Index

A note on the digital index

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Symbols

* (multiplication) operator
in matrix operations, Matrix Multiplication: The * Operator, Scalar Multiplication: The * Operator, Vector Multiplication: The * Operator
in quaternion operations, Quaternion multiplication: The * operator, Vector multiplication: The * operator, Quaternion Multiplication: The * Operator, Scalar Multiplication: The * Operator, Vector Multiplication: The * Operator
in vector operations, Vector Dot Product: The * Operator, Scalar Multiplication: The * Operator
*= (multiplication) operator
in matrix operations, Scalar Multiplication: The *= Operator
in quaternion operations, Scalar Multiplication: The *= Operator
in vector operations, Scalar Multiplication: The *= Operator
+ (addition) operator
in matrix operations, Matrix Addition: The + Operator
in quaternion operations, Quaternion Addition: The + Operator
in vector operations, Vector Addition: The + Operator
+= (addition) operator
in matrix operations, Matrix Addition: The += Operator
in quaternion operations, Quaternion Addition: The += Operator
in vector operations, Vector Addition: The += Operator
/ (division) operator
in matrix operations, Scalar Divide: The / Operator
in vector operations, Scalar Division: The / Operator
/= (division) operator
in matrix operations, Scalar Division: The /= Operator
in quaternion operations, Scalar Division: The /= Operator, Scalar Division: The / Operator
in vector operations, Scalar Division: The /= Operator
^ (cross-product) operator, in vector operations, Vectors, Vector Cross Product: The ^ Operator
~ (conjugate) operator in quaternion operations, Conjugate: The ~ operator, Conjugate: The ~ Operator
− (conjugate) operator in vector operations, Conjugate: The − Operator
− (subtraction) operator
in matrix operations, Matrix Subtraction: The − Operator
in quaternion operations, Quaternion Subtraction: The − Operator
in vector operations, Vector Subtraction: The − Operator
−= (subtraction) operator
in matrix operations, Matrix Subtraction: The −= Operator
in quaternion operations, Quaternion Subtraction: The −= Operator
in vector operations, Vector Subtraction: The −= Operator

A

Abbott, Ira H., Lift and Drag
acceleration
about, Velocity and Acceleration
accelerometer theory on, Accelerometer Theory
angular, Units and Measures, Angular Velocity and Acceleration–Angular Velocity and Acceleration, Rigid-Body Kinetics
average, Velocity and Acceleration
centrifugal, Steering
centripetal, Angular Velocity and Acceleration, Steering
constant, Constant Acceleration–Constant Acceleration
equations for, Particle Kinetics in 2D
equations of motion and, Particle Kinetics in 2D
instantaneous, Velocity and Acceleration
linear, Newton’s Laws of Motion, Units and Measures, Units and Measures, Newton’s Second Law of Motion, Force and Torque, Calculating Forces
nonconstant, Nonconstant Acceleration
relative, Angular Velocity and Acceleration
rotational, Force and Torque
second derivatives of, Velocity and Acceleration
tangential, Angular Velocity and Acceleration
velocity and, Velocity and Acceleration–Velocity and Acceleration
acceleration vector, computing, Newton’s Second Law of Motion, Numerical Differentiation
accelerometers
about, Accelerometers–Accelerometer Theory
common specifications, Common Accelerometer Specifications
controlling sprites example, Using Tilt to Control a Sprite–Two Degrees of Freedom
data clipping, Data Clipping
digital, Kinetics
MEMS, Accelerometer Theory–MEMS Accelerometers
sensing orientation with, Simple Particle Model, Sensing Orientation
sensing tilt, Sensing Tilt–Two Degrees of Freedom
active stereoization, Programming Considerations–Active Stereoization
ACVs (air cushion vehicles) (see hovercraft)
adaptive step size method, Euler’s Method
addition (+) operator
in matrix operations, Matrix Addition: The + Operator
in quaternion operations, Quaternion Addition: The + Operator
in vector operations, Vector Addition: The + Operator
addition (+=) operator
in matrix operations, Matrix Addition: The += Operator
in quaternion operations, Quaternion Addition: The += Operator
in vector operations, Vector Addition: The += Operator
aerodynamic drag
in billiards example, Calculating Forces
in cars, Resistance
on hovercraft, Force Effectors, Resistance–Resistance
aerostatic lift, How Hovercraft Work
ailerons, in aircraft, Flight Controls, Geometry, Control
aim (guns)
breathing and body position, Breathing and Body Position–Breathing and Body Position
defined, Projectile Motion
elevation adjustments, Bullet drop: Gravity and air resistance
shooting positions, Breathing and Body Position
taking aim, Taking Aim
zeroing the sights, Zeroing the Sights–Wind
air cushion vehicles (ACVs) (see hovercraft)
air drag
particle simulation, Implementing External Forces
for ships and boats, General Resistance
shooting guns example, Drag
aircraft
control surfaces in, Geometry
controlling, Control
flight controls in, Rotation in 3D Rigid-Body Simulators, Flight Controls–Flight Controls
forces acting on, Aircraft, Lift and Drag–Other Forces
geometry of, Geometry
modeling, Modeling–Modeling
parts of, Geometry
quaternion operations in, Quaternions in 3D Simulators–Quaternions in 3D Simulators
weather helm and, Resistance
airfoil
about, Geometry
lift and drag forces, Lift and Drag–Lift and Drag
stalled, Lift and Drag
alpha (opacity), Optical Tracking
altitude
barometers and, Barometers
defined, Gaming from One Place to Another
gravity and, Force Fields
trilateration technique and, Two-Dimensional Mathematical Treatment
anaglyphs, complementary-color, Complementary-Color Anaglyphs
Anderson, Byron, Propulsion
angle of attack
critical, Lift and Drag
defined, Geometry
lift and drag forces, Lift and Drag
in lift and drag, Lift and Drag
stalls and, Lift and Drag
angular acceleration
angular velocity and, Angular Velocity and Acceleration–Angular Velocity and Acceleration
rigid-body kinetics and, Rigid-Body Kinetics
units and symbols for, Units and Measures
angular displacement, Angular Velocity and Acceleration, Angular Velocity and Acceleration
angular effects in collision response, Angular Effects–Angular Effects
angular impulse
in collisions, Linear and Angular Impulse–Linear and Angular Impulse
golf example, Friction
in impulse-momentum principle, Impulse-Momentum Principle
angular kinetic energy, Impact
angular momentum
equation for, Inertia Tensor
laws of motion and, Newton’s Second Law of Motion
angular motion
defined, Mass, Center of Mass, and Moment of Inertia
particle explosions and, Particle Explosions
rigid-body kinetics and, Rigid-Body Kinetics–Rigid-Body Kinetics
angular velocity
angular acceleration and, Angular Velocity and Acceleration–Angular Velocity and Acceleration
Euler integration and, Integration
laws of motion and, Newton’s Second Law of Motion
rotation in 3D rigid-body simulation and, Rotation Matrices, Quaternions
units and symbols for, Units and Measures
anisotropic materials, Newton’s Second Law of Motion
antipodal locations, Distance
Archimedes’ principle of buoyancy, Stability
arm rod (golf swings), Modeling a Golf Swing
aspect ratio, aircraft wing area, Geometry
atan function, Using Tilt to Control a Sprite
atan2 function, Great-Circle Heading
atmospheric pressure, Under Pressure, Barometers
atomic clock drift, Two-Dimensional Mathematical Treatment
attentuation in sound, Attenuation
automobiles (see cars)
autosterescopy, Autostereoscopy
average acceleration, Velocity and Acceleration

B

backward difference scheme, Numerical Differentiation
ballistic coefficient (BC), Projectile Motion
ballistics and firearms, Projectile Motion
(see also shooting guns example)
about, Projectile Motion
particle explosions, Particle Explosions–Particle Explosions
projectile motion, Projectile Motion–Projectile Motion
recoil and impact, Recoil and Impact
taking aim, Taking Aim–Breathing and Body Position
Bancroft, Stephen, Two-Dimensional Mathematical Treatment
barometers, Pressure Sensors and Load Cells, Barometers–Barometers
baseball examples
collisions in, Impact–Impact
Magnus effect in, Magnus Effect
BC (ballistic coefficient), Projectile Motion
Bernouilli, David, Drag
Bernoulli’s equation, Drag, Lift and Drag
billiards
about, Billiards–Billiards
calculating forces, Calculating Forces–Calculating Forces
collision example, Impact–Impact
handling collisions, Handling Collisions–Handling Collisions
implementing example, Implementation–Implementation
initializing example, Initialization–Stepping the Simulation
stepping simulation, Stepping the Simulation
binaural recording, How We Hear in 3D
binocular disparity, Binocular Vision
binocular rivalry, Complementary-Color Anaglyphs
binocular vision, Binocular Vision–Binocular Vision
biomechanics, Sports, Sports
(see also sports)
boats (see ships and boats)
Borst, Henry V., Lift and Drag
boundary layer in fluid dynamic drag, Drag, Virtual mass
bounding boxes, Collision Detection
bounding circle check, Linear Collision Response, Angular Effects
bounding spheres, Collision Detection
Bourg, David M., Particles
Bradski, Gary, OpenCV
breadth-to-draft ratio, General Resistance
breadth-to-length ratio, Virtual mass
buoyancy
about, Buoyancy–Buoyancy
calculating, Buoyancy
pressure and, Buoyancy
in ship stability, Stability
buttons, pressure-sensitive, Button Mashing–Button Mashing

