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

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.