3D PRINTERS: A NEW CHALLENGE FOR MATHEMATICAL MODELING

Abstract. This short communication aims at creating a bridge between 3D printing and advanced mathematical methods. We review some features of 3D printing in order to show how 3D printers ’ software can benefit from mathematical methods. To prove the feasibility of one possible PDE-based approach, we use a classical model for the Shape-from-Shading problem to create a 3D object starting from a single 2D photograph, and we 3D-print it! 1. New modeling needs. Is a new industrial revolution coming? Many people think so: 3D printers are able to create almost any solid object one can image and replicate existing ones. Nowadays, the price of a 3D printer is small enough to allow many people to have one at home, and create their own plastic objects (works of art, toys, glasses, covers for cell phones, spare parts of any kind, etc.). Within a decade, some products may be downloaded from the Internet for printing at home, causing a revolution in the market of such a small objects. One can also print at home some parts of an object and buy the others at shops, then assemble the final product by himself. Most important, the number of printable materials is growing and it is already possible printing an objec