Exemplify bresenham line generation algorithm by digitizing, Computer Graphics

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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 pk > 0 then increase both X and Y

and pk  +1= pk + 2Δy - 2Δx

If pk < 0 then increase X and not Y

and pk + 1 = pk + 2Δy

 


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