CS_DEF


ID_NAME	= `<name_of_coord_system>`	Name of the coordinate system
CS_TYPE	= RECTANGULAR = CYLINDRICAL = SPHERICAL	Type of new coordinate system
DEF_TYPE	= LOCAL	`LOCAL` definition refers to an existing coordinate system
	= NODE	Definition using three nodes
	= VECTOR	Definition using an origin and three vectors

Items for DEF_TYPE = LOCAL


CS_REF	= `<name_of_coord_system>`	Existing reference coordinate system
ORIGIN_123	= `<coord_1>, <coord_2>, <coord_3>`	Coordinate values of the origin
ROTATION_321	= `<rot_3>, <rot_2>, <rot_1>`	Rotations that should be superimposed on the reference coordinate system

Items for DEF_TYPE = NODE


CS_AXIS		Specifies the axis and the plane defined by the three nodes.
	= X_XY	X-axis and the X-Y plane are defined by the three nodes.
	= X_XZ	X-axis and X-Z plane are defined by the nodes.
	= Z_XZ	Z-axis and X-Z plane are defined by the nodes.
NODE_ORIGIN	= `<node_id_of_origin>`	ID of node which defines the origin
NODE_AXIS	= `<node_id_on_axis>`	ID of the node on the axis
NODE_PLANE	= `<node_id_on_plane>`	ID of the node on the given plane and the second axis

Items for DEF_TYPE = VECTOR


ORIGIN	= `<coord_1>, <coord_2>, <coord_3>`	Coordinate values of the origin
VECTOR_X	= `<coord_1>, <coord_2>, <coord_3>`	Direction of the first reference vector.
VECTOR_Y	= `<coord_1>, <coord_2>, <coord_3>`	Direction of the second reference vector.
VECTOR_Z	= `<coord_1>, <coord_2>, <coord_3>`	Direction of the third reference vector.

Remark

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

$abs (\det ([m])) = abs (\det ([VECTOR_X, VECTOR_Y, VECTOR_Z])) = 1$
The rotation angles in the command ROTATION_321 are in degrees. The single rotations are carried out in series around the axis of the local Cartesian coordinate. The following figure shows the rotations for ROTATION_321 = 180.0, 0.0, 90.0:
The longitudinal axis of a cylindrical coordinate system is defined by the z-axis of the referenced rectangular coordinate system. Respectively, the polar axis equals the x-axis, as shown in the following image:

Examples

The following command defines a cylindrical coordinate system with origin (10,20,0) with respect to the global Cartesian coordinate system CS_0. The polar axis and longitudinal axis are obtained by rotating the x-axis and z-axis of CS_0 respectively by 45° around the z-axis and by 15° around the y-axis of CS_0.


CS_DEF
  ID_NAME      = my_cs_01
  CS_TYPE      = CYLINDRICAL
  DEF_TYPE     = LOCAL
  CS_REF       = cs_0
  ORIGIN_123   = 10.0, 20.0, 30.0
  ROTATION_321 = 45.0, 15.0, 0.0
END_

The following command defines a rectangular (Cartesian) coordinate system with origin through the node with ID number 10. The x-axis is defined by the nodes 10 and 100. Node 101 defines a point in the x-y plane.


CS_DEF
  ID_NAME     = my_cs_02
  CS_TYPE     = RECTANGULAR
  DEF_TYPE    = NODE
  CS_AXIS     = X_XY
  NODE_ORIGIN = 10
  NODE_AXIS   = 100
  NODE_PLANE  = 101
END_

The following command defines a rectangular (Cartesian) coordinate system with origin (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  = my_cs
  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_