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by David M Bourg, Bryan Bywalec
Physics for Game Developers, 2nd Edition
Preface
Who Is This Book For?
What We Assume You Know
Mechanics
Digital Physics
Arrangement of This Book
Conventions Used in This Book
Using Code Examples
Safari® Books Online
How to Contact Us
Acknowledgments
I. Fundamentals
1. Basic Concepts
Newton’s Laws of Motion
Units and Measures
Coordinate System
Vectors
Derivatives and Integrals
Mass, Center of Mass, and Moment of Inertia
Newton’s Second Law of Motion
Inertia Tensor
Relativistic Time
2. Kinematics
Velocity and Acceleration
Constant Acceleration
Nonconstant Acceleration
2D Particle Kinematics
3D Particle Kinematics
X Components
Y Components
Z Components
The Vectors
Hitting the Target
Kinematic Particle Explosion
Rigid-Body Kinematics
Local Coordinate Axes
Angular Velocity and Acceleration
3. Force
Forces
Force Fields
Friction
Fluid Dynamic Drag
Pressure
Buoyancy
Springs and Dampers
Force and Torque
Summary
4. Kinetics
Particle Kinetics in 2D
Particle Kinetics in 3D
X Components
Y Components
Z Components
Cannon Revised
Rigid-Body Kinetics
5. Collisions
Impulse-Momentum Principle
Impact
Linear and Angular Impulse
Friction
6. Projectiles
Simple Trajectories
Drag
Magnus Effect
Variable Mass
II. Rigid-Body Dynamics
7. Real-Time Simulations
Integrating the Equations of Motion
Euler’s Method
Better Methods
Summary
8. Particles
Simple Particle Model
Integrator
Rendering
The Basic Simulator
Implementing External Forces
Implementing Collisions
Particle-to-Ground Collisions
Particle-to-Obstacle Collisions
Tuning
9. 2D Rigid-Body Simulator
Model
Transforming Coordinates
Integrator
Rendering
The Basic Simulator
Tuning
10. Implementing Collision Response
Linear Collision Response
Angular Effects
11. Rotation in 3D Rigid-Body Simulators
Rotation Matrices
Quaternions
Quaternion Operations
Magnitude
Conjugate: The ~ operator
QVRotate
Quaternion multiplication: The * operator
Vector multiplication: The * operator
MakeQFromEulerAngles
MakeEulerAnglesFromQ
Quaternions in 3D Simulators
12. 3D Rigid-Body Simulator
Model
Integration
Flight Controls
13. Connecting Objects
Springs and Dampers
Connecting Particles
Rope
Spring structure and variables
Initialize the particles and springs
Update the simulation
Connecting Rigid Bodies
Links
Basic structures and variables
Initialize
Update
Rotational Restraint
14. Physics Engines
Building Your Own Physics Engine
Physics Models
Simulated Objects Manager
Collision Detection
Collision Response
Force Effectors
Numerical Integrator
III. Physical Modeling
15. Aircraft
Geometry
Lift and Drag
Other Forces
Control
Modeling
16. Ships and Boats
Stability and Sinking
Stability
Sinking
Ship Motions
Heave
Roll
Pitch
Coupled Motions
Resistance and Propulsion
General Resistance
Planing craft
Virtual mass
Guidance speeds
Propulsion
Maneuverability
Rudders and Thrust Vectoring
Propeller walk
17. Cars and Hovercraft
Cars
Resistance
Power
Stopping Distance
Steering
Hovercraft
How Hovercraft Work
Resistance
Steering
18. Guns and Explosions
Projectile Motion
Taking Aim
Zeroing the Sights
Bullet drop: Gravity and air resistance
Wind
Breathing and Body Position
Recoil and Impact
Explosions
Particle Explosions
Polygon Explosions
19. Sports
Modeling a Golf Swing
Solving the Golf Swing Equations
Billiards
Implementation
Initialization
Stepping the Simulation
Calculating Forces
Handling Collisions
IV. Digital Physics
20. Touch Screens
Types of Touch Screens
Resistive
Capacitive
Infrared and Optical Imaging
Exotic: Dispersive Signal and Surface Acoustic Wave
Step-by-Step Physics
Resistive Touch Screens
One-dimensional resistive touch sensor
Four-wire resistive touch screen
Capacitive Touch Screens
Self-capacitance
Mutual capacitance
Example Program
Multitouch
Other Considerations
Haptic Feedback
Modeling Touch Screens in Games
Difference from Mouse-Based Input
Custom Gestures
21. Accelerometers
Accelerometer Theory
MEMS Accelerometers
Common Accelerometer Specifications
Data Clipping
Sensing Orientation
Sensing Tilt
Using Tilt to Control a Sprite
Two Degrees of Freedom
22. Gaming from One Place to Another
Location-Based Gaming
Geocaching and Reverse Geocaching
Mixed Reality
Street Games
What Time Is It?
