smesh/doc/salome/gui/SMESH/input/about_meshes.doc

/*!

\page about_meshes_page About meshes

\n \b MESH represents a discretization of a geometrical CAD model into
a set of entities with a simple topology. In MESH there are two
options of creation of meshes, you can:

<ul>
<li>generate meshes on the basis of geometrical shapes produced in the GEOM module,</li>
<li>create your own meshes using the MESH functions destined for modification of generated meshes.</li>
</ul>

The topology of a mesh is described by the relationships between its
entities including:

<ul>
<li>\b Node &mdash; 0D object of a mesh presented by a point with coordinates (x, y, z).</li>
<li>\b Edge &mdash; 1D element of a mesh defined by two nodes.</li>
<li>\b Face &mdash; 2D element of a mesh defined by three or four edges (closed contour).</li>
<li>\b Volume &mdash; 3D element of a mesh defined by several faces.</li>
</ul>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;These entities are
considered as topological entities and they don't
imply any geometric representation. Only \b Nodes reference  geometric
representations of points with definite coordinates. The node entity
will contain  additional information about its position in the space
and its relations with the meshed CAD model. Its position could be
described in the following way:

<ul>
<li><b>2D position</b>. It is a free position defined by only two coordinates x,y.</li>
<li><b>3D position</b>. It is a free position defined by three coordinates x,y and z. </li>
<li><b>Surface position</b>. It characterizes the position of a node on a
geometric surface and is defined by the u,v position in the parametric
space of the corresponding surface.</li>
<li><b>Line position</b>. It characterizes the position of a node on a
geometric curve and is defined by the u parameter and the
corresponding curve.</li>
<li><b>Vertex position</b>. It characterizes the position of a node on a
geometric point of the meshed CAD model and is defined by the x,y,z
coordinates of the corresponding vertex.</li>
</ul>

<br><h2>Connections</h2>

Each mesh entity bounds 0 or more mesh entities of higher
dimension. In the same way each mesh entity is bounded by 0 or more
mesh entities of lower dimension:

<ul>
<li>A node bounds edges, faces and volumes</li>
<li>An edge bounds faces, and volumes</li>
<li>A face bounds volumes</li>
<li>A volume is bounded by faces, edges and nodes</li>
<li>A face is bounded by edges, and nodes</li>
<li>An edge is bounded by nodes</li>
</ul>

You can notice that there are two types of connections: \b inverse and
\b direct connections.

<br><h2>Inverse connections</h2>

This relationship has a particularity that the order of bounded
entities has not a direct meaning. Also the number of bounded entities
is not fixed.

\b Example: The edges surrounding a node. The 3rd edge has no more
sense that the 5th one.

<br><h2>Direct connections</h2>

This relationship has a particularity that the order of bounding
entities is meaningful. The number of bounding entities is fixed and
depends on the type of the entity (hexahedron, tetrahedron,?).

\b Example: An edge is composed of two nodes. A face is composed of 3
or 4 edges depending if we are dealing with triangles or quadrangles.

The connections are not only restricted to entities of one dimension
higher or lower. For example some algorithms may be interested to
retrieve all the faces surrounding a node.

*/