C

cannon ball game example (see shooting guns example)
capacitive touch screens, Capacitive, Capacitive Touch Screens–Mutual capacitance
capsizing ships and boats, Stability, Sinking
cars
about, Cars
power and, Power
resistance and, Resistance
steering, Steering–Steering
stopping distance in, Stopping Distance
Cartesian coordinate system
about, Coordinate System
2D particle kinematics and, 2D Particle Kinematics
Cavendish, Henry, Force Fields
cavitation, Propulsion
center of gravity (see center of mass)
center of mass
calculating, Mass, Center of Mass, and Moment of Inertia–Mass, Center of Mass, and Moment of Inertia
defined, Mass, Center of Mass, and Moment of Inertia
impact and, Impact
load cells and, Center of gravity–Center of gravity
local coordinate system and, Local Coordinate Axes
quaternion rotation and, Quaternions
rigid-body kinematics and, Rigid-Body Kinematics
in ship stability, Stability
torque and, Force and Torque
2D example, Mass, Center of Mass, and Moment of Inertia
center of percussion, Impact
center of pressure, Force Effectors
central difference, second-order, Numerical Differentiation
central impact, Impact, Linear Collision Response
centrifugal acceleration, Steering
centripetal acceleration, Angular Velocity and Acceleration, Steering
chord length, aircraft wings, Geometry
chord line, Geometry
circular cylinder, mass moment of inertia formula, Mass, Center of Mass, and Moment of Inertia
circular cylindrical shell, mass moment of inertia formula, Mass, Center of Mass, and Moment of Inertia
circular polarization of light, Linear and Circular Polarization–Linear and Circular Polarization
cloth simulation, Connecting Objects
coefficient of restitution
applying formula for, Impact
collision response and, Collision Response
defined, Impact
physics models and, Physics Models
coefficient of rolling resistance, Resistance
coefficients of friction, Friction, Physics Models
collision detection
about, Collisions, Linear Collision Response, Collision Detection
billiards example, Handling Collisions–Handling Collisions
bounding circle check, Linear Collision Response, Angular Effects
collision response and, Collision Response
continuous, Collision Detection
particle-to-ground, Particle-to-Ground Collisions–Particle-to-Ground Collisions
particle-to-obstacle, Particle-to-Obstacle Collisions–Particle-to-Obstacle Collisions
physics engines and, Building Your Own Physics Engine, Collision Detection
vertex-edge collisions, Angular Effects–Angular Effects
vertex-vertex collisions, Angular Effects–Angular Effects
collision response
about, Collisions
angular effects in, Angular Effects–Angular Effects
billiards example, Handling Collisions–Handling Collisions
collision detection and, Collision Response
conservation of momentum principle, Impact, Impact, Recoil and Impact
implementing, Implementing Collision Response–Angular Effects
impulse-momentum principle, Impulse-Momentum Principle, Collision Response
linear, Linear Collision Response–Linear Collision Response
particle-to-ground, Particle-to-Ground Collisions–Particle-to-Ground Collisions
particle-to-obstacle, Particle-to-Obstacle Collisions–Particle-to-Obstacle Collisions
physics engines and, Building Your Own Physics Engine, Collision Response
collisions
about, Collisions
angular impulse in, Linear and Angular Impulse–Linear and Angular Impulse, Friction
baseball and bat example, Impact–Impact
billiard ball example, Impact–Impact, Billiards
friction and, Friction–Friction
golf example, Friction–Friction
handling in billiards example, Handling Collisions–Handling Collisions
impact force and, Impact–Impact
implementing in particle simulation, Implementing Collisions–Particle-to-Obstacle Collisions
impulse-momentum principle, Impulse-Momentum Principle, Collision Response
inelastic, Impact
line of action of, Impact
linear impulse in, Linear and Angular Impulse–Linear and Angular Impulse, Linear Collision Response
penetration in, Linear Collision Response, Linear Collision Response, Collision Response
plastic, Impact
compartments in ships and boats, Sinking
complementary-color anaglyphs, Complementary-Color Anaglyphs
condensation, What Is Sound?
condition table, motion-identifying, Center of gravity
conjugate operator
in quaternion operations, Conjugate: The ~ operator, Conjugate: The ~ Operator
in vector operations, Conjugate: The − Operator
connecting objects
about, Connecting Objects
connecting particles, Connecting Particles–Update the simulation
connecting rigid bodies, Connecting Rigid Bodies–Rotational Restraint
hanging rope or vine example, Connecting Particles–Update the simulation
linked-chain example, Connecting Rigid Bodies–Rotational Restraint
conservation of momentum principle, Impact, Impact, Recoil and Impact
constant acceleration, Constant Acceleration–Constant Acceleration
contact forces
about, Forces
in billiards example, Calculating Forces
center of mass and, Force and Torque
collision response and, Collision Response
friction as, Friction–Friction
contact manifold, Collision Detection, Handling Collisions
continuous collision detection, Collision Detection
convergence distance, The Left and Right Frustums, Active Stereoization
conversion functions, in quaternion operations, Conversion Functions
coordinate systems
accelerometer example, Sensing Orientation
Cartesian, Coordinate System, 2D Particle Kinematics
in particle simulation, Simple Particle Model
geographic, Gaming from One Place to Another, Two-Dimensional Mathematical Treatment
local, Local Coordinate Axes
rotating, Rotation Matrices
3D rigid-body simulation, 3D Rigid-Body Simulator
coordinate transformation, 2D rigid-body simulation, Transforming Coordinates
coupled motions, Ship Motions, Coupled Motions
critical attack angle, Lift and Drag
cross track error, Rhumb Line
cross-product (^) operator, in vector operations, Vectors, Vector Cross Product: The ^ Operator

D

dampers
about, Springs and Dampers
connecting objects, Springs and Dampers
equation for, Springs and Dampers, Springs and Dampers
uses for, Springs and Dampers
data clipping in accelerometers, Data Clipping
degrees of freedom
controlling sprites example, Two Degrees of Freedom–Two Degrees of Freedom
rigid bodies and, Rotation in 3D Rigid-Body Simulators, Sensing Orientation
ships and boats, Sinking, Ship Motions–Pitch
DegreesToRadians function, Conversion Functions
density
sound and, What Is Sound?
uniform, Rigid-Body Kinetics
units and symbols for, Units and Measures, Units and Measures
depth from focus (cameras), Kinect
derivatives
defined, Derivatives and Integrals
second, Velocity and Acceleration
determinant, in matrix operations, Determinant
differentiation schemes (optical tracking), Numerical Differentiation–Numerical Differentiation
digital accelerometers, Kinetics
digital signal processing, Accelerometers
dihedral angle, Modeling
direct central impact, Impact
direct force effectors, Force Effectors
direct impact, Impact
direction
acceleration and, Newton’s Second Law of Motion
in vector operations, Vectors
of rotation, Angular Velocity and Acceleration, Force and Torque
tensors and, Newton’s Second Law of Motion
velocity and, Velocity and Acceleration, X Components–X Components
wind, Particle Kinetics in 3D
direction angles, Magnitude
direction cosines, vector, X Components, Magnitude
disparity maps, OpenCV
dispersive signal technology, Exotic: Dispersive Signal and Surface Acoustic Wave
displacement
about, Velocity and Acceleration, Ships and Boats
accelerometer theory on, Accelerometer Theory
angular, Angular Velocity and Acceleration, Angular Velocity and Acceleration
distance traveled versus, Velocity and Acceleration
formula for, Constant Acceleration
volume of ships and, Stability
weight of ship and, Stability
distance
calculating between latitude and longitude coordinates, Location, Location, Location–Rhumb Line
convergence, The Left and Right Frustums, Active Stereoization
equations of motion and, Particle Kinetics in 2D
intraocular, Active Stereoization
skidding, Stopping Distance
stopping, Stopping Distance
distance tolerance, Linear Collision Response, Collision Response
distance traveled
displacement versus, Velocity and Acceleration
equations for, Particle Kinetics in 2D
second derivatives of, Velocity and Acceleration
time and, Velocity and Acceleration
division (/) operator
in matrix operations, Scalar Divide: The / Operator
in vector operations, Scalar Division: The / Operator
division (/=) operator
in matrix operations, Scalar Division: The /= Operator
in quaternion operations, Scalar Division: The /= Operator, Scalar Division: The / Operator
in vector operations, Scalar Division: The /= Operator
Doppler effect, Speed of Sound, Doppler Effect
dot-product (*) operator, Vectors, Vector Dot Product: The * Operator
drag coefficient
aircraft and, Other Forces
calculating, Drag
cars and, Resistance
fluid dynamic drag and, Fluid Dynamic Drag
hovercraft and, Resistance
physics models and, Physics Models
terminal velocity and, Drag
drag forces
aircraft in flight and, Aircraft, Lift and Drag–Lift and Drag, Other Forces
on cars, Resistance
fluid dynamic, Fluid Dynamic Drag
on hovercraft, Resistance–Resistance
nonconstant acceleration and, Nonconstant Acceleration
particle kinetics in 3D, Particle Kinetics in 3D
resistance in ships and, General Resistance–General Resistance
speed and, Drag
viscous, Fluid Dynamic Drag

