Game Development Reference
In-Depth Information
Velocity is updated with
p = ˙
˙
+ ¨
p
pt
Orientation is updated with
δt
2 ω
θ
ˆ
=
θ
ˆ
+
θ
ˆ
ˆ
where ω
ˆ
is the quaternion form of the angular velocity and t is the duration to up-
date by.
Angular velocity is updated exactly the same as linear velocity:
θ = θ
+ θ t
D.5
P HYSICS
Newton's second law of motion gives us
m p
f
=
ma
=
where m is the mass and p is the position of an object. Or
m 1 f
p
¨
=
in terms of position.
Euler's equivalent for rotation is
θ
I 1 τ
=
where I is the inertia tensor and τ is the torque.
The force of gravity is
f
=
mg
where g is around 10 m/s 2
on earth, but is often replaced by 20 m/s 2
for added speed
in games.
Forces through an object's center of mass can be combined using D'Alembert's
principle:
f
=
f i
i
Forces not through the center of mass also have a torque component:
τ
=
p f ×
f
where p f is the position of application of the force, relative to the center of mass.
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