Physics for Flash Games, Animation, and Simulations by Ramtal, Dev -- Read -- Imperial Library of Trantor

Index

Cover Title Copyright Dedication Contents at a Glance Contents About the Authors About the Technical Reviewer About the Cover Image Artist Acknowledgments Preface

What this book will (and won't) teach you Overview of this book Source code and examples

Part I: The Basics

Chapter 1: Introduction to Physics Programming

Why model real physics?

Creating realistic animation effects Creating realistic games Building simulations and models Generating art from code Can't I just use a physics engine?

What is physics?

Everything behaves according to the laws of physics The laws can be written as math equations Predicting motion

Programming physics

The difference between animation and simulation The laws of physics are simple Hence, they can be readily coded up! The four steps for programming physics

A simple example

A bouncing ball: the physics Coding up a bouncing ball in 2D

Summary

Chapter 2: Selected ActionScript 3.0 Topics

ActionScript 3.0 classes

Classes and objects Structure of an AS3.0 class Functions, methods and constructors Properties Static methods and properties Inheritance

ActionScript 3.0 language basics

Variables and constants Data types Operators Math Logic Loops

Events in ActionScript 3.0

Event listeners and handlers Events and user interaction Drag and drop

The Flash coordinate system

2D coordinates 3D in Flash

The Flash drawing API

Drawing lines and curves Creating fills and gradients Example: Bouncing ball in a box

Producing animation using code

Using the built-in frame stepping as a clock Using the Timer class Using getTimer() to compute elapsed time Precalculating motion

Collision detection

Using the hitTestObject() method Using the hitTestPoint() method Distance-based collision detection Advanced collision detection

Summary

Chapter 3: Some Math Background

Coordinates and simple graphs

Building a plotter: the Graph class Plotting functions using the Graph class Straight lines Polynomial curves Things that grow and decay: exponential and log functions Making an object move along a curve Distance between two points

Basic trigonometry

Degrees and radians The sine function The cosine function The tangent function The inverse trig functions Using trig functions for animation

Vectors and basic vector algebra

What are vectors? Vectors and scalars Adding and subtracting vectors Resolving vectors: vector components Multiplying vectors: Scalar or dot product Multiplying vectors: Vector or cross product Building a Vector class with vector algebra

Simple calculus ideas

Slope of a line: gradient Rates of change: derivatives Doing sums: integrals

Summary

Chapter 4: Basic Physics Concepts

General physics concepts and notation

Physical quantities and units Scientific notation

Things: particles and other objects in physics

What is a particle? Particle properties Building a Particle class Moving particles: the Mover class Extending the Particle class

Describing motion: kinematics

Concepts: displacement, velocity, speed, acceleration Combining vector quantities Describing motion using graphs Equations of motion for uniform acceleration Applying the equations to projectile motion More motion-related concepts: inertia, mass, and momentum

Predicting motion: forces and dynamics

The cause of motion: forces The relationship between force, mass, and acceleration Types of forces Combining forces: force diagrams and resultant force Forces in equilibrium An example: object falling under gravity and drag

Energy concepts

The notion of work in physics The capacity to do work: energy Energy transfer, conversion, and conservation Potential and kinetic energy Power Example: a rudimentary “car” simulation

Summary

Part II: Particles, Forces, and Motion

Chapter 5: The Laws Governing Motion

Newton’s laws of motion

Newton’s first law of motion (N1) Newton’s second law of motion (N2) Newton’s third law of motion (N3)

Applying Newton’s laws

General method for applying F = ma The Forcer class The Forces class A simple example: projectile with drag A more complicated example: floating ball

Newton’s second law as a differential equation

Taking a deeper look at F = ma An example: Fall under gravity and drag revisited

The principle of energy conservation

Conservation of mechanical energy An example: Energy changes in a projectile

The principle of momentum conservation

Example: 1D elastic collision between two particles

Laws governing rotational motion Summary

Chapter 6: Gravity, Orbits, and Rockets

Gravity

Gravity, weight, and mass Newton’s universal law of gravitation Creating the gravity function

Orbits

Orbiter class Escape velocity Two-body motion

Local gravity

The force of gravity near the Earth’s surface Variation of gravity with height Gravity on other celestial bodies

Rockets

It is rocket science! Modeling the thrust of a rocket Building a rocket simulation

Summary

Chapter 7: Contact and Fluid Forces

Contact forces

Normal contact forces Tension and compression Friction Example: Sliding down a slope

Pressure

The meaning of pressure Density Variation of pressure with depth in a fluid Static and dynamic pressure

Upthrust (buoyancy)

Archimedes's Principle Apparent weight Submerged objects Floating objects Example: Balloon

Drag

Drag law for low velocities Drag law for high velocities Which drag law should I use? Adding drag to the balloon simulation Example: Floating ball Terminal velocity Example: Parachute

Lift

Lift coefficients Example: An airplane

Wind and turbulence

Force due to the wind Wind and drag Steady and turbulent flow Example: Air bubbles in a steady wind Modeling turbulence

