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)
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|
5
|
6
|
(26, 15)
|
|
6
|
2
|
(27, 16)
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|
7
|
- 2
|
(28, 16)
|
|
8
|
14
|
(29, 17)
|
|
9
|
10
|
(30, 18)
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|
|
← [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