Conformal mesh deformations with Möbius transformations

Amir Vaxman; Christian Müller; Ofir Weber

doi:10.1145/2766915

Conformal mesh deformations with Möbius transformations

Amir Vaxman, Christian Müller, Ofir Weber

Bar-Ilan University - The Alexander Kofkin Faculty of Engineering

Vienna University of Technology

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

28 Scopus citations

Abstract

We establish a framework to design triangular and circular polygonal meshes by using face-based compatible Möbius transformations. Embracing the viewpoint of surfaces from circles, we characterize discrete conformality for such meshes, in which the invariants are circles, cross-ratios, and mutual intersection angles. Such transformations are important in practice for editing meshes without distortions or loss of details. In addition, they are of substantial theoretical interest in discrete differential geometry. Our framework allows for handle-based deformations, and interpolation between given meshes with controlled conformal error.

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/10.1145/2766915
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.

Funding

Funders	Funder number
Austrian Science Fund	I 706-N26

Keywords

Circular meshes
Discrete conformal transformations
Handle-based editing
Interpolation
Möbius transformations

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10.1145/2766915

Cite this

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AB - We establish a framework to design triangular and circular polygonal meshes by using face-based compatible Möbius transformations. Embracing the viewpoint of surfaces from circles, we characterize discrete conformality for such meshes, in which the invariants are circles, cross-ratios, and mutual intersection angles. Such transformations are important in practice for editing meshes without distortions or loss of details. In addition, they are of substantial theoretical interest in discrete differential geometry. Our framework allows for handle-based deformations, and interpolation between given meshes with controlled conformal error.

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KW - Discrete conformal transformations

KW - Handle-based editing

KW - Interpolation

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BT - Proceedings of ACM SIGGRAPH 2015

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Y2 - 9 August 2015 through 13 August 2015

ER -

Conformal mesh deformations with Möbius transformations

Abstract

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Keywords

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