.. _BC-Cgeometry-Structure:

==============================================
Computational and Constructive Solid Geometry
==============================================

.. index::
   BC-Cgeometry-Introduction
   BC-Cgeometry-Base-Classes
    
.. _BC-Cgeometry-Introduction:

Introduction
############

A set of base classes to describe the location and shape of objects using
concepts from the fields of computer graphics, computational geometry,
and constructive solid geometry (CSG).

.. _BC-Cg-Introduction-Base-Classes:

Base Classes
############

The following base classes are defined to incentivize the use of NeXus for
using computational-geometry-based descriptions. In what follows, base classes
for frequently used shapes and geometric primitives are proposed:

:ref:`NXcg_primitive`
    Base class from which most other NXcg classes that define specific primitives inherit.

:ref:`NXcg_ellipsoid`
    A description for a set of possibly dissimilar oriented ellipsoids.

:ref:`NXcg_cylinder`
    A description for a set of possibly dissimilar oriented cylinders.

:ref:`NXcg_point`
    A collection of points with labels.

:ref:`NXcg_polyline`:
    A collection of lines and linear segments.

:ref:`NXcg_triangle`
    A collection of triangles.

:ref:`NXcg_parallelogram`
A collection of possibly dissimilar parallelograms.

:ref:`NXcg_polygon`
    A collection of polygons.

:ref:`NXcg_polyhedron`
    A collection of polyhedra.

:ref:`NXcg_roi`
    A container to host a number of different types of primitives.

:ref:`NXcg_tetrahedron`
    A collection of tetrahedra.

:ref:`NXcg_hexahedron`
    A collection of hexahedra with capabilities to represent
    also simpler (bounding) boxes for e.g. binary trees.

An example how to use these classes follows:

.. literalinclude:: cube_example.txt
    :tab-width: 4
    :linenos:
    :language: text

These base classes describe data structures used for more complex geometries:

:ref:`NXcg_face_list_data_structure`
    In essence, the usual way how polygon/polyhedra data are reported:
    A list of vertices and faces with identifier and properties.

:ref:`NXcg_half_edge_data_structure`
    A half-edge data structure (also known as a doubly connected edge list)
    is a useful complementary descriptor for polygon/polyhedra which enables
    topological analyses and traversal of the graph of how polygons and
    polyhedra are connected.

:ref:`NXcg_unit_normal`
    As an additional structuring element especially for meshes, well-documented
    normal information is crucial for distance computations.

:ref:`NXcg_alpha_complex`
    Alpha shapes and alpha wrappings, specifically the special case of the
    convex hull, are frequently used geometrical models for describing
    a boundary or edge to a set of geometric primitives.

    Next, a few base classes are defined for documenting discretized representations
    of material (area or volume) which can be useful not only for stencil-based methods:

:ref:`NXcg_grid`
    A grid of cells.

:ref:`NXisocontour`
    A description for isocontour descriptions.

:ref:`NXdelocalization`
    An approach to document procedures whereby a scalar field
    is smoothed in a controlled manner.

:ref:`NXsimilarity_grouping`
    A description for clustering of objects (such as atoms or features).

:ref:`NXrotations`
    A set of parameters to describe the relative orientation of
    members of a set of features/objects.