Section 1.3 (Figure 1.23(c)) paintings that correctly handle perspective.

Steven M LaValle 2020-11-11