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B Technical Appendix
B.1 Definition of Coordinates and Rotations
B.1.1 Room Calibration
The calibration angle defines origin and axes of the coordinate system. This can be done
in two different ways:
Type longer arm shorter arm
’ normal ’ +X axis +Y axis
’ powerwall ’ +X axis -Z axis
For example, a room calibration of type ’ normal ’ would result in a coordinate system like
the following:
1. The marker located in the crossing point of the two arms is defining the origin of the
coordinate system.
2. The longer arm of the calibration tool defines the +X axis.
3. The shorter arm of the calibration tool defines the +Y axis. (i.e., the tool markers
define the X/Y plane.)
4. The Z axis is added in order to give a right-handed coordinate system.
B.1.1.1 Room Adjustment
DTrack2 allows to modify the room coordinate system by specifying these seven values:
•
l
x
, l
y
, l
z
for a translational offset (denoted x, y, z in the GUI),
•
η
,
θ
,
φ
for a rotation (denoted rx, ry, rz in the GUI).
•
s for a scaling factor.
These offsets are defined as a shift and/or rotation and/or scaling of the room coordinate
system relative to the original one. Mathematically a point
~ x
orig
in the original room is
transformed into a point ~ x
mod
in the modified room coordinate system by:
~ x
mod
= ( R
T
·
~ x
orig
−
~l
)
·
s
where the rotation matrix R is calculated from η , θ and φ like defined in section B.1.3.
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