Bresenham's Line Drawing Algorithm

Presented by J.E. Bresenham in 1965 (IBM Systems journal 4, No. 1 pg 25-30

Drawing a line in a 2D plane requires four pieces of information, two
cooridinate pairs (x1,y1) and (x2,y2), the endpoints. We could calculate
the slope of the line from these two endpoints as

                  y2-y1
             m = -------
                  x2-x1

and then use the formula

              y = mx + b

to plot points on the x,y plane. The problem with this is it involves
floating point arithmetic and division. Even thought today's newer CPU's
may have a floating point coprocessor, using integer (whole numbers)
arithmetic is still faster. We can also avoid the slow process of dividing.

The Bresenham's Algorithm uses a method known as "incremental division".
For instance, the number 45 can be divided by 3 by subtracting 3 until what
you have left is less than 3. The number of times you subtracted is 45/3.
What you have left is the remainder.

As it turns out, the reason you need division in drawing lines is to
determing the rise vs run or x vs y of a line. That is, how far in the x
direction should I draw until the y coordinate should change?. We don't
need to know the slope at the beginning, but just how many x's in a number
of y's or vice-versa.
One point before we continue: The Major axis is the one in which the line
travels furthest, and the other is the Minor axis, e.g. for the line
(1,1)(7,9), y is the Major axis.
Bresenham's algorithm does this: Begin drawing at the starting point. Each
time through the loop, move one pixel in the major axis toward the endpoint
and check to see if it is necessary to move one pixel in the minor axis.