Two-Dimensional Mathematical Treatment
Location, Location, Location
Distance
Great-Circle Heading
Rhumb Line
23. Pressure Sensors and Load Cells
Under Pressure
Example Effects of High Pressure
Button Mashing
Load Cells
Tiny scales
Center of gravity
Barometers
24. 3D Display
Binocular Vision
Stereoscopic Basics
The Left and Right Frustums
Types of Display
Complementary-Color Anaglyphs
Linear and Circular Polarization
Liquid-Crystal Plasma
Autostereoscopy
Advanced Technologies
Programming Considerations
Active Stereoization
Passive Stereoization
25. Optical Tracking
Sensors and SDKs
Kinect
OpenCV
Numerical Differentiation
26. Sound
What Is Sound?
Characteristics of and Behavior of Sound Waves
Harmonic Wave
Superposition
Speed of Sound
Attenuation
Reflection
Doppler Effect
3D Sound
How We Hear in 3D
A Simple Example
A. Vector Operations
Vector Class
Magnitude
Normalize
Reverse
Vector Addition: The += Operator
Vector Subtraction: The −= Operator
Scalar Multiplication: The *= Operator
Scalar Division: The /= Operator
Conjugate: The − Operator
Vector Functions and Operators
Vector Addition: The + Operator
Vector Subtraction: The − Operator
Vector Cross Product: The ^ Operator
Vector Dot Product: The * Operator
Scalar Multiplication: The * Operator
Scalar Division: The / Operator
Triple Scalar Product
B. Matrix Operations
Matrix3×3 Class
Determinant
Transpose
Inverse
Matrix Addition: The += Operator
Matrix Subtraction: The −= Operator
Scalar Multiplication: The *= Operator
Scalar Division: The /= Operator
Matrix Functions and Operators
Matrix Addition: The + Operator
Matrix Subtraction: The − Operator
Scalar Divide: The / Operator
Matrix Multiplication: The * Operator
Scalar Multiplication: The * Operator
Vector Multiplication: The * Operator
C. Quaternion Operations
Quaternion Class
Magnitude
GetVector
GetScalar
Quaternion Addition: The += Operator
Quaternion Subtraction: The −= Operator
Scalar Multiplication: The *= Operator
Scalar Division: The /= Operator
Conjugate: The ~ Operator
Quaternion Functions and Operators
Quaternion Addition: The + Operator
Quaternion Subtraction: The − Operator
Quaternion Multiplication: The * Operator
Scalar Multiplication: The * Operator
Vector Multiplication: The * Operator
Scalar Division: The / Operator
QGetAngle
QGetAxis
QRotate
QVRotate
MakeQFromEulerAngles
MakeEulerAnglesFromQ
Conversion Functions
D. Bibliography
General Physics and Dynamics
Mathematics and Numerical Methods
Computational Geometry
Projectiles
Sports Ball Physics
Aerodynamics
Hydrostatics and Hydrodynamics
Automobile Physics
Real-time Physics Simulations
Digital Physics
Index
About the Authors
Colophon
Copyright
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