Survey on Discrete Surface Ricci Flow

Ricci flow deforms the Riemannian metric proportionally to the curvature, such that the curvature evolves according to a nonlinear heat diffusion process, and becomes constant eventually. Ricci flow is a powerful computational tool to design Riemannian metrics by prescribed curvatures This work surv...

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Bibliographic Details
Published inJournal of computer science and technology Vol. 30; no. 3; pp. 598 - 613
Main Author 章敏 曾薇 郭任 罗锋 顾险峰
Format Journal Article
LanguageEnglish
Published New York Springer US 01.05.2015
Springer Nature B.V
Department of Computer Science, State University of New York at Stony Brook, Stony Brook, NY 11794-4400, U.S.A.%School of Computing and Information Sciences, Florida International University, Miami, Florida 33199, U.S.A.%Department of Mathematics, 0regon State University, Corvallis, 0R 97331-4605, U.S.A.%Department of Mathematics, Rutgers University, Piscataway, NJ 08854, U.S.A
Subjects
Algorithms
Analysis
Artificial Intelligence
Computation
Computer Science
Constants
Curvature
Data Structures and Information Theory
Design
Design engineering
Diffusion
Fluid mechanics
Information Systems Applications (incl.Internet)
Mathematical analysis
Nonlinearity
Registration
Software
Software Engineering
Studies
Survey
Theory of Computation
Topological manifolds
形状分析
扩散工艺
曲率
曲面离散
计算工具
计算算法
非线性
黎曼度量
discrete
uniformization theory
Ricci flow
Riemannian metric
Ricci energy
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Summary:Ricci flow deforms the Riemannian metric proportionally to the curvature, such that the curvature evolves according to a nonlinear heat diffusion process, and becomes constant eventually. Ricci flow is a powerful computational tool to design Riemannian metrics by prescribed curvatures This work surveys the theory of discrete surface Ricci flow registration and shape analysis. Surface Ricci flow has been generalized to the discrete setting. its computational algorithms, and the applications for surface
Bibliography:Ricci flow, discrete, Riemannian metric, Ricci energy, uniformization theory
11-2296/TP
Ricci flow deforms the Riemannian metric proportionally to the curvature, such that the curvature evolves according to a nonlinear heat diffusion process, and becomes constant eventually. Ricci flow is a powerful computational tool to design Riemannian metrics by prescribed curvatures This work surveys the theory of discrete surface Ricci flow registration and shape analysis. Surface Ricci flow has been generalized to the discrete setting. its computational algorithms, and the applications for surface
Min Zhang, Wei Zeng, Ren Guo, Feng Luo, Xianfeng David Gu （1Department of Computer Science, State University of New York at Stony Brook, Stony Brook, NY 11794-4400, U.S.A 2School of Computing and Information Sciences, Florida International University, Miami, Florida 33199, U.S.A. 3Department of Mathematics, Oregon State University, Corvallis, OR 97331-4605, U.S.A. 4Department of MaLhematics, Rutgers University, Piscataway, NJ 08854, U.S.A.）
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ISSN:1000-9000
1860-4749
DOI:10.1007/s11390-015-1548-8