Computational Geometry

  1. Mathematical and Algorithmic Foundations
    1. Models of Computation
      1. RAM Model
        1. Real RAM Model
          1. Word RAM Model
            1. Pointer Machine Model
              1. Algebraic Decision Trees
              2. Asymptotic Analysis
                1. Big O Notation
                  1. Omega Notation
                    1. Theta Notation
                      1. Worst-Case Analysis
                        1. Average-Case Analysis
                          1. Amortized Analysis
                            1. Output-Sensitive Analysis
                            2. Basic Geometric Objects
                              1. Points
                                1. Coordinate Systems
                                  1. Cartesian Coordinates
                                    1. Polar Coordinates
                                      1. Spherical Coordinates
                                      2. Homogeneous Coordinates
                                        1. Point Arithmetic
                                        2. Vectors
                                          1. Vector Representation
                                            1. Vector Addition
                                              1. Scalar Multiplication
                                                1. Dot Product
                                                  1. Geometric Interpretation
                                                    1. Algebraic Computation
                                                    2. Cross Product
                                                      1. Geometric Interpretation
                                                        1. Algebraic Computation
                                                      2. Lines
                                                        1. Line Equations
                                                          1. Implicit Form
                                                            1. Parametric Form
                                                              1. Two-Point Form
                                                                1. Point-Slope Form
                                                                2. Rays
                                                                  1. Line Segments
                                                                    1. Distance Computations
                                                                    2. Polygons
                                                                      1. Simple Polygons
                                                                        1. Convex Polygons
                                                                          1. Star-Shaped Polygons
                                                                            1. Monotone Polygons
                                                                              1. Polygon Representation
                                                                                1. Vertex List
                                                                                  1. Edge List
                                                                                    1. Adjacency Structures
                                                                                  2. Polyhedra
                                                                                    1. Convex Polyhedra
                                                                                      1. Non-Convex Polyhedra
                                                                                        1. Euler's Formula
                                                                                          1. Platonic Solids
                                                                                        2. Data Structures for Geometric Objects
                                                                                          1. Implicit Representations
                                                                                            1. Parametric Representations
                                                                                              1. Boundary Representations
                                                                                                1. Winged-Edge Data Structure
                                                                                                  1. Doubly Connected Edge List
                                                                                                    1. Half-Edge Data Structure
                                                                                                      1. Quad-Edge Data Structure

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                                                                                                    1. Introduction to Computational Geometry

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                                                                                                    3. Fundamental Geometric Predicates