\page basic_meshing_algos_page Basic meshing algorithms
\n The MESH module contains a set of meshing algorithms, which are
-used for meshing entities (1D, 2D, 3D) composing geometrical objects.
+used for meshing entities (1D, 2D, 3D sub-shapes) composing
+geometrical objects.
+
+An algorithm represents either an implementation of a certain meshing
+technique or an interface to the whole meshing program generating elements
+of several dimensions.
<ul>
<li>For meshing of 1D entities (<b>edges</b>):</li>
-
+\anchor a1d_algos_anchor
<ul>
-<li>Wire Discretisation meshing algorithm - splits a wire into a
-number of mesh segments following any 1D hypothesis.</li>
-<li>Composite Side Discretisation algorithm - allows to apply any 1D
-hypothesis to a whole side of a geometrical face even if it is
-composed of several edges provided that they form C1 curve, have the
-same hypotheses assigned and form one side in all faces of the main
-shape of a mesh.</li>
+<li><em>Wire Discretization</em> meshing algorithm - splits an edge into a
+number of mesh segments following an 1D hypothesis.
+</li>
+<li><em>Composite Side Discretization</em> algorithm - allows to apply a 1D
+ hypothesis to a whole side of a geometrical face even if it is
+ composed of several edges provided that they form C1 curve in all
+ faces of the main shape.</li>
</ul>
<li>For meshing of 2D entities (<b>faces</b>):</li>
<ul>
-<li>Triangle meshing algorithms (Mefisto) - Faces are split into triangular elements.</li>
-<li>Quadrangle meshing algorithm (Mapping) - quadrilateral Faces are split into
-quadrangular elements.</li>
+<li><em>Triangle (Mefisto)</em> meshing algorithm - splits faces
+ into triangular elements.</li>
+<li>\subpage quad_ijk_algo_page "Quadrangle (Mapping)" meshing
+ algorithm - splits faces into quadrangular elements.</li>
</ul>
\image html image123.gif "Example of a triangular 2D mesh"
\image html image124.gif "Example of a quadrangular 2D mesh"
-<li>For meshing of 3D entities (<b>volume objects</b>):</li>
+<li>For meshing of 3D entities (<b>solid objects</b>):</li>
<ul>
-<li>Hexahedron meshing algorithm (i,j,k) - 6-sided Volumes are split into
-hexahedral (cubic) elements.</li>
-<li>\subpage cartesian_algo_page</li>
-internal parts of Volumes are split into hexahedral elements forming a
-Cartesian grid; polyhedra and other types of elements are generated
-where the geometrical boundary intersects Cartesian cells.</li>
+<li><em>Hexahedron (i,j,k)</em> meshing algorithm - solids are
+ split into hexahedral elements thus forming a structured 3D
+ mesh. The algorithm requires that 2D mesh generated on a solid could
+ be considered as a mesh of a box, i.e. there should be six nodes shared
+ by three quadrangles and the rest nodes should be shared by four
+ quadrangles.
+\image html hexa_ijk_mesh.png "Structured mesh generated by Hexahedron (i,j,k) on a solid bound by 16 faces"
+</li>
+
+<li>\subpage cartesian_algo_page "Body Fitting" meshing
+ algorithm - solids are split into hexahedral elements forming
+ a Cartesian grid; polyhedra and other types of elements are generated
+ where the geometrical boundary intersects Cartesian cells.</li>
</ul>
\image html image125.gif "Example of a tetrahedral 3D mesh"
\image html image126.gif "Example of a hexahedral 3D mesh"
</ul>
-Some of 3D meshing algorithms also can generate 3D meshes from 2D meshes, working without
-geometrical objects. Such algorithms are
-<ul>
-<li>Hexahedron meshing algorithm (i,j,k),</li>
-<!-- <li>GHS3D meshing algorithm (commercial)</li> -->
-</ul>
+Some 3D meshing algorithms, such as Hexahedron(i,j,k) and some
+commercial ones, also can generate 3D meshes from 2D meshes, working
+without geometrical objects.
There is also a number of more specific algorithms:
<ul>
+<li>\subpage prism_3d_algo_page "for meshing prismatic 3D shapes"</li>
+<li>\subpage quad_from_ma_algo_page "for meshing faces with sinuous borders"</li>
+<li> <em>Polygon per Face</em> meshing algorithm - generates one mesh
+ face (either a triangle, a quadrangle or a polygon) per a geometrical
+ face using all nodes from the face boundary.</li>
<li>\subpage projection_algos_page "for meshing by projection of another mesh"</li>
<li>\subpage import_algos_page "for meshing by importing elements from another mesh"</li>
<li>\subpage radial_prism_algo_page "for meshing geometrical objects with cavities"</li>
+<li>\subpage radial_quadrangle_1D2D_algo_page "for meshing special faces (circles and parts of circles)"</li>
+<li>\subpage use_existing_page "Use Edges to be Created Manually" and
+\ref use_existing_page "Use Faces to be Created Manually" algorithms can be
+used to create a 1D or a 2D mesh in a python script.</li>
<li>\subpage segments_around_vertex_algo_page "for defining the local size of elements around a certain node"</li>
-<li>\subpage prism_3d_algo_page "for meshing prismatic shapes"</li>
-<li>\subpage radial_quadrangle_1D2D_algo_page "for meshing special 2d faces (circles and part of circles)"</li>
</ul>
-\ref use_existing_anchor "Use existing edges" and
-\ref use_existing_anchor "Use existing faces" algorithms can be
-used to create an 1D or a 2D mesh in a python script.
\ref constructing_meshes_page "Constructing meshes" page describes in
detail how to apply meshing algorithms.
