Q-MAGIC: Quad-only Mesh Autoregressive Generation via Singularity-Aware Circular Relative Offset Tokenization

Yuming Zhao; Zezeng Li; Weimin Wang; Xiang Wu; Na Lei

cs.CVOct 14, 2026

Q-MAGIC: Quad-only Mesh Autoregressive Generation via Singularity-Aware Circular Relative Offset Tokenization

Authors: Yuming Zhao, Zezeng Li, Weimin Wang, Xiang Wu, Na Lei

Organizations: Dalian University of Technology, China · École Centrale de Lyon, France

Abstract

Autoregressive models have proven effective for triangular mesh generation by transforming it into predicting the next face, converting the non-differentiable connectivity prediction into a sequence of token predictions. However, generating quad-only meshes remains challenging because quad faces impose stricter topological constraints than triangles. The model must not only serialize quad faces into a valid token sequence, but also support unambiguous connectivity reconstruction during de-serialization. To address this, we propose Q-MAGIC, a novel autoregressive model for quad mesh generation. We first introduce a tailored serialization scheme for quad meshes, which requires at least two new vertices for the next face and is less flexible than triangles due to strict wiring constraints. To meet these requirements and reduce serialization length, we propose a singularity-aware serialization that prioritizes wiring from singular points, leading to more coherent traversals. Additionally, we propose a circular relative offset tokenization that encodes geometry mainly via local relative offsets. Built upon this representation, an autoregressive Transformer learns the underlying distribution of quad meshes via next-token prediction, enabling effective quad mesh generation. Extensive experiments demonstrate that Q-MAGIC produces more compact sequences while consistently improving geometric fidelity and mesh quality compared to state-of-the-art methods.

Figures & tables

Figure 1: Overview of the Q-MAGIC. We adopt a singularity-aware serialization strategy that prioritizes critical singularities in the sequence. In our token representation, geometric information is mainly encoded by circular relative offsets, and block tokens are inserted only when necessary to re-anchor the spatial location, enabling a compact representation. During inference, Q-MAGIC conditions on point clouds and autoregressively generates quad meshes.

Figure 2: Overview of circular relative offset tokenization. Left: each vertex is represented by a block–offset pair $(B,O)$ . Right: For intra-block moves, we emit only $\Delta o_{n}$ (wrapping to the bounded interval when needed); when crossing a block boundary, we emit the new block index $B$ and then continue with relative offsets. Bottom: the resulting token sequence with BOS/EOS, consisting of block tokens and circular relative offset tokens.

Figure 3: De-serialization in Q-MAGIC. (a) Consecutive records recover the shared vertex from the last vertex of the previous face. (b,c) Directly connecting adjacent tokens for non-consecutive records may generate invalid red dashed quads. We resolve this issue via a novel de-serialization scheme. Quads are reconstructed from the recorded non-center vertices under the face of the current local patch, ensuring consistent local topology.

Method	QGPT	MAV2	EG	DM	BPT	Ours
Avg. Len.	43106	29000	28497	20675	14104	12655
Comp. Ratio	1	0.67	0.66	0.48	0.33	0.29

Table 1: Average sequence length comparison. QGPT, MAV2, EG, and DM denote QuadGPT, MeshAnythingV2, EdgeRunner and DeepMesh. Our serialization yields the lowest token length on the same mesh set.

Figure 4: Visualization results and close-up views of generated quad meshes. Our method can better preserve continuous boundary loops and structured quad layouts in detail-sensitive regions, producing more regular and stable quad meshes.

Model	Point2Quad	TMGPT	QuadGPT	BPT	Ours
SJ $\uparrow^{1}_{-1}$	0.9726	0.8879	0.9727	0.9762	0.9829
WT $\uparrow^{1}_{0}$	0.9995	0.8921	0.9836	0.9873	0.9996
MF $\uparrow^{1}_{0}$	1	0.9989	0.9998	0.9998	0.9999
CD $\downarrow^{\infty}_{0}$	0.0717	0.1704	0.0854	0.0719	0.0684
HD $\downarrow^{\infty}_{0}$	0.1069	0.3255	0.1374	0.1299	0.1058
SR $\downarrow^{1}_{0}$	0.3050	0.8715	0.2164	0.4000	0.2310

Table 2: Quantitative comparison.

\uparrow^{a}_{b}

and

\downarrow^{a}_{b}

denote that larger and smaller values are better, respectively. Here,

a

and

b

represent the upper and lower bounds.SJ, WT, MF, CD, HD, SR and US denote Scaled Jacobian, Watertightness, Manifoldness, Chamfer distance, Hausdorff distance, singularity rate and user study.

Metrics	Random	Singularity-aware
Scaled Jacobian $\uparrow^{1}_{-1}$	0.8862	0.9829
Watertightness $\uparrow^{1}_{0}$	0.9429	0.9996
Manifoldness $\uparrow^{1}_{0}$	0.9986	0.9999
Chamfer distance $\downarrow^{\infty}_{0}$	0.2202	0.0684
Hausdorff distance $\downarrow^{\infty}_{0}$	0.3906	0.1058

Table 3: Ablation study on patch serialization policies under circular relative offset tokenization (Random vs. singularity-aware).

Metrics	Block-offset	Circ. relative offset
Scaled Jacobian $\uparrow^{1}_{-1}$	0.7442	0.9829
Watertightness $\uparrow^{1}_{0}$	0.6635	0.9996
Manifoldness $\uparrow^{1}_{0}$	0.9993	0.9999
Chamfer distance $\downarrow^{\infty}_{0}$	0.3161	0.0684
Hausdorff distance $\downarrow^{\infty}_{0}$	0.5487	0.1058

Table 4: Ablation study on serialization scheme under the default singularity-aware traversal (Circular relative offset vs. Block-offset).

Figure 5: Qualitative ablation on serialization schemes.

Figure 6: Qualitative ablation on patch traversal order.

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3D mesh generation creates and edits connected 3D surfaces for digital content, reconstruction, animation, and simulation.

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The generation of production-ready quad-dominant meshes is a cornerstone of modern 3D content creation. Generating anisotropic quad-dominant meshes from point clouds is challenging, as existing methods are typically limited to producing either pure triangular meshes or pure quadrilateral meshes with isotropic densities. In this paper, we present QuadLink, a unified framework consisting of three stages for quad-dominant mesh generation by linking points into structured faces. QuadLink formulates polygonal mesh generation as a hybrid centroid-conditioned vertex linking model: it first predicts a unified set of anchors (vertices and face centroids), then learns centroid-conditioned links that associate vertices with face centroids, and finally assembles polygonal faces with a quad-first strategy guided by robust geometric verification strategies. This link-based formulation enables efficient generation of sparse and anisotropic quad-dominant meshes with coherent edge flow and meanwhile supporting hybrid polygonal topology. To construct training data for this model, we further introduce a Tri-to-Quad Operator that converts artistic triangle meshes into quad-dominant training data via global merge selection. Extensive experiments show that QuadLink produces production-ready quad-dominant meshes from point clouds and achieves improved geometric fidelity and topological quality compared to prior baselines. Our method natively supports hybrid polygonal topology, generalizing to arbitrary n-gon meshes without architectural changes.

Abstract

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