Coordinate System Definition For 5Dof Targets (With And Without Cylinder Markers); Coordinate System Definition For Two 5Dof Targets With Cylinder Markers; 6Dof Results - Art ARTTRACK1 System User Manual

B Technical Appendix
- like done with setting
one marker of the body, according to the rules given for setting
B.1.2.4 Coordinate System Definition for 5DOF Targets (with and without cylinder
markers)
Body calibration setting
In the body coordinate system all markers of the target are on the selected axis. The
origin is in the middle between the two markers with the largest distance to each other.
The orientation is defined by the marker with the smallest distance to the origin. Its
position has a negative sign. The other two directions are undetermined due to the one
degree of freedom.
B.1.2.5 Coordinate System Definition for two 5DOF Targets with cylinder markers
Body calibration setting
The body is expected to consist of two about perpendicularly connected 5DOF targets.
These are placed on the two axes. The origin is placed at the position where the two
5DOF targets intersect. The first axis is assigned to the 5DOF target which includes the
marker with the largest distance to the origin. The other 5DOF target is placed in the
plane created by the two axes.
B.1.3 6DOF Results
Position and Orientation
Position and orientation of a target are expressed by an affine transformation ( ,
transforms a vector
I.e., the coordinates give the position of the origin of the body coordinate system (marker
#1 or center of gravity, as described above), measured in room coordinates.
The 3 3 rotation matrix
of the matrix are the axes (X, Y, Z) of the body coordinate system, expressed in room
coordinates.
Description by Rotation Angles
The rotation matrix can be replaced by three consecutive rotations
, rotation axis ). The angles, as given in the
equation:
252
due to room. The origin of the body coordinate system is given by
x/y /z:
xy /yx/yz/zy /zx/xz:
from the body coordinate system to the room coordinate system:
=
room
describes the rotation part of the transformation. The columns
= ( )
x
due to body
+
body
DTrack2
data output, are defined by the
( ) ( )
y z
.
) that
( ) (rotation angle
i