E

Einstein, Albert, Relativistic Time, Accelerometer Theory
electromagnetic waves, Linear and Circular Polarization
elevators, in aircraft, Flight Controls, Control
engineering strain, Tiny scales
equal and opposite forces, Springs and Dampers, Numerical Integrator
equations of motion
defined, Kinetics
linked-chain example, Update
numerical integrators and, Numerical Integrator
particle kinetics in 2D, Particle Kinetics in 2D–Particle Kinetics in 2D
particle kinetics in 3D, Particle Kinetics in 3D
in particle simulation, Integrator
real-time simulations and, Integrating the Equations of Motion–Integrating the Equations of Motion
in 2D rigid-body simulation, Transforming Coordinates
Euler angles
constructing quaternions from, MakeQFromEulerAngles, MakeQFromEulerAngles
extracting from quaternions, MakeEulerAnglesFromQ, Integration, MakeEulerAnglesFromQ
steering cars and, Steering
in 3D motion, Local Coordinate Axes, Rotation in 3D Rigid-Body Simulators
Euler’s method
for billiards example, Stepping the Simulation
improved, Better Methods–Better Methods
modeling golf swings, Solving the Golf Swing Equations
in particle simulation, Integrator
in real-time simulations, Euler’s Method–Euler’s Method
in 3D rigid-body simulation, Integration
in 2D rigid-body simulation, Integrator
exotic touch screens technologies, Exotic: Dispersive Signal and Surface Acoustic Wave
explosions
about, Explosions
kinematic particle explosion, Kinematic Particle Explosion–Kinematic Particle Explosion
kinematic particle explosions, Particle Explosions–Particle Explosions
particle, Particle Explosions–Particle Explosions
polygon, Polygon Explosions–Polygon Explosions
external ballistics, Projectile Motion

F

fade effect, Kinematic Particle Explosion
far zero, Bullet drop: Gravity and air resistance
field forces
about, Forces, Force Fields
center of mass and, Force and Torque
filters
accelerometers and, Accelerometers
polarized light and, Linear and Circular Polarization
in 3D sound, How We Hear in 3D
firearms (see ballistics and firearms)
fireworks exploding, Kinematic Particle Explosion
flag model, Connecting Objects
flaps, in aircraft, Flight Controls, Geometry, Lift and Drag, Control
flight controls, 3D rigid-body simulation, Rotation in 3D Rigid-Body Simulators, Flight Controls–Flight Controls, Modeling–Modeling
flight simulation (see aircraft)
fluid dynamic drag
about, Fluid Dynamic Drag
around a sphere, Drag–Drag
boundary layer in, Drag, Virtual mass
drag coefficient, Fluid Dynamic Drag, Drag
laminar flow, Fluid Dynamic Drag
in projectiles, Drag–Drag
Reynolds number, Drag
separation point in, Drag
of spinning sphere, Magnus Effect
turbulent flow, Fluid Dynamic Drag
turbulent wake, Drag
football simulation game, Kinematic Particle Explosion
force
about, Forces
aggregating, Numerical Integrator
on aircraft in flight, Aircraft, Lift and Drag–Other Forces
buoyancy, Buoyancy–Buoyancy
calculating in billiards example, Calculating Forces–Calculating Forces
equal and opposite, Springs and Dampers, Numerical Integrator
fluid dynamic drag, Fluid Dynamic Drag
impact, Impact–Impact
impulse, Impulse-Momentum Principle
linear acceleration and, Force and Torque
Newton’s second law of motion and, Newton’s Laws of Motion, Newton’s Second Law of Motion
pressure versus, Pressure
springs and dampers, Springs and Dampers
static, Friction
torque versus, Force and Torque–Force and Torque
units and symbols for, Units and Measures, Units and Measures
force effectors, Force Effectors
forces at a distance, Forces, Force Fields
forward azimuth, Great-Circle Heading
FourSquare app, Mixed Reality
frequency
measuring for accelerometers, Accelerometers
measuring for sound, What Is Sound?
friction
about, Friction–Friction
in billiards example, Calculating Forces
calculating, Friction
coefficients of, Friction
collisions and, Friction–Friction
recoil and, Recoil and Impact
skidding distance and, Stopping Distance
frictional drag
aircraft and, Other Forces
Bernouilli’s equation and, Drag
moving through fluid and, Units and Measures, General Resistance
frustum, viewing, The Left and Right Frustums–The Left and Right Frustums
fuselage, in aircraft, Geometry
fusion in binocular vision, Binocular Vision

G

game engines, Building Your Own Physics Engine, Aircraft
geocaching, Geocaching and Reverse Geocaching
geographic coordinate system, Gaming from One Place to Another, Two-Dimensional Mathematical Treatment
Gillespie, Thomas, Steering
Global Positioning System (GPS)
about, Gaming from One Place to Another, What Time Is It?, Barometers
calculating between latitude and longitude, Location, Location, Location–Rhumb Line
location-based gaming and, Location-Based Gaming
trilateration technique, Two-Dimensional Mathematical Treatment–Two-Dimensional Mathematical Treatment
GM (stability index), Stability
golf examples
in collisions, Friction–Friction
Magnus effect in, Magnus Effect
modeling golf swings, Modeling a Golf Swing–Solving the Golf Swing Equations
physics engine considerations, Building Your Own Physics Engine
two-rod model, Modeling a Golf Swing
Google Maps, Barometers
GPS (Global Positioning System)
about, Gaming from One Place to Another, What Time Is It?, Barometers
calculating between latitude and longitude, Location, Location, Location–Rhumb Line
location-based gaming and, Location-Based Gaming
trilateration technique, Two-Dimensional Mathematical Treatment–Two-Dimensional Mathematical Treatment
gravitational force
accelerometer theory on, Accelerometer Theory
aircraft in flight and, Aircraft
as force effector, Force Effectors
Newton’s law of grativation, Force Fields
particle simulation and, Simple Particle Model–Simple Particle Model
projectiles and, Projectiles
zeroing the sights and, Bullet drop: Gravity and air resistance–Bullet drop: Gravity and air resistance
great-circle heading, Location, Location, Location, Great-Circle Heading
Greenwich Observatory (UK), Gaming from One Place to Another, What Time Is It?
grid partitioning, game space, Collision Detection
ground plane, particle-to-ground collisions, Particle-to-Ground Collisions–Particle-to-Ground Collisions
guns, shooting (see ballistics and firearms)
gyroscopes, Sensing Orientation

H

Hamilton, William, Quaternions
haptic feedback in touch screens, Haptic Feedback
harmonic wave, What Is Sound?, Harmonic Wave
Harr-like features (optical tracking), OpenCV
haversine formula for distance, Distance
head-related transfer functions (HRTFs), How We Hear in 3D
heave motion in ships and boats, Ship Motions, Heave
hectoPascals (hPa), Barometers
heuristic subroutines, Passive Stereoization
high lift devices, Lift and Drag
high-pass filters (accelerometers), Accelerometers
higher-order terms, Euler’s Method
Hoerner, Sighard F., Lift and Drag, Other Forces
holographs, Advanced Technologies
Hooke’s law, Springs and Dampers, Springs and Dampers
horsepower in cars, Power
hovercraft
about, Hovercraft–How Hovercraft Work
aerodynamic drag on, Force Effectors, Resistance–Resistance
implementing collision response, Implementing Collision Response–Angular Effects
resistance in, Resistance–Resistance
steering, How Hovercraft Work, Steering
2D rigid-body simulation, 2D Rigid-Body Simulator–Tuning
hPa (hectoPascals), Barometers
HRTFs (head-related transfer functions), How We Hear in 3D
hull in ships and boats, Ships and Boats
hull speed, Guidance speeds
human action modeling (see sports)
hydrodynamic lift, Ships and Boats
hydrostatic pressure, Pressure, Example Effects of High Pressure

