.. auto-generated by script ../../../../utils/nxdl2rst.py from the NXDL source NXtransformations.nxdl.xml

.. index::
    ! NXtransformations (base class)
    ! transformations (base class)
    see: transformations (base class); NXtransformations

.. _NXtransformations:

=================
NXtransformations
=================

**Status**:

  base class, extends :ref:`NXobject`

**Description**:

  Collection of axis-based translations and rotations to describe a geometry.
  May also contain axes that do not move and therefore do not have a transformation
  type specified, but are useful in understanding coordinate frames within which
  transformations are done, or in documenting important directions, such as the
  direction of gravity.

  A nested sequence of transformations lists the offset and rotation steps
  needed to describe the position and orientation of any movable or fixed device.

  There will be one or more transformations (axes) defined by one or more fields
  for each transformation.  The all-caps name ``AXISNAME`` designates the
  particular axis generating a transformation (e.g. a rotation axis or a translation
  axis or a general axis).   The attribute ``units="NX_TRANSFORMATION"`` designates the
  units will be appropriate to the ``transformation_type`` attribute:

  * ``NX_LENGTH`` for ``translation``
  * ``NX_ANGLE`` for ``rotation``
  * ``NX_UNITLESS`` for axes for which no transformation type is specified

  This class will usually contain all axes of a sample stage or goniometer or
  a detector.  The NeXus default McSTAS coordinate frame is assumed, but additional
  useful coordinate axes may be defined by using axes for which no transformation
  type has been specified.

  The entry point (``depends_on``) will be outside of this class and point to a
  field in here. Following the chain may also require following ``depends_on``
  links to transformations outside, for example to a common base table.  If
  a relative path is given, it is relative to the group enclosing the ``depends_on``
  specification.

  For a chain of three transformations, where :math:`T_1` depends on :math:`T_2`
  and that in turn depends on :math:`T_3`, the final transformation :math:`T_f` is

  .. math:: T_f = T_3 T_2 T_1

  In explicit terms, the transformations are a subset of affine transformations
  expressed as 4x4 matrices that act on homogeneous coordinates, :math:`w=(x,y,z,1)^T`.

  For rotation and translation,

  .. math:: T_r &= \begin{pmatrix} R & o \\ 0_3 & 1 \end{pmatrix} \\ T_t &= \begin{pmatrix} I_3  & t + o \\ 0_3 & 1 \end{pmatrix}

  where :math:`R` is the usual 3x3 rotation matrix, :math:`o` is an offset vector,
  :math:`0_3` is a row of 3 zeros, :math:`I_3` is the 3x3 identity matrix and
  :math:`t` is the translation vector.

  :math:`o` is given the ``offset`` attribute, :math:`t` is given by the ``vector``
  attribute multiplied by the field value, and :math:`R` is defined as a rotation
  about an axis in the direction of ``vector``, of angle of the field value.

  NOTE

  One possible use of ``NXtransformations`` is to define the motors and
  transformations for a diffractometer (goniometer).  Such use is mentioned
  in the ``NXinstrument`` base class.  Use one ``NXtransformations`` group 
  for each diffractometer and name the group appropriate to the device.
  Collecting the motors of a sample table or xyz-stage in an NXtransformation
  group is equally possible.

**Symbols**:

  No symbol table

**Groups cited**:
  none

**Structure**:

  .. index:: AXISNAME (field)

  **AXISNAME**: (optional) :ref:`NX_NUMBER <NX_NUMBER>` {units=\ :ref:`NX_TRANSFORMATION <NX_TRANSFORMATION>`}

    Units need to be appropriate for translation or rotation

    The name of this field is not forced.  The user is free to use any name
    that does not cause confusion.  When using more than one ``AXISNAME`` field,
    make sure that each field name is unique in the same group, as required
    by HDF5.

    The values given should be the start points of exposures for the corresponding
    frames.  The end points should be given in ``AXISNAME_end``.

    .. index:: transformation_type (field attribute)

    **@transformation_type**: (optional) :ref:`NX_CHAR <NX_CHAR>`

      The transformation_type may be ``translation``, in which case the
      values are linear displacements along the axis, ``rotation``,
      in which case the values are angular rotations around the axis.

      If this attribute is omitted, this is an axis for which there
      is no motion to be specifies, such as the direction of gravity,
      or the direction to the source, or a basis vector of a
      coordinate frame.

      Any of these values: ``translation`` | ``rotation``

    .. index:: vector (field attribute)

    **@vector**: (optional) :ref:`NX_NUMBER <NX_NUMBER>`

      Three values that define the axis for this transformation.
      The axis should be normalized to unit length, making it
      dimensionless.  For ``rotation`` axes, the direction should be
      chosen for a right-handed rotation with increasing angle.
      For ``translation`` axes the direction should be chosen for
      increasing displacement.

    .. index:: offset (field attribute)

    **@offset**: (optional) :ref:`NX_NUMBER <NX_NUMBER>`

      A fixed offset applied before the transformation (three vector components).

    .. index:: offset_units (field attribute)

    **@offset_units**: (optional) :ref:`NX_CHAR <NX_CHAR>`

      Units of the offset.  Values should be consistent with NX_LENGTH.

    .. index:: depends_on (field attribute)

    **@depends_on**: (optional) :ref:`NX_CHAR <NX_CHAR>`

      Points to the path to a field defining the axis on which this
      depends or the string ".".

  .. index:: AXISNAME_end (field)

  **AXISNAME_end**: (optional) :ref:`NX_NUMBER <NX_NUMBER>` {units=\ :ref:`NX_TRANSFORMATION <NX_TRANSFORMATION>`}

    ``AXISNAME_end`` is a placeholder for a name constructed from the actual
    name of an axis to which ``_end`` has been appended.

    The values in this field are the end points of the motions that start
    at the corresponding positions given in the ``AXISNAME`` field.

  .. index:: AXISNAME_increment_set (field)

  **AXISNAME_increment_set**: (optional) :ref:`NX_NUMBER <NX_NUMBER>` {units=\ :ref:`NX_TRANSFORMATION <NX_TRANSFORMATION>`}

    ``AXISNAME_increment_set`` is a placeholder for a name constructed from the actual
    name of an axis to which ``_increment_set`` has been appended.

    The value of this optional field is the intended average range through which
    the corresponding axis moves during the exposure of a frame.  Ideally, the
    value of this field added to each value of ``AXISNAME`` would agree with the
    corresponding values of ``AXISNAME_end``, but there is a possibility of significant
    differences.  Use of ``AXISNAME_end`` is recommended.

**NXDL Source**:
  https://github.com/nexusformat/definitions/blob/master/base_classes/NXtransformations.nxdl.xml