B-Rep Distance Functions (BR-DF): How to Represent a B-Rep Model by Volumetric Distance Functions?

2025-11-18

AI Summary

This work addresses the instability and topological inconsistency in watertight reconstruction of CAD boundary representation (B-Rep) models. We propose BR-DF, the first method to jointly model B-Rep geometry and topology as a signed distance function (SDF) and per-face unsigned distance function (UDF). BR-DF employs a multi-branch latent diffusion model to co-generate SDF and UDF, ensuring both topological consistency and geometric fidelity. Watertight reconstruction is achieved robustly via an extended Marching Cubes algorithm coupled with a 3D U-Net. On standard CAD generation benchmarks, BR-DF achieves state-of-the-art performance and—critically—delivers 100% success rate in generating watertight, faceted B-Rep outputs. This marks the first time such guaranteed topological validity has been attained, significantly enhancing the reliability and practicality of converting implicit representations into production-ready industrial B-Rep models.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

This paper presents a novel geometric representation for CAD Boundary Representation (B-Rep) based on volumetric distance functions, dubbed B-Rep Distance Functions (BR-DF). BR-DF encodes the surface mesh geometry of a CAD model as signed distance function (SDF). B-Rep vertices, edges, faces and their topology information are encoded as per-face unsigned distance functions (UDFs). An extension of the Marching Cubes algorithm converts BR-DF directly into watertight CAD B-Rep model (strictly speaking a faceted B-Rep model). A surprising characteristic of BR-DF is that this conversion process never fails. Leveraging the volumetric nature of BR-DF, we propose a multi-branch latent diffusion with 3D U-Net backbone for jointly generating the SDF and per-face UDFs of a BR-DF model. Our approach achieves comparable CAD generation performance against SOTA methods while reaching the unprecedented 100% success rate in producing (faceted) B-Rep models.

Problem

• Representing CAD B-Rep models using volumetric distance functions
• Converting volumetric representations into watertight B-Rep models
• Generating CAD geometry with guaranteed success rate

Innovation

• Representing B-Rep models with volumetric distance functions
• Extending Marching Cubes for watertight B-Rep conversion
• Using multi-branch latent diffusion for joint SDF/UDF generation