I

impact
billiard characteristics for, Billiards
center of mass and, Impact
central, Impact, Linear Collision Response
collisions and, Impact–Impact
conservation of momentum principle, Impact, Impact, Recoil and Impact
direct, Impact
direct central, Impact
oblique, Impact
improved Euler method, Better Methods–Better Methods
impulse
angular, Impulse-Momentum Principle, Linear and Angular Impulse–Linear and Angular Impulse, Friction
defined, Impulse-Momentum Principle
linear, Impulse-Momentum Principle, Linear and Angular Impulse–Linear and Angular Impulse, Linear Collision Response
projectiles and, Projectiles
impulse torque, Impulse-Momentum Principle
impulse-momentum principle, Impulse-Momentum Principle, Collision Response
indirect force effectors, Force Effectors
induced drag, Resistance
inelastic collisions, Impact
inertia tensors
about, Inertia Tensor
angular momentum equation, Inertia Tensor
calculating, Inertia Tensor, Model
products of inertia, Inertia Tensor
symmetry and, Inertia Tensor
transfer of axis formula, Inertia Tensor
inertia, defined, Steering
infrared touch screens, Infrared and Optical Imaging
initial value problem, Integrating the Equations of Motion
instantaneous acceleration, Velocity and Acceleration
instantaneous velocity
calculating, Constant Acceleration
defined, Velocity and Acceleration
integral photography, Advanced Technologies
integrals, defined, Derivatives and Integrals
integrators
3D rigid-body simulation, Integration–Integration
about, Particles
numerical, Numerical Integrator
particle simulation, Integrator
2D rigid-body simulation, Integrator–Integrator
intensity of sound, What Is Sound?
interaural delay, How We Hear in 3D
internal ballistics, Projectile Motion
International System of Units (SI), Units and Measures
International Towing Tank Conference (ITTC), General Resistance
intraocular distance, Active Stereoization
inverse, in matrix operations, Inverse
isotropic materials, Newton’s Second Law of Motion
ITTC ( International Towing Tank Conference), General Resistance

J

jittering problem in objects, Collision Response
Jorgensen, Theodore P., Modeling a Golf Swing–Solving the Golf Swing Equations

K

Kaehler, Adrian, OpenCV
Kinect system, Kinect
kinematic viscosity, Units and Measures
kinematics
about, Kinematics
angular velocity and acceleration, Angular Velocity and Acceleration–Angular Velocity and Acceleration
constant acceleration, Constant Acceleration–Constant Acceleration
local coordinate axes, Local Coordinate Axes
nonconstant acceleration, Nonconstant Acceleration
particle explosion, Kinematic Particle Explosion–Kinematic Particle Explosion, Particle Explosions–Particle Explosions
rigid-body, Rigid-Body Kinematics
3D particle, 3D Particle Kinematics–Hitting the Target
2D particle, 2D Particle Kinematics–2D Particle Kinematics
velocity and acceleration, Velocity and Acceleration–Velocity and Acceleration
kinetic energy
about, Impact
of bullets, Recoil and Impact, Particle Explosions–Particle Explosions
converting, Impact
of sound waves, What Is Sound?
kinetic weapons, Recoil and Impact
kinetics
about, Kinetics–Kinetics
problem-solving guidelines, Kinetics
rigid-body, Rigid-Body Kinetics–Rigid-Body Kinetics
3D particle, Particle Kinetics in 3D–Cannon Revised
2D particle, Particle Kinetics in 2D–Particle Kinetics in 2D
kneeling (shooting position), Breathing and Body Position
Kutta condition, Lift and Drag
Kutta-Joukouski theorem, Magnus Effect

L

laminar flow, Fluid Dynamic Drag
latitude
calculating distance between longitude and, Location, Location, Location–Rhumb Line
defined, Gaming from One Place to Another
trilateration technique and, Two-Dimensional Mathematical Treatment–Two-Dimensional Mathematical Treatment
LC (liquid-crystal) shutter glasses, Liquid-Crystal Plasma
LED technology, Infrared and Optical Imaging
length
of aircraft wings, Geometry
of ships and boats, Ships and Boats
units and symbols for, Units and Measures, Units and Measures
lenticular lenses, Autostereoscopy
lift force
about, Magnus Effect–Magnus Effect
aerostatic lift, How Hovercraft Work
aircraft in flight and, Aircraft, Lift and Drag–Lift and Drag
calculating, Magnus Effect
lift-to-drag ratio, Lift and Drag
light
polarization of, Linear and Circular Polarization–Linear and Circular Polarization
speed of, Relativistic Time–Relativistic Time, Two-Dimensional Mathematical Treatment
linear acceleration
in billiards example, Calculating Forces
force and, Force and Torque
Newton’s second law of motion and, Newton’s Laws of Motion, Newton’s Second Law of Motion
units and symbols for, Units and Measures, Units and Measures
linear collision response, Linear Collision Response–Linear Collision Response
linear impulse
in collisions, Linear and Angular Impulse–Linear and Angular Impulse, Linear Collision Response
in impulse-momentum principle, Impulse-Momentum Principle
linear kinetic energy, Impact
linear momentum, Newton’s Second Law of Motion
linear motion, Mass, Center of Mass, and Moment of Inertia
linear polarization of light, Linear and Circular Polarization–Linear and Circular Polarization
linear velocity
equation for, Angular Velocity and Acceleration
linked-chain example, Update
units and symbols for, Units and Measures
linked-chain example, Connecting Rigid Bodies–Rotational Restraint
liquid-crystal (LC) shutter glasses, Liquid-Crystal Plasma
liquid-crystal plasma displays, Liquid-Crystal Plasma
load cells
center of gravity and, Center of gravity–Center of gravity
defined, Pressure Sensors and Load Cells
gaming uses for, Pressure Sensors and Load Cells, Load Cells
strain gauges and, Tiny scales
local coordinate system, Local Coordinate Axes, Geometry
locality principle, Relativistic Time
location-based gaming
about, Location-Based Gaming
geographic coordinate system and, Gaming from One Place to Another
longitude
calculating distance between latitude and, Location, Location, Location–Rhumb Line
defined, Gaming from One Place to Another
origin of determining, What Time Is It?
trilateration technique and, Two-Dimensional Mathematical Treatment–Two-Dimensional Mathematical Treatment
longitudinal waves, Linear and Circular Polarization
Lorentz factor, Relativistic Time
Lorentz transformation, Relativistic Time–Relativistic Time
loudness in sound, What Is Sound?
low-pass filters (accelerometers), Accelerometers

