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A Hitchhiker's Guide to Virtual Reality
book

A Hitchhiker's Guide to Virtual Reality

by Karen McMenemy, Robin Stuart Ferguson
July 2007
Beginner to intermediate content levelBeginner to intermediate
604 pages
17h 36m
English
A K Peters/CRC Press
Content preview from A Hitchhiker's Guide to Virtual Reality
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542 A. Rotation with Quaternions
For a normalized quaternion [w, x, y, z], the corresponding 4 × 4matrix
is
1 2y
2
2z
2
2xy + 2wz 2xz 2wy 0
2xy 2wz 1 2x
2
2z
2
2yz + 2wx 0
2xz + 2wy 2yz 2wx 1 2x
2
2y
2
0
0001
.
It is important to note that a 4 × 4 matrix can encapsulate positional
transformations as well as rotational ones. A unit quaternion only describes
pure rotations. So, when quaternions are combined, the complex rotation
they represent is with respect to axes passing through the coordinate origin
(0, 0, 0).
A.3 Converting a Matrix to a Quaternion
If the rotational matrix is given by
M =
a
00
a
01
a
02
0
a
10
a
11
a
12
0
a
20
a
21
a
22
0
0001
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Publisher Resources

ISBN: 9781568814773