Page 44 - DCAP313_LAB_ON_COMPUTER_GRAPHICS

Lab on Computer Graphics

Notes
(x, y) Πdescription

(0, 0) –2 illuminate pixel (0, 0)
1 increment ε by ∆y
(1, 0) increment x by 1
(1, 0) 1 illuminate pixel (1, 0)
since Π> 0
(1, 1) increment y by 1
–4 decrement Œ by 5
–1 increment ε by ∆y
(2, 1) increment x by 1

(2, 1) –1 illuminate pixel (2, 1)
2 increment ε by ∆y
(3, 1) increment x by 1

(3, 1) 2 illuminate pixel (3, 1)
since Π> 0
(3, 2) increment y by 1
–3 decrement Œ by 5
0 increment ε by ∆y
(4, 2) increment x by 1
(4, 2) 0 illuminate pixel (4, 2)

for i = 1 to x 2 – 1
x
illuminate (i, j)
if ( ≥ 0)
j + = 1
–
 – = ∆x
end if
i + = 1
–
 + = ∆y
next i
finish
3.2.3 Bresenham’s Algorithm for Lines with Arbitrary Endpoints

Bresenham’s algorithm is limited by the detail that the lines to be drawn have endpoints with
integer coordinates. Now we consider a version of Bresenham’s algorithm for lines that have
endpoints with real coordinates. The only problem to conquer is the initial setting of the error.
Once this is done, the algorithm proceeds as before.
Consider a line with initial point (x 1 , y 1 ) and terminal point (x 2 , y 2 ) in device space, where we
assume the points are not the same. To calculate the correct in this case, we refer to the following
figure.

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