Section: New Results

Highlights of the Year

Fabrication: We proposed a novel technique to automatically generate support structures for additive manufacturing with filament based processes. The deposited filament has to be properly supported at all times, which complicates printing of overhanging shapes: a disposable support has to be generated to temporarily hold the filament deposited above. Existing techniques either generate large structures, wasting material, or generate very thin structures that are hard to print and prone to failure. In contrast, our technique optimizes a scaffolding which is made of vertical pillars and horizontal bridges – such horizontal bridges print properly as long and the filament is deposited in straight line from one pilar to the next. We showed how to formulate scaffolding generation as a minimization problem and proposed a heuristic algorithm based on an efficient plane sweeping approach. The work was published [9] in ACM Transactions on Graphics in 2014 (proceedings of SIGGRAPH 2014). It is integrated within our 3D modeler for additive manufacturing, IceSL.

Optimal transport: this is an active research topics in the mathematics community. Given two measures $\mu$ and $\nu$, optimal transport defines a distance between $\mu$ and $\nu$, as the minimum cost of “morphing” $\mu$ into $\nu$. This distance (called the Wasserstein distance) structures the space of measures and offers new ways of solving some highly non-linear PDEs (Monge-Ampere, Fokker-Plank ...). This requires a numerical way of computing the Wasserstein distance and its gradients. We studied a semi-discrete technique [21] submitted to ESAIM J. M2AN), that optimizes power diagrams. This is to our knowledge the first numerical implementation of optimal transport for volumetric densities (computes the Wasserstein distance between a sum of Dirac masses and a piece-wise linear density supported on a tetrahedral mesh).