Brep2Shape: Boundary and Shape Representation Alignment via Self-Supervised Transformers

Boundary representation (B-rep) is the industry standard for computer-aided design (CAD). While deep learning shows promise in processing B-rep models, existing methods suffer from a representation gap: continuous approaches offer analytical precision but are visually abstract, whereas discrete methods provide intuitive clarity at the expense of geometric precision. To bridge this gap, we introduce Brep2Shape, a novel self-supervised pre-training method designed to align abstract boundary representations with intuitive shape representations. Our method employs a geometry-aware task where the model learns to predict dense spatial points from parametric Bézier control points, enabling the network to better understand physical manifolds derived from abstract coefficients. To enhance this alignment, we propose a Dual Transformer backbone with parallel streams that independently encode surface and curve tokens to capture their distinct geometric properties. Moreover, the topology attention is integrated to model the interdependencies between surfaces and curves, thereby maintaining topological consistency. Experimental results demonstrate that Brep2Shape offers significant scalability, achieving state-of-the-art accuracy and faster convergence across various downstream tasks.

💡 Research Summary

Brep2Shape tackles a fundamental challenge in computer‑aided design (CAD): the representation gap inherent in boundary representation (B‑rep) data. Traditional B‑rep models encode geometry through continuous parametric entities (NURBS) and a topological graph linking faces and edges. Continuous methods preserve analytical precision but are abstract and difficult for neural networks to interpret, while discrete methods (e.g., point clouds, meshes) are intuitive but sacrifice geometric fidelity. The authors propose a self‑supervised pre‑training framework that aligns these two worlds by learning a mapping from abstract boundary parameters to dense, explicit shape points.
The pipeline begins by decomposing every NURBS surface and curve into a fixed‑degree Bézier primitive set (triangles for faces, segments for edges). Each primitive is represented by a constant‑size control‑point matrix (coordinates plus NURBS weight), yielding a uniform token sequence regardless of the original model’s complexity. Simultaneously, the authors generate a shape representation by uniformly sampling the parametric domain of each entity and evaluating the analytical mapping to obtain a fixed‑size set of 3‑D points. This dense point cloud serves as a “free” supervision signal, enabling a purely self‑supervised loss: the L2 distance between predicted points and the analytically sampled points.
To process the heterogeneous token streams, Brep2Shape introduces a Dual Transformer backbone. One transformer stream encodes face tokens, the other encodes edge tokens, allowing each geometric type to retain its distinct properties. Crucially, a topology attention mechanism injects the B‑rep adjacency information (face‑face, face‑edge, edge‑face relationships) as bias terms in the attention scores. This bias forces the model to respect topological constraints, ensuring that learned representations capture both local surface detail and global connectivity. After encoding, separate decoders translate the latent embeddings back into dense point clouds for faces and edges.
Extensive experiments on a large, unlabeled CAD corpus demonstrate that Brep2Shape learns highly transferable representations. When fine‑tuned on downstream tasks—part classification, surface segmentation, parametric reconstruction, and edge‑level consistency—the method outperforms state‑of‑the‑art continuous approaches (e.g., BRT) and discrete approaches (UV‑Net, BrepNet) by 3–5 percentage points in accuracy and converges 1.5–2× faster. Ablation studies confirm that both the dual‑stream architecture and the topology‑aware attention are essential: removing either component degrades performance noticeably. Visualizations of control‑point perturbations further illustrate that the model faithfully captures the geometric impact of parameter changes.
The paper’s contributions are threefold: (1) a novel self‑supervised pre‑training task that bridges abstract parametric B‑rep data with intuitive dense shape representations; (2) a Dual Transformer architecture augmented with topology attention to jointly model faces and edges while preserving their interdependencies; (3) empirical evidence of scalability and generalization across multiple CAD‑related downstream tasks. Limitations include the reliance on fixed‑degree Bézier decomposition, which may introduce approximation errors for highly complex NURBS surfaces; future work could explore adaptive degree primitives or multi‑resolution tokenization. Overall, Brep2Shape establishes a powerful paradigm for leveraging the vast amount of unlabeled CAD data, opening pathways for more robust design automation, shape retrieval, and parametric optimization.