Efficient contouring of functionally represented objects for additive manufacturing. (December 2020) - Popov, Dmitry; Maltsev, Evgenii; Fryazinov, Oleg; Pasko, Alexander; Akhatov, Iskander
Abstract: Functionally (implicitly) defined 3D objects allow us to quite easily model parts with complex topology such as lattices and organic-like structures with a high level of flexibility. Previous works in this area are based on the direct generation of CNC programs for the 3D printing of these objects and are backed by the growing support for this input format from hardware manufacturers. Efficient contouring of functionally defined models, however, is not an easy task. In this paper, we develop an algorithm for contour extraction of implicitly defined objects for direct additive manufacturing (AM). By comparing various adaptive and exhaustive (non-adaptive) methods of the function representation contouring for AM (FRepCAM), we make a set of recommendations for its usage depending on the specific resolution of the printer. In particular, we use a novel criterion based on affine arithmetic to maintain efficiency while preserving the robustness of the contouring process. The techniques mentioned were evaluated for algebraic and non-algebraic solids and heterogeneous models under a resolution that is comparable with that of current AM technology. The results show that the chosen adaptation criteria allow us to efficiently obtain a contour for complex models and generally outperform those of traditional algorithms based on exhaustive enumeration, especially for high-resolution contouring. In addition, the results present proof of the printability of implicitly defined objects with different 3D printing techniques. Graphical abstract: Highlights: We revisit the concept of direct manufacturing with geometry represented by function representation (FRep) when the slices are generated directly without an intermediate step of surface generation. We compare various adaptive and exhaustive (non-adaptive) methods of the contour extraction of the FRep curves including exhaustive enumeration and reliable methods based on interval arithmetic. A novel criterion based on the affine arithmetic to keep efficiency while preserving robustness of the contouring process is presented. We make a set of recommendations for their usage depending on the specific resolution of a printer. We present the results of contouring with the resolution of up to 10 μ m.