Physics for Game Developers by Bourg, David M. -- Read -- Imperial Library of Trantor

Index

Physics for Game Developers 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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