M

magnitude
in polygon explosions, Polygon Explosions
in quaternion operations, Magnitude, Magnitude
scalars and, Vectors
tensors and, Newton’s Second Law of Motion
of torque, Force and Torque
in vector operations, Vectors, Magnitude
of velocity, Velocity and Acceleration
Magnus effect, Magnus Effect–Magnus Effect
MakeEulerAnglesFromQ function, MakeEulerAnglesFromQ, Integration, MakeEulerAnglesFromQ
MakeQFromEulerAngles function, MakeQFromEulerAngles, MakeQFromEulerAngles
maneuverability of ships and boats, Maneuverability
mass, Accelerometer Theory
(see also center of mass)
accelerometer theory on, Accelerometer Theory
calculating, Mass, Center of Mass, and Moment of Inertia
defined, Mass, Center of Mass, and Moment of Inertia
Newton’s second law of motion and, Newton’s Laws of Motion, Newton’s Second Law of Motion
2D example, Mass, Center of Mass, and Moment of Inertia
units and symbols for, Units and Measures, Units and Measures, Units and Measures
variable, Variable Mass
virtual, Virtual mass
mass flow rate, Resistance
mass moment of inertia
calculating, Mass, Center of Mass, and Moment of Inertia–Mass, Center of Mass, and Moment of Inertia
defined, Mass, Center of Mass, and Moment of Inertia
physics models and, Physics Models
2D example, Mass, Center of Mass, and Moment of Inertia–Mass, Center of Mass, and Moment of Inertia
units and symbols for, Units and Measures
mass properties
center of mass, Mass, Center of Mass, and Moment of Inertia, Mass, Center of Mass, and Moment of Inertia–Mass, Center of Mass, and Moment of Inertia
defined, Mass, Center of Mass, and Moment of Inertia
mass, Mass, Center of Mass, and Moment of Inertia, Mass, Center of Mass, and Moment of Inertia
mass moment of inertia, Mass, Center of Mass, and Moment of Inertia, Mass, Center of Mass, and Moment of Inertia–Mass, Center of Mass, and Moment of Inertia
2D example, Mass, Center of Mass, and Moment of Inertia–Mass, Center of Mass, and Moment of Inertia
matrix addition, Matrix Addition: The += Operator, Matrix Addition: The + Operator
matrix functions and operators
matrix addition, Matrix Addition: The += Operator, Matrix Addition: The + Operator
matrix multiplication, Matrix Multiplication: The * Operator
matrix subtraction, Matrix Subtraction: The −= Operator, Matrix Subtraction: The − Operator
scalar division, Scalar Division: The /= Operator, Scalar Divide: The / Operator
scalar multiplication, Scalar Multiplication: The *= Operator, Scalar Multiplication: The * Operator
vector multiplication, Vector Multiplication: The * Operator
matrix multiplication, Matrix Multiplication: The * Operator
matrix operations
matrix functions and operators, Matrix Functions and Operators–Vector Multiplication: The * Operator
Matrix3x3 class, Matrix3×3 Class–Scalar Division: The /= Operator
matrix subtraction, Matrix Subtraction: The −= Operator, Matrix Subtraction: The − Operator
Matrix3x3 class
about, Matrix3×3 Class
det method, Determinant
Inverse method, Inverse
matrix addition, Matrix Addition: The += Operator
matrix subtraction, Matrix Subtraction: The −= Operator
scalar division, Scalar Division: The /= Operator
scalar multiplication, Scalar Multiplication: The *= Operator
Transpose method, Transpose
mean camber line, Geometry
measures (see units and measures)
MEMS (microelectromechanical systems), Accelerometers–MEMS Accelerometers, Barometers
Mercator projection, Rhumb Line
metacenter, in ship stability, Stability
microelectromechanical systems (MEMS), Accelerometers–MEMS Accelerometers, Barometers
mixed-reality games, Mixed Reality
Miyamoto, Shigeru, Load Cells
models
3D rigid-body simulation, Model–Model
about, Particles
aircraft flight, Modeling–Modeling
connecting objects examples, Connecting Objects–Rotational Restraint
particle simulation, Simple Particle Model–Simple Particle Model
physics, Physics Models
2D rigid-body simulation, Model
modulo operator, Great-Circle Heading
moment (see torque)
moment of inertia
calculating, Mass, Center of Mass, and Moment of Inertia–Mass, Center of Mass, and Moment of Inertia, Inertia Tensor, Model
defined, Mass, Center of Mass, and Moment of Inertia
laws of motion and, Newton’s Second Law of Motion
rigid-body kinetics and, Rigid-Body Kinetics
3D example, Newton’s Second Law of Motion
2D example, Mass, Center of Mass, and Moment of Inertia–Mass, Center of Mass, and Moment of Inertia
momentum
angular, Newton’s Second Law of Motion, Inertia Tensor
conservation of momentum principle, Impact, Impact, Recoil and Impact
linear, Newton’s Second Law of Motion
momentum drag, Resistance
motion
angular, Mass, Center of Mass, and Moment of Inertia, Rigid-Body Kinetics–Rigid-Body Kinetics, Particle Explosions
coupled, Ship Motions, Coupled Motions
linear, Mass, Center of Mass, and Moment of Inertia
plane, Rigid-Body Kinematics
projectile, Projectile Motion–Projectile Motion
ship, Ship Motions–Coupled Motions
motion-identifying condition table, Center of gravity
mouse-based input versus touch screens, Difference from Mouse-Based Input
movement parallax, Binocular Vision
multiplication (*) operator
in matrix operations, Matrix Multiplication: The * Operator, Scalar Multiplication: The * Operator, Vector Multiplication: The * Operator
in quaternion operations, Quaternion multiplication: The * operator, Vector multiplication: The * operator, Quaternion Multiplication: The * Operator, Scalar Multiplication: The * Operator, Vector Multiplication: The * Operator
in vector operations, Vector Dot Product: The * Operator, Scalar Multiplication: The * Operator
multiplication (*=) operator
in matrix operations, Scalar Multiplication: The *= Operator
in quaternion operations, Scalar Multiplication: The *= Operator
in vector operations, Scalar Multiplication: The *= Operator
muzzle velocity, Projectile Motion

N

NACA foil sections, Lift and Drag
neutral axis, Mass, Center of Mass, and Moment of Inertia
Newton, Isaac, Newton’s Laws of Motion
Newton’s laws
conservation of momentum principle, Impact, Impact, Recoil and Impact
equal and opposite forces, Springs and Dampers, Numerical Integrator
equations of motion and, Kinetics, Particle Kinetics in 2D
Impulse-Momentum Principle and, Impulse-Momentum Principle
of motion, Accelerometer Theory
of gravitation, Force Fields
of motion, Newton’s Laws of Motion, Units and Measures, Newton’s Second Law of Motion–Newton’s Second Law of Motion, Forces, Force Fields
nonconstant acceleration, Nonconstant Acceleration
normalize, in vector operations, Normalize
numerical integrators, Numerical Integrator

O

object detection (optical tracking), OpenCV
Objective-C
accelerometer code example, Two Degrees of Freedom–Two Degrees of Freedom
calculating distances code example, Distance, Rhumb Line
objects
aggregating forces, Numerical Integrator
collision detection considerations, Collision Detection
connecting, Connecting Objects–Rotational Restraint
jittering problem, Collision Response
simulated objects manager for, Simulated Objects Manager
weight of, Units and Measures, Stability, Projectile Motion
oblique impact, Impact
occlusion in volumetric displays, Advanced Technologies
off-axis method (cameras), The Left and Right Frustums
opacity (alpha), Optical Tracking
OpenAL API
about, Sound
alDistanceModel function, Attenuation
alSpeedOfSound function, Speed of Sound
AL_SPEED_OF_SOUND property, Speed of Sound
Doppler effect, Doppler Effect
reverberation special effect, Reflection
3D sound example, A Simple Example–A Simple Example
OpenCV method for 3D reconstruction, OpenCV
optical sensors and tracking
about, Optical Tracking, Sensors and SDKs
Kinect system, Kinect
numerical differentiation, Numerical Differentiation–Numerical Differentiation
OpenCV method for 3D reconstruction, OpenCV
optimal imaging techniques, Infrared and Optical Imaging
orientation
computing in 2D rigid-body simulation, Model, Integrator
defining in cannon ball game example, X Components
expressing in 3D rigid-body simulations, Rotation in 3D Rigid-Body Simulators, Rotation Matrices
importance in rigid bodies, Kinematics
quaternions and, Quaternions, Quaternions in 3D Simulators–Quaternions in 3D Simulators, Model, Integration
sensing with accelerometers, Simple Particle Model, Sensing Orientation
tracking during body rotation, Local Coordinate Axes
out-of-screen effects, Active Stereoization
overshoot angle, Rudders and Thrust Vectoring
oversteering cars, Steering

