Computational Geometry

  1. Line Segment Intersection
    1. Problem Formulation
      1. Intersection Detection
        1. Intersection Reporting
          1. Intersection Counting
            1. Applications
              1. Map Overlay
                1. VLSI Design
                  1. Computer Graphics
                2. Brute-Force Approach
                  1. Algorithm Description
                    1. Time Complexity
                      1. Space Complexity
                      2. Sweep-Line Paradigm
                        1. Sweep-Line Concept
                          1. Event-Driven Simulation
                            1. Event Points
                              1. Segment Endpoints
                                1. Intersection Points
                                2. Event Queue
                                  1. Priority Queue Implementation
                                    1. Event Ordering
                                    2. Status Structure
                                      1. Active Segments
                                        1. Balanced Search Trees
                                          1. Status Updates
                                        2. Bentley-Ottmann Algorithm
                                          1. Algorithm Overview
                                            1. Event Processing
                                              1. Left Endpoint Events
                                                1. Right Endpoint Events
                                                  1. Intersection Events
                                                  2. Status Maintenance
                                                    1. Intersection Detection
                                                      1. Time Complexity Analysis
                                                        1. Space Complexity Analysis
                                                          1. Output Sensitivity
                                                          2. Degeneracy Handling
                                                            1. Overlapping Segments
                                                              1. Shared Endpoints
                                                                1. Vertical Segments
                                                                  1. Multiple Intersections
                                                                    1. Numerical Precision Issues

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                                                                  4. Convex Hulls

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                                                                  6. Polygon Triangulation