STL Files and Triangle Meshes

Parametric Surface and Triangulated Representation

The STL-format is the industrial standard for handling triangulated meshes. STL-files contain a plain list of three-dimensional corner point coordinates and flat triangles. The triangles, also referred to as faces, are defined by three corner points and have an inside and an outside. Adjacent triangles may use common corner points and share the same edges, which results in a coherent triangle mesh. The generality and simplicity of this concept makes STL-files compatible to a lot of applications.

However, they do not contain any topological information about the mesh. This may cause errors when CAD files with different file formats are converted to STL, especially if they are created with poorly engineered algorithms. The netfabb Studio software is a specialized software to detect and repair these kinds of damages and create faultless meshes without holes, deformations or intersections. These meshes can then be converted into slice files ready for additive manufacturing.

The STL format aims for a precise approximation of bodies in three-dimensional space. Although other CAD formats have advantages in that respect, a variety of applications need a surface representation consisting of flat triangles. These are:

- Accelerated rendering in multimedia applications

- Solving partial differential equations

- Computer aided engineering

- Rapid prototyping and additive manufacturing

However, a simple collection of triangles will not always create a solid body. For a good triangle mesh that can be used for 3D printing, the mesh has to be valid, closed, oriented and should not contain any self-intersections.

Validity:

Two edges of adjacent triangles which lie on top of each other are only regarded as one edge, if they have equal end points. Thus, the simple mesh in the first image below consists of two triangles and has exactly five edges: four border edges and one interior edge. Border edges belong to only one triangle, while interior edges connect two triangles.

A mesh is only regarded as valid, if interior edges have the same corner points for both adjacent triangles. Only then, all neighbouring triangles are connected by a whole interior edge. No neighboring triangles are split and a smooth topology is created.

This validity is an essential property of most calculations. If two edges have only one common corner point, they will be defined as two border edges, even if they are on top of each other.

A simple mesh with 5 edges: four border edges and one interior edge

An invalid triangulation (left) compared to a valid triangulation (right)

One valid and one arbitrary chaotic mesh

Closedness:

Parts can only be used for 3D printing, if their surface is closed. This means that there are no holes and no border edges. Every edge has to be attached to exactly two triangles and all neighbouring triangles have to share an interior edge.

Closedness may separate a mesh into several components called shells.

A closed surface (left) and a surface with holes (right)

A mesh consisting of 60 disjoint shells

Two disconnected (left) and two connected triangles (right)

Orientability:

For the conversion of triangle meshes into slice data ready for 3D printing, it is vital that the parts are oriented correctly. The orientation defines the outside and the inside of a part.

The orientation of a part is determined by the orientation of all triangles. The order of the points defining a triangle defines its orientation by the "right-hand-rule" (see image). If the orientations of all neighbouring triangles conform to each other and there are no flipped triangles, a closed shell separates between outside and inside. But if there are flipped triangles, this may not be possible. Thus, even closed parts may be faulty.

The orientation of a triangle is determined by the order of its points

Self-Intersections:

Finally, the surface of a solid body should not contain any self-intersections. These occur whenever triangles or surfaces of one part cut through each other. For many applications, self-intersections are very impractical, especially if the mesh shall be processed further.

For most additive fabrication processes, three-dimensional data has to be converted into two-and-a-half-dimensional slice data. Here, self-intersections in the original data result in self-intersection in the slices. These might cause constructional failures or instabilities. Therefore, it is essential to remove self-intersections during the preparation of files.

Self-Intersection: The two cubic shells cut through each other

Left: A mesh consisting of two shells with self-intersection. Right:A mesh consisting of one, non-intersecting shell