Mesh BDF: Barycentric Dominance Field for 3D Native Mesh Generation

2026-06-30

AI Summary

Existing autoregressive approaches to native 3D mesh generation are limited by constraints on face count, vertex resolution, and texture support. This work proposes the Barycentric Dominance Field (BDF), which for the first time encodes discrete mesh topological connectivity as a continuous signal defined over the surface of a triangle mesh. This formulation seamlessly integrates with mainstream 3D diffusion-based generative models without requiring any architectural modifications. The method enables high-quality, scalable, and robust native mesh synthesis, significantly outperforming state-of-the-art autoregressive methods in both geometric detail fidelity and topological completeness.

Abstract

Autoregressive (AR) modeling has recently achieved remarkable progress in native 3D mesh generation, largely due to its natural ability to handle variable-length, discrete data structures. However, the inherent constraints of the AR paradigm severely restrict the generated meshes, leading to limited face counts, bounded vertex resolutions, and difficulties in supporting textures. To overcome these bottlenecks, we propose the Barycentric Dominance Field (BDF), a continuous representation defined on triangular mesh surfaces that elegantly encodes vertex topological connectivity. BDF bridges the fundamental gap between discrete mesh topology and continuous diffusion-based generative modeling by transforming connectivity into a continuous surface signal. As an intrinsic mesh property, BDF shares strong similarities with texture maps, enabling its seamless integration into existing 3D diffusion pipelines without requiring architectural modifications. Extensive experiments demonstrate that BDF empowers diffusion models to generate native meshes with significantly higher quality, greater scalability, and stronger robustness compared to state-of-the-art autoregressive methods.

Problem

• autoregressive modeling
• 3D mesh generation
• mesh topology
• texture support
• vertex resolution

Innovation

• Barycentric Dominance Field
• 3D mesh generation
• diffusion models
• continuous representation
• mesh topology