Notes

The calculated cardan angles are given as a triple.
Corresponding to the rotation order the first value in the tripple is always the rotation angle about the axis the first rotation is around, the second value is the rotation angle about the second rotation is around and the last value is the rotation angle the third rotation es around.

The rotation from the „parentCoordinateSystem“ to the „childCoordinateSystem“ is expressed in angles about the axes of the moving „childCoordinateSystem“. If you want to calculate angles around the fix axes of the „parentCoordinateSystem“ you can simple revert parent and child coordinate system and the sign of the resulting angles.

Instead, Vicon-BodyBuilder calculates the angles around the fix axes of the parent coordinate system.

The equations show that each rotation can be defined by two different values of the Cardan or Euler angles set. For example if Cardan angles are used, the rotation defined by the angles a1, a2 and a3 is the same as the rotation defined by the angles PI + a1, PI - a2 and PI + a3. The choice of the solution depends on the attribute method. Have a look at the following example:

  <!-- The first axis (x) shows to the front, the second (y) directs to left, the third (z) up -->
  <CoordinateSystem name="A"
    Position="vec(0,0,0)"
    FirstAxis="vec(1,0,0)"
    DefiningVector="vec(0,0,1)
    orientation="xyz"/>
 
  <!-- The first axis (x) shows to the back, the second (y) directs to left, the third (z) down -->
  <CoordinateSystem name="B"
    Position="vec(0,0,0)
    FirstAxis="vec(-1,0,0)"
    DefiningVector="vec(0,0,-1)"
    orientation="xyz"/>
 
  <EulerCardanAngles name="AB"
    parentCoordinateSystem="A"
    childCoordinateSystem="B"
    decompositionOrder="yxz"/>

In principle there exists two solution to rotation coordinate system A into B:

With no further attributes set in the EulerCardanAngles element this results in the solutiuon [-180 0 -180]. But also the solution [180 0 0] is correct. You can get it by set of further attributes.

Created trajectories and parameters

Examples

    <EulerCardanAngles name="A"
    	parentCoordinateSystem="B"
    	childCoordinateSystem="C"/>

ToDo: Schön wäre es wenn ich in der Nähe des GimbalLock eine entsprechende Phase erzeugen könnte. Dafür dann am besten ein zusätzliches Attribut einführen das definiert wann ich in der Nähe des Gimbal Locks bin, also z.B einen Winkelabstand in Grad z.B. 1 Grad …

A ProjectionAngle element defines the angle between two vectors which are projected into a plane defined by its normal vector.

There are two possiblities to defined the two vectors.

In the first (deprectated) version the two vectors are defined by a common point laying in the projection plane (JointCenter) and two other points given in absolute coordinates which were projected into the plane before the angle is calculated.

In the second version the two vectors are given directly by directed vectors also given in the global coordinate system.

The angle is defined from the second to the first vector with the left(?) hand rule (thumb in direction of the normal vector of the projection plane). Es wird davon ausgegangen, dass die angegebenen Vektoren in einem rechtshändigem Koordinatensystem formuliert sind. Ist das nicht der Fall bekommt man pi minus dem Winkel zurück.

Liegen die Vektoren in einem linkshändigem Koordinatensystem vor, dann ist es am einfachsten das Vorzeichen aller z-Kompoenten zu wechseln d.h. sowohl die der Hebelarme als auch die der angegebenen Achse für die Orientierung (Normalenvektor der Projektionsebene).

Attributes

  forceContinuousValues

  	If set to "true" jumps in the values based on the circular behavoir of angles are eliminated by adding an offset value of 180 or 360 degree depending on the unsigned flag after leaving the cycle ranges.
  	false
  	No

  debug

  	  	false
  	No

  visible

  	  	
  	No

  includes

  	comma seperated list of switches 	
  	No

  excludes

  	  	
  	No

  calibrateIncludes

  	  	
  	No

  calibrateExcludes

  	  	
  	No

  average

  	Additional calculation of the trial average. The value is saved as a parameter with the name of the element and "Average" as a suffix: <name of the element>Average 	
  	No

  unit

  	"deg" oder "rad" (not implemented yet)
  	deg
  	No