At the heart of the algorithms described are so-called “displaced signed distance fields”, which augment the near ubiquitous signed distance field representation with a displacement field, specifying the offset from the input approximation to the true surface. This implicitly encodes smoothly curved or fine-detailed surfaces with respect to a coarse tessellation. For 3D printing, the models generated by human operators or by a scanning pipeline must be converted into polygon meshes. For a fixed print size, a fixed number of polygons suffices to print the object at the precision of the printer, but for larger print sizes, they must more finely tessellated, potentially with many more polygons.
The example of a plain sphere illustrates the problem: the printed sphere may appear round with a certain number of polygons, but if the object is printed larger with the same polygon mesh, the sphere no longer appears round. Displaced signed distance fields encode the difference between the piecewise flat input mesh and the true surface of the sphere, at the precision of the 3D printer.
Displaced signed distance fields represent the surface of the shape implicitly, allowing for volumetric regularization of the implicit function and robust computation from incomplete or self-overlapping surface data. This is especially relevant in 3D printing, as information processed in situ cannot be corrected. The new algorithms of the Cuttlefish® 3D printer driver thus facilitate highly detailed and smooth surfaces from low-poly meshes, in a robust, streaming compatible approach.