BrepGPT: Autoregressive B-rep Generation with Voronoi Half-Patch
📝 Abstract
Fig. 1. Top: B-rep models generated by BrepGPT. Bottom: Visualization of corresponding Voronoi Half-Patches, where distinct colors represent regions in the parametric space of each face that are geometrically closest to their respective boundary curves. Boundary representation (B-rep) is the de facto standard for CAD model representation in modern industrial design. The intricate coupling between geometric and topological elements in B-rep structures has forced existing generative methods to rely on cascaded multi-stage networks, resulting in error accumulation and computational inefficiency. We present BrepGPT, a
💡 Analysis
Fig. 1. Top: B-rep models generated by BrepGPT. Bottom: Visualization of corresponding Voronoi Half-Patches, where distinct colors represent regions in the parametric space of each face that are geometrically closest to their respective boundary curves. Boundary representation (B-rep) is the de facto standard for CAD model representation in modern industrial design. The intricate coupling between geometric and topological elements in B-rep structures has forced existing generative methods to rely on cascaded multi-stage networks, resulting in error accumulation and computational inefficiency. We present BrepGPT, a
📄 Content
Boundary representation (B-rep) [Weiler 1986] serves as the cornerstone of modern Computer-Aided Design (CAD) systems, enabling accurate modeling of intricate 3D shapes through geometrically defined faces, edges, and vertices, as well as their topological interrelations. Its hierarchical structure offers advantages compared to other representation formats, particularly in capturing smooth freeform surfaces, preserving geometric precision, and supporting robust design semantics. These features are essential in engineering workflows, where correctness, manufacturability, and structural analysis depend on exact geometry and rigid connectivity constraints. As a result, the B-rep representation facilitates a wide range of downstream tasks, including editing, analysis, simulation, etc.
Despite its importance, B-rep modeling poses significant difficulties for automatic generation. The hybrid nature of B-reps, combining continuous geometric parameters with discrete topological structures, makes the design space highly complex. Furthermore, the data structure of the B-rep representation changes for each 3D shape. B-rep models may comprise a varying number of faces, each containing boundary edges with arbitrary counts and optional inner loops. Such variability presents a challenge in directly applying deep learning techniques, which are generally tailored to inputs of fixed dimensionality. While recent generative models have demonstrated success on alternative 3D formats (e.g., meshes, point clouds, voxels, and implicit fields) [Chen and Wang 2024;Li et al. 2023cLi et al. , 2024c;;Shi et al. 2022;Sun et al. 2024], they fall short of capturing the stringent accuracy and consistency requirements of CAD models. Many CAD-oriented approaches sidestep B-rep generation by instead synthesizing sketch-and-extrude construction sequences [Ma et al. 2024a;Ren et al. 2022;Wu et al. 2021;Xu et al. 2023Xu et al. , 2022]], which fit well-established sequence generation techniques but are restricted by limited operation types and dataset availability.
Existing B-rep generation methods are typically built on hierarchical representations, which inherently lead to multi-stage generation pipelines that suffer from stage-to-stage inconsistencies. SolidGen [Jayaraman et al. 2022] emphasizes discrete data structures, sequentially defining vertices, edges, and faces via pointer networks. Its primary limitation lies in the inability to handle freeform surfaces. In contrast, BrepGen [Xu et al. 2024a] adopts a surface-based representation similar to UV-Net [Jayaraman et al. 2021], where face geometry is captured by uniformly sampling grid points in the parametric space. After generating boundaryless faces, the boundary edges for each face are further generated. While capable of representing freeform surfaces, its padding strategy, which ensures fixed input lengths for the diffusion module, introduces computational overhead and sensitivity to deduplication procedures. DTGBrep-Gen [Li et al. 2025a] seeks to explicitly separate topology from geometry by first generating edge-face and edge-vertex adjacency relationships, followed by the detailed geometry generation using a series of diffusion models. While this explicit separation provides interpretability, the sequential nature of multiple diffusion models increases computational complexity and inference time.
To overcome the inherent drawbacks of hierarchical B-rep representations, we introduce a unified sequential encoding scheme that consolidates the entire B-rep structure into a single-level coherent representation. Concretely, we encode the continuous surface and curve geometry, as well as the discrete topology of B-reps, into vertex-based features. Each vertex feature consists of three components: 1) its 3D coordinates, 2) features capturing connectivity between vertices, and 3) information about adjacent half-edges, including their local geometric details, next-edge relationships, and inner/outer classifications within loops. To bridge the gap between different primitive levels, we propose the Voronoi Half-Patch (VHP) structure, which implements the third component of our vertexbased representation. The VHP is defined for each half-edge in the B-rep model, effectively decomposing the complete B-rep information into local half-edge-centric units. This decomposition occurs in two ways: geometrically, we partition each surface in its parametric domain using Voronoi diagrams, assigning the nearest surface region to its corresponding half-edge; topologically, we encode the next-edge relationships through sampling along adjacent half-edges, enabling the reconstruction of face boundary loops through sequential half-edge traversal. The name Voronoi Half-Patch reflects its key characteristics: Voronoi refers to the parametric space partitioning mechanism, Half denotes its basis in the half-edge data structure, and Patch signifies its representation of both curve geometry and associated surface re
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