Page 46 - DCAP313_LAB_ON_COMPUTER_GRAPHICS

Lab on Computer Graphics

Notes
(x, y)  description
(0, 0) –0.57042 illuminate pixel (0, 0)
0.14789 increment  by 0.71831
(1, 0) increment x by 1
(1, 0) 0.14789 illuminate pixel (1, 0)
since ε > 0
(1, 1) increment y by 1
–0.85211 decrement ε by 1
–0.1338 increment ε by 0.71831
(2, 1) increment x by 1
(2, 1) –0.1338 illuminate pixel (2, 1)
0.58451 increment ε by 0.71831
(3, 1) increment x by 1
(3, 1) 0.58451 illuminate pixel (3, 1)
since ε > 0
(3, 2) increment y by 1
–0.41549 decrement ε by 1
0.30282 increment ε by 0.71831
(4, 2) increment x by 1
(4, 2) 0.30282 illuminate pixel (4, 2)

Assuming that the DA is the x-axis, the algorithmic description of Bresenham’s algorithm for
lines with arbitrary endpoints is as follows:
Bresenham’s Algorithm
The points (x 1 , y 1 ) and (x 2 , y 2 ) are assumed not equal

And have arbitrary real coordinates is assumed to be real.
Let ∆x = x 2 – x 1

Let ∆y = y 2 – y 1
Dy
Let m =
Dx
Let i 1 = y Í Î 1 ˙ ˚

Let j = y Í Î 1 ˙ ˚

Let i 2 = 2 ˙ ˚
x Í Î
))
Ê D ( y 1 - (x - i 1 ˆ
Let  = – 1 - (y 1 - ) - D x 1 ˜ ¯
j
Á
Ë
for i = 1 to i 2
i
illuminate (i, j)
if ( ≥ 0)
j + = 1
 – = 1.0

40 LOVELY PROFESSIONAL UNIVERSITY