Neural SDF-Based CAD Parts

• Neural SDF-based CAD parts are advanced 3D representations using neural networks to model geometric surfaces via signed distance functions for CAD applications.
• They enable high-fidelity reconstruction, precise segmentation, and effective deformation while ensuring surface regularity and semantic coherence.
• Cutting-edge methods integrate dynamic CSG trees, curvature regularization, and scalable architectures to support efficient, interactive CAD workflows.

Neural SDF-based CAD parts refer to the application of neural networks—particularly implicit neural representations built on signed distance functions (SDF)—to model, reconstruct, segment, synthesize, and manipulate computer-aided design (CAD) components in 3D space. SDFs encode shapes via functions $f(\mathbf{x})$, with the zero-level set $f(\mathbf{x})=0$ defining the surface. Neural SDF approaches have demonstrated state-of-the-art performance on tasks from high-fidelity surface modeling to semantically consistent segmentation, parametric part-aware synthesis, and deformation. Key advances include dynamic CSG tree discovery, curvature-aware regularization, interactive editing interfaces, scalable architectural designs for large assemblies, and unified pipelines that combine geometry, semantics, and photorealistic rendering. Methods typically train multilayer perceptrons (MLPs)—often using SIREN sinusoidal activations—subject to reconstruction, developability, and segmentation losses. The field continues to evolve through efficient architectural innovations and practical integrations with established CAD workflows.

1. Implicit SDF Representations for CAD Geometry

Neural SDF representations encode the geometry of CAD parts via networks that output the signed distance to the nearest surface for each point in space. For a shape $S$, the SDF $f(\mathbf{x})$ is given by: $$f(\mathbf{x}) = \begin{cases} +d(\mathbf{x}, \partial S), & \mathbf{x} \notin S \ -d(\mathbf{x}, \partial S), & \mathbf{x} \in S \end{cases}$$ where $d(\mathbf{x}, \partial S)$ is the Euclidean distance to the boundary. Neural implicit methods, notably leveraging sinusoidal activations (SIREN) (Kania et al., 2020, Vasilopoulos et al., 2023, Dong et al., 20 Apr 2024, Yin et al., 19 Jun 2025), scale efficiently, enable gradient-based surface normal computation, and yield surfaces of arbitrary resolution.

To enable surface extraction and rendering, volume density is computed from the SDF using parametric functions, e.g.: $$\sigma(\mathbf{x}) = s e^{-s f(\mathbf{x})} / [1 + e^{-s f(\mathbf{x})}]^2$$ Further, neural SDFs support continuous differentiable operations, essential for downstream CAD tasks such as blending, CSG, and deformation.

2. Structured, Part-Aware, and Segmentation-Aware Modeling

Accurate representation of composite CAD parts demands modeling structured assemblies and segmenting objects into meaningful components. Approaches fall in two categories:

• Explicit part-aware modeling, as in PartSDF (Talabot et al., 18 Feb 2025), where each CAD part is assigned a latent code $z_p$, pose parameter $p_p$, and a local SDF network, allowing manipulation and optimization at the part level. The network uses latent modulation and cross-part 1D convolutions, recovering the global SDF as the minimum over component SDFs.
• Dynamic segmentation and instance discovery applies methods such as ClusteringSDF (Wu et al., 21 Mar 2024) and Joint Neural SDF Reconstruction and Semantic Segmentation (Fan et al., 4 Oct 2025), fusing geometric and semantic pathways in a neural SDF backbone with segmentation heads. Supervision can use mesh-level part fields or unsupervised clustering with probabilistic simplex losses.

Performance evaluations confirm that part-aware architectures, supervised with ground truth or automated labels, yield superior Chamfer distances, Intersection over Union (IoU), and segmentation consistency, while also facilitating optimization and generation tasks.

3. Curvature, Developability, and Geometric Regularity

CAD-style surfaces are often piecewise developable, composed of planar, cylindrical, or conical regions. To favor such geometric properties, methods regularize principal curvatures:

• Gaussian curvature penalization is applied in NeurCADRecon (Dong et al., 20 Apr 2024): minimizing

$$L_\text{Gauss} = \frac{1}{|\Omega|} \int_{\Omega} DT(|k_\text{Gauss}(\mathbf{x})|)\,d\mathbf{x}$$

where $k_\text{Gauss}(\mathbf{x})$ is derived from the SDF Hessian, and $DT(\cdot)$ is a double-trough tolerance function permitting sharp tips.

• Mixed second-derivative proxies in FlatCAD (Yin et al., 19 Jun 2025): regularizing the off-diagonal Weingarten map term $S_{12}$, approximated by finite difference

$$D_{uv}^+ = \frac{f_{uv} - f_u - f_v + f_0}{h^2} \simeq u^\top H_f(x) v$$

and normalized by $\|\nabla f(x)\|$, encourages uniform curvature without demanding full Hessian computation.

Proxy-based regularization was shown to halve GPU memory usage and wall-clock time, matching or exceeding Hessian-based methods’ fidelity on benchmarks.

