DualBrep: A Dual-Field Continuous Representation for B-rep Modelling

2026-06-30

AI Summary

This work addresses the challenges posed by the heterogeneous nature of geometry and topology in traditional boundary representation (B-rep) modeling, as well as the non-differentiability of discrete graph structures, which hinder end-to-end deep learning optimization. To overcome these limitations, the authors propose a continuous dual-field representation that unifies B-rep geometry and topology within a continuous Euclidean space for the first time. This is achieved by jointly encoding topological structure through a signed distance function (SDF) and an unsigned distance field (UDF), which are compressed into a shared latent space—thereby avoiding fixed padding or sequential processing. Integrated with Voronoi partitioning, a flow-matching generative model, and a neural reconstructor, the method enables flexible modeling of arbitrary face counts and surface types, directly producing complete B-rep models from point clouds in both inverse and generative tasks while circumventing error accumulation inherent in sequential prediction.

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.

Problem

• B-rep
• continuous representation
• deep learning
• topology-geometry heterogeneity
• CAD modeling

Innovation

• Dual-field representation
• Boundary Representation (B-rep)
• Signed Distance Function (SDF)
• Flow Matching
• Neural B-rep reconstruction