Biomedical Engineering Reference
In-Depth Information
of the head turn [
13
]. For instance, if a user rotates the head by a yaw angle of 90
◦
,
again
g
R
[
y
]
=
1 maps this motion one-to-one to a 90
◦
rotation of the virtual camera
in the VE. Applying a gain of
g
R
[
y
]
=
5 results in the user having to rotate the head
by 180
◦
physically in order to achieve a 90
◦
virtual rotation. A gain of
g
R
[
y
]
=
0
.
2
results in the user having to rotate the head by only 45
◦
physically in order to achieve
a90
◦
virtual rotation.
In case such rotation gains cause differences between a user's head orientation
in tracking coordinates, and a camera orientation in virtual scene coordinates, this
requires us to adapt the direction of subsequent translational movements to the offset
between the real and virtual head orientation. We can account for such offsets by
introducing user-centric reference coordinates for translational movements in the real
and virtual environment (see Sect.
10.4.1
). For instance, in the example above, we
can account for offsets between real and virtual yaw orientation angles by defining
local coordinate transforms for position changes:
⎛
⎞
⎛
⎞
x
(
n
)
100
x
(
n
−
1
)
v
y
(
n
)
v
010
y
(
n
−
1
)
⎝
⎠
=
⎝
⎠
·
v
z
(
n
)
v
001
z
(
n
−
1
)
v
1
v
000 1
⎛
⎝
⎞
⎠
·
⎛
⎝
⎞
⎠
·
y
(
n
−
1
)
y
(
n
−
1
)
y
(
n
−
1
)
y
(
n
−
1
)
cos
(
˜
)
0
sin
(
˜
)
0
cos
(
−˜
)
0
sin
(
−˜
)
0
v
v
r
r
0
1
0
0
0
1
0
0
y
(
n
−
1
)
y
(
n
−
1
)
y
(
n
−
1
)
y
(
n
−
1
)
−
(
˜
)
(
˜
)
−
(
−˜
)
(
−˜
)
sin
0
cos
0
sin
0
cos
0
v
v
r
r
0
0
0
1
0
0
0
1
⎛
⎞
x
(
n
)
Δ
r
⎝
⎠
,
y
(
n
)
Δ
r
z
(
n
)
Δ
r
1
in which head position changes in tracking coordinates are first transformed into a
local coordinate system relative to the yaw orientation angle of the user's head in
the previous rendering frame, and then transformed into the local coordinate system
relative to the yaw orientation angle of the camera object in virtual coordinates at the
previous rendering frame. Using this simple coordinate transformation, we can apply
yaw rotation gains without changing the mapping of head translations relative to the
user's head orientation. At this point it should be noted that similar transformations
can be applied for pitch and roll transformations, e.g., to simulate virtual slopes [
17
].
However, since pitch and roll angles are usually applied sequentially relative to the
virtual camera yawangle (see Sect.
10.2
), inmost cases it is not necessary to introduce
such coordinate transformations to account for applied pitch or roll gains (cf. [
2
]).