4. Scalable, Modular, and Efficient Architectures

Large-scale and complex CAD assemblies benefit from scalable SDF modeling:

• Divide-and-conquer architectures (Yang et al., 15 Jan 2025) partition objects or scenes into overlapping regions, assigning independent local SDF networks and blending outputs via softmaxed weights: $$f_{ij}(x) = \omega_i(x)\,f_i(x) + \omega_j(x)\,f_j(x)$$ Registration across overlapping regions uses least-squares transformations and volume rendering alignment. This modular design allows independent part extraction, localized editing, and parallelizable training.
• Hierarchical online incremental approaches (Vasilopoulos et al., 2023) combine coarse voxel grids (for global backbone) and local SDF networks (for fine detail), incrementally updating as new sensor data arrives. These methods avoid catastrophic forgetting and are space-efficient, supporting interactive CAD workflows.

5. SDF-Based Boolean and Constructive Solid Geometry Operations

Constructive Solid Geometry (CSG) operations (union, intersection, difference) are central to CAD editing. UCSG-Net (Kania et al., 2020) learns a parse tree of primitives and Boolean operators in an unsupervised manner using differentiable occupancy functions. Occupancy for each primitive is soft-binarized as

$\mathcal{O} = \left[1 - D / \alpha \right]_{0,1}$

with learnable steepness parameter $\alpha$. Differentiable Boolean compositions are then applied: $$\begin{aligned} A \cup^* B &= [A + B]_{0,1}\ A \cap^* B &= [A + B - 1]_{0,1}\ A -^* B & = [A - B]_{0,1} \end{aligned}$$ Dynamic selection of operand primitives and operators via softmax and Gumbel-Softmax sampling builds interpretable CSG trees replicable within CAD software, supporting modification and reverse engineering.

6. Interactive Editing, Deformation, and Generative Modeling

Direct manipulation and generation of CAD surfaces via neural SDFs have been enabled:

• Interactive sculpting frameworks such as INST-Sculpt (Rubab et al., 5 Feb 2025) leverage stroke-based locality, custom brush profiles, and tubular sampling to provide region-specific surface edits. The deformation loss

$L_\text{deformation} = \mathbb{E}[|f_\theta(p')|]$

aligns the displaced surface points on the updated SDF.

• Decomposition and segmentation for mesh manipulation is achieved via learned SDF diameter fields (Roy, 2023) and graph-cut algorithms, which segment CAD models into semantically consistent regions, facilitating design editing and mapping.
• Generative modeling: SDF-3DGAN (Jiang et al., 2023) develops neural SDF-based GANs, exploiting ray marching, surface sampling, and normal-consistent losses for high-fidelity object generation trained on 2D images. Mosaic-SDF (Yariv et al., 2023) introduces local grid-based SDF representations for flow-model-based, class-conditioned, and text-to-3D CAD generation, compatible with transformer architectures.

7. Semantic Structuring, Part Retrieval, and Assembly Applications

Neural SDF-based representations support part-aware retrieval and semantic labeling:

• Graph neural network approaches for CAD part retrieval, such as GC-CAD (Quan et al., 13 Jun 2024), use contrastive learning on graph-structured BRep models, enabling label-free, efficient retrieval with substantial accuracy and speed improvements over previous methods.
• Joint reconstruction and segmentation frameworks (Fan et al., 4 Oct 2025) attach segmentation heads to SDF trunks (e.g., FlatCAD), producing geometry-aligned, part-label-coherent predictions (assessed via mIoU and segmentation consistency), robust to arbitrary part cardinalities and unsupervised labels.

Tables below summarize key loss terms and regularizers in neural SDF-based CAD modeling:

Loss Term	Formula/Definition	Purpose
Dirichlet (Manifold) Loss	$L_{DM} = (1/N) \sum_{x \in X_{man}} |f(x)|$	Surface fidelity
Eikonal Loss	$$L_E = (1/|Z|) \sum_{z \in Z} (\|\nabla f(z)\|^2_2 - 1)^2$$	Unit gradient enforcement
Gaussian Curvature Loss	$$L_{Gauss} = (1/|\Omega|) \int_\Omega DT(|k_{Gauss}|) dx$$	Developability (curvature)
Weingarten Mix Proxy	$$|S_{12}(x_0)| \approx |D_{uv}^+(x_0)|/\|\nabla f(x_0)\|$$	Curvature regularization

References and Research Directions

Foundational models and regularization methods for neural SDF-based CAD part representation include UCSG-Net (Kania et al., 2020), FlatCAD (Yin et al., 19 Jun 2025), NeurCADRecon (Dong et al., 20 Apr 2024), ClusteringSDF (Wu et al., 21 Mar 2024), PartSDF (Talabot et al., 18 Feb 2025), Scalable SDF implicit frameworks (Yang et al., 15 Jan 2025), GC-CAD (Quan et al., 13 Jun 2024), and interactive sculpting via INST-Sculpt (Rubab et al., 5 Feb 2025). Research continues in integrating finer boundary-aware segmentation (Fan et al., 4 Oct 2025), exploiting LiDAR for SDF initialization and regularization (Liu et al., 13 Mar 2025), and synthesizing CAD assemblies via flow-based generative models (Yariv et al., 2023).

Significance

Neural implicit SDF-based approaches unify high-resolution geometric modeling, semantic part structuring, efficient retrieval, scalable reconstruction, and generative synthesis for CAD workflows. Their adaptability, efficiency, and regularizability make them especially suitable for modern engineering design, manufacturing, prototyping, and assembly-level automation.