Wendy Stahler [Wendy Stahler] - Beginning Math and Physics for Game Programmers
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Whether youre a hobbyist or a budding game design pro, yourobjective is probably the same: To create the coolest gamespossible using todays increasingly sophisticated technology. To dothat, however, you need to understand some basic math and physicsconcepts. Not to worry: You dont need to go to night school if youget this handy guide! Through clear, step-by-step instructions,author Wendy Stahler covers the trigonometry snippets, vectoroperations, and 1D/2D/3D motion you need to improve your level ofgame development. Each chapter includes exercises to make thelearning stick, and Visualization Experience sections are sprinkledthroughout that walk you through a demo of the chapters content.By the end of the volume, youll have a thorough understanding ofall of the math and physics concepts, principles, and formulas youneed to control and enhance your users gaming experience.
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| Symbol | Name | Description |
|---|---|---|
| Alpha | Often used to represent an angle | |
| Delta | Means change in | |
| Epsilon | Coefficient of restitution | |
| f '( t ) | The derivative of function f with respect to t | |
| Mu | Coefficient of friction | |
| Omega | Used here to represent angular velocity | |
| Pi | Constant 3.14 | |
| Theta | Often used to represent an angle |
equals the slope between two points on position v . Time graph for any time interval a t b .
at t = a for any function f ( t ) that gives position as a function of time.
v = f '( t )
for any position equation that's a function of time, f ( t ).
equals the slope between two points on velocity v . Time graph for any time interval a t b .
for any function f ( t ) that gives velocity as a function of time.
a = v '( t )
for any velocity equation that's a function of time, v ( t ).
a = v '( t ) = y ''( t )
for any velocity equation that's a function of time, v ( t ), and any position equation that's a function of time, y ( t ).
r = r f r i
for position vectors r i (initial) and r f (final).
for any displacement vector r and time interval t .
v f = v i + at
x = ( v f + v i) t
x = v i t + at 2
for vectors a, v f, v i, and x and scalar t .
a y = 9.8m/s2
v fy = v iy + at
y = v iy t + a y t 2
a x = 0m/s2
v x = x / t
w = m g
where m = mass and g = acceleration due to gravity (9.8m/s2 on Earth).
1N = 1kg*m/s2
1N = 0.2248lbs
FS = SN
where N is the normal force.
FK = KN
where N is the normal force.
Use arrows of relative lengths to represent forces.
Draw all arrows originating from the center of the object and pointing in the appropriate direction.
If Fnet = 0, no change in motion occurs.
Fnet = m a
where m is mass and a is acceleration.
For every force there is an equal and opposite force, or, when two objects come into contact, they exert equal and opposite forces upon each other.
W = F x
where x = displacement and F = force in the direction of displacement.
KE = mv 2
where m = mass and v = speed.
W = KE = KE f KE i
or
where the force and displacement are in the same direction and v is speed.
GPE = mgy
where m = mass, g = acceleration due to gravity, and y = height.
KE i + PE i = KE f + PE f
or
KE i + PE i = KE f + PE f + E o
or
where E o represents other energy (heat/sound).
If the stationary boundary is vertical, v f = [ v ix v iy] and if the stationary boundary is horizontal, v f = [ v ix v iy] for incoming velocity v i = [ v ix v iy].
v f = 2 * P + v i
where v i = the incoming velocity and P = the projection of v i onto the normal of the boundary line.
p = mv
where m = mass and v = velocity.
Impulse = Ft
where F = net force and t = a very small amount of time.
Impulse = Ft = ( p )
where F = net force, t = a very small amount of time, and p = momentum.
m 1 v 1i + m 2 v 2i = m 1 v 1f + m 2 v 2f
where the 1 subscript represents object 1 and the 2 subscript represents object 2.
( v 1f v 2f) = ( v 1i v 2i)
where = coefficient of restitution (0 < < 1).
= s / r
where s = arc length and r = radius.
where = angular displacement and t = time.
where = angular displacement and t = time.
v t = r
where = instantaneous angular velocity and r = radius.
a t = r
where = instantaneous angular acceleration and r = radius.
The graph of an equation of the form A x + B y = C, where A and B are not both 0, is a straight line.
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