The unified discrete surface Ricci flow Public Deposited

http://ir.library.oregonstate.edu/concern/articles/4f16c478k

This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Elsevier and can be found at:  http://www.journals.elsevier.com/graphical-models/

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  • The unified surface Ricci flow
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  • Ricci flow deforms the Riemannian metric proportionally to the curvature, such that the curvature evolves according to a heat diffusion process and eventually becomes constant everywhere. Ricci flow has demonstrated its great potential by solving various problems in many fields, which can be hardly handled by alternative methods so far. This work introduces the unified theoretic framework for discrete Surface Ricci Flow, including all the common schemes: Tangential Circle Packing, Thurston’s Circle Packing, Inversive Distance Circle Packing and Discrete Yamabe Flow. Furthermore, this work also introduces a novel schemes, Virtual Radius Circle Packing and the Mixed Type schemes, under the unified framework. This work gives explicit geometric interpretation to the discrete Ricci energies for all the schemes with all back ground geometries, and the corresponding Hessian matrices. The unified frame work deepens our understanding to the the discrete surface Ricci flow theory, and has inspired us to discover the new schemes, improved the flexibility and robustness of the algorithms, greatly simplified the implementation and improved the efficiency.
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  • Zhang, M., Guo, R., Zeng, W., Luo, F., Yau, S. T., & Gu, X. (2014). The unified discrete surface Ricci flow. Graphical Models, 76(5), 321-339. doi:10.1016/j.gmod.2014.04.008
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  • description.provenance : Submitted by Deanne Bruner (deanne.bruner@oregonstate.edu) on 2015-05-11T22:49:00Z No. of bitstreams: 1 GuoRenMathematicsUnifiedSurfaceRicciFlow.pdf: 1290411 bytes, checksum: de4c6f0acf692c982c6ef5fbdb1935f0 (MD5)
  • description.provenance : Approved for entry into archive by Deanne Bruner(deanne.bruner@oregonstate.edu) on 2015-05-11T22:49:45Z (GMT) No. of bitstreams: 1 GuoRenMathematicsUnifiedSurfaceRicciFlow.pdf: 1290411 bytes, checksum: de4c6f0acf692c982c6ef5fbdb1935f0 (MD5)
  • description.provenance : Made available in DSpace on 2015-05-11T22:49:45Z (GMT). No. of bitstreams: 1 GuoRenMathematicsUnifiedSurfaceRicciFlow.pdf: 1290411 bytes, checksum: de4c6f0acf692c982c6ef5fbdb1935f0 (MD5) Previous issue date: 2014-09

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