Biomedical Engineering Reference
In-Depth Information
10.3.2 Reference Coordinates
A simple extension of isometric mappings is to introduce virtual reference coordi-
nates . Since one-to-one mappings only allow a user to explore a volume in the virtual
scene that is exactly as large as the interaction volume in the laboratory, it becomes
important to map the user's movements to specific regions of interest in the virtual
scene. This can be accomplished by introducing an intermediate reference coordinate
system when transferring position and orientation data from tracking coordinates to
virtual scene coordinates. Introducing such virtual reference coordinates, the corre-
sponding pseudo code in Sect. 10.3.1 changes to:
Algorithm 2 Isometric mapping with reference coordinates
for all rendering frames n
∈ N 0 do
// Get current head tracking state:
( x ( n )
, y ( n )
, z ( n )
3 )
) tracked head position (in R
r
r
r
y ( n )
p ( n )
r ( n )
3 )
( ˜
, ˜
, ˜
)
tracked head orientation (in
[
0
,
360
)
r
r
r
// Set virtual camera state:
· (
r ( n )
r ( n )
r ( n )
r ( n )
x x
y x
z x
p x
r ( n )
r ( n )
r ( n )
r ( n )
x ( n )
y ( n )
z ( n )
x ( n )
y ( n )
z ( n )
T
x y
y y
z y
p y
T
(
,
,
,
1
)
,
,
,
1
)
// position
v
v
v
r
r
r
r ( n )
r ( n )
r ( n )
r ( n )
x z
p z
0001
y z
z z
( y ( n )
, p ( n )
, r ( n )
) ( y ( n )
, p ( n )
, r ( n )
)
// orientation
v
v
v
r
r
r
end for
×
In the pseudo code, the 4
4 transformation matrix for homogenous coordinates
defines a reference position r ( n )
r ( n )
r ( n )
r ( n )
3
= (
,
,
) ∈ R
in the virtual scene, as
p
p x
p y
p z
well as coordinate axes with the direction vectors r ( n )
r ( n )
r ( n )
r ( n )
3 ,
= (
,
,
) ∈ R
x
x x
x y
x z
r ( n )
r ( n )
r ( n )
r ( n )
3 , and r ( n )
r ( n )
r ( n )
r ( n )
3 along the trans-
formed x -, y - and z -axes of the reference coordinates. The virtual yaw, pitch and roll
transformations are applied to the reference coordinate axes. Figure 10.1 illustrates
reference coordinates that are used to move the virtual interaction volume (limited by
the size of the laboratory workspace
= (
,
,
) ∈ R
= (
,
,
) ∈ R
y
y x
y y
y z
z
z x
z y
z z
3 ) to regions of interest.
To account for changing regions of interest in the virtual scene, reference coordi-
nates can be changed at run time. In particular, teleportation of the user's virtual view-
point can be implemented by abrupt changes of the reference coordinates, whereas
continuous traveling can be implemented by iterative changes in reference positions
and orientations [ 3 , 18 , 24 ].
(
lab x ,
lab y ,
lab z ) ∈ R
 
 
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