PaperlayerView exact revision on arXiv

Source-linked AI summary

HoLa: B-Rep Generation using a Holistic Latent Representation

Yilin Liu, Duoteng Xu, Xingyao Yu, Xiang Xu, Daniel Cohen-Or, Hao Zhang, Hui Huang

arXiv:2504.14257v3cs.GRcs.CV

TL;DR

B-Rep generation must represent continuous primitive geometry together with discrete topological relations, and prior generation can produce ambiguous or incoherent primitives. HoLa unifies geometry and topology in a surface-based latent space and recovers curves through surface intersections; experiments report higher validity and diversity than state-of-the-art alternatives.

  • Problem

    B-Reps combine continuous geometric parameters with discrete topology, while generated primitives can be ambiguous or incoherent.

    Source: §1 · p. 2

  • Method

    HoLa encodes geometry and topology in surface latents and uses neural intersection modules to recover curve geometry and relations during decoding.

    Source: §1 · p. 2

  • Results

    HoLa generates more plausible B-Reps with higher validity and greater diversity than state-of-the-art alternatives.

    Source: §1 · p. 2

  • Takeaways & Limitations

    A single latent space simplifies training and supports quality and diversity in conditional B-Rep generation.

    Source: §6 · p. 21

    Generated surface inconsistencies can cause inaccurate trimming and non-watertight B-Reps.

    Source: §5.6 · p. 21

Abstract

from arXiv · show

We introduce a novel representation for learning and generating Computer-Aided Design (CAD) models in the form of $\textit{boundary representations}$ (B-Reps). Our representation unifies the continuous geometric properties of B-Rep primitives in different orders (e.g., surfaces and curves) and their discrete topological relations in a $\textit{holistic latent}$ (HoLa) space. This is based on the simple observation that the topological connection between two surfaces is intrinsically tied to the geometry of their intersecting curve. Such a prior allows us to reformulate topology learning in B-Reps as a geometric reconstruction problem in Euclidean space. Specifically, we eliminate the presence of curves, vertices, and all the topological connections in the latent space by learning to distinguish and derive curve geometries from a pair of surface primitives via a neural intersection network. To this end, our holistic latent space is only defined on surfaces but encodes a full B-Rep model, including the geometry of surfaces, curves, vertices, and their topological relations. Our compact and holistic latent space facilitates the design of a first diffusion-based generator to take on a large variety of inputs including point clouds, single/multi-view images, 2D sketches, and text prompts. Our method significantly reduces ambiguities, redundancies, and incoherences among the generated B-Rep primitives, as well as training complexities inherent in prior multi-step B-Rep learning pipelines, while achieving greatly improved validity rate over current state of the art: 82% vs. $\approx$50%.

1 Introduction

B-Rep learning must reconcile continuous primitive geometry with discrete topology, while prior generation pipelines separate primitive types and can produce incoherent or invalid models. HoLa encodes geometry and topology in a surface-based latent space, recovers curves from surface pairs, and supports conditional generation with improved plausibility, validity, and diversity.

1 Introduction

  • B-Rep learning must combine continuous geometric parameters for primitives with their discrete topological relationships.B-Reps comprise surfaces, curves, vertices, and topological relations.Source: §1 · p. 2
  • Prior generation pipelines use separate primitive generators without explicit topology constraints, contributing to ambiguity, incoherence, invalid outputs, or post-processing.Surface and curve generators may be unaware whether two surfaces connect through a curve.Source: §1 · p. 2
  • HoLa unifies primitive geometry and topology in a latent space, using a neural intersection module to recover curve geometry from pairs of surface latents.The representation is defined over surfaces, while encoding the geometry and topological relationships of lower-order primitives.Source: §1 · p. 2
  • A VAE learns the holistic latent representation, and latent diffusion generates B-Reps from noise, point clouds, images, sketches, or text.The VAE encodes primitive geometry and connections; intersection modules decode curves and their topological relationships.Source: §1 · p. 2
  • HoLa generates more plausible B-Reps with higher validity and greater diversity than state-of-the-art alternatives.The unified latent space also allows retraining one diffusion model, rather than separate primitive models, when input conditions change.Source: §1 · p. 2

2 Related Work

Related work spans graph-based B-Rep representations, multi-step B-Rep generation, alternative CAD representations, and conditional CAD generation. These approaches offer ways to encode or generate CAD, but face challenges in capturing fine topology, coordinating primitive types, or handling complex inputs.

