Game Development Reference

In-Depth Information

A

C
OMMON
I
NERTIA

A
PPENDIX

T
ENSORS

physical primitives. This can be used to generate an inertia tensor for almost

any game object.

Inertia tensors are discussed in chapter 10.

This appendix provides formulae for calculating the inertia tensor of a range of

A.1

D
ISCRETE
M
ASSES

The inertia tensor of any set of masses, connected together to form a rigid body, is

⎡

⎣

⎤

⎦

I
x

−

I
xy
−

I
xz

I

=

−

I
xy

I
y

−

I
yz

[A.1]

−

I
xz
−

I
yz

I
z

where

n

m
i
a
p
i

I
a
=

i

=

1

and

n

=

I
ab

m
i
a
p
i
b
p
i

i

=

1