Join Our Newsletter

Free Online Productivity Tools
i2Speak
i2Symbol
i2OCR
iTex2Img
iWeb2Print
iWeb2Shot
i2Type
iPdf2Split
iPdf2Merge
i2Bopomofo
i2Arabic
i2Style
i2Image
i2PDF
iLatex2Rtf
Sci2ools

IMAMS

2007

2007

Conformal geometry is in the core of pure mathematics. Conformal structure is more ﬂexible than Riemaniann metric but more rigid than topology. Conformal geometric methods have played important roles in engineering ﬁelds. This work introduces a theoretically rigorous and practically efﬁcient method for computing Riemannian metrics with prescribed Gaussian curvatures on discrete surfaces - discrete surface Ricci ﬂow, whose continuous counter part has been used in the proof of Poincar´e conjecture. Continuous Ricci ﬂow conformally deforms a Riemannian metric on a smooth surface such that the Gaussian curvature evolves like a heat diffusion process. Eventually, the Gaussian curvature becomes constant and the limiting Riemannian metric is conformal to the original one. In the discrete case, surfaces are represented as piecewise linear triangle meshes. Since the Riemannian metric and the Gaussian curvature are discretized as the edge lengths and the angle deﬁcits, the discrete ...

Related Content

Added |
29 Oct 2010 |

Updated |
29 Oct 2010 |

Type |
Conference |

Year |
2007 |

Where |
IMAMS |

Authors |
Miao Jin, Junho Kim, Xianfeng David Gu |

Comments (0)