research-article

High-Order Directional Fields

Authors:

Iwan Boksebeld,

Amir VaxmanAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 41, Issue 6

Article No.: 254, Pages 1 - 17

https://doi.org/10.1145/3550454.3555455

Published: 30 November 2022 Publication History

Abstract

We introduce a framework for representing face-based directional fields of an arbitrary piecewise-polynomial order. Our framework is based on a primal-dual decomposition of fields, where the exact component of a field is the gradient of piecewise-polynomial conforming function, and the coexact component is defined as the adjoint of a dimensionally-consistent discrete curl operator. Our novel formulation sidesteps the difficult problem of constructing high-order non-conforming function spaces, and makes it simple to harness the flexibility of higher-order finite elements for directional-field processing. Our representation is structure-preserving, and draws on principles from finite-element exterior calculus. We demonstrate its benefits for applications such as Helmholtz-Hodge decomposition, smooth PolyVector fields, the vector heat method, and seamless parameterization.

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Cited By

Gong XHigham DZygalakis KBianconi G(2024)Higher-order connection Laplacians for directed simplicial complexesJournal of Physics: Complexity10.1088/2632-072X/ad353b5:1(015022)Online publication date: 28-Mar-2024
https://doi.org/10.1088/2632-072X/ad353b
Edelstein MGuillen NSolomon JBen-Chen M(2023)A Convex Optimization Framework for Regularized Geodesic DistancesACM SIGGRAPH 2023 Conference Proceedings10.1145/3588432.3591523(1-11)Online publication date: 23-Jul-2023
https://dl.acm.org/doi/10.1145/3588432.3591523

Index Terms

High-Order Directional Fields
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling

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cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 41, Issue 6

December 2022

1428 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/3550454

Issue’s Table of Contents

Copyright © 2022 ACM.

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Publication History

Published: 30 November 2022

Published in TOG Volume 41, Issue 6

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Cited By

Gong XHigham DZygalakis KBianconi G(2024)Higher-order connection Laplacians for directed simplicial complexesJournal of Physics: Complexity10.1088/2632-072X/ad353b5:1(015022)Online publication date: 28-Mar-2024
https://doi.org/10.1088/2632-072X/ad353b
Edelstein MGuillen NSolomon JBen-Chen M(2023)A Convex Optimization Framework for Regularized Geodesic DistancesACM SIGGRAPH 2023 Conference Proceedings10.1145/3588432.3591523(1-11)Online publication date: 23-Jul-2023
https://dl.acm.org/doi/10.1145/3588432.3591523

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