Digitize the line with endpoints (2,2) and (10,5) using DDA

The Digital Differential Analyzer (DDA) algorithm is used to rasterize lines in computer graphics, converting a line from continuous coordinates to discrete pixels on a raster grid. Here’s how you can use the DDA algorithm to digitize the line with endpoints (2,2) and (10,5):

### **Steps for DDA Algorithm**

1. **Calculate Line Parameters**:

  - Determine the differences in x and y coordinates between the endpoints.

  - Compute the number of steps required to draw the line, which is based on the larger of the differences in x or y coordinates.

2. **Calculate Increment Values**:

  - Compute the increments for x and y coordinates based on the number of steps.

3. **Iterate and Plot Points**:

  - Start at the initial point and incrementally plot the next points according to the calculated increments.

### **Detailed Calculation**

**1. Calculate Line Parameters**

- **Endpoints**: (x0, y0) = (2, 2) and (x1, y1) = (10, 5)

- **Δx (change in x)**: x1 - x0 = 10 - 2 = 8

- **Δy (change in y)**: y1 - y0 = 5 - 2 = 3

**2. Compute Number of Steps**

The number of steps is the maximum of the absolute values of Δx and Δy:

- **Steps**: max(|Δx|, |Δy|) = max(8, 3) = 8

**3. Calculate Increment Values**

- **Increment for x**: Δx / steps = 8 / 8 = 1

- **Increment for y**: Δy / steps = 3 / 8 = 0.375

**4. Iteration and Plotting**

Start at (x0, y0) = (2, 2). For each step, calculate the next point by adding the increments and round to the nearest integer for pixel positions:

- **Initial Point**: (x, y) = (2, 2)

  **For each step**:

  x = x + increment_x

  y = y + increment_y

Let’s calculate the points for each step:

1. **Step 0**:

  x = 2 + (0 * 1) = 2

  y = 2 + (0 * 0.375) = 2

  - **Plot**: (2, 2)

2. **Step 1**:

   x = 2 + (1 * 1) = 3

  y = 2 + (1 * 0.375) = 2.375

  - **Plot**: (3, 2)

3. **Step 2**:

   x = 2 + (2 * 1) = 4

  y = 2 + (2 * 0.375) = 2.75

  - **Plot**: (4, 3)

4. **Step 3**:

  x = 2 + (3 * 1) = 5

   y = 2 + (3 * 0.375) = 3.125

  - **Plot**: (5, 3)

5. **Step 4**:

  x = 2 + (4 * 1) = 6

  y = 2 + (4 * 0.375) = 3.5

  - **Plot**: (6, 4)

6. **Step 5**:

  x = 2 + (5 * 1) = 7

  y = 2 + (5 * 0.375) = 3.875

  - **Plot**: (7, 4)

7. **Step 6**:

  x = 2 + (6 * 1) = 8

  y = 2 + (6 * 0.375) = 4.25

  - **Plot**: (8, 4)

8. **Step 7**:

  x = 2 + (7 * 1) = 9

  y = 2 + (7 * 0.375) = 4.625

  - **Plot**: (9, 5)

9. **Step 8**:

  x = 2 + (8 * 1) = 10

  y = 2 + (8 * 0.375) = 5

  - **Plot**: (10, 5)

### **Summary of Points**

Using the DDA algorithm, the points to plot for the line from (2, 2) to (10, 5) are approximately:

(2, 2)

(3, 2)

(4, 3)

(5, 3)

(6, 4)

(7, 4)

(8, 4)

(9, 5)

(10, 5)

These points represent the discrete pixels that form the line on a raster grid, effectively digitizing the continuous line segment.

Hope you got this.