Cyrus/Beck Overview

1) Do the trivial accept/reject test on each line. For lines that
   don't get accepted or rejected you will have to clip them

2) We need to clip each boundary (N,S,E,W) with the line.  So
   first, calculate D = <P1-P0>, where P0 is the start point, and
   P1 is the end point of the line.

3) Create your normals, N.  N is relative to the clipping edge
   you're using: North: N = <0,1>; East: N = <1,0>; 
   South: N = <0,-1> ; West: N = <-1,0>.

3) Now, do the t calculation for each clipping edge, using the
   proper normal, N, that corresponds to its clipping edge.  For
   each edge, first calculate (N dot D).  If this is less than
   zero, then this t value is an entering point.  If it's greater
   than zero, it's a leaving point.  If it's equal to zero, then
   the line is parallel to that clipping edge, and there is no
   intersection

5)  Now calculate the t value for each clip edge:

        N dot [P0 - Pei]
    t = ----------------
          - [N dot D]

    where Pei is ANY point on the clip edge being tested.

6) You will have up to 4 t values, one for each edge.  Throw out
   any where t<0 or t>1.  They aren't on the line segment.  For
   those that remain, recall that we classified them as entering
   or leaving points.  Remember that N dot D tells you if they
   are entering or leaving. Take the largest t value for the
   entering points (PEmax) and the smallest t value for the
   leaving points (PLmin) and check if:

    PEmax < PLmin

    If this is the case, then those 2 t values are the new
    endpoints of the clipped line.  Convert the t values to (x,y)
    coordinates using the parametric line equation:

       P(t) = P0(1-t) + P1(t)

    then send these new endpoints to Bresenham.