Biomedical Engineering Reference
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of the tracking volume. Most advanced redirection techniques, however, manipulate
position or orientation changes relative to specific coordinates (e.g., determined from
the user's head or body state) in the real and virtual world. We can account for such
frames of reference by introducing local coordinate transforms, for which the virtual
camera transformation at frame n
∈ N
changes to:
=
·
,
x ( n )
100 x ( n 1 )
x ( n )
Δ
v
y ( n )
v
010 y ( n 1 )
r
y ( n )
Δ
v
z ( n )
v
001 z ( n 1 )
r
M v ·
M r ·
z ( n )
Δ
v
1
v
000 1
r
1
with homogeneous coordinates and 4
4 matrices M r and M v defining local coor-
dinate transformations in real and virtual coordinates, respectively. An example of
such transformations is discussed in the following section.
×
10.4.2 Scaling Self-Motions
The most often found redirection techniques are based on nonisometric mappings
of user-centric translations or rotations to virtual camera motions. Such mappings
can be described by self-motion gains , which define ratios between real and virtual
self-motions. Two types of self-motion gains are distinguished in immersive virtual
environments, i.e., rotation gains and translation gains .
Rotation Gains
Rotation gains define the ratio between physical head turns and virtual camera rota-
tions [ 16 , 32 ]. Assuming a relative change in the orientation of the user's head has
been determined for frame n
y ( n )
p ( n )
r ( n )
3 , rotation gains
∈ N
as
˜
˜
˜
) ∈ R
r
r
r
3 define the resulting virtual camera rotation, which
g R
= (
g R [ y ] ,
g R [ p ] ,
g R [ r ] ) ∈ R
changes to:
=
+
·
y ( n )
y ( n 1 )
y ( n )
˜
˜
Δ ˜
g R [ y ]
00
v
v
˜
r
p ( n )
p ( n 1 )
p ( n )
0
0
00 g R [ r ]
g R [ p ]
˜
Δ ˜
v
v
r
r ( n )
r ( n 1 )
r ( n )
˜
˜
Δ ˜
v
v
r
Most redirection techniques focus on scaling yaw rotations [ 13 , 22 , 23 ], for which
an applied rotation gain g R [ y ] ∈ R
y ( n )
causes a tracked real-world head rotation
Δ ˜
r
y ( n )
y ( n )
to cause a virtual camera rotation of g R [ y ] · Δ ˜
, instead of
Δ ˜
. This means that
r
r
if g R [ y ] =
1 the virtual scene remains stable considering a user's head orientation
change. In case of g R [ y ] >
1 the virtual scene appears to rotate against the direction
of the head turn, whereas a gain g R [ y ] <
1 causes the scene to rotate with the direction
 
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