research-article

Bounded distortion harmonic shape interpolation

Authors:

Ofir WeberAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 35, Issue 4

Article No.: 105, Pages 1 - 15

https://doi.org/10.1145/2897824.2925926

Published: 11 July 2016 Publication History

Abstract

Planar shape interpolation is a classic problem in computer graphics. We present a novel shape interpolation method that blends C^∞ planar harmonic mappings represented in closed-form. The intermediate mappings in the blending are guaranteed to be locally injective C^∞ harmonic mappings, with conformal and isometric distortion bounded by that of the input mappings. The key to the success of our method is the fact that the blended differentials of our interpolated mapping have a simple closed-form expression, so they can be evaluated with unprecedented efficiency and accuracy. Moreover, in contrast to previous approaches, these differentials are integrable, and result in an actual mapping without further modification. Our algorithm is embarrassingly parallel and is orders of magnitude faster than state-of-the-art methods due to its simplicity, yet it still produces mappings that are superior to those of existing techniques due to its guaranteed bounds on geometric distortion.

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Cited By

da Silva HRibeiro Tde C. Costa RMoreira JSerra ESpezzano F(2024)Moving Region Representations on the Spread of a Forest FireProceedings of the 33rd ACM International Conference on Information and Knowledge Management10.1145/3627673.3679111(5343-5347)Online publication date: 21-Oct-2024
https://dl.acm.org/doi/10.1145/3627673.3679111
Huang ZLiu SFu X(2024)High-order shape interpolationComputer Aided Geometric Design10.1016/j.cagd.2024.102301111(102301)Online publication date: Jun-2024
https://doi.org/10.1016/j.cagd.2024.102301
Wang YGuo MSolomon J(2023)Variational quasi-harmonic maps for computing diffeomorphismsACM Transactions on Graphics10.1145/359210542:4(1-26)Online publication date: 26-Jul-2023
https://dl.acm.org/doi/10.1145/3592105
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Index Terms

Bounded distortion harmonic shape interpolation
1. Computing methodologies
  1. Computer graphics

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Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 35, Issue 4

July 2016

1396 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/2897824

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Copyright © 2016 ACM.

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Publication History

Published: 11 July 2016

Published in TOG Volume 35, Issue 4

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Cited By

da Silva HRibeiro Tde C. Costa RMoreira JSerra ESpezzano F(2024)Moving Region Representations on the Spread of a Forest FireProceedings of the 33rd ACM International Conference on Information and Knowledge Management10.1145/3627673.3679111(5343-5347)Online publication date: 21-Oct-2024
https://dl.acm.org/doi/10.1145/3627673.3679111
Huang ZLiu SFu X(2024)High-order shape interpolationComputer Aided Geometric Design10.1016/j.cagd.2024.102301111(102301)Online publication date: Jun-2024
https://doi.org/10.1016/j.cagd.2024.102301
Wang YGuo MSolomon J(2023)Variational quasi-harmonic maps for computing diffeomorphismsACM Transactions on Graphics10.1145/359210542:4(1-26)Online publication date: 26-Jul-2023
https://dl.acm.org/doi/10.1145/3592105
Fargion GWeber O(2022)Globally Injective Flattening via a Reduced Harmonic SubspaceACM Transactions on Graphics10.1145/3550454.355544941:6(1-17)Online publication date: 30-Nov-2022
https://dl.acm.org/doi/10.1145/3550454.3555449
Dongbo SRenjie C(2022)Harmonic Shape Interpolation on Multiply‐connected Planar DomainsComputer Graphics Forum10.1111/cgf.1459841:5(1-11)Online publication date: 6-Oct-2022
https://doi.org/10.1111/cgf.14598
Aydınlılar MSahillioğlu Y(2021)Part-based data-driven 3D shape interpolationComputer-Aided Design10.1016/j.cad.2021.103027136(103027)Online publication date: Jul-2021
https://doi.org/10.1016/j.cad.2021.103027
Rossignac J(2020)Corner-operated Tran-similar (COTS) Maps, Patterns, and LatticesACM Transactions on Graphics10.1145/326734639:1(1-14)Online publication date: 7-Feb-2020
https://dl.acm.org/doi/10.1145/3267346
Lu SDing XGao FChen J(2020)Shape Manipulation of Diffusion Curves ImagesIEEE Access10.1109/ACCESS.2020.29824578(57158-57167)Online publication date: 2020
https://doi.org/10.1109/ACCESS.2020.2982457
Hefetz EChien EWeber O(2019)A Subspace Method for Fast Locally Injective Harmonic MappingComputer Graphics Forum10.1111/cgf.1362338:2(105-119)Online publication date: 7-Jun-2019
https://doi.org/10.1111/cgf.13623
Fan XBermano AKim VPopović JRusinkiewicz SWyvill BFu H(2018)TooncapProceedings of the Joint Symposium on Computational Aesthetics and Sketch-Based Interfaces and Modeling and Non-Photorealistic Animation and Rendering10.1145/3229147.3229149(1-12)Online publication date: 17-Aug-2018
https://dl.acm.org/doi/10.1145/3229147.3229149
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