NeurFrame: Learning Continuous Frame Fields for Structured Mesh Generation

TL;DR

NeurFrame introduces a neural network that learns continuous, high-resolution frame fields to generate high-quality structured meshes for complex geometries, improving efficiency and mesh quality over prior methods.

Contribution

The paper presents NeurFrame, a neural framework for continuous frame field representation that enables efficient, high-quality mesh generation without dense discretizations.

Findings

Produces smooth frame fields guiding mesh generation

Achieves fewer singularities and better distribution in meshes

Lower computational cost compared to prior neural methods

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.