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

.. index::
    ! NXcg_half_edge_data_structure (base class)
    ! cg_half_edge_data_structure (base class)
    see: cg_half_edge_data_structure (base class); NXcg_half_edge_data_structure

.. _NXcg_half_edge_data_structure:

=============================
NXcg_half_edge_data_structure
=============================

**Status**:

  base class, extends :ref:`NXobject`

**Description**:

  Computational geeometry description of a half-edge data structure.

  Such a data structure can be used to efficiently circulate around faces
  and iterate over vertices of a planar graph.

**Symbols**:

  The symbols used in the schema to specify e.g. dimensions of arrays.

  **d**: The dimensionality, which has to be at least 2.

  **n_v**: The number of vertices.

  **n_f**: The number of faces.

  **n_he**: The number of half-edges.

**Groups cited**:
  none

**Structure**:

  .. _/NXcg_half_edge_data_structure/dimensionality-field:

  .. index:: dimensionality (field)

  **dimensionality**: (optional) :ref:`NX_POSINT <NX_POSINT>` {units=\ :ref:`NX_UNITLESS <NX_UNITLESS>`}


  .. _/NXcg_half_edge_data_structure/number_of_vertices-field:

  .. index:: number_of_vertices (field)

  **number_of_vertices**: (optional) :ref:`NX_POSINT <NX_POSINT>` {units=\ :ref:`NX_UNITLESS <NX_UNITLESS>`}


  .. _/NXcg_half_edge_data_structure/number_of_faces-field:

  .. index:: number_of_faces (field)

  **number_of_faces**: (optional) :ref:`NX_POSINT <NX_POSINT>` {units=\ :ref:`NX_UNITLESS <NX_UNITLESS>`}


  .. _/NXcg_half_edge_data_structure/number_of_half_edges-field:

  .. index:: number_of_half_edges (field)

  **number_of_half_edges**: (optional) :ref:`NX_POSINT <NX_POSINT>` {units=\ :ref:`NX_UNITLESS <NX_UNITLESS>`}


  .. _/NXcg_half_edge_data_structure/vertex_identifier_offset-field:

  .. index:: vertex_identifier_offset (field)

  **vertex_identifier_offset**: (optional) :ref:`NX_INT <NX_INT>` {units=\ :ref:`NX_UNITLESS <NX_UNITLESS>`}

    In this half-edge data structure vertex identifiers start at 1.
    Vertices are identified with consecutive integers up to number_of_vertices.
    This field can be used to document which constant integer has to be
    added to another set of vertex_identifier to assure that these other
    identifiers also start at 1.

  .. _/NXcg_half_edge_data_structure/face_identifier_offset-field:

  .. index:: face_identifier_offset (field)

  **face_identifier_offset**: (optional) :ref:`NX_INT <NX_INT>` {units=\ :ref:`NX_UNITLESS <NX_UNITLESS>`}

    In this half-edge data structure face identifiers start at 1.
    Faces are identified with consecutive integers up to number_of_faces.
    This field can be used to document which constant integer has to be
    added to another set of face_identifier to assure that these other
    identifiers also start at 1.

    The face identifier zero is reserved for the NULL face !

  .. _/NXcg_half_edge_data_structure/half_edge_identifier_offset-field:

  .. index:: half_edge_identifier_offset (field)

  **half_edge_identifier_offset**: (optional) :ref:`NX_INT <NX_INT>` {units=\ :ref:`NX_UNITLESS <NX_UNITLESS>`}

    In this half-edge data structure half-edge identifiers start at 1.
    Half-edges are identified with consecutive integers up to number_of_half_edges.
    This field can be used to document which constant integer has to be
    added to another set of half_edge_identifier to assure that these other
    identifiers also start at 1.

  .. _/NXcg_half_edge_data_structure/position-field:

  .. index:: position (field)

  **position**: (optional) :ref:`NX_NUMBER <NX_NUMBER>` (Rank: 2, Dimensions: [n_v, d]) {units=\ :ref:`NX_LENGTH <NX_LENGTH>`}

    The position of the vertices.

  .. _/NXcg_half_edge_data_structure/vertex_incident_half_edge-field:

  .. index:: vertex_incident_half_edge (field)

  **vertex_incident_half_edge**: (optional) :ref:`NX_UINT <NX_UINT>` (Rank: 1, Dimensions: [n_v]) {units=\ :ref:`NX_UNITLESS <NX_UNITLESS>`}

    Identifier of the incident half-edge.

  .. _/NXcg_half_edge_data_structure/face_half_edge-field:

  .. index:: face_half_edge (field)

  **face_half_edge**: (optional) :ref:`NX_UINT <NX_UINT>` (Rank: 1, Dimensions: [n_f]) {units=\ :ref:`NX_UNITLESS <NX_UNITLESS>`}

    Identifier of the (starting)/associated half-edge of the face.

  .. _/NXcg_half_edge_data_structure/half_edge_vertex_origin-field:

  .. index:: half_edge_vertex_origin (field)

  **half_edge_vertex_origin**: (optional) :ref:`NX_UINT <NX_UINT>` (Rank: 1, Dimensions: [n_he]) {units=\ :ref:`NX_UNITLESS <NX_UNITLESS>`}

    The identifier of the vertex from which this half-edge is outwards pointing.

