Mathematics for Game Development

  1. Physics Simulation
    1. Kinematics
      1. Motion Fundamentals
        1. Position
          1. Displacement
            1. Velocity
              1. Acceleration
              2. One-Dimensional Motion
                1. Constant Velocity
                  1. Constant Acceleration
                    1. Kinematic Equations
                    2. Two-Dimensional Motion
                      1. Vector Components
                        1. Projectile Motion
                          1. Circular Motion
                          2. Three-Dimensional Motion
                            1. 3D Kinematics
                              1. Spatial Trajectories
                            2. Dynamics and Forces
                              1. Newton's Laws of Motion
                                1. First Law of Motion
                                  1. Inertia
                                    1. Equilibrium
                                    2. Second Law of Motion
                                      1. Force and Acceleration
                                        1. Mass Effects
                                        2. Third Law of Motion
                                          1. Action-Reaction Pairs
                                            1. Force Interactions
                                          2. Force Analysis
                                            1. Force Vectors
                                              1. Net Force Calculation
                                                1. Force Diagrams
                                                2. Common Forces
                                                  1. Gravitational Force
                                                    1. Constant Gravity
                                                      1. Universal Gravitation
                                                        1. Gravitational Fields
                                                        2. Normal Force
                                                          1. Friction Forces
                                                            1. Static Friction
                                                              1. Kinetic Friction
                                                                1. Friction Coefficients
                                                                2. Drag Forces
                                                                  1. Linear Drag
                                                                    1. Quadratic Drag
                                                                      1. Terminal Velocity
                                                                      2. Spring Forces
                                                                        1. Hooke's Law
                                                                          1. Spring Constants
                                                                            1. Elastic Potential Energy
                                                                          2. Momentum and Impulse
                                                                            1. Linear Momentum
                                                                              1. Impulse-Momentum Theorem
                                                                                1. Conservation of Momentum
                                                                              2. Collision Detection
                                                                                1. Bounding Volume Hierarchies
                                                                                  1. Bounding Spheres
                                                                                    1. Sphere Definition
                                                                                      1. Sphere-Sphere Intersection
                                                                                        1. Sphere-Point Tests
                                                                                        2. Axis-Aligned Bounding Boxes
                                                                                          1. AABB Definition
                                                                                            1. AABB-AABB Intersection
                                                                                              1. AABB-Point Tests
                                                                                              2. Oriented Bounding Boxes
                                                                                                1. OBB Definition
                                                                                                  1. OBB-OBB Intersection
                                                                                                    1. Separating Axis Theorem
                                                                                                  2. Primitive Collision Tests
                                                                                                    1. Point-Primitive Tests
                                                                                                      1. Line-Primitive Tests
                                                                                                        1. Plane-Primitive Tests
                                                                                                        2. Ray Casting
                                                                                                          1. Ray Definition
                                                                                                            1. Ray-Sphere Intersection
                                                                                                              1. Ray-Plane Intersection
                                                                                                                1. Ray-Box Intersection
                                                                                                                  1. Ray-Triangle Intersection
                                                                                                                  2. Spatial Partitioning
                                                                                                                    1. Uniform Grids
                                                                                                                      1. Grid Structure
                                                                                                                        1. Object Assignment
                                                                                                                          1. Query Optimization
                                                                                                                          2. Hierarchical Structures
                                                                                                                            1. Quadtrees
                                                                                                                              1. Octrees
                                                                                                                                1. BSP Trees
                                                                                                                                2. Hash-Based Methods
                                                                                                                              2. Collision Response
                                                                                                                                1. Collision Types
                                                                                                                                  1. Elastic Collisions
                                                                                                                                    1. Inelastic Collisions
                                                                                                                                      1. Perfectly Inelastic Collisions
                                                                                                                                      2. Conservation Laws
                                                                                                                                        1. Conservation of Momentum
                                                                                                                                          1. Conservation of Energy
                                                                                                                                            1. Energy Loss in Collisions
                                                                                                                                            2. Impulse Calculations
                                                                                                                                              1. Collision Impulse
                                                                                                                                                1. Impulse Application
                                                                                                                                                  1. Multiple Contact Points
                                                                                                                                                  2. Restitution
                                                                                                                                                    1. Coefficient of Restitution
                                                                                                                                                      1. Bouncing Behavior
                                                                                                                                                        1. Energy Dissipation
                                                                                                                                                        2. Friction in Collisions
                                                                                                                                                          1. Static Friction Response
                                                                                                                                                            1. Dynamic Friction Response
                                                                                                                                                              1. Friction Impulse

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                                                                                                                                                          7. Calculus for Motion and Physics

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                                                                                                                                                          9. Probability and Randomness