NeurFrame: Learning Continuous Frame Fields for Structured Mesh Generation

2026-03-13

AI Summary

This work addresses the persistent challenge of generating high-quality structured meshes—quadrilateral in 2D and hexahedral in 3D—in the presence of complex geometries and singularities. Existing field-guided approaches are limited by discrete representations that struggle to balance continuity and computational efficiency. To overcome this, we propose NeurFrame, the first neural implicit framework for continuous frame field modeling. NeurFrame leverages self-supervised learning to reconstruct a continuous, infinite-resolution frame field from sparse discrete samples, uniformly guiding both surface and volume mesh generation. By eliminating the need for dense tetrahedralization and employing a unified neural architecture, our method significantly reduces computational overhead. Furthermore, through embedded geometric constraints and unsupervised loss optimization, NeurFrame produces smoother frame fields with fewer and better-distributed singularities, thereby enhancing the quality of resulting structured meshes.

Technology Category

• Computer Vision: 3D Computer Vision
• Machine Learning: Learning with Manifolds
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Bridging structured and unstructured data
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Structured meshes, composed of quadrilateral elements in 2D and hexahedral elements in 3D, are widely used in industrial applications and engineering simulations due to their regularity and superior accuracy in finite element analysis. Generating high-quality structured meshes, however, remains challenging, especially for complex geometries and singularities. Field-guided approaches, which construct cross fields in 2D and frame fields in 3D to encode element orientation, are promising but are typically defined on discrete meshes, limiting continuity and computational efficiency. To address these challenges, we introduce \emph{NeurFrame}, a neural framework that represents frame fields continuously over the domain, supporting infinite-resolution evaluation. Trained in a self-supervised manner on discrete mesh samples, NeurFrame produces smooth, high-quality frame fields without relying on dense tetrahedral discretizations. The resulting fields simultaneously guide high-quality quadrilateral surface meshes and hexahedral volumetric meshes, with fewer and better-distributed singularities. By using a single network, NeurFrame also achieves lower computational cost compared to prior self-supervised neural methods that jointly optimize multiple fields.

Problem

• structured mesh generation
• frame fields
• singularities
• computational efficiency
• geometric complexity

Innovation

• Neural Implicit Representation
• Frame Fields
• Structured Mesh Generation
• Self-supervised Learning
• Singularity Optimization