__END__
 1  0 1 5 4
 1  1 6 1 16
-1 -2 2 1 8

A line from A(   1.0,   0.0 )
       to   B(   1.0,   5.0 )
of width sqrt(   4.0 )
is a box, counter-clock-wise:
            W(   2.0,   0.0 )
            X(   2.0,   5.0 )
            Y(   0.0,   5.0 )
            Z(   0.0,   0.0 )

          w=2
        |<--->|

        |
       (Y)(B)(X)
        |  #
       4+  #
        |  #
       3+  #
        |  #
       2+  #
        |  #
       1+  #
        |  #
--+--+-(Z)(A)(W)-+--
 -2 -1  0  1  2


A line from A(   1.0,   1.0 )
       to   B(   6.0,   1.0 )
of width sqrt(  16.0 )
is a box, counter-clock-wise:
            W(   1.0,  -1.0 )
            X(   6.0,  -1.0 )
            Y(   6.0,   3.0 )
            Z(   1.0,   3.0 )

     |
    4+
     |
    3+ (Z)            (Y)   ---
     |                       ^
    2+                       |
     |                       |
    1+ (A)############(B)   w=4
     |                       |
--+--+--+--+--+--+--+--+--+- |
 -1  0  1  2  3  4  5  6  7  v
   -1+ (W)            (X)   ---
     |
   -2+
     |

A line from A(  -1.0,  -2.0 )
       to   B(   2.0,   1.0 )
of width sqrt(   8.0 )
is a box, counter-clock-wise:
            W(   0.0,  -3.0 )
            X(   3.0,   0.0 )
            Y(   1.0,   2.0 )
            Z(  -2.0,  -1.0 )

           |
          3+     /
           |      \
          2+ (Y)   w=2*(2**.5)
           |         \
          1+    (B)    /
           |   //
--+--+--+--+--+--+-(X)-+--
 -3 -2 -1  0//1  2  3  4
    (Z)  -1+
         //|
       (A) -2
           |
        -3(W)
           |
         -4+
           |