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

TL;DR

This work introduces B-Rep Distance Functions (BR-DF), a volumetric representation that couples a global Signed Distance Function with per-face Unsigned Distance Functions to encode both geometry and topology of watertight CAD B-Rep models. An extension of Marching Cubes, termed Marching Cubes and Triangles (MCT), guarantees to reconstruct a valid faceted B-Rep from BR-DF, providing 100% success in topologically valid outputs. The authors also present a diffusion-based BR-DF generative framework with a 3D U-Net backbone and 3D VQ-VAEs to jointly synthesize SDF and UDF fields, achieving performance on par with state-of-the-art CAD generation methods while ensuring watertightness. Constructive geometry operations on BR-DF demonstrate potential for combining parts, and extensive experiments on DeepCAD and ABC datasets confirm robustness, with ablation studies highlighting the benefit of the two-stage generation and showing where failures arise (primarily in BR-DF generation rather than MCT). Overall, BR-DF offers a principled, watertight, volumetric pathway for CAD B-Rep generation and manipulation, with implications for reliable generative design and downstream CAD workflows.

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.

Figures (14)

• Figure 1: BR-DF is a geometric representation for Boundary Representation (B-Rep) models. An SDF encodes surface geometry. UDFs encode vertices, edges, faces, and their connectivity. An extension of the Marching Cubes converts BR-DF to a faceted B-Rep model.
• Figure 2: MCT algorithm: 1) Given the volumetric UDFs for each face, interpolate a UDF value at each mesh vertex; 2) Select the face with the smallest UDF at each mesh vertex; and 3) Extract B-Rep vertices and edges by applying the 3-way rules.
• Figure 3: The multi-branch diffusion architecture. Top and bottom represent the face and surface branches, respectively. The number of faces corresponds to the generated bounding boxes during inference and the ground truth bounding boxes during training. Three inter-branch cross-attention modules (f2f, f2s, s2f) are added.
• Figure 4: Unconditional generation results on DeepCAD dataset deepcad. Our method achieves comparable performance to the state-of-the-art methods, while maintaining 100% success rate.
• Figure 5: Unconditional generation results on the ABC dataset abc.