Summary

Chapter 8: Restoring Forces: Springs and Oscillations

Springs and oscillations: Basic concepts

Spring-like motion Restoring force, damping, and forcing Hooke’s law

Free oscillations

The spring force function Creating a basic oscillator Simple harmonic motion Oscillations and numerical accuracy

Damped oscillations

Damping force The effect of damping on oscillations Analytical solutions for oscillations with damping

Forced oscillations

Driving forces Example: A periodic driving force Example: A random driving force Gravity as a driving force: bungee jumping Example: Driving force by user interaction

Coupled oscillators: Multiple springs and objects

Example: A chain of objects connected by springs

Summary

Chapter 9: Centripetal Forces: Rotational Motion

Kinematics of uniform circular motion

Angular displacement Angular velocity Angular acceleration Period, frequency, and angular velocity Relation between angular velocity and linear velocity Example: A rolling wheel Particles with spin Example: Satellite around a rotating Earth

Centripetal acceleration and centripetal force

Centripetal acceleration Centripetal acceleration, velocity and angular velocity Centripetal force Common misconceptions about centripetal force Example: Revisiting the satellite animation Example: Circular orbits with gravitational force Example: Car moving around a bend

Non-uniform circular motion

Tangential force and acceleration Example: A simple pendulum

Summary

Chapter 10: Long-Range Forces

Particle interactions and force fields

Interaction at a distance From particle interactions to force fields

Newtonian gravitation

Gravitational field due to a particle Gravity with multiple orbiters Gravity with multiple attractors Particle trajectories in a gravity field Building a simple black hole game

Electrostatic force

Electric charge Coulomb's law of electrostatics Charged particle attraction and repulsion Electric fields

Electromagnetic force

Magnetic fields and forces The Lorentz force law

Other force laws

Central forces Gravity with a spring force law? Multiple attractors with different laws of gravity

Summary

Part III: Multi-particle and Extended Systems

Chapter 11: Collisions

Collisions and their modeling Bouncing off horizontal or vertical walls

Elastic bouncing Implementing energy loss due to bouncing

Bouncing off inclined walls

Collision detection Repositioning the particle Calculating the new velocity Velocity correction just before collision An example of a ball bouncing off an inclined wall Example of ball bouncing off multiple inclined walls

Collisions between particles in 1D

Repositioning the particles Elastic collisions Inelastic collisions

Collisions between particles in 2D

An example: 2D collisions between two particles Example: multiple particle collisions Example: multiple particle collisions with bouncing

Summary

Chapter 12: Particle Systems

Introduction to particle system modeling Creating animated effects using particles

A simple example: splash effect with particles Creating a particle emitter Creating a smoke effect Creating a fire effect Creating fireworks

Particle animations with long-range forces

Particle paths in a force field Building a wormhole

Interacting particle systems

Multiple particles under mutual gravity A simple galaxy simulation

Summary

Chapter 13: Extended Objects

Rigid bodies

Basic concepts of rigid body modeling Modeling rigid bodies Rotational dynamics of rigid bodies Simulating rigid body dynamics Example: a simple wind turbine simulation Example: Rolling down an inclined plane Rigid body collisions and bouncing Example: Simulating a single bouncing block Example: Colliding blocks

Deformable bodies

Mass-spring systems Rope simulation Cloth simulation

Summary

Part IV: Building More Complex Simulations

Chapter 14: Numerical Integration Schemes

General principles

Statement of the problem Characteristics of numerical schemes Types of integration schemes Modifying Forcer to allow for different integration schemes

Euler integration

Explicit Euler Implicit Euler Semi-implicit Euler Comparing the explicit and semi-implicit Euler schemes Why use Euler and why not?

Runge-Kutta integration

Second-order Runge-Kutta scheme (RK2) Fourth-order Runge-Kutta scheme (RK4) Stability and accuracy of RK2 and RK4 compared with Euler

Verlet integration

Position Verlet Velocity Verlet Testing the stability and accuracy of the Verlet schemes

Summary

Chapter 15: Other Technical Issues

Doing physics in 3D

3D versus 2D physics 3D math Creating classes for 3D objects and motion Creating 3D models Example: A rotating cube Integrating with 3D engines Looking ahead to Stage3D

Building scale models

Scaling for realism A simple example Choosing units Scaling factors and parameter values Rescaling equations

Building accurate simulations

Using Number for calculations Choosing an appropriate integration scheme Using an appropriate timestep Using accurate initial conditions Dealing with boundaries carefully

Summary

Chapter 16: Simulation Projects

Build a submarine

Brief review of the physics The visual setup The setup code The basic motion code Adding controls and visual effects The full mover code Further ideas

Build a flight simulator

Physics and control mechanisms of aircraft What we will create Creating the visual setup Coding up the physics Implementing the controls Displaying flight information Test flying the simulator Further things to do

Create an accurate solar system model

What we will create The physics Coding up an appropriate integration scheme Building an idealized single-planet simulation Choosing appropriate scaling factors Obtaining planetary data and initial conditions Basic solar system model Incorporating accurate initial conditions Comparing the model results with NASA data Other things to do

Summary

Index

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