Game Physics Cookbook (Gabor Szauer 著)

Chapter1: Vectors

Chapter2: Matrices

Chapter3: Matrix Transformations

Chapter4: 2D Primitive Shapes

Chapter5: 2D Collisions

Chapter6: 2D Optimizations

Chapter7: 3D Primitive Shapes

Chapter8: 3D Point Tests

Chapter9: 3D Shape Intersections

Chapter10: 3D Line Intersections

Chapter11: Triangles and Meshes

Chapter12: Models and Scenes

Chapter13: Camera and Frustum

Chapter14: Constraint Solving

Chapter15: Manifolds and Impulses

Chapter16: Springs and Joints

Appendix: Advanced Topics

 

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 

　　http://box2d.org/files/GDC2006/Box2D_Lite.zip

　　http://box2d.org/files/GDC2006/GDC2006_Catto_Erin_PhysicsTutorial.ppt
Box2D

　　https://github.com/erincatto/Box2D
Dyn4j

　　http://www.dyn4j.org
Bullet

　　http://bulletphysics.org/wordpress
ODE

　　http://www.ode.org
JigLib

　　http://www.rowlhouse.co.uk/jiglib
React 3D

　　http://www.reactphysics3d.com
Qu3e

　　https://github.com/RandyGaul/qu3e
Cyclone Physics

　　https://github.com/idmillington/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