Octahedral fields for feature-aligned cross-fields

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 use these new energies to generate feature-aligned cross fields and demonstrate the applicability of our method to quad-meshing.