Give a line AB where A(0,0) and B(1,3). Find out all coordinates of line AB using DDA algorithm.

Steps to Solve

1. Identify the coordinates and calculate the difference We have two points, A(0,0) and B(1,3). We denote these points as: $$ A(x_0, y_0) = (0, 0) $$ $$ B(x_1, y_1) = (1, 3) $$

Next, we find the differences in the x and y coordinates: $$ \Delta x = x_1 - x_0 = 1 - 0 = 1 $$ $$ \Delta y = y_1 - y_0 = 3 - 0 = 3 $$

2. Calculate the number of steps Determine the number of steps required to draw the line. This is done by taking the maximum of the absolute values of $\Delta x$ and $\Delta y$: $$ \text{steps} = \text{round}(\max(|\Delta x|, |\Delta y|)) = \text{round}(\max(1, 3)) = 3 $$

3. Calculate the increments The increments in x and y coordinates for each step: $$ x_{\text{inc}} = \frac{\Delta x}{\text{steps}} = \frac{1}{3} \approx 0.33 $$ $$ y_{\text{inc}} = \frac{\Delta y}{\text{steps}} = \frac{3}{3} = 1 $$

4. Generate the line points Now we can calculate the coordinates of the points along the line segment. Start at point A(0,0) and incrementally add $x_{\text{inc}}$ and $y_{\text{inc}}$ for each step:

• Step 0: $$ (x, y) = (0 + 0 \cdot 0.33, 0 + 0 \cdot 1) = (0, 0) $$
• Step 1: $$ (x, y) = (0 + 1 \cdot 0.33, 0 + 1 \cdot 1) = (0.33, 1) $$
• Step 2: $$ (x, y) = (0 + 2 \cdot 0.33, 0 + 2 \cdot 1) = (0.66, 2) $$
• Step 3: $$ (x, y) = (0 + 3 \cdot 0.33, 0 + 3 \cdot 1) = (1, 3) $$

5. List of generated points The points along the line segment from A to B are:

• (0, 0)
• (0.33, 1)
• (0.66, 2)
• (1, 3)