2.1 Representation Learning of B-Reps

  • Homogeneous graphs model surface attributes but can miss edge loops and vertices, while heterogeneous graphs capture richer primitive relationships yet complicate downstream generation.Examples include UV-Net and BRepNet for homogeneous graphs, and AutoMate for heterogeneous graphs.Source: §2.1 · p. 3

2.2 3D reconstruction and generation using B-Rep

  • Prior B-Rep generation uses multi-step primitive pipelines or separate surface and curve generators, whereas HoLa embeds primitive geometry and topology in one latent vector.SolidGen selects lower-order primitives to form surfaces; BRepGen separates topology from geometry learning, contributing to ambiguity and inconsistency.Source: §2.2 · p. 3

2.3 Constructive Solid Geometry and Sketch-and-Extrude

  • Neural CSG reconstruction can yield non-optimal trees and redundant primitives, while sketch-and-extrude models face fixed command order, limited operations, and error accumulation.Collecting construction histories for sketch-and-extrude models is more complex, and the passage reports B-Rep datasets are approximately five times larger.Source: §2.3 · p. 3

2.4 Conditional CAD model generation

  • Most generic 3D generation focuses on meshes or signed distance functions, which inadequately capture CAD sharp features and complex topology; conditional CAD methods also face ambiguous 2D inputs.The reviewed CAD methods often rely on command-based generation, and the authors report no prior direct B-Rep generation from diverse conditional inputs.Source: §2.4 · pp. 3–4

3 Overview

The framework combines a VAE that learns a surface-based holistic latent space with a latent diffusion model that generates latent vectors under varied conditions. Decoding recovers lower-order primitives and their connections to reconstruct the B-Rep.

3 Overview

  • The input B-Rep is represented by sampled parametric surfaces and curves, with surface-to-curve connections encoded as binary adjacency matrices.Surface samples use a 16×16×3 grid and curve samples use 16×3 points; vertices are merged into curve endpoints in the final representation.Source: §3 · p. 4
  • A VAE propagates curve and vertex features to surface primitives, forming a latent per surface; intersection modules recover lower-order features for decoding.The decoder reconstructs the input B-Rep from the sampled surface latent and recovered features.Source: §3 · p. 4, Figure 5 · p. 5, Figure 4 · p. 5
  • A latent diffusion model denoises latent vectors conditioned on images, point clouds, sketches, or text, then intersection and decoder networks produce the final B-Rep.Without a condition, the condition vector is set to zero; post-processing converts the output into a watertight CAD model using OpenCascade.Source: §3 · p. 4

4 Methodology

HoLa encodes B-Rep geometry and topology in a unified surface latent, then decodes curves and their topological relations from surface latents. The methodology uses this representation for conditional latent diffusion and watertight CAD reconstruction.

4. Methodology

  • HoLa encodes geometry and topology in a unified surface latent, then recovers curves, vertices, and topological connections during decoding.The encoder propagates curve features to surfaces using their topological connections, followed by self-attention and mapping to latent Gaussian parameters.Source: §4 · p. 5, §4.1 · p. 5

4.1 Encoder

  • The encoder extracts geometric features from sampled surface and curve points, then a graph neural network propagates curve features to connected surfaces.Self-attention aggregates surface features, which are mapped to the mean and variance of the latent Gaussian.Source: §4.1 · p. 5

4.2 Decoder and Loss Function

  • A neural intersection module predicts whether surface pairs intersect and recovers their curve features, while reconstruction, intersection-classification, and KL losses supervise decoding.It predicts oriented half-curves: counterclockwise for outer boundaries and clockwise for holes; swapping surface order inverts the half-curve orientation.Source: §4.2 · p. 6

