1. The document discusses the Digital Differential Analyzer (DDA) line drawing algorithm, which is used to approximate and draw line segments on a discrete pixel grid. 2. The DDA algorithm works by calculating the slope of the line between two endpoints, then incrementally stepping from pixel to pixel and calculating the corresponding y-value. 3. The algorithm handles both horizontal, vertical, and diagonal lines by calculating the change in x and y between endpoints and using those values to determine how much to increment x and y with each step.

1. DDA Line Drawing
Algorithm
Muhammad Hamza
157101
Bioinformatics 7th
Graphics andVisualization
Presented to: Sir Muhammad Rizwan
Govt Post Graduate College Mandian
Abbottabad

2. Talk Sequence:
• What is Line
• Line Equation
• Slope of Line
• Examples of Drawing Line
• DDA

3. DDA Line Drawing Algorithm
• DDA stands for Digital Differential Analyzer
• A line drawing algorithm is a graphical algorithm for approximating a line
segment on discrete graphical media.
• This algorithm is used to draw a line on computer pixels.

4. What is a Line?
• A line in Computer graphics typically refers to line segment, which is a
portion of straight line that extends indefinitely in opposite direction.
• It is defined by its two end points & the slope intercept equation for a line:
y = mx + b
where, m = Slope of the line
b = the y intercept of a line

5. • The two endpoints of a line segment are specified at positions (x1,y1) and
(x2,y2).

6. Slope Conditions for Algorithms
• 1. ∆ y/ ∆ x > 1 when 0 >45
• 2. ∆ y/ ∆ x < 1 when 0 <45
• 3. ∆ y /∆ x = 1 when 0 =45
1
2
3

7. 9
8
7
6
5
4
3
2
1
(x1,y1)(x2,y2)
(2,2) (9,2)
∆ x=9-2=7
∆ y=2-2=0
m= ∆ y/ ∆ x=0/7=0
xinc=7/7=1
yinc=0/7=0
X Y
2 2
3 2
4 2
5 2
6 2
7 2
8 2
9 2
1 2 3 4 5 6 7 8 9 10
For Horizontal line

8. 9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 10
(x1,y1)(x2,y2)
(2,2) (9,2)
∆ x=9-2=7
∆ y=2-2=0
m= ∆ y/ ∆ x=0/7=0
xinc=7/7=1
yinc=0/7=0
X Y
2 2
3 2
4 2
5 2
6 2
7 2
8 2
9 2
For Horizontal line

9. 9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 10
(x1,y1)(x2,y2)
(2,3) (2,8)
∆ x=2-2=0
∆ y=8-2=6
m= ∆ y/ ∆ x=6/0=∞
xinc=0/6=0
yinc=6/6=1
X Y
2 3
2 4
2 5
2 6
2 7
2 8
For Vertical line

10. 9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 10
(x1,y1)(x2,y2)
(2,3) (2,8)
∆ x=2-2=0
∆ y=8-2=6
m= ∆ y/ ∆ x=6/0=∞
xinc=0/6=0
yinc=6/6=1
X Y
2 3
2 4
2 5
2 6
2 7
2 8
For Vertical line

11. 9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 10
(x1,y1)(x2,y2)
(1,2) (9,5)
∆ x=9-1=8
∆ y=5-2=3
m= ∆ y/ ∆ x=3/8=0.37
xinc=8/8=1
yinc=3/8=0.37
X Y
1 2
2 2.37=2
3 2.74=3
4 3.11=3
5 3.48=3
6 3.85=4
7 4.22=4
8 4.59=5
9 4.96=5
For any Diagonal line

12. 9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 10
(x1,y1)(x2,y2)
(1,2) (9,5)
∆ x=9-1=8
∆ y=5-2=3
m= ∆ y/ ∆ x=3/8=0.37
xinc=8/8=1
yinc=3/8=0.37
X Y
1 2
2 2.37=2
3 2.74=3
4 3.11=3
5 3.48=3
6 3.85=4
7 4.22=4
8 4.59=5
9 4.96=5
For any Diagnal line

13. DDA Algorithm
dx-=x2-x1;
dy=y2-y1;
If(abs(dx) > abs(dy))
Steps=abs(dx);
else
Steps=abs(dy);
xinc=dx/steps;
yinc=dy/steps;
For(i-1, i<=step, i++)
{
putpixel(x1,y1);
x1=x1+xinc;
y1=y1+yinc;
}

14. Limitation
• There are no decimal points in coordinate system
• Time consuming because algorithm may generate floating numbers
• Line generated will not be smooth.

15. References:
• https://www.tutorialspoint.com/computer_graphics/line_generation_algorit
hm.htm
• http://personales.unican.es/iglesias
• https://www.geeksforgeeks.org/dda-line-generation-algorithm
• https://www.tutorialspoint.com/.../line_generation_algorithm.htm
• www.codingalpha.com/dda-line-drawing-algorithm-c-program