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BRepNet: A topological message passing system for solid models
Joseph G. Lambourne, Karl D. D. Willis, Pradeep Kumar Jayaraman, Aditya Sanghi, Peter Meltzer, Hooman Shayani
TL;DR
B-rep segmentation is valuable for automating CAD-related tasks, but progress has been limited by complex data structures and scarce labelled datasets. The paper introduces BRepNet, which convolves directly over B-rep topology, and releases over 35,000 annotated models. BRepNet outperforms point-cloud and mesh techniques on Fusion 360 Gallery segmentation while also offering parameter efficiency.
Problem
B-rep segmentation supports automation of CAD, CAE, and CAPP tasks, but complex data structures and limited labelled datasets have hindered research progress.
Method
BRepNet applies convolution directly to B-rep faces, edges, and coedges by assigning learnable parameters to topologically defined neighboring entities and walks.
Results
BRepNet achieves higher performance and parameter efficiency than point-cloud and mesh techniques on the Fusion 360 Gallery segmentation problem.
Takeaways & Limitations
The Fusion 360 Gallery dataset provides over 35,000 segmented 3D models in B-rep, mesh, and point-cloud formats for research on B-rep segmentation.
Takeaways & Limitations
The mesh comparison excludes 13% of B-rep models because the algorithm failed to generate meshes meeting the specified criteria.
Abstract
from arXiv · showhide
Boundary representation (B-rep) models are the standard way 3D shapes are described in Computer-Aided Design (CAD) applications. They combine lightweight parametric curves and surfaces with topological information which connects the geometric entities to describe manifolds. In this paper we introduce BRepNet, a neural network architecture designed to operate directly on B-rep data structures, avoiding the need to approximate the model as meshes or point clouds. BRepNet defines convolutional kernels with respect to oriented coedges in the data structure. In the neighborhood of each coedge, a small collection of faces, edges and coedges can be identified and patterns in the feature vectors from these entities detected by specific learnable parameters. In addition, to encourage further deep learning research with B-reps, we publish the Fusion 360 Gallery segmentation dataset. A collection of over 35,000 B-rep models annotated with information about the modeling operations which created each face. We demonstrate that BRepNet can segment these models with higher accuracy than methods working on meshes, and point clouds.
1. Introduction
B-rep segmentation is important for automating CAD-related tasks, but complex structures and limited labelled data have hindered progress. BRepNet directly exploits B-rep topology, alongside a new dataset of over 35,000 annotated models, and outperforms mesh- and point-cloud-based techniques on Fusion 360 Gallery segmentation.
- B-rep models compactly combine trimmed parametric surfaces with adjacency relationships, supporting both prismatic and free-form CAD objects.The representation uses primitive curves and surfaces for prismatic shapes and NURBS for free-form objects.
- Complex data structures, limited labelled datasets, and lost parametric feature history have constrained B-rep segmentation research and practical workflows.Feature history is often lost when models move between CAD applications, motivating segmentation-based recovery.
- Automated B-rep segmentation supports laborious CAD, CAE, and CAPP tasks such as model simplification and manufacturing-oriented grouping.These tasks otherwise require users to repeatedly select groups of faces or edges.
- Over 35,000 3D models are released in the Fusion 360 Gallery segmentation dataset with labels revealing the modeling operations used to create faces.The dataset includes B-rep, mesh, and point-cloud representations.
- BRepNet defines convolutional kernels around coedges, assigning learnable parameters to ordered neighboring faces, edges, and coedges.This arrangement lets feature vectors from topologically well-defined locations be concatenated and processed by matrix/vector multiplication.
- BRepNet achieves higher performance and parameter efficiency than techniques based on point clouds and meshes on the Fusion 360 Gallery segmentation problem.The paper reports experimental results including ablations and comparisons with other representations and methods.
2. Related work
Prior B-rep segmentation methods used heuristics, voxels, point clouds, meshes, or graph representations, each retaining only part of the original structure or incurring representation-specific costs. BRepNet instead operates around B-rep topology, whose entities can be traversed through explicit instruction sequences.
- Earlier neural methods converted B-reps into face adjacency graphs and processed heuristically selected connected components.These methods extracted node features from faces and arc attributes from edges before network processing.
- Voxel methods face cubic storage complexity, limiting the size of geometric features detectable with current GPU hardware.This is especially restrictive because CAD models often contain small but important features.
- Point-cloud segmentation can under-sample small-area faces, causing them to be incorrectly classified.The representation typically requires many uniformly sampled surface points.
