Midpoint Algorithm (Bresenham)

     y = (dy/dx)x+b   //slope-intercept

     0 = dy x - dx y + c = Ax + By + C

         (x+1, y+1)                  F(x,y)        = dy x - dx y + c
                NE                   F(x+1, y+1/2) = dy(x+1) - dx(y+1/2) + c
(x+1, y+1/2) ^  O
              \ |                Midpoint: Delta F  = F(x+1, y+1/2) - F(x,y) = dy - 1/2dx
               \|  --Line                  Delta NE = F(x+1, y+1) - F(x,y)   = dy - dx       (USEFUL TO DETERMINE WHICH DIRECTION A PIXEL WILL BE RASTORIZED)
    (x,y)      ---/                        Delta E  = F(x+1, y) - F(x,y)     = dy
          O---/ |
                O                          To avoid floats Bresenham multiplies the implicit equation by 2
                E (x+1, y)                 Delta F  = F(x+1, y+1/2) - F(x,y) = dy - 1/2dx   => 2dy - dx
                                           Delta NE = F(x+1, y+1) - F(x,y)   = dy - dx      => 2dy - 2dx
                                           Delta E  = F(x+1, y) - F(x,y)     = dy           => 2dy


     EXAMPLE





                  |   |   |   |   |   |   |   |   |   |   |   |              F = 0
                  |   |   |   |   |   |   |   |   |   |   |   |              Draw(2,2)
                  |   |   |   |   |   |   |   |(.)|---|---|---|-(8,7)
                  |   |   |   |   |   |   |(/)|   |   |   |   |              F(x,y) = 2(5x - 6y + 2) = 10x - 12y + 4          //Check F + Delta F = 0 + 4
                  |   |   |   |   |   |(/)|   |   |   |   |   |              F(2,3) = 20 - 36 + 4 = -12                       //Since F + Delta F > 0 choose NE
                  |   |   |   |(/)|(/)|   |   |   |   |   |   |              F(7,1) = 70 - 12 + 4 = 62                        //Draw (3,3)
                  |   |   |(/)|   |   |   |   |   |   |   |   |
           (2,2)--|---|(.)|   |   |   |   |   |   |   |   |   |              Delta F = 2dy - dx = 10 - 6 = 4
                  |   |   |   |   |   |   |   |   |   |   |   |              Draw(3,3)

                                                       ---------------------------------------------------------------------------------------------
                  F = F + Delta NE   = -2              |   Check F + Delta F = 6 + 4 = 10
                  Check F + Delta F  = -2 + 4 = 2      |   10 > 0, choose NE
                  Since 2 > 0, Choose NE               |   Draw(6,5)
                  Draw(4,4)                            |   F = F + Delta NE = 6 - 2 = 4
                  F = F + Delta NE = -2 - 2 = -4       |
                                                       |   Check F + Delta F = 4 + 4 = 8
                  Check F + Delta F = -4 + 4 = 0       |   8 > 0, choose NE
                  Since 0 <= 0, Choose E               |   Draw(7,6)
                  Draw(5,4)                            |   F = 4 - 2 = 2
                  F = F + Delta E = -4 + 10 = 6        |
-----------------------------------------------------------------------------------------------------------------------------------------------------
                  m = 5/6                                Draw(6,5)
                  Draw(2,2)                              6 1/6
                  y = y + m = 2 5/6                      Draw(7,6)
                  x++                                    7
                  Draw(3,3)                              Draw(8,7)
                  x++
                  y = y + m = 2 5/6 + 5/6 = 3 4/6                             DDR Method
                  Draw(4,4)                                                 (Line changes are slight between the two algorithm)
                  x++
                  y = y + m = 3 4/6 + 5/6 = 4 3/6
                  Draw(5,5)
                  x++
                  y = 4 3/6 + 5/6 = 5 2/6
------------------------------------------------------------------------------------------------------------------------------------------------------


                  |   |   |   |   |   |   |   |   |   |   |   |              F = 0       dy = 1
                  |   |   |   |   |   |   |   |   |   |   |   |              Draw(1,1)   dx = 7
                  |   |   |   |   |   |   |   |   |   |   |   |
                  |   |   |   |   |   |   |   |   |   |   |   |              Delta F = -5
                  |   |   |   |   |   |   |   |   |   |   |   |              Delta NE = -12
                  |   |   |   |   |   |   |   |   |   |   |   |              Delta E = 2
                  |   |   |   |   |   |   |   |   |   |   |   |
                  |   |   |   |   |(.)|(.)|(.)|(.)|---|---|---|---(8,2)      F + Delta F = 0 - 5 <= 0
          (1,1)---|(.)|(.)|(.)|(.)|   |   |   |   |   |   |   |              Draw(2,1)
                                                                             F + Delta E = 2
                  ----------------------------------------------------------------------------------------------------------------------------------------
                  F + Delta F = 2 - 5 <= 0                 F + Delta F = -6 - 5 <= 0
                  Draw(3,1)                                Draw(6,2)
                  F + Delta E = 4                          F + Delta E = -4

                  F + Delta F = 4 - 5 <= 0                 F + Delta F = -4 - 5 <= 0
                  Draw(4,1)                                Draw(7,2)
                  F + Delta E = 6                          F + Delta E = -2

                  F + Delta F = 6 - 5 > 0                  Draw(8,2)
                  Draw(5,2)
                  F + Delta NE = -6