# Bresenham Circle Drawing vs. Midpoint Circle Drawing

## What's the Difference?

Bresenham Circle Drawing and Midpoint Circle Drawing are both algorithms used to draw circles on a computer screen. While Bresenham Circle Drawing uses integer arithmetic to determine the pixels closest to the true circle path, Midpoint Circle Drawing uses floating-point arithmetic to calculate the pixels that lie on the circle's circumference. Bresenham Circle Drawing is known for its efficiency and speed, making it a popular choice for drawing circles in computer graphics. On the other hand, Midpoint Circle Drawing is more accurate and produces smoother circles, but it may be slower due to the use of floating-point calculations. Ultimately, the choice between the two algorithms depends on the specific requirements of the application.

## Comparison

Attribute | Bresenham Circle Drawing | Midpoint Circle Drawing |
---|---|---|

Algorithm type | Incremental | Incremental |

Pixel selection | Octant selection | Octant selection |

Pixel decision parameter | Decision parameter based on midpoint | Decision parameter based on midpoint |

Pixel update parameter | Update parameter based on decision parameter | Update parameter based on decision parameter |

Optimization | Optimized for integer arithmetic | Optimized for integer arithmetic |

## Further Detail

### Introduction

Circle drawing algorithms are essential in computer graphics for rendering circles efficiently. Two popular algorithms for drawing circles are Bresenham's circle drawing algorithm and Midpoint circle drawing algorithm. Both algorithms have their own set of attributes and advantages, which we will explore in this article.

### Algorithm Overview

Bresenham's circle drawing algorithm is based on the idea of using integer arithmetic to plot points on a circle. It is a simple and efficient algorithm that avoids floating-point arithmetic. The algorithm calculates the next pixel position based on the current pixel position and the decision parameter. On the other hand, the Midpoint circle drawing algorithm is based on the idea of using a decision parameter to determine the next pixel position. It is also an efficient algorithm that avoids floating-point arithmetic.

### Accuracy

One of the key differences between Bresenham's and Midpoint circle drawing algorithms is their accuracy in drawing circles. Bresenham's algorithm is known for its high accuracy in drawing circles, as it uses integer arithmetic to calculate pixel positions. This results in a more precise circle compared to the Midpoint algorithm. On the other hand, the Midpoint algorithm may introduce slight inaccuracies in the circle drawing due to its decision parameter calculation.

### Efficiency

Efficiency is another important factor to consider when comparing Bresenham's and Midpoint circle drawing algorithms. Bresenham's algorithm is known for its efficiency in terms of computational complexity. It requires fewer operations to draw a circle compared to the Midpoint algorithm. This makes Bresenham's algorithm a preferred choice for applications where performance is critical. On the other hand, the Midpoint algorithm is also efficient but may require slightly more operations to draw a circle compared to Bresenham's algorithm.

### Implementation

When it comes to implementation, both Bresenham's and Midpoint circle drawing algorithms are relatively easy to implement. Bresenham's algorithm involves calculating the decision parameter and updating pixel positions based on it. The implementation of Bresenham's algorithm is straightforward and can be easily understood. Similarly, the Midpoint algorithm involves calculating the decision parameter and updating pixel positions accordingly. The implementation of the Midpoint algorithm is also simple and can be easily implemented in code.

### Robustness

Robustness is another factor to consider when comparing Bresenham's and Midpoint circle drawing algorithms. Bresenham's algorithm is known for its robustness in handling different circle sizes and positions. It can draw circles of varying sizes with high accuracy and efficiency. On the other hand, the Midpoint algorithm may not be as robust as Bresenham's algorithm when it comes to handling different circle sizes and positions. It may introduce slight inaccuracies in drawing circles of certain sizes.

### Conclusion

In conclusion, both Bresenham's and Midpoint circle drawing algorithms have their own set of attributes and advantages. Bresenham's algorithm is known for its high accuracy and efficiency, making it a preferred choice for applications where precision and performance are critical. On the other hand, the Midpoint algorithm is also efficient and easy to implement but may introduce slight inaccuracies in drawing circles. Ultimately, the choice between the two algorithms depends on the specific requirements of the application and the trade-offs between accuracy, efficiency, and robustness.

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