DDA (Digital Differential Analyzer) Algorithm Computer Graphics

• The Digital Differential Analyzer (DDA) algorithm is a straightforward method for scan-converting lines in computer graphics.
• It calculates the intermediate points between two given points (endpoints of a line) and plots them to draw the line.

Example: Drawing a Line from (1, 1) to (5, 4)

1. Calculate Differences

• Determine the change in x (Δ x) and y (Δ y) between the endpoints (1, 1) and (5, 4).
• Δx (change in x) = X2-X1 i.e 5 - 1 = 4
• Δy (change in y) = Y2-Y1 i.e 4 - 1 = 3

2. Determine Steps

• Find the maximum of the absolute values of Δx and Δy to determine the number of steps needed for the algorithm.
• Steps = max(|Δx|, |Δy|) = max(4, 3) = 4

3. Calculate Increment Values

• Divide Δ x and Δ y by the number of steps to calculate the increments along the x and y directions, respectively.
• X-Increment = Δx / Steps = 4 / 4 = 1
• Y-Increment = Δy / Steps = 3 / 4 = 0.75

4. Initialize Current Points

• Start at (1, 1)

5. Scan Convert:

• Plot the point (1, 1).
• Update the current point:

1Initialize Current Points:
2Start at (1, 1)
3
4Iteration 1:
5    x_new = x_old + X-Increment = 1 + 1 = 2
6    y_new = y_old + Y-Increment = 1 + 0.75 = 1.75
7    Current Point: (2, 1.75)
8
9Iteration 2:
10    x_new = x_old + X-Increment = 2 + 1 = 3
11    y_new = y_old + Y-Increment = 1.75 + 0.75 = 2.5
12    Current Point: (3, 2.5)
13
14Iteration 3:
15    x_new = x_old + X-Increment = 3 + 1 = 4
16    y_new = y_old + Y-Increment = 2.5 + 0.75 = 3.25
17    Current Point: (4, 3.25)
18
19Iteration 4:
20    x_new = x_old + X-Increment = 4 + 1 = 5
21    y_new = y_old + Y-Increment = 3.25 + 0.75 = 4
22    Current Point: (5, 4)
23
24Iteration 5:
25    x_new = x_old + X-Increment = 5 + 1 = 6
26    y_new = y_old + Y-Increment = 4 + 0.75 = 4.75
27    Current Point: (6, 4.75)
28

• Repeat the process until reaching the endpoint (5, 4).

Visualization:

• (1, 1) -> (2, 1.75) -> (3, 2.5) -> (4, 3.25) -> (5, 4)
• The DDA algorithm essentially takes steps along the line, plotting points at each step.
• It calculates the increments needed in the x and y directions to distribute pixels along the line evenly.
• In this example, it draws a line from (1, 1) to (5, 4) by incrementing both x and y values in a smooth manner.

Conclusion

• The DDA algorithm efficiently calculates and plots intermediate points along a line, ensuring a smooth distribution of pixels.
• In the example above, it draws a line from (1, 1) to (5, 4) by continuously incrementing both x and y values.