QuickCurve: revisiting slightly non-planar 3D printing

TL;DR

This work tackles the staircase defects inherent in planar slicing by introducing QuickCurve, a method that optimizes a non-planar slicing surface $ S$ to reproduce top surfaces of a model with curvature-aware deposition on 3-axis printers. The approach uses a single least-squares optimization, augmented by per-component vertical offsets $z_c$ and a gradient-target term $H_{target}$ derived from a target slope $ heta_{target}$, all while enforcing a collision-safe constraint $ heta_{max}$ and employing a post-processing step to guarantee manufacturability. Toolpaths are oriented according to surface curvature, enabling either alignment with the maximum or minimum principal curvature, and a filtering stage with radius $ ho$ removes tiny surface features that could corrupt curved regions. The method is demonstrated on various models, showing improved surface finish on top surfaces and offering a favorable trade-off between computational efficiency and generality compared with existing volume-deformation or pure-curved-layer approaches. Overall, QuickCurve provides a practical, efficient framework for achieving curved surface deposition on standard 3-axis printers, with a tunable balance between curved and planar regions and strong potential for integration with multi-axis platforms in the future.

Abstract

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.

Figures (16)

• Figure 1: Our technique starts from a 3D model to be 3D printed (left) using non-planar deposition to reproduce the top surface accurately (second, bottom). Our technique optimizes for a slicing surface (second, top) that is used to extract non-planar layers (third). The rightmost figure illustrates how the optimized slicing surface (dashed line) will precisely align with the top surfaces, extracting a layer that follows the curvature. We further propose a novel strategy capable of aligning the toolpaths along the curvature. Our approach allows complex parts to be printed with a non-planar surface finish (rightmost). (Zoom in for details).
• Figure 2: The two-towers model. The approach of Ahlers et al. ahlers_19_3d used in this Figure cannot curve the middle part as it would produce collisions during printing. The result of our approach follows all surfaces, with curved layers throughout the part as shown in Figure \ref{['fig:teaser']}.
• Figure 3: From left to right: A shape with sloped surfaces, the slicing surface optimized by our approach, the obtained trajectories. All surfaces are exactly reproduced (zoom for details). Note how the vertical ridges do not prevent curving the top surfaces.
• Figure 4: Left: The green surfaces are specified in $\Theta$, the red ones are free as their slopes exceed $\theta_{target}$. The relative heights of the green surfaces makes it impossible to find a slicing surface with slopes everywhere below $\theta_{max}$. Right: By allowing the green surfaces to 'float' up and down during optimization, our method computes the dashed line as a slicing surface. It exactly reproduces all surfaces in $\Theta$.
• Figure 5: Top: Half a cylinder (left) and the trajectories produced by our technique (right). Note the curved top. Bottom: Showing half of the bottom layers (left) reveals the shape of the slicing surface (right). The back of the slicing surface is a smooth free region where the extruder travels when the print starts.