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3D Game Engine Design, 2nd Edition
book

3D Game Engine Design, 2nd Edition

by David Eberly
November 2006
Intermediate to advanced content levelIntermediate to advanced
1040 pages
26h 31m
English
CRC Press
Content preview from 3D Game Engine Design, 2nd Edition
17.5 The Curse of Nonuniform Scaling 779
where R is a rotation matrix and S is a scaling matrix, diagonal and with positive
diagonal entries. The technical problem, and one many programmers do not expect,
is that it is not always possible to factor M in this manner.
Example
17.1
Consider the attempt to factor the following matrix:
M =
11
01
= RS =
cos θ sin θ
sin θ cos θ

d
0
0
0 d
1
=
d
0
cos θ d
1
sin θ
d
0
sin θd
1
cos θ
where d
0
> 0 and d
1
> 0. Equating the off-diagonal terms, we have 0 = d
0
sin θ and
1 =−d
1
sin θ . Since d
0
> 0, the first equation forces sin θ = 0. The second equation
does not allow sin θ = 0. Even if you allowed d
0
= 0, the equation d
0
cos θ =1
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Publisher Resources

ISBN: 9781482267303