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Appendix
B
B.1 Definition of Coordinates and Rotations
Expressed in trigonometric functions, that means:
R =


cos φ cos θ
−
sin φ cos θ sin θ
sin φ cos η + cos φ sin θ sin η cos φ cos η
−
sin φ sin θ sin η
−
cos θ sin η
sin φ sin η
−
cos φ sin θ cos η cos φ sin η + sin φ sin θ cos η cos θ cos η


Note that per definitionem the angles can only have the values:
−
180
◦
≤
φ
≤
180
◦
,
−
90
◦
≤
θ
≤
90
◦
,
−
180
◦
≤
η
≤
180
◦
Z
Note: rotation angles can show strange behaviour at certain orienta-
tions. In particular, for orientations close to
θ =
±
90
◦
the other two
angles can experience large odd-looking changes (so called “Gimbal
Lock”).
When connecting DTrack2 to an application, often problems appear caused by different
definitions of rotation angles. To avoid that, we recommend to use rotation matrices.
B.1.4 3DOF Data
Besides the tracking of 6DOF bodies, DTrack2 is able to calculate the coordinates of
single markers, i.e. markers that can not be recognized as part of a rigid body. The
output values are the coordinates of these markers, measured in room coordinates.
In some situations, a rigid body within the measurement volume is (temporarily) not cor-
rectly recognized by the software. In these cases, its markers appear as 3DOF objects.
3DOF markers are tracked (as long as possible) and labeled with an ID number. When a
3DOF marker vanishes (or is recognized as part of a 6DOF body), its ID number will not
be used any more, as long as the tracking is active.
B.1.5 Flystick devices
DTrack2
is supporting the following input devices:
• Flystick1,
•
Flystick2 and
• Flystick3.
Each of the afore mentioned devices is equipped with buttons (4 - 8) and a small joystick.
Input transactions are transmitted wirelessly to the controller and added to the 6DOF
tracking result of the Flystick body.
There are two types of output formats available, called
6df
and
6df2
(details see chapter
B.2.5 on page 261 and chapter B.2.6 on page 262); they differ in the number of carried
input controls. Only the newer
6df2
format is capable of processing analogue values (or
controllers) as produced by a joystick. Both formats use the same order of buttons (details
see below):
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