Mathematics for Game Development

  1. Curves and Splines
    1. Parametric Curves
      1. Parametric Representation
        1. Parameter Domain
          1. Curve Parameterization
            1. Arc Length Parameterization
            2. Linear Parametric Curves
              1. Line Segments
                1. Ray Representation
                2. Curve Properties
                  1. Continuity
                    1. Smoothness
                      1. Curvature
                    2. Interpolation Methods
                      1. Linear Interpolation
                        1. Formula and Implementation
                          1. Geometric Interpretation
                          2. Bilinear Interpolation
                            1. 2D Extension
                              1. Surface Interpolation
                              2. Higher-Order Interpolation
                                1. Polynomial Interpolation
                                  1. Lagrange Interpolation
                                    1. Spline Interpolation
                                  2. Bézier Curves
                                    1. Linear Bézier Curves
                                      1. Two Control Points
                                        1. Linear Interpolation
                                        2. Quadratic Bézier Curves
                                          1. Three Control Points
                                            1. Curve Construction
                                            2. Cubic Bézier Curves
                                              1. Four Control Points
                                                1. Curve Properties
                                                2. Control Point Influence
                                                  1. Geometric Interpretation
                                                    1. Curve Shaping
                                                    2. De Casteljau's Algorithm
                                                      1. Recursive Construction
                                                        1. Numerical Stability
                                                          1. Curve Subdivision
                                                          2. Bézier Curve Properties
                                                            1. Convex Hull Property
                                                              1. Endpoint Interpolation
                                                                1. Tangent Vectors
                                                              2. Spline Curves
                                                                1. B-Splines
                                                                  1. Basis Functions
                                                                    1. Control Points
                                                                      1. Knot Vectors
                                                                      2. NURBS
                                                                        1. Rational Basis Functions
                                                                          1. Weights
                                                                            1. Homogeneous Coordinates
                                                                            2. Catmull-Rom Splines
                                                                              1. Interpolating Splines
                                                                                1. Tangent Calculation
                                                                              2. Curve Applications
                                                                                1. Animation Paths
                                                                                  1. Character Movement
                                                                                    1. Camera Paths
                                                                                      1. Object Trajectories
                                                                                      2. User Interface
                                                                                        1. Smooth Transitions
                                                                                          1. Easing Functions
                                                                                          2. Level Design
                                                                                            1. Track Design
                                                                                              1. Path Creation
                                                                                                1. Terrain Modeling
                                                                                                2. Path Following
                                                                                                  1. Curve Following Algorithms
                                                                                                    1. Speed Control
                                                                                                      1. Look-Ahead Systems

                                                                                                  Previous

                                                                                                  9. Probability and Randomness

                                                                                                  Go to top

                                                                                                  Next

                                                                                                  11. Specialized Topics