Polygon mesh

A polygon mesh (often just called a mesh or mesh model) is a representation of a 3D object's surface made of vertices, edges and faces, most often triangles. Each vertex has its own coordinates, and each face references three or more vertices. A mesh describes only the surface, not design features, dimensions or parameters.

Unlike a CAD model, which describes surfaces with exact mathematics (planes, cylinders, NURBS surfaces), a mesh only approximates curved surfaces with flat facets. A cylinder in a mesh is really a many-sided prism, and the accuracy of the approximation depends on facet size. When exporting from a CAD system, it is controlled by the chordal deviation and angle tolerance; in a scan, by the density of measured points. The mesh of a scanned part typically has hundreds of thousands to millions of triangles.

In 3D scanning, the mesh is generated from the point cloud by triangulation. Cleanup follows: removing noise and outliers, filling holes, smoothing and decimation, that is, reducing the triangle count where it is not needed. For 3D printing and most other operations, the mesh must be closed (watertight), with no self-intersections, no flipped normals and no edges shared by more than two faces (non-manifold edges).

The most common formats are STL (triangles only, with no colors and no unit information), OBJ (also supports color textures), PLY (common for scanner data, including point colors) and 3MF (carries units, colors and other data for 3D printing).

A mesh is enough wherever you need the shape but not parametric geometry: 3D printing (slicers work with meshes), visualization and presentations, digital archives, comparing a manufactured part with its CAD model, and designing parts that fit organic shapes, such as orthoses, handles or covers for a scanned body part or machine. In a CAD system, a mesh can be inserted as a reference body and a mating part designed around it.

You need a CAD model instead of a mesh when the part will be machined, dimensioned on a drawing, toleranced or modified further. In a mesh, you cannot simply enlarge a hole diameter or move a hole, and precise flat and cylindrical surfaces are hard to program from it. Conversion to a CAD model is the job of scan to CAD.

STL carries no units. A file created in millimeters can therefore be read in inches, and the part becomes 25.4 times larger. Always state the units when you hand over data, or use 3MF. When exporting from CAD for 3D printing, set a fine enough chordal deviation, or facets will show on curved surfaces, but not a needlessly fine one, or the file will run to hundreds of megabytes.

With meshes from scanning, ask what was edited. Smoothing removes noise but also sharp edges and fine details, and filled holes contain a computed shape, not a measured one. For measurement and comparison, ask for a mesh with minimal edits or with the filled areas marked, and agree on the coordinate system it is aligned in.

Do not confuse a polygon mesh with the finite element mesh used in finite element analysis (FEA), which divides a solid into elements for structural or thermal calculations.