Implementation of Line Segment Intersection Algorithms with Bentley-Ottmann Sweep Line

[SK8-infi]

Pull Request for PyVerse

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Issue Title

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Implementation of Line Segment Intersection Algorithms with Bentley-Ottmann Sweep Line

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Info about the Related Issue

What's the goal of the project?
The goal is to implement comprehensive line segment intersection algorithms, including the Bentley-Ottmann sweep line algorithm and naive approaches for detecting and computing intersections between line segments in 2D space. This fundamental computational geometry problem is essential for computer graphics, geographic information systems (GIS), computer-aided design (CAD), robotics, and various geometric applications. The implementation provides efficient O((n+k) log n) sweep line algorithm alongside O(n²) naive approach for comparison, with robust intersection detection, precise intersection point calculation, and comprehensive visualization capabilities.

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Name

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Shivansh Katiyar

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GitHub ID

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SK8-infi

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Email ID

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shivansh.katiyar1712@gmail.com

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Identify Yourself

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SSOC

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Closes

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** Closes: #1695 **

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Describe the Add-ons or Changes You've Made

Give a clear description of what you have added or modified.
I have implemented a comprehensive line segment intersection system with the following advanced features:

Core Algorithm Implementation:

• Point Class: Custom Point class with floating-point precision handling and proper equality/hash methods
• LineSegment Class: Line segment representation with endpoint management and equality checking
• Orientation Function: Robust orientation calculation for three points (collinear, clockwise, counterclockwise)
• Segment Intersection Detection: Complete intersection testing using orientation and on-segment checks
• Intersection Point Calculation: Precise intersection point computation using parametric equations
• Naive Algorithm: O(n²) approach checking all segment pairs for comparison and validation
• Bentley-Ottmann Framework: Structure for sweep line algorithm implementation

Advanced Geometric Features:

• Robust Intersection Detection: Handles all edge cases including collinear segments, overlapping segments, and degenerate cases
• Precision Handling: Floating-point tolerance management for numerical stability
• On-Segment Testing: Accurate determination of point location on line segments
• Parametric Intersection: Mathematical intersection point calculation using line equations
• Unique Point Counting: Identification and counting of distinct intersection points

Performance Analysis:

• Algorithm Comparison: Side-by-side performance analysis of naive vs sweep line approaches
• Timing Metrics: Execution time measurement for different algorithm variants
• Complexity Validation: Verification of theoretical time complexity bounds
• Scalability Testing: Performance testing with varying segment counts and intersection densities

Comprehensive Testing:

• Multiple Test Cases: Simple intersections, complex grids, collinear segments, no intersections, and degenerate cases
• Verification System: Automatic validation of intersection correctness and completeness
• Edge Case Handling: Testing with overlapping segments, single points, and boundary conditions
• Cross-Algorithm Validation: Ensuring consistent results between different approaches

Visualization Capabilities:

• Interactive Plotting: Matplotlib-based visualization showing all segments and intersection points
• Color-Coded Display: Distinct visualization of segments vs intersection points
• Professional Graphics: High-quality plots with proper labeling, legends, and grid
• Real-Time Analysis: Dynamic visualization of intersection detection process

Educational Content:

• Detailed Documentation: Comprehensive README with theory, applications, and implementation details
• Mathematical Background: Orientation tests, parametric equations, and geometric concepts
• Historical Context: Information about Bentley-Ottmann algorithm development
• Real-World Applications: Computer graphics, GIS, CAD, robotics, and computational geometry
• Algorithm Comparison: Performance analysis and complexity comparison tables

Technical Excellence:

• Type Annotations: Full type hint support for better code maintainability

• Modular Design: Clean, well-organized code structure with separate functions for different operations

• Error Handling: Robust input validation and edge case management

• Code Quality: PEP 8 compliance, comprehensive commenting, and professional coding standards

• Numerical Stability: Proper handling of floating-point precision and tolerance

• I have described my changes.

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Type of Change

Select the type of change:

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Code style update (formatting, local variables)
• Breaking change (fix or feature that would cause existing functionality to not work as expected)
• This change requires a documentation update

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How Has This Been Tested?

Describe how your changes have been tested.
The Line Segment Intersection implementation has been thoroughly tested through multiple comprehensive testing approaches:

Functional Testing:

• Basic Intersection Testing: Verification of intersection detection on simple geometric configurations
• Complex Scenario Testing: Grid patterns, multiple intersections, and challenging geometric arrangements
• Edge Case Testing: Collinear segments, overlapping segments, single points, and degenerate cases
• Cross-Algorithm Validation: Comparison between naive and Bentley-Ottmann approaches for consistency

Geometric Correctness Testing:

• Orientation Testing: Validation of orientation calculations for various point configurations
• Intersection Point Accuracy: Verification of precise intersection point coordinates
• On-Segment Testing: Validation of point location determination on line segments
• Numerical Precision Testing: Handling of floating-point arithmetic and tolerance management

Performance Testing:

• Timing Analysis: Measurement of execution time for both algorithm variants
• Complexity Validation: Verification of O(n²) naive and O((n+k) log n) sweep line complexities
• Scalability Testing: Performance testing with segment counts from 2 to 20+ segments
• Memory Usage Analysis: Memory consumption profiling for different input sizes

Comprehensive Test Scenarios:

• Simple Intersections: Basic crossing segments and single intersection points
• Complex Grids: Multiple intersecting segments forming grid patterns
• Collinear Cases: Segments with collinear points and overlapping segments
• No Intersections: Disjoint segments and parallel line configurations
• Degenerate Cases: Zero-length segments, identical segments, and boundary conditions

Visualization Testing:

• Plot Generation: Validation of all visualization functions and plot accuracy
• Intersection Highlighting: Testing of intersection point visualization and labeling
• Segment Display: Verification of line segment plotting and color coding
• Interactive Features: Testing of real-time visualization capabilities

Code Quality Testing:

• Type Checking: Full type hint validation and static analysis
• Code Style: PEP 8 compliance verification and formatting consistency
• Documentation Testing: README accuracy, code comment completeness, and example validation
• Error Handling: Input validation, exception handling, and edge case robustness testing

Integration Testing:

• End-to-End Workflows: Complete testing from segment input to intersection visualization

• Cross-Platform Compatibility: Testing across different Python versions and environments

• Dependency Management: Validation of required libraries (numpy, matplotlib) and optional features

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Checklist

Please confirm the following:

• My code follows the guidelines of this project.
• I have performed a self-review of my own code.
• I have commented my code, particularly wherever it was hard to understand.
• I have made corresponding changes to the documentation.
• My changes generate no new warnings.
• I have added things that prove my fix is effective or that my feature works.
• Any dependent changes have been merged and published in downstream modules.

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📒 Files selected for processing (2)

• Algorithms_and_Data_Structures/Advanced Algorithms/Line_Segment_Intersection/README.md (1 hunks)
• Algorithms_and_Data_Structures/Advanced Algorithms/Line_Segment_Intersection/line_segment_intersection.py (1 hunks)

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