# CrossGen: Learning and Generating Cross Fields for Quad Meshing

arXiv: https://arxiv.org/abs/2506.07020 · HTML: https://mlsanity.com/paper/2506.07020/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2025.

## Built on by (most cited first, 11 of 11)

- [QuadGPT: Native Quadrilateral Mesh Generation with Autoregressive Models](https://mlsanity.com/paper/2509.21420/) (2025)
- [HY3D-Bench: Generation of 3D Assets](https://mlsanity.com/paper/2602.03907/) (2026)
- [MeshMosaic: Scaling Artist Mesh Generation via Local-to-Global Assembly](https://mlsanity.com/paper/2509.19995/) (2025)
- [Mesh-Pro: Asynchronous Advantage-guided Ranking Preference Optimization for Artist-style Quadrilateral Mesh Generation](https://mlsanity.com/paper/2603.00526/) (2026)
- [Strips as Tokens: Artist Mesh Generation with Native UV Segmentation](https://mlsanity.com/paper/2604.09132/) (2026)
- [MeshWeaver: Sparse-Voxel-Guided Surface Weaving for Autoregressive Mesh Generation](https://mlsanity.com/paper/2606.04688/) (2026)
- [TriFlow: Generating Artist-Like 3D Mesh Topology via Nearest-Vertex Vector Fields](https://mlsanity.com/paper/2606.20131/) (2026)
- [QuadLink: Autoregressive Quad-Dominant Mesh Generation via Point-Relation Learning](https://mlsanity.com/paper/2605.16813/) (2026)
- [Look Both Ways Before You Cross: Lifting Cross Fields From 2D Visual Priors](https://mlsanity.com/paper/2605.26062/) (2026)
- [SQuadGen: Generating Simple Quad Layouts via Chart Distance Fields](https://mlsanity.com/paper/2604.27329/) (2026)
- [Q-MAGIC: Quad-only Mesh Autoregressive Generation via Singularity-Aware Circular Relative Offset Tokenization](https://mlsanity.com/paper/2610.19777/) (2026)

## Abstract (arXiv)

Cross fields play a critical role in various geometry processing tasks, especially for quad mesh generation. Existing methods for cross field generation often struggle to balance computational efficiency with generation quality, using slow per-shape optimization. We introduce CrossGen, a novel framework that supports both feed-forward prediction and latent generative modeling of cross fields for quad meshing by unifying geometry and cross field representations within a joint latent space. Our method enables extremely fast computation of high-quality cross fields of general input shapes, typically within one second without per-shape optimization. Our method assumes a point-sampled surface, also called a em point-cloud surface, as input, so we can accommodate various surface representations by a straightforward point sampling process. Using an auto-encoder network architecture, we encode input point-cloud surfaces into a sparse voxel grid with fine-grained latent spaces, which are decoded into both SDF-based surface geometry and cross fields(see the teaser figure). We also contribute a dataset of models with both high-quality signed distance fields (SDFs) representations and their corresponding cross fields, and use it to train our network. Once trained, the network is capable of computing a cross field of an input surface in a feed-forward manner, ensuring high geometric fidelity, noise resilience, and rapid inference. Furthermore, leveraging the same unified latent representation, we incorporate a diffusion model for computing cross fields of new shapes generated from partial input, such as sketches. To demonstrate its practical applications, we validate CrossGen on the quad mesh generation task for a large variety of surface shapes. Experimental results...