Orthographic projection

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

  1. A jumble of objects would be superimposed, rather than hiding parts of a model that are in front of another.
  2. The display wound extend infinitely in all directions (except $ z$). If the display is a small rectangle in the $ xy$ plane, then the model parts that are outside of its range can be eliminated.
  3. Objects that are closer should appear larger than those further away. This happens in the real world. Recall from Section 1.3 (Figure 1.22(c)) paintings that correctly handle perspective.
The first two problems are important graphics operations that are deferred until Chapter 7. The third problem is addressed next.

Steven M LaValle 2016-12-31