Graphics Reference
In-Depth Information
Shoemake ([Shoe91]) discusses how quaternions can be expressed as 4 ¥ 4 homoge-
neous matrices so that one can take advantage of fast matrix multiplication in hard-
ware.
20.4
E
XERCISES
Section 20.2
20.2.1
Prove Proposition 20.2.1.
20.2.2
Prove Proposition 20.2.2.
20.2.3
Prove Proposition 20.2.3.
20.2.4
Prove Proposition 20.2.4.
20.2.5
Prove Proposition 20.2.5.
20.2.6
Prove Proposition 20.2.6.
Prove that if
u
,
v
Œ
R
2
are orthogonal unit vectors, them (
u
¥
v
) ¥
u
=
u
.
20.2.7
Section 20.3
20.3.1
Prove Proposition 20.3.4.
Find a unit quaternion
q
that represents the rotation R of
R
3
20.3.2
about the origin with
matrix
Ê
1
3
1
3
1
3
ˆ
Á
Á
Á
˜
˜
˜
1
2
1
2
M =
-
0
.
1
6
1
6
2
6
-
Ë
¯