  .. _/NXcg_half_edge_data_structure/half_edge_twin-field:

  .. index:: half_edge_twin (field)

  **half_edge_twin**: (optional) :ref:`NX_UINT <NX_UINT>` (Rank: 1, Dimensions: [n_he]) {units=\ :ref:`NX_UNITLESS <NX_UNITLESS>`}

    Identifier of the associated oppositely pointing half-edge.

  .. _/NXcg_half_edge_data_structure/half_edge_incident_face-field:

  .. index:: half_edge_incident_face (field)

  **half_edge_incident_face**: (optional) :ref:`NX_UINT <NX_UINT>` (Rank: 1, Dimensions: [n_he]) {units=\ :ref:`NX_UNITLESS <NX_UNITLESS>`}

    If the half-edge is a boundary half-edge the
    incident face identifier is NULL, i.e. 0.

  .. _/NXcg_half_edge_data_structure/half_edge_next-field:

  .. index:: half_edge_next (field)

  **half_edge_next**: (optional) :ref:`NX_UINT <NX_UINT>` (Rank: 1, Dimensions: [n_he]) {units=\ :ref:`NX_UNITLESS <NX_UNITLESS>`}

    Identifier of the next half-edge.

  .. _/NXcg_half_edge_data_structure/half_edge_prev-field:

  .. index:: half_edge_prev (field)

  **half_edge_prev**: (optional) :ref:`NX_UINT <NX_UINT>` (Rank: 1, Dimensions: [n_he]) {units=\ :ref:`NX_UNITLESS <NX_UNITLESS>`}

    Identifier of the previous half-edge.

  .. _/NXcg_half_edge_data_structure/weinberg_vector-field:

  .. index:: weinberg_vector (field)

  **weinberg_vector**: (optional) :ref:`NX_CHAR <NX_CHAR>`

    Users are referred to the literature for the background of L. Weinberg's
    work about topological characterization of planar graphs:

    * `L. Weinberg 1966a, <https://dx.doi.org/10.1109/TCT.1964.1082216>`_  
    * `L. Weinberg, 1966b, <https://dx.doi.org/10.1137/0114062>`_  
    * `E. A. Lazar et al. <https://doi.org/10.1103/PhysRevLett.109.095505>`_

    and how this work can e.g. be applied in space-filling tessellations
    of microstructural objects like crystals/grains.


Hypertext Anchors
-----------------

List of hypertext anchors for all groups, fields,
attributes, and links defined in this class.


* :ref:`/NXcg_half_edge_data_structure/dimensionality-field </NXcg_half_edge_data_structure/dimensionality-field>`
* :ref:`/NXcg_half_edge_data_structure/face_half_edge-field </NXcg_half_edge_data_structure/face_half_edge-field>`
* :ref:`/NXcg_half_edge_data_structure/face_identifier_offset-field </NXcg_half_edge_data_structure/face_identifier_offset-field>`
* :ref:`/NXcg_half_edge_data_structure/half_edge_identifier_offset-field </NXcg_half_edge_data_structure/half_edge_identifier_offset-field>`
* :ref:`/NXcg_half_edge_data_structure/half_edge_incident_face-field </NXcg_half_edge_data_structure/half_edge_incident_face-field>`
* :ref:`/NXcg_half_edge_data_structure/half_edge_next-field </NXcg_half_edge_data_structure/half_edge_next-field>`
* :ref:`/NXcg_half_edge_data_structure/half_edge_prev-field </NXcg_half_edge_data_structure/half_edge_prev-field>`
* :ref:`/NXcg_half_edge_data_structure/half_edge_twin-field </NXcg_half_edge_data_structure/half_edge_twin-field>`
* :ref:`/NXcg_half_edge_data_structure/half_edge_vertex_origin-field </NXcg_half_edge_data_structure/half_edge_vertex_origin-field>`
* :ref:`/NXcg_half_edge_data_structure/number_of_faces-field </NXcg_half_edge_data_structure/number_of_faces-field>`
* :ref:`/NXcg_half_edge_data_structure/number_of_half_edges-field </NXcg_half_edge_data_structure/number_of_half_edges-field>`
* :ref:`/NXcg_half_edge_data_structure/number_of_vertices-field </NXcg_half_edge_data_structure/number_of_vertices-field>`
* :ref:`/NXcg_half_edge_data_structure/position-field </NXcg_half_edge_data_structure/position-field>`
* :ref:`/NXcg_half_edge_data_structure/vertex_identifier_offset-field </NXcg_half_edge_data_structure/vertex_identifier_offset-field>`
* :ref:`/NXcg_half_edge_data_structure/vertex_incident_half_edge-field </NXcg_half_edge_data_structure/vertex_incident_half_edge-field>`
* :ref:`/NXcg_half_edge_data_structure/weinberg_vector-field </NXcg_half_edge_data_structure/weinberg_vector-field>`

**NXDL Source**:
  https://github.com/nexusformat/definitions/blob/main/base_classes/NXcg_half_edge_data_structure.nxdl.xml