Unterschiede

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--- modellingcomponents:elements:angles:eulercardanangles [2017/05/31 23:22] – [Configuration] oliver
+++ modellingcomponents:elements:angles:eulercardanangles [2021/11/22 15:42] (aktuell) – [Euler/Cardan Angles] oliver
@@ Zeile 1: / Zeile 1: @@
 ===== Euler/Cardan Angles =====
-A triple of Euler angles defines the angles of three rotations where the first and the last are around the same but rotated axis. A triple or rotation angles are called Cardan angles if each rotation is around a different axis where alle three axes are orthogonal.
+Euler angles define the sequence of three rotation angles, where the first and the last are around the same but rotated axis. A triple of rotation angles is called Cardan angles, if each rotation is around a different axis, where all three axes are orthogonal.
 ==== Configuration ====
 ^ Attribute ^ Default ^ Description ^ Required ^
@@ Zeile 14: / Zeile 14: @@
 ==== Notes ====
-The calculated cardan angles are given as a triple.\\
+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.
-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.
+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 equations show that each rotation can be defined by two different value-triples of the Cardan or Euler angles parameterisation. 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:
 <code xml>
   <!-- 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)"
+                    Position="vec(0,0,0)"
-    FirstAxis="vec(1,0,0)"
+                    FirstAxis="vec(1,0,0)"
-    DefiningVector="vec(0,0,1)
+                    DefiningVector="vec(0,0,1)
-    orientation="xyz"/>
+                    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)
+                    Position="vec(0,0,0)
-    FirstAxis="vec(-1,0,0)"
+                    FirstAxis="vec(-1,0,0)"
-    DefiningVector="vec(0,0,-1)"
+                    DefiningVector="vec(0,0,-1)"
-    orientation="xyz"/>
+                    orientation="xyz"/>
   <EulerCardanAngles name="AB"
-    parentCoordinateSystem="A"
+                     parentCoordinateSystem="A"
-    childCoordinateSystem="B"
+                     childCoordinateSystem="B"
-    decompositionOrder="yxz"/>
+                     decompositionOrder="yxz"/>
 </code>
-In principle there exists two solution to rotation coordinate system A into B:
+In principle there exists two possibilities to rotate 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.
+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 setting additional attributes.
 ==== Created trajectories and parameters ====
@@ Zeile 54: / Zeile 53: @@
 ^ MeanStd | double  | |  No  |
-==== Examples ====
-<code xml>
-    <EulerCardanAngles name="A"
-    	parentCoordinateSystem="B"
-    	childCoordinateSystem="C"/>
-</code>