P

parallax, Binocular Vision
parallax barrier in autostereoscopy, Autostereoscopy
parallel axis theorem, Mass, Center of Mass, and Moment of Inertia, Mass, Center of Mass, and Moment of Inertia
parameter tuning, Projectiles
particle explosions, Kinematic Particle Explosion–Kinematic Particle Explosion, Particle Explosions–Particle Explosions
particle kinematics
particle explosions, Kinematic Particle Explosion–Kinematic Particle Explosion, Particle Explosions–Particle Explosions
3D, 3D Particle Kinematics–Hitting the Target
2D, 2D Particle Kinematics–2D Particle Kinematics
particle kinetics
3D, Particle Kinetics in 3D–Cannon Revised
2D, Particle Kinetics in 2D–Particle Kinetics in 2D
particle simulation
about, Particles–Particles
basic simulator, The Basic Simulator–The Basic Simulator
implementing collisions, Implementing Collisions–Particle-to-Obstacle Collisions
implementing external forces, Implementing External Forces–Implementing External Forces
integrating particles, Integrator
rendering particles, Rendering
simple model, Simple Particle Model–Simple Particle Model
tuning, Tuning
particle-to-ground collisions, Particle-to-Ground Collisions–Particle-to-Ground Collisions
particle-to-obstacle collisions, Particle-to-Obstacle Collisions–Particle-to-Obstacle Collisions
particles
about, Kinematics
cloth simulation, Connecting Objects
connecting, Connecting Particles–Update the simulation
hanging rope or vine example, Connecting Particles–Update the simulation
integrating in simulator, Integrator
rendering in simulator, Rendering
uses for, Particles
passive stereoization, Programming Considerations, Passive Stereoization
pattern recognition, Optical Tracking
penalty methods, Collisions
penetration in collisions, Linear Collision Response, Linear Collision Response, Collision Response
percussion, center of, Impact
photodetectors, Infrared and Optical Imaging
photons, defined, Relativistic Time
physics engines
about, Physics Engines
building, Building Your Own Physics Engine–Building Your Own Physics Engine
collision detection in, Building Your Own Physics Engine, Collision Detection
collision response in, Building Your Own Physics Engine, Collision Response
force effectors and, Force Effectors
general-purpose, Building Your Own Physics Engine
numerical integrators and, Numerical Integrator
physics models, Physics Models
purpose-built, Building Your Own Physics Engine
simulated objects manager, Simulated Objects Manager
physics models, Physics Models
piezoresisters, MEMS Accelerometers, Barometers
piezoresistive strain gauge, Tiny scales
pinned joint, Rotational Restraint
pitch
flight control action for, Rotation in 3D Rigid-Body Simulators, Flight Controls, Flight Controls, Control
local coordinate axes and, Local Coordinate Axes, Geometry
quarter-chord point and, Lift and Drag, Control
in ships and boats, Stability, Ship Motions, Pitch
in sound, What Is Sound?
plane motion, Rigid-Body Kinematics
planing vessels, Ships and Boats, Planing craft
plastic collisions, Impact
plenum chamber (hovercraft), How Hovercraft Work
point sound source, Attenuation
point-blank weapons, Taking Aim
polarization of light, Linear and Circular Polarization–Linear and Circular Polarization
polling rate, Accelerometers
polygon explosions, Polygon Explosions–Polygon Explosions
pounds per square foot (psf), Pressure
pounds per square inch (psi), Pressure
power
of car engines, Power
defined, Power
hovercraft hover height and, How Hovercraft Work
of sound wave, What Is Sound?
pressure
atmospheric, Under Pressure, Barometers
Bernoulli’s equation and, Drag, Lift and Drag
buoyancy and, Buoyancy
center of, Force Effectors
defined, Under Pressure
force versus, Pressure
hydrostatic, Pressure, Example Effects of High Pressure
sound and, What Is Sound?
units and symbols for, Units and Measures, Under Pressure
pressure drag, General Resistance, Resistance
pressure sensors
about, Pressure Sensors and Load Cells–Example Effects of High Pressure
load cells and, Load Cells–Center of gravity
pressure-sensitive buttons and, Button Mashing–Button Mashing
principal axes, Inertia Tensor
products of inertia, Inertia Tensor
projectiles
about, Projectiles–Projectiles
bullets in motion, Projectile Motion–Projectile Motion
drag and, Drag–Drag
football simulation game, Kinematic Particle Explosion
golf ball flight, Modeling a Golf Swing
hitting the target example, Hitting the Target–Hitting the Target
impulse forces, Impulse-Momentum Principle
Magnus effect, Magnus Effect–Magnus Effect
particle explosions as, Kinematic Particle Explosion–Kinematic Particle Explosion, Particle Explosions–Particle Explosions
recoil and impact, Recoil and Impact
simple trajectories, Simple Trajectories–Simple Trajectories
taking aim, Taking Aim–Breathing and Body Position
terminal velocity and, Drag
variable mass and, Variable Mass
prone (shooting position), Breathing and Body Position
propeller walk, Propeller walk
propulsion of ships and boats, Propulsion
pseudoranges, Two-Dimensional Mathematical Treatment
psf (pounds per square foot), Pressure
psi (pounds per square inch), Pressure

Q

QGetAngle function, QGetAngle
QGetAxis function, QGetAxis
QRotate function, QRotate
quantum tunneling, Common Accelerometer Specifications
quarter-chord point, Lift and Drag, Control
quaternion addition, Quaternion Addition: The += Operator, Quaternion Addition: The + Operator
Quaternion class
about, Quaternion Operations, Quaternion Class
conjugate operator, Conjugate: The ~ operator, Conjugate: The ~ Operator
GetScalar method, GetScalar
GetVector method, GetVector
Magnitude method, Magnitude, Magnitude
quaternion addition, Quaternion Addition: The += Operator
quaternion subtraction, Quaternion Subtraction: The −= Operator
scalar division, Scalar Division: The /= Operator
scalar multiplication, Scalar Multiplication: The *= Operator
quaternion functions and operators
conjugate operator, Conjugate: The ~ operator, Conjugate: The ~ Operator
conversion functions, Conversion Functions
DegreesToRadians function, Conversion Functions
MakeEulerAnglesFromQ function, MakeEulerAnglesFromQ, Integration, MakeEulerAnglesFromQ
MakeQFromEulerAngles function, MakeQFromEulerAngles, MakeQFromEulerAngles
QGetAngle function, QGetAngle
QGetAxis function, QGetAxis
QRotate function, QRotate
quaternion addition, Quaternion Addition: The += Operator, Quaternion Addition: The + Operator
quaternion multiplication, Quaternion multiplication: The * operator, Quaternion Multiplication: The * Operator
quaternion subtraction, Quaternion Subtraction: The −= Operator, Quaternion Subtraction: The − Operator
QVRotate function, QVRotate, Quaternions in 3D Simulators, Model, QVRotate
RadiansToDegrees function, Conversion Functions
scalar division, Scalar Division: The /= Operator, Scalar Division: The / Operator
scalar multiplication, Scalar Multiplication: The *= Operator, Scalar Multiplication: The * Operator
vector multiplication, Vector multiplication: The * operator, Vector Multiplication: The * Operator
quaternion multiplication, Quaternion multiplication: The * operator, Quaternion Multiplication: The * Operator
quaternion operations
Quaternion class, Quaternion Operations, Quaternion Class–Conjugate: The ~ Operator
quaternion functions and operators, Quaternion Functions and Operators–Conversion Functions
for rigid-body rotation, Quaternions–MakeEulerAnglesFromQ
3D simulation and, Quaternions in 3D Simulators–Quaternions in 3D Simulators
quaternion subtraction, Quaternion Subtraction: The −= Operator, Quaternion Subtraction: The − Operator
QVRotate function, QVRotate, Quaternions in 3D Simulators, Model, QVRotate

R

RadiansToDegrees function, Conversion Functions
rarefaction, What Is Sound?
real-time simulations
about, Real-Time Simulations
equations of motion and, Integrating the Equations of Motion–Integrating the Equations of Motion
Euler’s method, Euler’s Method–Euler’s Method
improved Euler method, Better Methods–Better Methods
physics engine considerations, Building Your Own Physics Engine
Runge-Kutta method in, Better Methods–Better Methods
Taylor’s theorem in, Euler’s Method, Better Methods
recoil of firearms, Recoil and Impact
rectangular cylinder, mass moment of inertia formula, Mass, Center of Mass, and Moment of Inertia
reflection in sound waves, Reflection
relative acceleration, Angular Velocity and Acceleration
relative normal velocity, Linear Collision Response
relative velocity
about, Angular Velocity and Acceleration
between connected objects, Springs and Dampers
collision detection and, Linear Collision Response, Linear Collision Response, Collision Detection
particle-to-ground collisions and, Particle-to-Ground Collisions
relativistic time, Relativistic Time–Relativistic Time, Two-Dimensional Mathematical Treatment
rendering
about, Particles
particle simulation, Rendering
simulated objects manager and, Simulated Objects Manager
2D rigid-body simulation, Rendering
residual resistance, General Resistance
resistance
in cars, Resistance
equation for, Particle Kinetics in 2D
in hovercraft, Resistance–Resistance
residual, General Resistance
rolling, Resistance, Calculating Forces
in ships and boats, General Resistance–Guidance speeds
zeroing the sights and, Bullet drop: Gravity and air resistance–Bullet drop: Gravity and air resistance
resistive touch screens, Resistive, Resistive Touch Screens–Four-wire resistive touch screen
restitution, coefficient of (see coefficient of restitution)
reverberation special effect, Reflection
reverse geocaching, Geocaching and Reverse Geocaching
reverse, in vector operations, Reverse
Reynolds number, Drag, General Resistance
rhumb line, Location, Location, Location, Rhumb Line
right hand rule, Force and Torque
rigid bodies
about, Kinematics
billiards example, Implementation
circular path of particles making up, Angular Velocity and Acceleration
connecting, Connecting Rigid Bodies–Rotational Restraint
conservation of momentum principle, Impact, Impact, Recoil and Impact
linked-chain example, Connecting Rigid Bodies–Rotational Restraint
penalty methods for, Collisions
rotation in 3D simulation, Rotation in 3D Rigid-Body Simulators–Quaternions in 3D Simulators
3D simulation for, 3D Rigid-Body Simulator–Flight Controls, Implementation
2D simulation for, 2D Rigid-Body Simulator–Tuning
rigid-body kinematics, Rigid-Body Kinematics
rigid-body kinetics, Rigid-Body Kinetics–Rigid-Body Kinetics
roadway bank, Steering
Robbins effect, Magnus Effect–Magnus Effect
roll
flight control action for, Rotation in 3D Rigid-Body Simulators, Flight Controls
local coordinate axes and, Local Coordinate Axes, Geometry
in ships and boats, Stability, Ship Motions, Roll
roll period, Roll
rolling resistance, Resistance, Calculating Forces
rope example, Connecting Particles–Update the simulation
rotation in 3D rigid-body simulation
about, Rotation in 3D Rigid-Body Simulators
quaternions and, Quaternions–Quaternions in 3D Simulators
rotation matrices and, Rotation Matrices–Rotation Matrices
rotational restraint, Rotational Restraint–Rotational Restraint
rotation matrices, Rotation Matrices–Rotation Matrices
rotational acceleration, Force and Torque
rotational inertia (see mass moment of inertia)
rotational restraint, Rotational Restraint–Rotational Restraint
rudders
in aircraft, Geometry, Control
in ships and boats, Rudders and Thrust Vectoring
Runge-Kutta method, Better Methods–Better Methods, Modeling a Golf Swing, Solving the Golf Swing Equations

