Surface Quadrilateral Meshing from Integrable Odeco Fields

TL;DR

This paper introduces a novel method for generating orthogonal quadrilateral meshes using integrable orthogonal frame fields based on odeco tensors, extending 2D formulations to 3D with improved performance.

Contribution

It extends 2D odeco integrability to 3D, defines energies in a finite element framework, and automatically places singularities for better mesh quality without user intervention.

Findings

Better performance with mesh sizing constraints

Lower distortion metrics compared to previous methods

Validated on smooth and feature-rich CAD models

Abstract

We present a method for generating orthogonal quadrilateral meshes subject to user-defined feature alignment and sizing constraints. The approach relies on computing integrable orthogonal frame fields, whose symmetries are implicitly represented using orthogonally decomposable (odeco) tensors. We extend the existing 2D odeco integrability formulation to the 3D setting, and define the useful energies in a finite element approach. Our frame fields are shear-free (orthogonal) by construction, and we provide terms to minimize area and/or stretch distortion. The optimization naturally creates and places singularities to achieve integrability, obviating the need for user placement or greedy iterative methods. We validate the method on both smooth surfaces and feature-rich CAD models. Compared to previous works on integrable frame fields, we offer better performance in the presence of mesh sizing constraints and achieve lower distortion metrics.