Mathematics for Game Development

  1. Geometric Transformations
    1. Transformation Fundamentals
      1. Coordinate Spaces
        1. Object Space
          1. World Space
            1. View Space
              1. Screen Space
              2. Transformation Pipeline
                1. Sequential Transformations
                  1. Local vs Global Transformations
                    1. Transformation Hierarchy
                    2. Transformation Properties
                      1. Linearity
                        1. Preservation of Properties
                          1. Invertibility
                        2. 2D Transformations
                          1. Translation in 2D
                            1. Vector Addition
                              1. Translation Matrices
                                1. Multiple Translations
                                2. Rotation in 2D
                                  1. Rotation About Origin
                                    1. Rotation Matrices
                                      1. Angle Conventions
                                        1. Rotation About Arbitrary Point
                                        2. Scaling in 2D
                                          1. Uniform Scaling
                                            1. Non-Uniform Scaling
                                              1. Scaling Matrices
                                                1. Scaling About Arbitrary Point
                                                2. Other 2D Transformations
                                                  1. Reflection
                                                    1. Shearing
                                                      1. Combined Effects
                                                    2. Matrix Representation of 2D Transformations
                                                      1. 2x2 Transformation Matrices
                                                        1. Rotation Matrices
                                                          1. Scaling Matrices
                                                            1. Limitations
                                                            2. Need for Translation
                                                              1. Translation as Matrix Operation
                                                                1. Limitations of 2x2 Matrices
                                                              2. Homogeneous Coordinates
                                                                1. 2D Homogeneous Coordinates
                                                                  1. Extending to 3D Representation
                                                                    1. Homogeneous Point Representation
                                                                      1. Conversion Between Forms
                                                                      2. 3x3 Transformation Matrices
                                                                        1. Translation in Homogeneous Form
                                                                          1. Rotation in Homogeneous Form
                                                                            1. Scaling in Homogeneous Form
                                                                              1. Combined Transformations
                                                                              2. Perspective Division
                                                                                1. W-Component Meaning
                                                                                  1. Perspective Transformations
                                                                                2. 3D Transformations
                                                                                  1. Translation in 3D
                                                                                    1. 4x4 Translation Matrices
                                                                                      1. Vector Representation
                                                                                      2. Rotation in 3D
                                                                                        1. Rotation About X-Axis
                                                                                          1. Rotation About Y-Axis
                                                                                            1. Rotation About Z-Axis
                                                                                              1. Arbitrary Axis Rotation
                                                                                                1. Euler Angles
                                                                                                2. Scaling in 3D
                                                                                                  1. Uniform Scaling
                                                                                                    1. Non-Uniform Scaling
                                                                                                      1. 4x4 Scaling Matrices
                                                                                                      2. Other 3D Transformations
                                                                                                        1. Reflection in 3D
                                                                                                          1. Shearing in 3D
                                                                                                        2. Combining Transformations
                                                                                                          1. Matrix Concatenation
                                                                                                            1. Order of Operations
                                                                                                              1. Right-to-Left Multiplication
                                                                                                                1. Transformation Chains
                                                                                                                2. Composite Transformations
                                                                                                                  1. Building Complex Transformations
                                                                                                                    1. Optimization Strategies
                                                                                                                    2. Inverse Transformations
                                                                                                                      1. Undoing Transformations
                                                                                                                        1. Inverse Matrix Calculation
                                                                                                                          1. Transformation Reversal

                                                                                                                      Previous

                                                                                                                      3. Linear Algebra: Matrices

                                                                                                                      Go to top

                                                                                                                      Next

                                                                                                                      5. Advanced Rotation: Quaternions