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.

翻译：增材制造通过逐层累积固化材料来构建实体物体，这一过程通常采用水平平面层进行。然而，熔丝打印机具备沿三维曲线挤压材料的能力。这种非平面沉积（亦称非平面打印）的思路催生了一系列研究趋势，旨在开发能从三维物体自动生成非平面沉积路径的算法。本文提出了一种针对此目标的新型算法。我们的方法优化了一个弯曲切片曲面。将该曲面与输入模型相交，可提取非平面层，目标是在避免碰撞的同时精确再现模型顶面。我们的公式推导出了一种简单高效的求解方案，仅需解决单个最小二乘问题。值得注意的是，该方法无需对输入进行四面体化或迭代求解器处理，同时比简单方法更具通用性。我们进一步探索了如何使路径沿表面主曲率方向定向、如何过滤破坏结果的虚假微小特征，以及如何在同个零件中实现平面与非平面策略的良好平衡。我们给出了完整的公式推导及其实现，并在多种3D打印模型上验证了该方法。