.. _basic_meshing_algos_page:

************************
Basic meshing algorithms
************************

The MESH module contains a set of meshing algorithms, which are	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.

.. _a1d_algos_anchor:

1D Entities
===========

* For meshing of 1D entities (**edges**):
* **Wire Discretization** meshing algorithm - splits an edge into a number of mesh segments following an 1D hypothesis.
* **Composite Side Discretization** 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.
* For meshing of 2D entities (**faces**):


	* **Triangle: Mefisto** meshing algorithm - splits faces into triangular elements.
	* :ref:`quad_ijk_algo_page` meshing algorithm - splits faces into quadrangular elements.

		.. image:: ../images/image123.gif
			:align: center 

		.. centered::
			"Example of a triangular 2D mesh"

		.. image:: ../images/image124.gif 
			:align: center 

		.. centered::
			"Example of a quadrangular 2D mesh"

	* For meshing of 3D entities (**solid objects**):


		* **Hexahedron (i,j,k)** 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 eight nodes shared by three quadrangles and the rest nodes should be shared by four quadrangles.
			.. image:: ../images/hexa_ijk_mesh.png 
				:align: center 

			.. centered::
				"Structured mesh generated by Hexahedron (i,j,k) on a solid bound by 16 faces"


		* :ref:`cartesian_algo_page` 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.
			.. image:: ../images/image125.gif 
				:align: center 

			.. centered::
				 "Example of a tetrahedral 3D mesh"

			.. image:: ../images/image126.gif 
				:align: center 

			.. centered::
				"Example of a hexahedral 3D mesh"


Some 3D meshing algorithms, such as Hexahedron(i,j,k) also can
generate 3D meshes from 2D meshes, working without geometrical
objects.

There is also a number of more specific algorithms:

	* :ref:`prism_3d_algo_page` - for meshing prismatic 3D shapes with hexahedra and prisms.
	* :ref:`quad_from_ma_algo_page` - for quadrangle meshing of faces with sinuous borders and rings.
	* **Polygon per Face** 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.
	* :ref:`projection_algos_page` - for meshing by projection of another mesh.
	* :ref:`import_algos_page` - for meshing by importing elements from another mesh.
	* :ref:`radial_prism_algo_page` - for meshing 3D geometrical objects with cavities with hexahedra and prisms.
	* :ref:`radial_quadrangle_1D2D_algo_page` - for quadrangle meshing of disks and parts of disks.
	* :ref:`use_existing_page` - to create a 1D or a 2D mesh in a python script.
	* :ref:`segments_around_vertex_algo_page` - for defining the length of mesh segments around certain vertices.


:ref:`constructing_meshes_page` page describes in detail how to apply meshing algorithms.

**See Also** a sample TUI Script of a :ref:`tui_defining_meshing_algos` operation.  


.. toctree::
	:maxdepth: 2

	quad_ijk_algo.rst
	cartesian_algo.rst
	prism_3d_algo.rst
	quad_from_ma_algo.rst
	projection_algos.rst
	use_existing_algos.rst
	radial_prism_algo.rst
	radial_quadrangle_1D2D_algo.rst
	define_mesh_by_script.rst
	segments_around_vertex_algo.rst