How to Take this Course

A Quick Review of Vector Math

Introduction & Learning Outcomes

What is Game Physics

Using the P5js Web Editor

Visualizing Errors in the Web Editor

Coding a Vec2 Class

Vector & Scalar Quantities

Vector Magnitude

Vector Equality

Vector Addition & Subtraction

Scaling Vectors

Methods for Vector Addition & Subtraction

Static Methods

Applications of Vector Addition & Subtraction

Is the Dot Product Commutative

Dot Product

Cross Product

Coding the Cross Product Method

Exercise Perpendicular 2D Vector

Perpendicular 2D Vector

Vec3 Methods

Exercise Vec3 Methods

Coding the Normalization Method

Vector Normalization

Scaling, Translating, and Rotating Vectors

Quick Review of Sine & Cosine

Vector Rotation Proof (y-component)

Coding the Vec2 Rotate Method

Vector Rotation Proof (x-component)

Vec2 C++ Header File

Vec2 Operator Overloading

A Quick Look at C++ Vec2 Syntax

Technologies & Dependencies

Folder Structure

Compiling using GCC & Linux

Makefile

Initial Project Files

Configuring Visual Studio on Windows

Particle Class

Particle Velocity

Introduction to Particle Physics

Using the + Operator to Add Vectors

Clamping Invalid DeltaTime Values

Controlling our Framerate

Framerate Independent Movement

Moving in a Constant Velocity

Keeping the Particle Inside the Window

Constant Acceleration

Changing the Particle's Velocity

Particle Integrate Function

Discrete vs. Continuous

Different Integration Methods

Integration & Movement Simulation

Applying Forces to Particles

Function to Add Force

Particles with Different Mass

The Weight Force

Inverse of the Mass

Applying Forces with the Keyboard

Drag Force Function

Drag Force

Unexpected Drag Behavior

Handling Mouse Clicks with SDL

Friction Force

Friction Force Function

Gravitational Attraction Force Function

Gravitational Attraction Force

Spring Force

Spring Force Function

Exercise Spring Forces

Multiple Particles Chain

Multiple Particles Soft body

Soft Bodies & Verlet Integration

Rigid-Bodies

Shapes

Shape Class

Shape Class Implementation

Angular Velocity & Angular Acceleration

Circle Shape

Torque & Moment of Inertia

Circle Shape Angular Motion

Box Vertices

Local Space vs. World Space

Body Update Function

Why Not a Shape Draw Function

No Draw Method in the Shape Class

Circle-Circle Collision Detection

Circle-Circle Collision Class

Circle-Circle Collision Implementation

Collision Contact Information

Implementing the Projection Method

Collision Information Code

Broad Phase & Narrow Phase

Objects with Infinite Mass

The Projection Method

Impulse Method & Momentum

Impulse

Simplifying the Impulse Method Formula

Is Linear Collision Response Enough

Coding the Linear Impulse Method

Deriving the Linear Impulse Formula

AABB Collision Detection

Polygon-Polygon Collision Code

Finding Minimum Separation with SAT

SAT Separating Axis Theorem

Code to Find SAT Minimum Separation

Refactoring the SAT Separation Function

Finding Extra Collision Information with SAT

Polygon-Polygon Collision Information

Linear & Angular Velocity At Point

Computing Linear & Angular Impulse

Post-Collision Velocity At Point

Collision Distance Vectors Ra-Rb

D Cross Product Simplification

Coding the Impulse Along Normal

Friction Impulse Along Tangent

Exercise Impulse Along Tangent

Removing Window Boundaries Check

Circle-Polygon Collision Detection

Finding Polygon's Nearest Edge with Circle

Exercise Circle-Polygon Edge Regions

Circle-Polygon Collision Information

Circle-Polygon Collision Resolution

Polygon with Multiple Vertices

Exercise Polygons with Multiple Vertices

Rendering Circle Texture

Loading SDL Textures

World Class

Implementing World Functions

Refactoring Function to Update Vertices

Local Solvers vs. Global Solvers

A Naive Iterative Positional Correction

Constrained Rigid-Body Physics

Example Velocity Constraint & Bias Factor

Position vs. Velocity Constraints

Example Distance Constraint & Bias Factor

The Constraint Class

Constraint Forces & Constrained Movement

VecN Class

Force-Based vs. Impulse-Based Constraints

Implementing VecN Functions

VecN Operator Overloading

Matrices

MatMN Class

Matrix Transpose

Matrix Multiplication

Matrix Multiplication Function

Seeing Beyond the Matrix

Constraint Class Inheritance

Generalized Velocity Constraint

Solving Violated Velocity Constraints

Distance Constraint

Joint Constraint Class

Converting World Space to Local Space

World List of Constraints

Refactoring Body Update

Populating the Distance Jacobian

Deriving the Distance Jacobian

Gauss-Seidel Method

Constrained Pendulum

Solving System of Equations (Ax=b)

Solving System of Constraints Iteratively

Adding the Bias Term

Warm Starting

Ragdoll with Joint Constraints

Preventing NaN Errors

Penetration Constraint

Deriving the Penetration Jacobian

Solving Penetration Constraints

Penetration Constraint Class

Penetration Warm Starting

Penetration Constraint Friction

Clamping Friction Magnitude Values

Penetration Constraint Bounciness

Unstable Stack of Boxes

Allowing for Multiple Contact Points

Reference & Incident Edges

Finding Incident Edge

Getting Ready for Clipping

Clipping Function

Testing Multi-Contact Boxes

Testing Multiple Objects & Constraints

Broad & Narrow Split

Continuous Collision Detection

Contact Caching

Euler Integration Review

MidPoint & RK4 Integrators

Stick Constraints

Verlet Integration

Conclusion & Next Steps