# 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.

## 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.

• Quadrangle: Mapping meshing algorithm meshing algorithm - splits faces into quadrangular elements.

“Example of a triangular 2D mesh”

“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.

“Structured mesh generated by Hexahedron (i,j,k) on a solid bound by 16 faces”

• Body Fitting 3D meshing algorithm 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.

“Example of a tetrahedral 3D mesh”

“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:

Constructing meshes page describes in detail how to apply meshing algorithms.

See Also a sample TUI Script of a Defining Meshing Algorithms operation.