Goal

Given two integer endpoints (x1,y1) and (x2,y2), light up the pixels that best approximate the straight line segment between them.

Idea

DDA = Digital Differential Analyzer. Use the line equation y = m*x + c with slope m = dy/dx. Step in the major axis by 1 and increment the minor axis by m (or 1/m).

Algorithm Steps

1. Compute dx = x2 - x1, dy = y2 - y1.
2. steps = max(|dx|, |dy|).
3. xInc = dx / steps, yInc = dy / steps.
4. Initialize x = x1, y = y1; plot (round x, round y).
5. Repeat steps times: x += xInc, y += yInc, plot (round x, round y).

Worked Example

Draw line from (2, 3) to (8, 6).

• dx = 6, dy = 3, |dx| > |dy| -> steps = 6.
• xInc = 1, yInc = 0.5.
• Pixels:

Pros and Cons

• Pros: Simple, easy to understand, easy to implement.
• Cons: Uses floating-point arithmetic and rounding in the inner loop -> slow on hardware without an FPU; accumulated rounding errors on long lines.

When to Use

• Teaching, software prototyping where speed is not critical.
• Real hardware uses Bresenham (next lesson) which is integer-only.