research-article

Robust fairing via conformal curvature flow

Authors:

Ulrich Pinkall,

Peter SchröderAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 32, Issue 4

Article No.: 61, Pages 1 - 10

https://doi.org/10.1145/2461912.2461986

Published: 21 July 2013 Publication History

Abstract

We present a formulation of Willmore flow for triangulated surfaces that permits extraordinarily large time steps and naturally preserves the quality of the input mesh. The main insight is that Willmore flow becomes remarkably stable when expressed in curvature space -- we develop the precise conditions under which curvature is allowed to evolve. The practical outcome is a highly efficient algorithm that naturally preserves texture and does not require remeshing during the flow. We apply this algorithm to surface fairing, geometric modeling, and construction of constant mean curvature (CMC) surfaces. We also present a new algorithm for length-preserving flow on planar curves, which provides a valuable analogy for the surface case.

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Cited By

Nabizadeh MRoy-Chowdhury RYin HRamamoorthi RChern A(2024)Fluid Implicit Particles on Coadjoint OrbitsACM Transactions on Graphics10.1145/368797043:6(1-38)Online publication date: 19-Dec-2024
https://dl.acm.org/doi/10.1145/3687970
Mattos Da silva LStein OSolomon J(2024)A Framework for Solving Parabolic Partial Differential Equations on Discrete DomainsACM Transactions on Graphics10.1145/366608743:5(1-14)Online publication date: 28-May-2024
https://dl.acm.org/doi/10.1145/3666087
Feng NCrane K(2024)A Heat Method for Generalized Signed DistanceACM Transactions on Graphics10.1145/365822043:4(1-19)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658220
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Index Terms

Robust fairing via conformal curvature flow
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
2. Theory of computation
  1. Randomness, geometry and discrete structures

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cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 32, Issue 4

July 2013

1215 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/2461912

Issue’s Table of Contents

Copyright © 2013 ACM.

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Publication History

Published: 21 July 2013

Published in TOG Volume 32, Issue 4

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Bundesministerium für Bildung und Forschung
Deutsche Forschungsgemeinschaft
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Hausdorff Research Institute for Mathematics
TU München Institute for Advanced Study

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Cited By

Nabizadeh MRoy-Chowdhury RYin HRamamoorthi RChern A(2024)Fluid Implicit Particles on Coadjoint OrbitsACM Transactions on Graphics10.1145/368797043:6(1-38)Online publication date: 19-Dec-2024
https://dl.acm.org/doi/10.1145/3687970
Mattos Da silva LStein OSolomon J(2024)A Framework for Solving Parabolic Partial Differential Equations on Discrete DomainsACM Transactions on Graphics10.1145/366608743:5(1-14)Online publication date: 28-May-2024
https://dl.acm.org/doi/10.1145/3666087
Feng NCrane K(2024)A Heat Method for Generalized Signed DistanceACM Transactions on Graphics10.1145/365822043:4(1-19)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658220
Noma YSellán SSharp NSingh KJacobson A(2024)Surface-Filling Curve Flows via Implicit Medial AxesACM Transactions on Graphics10.1145/365815843:4(1-12)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658158
Corman E(2024)Curvature-Driven Conformal DeformationsACM Transactions on Graphics10.1145/365814543:4(1-16)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658145
Li YNumerow LThomaszewski BCoros S(2024)Differentiable Geodesic Distance for Intrinsic Minimization on Triangle MeshesACM Transactions on Graphics10.1145/365812243:4(1-14)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658122
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Basset JBénard PBarla P(2024)SMEAR: Stylized Motion Exaggeration with ARt-directionACM SIGGRAPH 2024 Conference Papers10.1145/3641519.3657457(1-11)Online publication date: 13-Jul-2024
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Li ZYang GZhao QDeng XGuibas LHariharan BWetzstein G(2024)Neural Control Variates with Automatic IntegrationACM SIGGRAPH 2024 Conference Papers10.1145/3641519.3657395(1-9)Online publication date: 13-Jul-2024
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