Computational Geometry

  1. Polygon Triangulation
    1. Triangulation Fundamentals
      1. Definition of Triangulation
        1. Properties of Triangulations
          1. Diagonal Definition
            1. Triangulation Existence
              1. Applications
                1. Mesh Generation
                  1. Computer Graphics
                    1. Finite Element Methods
                  2. Combinatorial Properties
                    1. Number of Triangulations
                      1. Catalan Numbers
                        1. Counting Triangulations
                          1. Dual Graphs
                          2. Triangulating Monotone Polygons
                            1. Monotone Polygon Definition
                              1. Types of Monotonicity
                                1. y-Monotone
                                  1. x-Monotone
                                  2. Triangulation Algorithm
                                    1. Stack-Based Approach
                                      1. Diagonal Addition
                                      2. Time Complexity
                                        1. Correctness Proof
                                        2. Polygon Partitioning
                                          1. Partitioning into Monotone Pieces
                                            1. Sweep-Line Approach
                                              1. Helper Vertices
                                                1. Diagonal Addition Strategy
                                                  1. Overall Triangulation Algorithm
                                                  2. Ear Clipping Method
                                                    1. Ear Definition
                                                      1. Ear Identification
                                                        1. Iterative Removal
                                                          1. Time Complexity
                                                          2. Optimal Triangulations
                                                            1. Weight Functions
                                                              1. Dynamic Programming Approach
                                                                1. Minimum Weight Triangulation

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                                                              5. Line Segment Intersection

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                                                              7. Proximity Problems