Example on Bresenham’s algorithm: Consider the line from (0, 0) to (-8,-4), use general Bresenham’s line algorithm to rasterize this line. Evaluate and tabulate all the steps involved. Solution: Given data, (x1, y1)= (0, 0) (x2, y2)= (-8,-4) ∆x=x2-x1=-8-0=8 ∴ S1=-1 ∆y=y2-y1=-4-0=4 ∴S2=-1 Decision Variable=e=2*(∆y)-(∆x) ∴e= 2*(4)-(8) =8-8 =0 ∴ e=0
∴ By using general Bresenham’s algorithm, The result in tabulated form as,
Ms. Punam R. Patil
Pixel
e
x
y
Initially (0,0)
0
0
0
(-1,0)
+8
-1
0
(-2,-1)
0
-2
-1
(-3,-1)
-8
-3
-1
(-4,-2)
0
-4
-2
(Computer Graphics & Multimedia)
Page 1
(-5,-2)
+8
-5
-2
(-6,-3)
0
-6
-3
(-7,-3)
+8
-7
-3
(-8,-4)
0
-8
-4
∴ By pictorial presentation in graph is as shown below,
(0, 0)
-1
-2
-3
-4
-5
-6
-7
-8
-1 -2 -3 -4 -5 -6
--- This is required solution for the given line using Bresenham’s algorithm.
Ms. Punam R. Patil
(Computer Graphics & Multimedia)
Page 2
Example on DDA algorithm: Consider the line from (3, 2) to (4, 7), use DDA line algorithm to rasterize this line. Evaluate and tabulate all the steps involved. Solution: Given data, 1. (x1, y1)= (3, 2) (x2, y2)= (4,7) 2. To find, ∆x=x2-x1=4-3=1 ∆y=y2-y1=7-2=5 3. Find out Length by checking condition, If (dx>=dy) then length=dx else length=dy end if ∴ Length=∆y=5 4. ∆x=∆x/Length =1/5= 0.2 ∆y=∆y/Length=5/5=1 5. Initial values, X=x1+0.5*sign (∆x) =3+0.5* (+) ∴ X=3.5 Y=y1+0.5*sign (∆y) =2+0.5*sign(+) Ms. Punam R. Patil
(Computer Graphics & Multimedia)
Page 3
∴ Y=2.5 6. ∴ Byloop, The result in tabulated form as, Iteration
Pixel
x
y
R(x)
R(y)
0
Initially (3,2)
3.5
2.5
3
2
1
(3,3)
3.7
3.5
3
3
2
(3,4)
3.9
4.5
3
4
3
(4,5)
4.1
5.5
4
5
4
(4,6)
4.3
6.5
4
6
Length=5
(4,7)
4.5
7.5
4
7
∴ By pictorial presentation in graph is as shown below,
7 6 5 4 3 2 1 (0, 0) 1
Ms. Punam R. Patil
2
3
4
5
6
(Computer Graphics & Multimedia)
Page 4
