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B Technical Appendix
B.1.6.2 Using a reference body
When using a reference body for a Measurement Tool , the module calculates the position
of the tip
~ x
S
ref
within the local coordinate system of the reference body:
~ x
S
room
= R
ref
·
~ x
S
ref
+ ~ s
ref
where
~ x
S
room
is the position of the tip in room coordinates, and
( ~ s
ref
, R
ref
)
position and
orientation (see B.1.3) of the reference body. The orientation of the Measurement Tool is
transformed in an analogous way.
B.1.6.3 Covariance of Measurement Tool tip
DTrack2 provides an estimation for the current uncertainty of the measured position of
the tool tip, expressed as a 3
×
3 covariance matrix Σ . Assuming a translational vector ~ e
S
representing the error of the measured tip position, the covariances are calculated as the
’expected values’ (
E () ) of:
~ x
S
meas
= ~ x
S
+ ~ e
S
σ
ij
= E ( e
S
i
·
e
S
j
)
Intuitively, the diagonal entries of Σ
tip
can be interpreted as the positional uncertainty in
world coordinates. Off-diagonal values describe the statistical dependency between two
values.
B.1.7 Fingertracking
The Fingertracking device allows to track a human’s entire hand, including fingers. The
output data consists of:
• position and orientation of the back of the hand (given in room coordinate system),
• number of the tracked fingers (
3
or
5
) and a value to distinguish between right and
left hand,
•
position and orientation of the outermost phalanxes, given in the hand coordinate
system; the radius of the finger tip to identify its position and orientation (more ex-
actly its surface),
•
angles between the single phalanxes as well as their respective lengths. These
values are calculated using tracked markers and empirical data.
Hand coordinate system The hand coordinate system is defined as follows:
•
the origin is in the joint, where the index finger is connected to the back of the hand.
•
the +X axis is oriented in direction of the outstretched index finger.
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