bluemira.structural.transformation
==================================

.. py:module:: bluemira.structural.transformation

.. autoapi-nested-parse::

   FE transformation matrices and methods



Functions
---------

.. autoapisummary::

   bluemira.structural.transformation._direction_cosine_matrix
   bluemira.structural.transformation._direction_cosine_matrix_debugging
   bluemira.structural.transformation.lambda_matrix
   bluemira.structural.transformation.cyclic_pattern


Module Contents
---------------

.. py:function:: _direction_cosine_matrix(dx: float, dy: float, dz: float) -> numpy.ndarray

   Calculates the direction cosine (transformation) matrix for an arbitrary
   vector in space. A number of painful edge cases are handled...

   Works such that the output dcm satisfies the following properties:

   local = dcm @ global
   global = dcm.T @ local

   :param dx: The absolute length of the vector in the x global coordinate
   :param dy: The absolute length of the vector in the y global coordinate
   :param dz: The absolute length of the vector in the z global coordinate

   :returns: * *The direction cosine matrix with reference to the global coordinate*
             * *system (3, 3)*


.. py:function:: _direction_cosine_matrix_debugging(dx, dy, dz, *, debug=False)

   Slow, ugly, safe


.. py:function:: lambda_matrix(dx: float, dy: float, dz: float) -> numpy.ndarray

   3-D transformation matrix, generalised to a 2-node beam.
   Effectively only handles the tiling of the direction cosine matrix
   transform.

   :param dx: The absolute length of the vector in the x global coordinate
   :param dy: The absolute length of the vector in the y global coordinate
   :param dz: The absolute length of the vector in the z global coordinate

   :rtype: The transformation matrix (12, 12)


.. py:function:: cyclic_pattern(geometry: bluemira.structural.geometry.Geometry, axis: numpy.ndarray, angle: float, n: int, *, include_first: bool = True) -> list[bluemira.structural.geometry.Geometry | bluemira.structural.geometry.DeformedGeometry]

   Build a cyclic pattern of a Geometry.

   :param geometry: The geometry to pattern
   :param axis: The axis vector about which to pattern
   :param angle: The pattern angle [degrees]
   :param n: The number of sectors to pattern
   :param include_first: Whether or not to include the first sector in the result

   :rtype: The patterned and merged geometry