Graphics - Line Drawing Samples

1. Drawing Algorithms
CS4815 1
B. Bartlett, M. Santos (CRIS)
Computer Graphics
B. Bartlett, M.
Santos
D2-037
Main Building.
ben.bartlett@ul.ie
matheus.santos@ul.ie
Spring 2025
Computer Graphics

2. Drawing Algorithms
CS4815 2
B. Bartlett, M. Santos (CRIS)
Examples - DDA
L1 = p(0,0) ; q(2,10)
L2 = p(10,7) ; q(2,4)
----------------------------
|
𝑚
| ≤ 1
|
𝑚
|> 1

3. Drawing Algorithms
CS4815 3
B. Bartlett, M. Santos (CRIS)
Which pixels?
L1: (0,0) (2,10)
Sampling in
0
0
1
2
1 2 3 4
3
4
5
6
7
8
9
10
𝑚 =
10
2
=5
0 0 0
1 1 5
2 2 10
𝑦 𝑘+1= 𝑦 𝑘 +m

4. Drawing Algorithms
CS4815 4
B. Bartlett, M. Santos (CRIS)
Which pixels?
L1: (0,0) (2,10)
Sampling in
0
0
1
2
1 2 3 4
3
4
5
6
7
8
9
10
𝑚 =
10
2
=5
0 0 0
1 0.2 1
2 0.4 2
3 0.6 3
4 0.8 4
5 1 5
6 1.2 6
7 1.4 7
8 1.6 8
9 1.8 9
10 2 10
𝑥𝑘+1= 𝑥𝑘 +
1
𝑚
|𝑚|>1

5. Drawing Algorithms
CS4815 5
B. Bartlett, M. Santos (CRIS)
Which pixels?
L2: (10,7) (2,4)
Sampling in
0
2
1
2
3 4 5 6
3
4
5
6
7
8
9
10
𝑚 =
3
8
0 2 4
1 3 4.375
2 4 4.75
3 5 5.125
4 6 5.5
5 7 5.875
6 8 6.25
7 9 6.625
8 10 7
𝑦 𝑘+1= 𝑦𝑘 +𝑚|𝑚|≤1
7 8 9 10

6. Drawing Algorithms
CS4815 6
B. Bartlett, M. Santos (CRIS)
Examples - Bresenham’s
L1 = p(0,0) ; q(2,10)
L2 = p(10,7) ; q(2,4)

7. Drawing Algorithms
CS4815 7
B. Bartlett, M. Santos (CRIS)
Which pixels?
L2: (10,7) (2,4)
Sampling in
0
2
1
2
3 4 5 6
3
4
5
6
7
8
9
10
𝑚 =
3
8
0 2 4 -2
1 3 4 4
2 4 5 -6
3 5 5 0
4 6 6 -10
5 7 6 -4
6 8 6 2
7 9 7 -8
8 10 7
7 8 9 10
Sampling in
Positive Slope

8. Drawing Algorithms
CS4815 8
B. Bartlett, M. Santos (CRIS)
Examples - Bresenham’s
L3 = p(-4,7) ; q(-2,-4)
L4 = p(5,2) ; q(11,4)
L5 = p(6,12) ; q(14,5)

9. Drawing Algorithms
CS4815 9
B. Bartlett, M. Santos (CRIS)
Which pixels?
L5: (6,12) (14,5)
Sampling in
2
6
3
4
7 8 9 10
5
6
7
8
9
10
11
12
𝑚=−
7
8
*
0 6 -12 6
1 7 -11 4
2 8 -10 2
3 9 -9 0
4 10 -8 -2
5 11 -8 12
6 12 -7 10
7 13 -6 8
8 14 -5
11 12 13 14
Sampling in
Negative Slope
Swap sign for calculations
L5: (6,-12) (14,-5)
(*) real value is equal to -*

10. Drawing Algorithms
CS4815 10
B. Bartlett, M. Santos (CRIS)
Which pixels?
L3: (-4,7) (-2,-4)
-3
-1
-2
-1
0 1 2 3
0
1
2
3
4
5
6
7
𝑚=−
11
2
* **
0 -4 2 -7
1 -3 2 -3
2 -2 2 1
3 -1 3 -17
4 0 3 -13
5 1 3 -9
6 2 3 -5
7 3 3 -1
8 4 3 3
9 5 4 -15
10 6 4 -11
11 7 4
4 5 6 7
Sampling in
Swap for calculations
L3: (7,-4) (-4,-2)
Since (-4 < 7), rearrange:
L3: (-4,-2)(7,-4)
Negative Slope
Swap sign for calculations
L3: (-4,2) (7,4)
(*) true value is equal to -**
(**) true value is equal to *
-2
-3
-4
-4