Octahedral Frames for Feature-Aligned Cross-Fields

TL;DR

This paper introduces a novel energy-based method for designing smooth, feature-aligned cross fields on surfaces using spherical harmonics, with applications in quad-meshing and extensive benchmarking.

Contribution

It presents a new class of energies for cross field design that align with surface features and provides theoretical analysis and practical benchmarks.

Findings

The method effectively aligns cross fields with sharp surface features.

The energies promote smoothness while respecting geometric creases.

Benchmark results show improved feature alignment over existing approaches.

Abstract

We present a method for designing smooth cross fields on surfaces that automatically align to sharp features of an underlying geometry. Our approach introduces a novel class of energies based on a representation of cross fields in the spherical harmonic basis. We provide theoretical analysis of these energies in the smooth setting, showing that they penalize deviations from surface creases while otherwise promoting intrinsically smooth fields. We demonstrate the applicability of our method to quad-meshing and include an extensive benchmark comparing our fields to other automatic approaches for generating feature-aligned cross fields on triangle meshes.