FoV-Net: Rotation-Invariant CAD B-rep Learning via Field-of-View Ray Casting

AI summary

Overview

Research area: 3D deep learning on CAD boundary representations (B-rep learning), a subfield of computer vision and geometric deep learning applied to computer-aided design.

Technical level: Advanced. The paper assumes familiarity with graph neural networks, parametric surface parameterization (UV maps), rotation groups such as SO(3), and CAD kernel operations like curve-face intersection. The core intuition is accessible, but the descriptor design and evaluation details are technically dense.

Scope: The paper introduces FoV-Net, a B-rep learning framework whose per-face descriptors are rotation- and translation-invariant by construction, and evaluates it on two classification and two segmentation benchmarks against UV-Net and AAGNet.

What This Paper Is About

State-of-the-art B-rep learning methods describe each CAD face using UV-grids that store absolute 3D coordinates and normals in the global frame, which makes them highly sensitive to the orientation of the part. The authors first measure how severe this problem is — models above 95% accuracy on aligned data can fall to as low as 10% under arbitrary SO(3) rotations — and then propose a way to encode each face's local geometry and surrounding structure without ever referring to a global coordinate system. The goal is a model that keeps the same accuracy no matter how a CAD model is oriented.

Key Contributions

1. The first systematic study quantifying rotation sensitivity in B-rep learning. The authors measure how UV-based methods (UV-Net, AAGNet) degrade under SO(3) rotations across classification and segmentation benchmarks, and show that accuracy can drop from over 95% to as low as 10%.

2. A rotation-invariant B-rep descriptor combining local geometry and surrounding structure. Each face is described by a Local Reference Frame (LRF) UV-grid for intrinsic surface geometry and by Outward Vision (OV) and Inward Vision (IV) grids produced by ray casting for structural context.

3. FoV-Net, a full architecture built on these descriptors. Lightweight CNNs encode the three grid types, an MLP fuses them with per-face attributes, and a 3-layer graph attention network (GAT) propagates features over the B-rep graph.

4. Evidence of data efficiency and of rotation sensitivity harming segmentation even on aligned data. On MFCAD++, FoV-Net reaches 80% accuracy with just 50 training samples, compared to roughly 60% for AAGNet and roughly 30% for UV-Net.

Main Findings

• Rotation collapse in existing methods: On SolidLetters, UV-Net loses 87.41 percentage points and AAGNet 82.65 percentage points under rotation. On TraceParts, UV-Net drops 54.33 pp and AAGNet 8.67 pp. On MFCAD++, UV-Net's accuracy collapses by 63.51 pp (77.86 pp IoU) and AAGNet drops 19.20 pp (33.40 pp IoU). On Fusion360, UV-Net and AAGNet lose 19.21 and 10.75 percentage points in accuracy, corresponding to 29.41 and 20.39 pp drops in IoU.

• FoV-Net is identical across orientations: On SolidLetters it scores 96.35 ± 0.16 on both rotated and original test sets; on TraceParts, 100.00 ± 0.00 on both; on Fusion360, 91.72 ± 0.17 accuracy and 73.81 ± 0.62 IoU on both; on MFCAD++, 99.33 ± 0.07 accuracy and 97.81 ± 0.24 IoU on both.

• Adding global UV features helps only when pose carries information: FoV-Net (UV) reaches 97.42 ± 0.17 on original SolidLetters (above FoV-Net's 96.35), which the authors attribute to pose cues such as b vs. d and p vs. q, but it collapses to 23.53 ± 0.61 on rotated data. On the segmentation tasks, FoV-Net outperforms FoV-Net (UV), suggesting global UV features add no useful positional information there.

• Rotation augmentation trades robustness for overall accuracy: On SolidLetters, UV-Net (aug) and AAGNet (aug) reach 94.97 ± 0.10 and 94.43 ± 0.22 on rotated data, but fall to 95.34 ± 0.12 and 94.95 ± 0.18 on original data, below their unaugmented counterparts. On Fusion360, UV-Net (aug) scores 86.04 ± 0.88 original accuracy, below unaugmented UV-Net's 88.34 ± 0.41.

• Segmentation is less rotation-sensitive than classification, but still affected: The authors suggest this is because faces occupy varying absolute positions even in aligned models, forcing UV-based methods to partially ignore pose cues.

• Component ablation on SolidLetters: FoV grids alone reach 95.79% and LRF UV alone 94.39%, while the combination reaches 96.35%. OV alone reaches 92.92% and IV alone 93.40%, with their combination at 95.79%. Per-face features alone yield 70.68%, and topology alone (node degree) drops to 37.72%.

• Resolution ablation on SolidLetters: Reducing the FoV grid from the original 6 × 12 to 4 × 8, 2 × 4, 1 × 4, and 1 × 1 produces gradual decline with only minor losses down to 4 × 2; performance drops more noticeably at 4 × 1 and collapses to 75.04% at 1 × 1, a single ray along the face normal.

• Data efficiency on MFCAD++: With training subsets ranging from 25 samples to the full dataset, FoV-Net reaches 80% accuracy with just 50 samples, versus roughly 60% for AAGNet and roughly 30% for UV-Net. AAGNet catches up to FoV-Net at 1,000 samples; UV-Net requires 10,000 samples.

Methodology in Plain English

The authors start from the observation that standard B-rep descriptors work like a photograph taken with the camera fixed to the world: rotate the object and every pixel value changes. Their fix is to attach a tiny coordinate system to each face instead, so that the description travels with the face.

