Game Development Reference
In-Depth Information
B.6
Chapter 6
(Page 189.)
3 −2
1
1.
= 34−(−2)1 = 14
4
2. The determinant is
3 −2
0
1
4
0
= 3(42−00) + (−2)(00−12) + 0(10−40) = 28.
0
0
2
We compute the cofactors
4
0
1
0
1
4
{11}
{12}
{13}
C
= +
= 8,
C
= −
= −2,
C
= +
= 0,
0
2
0
2
0
0
−2
0
3
0
3 −2
0
{21}
{22}
{23}
C
= −
= 4,
C
= +
= 6,
C
= −
= 0,
0
2
0
2
0
−2
0
3
0
3 −2
1
C
{31}
= +
C
{32}
= −
C
{33}
= +
= 0,
= 0,
= 14,
4
0
1
0
4
and put them into the classical adjoint:
2
3
2
4
C
{11}
3
2
3
C
{21}
C
{31}
3 −2
0
8
4
0
4
5
5
4
5
adj
1
4
0
=
C
{12}
C
{22}
C
{32}
=
−2
6
0
.
0
0
2
C
{13}
C
{23}
C
{33}
0
0
14
Dividing by the determinant gives us the inverse:
2
3
5
−1
2
3
2
3
3 −2
0
8
4
0
2/7
1/7
0
1
28
4
4
5
4
5
1
4
0
=
−2
6
0
=
−1/14
3/14
0
.
0
0
2
0
0
14
0
0
1/2
3. The matrix is orthogonal within the appropriate tolerance.
4. Because the matrix is orthogonal, its inverse is simply its transpose:
2
4
−0.1495 −0.1986 −0.9685
3
5
−1
2
4
−0.1495 −0.1986 −0.9685
3
5
T
−0.8256
0.5640
0.0117
=
−0.8256
0.5640
0.0117
−0.5439 −0.8015
0.2484
−0.5439 −0.8015
0.2484
2
4
−0.1495 −0.8256 −0.5439
3
5
=
−0.1986
0.5640
−0.8015
.
−0.9685
0.0117
0.2484
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