用体素距离函数表示CAD模型，生成成功率100%。
B-Rep Distance Functions (BR-DF): How to Represent a B-Rep Model by Volumetric Distance Functions?
- 将CAD的顶点、边、面等拓扑信息编码为面级无符号距离函数。
- 基于扩展的等值面算法，可稳定生成闭合的多面体CAD模型。
- 结合扩散模型实现几何与拓扑联合生成，成功率突破100%。
本文提出一种新型几何表示方法——边界表示（B-Rep）体素距离函数（BR-DF），将CAD模型的表面网格几何编码为有符号距离函数（SDF），同时将顶点、边、面及其拓扑信息编码为面级无符号距离函数（UDF）。通过扩展的Marching Cubes算法，可直接将BR-DF转换为封闭的（多面体化）CAD B-Rep模型，且该转换过程始终成功。利用BR-DF的体素特性，我们设计了基于3D U-Net骨干网络的多分支潜在扩散模型，用于联合生成SDF与面级UDF。实验表明，该方法在生成性能上达到现有最优水平，同时实现了前所未有的100%（多面体）B-Rep模型生成成功率。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。