Line Intersection Detector

• Draw segments: Click twice on the canvas to create a line segment
• Add more segments: Keep clicking to add additional line segments
• View intersections: Red dots automatically appear where segments intersect
• Clear canvas: Use the "Clear All" button to start over
• Undo: Remove the most recently drawn segment

This app uses computational geometry to detect line segment intersections:

• Basic approach: Checks all pairs of line segments for intersections
• Intersection test: Uses vector cross products and parametric equations
• Time complexity: O(n²) for n line segments (naive approach)
• Practical optimization: Bentley-Ottmann sweep line algorithm can achieve O((n + k) log n) where k is the number of intersections

• Computer Graphics: Rendering, clipping, hidden surface removal
• CAD Systems: Detecting overlaps in engineering drawings
• GIS: Map overlay operations, route planning
• Robotics: Path planning and collision detection
• Game Development: Collision detection, ray casting

Two line segments intersect if:

• Orientation test: The segments straddle each other (opposite orientations)
• Parametric form: Each segment can be expressed as P = P1 + t(P2 - P1) where 0 ≤ t ≤ 1
• Intersection point: Solve the system of parametric equations to find the intersection coordinates
• Cross product: Used to determine if points are on opposite sides of a line

• Parallel segments: No intersection unless collinear
• Collinear segments: May overlap (not detected as point intersection)
• Endpoint touching: Counted as intersection
• Degenerate segments: Single points (length 0) are handled