Surface Quadrilateral Meshing from Integrable Odeco Fields

2026-04-04

AI Summary

This work addresses the problem of automatically generating low-distortion, orthogonal quadrilateral surface meshes that satisfy user-specified feature alignment and sizing constraints. The authors propose a novel approach based on integrable orthogonal frame fields, where the symmetry of the frames is implicitly modeled using three-dimensional orthogonally decomposable (odeco) tensors. Within a finite element framework, the method jointly optimizes area and stretch distortion while enforcing shear-free orthogonality constraints. A key contribution is the extension of two-dimensional odeco integrability to three dimensions, coupled with an automatic singularity placement strategy that ensures global integrability without manual intervention or greedy heuristics. Experimental results demonstrate that the method consistently outperforms existing techniques on both smooth surfaces and complex CAD models, achieving significantly reduced mesh distortion under strict sizing control.

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.

Problem

• quadrilateral meshing
• integrable frame fields
• odeco tensors
• feature alignment
• mesh sizing constraints

Innovation

• integrable frame fields
• odeco tensors
• quadrilateral meshing
• orthogonal parameterization
• singularity placement