Definition by Origin and Vectors

Another possibility to define a coordinate system is by an origin and three vectors.

In Tosca Structure.gui, the origin and three vectors are used in order to define a coordinate system. This is done using VECTOR radio button as shown in the following figure (this is equivalent to setting DEF_TYPE = VECTOR in CS_DEF command):



Then, the coordinates of the origin (with respect to the coordinate system CS_0) and the three vectors are to be chosen. The directions of the axes of the coordinate system are constructed by setting the X,Y, Z axes to the VECTOR_X, VECTOR_Y and VECTOR_Z entries, respectively.

The rotation matrix given by VECTOR_X, VECTOR_Y, VECTOR_Z must have a determinant of 1, ie:

absdetm=absdetVECTOR_X, VECTOR_Y, VECTOR_Z=1

Examples

As shown in the following figure, a Cartesian coordinate system with the name CS_16 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 (10, 10, 10). The x-axis is defined by the vector (-1,0,0), y-axis with the vector (0,-1,0) and the z-axis with (0,0,-1).:


CS_DEF
  ID_NAME  = CS_16
  CS_TYPE  = RECTANGULAR
  DEF_TYPE = VECTOR
  ORIGIN   = 10,10,10
  VECTOR_X = -1,0,0
  VECTOR_Y = 0,-1,0
  VECTOR_Z = 0,0,-1
END_