example exemplify the bresenham line generation

Question

Example: Exemplify the Bresenham line generation algorithm through digitizing the line along with end points (20, 10) and (30, 18)

Solution: m =    (y2 - y1)/( x2 - x1)

 =   (Δy) /(Δx)

=   (18 -10)/( 30 - 20)  = 0.8-------------------(1)

=> Δy = 8 and Δx = 10-------------------(2)

value of initial decision parameter (p0) = 2Δy - Δx= 2 * 8 - 10 = 6 -----------------(3) value of increments for calculating successive decision parameters are:

2Δy = 2 * 8 = 16;                                                  -------------------(4)

2Δy - 2Δx = 2 * 8 - 2 * 10 = - 4                          -------------------(5)

So plot first point (x₀, y₀) = (20, 10) in frame buffer at this time determine successive pixel positions beside line path from decision parameters value (20, 10).

k 0 pk 6   (xk + 1, yk + 1) (21, 11) 1 2 (22, 12) 2 - 2 (23, 12) 3 14 (24, 13) 4 10 (25, 14) 5 6 (26, 15) 6 2 (27, 16) 7 - 2 (28, 16) 8 14 (29, 17) 9 10 (30, 18)

← [use step (d) of algorithm Δ x times]

If p_k > 0 then increase both X and Y

and p_k  +1= p_k + 2Δy - 2Δx

If p_k < 0 then increase X and not Y

and p_k + 1 = p_k + 2Δy