Definition by Origin and Rotation Angles

A third possibility to define a coordinate system is by an origin and rotation angles.

In Tosca Structure.gui, instead of using three points with given coordinates, the origin and the rotation angles around the three axes are used in order to define a coordinate system. This is done using Local radio button as shown in the following figure (this is equivalent to setting DEF_TYPE = LOCAL in CS_DEF command):



Then, the coordinates of the origin (with respect to the coordinate system specified in Reference CS field) and the three rotation angles are to be chosen. The directions of the axes of the coordinate system are constructed in the following manner:

  • first, the axes X, Y, Z of the reference coordinate system are taken.
  • then, the axes are rotated around z-axis by the first angle in Rotation fields (labeled with 3): axes X’, Y’, Z’ = Z are produced.
  • the resulting axes are rotated around Y’ by the second angle (field labeled with 2): axes X’’, Y’’ = Y’, Z’’ are produced.
  • finally, these axes are rotated around X’’ by the third angle (field labeled with 1): axes X’’’ = X’’, Y’’’, Z’’’ are produced that give the directions for the coordinate system axes.

All rotations are performed in positive (counter-clockwise) directions. the values of the angles are in degrees.

Examples

As shown in the following figure, a Cartesian coordinate system with the name CS_14 should be defined relative to the global Cartesian coordinate system CS_0. The point of origin of the new coordinate system should have the coordinates (30, 20, 0). Then, a cylindrical coordinate system CS_15 should be defined relative to CS_14 with the origin at the point (60, 5, 0). CS_15 should be rotated 15° around Z axis: The result coordinate system CS_15 defines a cylindrical coordinate system with origin (90,25,0) with respect to the global Cartesian coordinate system CS_0. The polar axis through the new origin is rotated by 15° around the z-axis. The longitudinal axis is parallel to the original z-axis through the new origin:


CS_DEF
  ID_NAME      = CS_14
  CS_TYPE      = RECTANGULAR
  DEF_TYPE     = LOCAL
  CS_REF       = CS_0
  ORIGIN_123   = 30,20,0
  ROTATION_321 = 0,0,0
END_



CS_DEF
  ID_NAME      = CS_15
  CS_TYPE      = CYLINDRICAL
  DEF_TYPE     = LOCAL
  CS_REF       = CS_14
  ORIGIN_123   = 60,5,0
  ROTATION_321 = 15,0,0
END_