Which Step Size Is Chosen in the DDA Algorithm and Why?

The Digital Differential Analyzer (DDA) algorithm is a fundamental line-drawing algorithm in computer graphics. One of the most common exam, interview, and academic questions related to this algorithm is:

Which step size is chosen in the DDA algorithm and why?

This article explains the exact step size used in the DDA algorithm, the reason behind it, and how it ensures accurate and efficient line rasterization on digital displays.

Understanding the DDA Algorithm (Quick Recap)

The DDA algorithm is used to draw a straight line between two points on a raster screen by incrementally calculating intermediate pixel positions.

If you want a full explanation of the algorithm itself, refer to:
👉 DDA Line Algorithm – Complete Explanation

Which Step Size Is Chosen in the DDA Algorithm?

✅ Step size in the DDA algorithm is chosen as:

[
\textbf{Steps} = \max(|dx|, |dy|)
]

Where:

• ( dx = x_2 – x_1 )
• ( dy = y_2 – y_1 )

Increment values are then calculated as:

[
x_{increment} = \frac{dx}{\text{Steps}}
]

[
y_{increment} = \frac{dy}{\text{Steps}}
]

Why Is This Step Size Chosen?

The step size is chosen as the maximum of |dx| and |dy| for accuracy, uniformity, and simplicity.

1️⃣ To Ensure Uniform Pixel Distribution

Choosing the maximum value ensures that:

• Each step moves exactly one pixel in the dominant direction
• The line does not skip pixels
• The line appears continuous and smooth

2️⃣ To Handle All Line Slopes Correctly

• If |dx| > |dy| → line is more horizontal
• If |dy| > |dx| → line is more vertical

By selecting the larger value, the algorithm:

• Adapts automatically to steep and shallow slopes
• Maintains consistent pixel spacing

3️⃣ To Simplify Floating-Point Calculations

DDA uses floating-point arithmetic.
Using the maximum difference:

• Keeps increments ≤ 1
• Reduces rounding errors
• Improves numerical stability

4️⃣ To Avoid Gaps and Overlapping Pixels

If a smaller step size were chosen:

• Pixels would be skipped (gaps)
• The line would appear broken

If a larger step size were chosen:

• Pixels would overlap
• The line would appear thicker or distorted

Example: Step Size Selection in DDA

Suppose:

• Start point: (2, 3)
• End point: (10, 7)

[
dx = 10 – 2 = 8
]
[
dy = 7 – 3 = 4
]

Step size:
[
\text{Steps} = \max(8, 4) = 8
]

Increments:
[
x_{inc} = 8 / 8 = 1
]
[
y_{inc} = 4 / 8 = 0.5
]

➡ Each iteration moves 1 pixel horizontally and 0.5 pixel vertically, producing a smooth straight line.

Why Not Use a Fixed Step Size?

Using a fixed step size would:

• Fail for steep lines
• Produce jagged edges
• Increase aliasing
• Reduce accuracy

The dynamic step size is what makes the DDA algorithm adaptable and reliable.

Advantages of This Step Size Choice

DDA Step Size vs Other Line Algorithms

Compared to Bresenham’s Line Algorithm:

• DDA uses floating-point arithmetic
• Bresenham uses integer arithmetic
• DDA is easier to understand
• Bresenham is faster in hardware implementations

Related reading:
👉 Cohen–Sutherland Line Clipping Algorithm

Exam-Ready Answer (Short & Direct)

In the DDA algorithm, the step size is chosen as the maximum of |dx| and |dy| to ensure uniform pixel plotting, handle all line slopes correctly, and avoid gaps or overlaps while drawing a straight line.

This answer is perfect for exams and interviews.

Conclusion

The step size in the DDA algorithm is a deliberate and mathematically sound choice. By selecting the maximum of horizontal and vertical differences, the algorithm achieves:

• Smooth line rendering
• Correct slope handling
• Efficient pixel plotting

This simple decision is what makes the DDA algorithm reliable in computer graphics systems.

 DDA ALGORITHM PSEUDOCODE (WITH EXPLANATION)

Pseudocode

Input: (x1, y1), (x2, y2)

dx = x2 - x1
dy = y2 - y1

steps = max(|dx|, |dy|)

x_increment = dx / steps
y_increment = dy / steps

x = x1
y = y1

for i = 1 to steps
    plot(round(x), round(y))
    x = x + x_increment
    y = y + y_increment
end for

Explanation

• steps ensures uniform progression
• Increment values keep movement ≤ 1 pixel
• Rounding converts floating values to pixel positions
• Loop executes predictable number of iterations

 DDA vs BRESENHAM COMPARISON (TABLE + DIAGRAM)

Comparison Table

Conceptual Diagram (Textual)

DDA Line:
(x, y) → (x+1, y+0.5) → (x+2, y+1.0)

Bresenham Line:
(x, y) → (x+1, y+1) → (x+2, y+1)

✔ DDA calculates real values
✔ Bresenham decides pixels using decision variables

 VIVA / EXAM QUESTIONS & ANSWERS

Q1. What is the step size in the DDA algorithm?

Answer:
The step size is the maximum of |dx| and |dy|.

Q2. Why is max(|dx|, |dy|) chosen?

Answer:
To ensure uniform pixel plotting and proper slope handling.

Q3. What type of arithmetic does DDA use?

Answer:
Floating-point arithmetic.

Q4. Which algorithm is faster: DDA or Bresenham?

Answer:
Bresenham’s algorithm.

Q5. Is DDA suitable for real-time graphics?

Answer:
No, due to floating-point overhead.