S

Saffer, Dan, Custom Gestures
scalar division
in matrix operations, Scalar Division: The /= Operator, Scalar Divide: The / Operator
in quaternion operations, Scalar Division: The /= Operator, Scalar Division: The / Operator
in vector operations, Scalar Division: The /= Operator, Scalar Division: The / Operator
scalar multiplication
in matrix operations, Scalar Multiplication: The *= Operator, Scalar Multiplication: The * Operator
in quaternion operations, Scalar Multiplication: The *= Operator, Scalar Multiplication: The * Operator
in vector operations, Scalar Multiplication: The *= Operator, Scalar Multiplication: The * Operator, Triple Scalar Product
scalars
defined, Vectors
examples of, Vectors
magnitude and, Vectors
tensors and, Newton’s Second Law of Motion
second derivatives, Velocity and Acceleration
second zero, Bullet drop: Gravity and air resistance
second-order central difference, Numerical Differentiation
separation point in fluid dynamic drag, Drag
ships and boats
about, Ships and Boats–Ships and Boats
geometry of, Ships and Boats
maneuverability of, Maneuverability–Propeller walk
parts of, Ships and Boats
propulsion of, Propulsion
resistance in, General Resistance–Guidance speeds
ship motions, Ship Motions–Coupled Motions
sinking, Sinking
stability of, Stability–Stability
2D particle kinetics example, Particle Kinetics in 2D–Particle Kinetics in 2D
types of, Ships and Boats
typical speeds for, Guidance speeds
shooting guns example
air drag and, Drag
challenges of, Projectile Motion
particle kinematics suggestions, Kinematic Particle Explosion
physics engine considerations, Building Your Own Physics Engine
taking aim, Taking Aim
3D particle kinematics, 3D Particle Kinematics–Hitting the Target
3D particle kinetics, Particle Kinetics in 3D–Cannon Revised
2D particle kinematics, 2D Particle Kinematics–2D Particle Kinematics
shooting positions, Breathing and Body Position
SI (International System of Units), Units and Measures
simulated objects manager, Simulated Objects Manager
simulations
cloth, Connecting Objects
football game, Kinematic Particle Explosion
force effectors in, Force Effectors
hitting the target example, Hitting the Target–Hitting the Target
implementing collision response, Implementing Collision Response–Angular Effects
particle, Particles–Tuning
physics engine considerations, Building Your Own Physics Engine
real-time, Real-Time Simulations–Summary, Building Your Own Physics Engine
springs and dampers in, Springs and Dampers
3D rigid-body, Rotation in 3D Rigid-Body Simulators–Quaternions in 3D Simulators, 3D Rigid-Body Simulator–Flight Controls
2D rigid-body, 2D Rigid-Body Simulator–Tuning
updating, Update the simulation–Update the simulation, Update–Update
sinking ships and boats, Sinking
skidding distance, Stopping Distance
skin friction
on aircraft, Other Forces
on cars, Resistance
on hovercraft, Resistance
planing vessels and, Planing craft
sliding friction force, Calculating Forces
sound and sound waves
about, Sound–What Is Sound?
characteristics of, Characteristics of and Behavior of Sound Waves–Doppler Effect
3D, 3D Sound–A Simple Example
span, aircraft wings, Geometry
special effects
fade effect, Kinematic Particle Explosion
out-of-screen effects, Active Stereoization
particle explosions, Kinematic Particle Explosion
reverberation, Reflection
specific weight, Buoyancy
speed
acceleration and, Velocity and Acceleration
calculating, Velocity and Acceleration
defined, Velocity and Acceleration
drag and, Drag
equations of motion and, Particle Kinetics in 2D
hull, Guidance speeds
of light, Relativistic Time–Relativistic Time, Two-Dimensional Mathematical Treatment
of sound, Speed of Sound
units and symbols for, Units and Measures, Velocity and Acceleration
velocity and, Velocity and Acceleration
spheres
bounding, Collision Detection
calculating distance along, Distance
fluid dynamic drag around, Drag–Drag
great-circle heading, Great-Circle Heading
Magnus effect and, Magnus Effect
mass moment of inertia formula, Mass, Center of Mass, and Moment of Inertia
spherical law of cosines, Distance
spherical shell, mass moment of inertia formula, Mass, Center of Mass, and Moment of Inertia
sports
about, Sports
baseball examples, Impact–Impact, Magnus Effect
billiards examples, Impact–Impact, Billiards–Handling Collisions
football game simulation, Kinematic Particle Explosion
golf examples, Friction–Friction, Magnus Effect, Building Your Own Physics Engine, Modeling a Golf Swing–Solving the Golf Swing Equations
spring-damper element formula, Springs and Dampers, Connecting Objects, Springs and Dampers
springs
about, Springs and Dampers
accelerometer theory on, Accelerometer Theory
cloth simulation, Connecting Objects
connecting objects, Springs and Dampers
equation for, Springs and Dampers, Springs and Dampers
swinging rope example, Rope–Update the simulation
uses for, Springs and Dampers
stability index (GM), Stability
stability of ships and boats, Stability–Stability
standing (shooting position), Breathing and Body Position
static forces, Friction
steering
in cars, Steering–Steering
in hovercraft, How Hovercraft Work, Steering
throttle, Rudders and Thrust Vectoring
Stein, Jonathan Y., Accelerometers
stereoization process
about, Programming Considerations
active stereoization, Programming Considerations–Active Stereoization
passive stereoization, Programming Considerations, Passive Stereoization
stereopsis, Binocular Vision
stereoscopic displays, 3D Display
(see also 3D display)
about, 3D Display, Stereoscopic Basics
viewing frustum, The Left and Right Frustums–The Left and Right Frustums
stopping distance in cars, Stopping Distance
strain energy, Impact
strain gauges, Tiny scales
street games, Street Games
subtraction (−) operator
in matrix operations, Matrix Subtraction: The − Operator
in quaternion operations, Quaternion Subtraction: The − Operator
in vector operations, Vector Subtraction: The − Operator
subtraction (−=) operator
in matrix operations, Matrix Subtraction: The −= Operator
in quaternion operations, Quaternion Subtraction: The −= Operator
in vector operations, Vector Subtraction: The −= Operator
summation in binocular vision, Binocular Vision
superelevation (roadway banking), Steering
superposition principle, Superposition
suppression in binocular vision, Binocular Vision
surface acoustic wave technology, Exotic: Dispersive Signal and Surface Acoustic Wave
surface area, units and symbols for, Units and Measures
symmetry, plane of, Inertia Tensor

