Fundamentals of Computational Conformal Geometry

David Xianfeng Gu; Feng Luo; Shing Tung Yau

doi:10.1007/s11786-011-0065-6

Fundamentals of Computational Conformal Geometry

David Xianfeng Gu
, Feng Luo
, Shing Tung Yau

Computer Science

Stony Brook University

Rutgers - The State University of New Jersey, New Brunswick
Harvard University

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

Computational conformal geometry is an inter-disciplinary field between mathematics and computer science. This work introduces the fundamentals of computational conformal geometry, including theoretic foundation, computational algorithms, and engineering applications. Two computational methodologies are emphasized, one is the holomorphic differentials based on Riemann surface theory and the other is surface Ricci flow from geometric analysis.

Original language	English
Pages (from-to)	389-429
Number of pages	41
Journal	Mathematics in Computer Science
Volume	4
Issue number	4
DOIs	https://doi.org/10.1007/s11786-011-0065-6
State	Published - Dec 2010

Keywords

Conformal geometry
Discrete surface
Holomorphic differential
Ricci flow

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10.1007/s11786-011-0065-6

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title = "Fundamentals of Computational Conformal Geometry",

abstract = "Computational conformal geometry is an inter-disciplinary field between mathematics and computer science. This work introduces the fundamentals of computational conformal geometry, including theoretic foundation, computational algorithms, and engineering applications. Two computational methodologies are emphasized, one is the holomorphic differentials based on Riemann surface theory and the other is surface Ricci flow from geometric analysis.",

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author = "Gu, \{David Xianfeng\} and Feng Luo and Yau, \{Shing Tung\}",

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doi = "10.1007/s11786-011-0065-6",

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AU - Gu, David Xianfeng

AU - Luo, Feng

AU - Yau, Shing Tung

PY - 2010/12

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N2 - Computational conformal geometry is an inter-disciplinary field between mathematics and computer science. This work introduces the fundamentals of computational conformal geometry, including theoretic foundation, computational algorithms, and engineering applications. Two computational methodologies are emphasized, one is the holomorphic differentials based on Riemann surface theory and the other is surface Ricci flow from geometric analysis.

AB - Computational conformal geometry is an inter-disciplinary field between mathematics and computer science. This work introduces the fundamentals of computational conformal geometry, including theoretic foundation, computational algorithms, and engineering applications. Two computational methodologies are emphasized, one is the holomorphic differentials based on Riemann surface theory and the other is surface Ricci flow from geometric analysis.

KW - Conformal geometry

KW - Discrete surface

KW - Holomorphic differential

KW - Ricci flow

UR - https://www.scopus.com/pages/publications/80255126145

U2 - 10.1007/s11786-011-0065-6

DO - 10.1007/s11786-011-0065-6

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VL - 4

SP - 389

EP - 429

JO - Mathematics in Computer Science

JF - Mathematics in Computer Science

IS - 4

ER -

Fundamentals of Computational Conformal Geometry

Abstract

Keywords

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