### What is Mesh and what are the types of Meshing

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 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.

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.

##### 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.

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.

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.

### What is Reverse Engineering ?

Let us start with an example. One day you get into your garage and find on the workbench a 'black box'. Stricken by curiosity, you build up an urge to discover what it 'is' and what it 'does'. You start with an inspection of the box's dimensions, color. Then you try to find its purpose and then how it operates. Not satisfied, you try to open it, break it apart, piece by piece in an attempt to understand what each component does and build up a pattern of how they would all interact together as one system. Finally you reach the end of your inquisition. You now fully (or partially) understand the box. This very approach is termed as Reverse Engineering.
Reverse engineering, also known as back engineering, is the process where a man-made object is dismantled completely to reveal its architecture, design or to extract knowledge from the object about its functioning and structural integrity.

##### Why do you need Reverse Engineering?

There might be innumerable reasons to adopt reverse engineering process. Some of the common cases are as follows:

• The original manufacturer of a particular product no longer produces it. In some cases, situations arise where original manufacturer ceased to exist, but a customer needs the product. Then there are cases where an original supplier is unable or unwilling to provide additional parts
• There is inadequate documentation or no documentation at all of the original design
• To enhance and strengthen the good features of a product based on its long-term usage
• To analyze the shortcomings of the product, thereby exploring new possibilities to improve product performance and features
• To update obsolete materials or replace outdated manufacturing processes with more current, less-expensive technologies
• The CAD model is not sufficient to support current manufacturing process; hence creating 3D models