Mesh

For those acquainted with mechanical design and reverse engineering, they can testify to the fact that the road to a new product design involves several steps. In reverse engineering, the summary of the entire process involves scanning, point cloud generation, meshing, computer-aided designing, prototyping and final production. This section covers a very crucial part of the process — Meshing or simply put, Mesh.

To put a simple definition, a mesh is a network that constitutes of cells and points.

Mesh generation is the practice of converting the given set of points into a consistent polygonal model that generates vertices, edges and faces that only meet at shared edges. It can have almost any shape in any size. Each cell of the mesh represents an individual solution, which when combined, results in a solution for the entire mesh.

 

mesh

Mesh is formed of facets which are connected to each other topologically. The topology is created using following entities:

  • Facet - A triangle connecting three data points
  • Edge - A line connecting two data points
  • Vertex - A data point
Mesh Property

Before we proceed to know the types of meshes, it is necessary to understand the various aspects that constitute a mesh. It is important to know the concept of a polygonal mesh.

A polygon mesh is a collection of vertices, edges and faces that defines the shape of a polyhedral object in 3D graphics and solid modeling. The faces usually consist of triangles, quadrilaterals or other simple polygons as that simplifies rendering. It may also be composed of more general concave polygons or polygons with holes.

Objects created with polygon meshes must store different types of elements. These include:

  • Vertex: A position (usually in 3D space) along with other information such as color, normal vector and texture coordinates
  • Edge: A connection between two vertices
  • Face: A closed set of edges, in which a triangle face has three edges, and a quad face has four edges
  • Surfaces: They are often called smoothing groups. Generally, surfaces are not required to group smooth regions

A polygon mesh may be represented in a variety of ways, using different methods to store the vertex, edge and face data. These include:

  • Face-vertex meshes
  • Winged edge meshes
  • Corner tables
  • Vertex-vertex meshes
Types of meshes

Meshes are commonly classified into two divisions, Surface mesh and Solid mesh. Let us go through each section one by one.

Surface Mesh: A surface mesh is a representation of each individual surface constituting a volume mesh. It consists of faces (triangles) and vertices. Depending on the pre-processing software package, feature curves may be included as well.

Generally, a surface mesh should not have free edges and the edges should not be shared by two triangles.

The surface should ideally contain the following qualities of triangle faces:

  • Equilateral sized triangles
  • No sharp angles/surface folds etc. within the triangle proximity sphere
  • Gradual variation in triangle size from one to the next

The surface mesh generation process should be considered carefully. It has a direct influence on the quality of the resulting volume mesh and the effort it takes to get to this step.

surface mesh

Solid Mesh: Solid mesh, also known as volume mesh, is a polygonal representation of the interior volume of an object. There are three different types of meshing models that can be used to generate a volume mesh from a well prepared surface mesh.

The three types of meshing models are as follows:

  • Tetrahedral - tetrahedral cell shape based core mesh
  • Polyhedral - polyhedral cell shape based core mesh
  • Trimmed - trimmed hexahedral cell shape based core mesh

Once the volume mesh has been built, it can be checked for errors and exported to other packages if desired.

solid mesh

Mesh type as per Grid structure

A grid is a cuboid that covers entire mesh under consideration. Grid mainly helps in fast neighbor manipulation for a seed point.

mesh grid

Meshes can be classified into two divisions from the grid perspective, namely Structured and Unstructured mesh. Let us have a look at each of these types.

Structured Mesh: Structured meshes are meshes which exhibits a well-known pattern in which the cells are arranged. As the cells are in a particular order, the topology of such mesh is regular. Such meshes enable easy identification of neighboring cells and points, because of their formation and structure. Structured meshes are applied over rectangular, elliptical, spherical coordinate systems, thus forming a regular grid. Structured meshes are often used in CFD.

structured mesh

Unstructured Mesh: Unstructured meshes, as the name suggests, are more general and can randomly form any geometry shape. Unlike structured meshes, the connectivity pattern is not fixed hence unstructured meshes do not follow a uniform pattern. However, unstructured meshes are more flexible. Unstructured meshes are generally used in complex mechanical engineering projects.

Unstructured Mesh