- Mesh methods apply convolutions to triangle-mesh edges or directed triangle edges, but converting B-reps to meshes introduces an additional representation step.The passage describes MeshCNN and directed-edge convolution as examples of mesh-based strategies.
- Graph-based B-rep segmentation translates the data structure into face adjacency graphs, losing information about the relative topological locations of nearby entities.The cited concurrent approaches differ in their geometric input features but share this graph conversion.
- B-rep topology contains faces, edges, loops, coedges, and vertices that can be traversed using instruction sequences such as {mate, next, mate, face}.Figure 2 represents such walks with products of incidence matrices including N, P, M, F, and E.
3. Method
BRepNet operates directly on B-rep topology by defining convolution neighborhoods around oriented coedges and propagating geometric features among faces, edges, and coedges. Its convolution units pool information across coedges, faces, and edges to produce per-face segmentation scores.
- 3.1. B-rep data structures: B-reps contain faces, edges, loops, coedges, and vertices connected through adjacency and incidence relationships.Coedges are directed entities that link neighboring coedges with their mating coedges, parent faces, and parent edges.
- 3.2. Topological walks: Topological walks reach neighboring entities by following next, previous, and mating coedge pointers, optionally terminating at a face or edge.The corresponding matrices are multiplied in instruction order to represent each walk.
- 3.3. Input feature extraction: BRepNet uses coordinate-free feature matrices for faces, edges, and coedges, including surface or curve types, geometric measurements, convexity, loop closure, and orientation.These features are standardized over the training set and reused with the same scaling for validation and testing.
- 3.4. Convolution: Convolutional kernels are defined relative to oriented coedges, concatenating hidden states from entities reached by specified topological walks.Directed coedges distinguish the faces on either side and avoid symmetric aggregation for that ambiguity.
- 3.4. Convolution: The network initializes hidden states from the face, edge, and coedge feature matrices and processes them through T convolution units before generating segmentation outputs.The architecture is illustrated as a stack of convolution units producing hidden states H(t).
- 3.4. Convolution: Each convolution unit applies an MLP to the assembled neighborhood features, then pools information from coedges onto parent faces and edges before producing new hidden states.Pooling lets information pass between separate loops of a face, while a final unit outputs per-face scores for the segmentation classes.
4. Fusion 360 Gallery segmentation dataset
The Fusion 360 Gallery segmentation dataset provides B-rep models and corresponding mesh and point-cloud representations labeled by the CAD operations that created their faces. It contains 35,858 models and includes several common additive and subtractive modeling operations.
- Dataset contribution: The dataset introduces segmentation information for B-rep models together with corresponding triangle meshes and point clouds.Its labels are based on the CAD modeling operations used to create each face, providing modeling-history information absent from existing datasets.
- Dataset contents: 35,858 3D models include per-face, per-triangle, and per-point segment labels across the B-rep, mesh, and point-cloud representations.The dataset uses common operations including extrude, chamfer, fillet, and revolve, with extrusions divided into additive and subtractive cases.
5. Experiments
Experiments evaluate BRepNet’s topology-aware kernels, input features, heuristic comparison, graph-network baseline, and direct B-rep processing against mesh and point-cloud alternatives. Results show useful loop ordering and geometric features, while direct B-rep methods achieve strong accuracy, IoU, and parameter efficiency.
- Kernel configuration: 0.98% higher IoU for the asymmetric kernel than the simple edge kernel indicates that coedge ordering information is useful for segmentation.The comparison uses equal numbers of faces, edges, and coedges; a Welch’s unequal variances t-test reports P = 0.0012.
- Kernel configuration: 92.52% accuracy and 77.10% IoU are achieved by the winged edge kernel, while expanding the kernel produces only marginal gains.The winged edge configuration contains a compact set of topological entities immediately adjacent to an edge.
- Input-feature ablations: 4.6% lower IoU results when edge convexity is removed, compared with 3.9% for curve type and 3.7% for surface type removal.Edge convexity, curve type, and surface type are identified as the primary input information used for segmentation; edge length and face area have much smaller effects.
- Heuristic method comparison: BRepNet achieves an IoU value 27% higher than ASM, although ASM’s recognized faces are geometrically consistent and its confusion concerns ambiguous modeling techniques.ASM cannot detect the RevolveEnd segment type, which is omitted from its average IoU calculation, and fails to identify a feature type for 13% of faces.