Three inputs are computed per face. First, an LRF UV-grid: the face is sampled over its 2D UV parameter domain, but the sampled points and normals are expressed relative to the face's own center and its orthonormal frame (built from the outward normal and the tangent along the parametric U direction). Because the frame rotates with the face, the resulting 10 × 10 × 7 tensor is identical for an identical face in any pose. Second, an Outward Vision grid: rays are fired from the face center over a hemisphere around the normal, and a 2D grid records, for each ray direction, whether it hit anything, how far away the first hit was, and the incidence angle at that hit. Third, an Inward Vision grid, computed the same way but over the opposite hemisphere around the negative normal, which probes the solid's interior and typically produces dense intersections. Ray intersections come from PythonOCC, the Python wrapper for the OpenCASCADE CAD kernel. Both vision grids are 6 × 12 × 3 (15-degree elevation and 30-degree azimuth steps).

Small 2D CNNs encode each grid separately (two convolutional layers of 32 then 64 channels for the vision grids; three layers of 32, 64, then 128 for the LRF UV grid), each followed by global average pooling and a projection to 64 dimensions. Circular padding handles the azimuth wrap-around. These are concatenated with a 7D per-face attribute vector (one-hot surface type of 6 dimensions plus area) and fused by a two-layer MLP with hidden dimension 256 into a single 64-D node embedding. A 3-layer GAT with 4 attention heads and hidden dimension 64 then passes messages between neighboring faces in the B-rep graph. Classification aggregates node embeddings with max pooling and a two-layer MLP; segmentation uses the final node embeddings directly per face.

Training uses Adam with learning rate 0.001 and batch size 64, early stopping with patience 30, on a single NVIDIA RTX A5000 (24 GB VRAM). Models are evaluated on original and randomly SO(3)-rotated test sets while validation sets stay unrotated, and every experiment is repeated five times with different random seeds.

Why This Matters

Impact on research: The paper reframes rotation sensitivity from a known caveat in UV-Net into a measured, quantified failure mode across current B-rep learning methods, and shows it also harms segmentation on aligned data in low-data regimes by letting models overfit pose-to-label correlations. It also brings ray casting — long used in graphics and point cloud processing — into B-rep learning as a way to capture structural context without sacrificing invariance.

Real-world applications:

• Cross-source CAD pipelines: Manufacturing workflows ingest CAD models from many suppliers and tools, so parts arrive in arbitrary orientations and must be classified and segmented without a canonical alignment step.
• Machining and tool reachability analysis: Ray casting has been used in industrial CAD to estimate surface accessibility and tool reachability, an area the authors identify as a natural fit for FoV descriptors.
• Feature recognition and part classification: Determining 26-way letter identity on SolidLetters, mechanical part category on TraceParts, and machining features such as pockets, holes, and chamfers on MFCAD++ maps directly onto automated inspection and process planning.
• Data-scarce industrial settings: Because FoV-Net performs well with few samples, it suits environments where intellectual property restrictions limit how much proprietary CAD data can be collected.

Industry relevance: The authors emphasize that data availability in industrial CAD is often constrained by IP concerns, so a method reaching strong accuracy from as few as 50 samples, without needing rotation augmentation and its associated computational cost and accuracy penalty, is practically valuable.

Future Directions

• Scaling to larger assemblies. Current experiments focus on single-part B-reps of simple to moderate complexity; the authors plan to explore larger assemblies and larger FoV grids, potentially using GPU acceleration or mesh-level ray casting.

• Replacing the equiangular ray mapping. The 3D-to-2D projection used for FoV grids introduces polar distortions similar to geographic map projections; spherical CNNs could provide more uniform directional parameterizations.

• Handling surface reparameterizations. FoV-Net guarantees rotation invariance, but UV-axis flips or swaps remain challenging; the authors point to UV-Net's D2-equivariant convolutions as a promising mitigation.

• Extending beyond invariance and beyond current benchmarks. The authors suggest that FoV descriptors capture structural context which today's benchmarks only weakly emphasize, and that datasets targeting structural tasks such as milling tool reachability would better highlight these strengths. They also note their architecture omits edge features for computational reasons, and that extensions to B-rep generation — where edge features are essential — are an important direction. Contrastive B-rep pretraining and unsupervised CAD retrieval are named as possible foundations.

Target Audience

Researchers and practitioners in geometric deep learning and CAD/CAE who work with B-rep data, particularly those building classification, segmentation, feature recognition, or retrieval systems for manufacturing. It is also relevant to engineers deploying CAD analysis pipelines where parts arrive without canonical orientation, and to readers interested in how rotation-invariant descriptors from point cloud learning transfer to structured CAD representations. Readers need a working grasp of GNNs, parametric surfaces, and 3D rotation concepts to follow the methodology in detail.

Authors’ abstract

Learning directly from boundary representations (B-reps) has significantly advanced 3D CAD analysis. However, state-of-the-art B-rep learning methods rely on absolute coordinates and normals to encode global context, making them highly sensitive to rotations. Our experiments reveal that models achieving over 95% accuracy on aligned benchmarks can collapse to as low as 10% under arbitrary $\mathbf{SO}(3)$ rotations. To address this, we introduce FoV-Net, the first B-rep learning framework that captures both local surface geometry and global structural context in a rotation-invariant manner. Each face is represented by a Local Reference Frame (LRF) UV-grid that encodes its local surface geometry, and by Field-of-View (FoV) grids that capture the surrounding 3D context by casting rays and recording intersections with neighboring faces. Lightweight CNNs extract per-face features, which are propagated over the B-rep graph using a graph attention network. FoV-Net achieves state-of-the-art performance on B-rep classification and segmentation benchmarks, demonstrating robustness to arbitrary rotations while also requiring less training data to achieve strong results.