DeepAI AI Chat
Log In Sign Up

Octahedral Frames for Feature-Aligned Cross-Fields

by   Paul Zhang, et al.

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.


page 1

page 2

page 7

page 8

page 9

page 10

page 11

page 12


Computing cross fields - A PDE approach based on the Ginzburg-Landau theory

Cross fields are auxiliary in the generation of quadrangular meshes. A m...

An Approach to Quad Meshing Based on Harmonic Cross-Valued Maps and the Ginzburg-Landau Theory

A generalization of vector fields, referred to as N-direction fields or ...

Loopy Cuts: Surface-Field Aware Block Decomposition for Hex-Meshing

We present a new fully automatic block-decomposition hexahedral meshing ...

Interpolation of subdivision features for curved geometry modeling

We present a nodal interpolation method to approximate a subdivision mod...

Algebraic Representations for Volumetric Frame Fields

Field-guided parametrization methods have proven effective for quad mesh...

Ginzburg-Landau energy and placement of singularities in generated cross fields

Cross field generation is often used as the basis for the construction o...

Representing three-dimensional cross fields using 4th order tensors

This paper presents a new way of describing cross fields based on fourth...