Neural Slicer for Multi-Axis 3D Printing

TL;DR

This work addresses curved-layer generation for multi-axis 3D printing across models with diverse representations by introducing a neural, representation-agnostic slicer. It learns a differentiable mapping $\lambda(\mathbf{q}(\mathbf{x}),\mathbf{s}(\mathbf{x}))$ on a caging mesh to produce a scalar field $G(\mathbf{x})$, whose isosurfaces form curved layers; losses defined on $\nabla G(\mathbf{x})$ directly encode manufacturing objectives like SF and SR. The approach combines ARAP-based deformation, SIREN-based NN architectures, and DC3-constrained optimization to achieve fast, robust slicing that is less sensitive to initial guesses and applicable to complex topologies, with validation via FEA and physical prints. It demonstrates significant improvements in overhang reduction and mechanical performance, and confirms the practicality of deploying a neural, differentiable slicer in multi-axis fabrication workflows. Limitations include isotropic assumptions for SR and reliance on a cage representation, pointing to future work on differentiable stress analysis and end-to-end hardware integration.

Abstract

We introduce a novel neural network-based computational pipeline as a representation-agnostic slicer for multi-axis 3D printing. This advanced slicer can work on models with diverse representations and intricate topology. The approach involves employing neural networks to establish a deformation mapping, defining a scalar field in the space surrounding an input model. Isosurfaces are subsequently extracted from this field to generate curved layers for 3D printing. Creating a differentiable pipeline enables us to optimize the mapping through loss functions directly defined on the field gradients as the local printing directions. New loss functions have been introduced to meet the manufacturing objectives of support-free and strength reinforcement. Our new computation pipeline relies less on the initial values of the field and can generate slicing results with significantly improved performance.

Figures (23)

• Figure 1: An illustration of the distortion caused by indirect optimization in $S^3$-Slicer: (a) the layers generated in the deformed space, and (b) curved layers in the model space obtained by the mapping. In the deformed space, the support-free requirement has been fulfilled -- i.e., the angle between the printing direction and surface normal is less than $135^\circ$. However, the angle expands when mapped back to the model space, resulting in a larger overhang area (see also the 3D printing result shown in Fig.\ref{['fig:result-ring']}).
• Figure 2: An overview of our neural slicer to generate curved layers for multi-axis 3D printing. (a) The input Yoga model $\mathcal{M}$ with its implicit solid $H(\mathbf{x})$ and the distribution of principal stresses obtained from voxel-based FEA. (b) A volumetric mesh $\mathcal{C}$ caging the input model $\mathcal{M}$ is constructed, serving as the intermediate representation in numerical computation. (c) Two continuous functions $\mathbf{q}(\mathbf{x})$ and $\mathbf{s}(\mathbf{x})$ specify the quaternion and the scaling ratios of local deformation for all $\mathbf{x}\in \mathbb{R}^3$, which are represented as neural networks (NN) to be optimized. (d) The function values of $\mathbf{q}(\mathbf{x})$ and $\mathbf{s}(\mathbf{x})$ are sampled to drive a differential deformation to obtain a deformed caging mesh $\mathcal{C}^d$ therefore also the mapping $\lambda(\mathbf{q}(\mathbf{x}),\mathbf{s}(\mathbf{x}))$. (e) The scalar field $G(\mathbf{x})$ is obtained from the mapping, with its gradient $\nabla G(\mathbf{x})$ serving as local printing directions (LPDs) that play a pivotal role in formulating the loss functions utilized for optimization. (f) After computing an optimized $G(\mathbf{x})$, its isosurfaces are extracted on the caging mesh $\mathcal{C}$ and trimmed by the implicit solid $H(\mathbf{x})$ to obtain the curved layers.
• Figure 3: The illustration of cage generation: (a) the implicit surface $H(\mathbf{x})$ (gray) of the input model $\mathcal{M}$ in an abstract representation (e.g., as a convolution surface of the skeletons illustrated in black curves), (b) the polygonal mesh of $H(\mathbf{x})=0$ (yellow) and the caging surface mesh (black), (c) the tetrahedral mesh (purple) caging the input model.
• Figure 4: The illustration of slicing process to generate the curved layers: (a) a scalar field $G(\mathbf{x})$ that is optimized on the volumetric caging mesh $\mathcal{C}$, (b) the isosurfaces of $G(\mathbf{x})$ as polygonal surface meshes $\{\mathcal{G}_i \}$ are extracted from $\mathcal{C}$'s tetrahedra -- the colors on an isosurface visualize the function values of $H(\mathbf{x})$, and (c) the curved layers $\{\mathcal{P}_i \}$ are obtained by trimming $\{\mathcal{G}_i \}$ with the implicit solid $H(\mathbf{x}) \leq 0$.
• Figure 5: The result generated by our Neural Slicer vs. the result by a planar slicer on the Shelf model: (a) the stress field under the given forces (shown as the arrows) and the model's cage used in the computation, (b) the curved layers (bottom) generated from the mapping determined by a deformed cage (top), (c) the histograms for evaluating the quality of results in terms of (top) the angles between LPDs and surface normals for the SF requirement and (bottom) the angles between LPDs and the maximal stresses for the SR requirement, (d) the results of FEA simulation by using anisotropic material orientations defined according to the LPDs for planar layers (top) and our curved layers (bottom).