Bounded distortion harmonic mappings in the plane

Renjie Chen; Ofir Weber

doi:10.1145/2766989

Bounded distortion harmonic mappings in the plane

Renjie Chen, Ofir Weber

Bar-Ilan University - The Alexander Kofkin Faculty of Engineering

University of North Carolina at Chapel Hill

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

29 Scopus citations

Abstract

We present a framework for the computation of harmonic and conformal mappings in the plane with mathematical guarantees that the computed mappings are C1, locally injective and satisfy strict bounds on the conformal and isometric distortion. Such mappings are very desirable in many computer graphics and geometry processing applications. We establish the sufficient and necessary conditions for a harmonic planar mapping to have bounded distortion. Our key observation is that these conditions relate solely to the boundary behavior of the mapping. This leads to an efficient and accurate algorithm that supports handle-based interactive shape-and-image deformation and is demonstrated to outperform other state-of-the-art methods.

Original language	English
Title of host publication	Proceedings of ACM SIGGRAPH 2015
Publisher	Association for Computing Machinery
Volume	34
Edition	4
ISBN (Electronic)	9781450333313
DOIs	https://doi.org/10.1145/2766989
State	Published - 27 Jul 2015
Event	ACM Special Interest Group on Computer Graphics and Interactive Techniques Conference, SIGGRAPH 2015 - Los Angeles, United States Duration: 9 Aug 2015 → 13 Aug 2015

Conference

Conference	ACM Special Interest Group on Computer Graphics and Interactive Techniques Conference, SIGGRAPH 2015
Country/Territory	United States
City	Los Angeles
Period	9/08/15 → 13/08/15

Bibliographical note

Publisher Copyright:
Copyright 2015 ACM.

Keywords

Bounded distortion
Conformal mappings
Harmonic mappings
Injective mappings
Planar deformation

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10.1145/2766989

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title = "Bounded distortion harmonic mappings in the plane",

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N2 - We present a framework for the computation of harmonic and conformal mappings in the plane with mathematical guarantees that the computed mappings are C1, locally injective and satisfy strict bounds on the conformal and isometric distortion. Such mappings are very desirable in many computer graphics and geometry processing applications. We establish the sufficient and necessary conditions for a harmonic planar mapping to have bounded distortion. Our key observation is that these conditions relate solely to the boundary behavior of the mapping. This leads to an efficient and accurate algorithm that supports handle-based interactive shape-and-image deformation and is demonstrated to outperform other state-of-the-art methods.

AB - We present a framework for the computation of harmonic and conformal mappings in the plane with mathematical guarantees that the computed mappings are C1, locally injective and satisfy strict bounds on the conformal and isometric distortion. Such mappings are very desirable in many computer graphics and geometry processing applications. We establish the sufficient and necessary conditions for a harmonic planar mapping to have bounded distortion. Our key observation is that these conditions relate solely to the boundary behavior of the mapping. This leads to an efficient and accurate algorithm that supports handle-based interactive shape-and-image deformation and is demonstrated to outperform other state-of-the-art methods.

KW - Bounded distortion

KW - Conformal mappings

KW - Harmonic mappings

KW - Injective mappings

KW - Planar deformation

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BT - Proceedings of ACM SIGGRAPH 2015

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T2 - ACM Special Interest Group on Computer Graphics and Interactive Techniques Conference, SIGGRAPH 2015

Y2 - 9 August 2015 through 13 August 2015

ER -

Bounded distortion harmonic mappings in the plane

Abstract

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Keywords

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