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 classical 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 also propose a multi-branch latent diffusion with 3D UNet 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.

BR-DF

BR-DF is a novel geometric representation for CAD Boundary Representation (B-Rep) models, where an SDF encodes surface geometry, and UDFs represent B-Rep vertices, edges, faces, and their connectivity. A simple extension of the Marching Cubes algorithm can reliably convert BR-DF into faceted B-Rep model with 100% success rate.

BRep Conversion

Step 1: Given the volumetric UDFs for each face, the UDF value at each mesh vertex is computed using linear interpolation. Step 2: Each mesh vertex selects the face with the smallest UDF value. Step 3: B-Rep vertices and edges are extracted by applying the 3-way rules as illustrated at the bottom of the figure.

Results

Unconditional generation results on DeepCAD dataset. Our method achieves comparable performance to the state-of-the-art methods, while maintaining 100% success rate.

Unconditional generation results on the ABC dataset.

Citation

Acknowledgements

This research is partially supported by NSERC Discovery Grants, NSERC Alliance Grants, and John R. Evans Leaders Fund (JELF). We thank the Digital Research Alliance of Canada and BC DRI Group for providing computational resources.