Write Midpoint Circle Drawing Algorithm. Give its advantages and disadvantages.

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The Midpoint Circle Drawing Algorithm is a fundamental computer graphics technique used to efficiently draw circles on pixel-based displays. Unlike naive approaches that use floating-point arithmetic and trigonometric functions, this algorithm employs only integer operations and leverages the eight-way symmetry of circles. By calculating points for just one octant and reflecting them to the other seven octants, it significantly reduces computational overhead while maintaining high accuracy. The algorithm follows a systematic approach. First, we input the circle's center coordinates and radius. We initialize the starting point at x equals zero and y equals radius, with a decision parameter p0 equals one minus radius. The main loop continues while x is less than or equal to y. In each iteration, we plot the current point and its seven symmetric counterparts, update the decision parameter based on whether it's positive or negative, increment x, and conditionally decrement y. The process stops when x becomes greater than y, ensuring we've covered one complete octant. The decision parameter is the heart of the algorithm's efficiency. At each step, we have two candidate pixels: the East pixel at coordinates x plus one, y, and the South-East pixel at x plus one, y minus one. The decision parameter p helps us choose which pixel is closer to the true circle boundary. If p is negative, we select the East pixel and update p by adding two x plus three. If p is greater than or equal to zero, we choose the South-East pixel and update p by adding two x minus two y plus five. This mathematical approach ensures optimal pixel selection without expensive distance calculations. The Midpoint Circle Drawing Algorithm offers several significant advantages over naive approaches. First, it achieves computational efficiency by using only integer arithmetic, eliminating expensive floating-point operations and square root calculations. This leads to high-speed execution, making it ideal for real-time graphics applications. The algorithm maintains high accuracy by systematically selecting pixels closest to the true circle boundary, resulting in smooth, visually appealing circles. Additionally, it's memory efficient with minimal storage requirements and simple data structures. The time complexity is linear in the radius, compared to quadratic complexity in naive methods, making it substantially faster for large circles. While highly efficient, the Midpoint Circle Algorithm has some limitations. The implementation complexity can be challenging for beginners, requiring careful handling of decision parameter logic and multiple conditional branches. The algorithm assumes a circle centered at the origin, necessitating coordinate transformation for arbitrary center positions, which adds computational overhead. Additionally, it's specifically optimized for circles and doesn't easily extend to other shapes like ellipses. However, these disadvantages are minor compared to its benefits. The algorithm remains the industry standard for circle rasterization due to its exceptional efficiency, accuracy, and speed, making it indispensable in computer graphics applications.