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

Gaochao Song1,2, Haohan Weng3, Luo Zhang4, Zibo Zhao3, Shenghua Gao1,2
1HKU 2Shenzhen Loop Area Institute, 3Tencent Hunyuan 3D, 4NTU
Paper Code (Coming 07/05) 🤗 Check Points (Coming)

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.

BDF Illustration

Given a triangle with vertices \( V_1, V_2, V_3 \), any interior point \( p \) can be uniquely expressed by its barycentric coordinates \( (w_1, w_2, w_3) \) satisfying \( w_1 + w_2 + w_3 = 1,\; w_i \ge 0 \). We define the Barycentric Dominance Field at \( p \) as $$ B(p) = \max(w_1,\; w_2,\; w_3). $$ \( B(p) \) takes its minimum value \( 1/3 \) at the centroid and reaches \( 1 \) at the three vertices. Drag the white point inside the triangle below to see how the barycentric weights and BDF value change in real time. The right panel visualizes \( B \) as a scalar field over the entire triangle surface, where white iso-lines denote BDF contours.

Interactive Triangle

BDF as a Scalar Field

Live Values

w1 (V1) 0.333
w2 (V2) 0.333
w3 (V3) 0.333
B(p) = 0.333
Range: \( B(p) \in [1/3,\; 1] \).
Min at centroid · max at vertices.
1/3 1

Pipeline

We adopt a sparse-voxel + flow-based 3D generation backbone (Trellis.2) and integrate BDF as an additional surface signal (like texture) alongside geometry. The pipeline consists of two main stages: (1) BDF Encoding & Decoding represents discrete mesh connectivity as a continuous BDF stored on voxel edges, with mesh recovery via vertex Non-Maximum Suppression and BDF-guided flood fill on a Dual-Contouring grid; (2) VAE + Flow Generation processes BDF in the same way as PBR textures, enabling unified, architecture-free integration into mature 3D VAE and diffusion frameworks.

BDF Encoding and Decoding Pipeline
Figure 1. BDF Encoding & Decoding. Top (Encoding): voxel edges intersecting the mesh surface store the BDF values of the intersection points; each sparse voxel keeps only three orthogonal edges (x, y, z) to avoid redundancy. Bottom (Decoding): mesh vertices are first identified via Non-Maximum Suppression on local BDF maxima, then a BDF-guided flood-fill propagates along contours to reconstruct an equivalent Voronoi-style mesh (like dual mesh).
BDF VAE and Flow Pipeline
Figure 2. VAE + Flow generation with BDF. By conceptualizing BDF as an intrinsic surface texture, we seamlessly plug it into existing 3D VAE and flow-matching diffusion frameworks without any architectural modifications, enabling unified native mesh and PBR texture generation in a single pipeline.

Citation

        @misc{song2026meshbdfbarycentricdominance,
        title={Mesh BDF: Barycentric Dominance Field for 3D Native Mesh Generation}, 
        author={Gaochao Song and Haohan Weng and Luo Zhang and Zibo Zhao and Shenghua Gao},
        year={2026},
        eprint={2606.31777},
        archivePrefix={arXiv},
        primaryClass={cs.CV},
        url={https://arxiv.org/abs/2606.31777}, 
        }