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2. when
= 0, a sliding or “horizontal shear” of the returned volume according to
the depth (cf. Fig. 4(c)),
3. when
γ
i
= 0 and/or when the actual overhanging position of the observer dif-
fers from the optimal one, a sliding or “vertical shear” of the returned volume
according to the depth and
4. when
δ
i
ρ
μ
= 1 and/or
= 1, an anamorphose producing uneven distortions of the
i
)(cf.Fig.4(d)).
The depth controlled-distortion is obtained by adjusting the enlarging factor(s)
k
i
2
and the distortion parameters
3axis(
X
versus
Z
for
μ
i
and
Y
versus
X
for
ρ
ε
i
(and so
a
i
=
ε
∗
k
i
2
(
ε
−
1)
/
d
i
2
),
μ
i
,
ρ
,
γ
i
and
δ
i
.
i
i
This latter condition on
δ
i
is more delicate because it depends on the height of the
viewer which inevitably affects the effective position towards the device. So the
chosen vertical sliding
δ
i
can be reached only for an observer whose overhanging
position is defined in the viewing settings for this observation position.
Thus, given the viewing settings and the desired distortion parameters, the shoot-
ing parameters can be calculated as follows:
P
i
2
=(
p
i
2
−
δ
i
d
i
2
)
/
(
k
i
2
ρμ
i
)
D
i
2
=
d
i
2
/
k
i
2
i
/
(
k
i
2
μ
i
/
(
k
i
2
ρμ
W
b
=
W
ε
i
)
H
b
=
H
ε
i
)
c
i
=(
e
i
+
γ
i
d
i
2
)
/
(
k
i
2
μ
i
)
f
i
imposed or chosen, individually
∀
i
∈{
1
...
n
}×{
1
...
m
}
,
by lot
∀
i
2
∈{
1
...
n
}
or on the whole
.
(15)
w
i
=
W
b
f
i
/
D
i
2
=
Wf
i
ε
i
/
(
μ
i
d
i
2
)
h
i
=
H
b
f
i
/
D
i
2
=
Hf
i
ε
i
/
(
μ
i
ρ
d
i
2
)
α
i
=
c
i
f
i
/
D
i
2
=
f
i
(
e
i
+
μ
i
d
i
2
)
β
i
=
P
i
2
f
i
/
D
i
2
=
f
i
(
p
i
2
−
δ
i
d
i
2
)
/
(
γ
i
d
i
2
)
/
(
μ
i
ρ
d
i
2
)
This depth controlled-distortion scheme allows to obtain the parameters of a shoot-
ing layout producing desired 3D content for any rendering device and any depth
distortions combination.
4.2
Perfect Depth Effect
A particular case of the depth controlled-distortion is a perfect depth effect (depth
perception without any distortion compared with the depth of the shot scene). To
produce a perfect depth effect (whatever the enlarging factor(s)
k
i
2
), we should
configure the shooting in order to avoid the 4 potential distortions. This is ob-
tained by making sure that the distortion parameters verify
ε
i
= 1,
μ
i
= 1,
ρ
= 1,
γ
i
= 0and
δ
i
= 0 is more delicate,
as it can be assured only for an observer complying to the defined overhanging
position.
δ
i
= 0 (cf. Fig. 4(a)). The latter condition
