Flatten The Complex: Joint B-Rep Generation via Compositional $k$-Cell Particles

TL;DR

This work addresses the challenge of generative B-Rep modeling by introducing Compositional $k$-Cell Particles that unify topology and geometry into a spatially grounded set representation. A two-stage CC-VAE encodes a B-Rep into a latent particle set over the Spatial Hasse Diagram, followed by a Rectified Flow that enables unconditional and multi-modal conditional generation. The method performs two-phase decoding to recover topology and realize geometry, enabling tasks from open-surface reconstruction and wireframe synthesis to local in-painting and multi-modal reconstructions from images or point clouds. The approach achieves high validity and editability compared to state-of-the-art methods, demonstrates strong generalization to non-solid topologies, and exhibits inference-time scalability by trading particle count for fidelity. Overall, the framework provides a scalable, global-context CAD generative model that jointly reasons about topology and geometry with explicit spatial grounding.

Abstract

Boundary Representation (B-Rep) is the widely adopted standard in Computer-Aided Design (CAD) and manufacturing. However, generative modeling of B-Reps remains a formidable challenge due to their inherent heterogeneity as geometric cell complexes, which entangles topology with geometry across cells of varying orders (i.e., $k$-cells such as vertices, edges, faces). Previous methods typically rely on cascaded sequences to handle this hierarchy, which fails to fully exploit the geometric relationships between cells, such as adjacency and sharing, limiting context awareness and error recovery. To fill this gap, we introduce a novel paradigm that reformulates B-Reps into sets of compositional $k$-cell particles. Our approach encodes each topological entity as a composition of particles, where adjacent cells share identical latents at their interfaces, thereby promoting geometric coupling along shared boundaries. By decoupling the rigid hierarchy, our representation unifies vertices, edges, and faces, enabling the joint generation of topology and geometry with global context awareness. We synthesize these particle sets using a multi-modal flow matching framework to handle unconditional generation as well as precise conditional tasks, such as 3D reconstruction from single-view or point cloud. Furthermore, the explicit and localized nature of our representation naturally extends to downstream tasks like local in-painting and enables the direct synthesis of non-manifold structures (e.g., wireframes). Extensive experiments demonstrate that our method produces high-fidelity CAD models with superior validity and editability compared to state-of-the-art methods.

Figures (9)

• Figure 1: Architecture of the CC-VAE. The framework encodes a B-Rep into a set of latent particles and reconstructs it via a compositional decoder. Left: The encoder fuses local surface details extracted from a dense point cloud with topological context propagated along the input Spatial Hasse Diagram via GCN layers. A Transformer encoder aggregates these features into the latent particle set subject to KL regularization. Right: The reconstruction proceeds in two stages. Phase I recovers the Spatial Hasse Diagram by predicting particle attributes and incidence links. Phase II performs compositional geometry synthesis, where specific geometry heads generate detailed geometry conditioned on features gathered via the connectivity recovered in Phase I.
• Figure 2: Illustration of the reformulation of the hierarchical B-Rep model into an unordered set of compositional $k$-cell particles, and the subsequent reconstruction of the original hierarchical structure..
• Figure 3: Qualitative results of unconditional generation on the ABC dataset after filtering out simple models. The results demonstrate that our method generates complex and realistic CAD models, particularly those featuring intricate details such as chamfers and holes.
• Figure 4: We plot the validity rate of generated models as a function of the minimum number of faces ($\min\text{-}k$). Markers 'x' indicate performance points reported in HoLa HoLa and Stitch-A-Shape StitchAShape.
• Figure 5: Given only the edge and vertex constraints,the model successfully predicts the missing faces to produce the complete solid B-Reps.