# About meshes

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

- generate meshes on the basis of geometrical shapes produced in the GEOM module,

- create your own meshes using the SMESH functions destined for modification of generated meshes. More about this functionality of SMESH see in the chapter "Modifying meshes".

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

- Node – 0D element of a mesh presented by a point with coordinates (x, y, z).

- Edge – 1D element of a mesh defined by two nodes.

- Face – 2D element of a mesh defined by three or four edges (closed contour).

- Volume – 3D element of a mesh defined by several faces.

These entities are considered as topological entities and they don't imply any geometric representation. Only 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:

- 2D position. It is a free position defined by only two coordinates x,y.

- 3D position. It is a free position defined by three coordinates x,y and z.

- Surface position. 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.

- Line position. It characterizes the position of a node on a geometric curve and is defined by the u parameter and the corresponding curve.

- Vertex position. 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.

#### Connections

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:

- A node bounds edges, faces and volumes

- An edge bounds faces, and volumes

- A face bounds volumes

- A volume is bounded by faces, edges and nodes

- A face is bounded by edges, and nodes

- An edge is bounded by nodes

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

#### Inverse connections

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.

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

Direct connections

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,…).

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.