Octahedral Frames for Feature-Aligned Cross Fields

Paul Zhang,Edward Chien,Justin Solomon,Josh Vekhter,David Bommes,Etienne Vouga

doi:10.1145/3374209

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.

Highlights

Solomon received generfaces are ubiquitous in computer graphics. 2-rotationally symmetric (RoSy) fields can be used to generate stripe patterns due to their ambivalence to rotaous support from Army Research Office grant W911NF-12-R-0011, National Science tion by π about the normal. 4-RoSy fields are heav
In the case p = 1, our cross field is discontinuous over all creases, but it is provably incentivized to align, it sometimes deviates due to the influence of neighboring creases
Significant effort has been put into extrinsic alignment of cross fields to curvature directions, they are not always appropriate substitutes for crease alignment

Summary

Introduction

N -rotationally symmetric (RoSy) tangential vector fields over surand NSF IIS-1910274. J. Solomon received generfaces are ubiquitous in computer graphics. 2-RoSy fields can be used to generate stripe patterns due to their ambivalence to rotaous support from Army Research Office grant W911NF-12-R-0011, National Science tion by π about the normal. Solomon received generfaces are ubiquitous in computer graphics. 2-RoSy fields can be used to generate stripe patterns due to their ambivalence to rotaous support from Army Research Office grant W911NF-12-R-0011, National Science tion by π about the normal. 4-RoSy fields (cross fields) are heav-

Methods

Results

Conclusion