Sweep Line Algorithm for Convex Hull in C

[Bhupendrakumar20]

issue resolved :#1562

Pull Request: Sweep Line Algorithm for Convex Hull in C

Description
This PR introduces a C implementation of the Sweep Line Algorithm to compute the convex hull for a set of 2D points. The convex hull is a minimal convex boundary that can enclose all given points. This sweep line approach enables efficient computation by processing points in sorted order and maintaining the hull dynamically, making it well-suited for large sets of points.

Features Implemented

1. Sorting Points: Points are sorted by x-coordinate, enabling efficient left-to-right processing.
2. Convex Hull Construction:
   • The algorithm uses the sweep line method to iteratively build both the lower and upper hulls.
   • Cross Product: This function helps determine the orientation of three points, essential for ensuring the hull's convexity.
3. Memory-Efficient Design: This implementation uses a linked list for dynamically managing points, reducing memory constraints compared to array-based approaches.

Files Added

• sweep_line_convex_hull.c: Contains the main C code implementing the sweep line approach for convex hull.
• README.md: Documentation covering the algorithm, usage, and example scenarios.

Code Overview

• Data Structures:
  • Point struct to store x and y coordinates.
  • Linked list used for handling dynamically increasing points on the hull.
• Key Functions:
  • compare: Helper function to sort points by x and y coordinates.
  • cross_product: Calculates the cross product of three points to determine left or right turns.
  • sweep_line_convex_hull: Computes the convex hull using the sweep line method.
• Main Function:
  • Initializes a set of points and calls sweep_line_convex_hull to calculate and print the vertices of the convex hull.

Example

Consider the input points:

{ (0, 3), (2, 2), (1, 1), (2, 1), (3, 0), (0, 0), (3, 3) }

Expected output (convex hull vertices in counter-clockwise order):

(0, 0)
(3, 0)
(3, 3)
(0, 3)

Testing

The code has been tested with:

• Basic configurations to verify output correctness.
• Edge cases such as collinear points, minimal input (2-3 points), and duplicate points.
• Larger datasets to ensure efficiency and correctness.

Checklist

• Implemented Sweep Line Algorithm for convex hull.
• Verified against known test cases for accuracy.
• Included comprehensive documentation in README.md.
• Code is formatted and commented for readability.

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Additional Notes
The Sweep Line Algorithm provides a foundation for computational geometry tasks that require efficient hull calculations. This PR supports integer coordinates; future extensions could add floating-point support or graphical visualizations.

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[Bhupendrakumar20]

@pankaj-bind kindly review the issue and possibly merge it