DDA Line Drawing Algorithm

1. Line Drawing Algorithms

Line drawing algorithms determine which pixels should be illuminated to represent a straight line on a raster display.

• Used in raster graphics
• Convert mathematical lines to pixels
• Examples: DDA, Bresenham

2. What is DDA Algorithm?

DDA is an incremental algorithm that calculates intermediate points between two endpoints by incrementing x and y values step by step.

• Uses floating-point calculations
• Simple and easy to understand

3. Basic Principle of DDA

The algorithm works by determining the number of steps required to draw the line and incrementing x and y coordinates accordingly.

• Steps = max(|dx|, |dy|)
• x increment = dx / steps
• y increment = dy / steps

4. Mathematical Formulation

dx = x2 - x1
dy = y2 - y1
steps = max(|dx|, |dy|)

x_inc = dx / steps
y_inc = dy / steps

5. Steps of DDA Algorithm

• Input starting and ending points
• Calculate dx and dy
• Determine number of steps
• Compute x and y increments
• Plot points incrementally

6. DDA Algorithm (Pseudocode)

x = x1
y = y1
for i = 1 to steps
    plot(round(x), round(y))
    x = x + x_inc
    y = y + y_inc

7. Example

To draw a line from (2, 3) to (10, 7):

• dx = 8, dy = 4
• steps = 8
• x_inc = 1, y_inc = 0.5

8. Advantages of DDA Algorithm

• Simple implementation
• Works for all line slopes
• Easy to understand

9. Disadvantages of DDA Algorithm

• Uses floating-point arithmetic
• Less efficient than Bresenham
• Rounding errors may occur

10. Applications of DDA Algorithm

• Basic graphics systems
• Educational purposes
• Line rasterization

Practice Questions

1. What is DDA algorithm?
2. Explain steps of DDA algorithm.
3. Write DDA pseudocode.
4. List advantages and disadvantages of DDA.
5. Draw a line using DDA algorithm.

Practice Task