Chapter1: Vectors
Introduction
Vector definition
Component-wise operations
Dot product
Magnitude
Normalizing
Cross product
Angles
Projection
Reflection
Chapter2: Matrices
Introduction
Matrix definition
Transpose
Multiplication
Identity matrix
Determinant of a 2x2 matrix
Matrix of minors
Cofactor
Determinant of a 3x3 matrix
Operations on a 4x4 matrix
Adjugate matrix
Matrix inverse
Chapter3: Matrix Transformations
Introduction
Matrix majors
Translation
Scaling
How rotations work
Rotation matrices
Axis angle rotation
Vector matrix multiplication
Transform matrix
View matrix
Projection matrix
Chapter4: 2D Primitive Shapes
Introduction
2D points
2D lines
Circle
Rectangle
Oriented rectangle
Point containment
Line intersection
Chapter5: 2D Collisions
Introduction
Circle to circle
Circle to rectangle
Circle to oriented rectangle
Rectangle to rectangle
Separating Axis Theorem
Rectangle to oriented rectangle
Oriented rectangle to oriented rectangle
Chapter6: 2D Optimizations
Introduction
Containing circle
Containing rectangle
Simple and complex shapes
Quad tree
Broad phase collisions
Chapter7: 3D Primitive Shapes
Introduction
Point
Line segment
Ray
Sphere
Axis Aligned Bounding Box
Oriented Bounding Box
Plane
Triangle
Chapter8: 3D Point Tests
Introduction
Point and sphere
Point and AABB
Point and Oriented Bounding Box
Point and plane
Point and line
Point and ray
Chapter9: 3D Shape Intersections
Introduction
Sphere-to-sphere
Sphere-to-AABB
Sphere-to-OBB
Sphere-to-plane
AABB-to-AABB
AABB-to-OBB
AABB-to-plane
OBB-to-OBB
OBB-to-plane
Plane-to-plane
Chapter10: 3D Line Intersections
Introduction
Raycast Sphere
Raycast Axis Aligned Bounding Box
Raycast Oriented Bounding Box
Raycast plane
Linetest Sphere
Linetest Axis Aligned Bounding Box
Linetest Oriented Bounding Box
Linetest Plane
Chapter11: Triangles and Meshes
Introduction
Point in triangle
Closest point triangle
Triangle to sphere
Triangle to Axis Aligned Bounding Box
Triangle to Oriented Bounding Box
Triangle to plane
Triangle to triangle
Robustness of the Separating Axis Theorem
Raycast Triangle
Linetest Triangle
Mesh object
Mesh optimization
Mesh operations
Chapter12: Models and Scenes
Introduction
The Model object
Operations on models
The Scene object
Operations on the scene
The Octree object
Octree contents
Operations on the Octree
Octree scene integration
Chapter13: Camera and Frustum
Introduction
Camera object
Camera controls
Frustum object
Frustum from matrix
Sphere in frustum
Bounding Box in frustum
Octree culling
Picking
Chapter14: Constraint Solving
Introduction
Framework introduction
Raycast sphere
Raycast Bounding Box
Raycast plane and triangle
Physics system
Integrating particles
Solving constraints
Verlet Integration
Chapter15: Manifolds and Impulses
Introduction
Manifold for sphere
Manifold for boxes
Rigidbody Modifications
Linear Velocity
Linear Impulse
Physics System Update
Angular Velocity
Angular Impulse
Chapter16: Springs and Joints
Introduction
Particle Modifications
Springs
Cloth
Physics System Modification
Joints
Appendix: Advanced Topics
Introduction
Generic collisions
Stability improvements
Springs
Open source physics engines
Box2D Lite
Box2D
Dyn4j
Bullet
ODE
JigLib
React 3D
Qu3e
Cyclone Physics
Books
Physics Modeling for Game Programmers
Conger, D. (2004). Physics modeling for game programmers. Boston, MA: Thomson/Premier.
By David Cogner, ISBN-13: 978-1592000937
Physics for Game Developers
Bourg, D. M., & Bywalec, B. (2013). Physics for game developers. Sebastopol, CA: O'Reilly Media.
By David M Bourg and Bryan Bywalec, ISBN-13: 978-1449392512
Game Physics Engine Development
Millington, I. (2010). Game physics engine development: how to build a robust commercial-grade physics engine for your game. Burlington, MA: Morgan Kaufmann.
By Ian Millington, ISBN-13: 978-0123819765
Game Physics
Eberly, D. H. (2010). Game physics. Burlington, MA: Morgan Kaufmann/Elsevier.
By David H. Eberly, ISBN-13: 978-0123749031
Real-Time Collision Detection
Ericson, C. (2004). Real-time collision detection. San Francisco, CA: Elsevier.
By Christer Ericson, ISBN-13: 978-1558607323
Game Physics: A Practical Introduction
By Ben Kenwright, ISBN-13: 978-1471033971
Online resources
http://valvesoftware.com/company/publications.html
http://allenchou.net/game-physics-series
http://randygaul.net/category/physics
http://gafferongames.com/game-physics
http://wildbunny.co.uk/blog/category/physics-2
http://chrishecker.com/Rigid_Body_Dynamics
http://www.xbdev.net/physics/index.php
http://brm.io/game-physics-for-beginners
http://www.gdcvault.com
http://box2d.org/files
https://www.gamedev.net/forum/20-math-and-physics
Summary