T

tangential acceleration, Angular Velocity and Acceleration
tangential velocity, Angular Velocity and Acceleration, Impact
Taylor’s theorem, Euler’s Method, Better Methods
tensors
about, Newton’s Second Law of Motion
inertia, Inertia Tensor–Inertia Tensor, Model
scalars and, Newton’s Second Law of Motion
vectors and, Newton’s Second Law of Motion
10/10 maneuver, Rudders and Thrust Vectoring
terminal ballistics, Projectile Motion
terminal velocity, Drag
3D display
about, 3D Display
binocular vision, Binocular Vision–Binocular Vision
programming considerations, Programming Considerations–Passive Stereoization
stereoscopic basics, Stereoscopic Basics–The Left and Right Frustums
types of, Types of Display–Advanced Technologies
3D particle kinematics
about, 3D Particle Kinematics
hitting the target, Hitting the Target–Hitting the Target
shooting guns example, 3D Particle Kinematics–Hitting the Target
vectors, The Vectors
x components, X Components–X Components
y components, Y Components
z components, Z Components
3D particle kinetics
about, Particle Kinetics in 3D–Particle Kinetics in 3D
shooting guns example, Particle Kinetics in 3D–Cannon Revised
x components, X Components
y components, Y Components
z components, Z Components
3D rigid-body simulation
about, 3D Rigid-Body Simulator
billiard ball example, Implementation
flight controls, Flight Controls–Flight Controls, Modeling–Modeling
integrator for, Integration–Integration
model for, Model–Model
quaternions in, Quaternions in 3D Simulators–Quaternions in 3D Simulators
rotation in, Rotation in 3D Rigid-Body Simulators–Quaternions in 3D Simulators
3D sound, 3D Sound–A Simple Example
throttle steering, Rudders and Thrust Vectoring
thrust
defined, Forces, Other Forces
flight control actions, Flight Controls, Aircraft
thrust vectoring, Rudders and Thrust Vectoring
thrust-to-propeller RPM ratio, Propulsion
thrust-to-throttle curve ratio, Propulsion
thrust-to-weight ratio, Other Forces
tilt
controlling sprite with, Using Tilt to Control a Sprite–Two Degrees of Freedom
sensing with accelerometers, Sensing Tilt
time
equations of motion and, Particle Kinetics in 2D
GPS background and, What Time Is It?–Two-Dimensional Mathematical Treatment
laws of motion and, Newton’s Second Law of Motion
relativistic, Relativistic Time–Relativistic Time
reliativistic, Two-Dimensional Mathematical Treatment
speed and, Velocity and Acceleration
tracking button position over, Button Mashing
units and symbols for, Units and Measures, Units and Measures
TNT equivalency, Polygon Explosions
toe-in method (cameras), The Left and Right Frustums
tons per centimeter immersion (TPCM), Heave
torque
about, Force and Torque
calculating, Force and Torque
force versus, Force and Torque–Force and Torque
impulse, Impulse-Momentum Principle
laws of motion and, Newton’s Second Law of Motion
magnitude of, Force and Torque
rotational acceleration and, Force and Torque
units and symbols for, Units and Measures
touch screens
about, Touch Screens
custom gestures and, Custom Gestures
example program, Example Program–Multitouch
haptic feedback, Haptic Feedback
modeling in games, Modeling Touch Screens in Games
mouse-based input versus, Difference from Mouse-Based Input
step-by-step physics, Resistive Touch Screens–Mutual capacitance
types of, Resistive
TPCM (tons per centimeter immersion), Heave
trajectories
football simulation game, Kinematic Particle Explosion
hitting the target example, Hitting the Target–Hitting the Target
simple, Simple Trajectories–Simple Trajectories
terminal velocity and, Drag
zeroing the sights, Zeroing the Sights–Wind
transfer functions (sound), How We Hear in 3D
transfer of axis formula, Inertia Tensor
transforming coordinates, 2D rigid-body simulation, Transforming Coordinates
transitional ballistics, Projectile Motion
transpose, in matrix operations, Transpose
transverse waves, Linear and Circular Polarization
trilateration technique, Two-Dimensional Mathematical Treatment–Two-Dimensional Mathematical Treatment
triple scalar product, Triple Scalar Product
triple vector product, Inertia Tensor
truncation error, Euler’s Method–Euler’s Method
tuning
particle simulation, Tuning
2D rigid-body simulation, Tuning
turbulent flow, Fluid Dynamic Drag
turbulent wake, Drag
two-rod model, Modeling a Golf Swing
2D particle kinematics, 2D Particle Kinematics–2D Particle Kinematics
2D particle kinetics, Particle Kinetics in 2D–Particle Kinetics in 2D
2D rigid-body simulation
about, 2D Rigid-Body Simulator
basic simulator, The Basic Simulator–The Basic Simulator
implementing collision response, Implementing Collision Response–Angular Effects
integrator for, Integrator–Integrator
model for, Model–Model
rendering, Rendering
tuning, Tuning

U

understeering cars, Steering
uniform density, Rigid-Body Kinetics
unit quaternion, Quaternions, Quaternions in 3D Simulators, Integration
units and measures
checking dimensional consistency, Units and Measures–Units and Measures
common mistakes when calculating, Units and Measures
for pressure, Pressure, Under Pressure
for sound, What Is Sound?
universal constant, Force Fields

V

variable mass, Variable Mass
vector addition, Vector Addition: The += Operator, Vector Addition: The + Operator
Vector class
about, Vector Class
conjugate operator, Conjugate: The − Operator
Magnitude method, Magnitude
Normalize method, Normalize
in particle simulation, Simple Particle Model
Reverse method, Reverse
scalar division and, Scalar Division: The /= Operator
scalar multiplication and, Scalar Multiplication: The *= Operator
vector addition and, Vector Addition: The += Operator
vector subtraction and, Vector Subtraction: The −= Operator
vector cross product, Vectors, Angular Velocity and Acceleration, Vector Cross Product: The ^ Operator
vector direction cosines, X Components, Magnitude
vector dot-product operator, Vectors, Vector Dot Product: The * Operator
vector functions and operators
conjugate operator, Conjugate: The − Operator
scalar division, Scalar Division: The /= Operator, Scalar Division: The / Operator
scalar multiplication, Scalar Multiplication: The *= Operator, Scalar Multiplication: The * Operator
triple scalar product, Triple Scalar Product
vector addition, Vector Addition: The += Operator, Vector Addition: The + Operator
vector cross product, Vectors, Angular Velocity and Acceleration, Vector Cross Product: The ^ Operator
vector dot product, Vectors, Vector Dot Product: The * Operator
vector subtraction, Vector Subtraction: The −= Operator, Vector Subtraction: The − Operator
vector multiplication
in matrix operations, Vector Multiplication: The * Operator
in quaternion operations, Vector multiplication: The * operator, Vector Multiplication: The * Operator
vector operations
direction in, Vectors
magnitude in, Vectors, Magnitude
Vector class, Vector Class–Conjugate: The − Operator
vector functions and operators, Vector Functions and Operators–Triple Scalar Product
vector subtraction, Vector Subtraction: The −= Operator, Vector Subtraction: The − Operator
vectors
acceleration, Newton’s Second Law of Motion, Numerical Differentiation
defined, Vectors
examples of, Vectors
orthogonal, Rotation Matrices
tensors and, Newton’s Second Law of Motion
3D particle kinematics and, The Vectors
time derivative of, Newton’s Second Law of Motion
velocity
about, Velocity and Acceleration–Velocity and Acceleration
acceleration and, Velocity and Acceleration–Velocity and Acceleration
angular, Units and Measures, Newton’s Second Law of Motion, Angular Velocity and Acceleration–Angular Velocity and Acceleration, Rotation Matrices, Quaternions, Integration
Bernoulli’s equation and, Drag
equations for, Particle Kinetics in 2D
instantaneous, Velocity and Acceleration, Constant Acceleration
linear, Units and Measures, Angular Velocity and Acceleration, Update
magnitude of, Velocity and Acceleration
muzzle, Projectile Motion
relative, Angular Velocity and Acceleration, Particle-to-Ground Collisions, Linear Collision Response, Linear Collision Response, Springs and Dampers, Collision Detection
Reynolds number and, Drag
second derivatives of, Velocity and Acceleration
tangential, Angular Velocity and Acceleration, Impact
terminal, Drag
vertex-edge collisions, Angular Effects–Angular Effects
vertex-vertex collisions, Angular Effects–Angular Effects
vertical force, Calculating Forces
vibration energy, Exotic: Dispersive Signal and Surface Acoustic Wave
viewing frustum, The Left and Right Frustums–The Left and Right Frustums
Vincenty formula, Distance
vines (swinging) example, Connecting Particles–Update the simulation
virtual mass, Virtual mass
viscosity
kinematic, Units and Measures
units and symbols for, Units and Measures
viscous drag, Resistance
volume of ships, displacement and, Stability
volumetric displays, 3D Display, Advanced Technologies
Von Doenhoff, Albert E., Lift and Drag
voxels, Advanced Technologies

W

wave drag, General Resistance, Resistance
weather helm, Resistance
weight of objects
about, Units and Measures
ammunition, Projectile Motion
buoyancy and, Stability
weighted average, Center of gravity–Center of gravity
wetted drag, Resistance–Resistance
wind force
as force effector, Force Effectors
particle kinetics in 3D, Particle Kinetics in 3D
in particle simulation, Implementing External Forces–Implementing External Forces
zeroing the sights and, Wind
wings, in aircraft, Geometry
wire-grid polarizer, Linear and Circular Polarization

X

x-axis, rotation around, Coordinate System, Rotation Matrices

Y

y-axis, rotation around, Coordinate System, Rotation Matrices
yaw
flight control action for, Rotation in 3D Rigid-Body Simulators, Flight Controls, Control
local coordinate axes and, Local Coordinate Axes, Geometry
in ships and boats, Ship Motions

Z

z-axis, rotation around, Coordinate System, Rotation Matrices
zero range, Bullet drop: Gravity and air resistance
zeroing the sights
about, Zeroing the Sights
gravity and resistance, Bullet drop: Gravity and air resistance–Bullet drop: Gravity and air resistance
wind and, Wind
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