Computational Geometry

  1. Fundamental Geometric Predicates
    1. Orientation Test
      1. Geometric Interpretation
        1. Cross Product Method
          1. Determinant Method
            1. Signed Area Computation
              1. Applications
                1. Convex Hull Construction
                  1. Polygon Testing
                    1. Line Intersection
                  2. In-Circle Test
                    1. Geometric Interpretation
                      1. Determinant Method
                        1. Algebraic Formulation
                          1. Applications
                            1. Delaunay Triangulation
                              1. Voronoi Diagrams
                            2. Point-in-Polygon Test
                              1. Ray Casting Algorithm
                                1. Winding Number Method
                                  1. Crossing Number Method
                                    1. Handling Edge Cases
                                    2. Robustness and Numerical Issues
                                      1. Floating-Point Precision Problems
                                        1. Rounding Errors
                                          1. Catastrophic Cancellation
                                            1. Overflow and Underflow
                                            2. Exact Arithmetic Methods
                                              1. Rational Arithmetic
                                                1. Interval Arithmetic
                                                  1. Adaptive Precision
                                                  2. Symbolic Perturbation
                                                    1. Simulation of Simplicity
                                                      1. Lexicographic Ordering
                                                      2. Handling Degenerate Cases
                                                        1. Collinear Points
                                                          1. Cocircular Points
                                                            1. Overlapping Objects

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                                                        2. Mathematical and Algorithmic Foundations

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                                                        4. Convex Hulls