Iterative carving for self-supporting 3D printed cavities

Additive manufacturing technologies fabricate objects layer by layer, adding material on top of already solidified layers. A key challenge is to ensure that there is always something below the layer being fabricated: otherwise added material simply falls under the effect of gravity -- this is a critical issue with most technologies. This difficulty is typically treated differently for the interior and the exterior of an object: the exterior is supported through structures akin to scaffoldings that are removed afterwards, while the interior volume is filled with a sparse, self-supporting infill pattern. The infill acts as a support for the tops and also provides mechanical strength to the final print. However, as objects grow in size even sparse infills become prohibitively expensive in time and material usage, and if made too sparse they no longer provide the required support. This prevents printing large objects with empty interiors. In this work we investigate how to compute as large as possible self-supporting empty cavities. Our technique is based on an iterated geometric carving algorithm, that is fast to compute and produces nested sets of inner walls. The walls have exactly the minimal printable thickness of the manufacturing process everywhere. Remarkably, our technique only manipulates two consecutive slices of the model at a time, sweeping through the model along the vertical direction, from top to bottom. We discuss an efficient, robust implementation in details, based on a filtered polygonal medial axis extraction and an exact polygon offsetting technique. Using our approach, we can print large parts on filament printers using as little as a single filament thickness, providing on order of magnitude reduction in print time and material use while \textit{guaranteeing} printability.