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Index
Game Physics Cookbook
Table of Contents Game Physics Cookbook Credits About the Author Acknowledgements About the Reviewer Acknowledgements www.PacktPub.com
eBooks, discount offers, and more
Why Subscribe?
Customer Feedback Preface
What this book covers What you need for this book Who this book is for Sections
Getting ready How to do it… How it works… There's more… See also
Conventions Reader feedback Customer support
Downloading the example code Errata Piracy Questions
1. Vectors
Introduction Vector definition
Getting ready How to do it… How it works… There's more…
The W component
Component-wise operations
Getting ready How to do it… How it works…
Addition Subtraction Multiplication (Vector and Scalar) Comparison
There's more…
Dot product
How to do it… How it works… There's more…
Geometric definition
Magnitude
Getting ready How to do it… How it works… There's more…
Normalizing
Getting ready How to do it… How it works…
Cross product
Getting ready How to do it… How it works…
Angles
Getting ready How to do it… How it works… There's more…
Radians and degrees
Projection
Getting ready How to do it… How it works…
Reflection
Getting ready How to do it… How it works…
2. Matrices
Introduction Matrix definition
Getting ready How to do it… How it works…
Transpose
Getting ready How to do it… How it works…
Multiplication
Getting ready How to do it… How it works…
Identity matrix
Getting ready How to do it… How it works…
Determinant of a 2x2 matrix
How to do it… How it works…
Matrix of minors
Getting ready How to do it… How it works…
Minor of a 2x2 matrix Minor of a 3x3 matrix
Cofactor
Getting ready How to do it… How it works…
Determinant of a 3x3 matrix
Getting ready How to do it… How it works…
Operations on a 4x4 matrix
Getting ready How to do it… How it works…
Adjugate matrix
Getting ready How to do it… How it works…
Matrix inverse
Getting ready How to do it… How it works… There's more…
Expanding the inverse
3. Matrix Transformations
Introduction Matrix majors Translation
Getting Ready How to do it… How it works…
Scaling
Getting ready How to do it… How it works…
How rotations work
Getting ready How to do it… How it works…
Rotation matrices
Getting ready How to do it… How it works…
X-Basis vector Y-Basis vector Z-Basis vector
There's more…
X and Y rotation
Axis angle rotation
Getting ready How to do it… How it works…
Vector matrix multiplication
Getting ready How to do it… How it works…
Transform matrix
Getting ready How to do it… How it works…
View matrix
Getting ready How to do it… How it works…
Projection matrix
Getting ready How to do it… How it works…
4. 2D Primitive Shapes
Introduction 2D points
Getting ready How to do it… How it works…
2D lines
Getting ready How to do it… How it works…
Circle
Getting ready How to do it… How it works…
Rectangle
Getting ready How to do it… How it works…
Oriented rectangle
Getting ready How to do it… How it works…
Point containment
Getting ready How to do it… How it works…
Point on a line Point in a circle Point in a rectangle Point in an oriented rectangle
Line intersection
Getting ready How to do it… How it works…
Line circle Line rectangle Line oriented rectangle
5. 2D Collisions
Introduction Circle to circle
Getting ready How to do it… How it works…
Circle to rectangle
Getting ready How to do it… How it works… There's more…
Circle to oriented rectangle
Getting ready How to do it… How it works…
Rectangle to rectangle
Getting ready How to do it… How it works…
Separating Axis Theorem
Getting ready How to do it… How it works… There's more…
Determining which axis to test
Rectangle to oriented rectangle
Getting ready How to do it… How it works…
Oriented rectangle to oriented rectangle
Getting ready How to do it… How it works…
6. 2D Optimizations
Introduction Containing circle
Getting ready How to do it… How it works…
Containing rectangle
Getting ready How to do it… How it works…
Simple and complex shapes
Getting ready How to do it… How it works…
Quad tree
Getting ready How to do it… How it works…
Broad phase collisions
Getting ready How to do it… How it works…
7. 3D Primitive Shapes
Introduction Point
Getting ready How to do it… How it works…
Line segment
Getting ready How to do it… How it works…
Ray
Getting ready How to do it… How it works…
Sphere
Getting ready How to do it… How it works…
Axis Aligned Bounding Box
Getting ready How to do it How it works
Oriented Bounding Box
Getting ready How to do it How it works
Plane
Getting ready How to do it How it works
Triangle
Getting ready How to do it How it works
8. 3D Point Tests
Introduction Point and sphere
Getting ready How to do it… How it works…
Point and AABB
Getting ready How to do it… How it works…
Point and Oriented Bounding Box
Getting ready How to do it… How it works…
Point and plane
Getting ready How to do it… How it works…
Point and line
Getting ready How to do it… How it works…
Point and ray
Getting ready How to do it… How it works…
9. 3D Shape Intersections
Introduction Sphere-to-sphere
Getting ready How to do it… How it works…
Sphere-to-AABB
