### Stable

Can easily handle geometries represented with over 20 Million triangles.

### Fast and Efficient

With enough recourses slicing any geometry can be reduced to a matter of seconds. But the algorithm also allows efficient and fast slicing of detailed geometry on low resources.

### Optimized workflow

The slicing algorithm works with an STL file. But the proposed new file format for geometry data would further increase slicing speed as indexing would be eliminated. And it could enable direct printing of geometry from the proposed 3D file, while slicing takes place in the background within the printer itself.

## The Key Element

The algorithm is based on a modified representation of the triangles in an STL file with tetragons (quadrangles) comprised of two triangles.

Notation of the tetragon is different from more common representations such as e.g. in a VTK file. The tetragon in the image is denoted with 2134 instead of the common approach with 2413. The former contains information about the two triangles building the tetragon and their normal orientations.

## Sort & Index

When starting from an STL file the first step is to eliminate redundant points and define the tetragons. A tetragon is defined for each edge.

The image shows an example of how the connectivities are written for the sketched triangles with normals pointing out of the screen. Each edge must have only one tetragon defined for it.

A simple indexing can be used to easily find an edge in the list, or rather all the connections of a vertex with other vertices.

Additional sorting of edges according to their locations on the slicing axis will further enhance speed.

## Slice

The first intersection is found with an efficient search that includes only edges close to the slicing plane. The following points to build the cross section can easily be found in an orderly fashion.

With the first intersection c_{1} in the image the second intersection can only exist in the edges 31, 32, 41 or 42. If a direction is already set (with a choice of clockwise or anti-clockwise rotation) the possibility is reduced to two edges. After the second intersection c_{2} is found in edge 41 the algorithm finds edge 41 in the list, where the other 2 possible edges for the next intersection are given.

## The File Format

The algorithm explained here starts from an STL file. To optimize speed, accuracy and stability of the slicing algorithm, the file format represented in the image is recommended.

This file format contains all the information in an STL file in a more compact form, and it is already sorted and indexed.

If this file format is used with the proposed algorithm slicing efficiency and stability in 3D printing would benefit immensely from it.

## You see the benefits

Then please don’t hesitate to contact us! We are looking for interested parties to implement the algorithm for commercial 3D printing and also for publishing comparisons with other methods to establish its benefits.

Keep in mind that a patent application has been filed. Please talk to us before implementing any code.