CrossGen: Learning and Generating Cross Fields for Quad Meshing

2025-06-08

AI Summary

Balancing efficiency and quality in cross-field modeling for quadrilateral mesh generation remains challenging. Method: We propose the first unified framework supporting both feedforward prediction and latent-space generation. Our approach jointly encodes point-cloud surfaces and cross-fields into a sparse voxel-based latent space, integrating signed distance function (SDF) geometry reconstruction, directional field parameterization, and diffusion modeling. We introduce a novel geometry-field joint implicit representation, enabling zero-iteration feedforward inference and sketch-guided generation. Contribution/Results: We construct the first large-scale SDF–cross-field paired dataset. Experiments demonstrate high-fidelity cross-field generation in under one second across diverse complex shapes—significantly outperforming conventional optimization-based methods. Our method exhibits strong robustness to input noise and end-to-end improves downstream quad-mesh quality and generation efficiency.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Natural Language Processing: Generation

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Multilingual and cross-lingual Web search
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

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, or called a point-cloud surface, as input, so we can accommodate various different 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. 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...

Problem

• Balancing efficiency and quality in cross field generation
• Enabling fast cross field computation without per-shape optimization
• Generating cross fields for quad meshing from point-cloud surfaces

Innovation

• Unifies geometry and cross fields in latent space
• Uses auto-encoder for fast feed-forward prediction
• Incorporates diffusion model for new shape generation