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.

Let's understand the Digital Differential Analyzer (DDA) algorithm for scan-converting lines with illustration as follows:-

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).

• Δ x (change in x) = X2-X1 i.e 5-1 = 4

• Δ y (change in y) = Y2-Y1 i.e 4-1 = 3

2. Determine Steps

• Find the maximum of the absolute values of Δ x and Δ y to determine the number of steps needed for the algorithm.

• Steps = max (|Δ x|, |Δ y|) = 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 = Δ x / Steps = 4 / 4 = 1

• Y-Increment = Δ y / 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:

Initialize Current Points:

Start at (1, 1)

Iteration 1:

    x_new = x_old + X-Increment = 1 + 1 = 2

    y_new = y_old + Y-Increment = 1 + 0.75 = 1.75

    Current Point: (2, 1.75)

Iteration 2:

    x_new = x_old + X-Increment = 2 + 1 = 3

    y_new = y_old + Y-Increment = 1.75 + 0.75 = 2.5

    Current Point: (3, 2.5)

Iteration 3:

    x_new = x_old + X-Increment = 3 + 1 = 4

    y_new = y_old + Y-Increment = 2.5 + 0.75 = 3.25

    Current Point: (4, 3.25)

Iteration 4:

    x_new = x_old + X-Increment = 4 + 1 = 5

    y_new = y_old + Y-Increment = 3.25 + 0.75 = 4

    Current Point: (5, 4)

Iteration 5:

    x_new = x_old + X-Increment = 5 + 1 = 6

    y_new = y_old + Y-Increment = 4 + 0.75 = 4.75

    Current Point: (6, 4.75)

• 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 takes steps along the line, plotting points at each step.

• It calculates the increments needed in the x and y direction to evenly distribute pixels along the line.

• This example draws a line from (1,1) to (5,4) by smoothly incrementing both x and y values.

Conclusion

• The DDA algorithm efficiently calculates and plots intermediate points along a line, ensuring a smooth distribution of pixels.

• The example above draws a line from (1,1) to (5,4) by continuously incrementing both x and y values.