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In-Depth Information
V
u
T(-
p
e
)
V
v
p
e
camera at
origin
V
w
V
u
p
a
V
v
V
w
p
EC
y
p
a
- p
e
x
z
M
wb2eb
camera still
at origin
Figure 14.19.
WC-to-EC transformation
.
Figure 14.19 shows that to transform vertex positions from
V
wc
(WC) to
V
ec
(EC), we first translate the eye position
p
e
to the origin by applying the
T
(
−
p
e
)
translation and then align the WC and EC orthonormal basis by
M
wb
2
eb
,or
V
ec
=
V
wc
T
(
−
p
e
)
M
wb
2
eb
=
V
wc
M
w
2
e
,
so
M
w
2
e
=
T
(
−
p
e
)
M
wb
2
eb
.
(14.4)
The inverse transform of
M
w
2
e
is
M
e
2
w
, an operator that transforms vertices from
EC to WC:
eb2wb.
eb
2
wb
is the reverse
of
wb
2
eb
and abbreviates
eye
basis to world basis
.
M
−
1
w
2
e
M
e
2
w
=
M
wb
2
eb
)
−
1
=(
T
(
−
p
e
)
(14.5)
M
−
1
wb
2
eb
T
−
1
=
(
−
p
e
)
=
M
eb
2
wb
T
(
p
e
)
.
Equation (14.5) says that to transform from EC back to WC, we first apply
M
eb
2
wb
to align the EC orthonormal basis with that of the WC, and then we translate by
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