\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.
+\n \b MESH represents a discrete approximation of a subset of the
+three-dimensional space by \ref mesh_entities "elementary geometrical
+elements".
-It is possible to \subpage constructing_meshes_page "construct meshes"
-on the basis of geometrical shapes produced in the GEOM module.
-It is also possible to
-\subpage constructing_submeshes_page "construct mesh on a part of the geometrical object",
-for example, a face, with different meshing parameters or using
-another meshing algorithm.
-
-Several created meshes can be \subpage building_compounds_page "combined into another mesh".
-
-The whole mesh or its part can be \subpage copy_mesh_page "copied" into another mesh.
-
-Meshing parameters of meshes and sub-meshes can be
-\subpage editing_meshes_page "edited", then only the mesh part
-depending on the changed parameters will be re-computed.
-
-Meshes can be edited using the MESH functions destined for
-\ref modifying_meshes_page "modification" of generated meshes.
-
-Meshes are stored in DAT, MED, UNV, STL, CGNS, GMF and SAUVE formats and can be
-\subpage importing_exporting_meshes_page "imported from and exported to"
- the file in these formats.
-
-The \b topology of a mesh is described by the relationships between its
-entities including:
-
-<ul>
-<li>\b Node — 0D object of a mesh presented by a point with coordinates (x, y, z).</li>
-<li>\b 0D element — element of a mesh defined by one node.</li>
-<li>\b Edge — 1D element of a mesh defined by two nodes.</li>
-<li>\b Face — 2D element of a mesh defined by three or four edges (closed contour).</li>
-<li>\b Volume — 3D element of a mesh defined by several faces.</li>
-<li>\b Ball element — discrete element of a mesh defined by a node and a diameter.</li>
-</ul>
-
- 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
-contains 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:
+A SALOME study can contain multiple meshes, but they do not
+implicitly compose one super-mesh, and finally each of them
+can be used (e.g. exported) only individually.
+Mesh module provides several ways to create the mesh:
<ul>
-<li><b>3D position</b>. It characterizes the position of a node in a
- solid geometry and is defined by three coordinates x,y and z and a
- reference to the solid geometrical entity. </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>
+ <li>The main way is to \subpage constructing_meshes_page "construct the mesh"
+ on the basis of the geometrical shape produced in the Geometry
+ module. This way implies selection of
+ - a geometrical object (<em>main shape</em>) and
+ - <em>meshing parameters</em> (\ref
+ basic_meshing_algos_page "meshing algorithms" and
+ characteristics (e.g. element size) of a
+ required mesh encapsulated in \ref about_hypo_page "hypothesis"
+ objects).
+
+ Construction of \subpage constructing_submeshes_page "sub-meshes"
+ allows to discretize some sub-shapes of the main shape, for example a face,
+ using the meshing parameters that differ from those used for other sub-shapes.<br>
+ Meshing parameters of meshes and sub-meshes can be
+ \subpage editing_meshes_page "edited". (Upon edition only mesh entities
+ generated using changed meshing parameters are removed and will be
+ re-computed).<br>
+ \note Algorithms and hypotheses used at mesh level are referred to as
+ \a global ones and those used at sub-mesh level are referred to as \a
+ local ones.
+ </li>
+ <li>Bottom-up way, using \ref modifying_meshes_page "mesh modification"
+ operations, especially \ref extrusion_page "extrusion" and \ref
+ revolution_page "revolution". To create an empty mesh not based on a
+ geometry, use the same dialog as to \ref constructing_meshes_page
+ "construct the mesh on geometry" but specify neither the geometry
+ nor meshing algorithms.
+ </li>
+ <li>The mesh can be \subpage importing_exporting_meshes_page "imported" from
+ (and exported to) the file in MED, UNV, STL, CGNS, DAT, GMF and
+ SAUVE formats.
+ </li>
+ <li>The 3D mesh can be generated from the 2D mesh not based on the geometry,
+ which was either \ref importing_exporting_meshes_page "imported" or created in
+ other way. To setup the meshing parameters of a mesh not based on a geometry,
+ just invoke \ref editing_meshes_page "Edit mesh / sub-mesh" command on
+ your 2D mesh.
+ </li>
+ <li>Several meshes can be \subpage building_compounds_page "combined"
+ into a new mesh.
+ </li>
+ <li>The whole mesh or its part (sub-mesh or group) can be
+ \subpage copy_mesh_page "copied" into a new mesh.
+ </li>
+ <li>A new mesh can be created from a transformed, e.g. \ref
+ translation_page "translated", part of the mesh.</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:
-
+Meshes can be edited using the MESH functions destined for
+\ref modifying_meshes_page "modification" of meshes.
+
+Attractive meshing capabilities include:
+- 3D and 2D \ref viscous_layers_anchor "Viscous Layers" (boundary
+ layers of highly stretched elements beneficial for high quality
+ viscous computations);
+- automatic conformal transition between tetrahedral and hexahedral
+ sub-meshes.
+
+The \b structure of a SALOME mesh is described by nodes and elements based on
+these nodes. The geometry of an element is defined by the sequence of
+nodes constituting it and
+the <a href="http://www.code-aster.org/outils/med/html/connectivites.html">
+ connectivity convention </a> (adopted from MED library). Definition of
+the element basing on the elements of a lower dimension is NOT supported.
+
+\anchor mesh_entities
+The mesh can include the following entities:
<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>
+<li>\b Node — a mesh entity defining a position in 3D
+ space with coordinates (x, y, z).</li>
+<li>\b Edge (or segment) — 1D mesh element linking two nodes.</li>
+<li>\b Face — 2D mesh element representing a part of
+ surface bound by links between face nodes. A face can be a
+ triangle, quadrangle or polygon.</li>
+<li>\b Volume — 3D mesh element representing a part of 3D
+ space bound by volume facets. Nodes of a volume describing each
+ facet are defined by
+ the <a href="http://www.code-aster.org/outils/med/html/connectivites.html">
+ MED connectivity convention.</a> A volume can be a tetrahedron, hexahedron,
+ pentahedron, pyramid, hexagonal prism or polyhedron.</li>
+<li>\b 0D element — mesh element defined by one node.</li>
+<li>\b Ball element — discrete mesh element defined by a
+ node and a diameter.</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.
-
+Every mesh entity has an attribute associating it to a sub-shape it is
+generated on (if any). The node generated on the geometrical edge or
+surface in addition stores its position in parametric space of the
+associated geometrical entity. This attribute is set up by meshing
+algorithms generating elements and nodes.
+
+Mesh entities are identified by integer IDs starting from 1.
+Nodes and elements are counted separately, i.e. there can be a node
+and element with the same ID.
+
+SALOME supports elements of second order, without a central node
+(quadratic triangle, quadrangle, polygon, tetrahedron, hexahedron,
+pentahedron and pyramid) and with central nodes (bi-quadratic triangle
+and quadrangle and tri-quadratic hexahedron).<br>
+Quadratic mesh can be obtained in three ways:
+- Using a global \ref quadratic_mesh_anchor "Quadratic Mesh"
+hypothesis. (Elements with the central node are not generated in this way).
+- Using \ref convert_to_from_quadratic_mesh_page operation.
+- Using an appropriate option of some meshing algorithms, which
+generate elements of several dimensions starting from mesh segments.
*/
