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

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.