4.3 Generation

  • The latent diffusion model denoises a fixed-length surface latent conditioned on a 256-dimensional input vector, with image and point-cloud features mapped into that vector.Multiple image features are averaged after adding view-pose encodings; PointNet extracts point-cloud features, and an MLP maps each condition to 256 dimensions.Source: §4.3 · pp. 6–7

4.4 Implementation Details

  • A single VAE (181M parameters) and diffusion model (205M) replace BRepGen’s two VAEs (88.6M) and four diffusion modules (202M total).The shared architecture avoids coordinating dependent components; VAE training balances positive and negative intersection pairs because true intersection pairs are much rarer than all possible face pairs.Source: §4.4 · p. 7

4.5 Post Processing

  • Post-processing fits C2-smooth B-splines, forms oriented wire loops to trim surfaces, and sews the surfaces into watertight B-Reps.For point-cloud conditions, test-time augmentation selects the generated model with the smallest Chamfer distance to the input among multiple noise samples.Source: §4.5 · p. 7

5 Experimental Results

Experiments evaluate unconditional and point-, text-, and image-conditioned generation, along with ablations and limitations. Results report higher unconditional validity, strong point-conditioned performance, and plausible outputs across varied inputs.

5.1 Unconditional B-Rep Generation

  • 82.68% validity for HoLa versus 47.74% for BRepGen after filtering simple models; qualitative samples also show more diverse and plausible shapes than the baselines.The Table 1 results average 10 runs, each comparing 3,000 generated models with 1,000 test models.Source: Table 1 · p. 8, §5.1 · pp. 10–11

5.2 Point Conditioned B-Rep Generation

  • 83.87% to 98.23% validity with 1 to 32 runs; single-sample HoLa matches baselines on Chamfer and exceeds them on geometry and topology F-scores.Under imperfect point-cloud inputs, performance remains comparable; standard generation takes 0.56 seconds per model, versus over 30 seconds for HPNet and SEDNet.Source: §5.2 · pp. 11, 14

5.3 Text-conditioned B-Rep Generation

  • HoLa generates plausible text-conditioned models, including from abstract out-of-distribution descriptions, while detailed prompts can misalign on parts, symmetry, or geometry.The section reports qualitative rather than quantitative results because text descriptions provide weak, often ambiguous supervision.Source: §5.3 · pp. 14, 16

5.4 Image-Conditioned B-Rep Generation

  • Multi-view conditioning performs best on Chamfer distance and geometry and topology F-scores; single-view and sketch inputs yield varied plausible completions in unseen regions.Multiple samples from the same single-view or sketch input vary in regions not visible in the input.Source: Table 6 · p. 16, §5.4 · p. 16

5.5 Ablation

  • Removing spatial resolution and half-edge representation sharply degrades performance; removing self-attention speeds training but lowers validity through reduced precision and recall.Intersection accuracy remains 99.99% across the ablation variants.Source: §5.5 · pp. 16, 21

5.6 Limitation

  • Generated-surface inconsistencies can cause inaccurate trimming and non-watertight models; fixed-count padding adds training noise, while 1D condition features may miss input complexity.The authors report that padding and deduplication noise can propagate to generated surfaces, and weak condition encoding can yield input-output inconsistencies.Source: §5.6 · p. 21

6 Conclusions

HoLa unifies B-Rep geometry and topology in a holistic latent space, tying topological connections to lower-order primitive geometry. The conclusion highlights simpler training and improved quality and diversity, while outlining directions for future work.

6 Conclusions

  • HoLa ties topological connections between primitives to lower-order primitive geometry, integrating those relationships into geometry reconstruction.The conclusion presents this fusion as supporting more accurate and expressive B-Rep generation.Source: §6 · p. 21
  • A single latent space simplifies training and enhances the quality and diversity of conditional B-Rep generation.Source: §6 · p. 21
  • Future work proposes compressing the latent into a global B-Rep vector and improving feature injection during conditional generation.The authors suggest these directions could improve compactness, quality, and validity.Source: §6 · p. 21

A Supplementary Material

The supplementary material includes additional conditional-generation results and examples of shape descriptions spanning varied forms and features.

A Supplementary Material

Loading 2504.14257v3…