polymerist.maths.lattices.bravais
=================================

.. py:module:: polymerist.maths.lattices.bravais

.. autoapi-nested-parse::

   Representations and calculation methods for crystallographic unit cells and lattice parameters



Attributes
----------

.. autoapisummary::

   polymerist.maths.lattices.bravais.COMMON_UNIT_LATTICE_VECTORS
   polymerist.maths.lattices.bravais.lattice_generator


Classes
-------

.. autoapisummary::

   polymerist.maths.lattices.bravais.LatticeParameters


Functions
---------

.. autoapisummary::

   polymerist.maths.lattices.bravais.identify_bravais_points_within_bbox


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

.. py:function:: identify_bravais_points_within_bbox(lattice_vectors: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[polymerist.genutils.typetools.numpytypes.D, polymerist.genutils.typetools.numpytypes.D], numbers.Number], bbox: polymerist.maths.lattices.coordinates.BoundingBox) -> tuple[polymerist.maths.lattices.coordinates.Coordinates, polymerist.maths.lattices.integral.CubicIntegerLattice]

   Locate all lattice points generated by a set of Bravais lattice vectors in D-dimensions which fall within a given bounding box
   Returns the coordinate vector of the internal lattice points and a CubicIntegerLattice containing the corresponding lattice vector multiplicities


.. py:class:: LatticeParameters

   For storing the lengths of and the angles between the 3 lattice vectors of a crystallographic unit cell


   .. py:attribute:: a
      :type:  float


   .. py:attribute:: b
      :type:  float


   .. py:attribute:: c
      :type:  float


   .. py:attribute:: alpha
      :type:  float


   .. py:attribute:: beta
      :type:  float


   .. py:attribute:: gamma
      :type:  float


   .. py:property:: lengths_are_positive
      :type: tuple[bool, Optional[str]]


      Check whether all axial lengths are well-defined (i.e. positive)


   .. py:method:: reduce_angles() -> None

      Ensure all angles are within the principal [0, 2*pi) interval



   .. py:property:: axial_lengths
      :type: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[3], float]


      View of just the axial lengths


   .. py:attribute:: lengths


   .. py:property:: angles
      :type: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[3], float]


      Property alias of angles() method for convenience


   .. py:method:: axial_angles(in_degrees: bool = False) -> numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[3], float]

      View of just the angles



   .. py:property:: volume
      :type: float


      The volume of the unit cell (in arbitrary units)


   .. py:method:: from_lattice_vectors(vectors: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[3, 3], float]) -> LatticeParameters
      :classmethod:


      Obtain axial lengths and inter-vector angles from a matrix of lattice vectors



   .. py:method:: to_lattice_vectors() -> numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[3, 3], float]

      The restricted lattice vectors corresponding to the lattice parameters,
      where vector A lies along the x-axis and vector B is in the xy-plane

      Vectors are returned as a 3x3 matrix, where each row represents a lattice vector



   .. py:property:: lattice_vectors
      :type: numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[3, 3], float]


      Property alias of to_lattice_vectors() method for convenience


.. py:data:: COMMON_UNIT_LATTICE_VECTORS
   :type:  dict[str, numpy.ndarray[polymerist.genutils.typetools.numpytypes.Shape[3, 3], float]]

.. py:data:: lattice_generator