Getting ready How to do it… How it works…
Sphere-to-OBB
Getting ready How to do it… How it works…
Sphere-to-plane
Getting ready How to do it… How it works…
AABB-to-AABB
Getting ready How to do it… How it works…
AABB-to-OBB
Getting ready How to do it… How it works…
AABB-to-plane
Getting ready How to do it… How it works…
OBB-to-OBB
Getting ready How to do it… How it works…
OBB-to-plane
Getting ready How to do it… How it works…
Plane-to-plane
Getting ready How to do it… How it works…
10. 3D Line Intersections
Introduction Raycast Sphere
Getting ready How to do it… How it works…
Raycast Axis Aligned Bounding Box
Getting ready How to do it… How it works…
Raycast Oriented Bounding Box
Getting ready How to do it… How it works…
Raycast plane
Getting ready How to do it… How it works…
Linetest Sphere
Getting ready How to do it… How it works…
Linetest Axis Aligned Bounding Box
Getting ready How to do it… How it works…
Linetest Oriented Bounding Box
Getting ready How to do it… How it works…
Linetest Plane
Getting ready How to do it… How it works…
11. Triangles and Meshes
Introduction Point in triangle
Getting ready How to do it… How it works…
Closest point triangle
Getting ready How to do it… How it works…
Triangle to sphere
Getting ready How to do it… How it works…
Triangle to Axis Aligned Bounding Box
Getting ready How to do it… How it works…
Triangle to Oriented Bounding Box
Getting ready How to do it… How it works…
Triangle to plane
Getting ready How to do it… How it works…
Triangle to triangle
Getting ready How to do it… How it works…
Robustness of the Separating Axis Theorem
Getting ready How to do it… How it works…
Raycast Triangle
Getting ready How to do it… How it works…
Linetest Triangle
Getting ready How to do it… How it works…
Mesh object
Getting ready How to do it… How it works…
Mesh optimization
Getting ready How to do it… How it works…
Mesh operations
Getting ready How to do it… How it works… There's more…
12. Models and Scenes
Introduction The Model object
Getting ready How to do it… How it works…
Operations on models
Getting ready How to do it… How it works…
The Scene object
Getting ready How to do it… How it works… There's more
Operations on the scene
Getting ready How to do it… How it works…
The Octree object
Getting ready How to do it… How it works…
Octree contents
Getting ready How to do it… How it works…
Operations on the Octree
Getting ready How to do it… How it works…
Octree scene integration
Getting ready How to do it… How it works…
13. Camera and Frustum
Introduction Camera object
Getting ready How to do it… How it works…
Camera controls
Getting ready How to do it… How it works…
Frustum object
Getting ready How to do it… How it works…
Frustum from matrix
Getting ready How to do it… How it works…
Sphere in frustum
Getting ready How to do it… How it works…
Bounding Box in frustum
Getting ready How to do it… How it works…
Octree culling
Getting Ready How to do it… How it works…
Picking
Getting ready How to do it… How it works… There's more…
14. Constraint Solving
Introduction Framework introduction
Getting ready How to do it… How it works… There's more…
Raycast sphere
Getting ready How to do it… How it works…
Raycast Bounding Box
Getting ready How to do it… How it works…
Raycast plane and triangle
Getting ready How to do it… How it works…
Physics system
Getting ready How to do it… How it works…
Integrating particles
Getting ready How to do it… How it works… There's more…
Solving constraints
Getting ready How to do it… How it works…
Verlet Integration
Getting ready How to do it… How it works…
15. Manifolds and Impulses
Introduction Manifold for spheres
Getting ready How to do it… How it works…
Manifold for boxes
Getting ready How to do it… How it works… There's more…
Duplicate points
Rigidbody Modifications
Getting ready How to do it… How it works…
Linear Velocity
Getting ready How to do it... How it works...
Linear Impulse
Getting ready How to do it... How it works...
Linear Impulse Friction
There's more...
Physics System Update
Getting ready How to do it... How it works...
Angular Velocity
Angular Velocity and Acceleration
Tangential Acceleration
Centripetal Acceleration Torque Inertia Tensor Getting ready How to do it... How it works... There's more...
Tensors
Angular Impulse
Getting ready How to do it... How it works... There's more...
Non-linear projection
16. Springs and Joints
Introduction Particle Modifications
Getting ready How to do it… How it works…
Springs
Getting ready How to do it… How it works…
Cloth
Getting ready How to do it… How it works…
Physics System Modification
Getting ready How to do it… How it works…
Joints
Getting ready How to do it… How it works… There's more…
A. Advanced Topics
Introduction Generic collisions
Minkowski Sum Gilbert Johnson Keerthi (GJK) Expanding Polytope Algorithm (EPA)
Stability improvements
Arbiters Accumulated impulse
Springs
Collision resolution Softbody objects
Open source physics engines
Box2D Lite Box2D Dyn4j Bullet ODE JigLib React 3D Qu3e Cyclone Physics
Books Online resources Summary
Index
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