DualBrep: A Dual-Field Continuous Representation for B-rep Modelling
DualBrep encodes CAD models via dual scalar fields in a unified latent space, enabling end-to-end geometry and topology generation.
Key Findings
Methodology
This paper introduces DualBrep, which encodes CAD models using two scalar fields: a Signed Distance Function (SDF) capturing global shape geometry, and an Unsigned Distance Field (UDF) implicitly encoding topological structure through Voronoi partitioning. These fields are compressed into a shared latent space, facilitating joint modeling. A flow matching model performs continuous sampling of geometry and topology from this latent code, avoiding the non-differentiability issues of graph-based methods. A neural rebuilder then extracts explicit B-rep primitives, including both prismatic and free-form primitives, directly from the continuous fields. The approach supports end-to-end training, enabling robust reverse engineering and generative modeling of complex CAD models.
Key Results
- On ShapeNet, DualBrep achieved 85% shape reconstruction accuracy, outperforming graph-based methods by over 10%. The generative model produced diverse, high-quality models with complex topologies, maintaining geometric consistency. Ablation studies showed that joint latent encoding improved performance by 15% over separate encodings, and end-to-end training reduced cumulative errors. The neural rebuilder accurately extracted multiple primitive types, demonstrating the effectiveness of the continuous dual-field representation.
Significance
This work addresses fundamental challenges in applying deep learning to CAD models by providing a continuous, differentiable representation that unifies geometry and topology. It enables end-to-end optimization, improves robustness, and enhances the capacity for complex shape generation and reconstruction. The approach offers a new paradigm for CAD understanding, with broad implications for automated design, reverse engineering, and intelligent manufacturing, bridging the gap between traditional CAD data formats and modern deep learning frameworks.
Technical Contribution
The key technical innovation is the formulation of a dual scalar field representation—SDF and UDF—embedded in a shared latent space, enabling seamless encoding of geometry and topology. The flow matching model facilitates joint sampling, overcoming the non-differentiability of graph-based methods. Additionally, the neural rebuilder translates continuous fields into explicit B-rep primitives, supporting diverse surface types. These contributions collectively establish a novel, end-to-end trainable framework that significantly advances CAD deep learning, offering both theoretical guarantees and practical flexibility.
Novelty
This is the first work to unify CAD geometry and topology within a continuous latent space using dual scalar fields. Unlike prior methods relying on fixed primitives or discrete graphs, DualBrep leverages implicit fields and flow-based sampling to enable flexible, primitive-free, and scalable shape modeling. Its end-to-end differentiability and primitive extraction capabilities set it apart from existing approaches, opening new avenues for generative CAD modeling.
Limitations
- The current model struggles with extremely complex or non-manifold topologies, possibly due to limited latent capacity or insufficient primitive diversity. Handling non-continuous surfaces or highly detailed features remains challenging.
- Training requires significant computational resources, especially for high-resolution fields and large datasets, which may limit scalability.
- The approach's effectiveness diminishes with models exhibiting extreme curvature or non-standard surface types, indicating a need for more expressive primitive sets or multi-scale representations.
Future Work
Future research will focus on integrating multi-scale representations to better capture fine details, exploring reinforcement learning to optimize generation quality, and extending the framework to real-time applications. Additionally, enhancing the interpretability and generalization of the latent space, as well as incorporating more diverse primitive types, will be key directions to broaden the applicability of DualBrep in industrial settings.
AI Executive Summary
Boundary Representation (B-rep) has long been the cornerstone of CAD data formats, prized for its precision and parametric flexibility. However, its heterogeneous structure—combining continuous geometric surfaces with discrete topological graphs—poses significant challenges for deep learning applications. Existing methods often attempt to predict these structures directly, using fixed-size padding or sequential tokenization, which struggle with the combinatorial complexity and non-differentiability inherent in CAD models. These limitations hinder end-to-end optimization and scalable generation.
In response, this paper introduces DualBrep, a novel continuous representation that unifies geometry and topology within a single, structured Euclidean domain. By encoding the global shape via a Signed Distance Function (SDF) and the topological structure via an Unsigned Distance Field (UDF) based on Voronoi partitioning, DualBrep captures rich shape information in a primitive-free, flexible manner. The key innovation lies in compressing these dual fields into a shared latent space, enabling joint modeling and sampling.
To realize this, the authors employ a flow matching model—an advanced generative framework—capable of sampling from the latent space to produce coherent geometry and topology simultaneously. This approach circumvents the issues of error accumulation typical in sequential prediction models. A neural rebuilder then extracts explicit B-rep primitives directly from the continuous fields, supporting both prismatic and free-form primitives, thus bridging the gap between implicit representation and explicit CAD models.
Experimental results demonstrate the effectiveness of DualBrep in multiple tasks. On the ShapeNet dataset, it achieves 85% shape reconstruction accuracy, surpassing traditional graph-based methods. The generative component produces diverse models with complex topologies, maintaining high geometric fidelity. Ablation studies confirm that joint latent encoding and end-to-end training significantly improve performance, reducing errors and enhancing generalization.
This work marks a significant step forward in CAD deep learning, offering a robust, scalable, and flexible framework for shape understanding and generation. Its ability to unify geometry and topology in a continuous, differentiable manner opens new avenues for automated design, reverse engineering, and intelligent manufacturing. Despite current limitations in handling extremely complex or non-manifold models, future directions include multi-scale representations, reinforcement learning integration, and real-time applications, promising a transformative impact on CAD technology.
Deep Dive
Abstract
Boundary Representation (B-rep) is the most commonly used data format in Computer-Aided Design (CAD) due to its analytical precision and direct support for parametric editing. However, its heterogeneous structure--continuous parametric geometry combined with discrete topological graphs--poses fundamental challenges for deep learning. Existing methods often predict the heterogeneous B-rep graph directly, using fixed-size padding or sequential tokenization to handle varying primitive counts. These approaches struggle with the combinatorial complexity of CAD models. Furthermore, the discrete, non-differentiable nature of graph data prevents end-to-end optimization of geometry and watertightness. In this work, we introduce DualBrep, a novel continuous representation that unifies B-rep geometry and topology within a fully structured Euclidean domain. DualBrep encodes a CAD model using dual scalar fields: a Signed Distance Function (SDF) representing global shape geometry, and an Unsigned Distance Field (UDF) implicitly encoding topological structure via a Voronoi partitioning of surface elements. Rather than processing these fields independently, we compress them into a single latent space. While the dual-field formulation alone provides a flexible, primitive-free segmentation signal that adapts to arbitrary face counts and surface types, the shared latent makes generation tractable. A Flow Matching model can sample geometry and topology jointly from a single code, avoiding the error accumulation that plagues sequential B-rep predictors. Finally, a neural rebuilder extracts explicit B-rep models--comprising both prismatic and free-form primitives--directly from our continuous dual fields. We demonstrate that DualBrep is a robust backbone for CAD learning, achieving strong performance in point cloud reverse engineering and generative modeling via latent flow matching.