- Representation and network comparisons: 13% of B-rep models fail the high-quality meshing process, motivating direct B-rep processing instead of conversion to meshes or point clouds.The generated meshes target close to 3,000 triangles each, and avoiding this specialized meshing requirement is described as a major advantage of direct B-rep operation.
- Representation and network comparisons: BRepNet and ECC outperform geometry-based methods by more than 16% accuracy and 37% IoU with just under one-quarter as many parameters.The ECC network has 359,558 parameters and achieves an IoU more than 5% below BRepNet’s winged edge configuration; its test performance may partly reflect training-epoch selection.
6. Conclusions
BRepNet operates directly on B-rep models and uses coedge-relative convolution to exploit local topological context. On Fusion 360 Gallery segmentation, it outperforms mesh and point-cloud methods and an edge-conditioned graph network.
- BRepNet operates directly on B-rep models using convolutional kernels defined relative to coedges.This lets the architecture use information from the next and previous coedges in face loops.
- BRepNet outperforms existing point-cloud and mesh techniques on the Fusion 360 Gallery segmentation task.
- Coedge-relative kernels give BRepNet better performance than an edge-conditioned convolution network with the same number of parameters.
A.1. Dataset statistics
The Fusion 360 Gallery dataset contains 35,858 labeled 3D models represented as B-reps, meshes, and point clouds. Its bodies vary in complexity and modeling history, while the face classes are substantially imbalanced and include rare, context-dependent categories.
- Half of the bodies have fewer than 9 faces, while the most complex body has 421 faces.Just over half use more than one CAD modeling operation, and 31% use at least two.
- Extrusions comprise 74% of modeling operations, making them the dominant construction feature.
- More than half of faces belong to ExtrudeSide, while RevolveEnd accounts for only 0.08% of faces.The dataset is therefore relatively imbalanced across segmentation classes.
A.1.1 Data preparation
The dataset is prepared by filtering Fusion 360 models to selected operations, removing duplicates, normalizing B-rep placement and scale, and extracting corresponding meshes and point clouds.
- Fusion 360 scripts suppress all features except extrusions, revolutions, fillets, and chamfers to generate the dataset bodies.The procedure modifies some shapes but increases the number of available B-rep bodies.
- Duplicate bodies are removed by matching face and edge counts, then checking surface area and volume within 1%.The duplicate-free result is verified using thumbnails.
- All B-reps are translated to place their bounding-box centers at the origin and uniformly scaled so the largest bounding-box length is 2 model units.
- Meshes and point clouds are extracted from the scaled B-rep models.
A.1.2 Input feature standardization
BRepNet input features are standardized using training-set statistics before being passed to the network.
- For each input feature, the training-set mean and standard deviation are used to compute standardized values x′.
A.1.3 Support for operation grouping and ordering problems
The dataset provides face-level operation identities and structural metadata to support grouping faces by modeling operation and reconstructing parametric histories. These annotations also support predicting extrusion directions and learning ordered modeling-operation sequences.
- Each B-rep face has an identifier for its creating operation, while extrusions and revolutions include Start, End, or Side classifications.
- Grouping points or triangles by their creating operation supports reconstruction of the model’s parametric history.
- Extrusion subdivisions based on Start, End, and Side information allow extrusion-direction prediction and profile-curve extraction.
- Predicting operation type and order supports learning sensible sequences for regenerating extruded volumes.
A.2. Kernels
BRepNet’s topological kernels are evaluated alongside graph, point-cloud, and mesh approaches, including class-level IoU analyses. The results emphasize advantages on rare classes whose identification depends on neighboring faces and edges, while performance varies by class distinctiveness.
- Kernel design: BRepNet kernels require no special handling when multiple topological walks terminate on the same entity.This can occur in arbitrary B-reps because local topology may cause repeated destinations.
- Training setup: BRepNet training used Adam with 0.001 learning rate and approximately 1000 faces per minibatch.
- Training setup: The Fusion 360 Gallery segmentation dataset was trained in under 12 minutes from random seed.
- Class-level results: BRepNet and ECC outperform PointNet++ and MeshCNN partly by correctly classifying rare classes using adjacent-face information.
- Class-level results: 49% IoU on RevolveEnd contrasts with zero identified faces for both PointNet++ and MeshCNN.RevolveEnd represents 0.08% of the dataset and requires neighboring-face and edge context.
- Class-level results: 97.57% IoU for BRepNet and 97.32% for ECC on Fillet demonstrate that distinctive geometric patterns are readily detected.
- Class-level results: Fillet faces remain easier to detect than CutSide faces despite their smaller areas and similar dataset frequency.