The PROJECTION of a point A in R^3 to the picture plane is defined to be
the intersection of the line m containing A and the viewing position with
the picture plane.  If A is the viewing position, its projection is empty.
If m is parallel to the picture plane then the projection of A is empty.

The projection of a line m in R^3 to the picture plane is defined to be
the union of the projection of its points.  


Some facts you can easily check: 

1. If the line contains the viewing point the projection will be 
a single point.  

2. If a line m not containing the viewing point is parallel to the 
viewing plane, then the projection of m is a line.  You will see a 
proof that this line must be parallel to m.

3. If a line m not containing the viewing point is not parallel to the
viewing plane, then its projection is a line minus a point.  The missing
point is the vanishing point, defined to be the intersection with the
picture plane of a line parallel to m through the viewing point.

The IMAGE of a point A in R^3 that is not the viewing point is defined 
to be the intersection of the ray k starting at the viewing point and 
passing through A with the picture plane.  Thus the image of A is either
the projection of A or empty.  Informally, "image" captures the notion
that you can't see what you're not looking at (see text before Figure 1.2).

In Chapter 3, we explore what images of lines can look like.