Computer Graphics

  1. Mathematical Foundations
    1. Number Systems and Precision
      1. Integer Representation
        1. Floating-Point Representation
          1. Fixed-Point Arithmetic
            1. Precision and Accuracy Issues
            2. Coordinate Systems
              1. 2D Coordinate Systems
                1. Cartesian Coordinates
                  1. Polar Coordinates
                    1. Screen Coordinates
                    2. 3D Coordinate Systems
                      1. Cartesian Coordinates
                        1. Cylindrical Coordinates
                          1. Spherical Coordinates
                          2. Homogeneous Coordinates
                            1. Purpose and Advantages
                              1. Point Representation
                                1. Vector Representation
                                  1. Transformations in Homogeneous Space
                                2. Vector Mathematics
                                  1. Vector Fundamentals
                                    1. Vector Definition and Notation
                                      1. Vector vs Point Distinction
                                        1. Vector Representation
                                        2. Vector Operations
                                          1. Vector Addition
                                            1. Vector Subtraction
                                              1. Scalar Multiplication
                                                1. Vector Magnitude
                                                  1. Vector Normalization
                                                  2. Dot Product
                                                    1. Mathematical Definition
                                                      1. Geometric Interpretation
                                                        1. Applications in Lighting
                                                          1. Applications in Angle Calculation
                                                          2. Cross Product
                                                            1. Mathematical Definition
                                                              1. Geometric Interpretation
                                                                1. Right-Hand Rule
                                                                  1. Applications in Normal Calculation
                                                                    1. Applications in Orientation Testing
                                                                  2. Matrix Mathematics
                                                                    1. Matrix Fundamentals
                                                                      1. Matrix Definition and Notation
                                                                        1. Matrix Types
                                                                          1. Matrix Dimensions
                                                                          2. Matrix Operations
                                                                            1. Matrix Addition
                                                                              1. Matrix Subtraction
                                                                                1. Scalar Multiplication
                                                                                  1. Matrix Multiplication
                                                                                    1. Matrix Properties
                                                                                    2. Special Matrices
                                                                                      1. Identity Matrix
                                                                                        1. Zero Matrix
                                                                                          1. Diagonal Matrix
                                                                                            1. Symmetric Matrix
                                                                                            2. Matrix Transformations
                                                                                              1. Matrix Inverse
                                                                                                1. Matrix Transpose
                                                                                                  1. Determinant Calculation
                                                                                                    1. Matrix Rank
                                                                                                  2. Geometric Transformations
                                                                                                    1. 2D Transformations
                                                                                                      1. Translation
                                                                                                        1. Rotation
                                                                                                          1. Scaling
                                                                                                            1. Shearing
                                                                                                              1. Reflection
                                                                                                              2. 3D Transformations
                                                                                                                1. Translation
                                                                                                                  1. Rotation about Coordinate Axes
                                                                                                                    1. Rotation about Arbitrary Axis
                                                                                                                      1. Scaling
                                                                                                                        1. Shearing
                                                                                                                        2. Transformation Matrices
                                                                                                                          1. Translation Matrices
                                                                                                                            1. Rotation Matrices
                                                                                                                              1. Scaling Matrices
                                                                                                                                1. Shearing Matrices
                                                                                                                                2. Composite Transformations
                                                                                                                                  1. Transformation Concatenation
                                                                                                                                    1. Order of Operations
                                                                                                                                      1. Inverse Transformations
                                                                                                                                        1. Transformation Hierarchies
                                                                                                                                      2. Interpolation and Approximation
                                                                                                                                        1. Linear Interpolation
                                                                                                                                          1. Polynomial Interpolation
                                                                                                                                            1. Spline Interpolation
                                                                                                                                              1. Bezier Curves and Surfaces
                                                                                                                                                1. B-Spline Curves and Surfaces

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                                                                                                                                              1. Introduction to Computer Graphics

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                                                                                                                                              3. 2D Graphics Fundamentals