Graphics Reference
In-Depth Information
(
r
0
, c
0
) pixel coordinates of origin in (
u, v
) space
y
v
w
x
z
f
u
(
x
i
, y
i
, z
i
)
global coordinates of point
(
u
i
, v
i
, f
) local coordinates of projected point
(
c
i
, r
i
)
pixel coordinates
(column and row) of projected point
FIGURE B.60
Coordinate systems used in the projection of a global point to pixel coordinates.
ðc
i
c
0
ÞðR
2
½x
i
y
i
z
i
þt
2
Þf
u
ðR
0
½x
i
y
i
z
i
þt
0
Þ¼
0
(B.174)
ðr
i
r
0
ÞðR
2
½x
i
y
i
z
i
þt
2
Þf
v
ðR
1
½x
i
y
i
z
i
þt
1
Þ¼
0
AW ¼
0
(B.175)
2
4
3
5
x
1
y
1
z
1
0
0
0
r
1
x
1
r
1
y
1
r
1
z
1
10
r
1
0
0
0
x
1
y
1
z
1
c
1
x
1
c
1
y
1
c
1
z
1
0
1
c
1
...
...
...
...
...
...
...
...
...
...
...
...
x
1
y
n
z
n
r
n
x
n
r
n
y
n
r
n
z
n
10
r
n
0
0
0
x
n
y
n
z
n
c
n
x
n
c
n
y
n
c
n
z
n
c
n
0
0
0
0
1
T
W
0
¼ f
u
R
0
þ c
0
R
2
¼½w
0
w
1
w
2
T
W
3
¼ f
v
R
1
þ r
0
R
2
¼½w
3
w
4
w
5
T
W
6
¼ R
2
¼½w
6
w
7
w
8
(B.176)
w
9
¼ f
u
t
0
þ c
0
t
2
w
10
¼ f
v
f
1
þ r
0
t
2
w
11
¼ t
2
T
W ¼½w
0
w
1
w
2
w
3
w
4
w
5
w
6
w
7
w
8
w
9
w
10
w
11
(B.177)
0
0
0
A
W
þ B
¼
0
(B.178)
0
0
0
min
kA
W
þ B
k
(B.179)
w
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