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

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.