Computational Geometry

  1. Arrangements and Duality
    1. Line Arrangements
      1. Arrangement Definition
        1. Faces
          1. Edges
            1. Vertices
            2. Combinatorial Complexity
              1. Vertex Count
                1. Edge Count
                  1. Face Count
                    1. Euler's Formula
                    2. Construction Algorithms
                      1. Incremental Construction
                        1. Line Addition
                          1. Face Updates
                            1. Complexity Analysis
                            2. Divide and Conquer
                              1. Recursive Construction
                                1. Merging Arrangements
                              2. Zone Theorem
                                1. Statement
                                  1. Proof Techniques
                                  2. Single Cell Complexity
                                    1. Many Faces Problem
                                    2. Duality Transform
                                      1. Point-Line Duality
                                        1. Transformation Rules
                                          1. Incidence Preservation
                                            1. Order Preservation
                                            2. Properties of Duality
                                              1. Involution Property
                                                1. Geometric Interpretations
                                                2. Applications
                                                  1. Ham Sandwich Theorem
                                                    1. Linear Programming
                                                      1. Range Searching
                                                      2. Projective Duality
                                                      3. Hyperplane Arrangements
                                                        1. Higher-Dimensional Arrangements
                                                          1. Complexity Bounds
                                                            1. Construction Methods
                                                              1. Applications
                                                                1. Linear Programming
                                                                  1. Optimization

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                                                              8. Geometric Data Structures and Searching

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                                                              10. Motion Planning