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Introduction & Learning Outcomes
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How to Take this Course
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What is Game Physics
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A Quick Review of Vector Math
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Vector & Scalar Quantities
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Using the P5js Web Editor
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Visualizing Errors in the Web Editor
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Coding a Vec2 Class
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Vector Magnitude
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Methods for Vector Addition & Subtraction
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Vector Equality
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Scaling Vectors
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Static Methods
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Applications of Vector Addition & Subtraction
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Dot Product
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Is the Dot Product Commutative?
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Cross Product
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Coding the Cross Product Method
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Exercise: Perpendicular 2D Vector
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Perpendicular 2D Vector
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Exercise: Vec3 Methods
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Vec3 Methods
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Vector Normalization
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Coding the Normalization Method
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Scaling, Translating, and Rotating Vectors
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Quick Review of Sine & Cosine
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Vector Rotation Proof (x-component)
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Vector Rotation Proof (y-component)
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Coding the Vec2 Rotate Method
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Concluding our JavaScript Vector Class
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A Quick Look at C++ Vec2 Syntax
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Technologies & Dependencies
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Folder Structure
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Initial Project Files
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Compiling using GCC & Linux
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Makefile
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Configuring Visual Studio on Windows
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Introduction to Particle Physics
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Particle Class
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Particle Velocity
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Using the + Operator to Add Vectors
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Controlling our Framerate
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Framerate Independent Movement
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Clamping Invalid DeltaTime Values
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Moving in a Constant Velocity
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Changing the Particle's Velocity
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Keeping the Particle Inside the Window
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Constant Acceleration
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Discrete vs. Continuous
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Integration & Movement Simulation
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Different Integration Methods
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Particle Integrate Function
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Applying Forces to Particles
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Particles with Different Mass
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The Weight Force
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Inverse of the Mass
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Applying Forces with the Keyboard
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Drag Force
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Drag Force Function
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Handling Mouse Clicks with SDL
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Unexpected Drag Behavior
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Friction Force
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Friction Force Function
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Gravitational Attraction Force
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Gravitational Attraction Force Function
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Spring Force
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Spring Force Function
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Exercise: Spring Forces
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Multiple Particles: Chain
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Multiple Particles: Soft body
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Soft Bodies & Verlet Integration
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Rigid-Bodies
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Shapes
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Shape Class
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Shape Class Implementation
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Circle Shape
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Angular Velocity & Angular Acceleration
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Torque & Moment of Inertia
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Circle Shape Angular Motion
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Box Vertices
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Local Space vs. World Space
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Body Update Function
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Why Not a Shape Draw Function?
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No Draw Method in the Shape Class
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Circle-Circle Collision Detection
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Circle-Circle Collision Class
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Circle-Circle Collision Implementation
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Collision Contact Information
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Collision Information Code
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The Projection Method
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Objects with Infinite Mass
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Impulse Method & Momentum
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Impulse
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Deriving the Linear Impulse Formula
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Simplifying the Impulse Method Formula
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Coding the Linear Impulse Method
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Is Linear Collision Response Enough?
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AABB Collision Detection
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SAT: Separating Axis Theorem
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Finding Minimum Separation with SAT
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Polygon-Polygon Collision Code
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Code to Find SAT Minimum Separation
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Refactoring the SAT Separation Function
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Finding Extra Collision Information with SAT
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Polygon-Polygon Collision Information
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Linear & Angular Velocity At Point
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Post-Collision Velocity At Point
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Computing Linear & Angular Impulse
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Collision Distance Vectors Ra-Rb
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2D Cross Product Simplification
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Coding the Impulse Along Normal
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Exercise: Impulse Along Tangent
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Friction Impulse Along Tangent
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Removing Window Boundaries Check
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Circle-Polygon Collision Detection
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Finding Polygon's Nearest Edge with Circle
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Exercise: Circle-Polygon Edge Regions
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Circle-Polygon Collision Information
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Circle-Polygon Collision Resolution
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Exercise: Polygons with Multiple Vertices
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Polygon with Multiple Vertices
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Rendering Circle Texture
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World Class
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Implementing World Functions
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Refactoring Function to Update Vertices
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Local Solvers vs. Global Solvers
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A Naive Iterative Positional Correction
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Constrained Rigid-Body Physics
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Position vs. Velocity Constraints
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Example Velocity Constraint & Bias Factor
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Example Distance Constraint & Bias Factor
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Constraint Forces & Constrained Movement
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Force-Based vs. Impulse-Based Constraints
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The Constraint Class
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VecN Class
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Implementing VecN Functions
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Matrices
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MatMN Class
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Matrix Transpose
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Matrix Multiplication
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Matrix Multiplication Function
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Seeing Beyond the Matrix
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Generalized Velocity Constraint
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Solving Violated Velocity Constraints
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Constraint Class Inheritance
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Distance Constraint
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Joint Constraint Class
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Converting World Space to Local Space
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World List of Constraints
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Refactoring Body Update
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Deriving the Distance Jacobian
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Populating the Distance Jacobian
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Solving System of Equations (Ax=b)
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Gauss-Seidel Method
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Constrained Pendulum
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Solving System of Constraints Iteratively
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Warm Starting
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Ragdoll with Joint Constraints
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Preventing NaN Errors
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Penetration Constraint
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Deriving the Penetration Jacobian
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Penetration Constraint Class
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Solving Penetration Constraints
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Penetration Warm Starting
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Penetration Constraint Friction
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Clamping Friction Magnitude Values
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Penetration Constraint Bounciness
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Unstable Stack of Boxes
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Allowing for Multiple Contact Points
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Reference & Incident Edges
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Finding Incident Edge
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Clipping Function
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Testing Multi-Contact Boxes
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Testing Multiple Objects & Constraints
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Contact Caching
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Continuous Collision Detection
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