Game Development Reference
In-Depth Information
()(
)
T
w
ci
w
oj
w
ci
Position:
t
=
R
t
t
,
ij
w
ci
w
ci
R
t
where i = 1... n and j = 1... m ,
is the orientation of camera i and
, its position,
w
oj
w
o t , its position.
Writing all orientation matrices into one large matrix yields:
and
R
is the orientation of frame j and
()
T
R
R
R
w
c
11
1
m
1
[
]
=
R
w
o
R
w
om
1
()
T
R
R
R
w
cn
.
M
o
1
n
nm
M
M
c
Let M = UWV T be the singular value decomposition ( SVD ) (Press, Teukolsky,
Vetterling & Flannery, 1992) of M . Let U' be the matrix consisting of the three
columns of U that correspond to the three largest singular values in W . Then
()
T
ci R are estimated as the orthonormal matrices that are closest to the
corresponding submatrices in U' (Horn, Hilden & Negahdaripour, 1988).
w
w
oj
R
can be computed in the same way from V .
()
T
After getting all
w
ci
, stacking all position vectors on top of each other results
R
in:
T
m
w
c
1
0
0
R
t
t
w
o
2
1
11
1
I
n
×
n
T
m
w
cn
1
0
0
R
t
w
om
t
2
n
1
=
w
c
t
0
0
T
m
1
R
w
c
t
1
2
1
1
m
,
I
n
×
n
w
cn
t
0
T
m
R
w
cn
t
0
1
2
nm
x
A
b
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