Biomedical Engineering Reference
In-Depth Information
scale translational movements. The latter approach can be implemented even without
additional user instrumentation by changing the mapping to:
⎛
⎝
⎞
⎠
=
⎛
⎝
⎞
⎠
·
⎛
⎝
⎞
⎠
·
x
(
n
)
100
x
(
n
−
1
)
y
(
n
−
1
)
y
(
n
−
1
)
cos
(
˜
)
0
sin
(
˜
)
0
v
y
(
n
)
v
010
y
(
n
−
1
)
v
v
0
1
0
0
v
z
(
n
)
v
001
z
(
n
−
1
)
y
(
n
−
1
)
y
(
n
−
1
)
−
sin
(
˜
)
0
cos
(
˜
)
0
v
v
v
1
v
000 1
0
0
0
1
⎛
⎝
⎞
⎠
,
⎛
⎝
⎞
⎠
·
⎛
⎝
⎞
⎠
·
x
(
n
)
y
(
n
−
1
)
y
(
n
−
1
)
Δ
g
T
[
x
]
000
0
g
T
[
y
]
00
00
g
T
[
z
]
0
0001
cos
(
−˜
)
0
sin
(
−˜
)
0
r
r
r
y
(
n
)
0
1
0
0
Δ
r
y
(
n
−
1
)
y
(
n
−
1
)
z
(
n
)
−
sin
(
−˜
)
0
cos
(
−˜
)
0
Δ
r
r
r
1
0
0
0
1
which allows to scale head position changes with separate gains relative to the user's
locomotion state. In particular, walking distances in the virtual heading direction can
be scaled with a gain
g
T
[
z
]
∈ R
, lateral distances can be scaled with a gain
g
T
[
x
]
∈ R
,
and vertical distances can be scaled with a gain
g
T
[
y
]
∈ R
.
10.4.3 Redirected Walking
Although scaling self-motions as introduced in Sect.
10.4.2
can be used to redirect
a user, e.g., by scaling head rotations to reorient the user away from an obstacle in
the physical workspace, the approach has practical limitations. In particular, assum-
ing the user walks straight ahead in the laboratory workspace without performing
head rotations, then the virtual travel distance can be scaled relative to the physical
walking distance, but at some point the user will eventually reach the end of the
physical workspace, and potentially collide with an obstacle. To avoid this problem,
researchers proposed various solutions [
7
,
14
,
19
,
20
,
22
,
23
,
26
,
32
,
34
,
38
,
39
],
including techniques based on instructing the user to stop walking and start rotating
the head, such that rotation gains can be applied to reorient the user away from physi-
cal obstacles [
22
,
38
]. However, the most prominent solution for unrestricted walking
was presented by Razzaque et al. [
23
], who proposed to use subtle virtual camera
rotations while a user performs translational movements in the physical laboratory
workspace. This causes the user to change the heading direction when walking in
the real world according to the rotations in the virtual environment. The approach
can be implemented with
curvature gains
.
Curvature Gains
Curvature gains define ratios between position changes of the user's head in the real
world and virtual camera rotations [
32
]. For example, when the user walks straight
ahead in the physical workspace, a curvature gain that causes reasonably small
