Polygon Mesh

When working on a shoe prototype from the file generated by the verification, we obtain what we call a polygonal mesh.
Let’s understand better the structure of what this represents.

In 3D computer graphics and solid modeling, a polygon mesh is a collection of vertices, edges and faces that defines the shape of a polyhedral object. The faces usually consist of triangles (triangle mesh), quadrilaterals (quads), or other simple convex polygons (n-gons), since this simplifies rendering, but may also be more generally composed of concave polygons, or even polygons with holes.

Volumetric meshes are distinct from polygon meshes in that they explicitly represent both the surface and volume of a structure, while polygon meshes only explicitly represent the surface (the volume is implicit).

Elements

Objects created with polygon meshes must store different types of elements. These include vertices, edges, faces, polygons and surfaces. In many When generating a digital file from a scanned shoe, we obtain polygons meshes that store different types of elements. This includes vertices, edges, faces, polygons and surfaces. In many applications, only vertices, edges and faces or polygons are stored.

A renderer can only support three-sided faces; therefore, polygons must be constructed with many of them, as shown above. However, many renderers support quads and polygons on the higher sides, or can convert polygons to triangles quickly, making it unnecessary to store a triangular mesh.

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. A polygon is a coplanar set of faces. In systems that support multi-sided faces, polygons and faces are equivalent. However, most rendering hardware supports only 3- or 4-sided faces, so polygons are represented as multiple faces. Mathematically a polygonal mesh may be considered an unstructured grid, or undirected graph, with additional properties of geometry, shape and topology.

Surfaces

Curves are 2D objects, and surfaces are their extension in 3D. Surfaces are also manipulated with control points. Very useful for simple shapes, but very organic and rounded. More often called smoothing groups, they are useful, but are not necessary for grouping smooth regions.

Consider shoes with a rounded upper. For smooth shading on the sides, all normal surfaces must point horizontally away from the center, ie outside the model. Rendered as a single surface, shaded by Phong, the vertices of the crease would have incorrect normals. Thus, some way is needed to determine where to stop smoothing to group smooth parts of a mesh, just as polygons group faces on three sides.

As an alternative to providing surfaces / smoothing groups, a mesh can contain other data to calculate the same data, such as a division angle (polygons with normal values ​​above this limit are automatically treated as separate smoothing groups or some technique such as division or chamfer is automatically applied to the edge between them). In addition, high resolution meshes are less subject to problems that would require smoothing groups, as their polygons are so small that they make the need irrelevant.

In addition, there is another alternative in the possibility of simply detaching the surfaces themselves from the rest of the mesh. Renderers do not attempt to smooth edges between non-contiguous polygons.

Groups

It is possible to separate all parts of a shoe into groups that define separate elements of the mesh.
This process is extremely useful for preparing the same model to receive different materials.

Materials

The materials will be defined, allowing different parts of the mesh to use different shaders when rendered. uppers, soles, heels, everything that makes up a shoe can receive independent materials.

UV coordinates

The mesh must be prepared to receive UV coordinates or UV mapping. That is, the 2d representation separated from the “unfolded” mesh to show which part of a two-dimensional texture map should be applied to different mesh polygons.
It is also possible that the meshes contain other information of vertex attributes, such as colors, tangent vectors, normal maps, gloss, etc.

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