QuickCurve: revisiting slightly non-planar 3D printing

Additive manufacturing builds physical objects by accumulating layers upon layers of solidified material. This process is typically done with horizontal planar layers. However, fused filament printers have the capability to extrude material along 3D curves. The idea of depositing out-of-plane, also known as non-planar printing, has spawned a trend of research towards algorithms that could generate non-planar deposition paths automatically from a 3D object. In this paper we introduce a novel algorithm for this purpose. Our method optimizes for a curved slicing surface. This surface is intersected with the input model to extract non-planar layers, with the objective of accurately reproducing the model top surfaces while avoiding collisions. Our formulation leads to a simple and efficient approach that only requires solving for a single least-square problem. Notably, it does not require a tetrahedralization of the input or iterative solver passes, while being more general than simpler approaches. We further explore how to orient the paths to follow the principal curvatures of the surfaces, how to filter spurious tiny features damaging the results, and how to achieve a good compromise of mixing planar and non-planar strategies within the same part. We present a complete formulation and its implementation, and demonstrate our method on a variety of 3D printed models.