This paper presents a new method to fabricate 3D models on a robotic printing system equipped with multi-axis motion. Materials are accumulated inside the volume along curved tool-paths so that the need of supporting structures can be tremendously reduced - if not completely abandoned - on all models. Our strategy to tackle the challenge of tool-path planning for multi-axis 3D printing is to perform two successive decompositions, first volume-to-surfaces and then surfaces-to-curves. The volume-to-surfaces decomposition is achieved by optimizing a scalar field within the volume that represents the fabrication sequence. The field is constrained such that its isovalues represent curved layers that are supported from below, and present a convex surface affording for collision-free navigation of the printer head. After extracting all curved layers, the surfaces-to-curves decomposition covers them with tool-paths while taking into account constraints from the robotic printing system. Our method successfully generates tool-paths for 3D printing models with large overhangs and high-genus topology. We fabricated several challenging cases on our robotic platform to verify and demonstrate its capabilities.

Additive manufacturing (AM) and topology optimization (TO) form a pair of complementary techniques in transforming digital models into physical replicas: AM enables a cost-effective fabrication of geometrically complex shapes, while TO provides a powerful design methodology for generating optimized models, which are typically complex from a geometric perspective. The potential of both techniques has recently been explored in graphics, resulting in fantastic applications especially regarding structural and aesthetic properties of fabricated models. In this tutorial, we start from the fundamentals of AM and TO, and proceed to advanced TO techniques which steer the optimization process, i.e., taking into account the manufacturing as well as aesthetic appearance.