COMPUTATIONAL CONFORMAL GEOMETRY

XIANFENG DAVID GU      ASSOCIATE PROFESSOR
WEI ZENG                        POSTDOCTORAL RESEARCHER

COMPUTER SCIENCE DEPARTMENT

STONY BROOK UNIVERSITY (SUNY @ STONY BROOK)

STONY BROOK, NEW YORK 11794

RICCI FLOW | HOLOMORPHIC 1-FORM | APPLICATIONS

 

　

UNIFORMIZATION THEOREM - RICCI FLOW

　
Ricci Flow - General Closed Surfaces Ricci Flow - General Open Surfaces Geometric Structures

(1) Spherical structure on S2, (2) Euclidean structure on R2, (3) Hyperbolic structure on Poincare Disk H2: Conformal Structures.
(4) Projective structure on Klein Model H2: another kind of Geometric Structure.
　

GLOBAL CONFORMAL PARAMETERIZATION - HOLOMORPHIC 1-FORM
Step1: Harmonic 1-Forms Step2: Conjugate Harmonic 1-Forms Step3: Holomorphic 1-Forms
　
Riemannian Mapping Annulus Conformal Mapping Generalized Koebe's Conformal Mapping
　

QUASI-CONFORMAL MAPPING
Qusi-Riemannian Mapping Quasi-Annulus Mapping Quasi-Koebe's Mapping
　

EXAMPLES

Hyper (front-back)

 Camel (front-back) Dino Bull
　
Stanford Bunny David (front-back-left-right) Bird
　

APPLICATIONS IN MEDICAL IMAGING

Brain Morphology Virtual Colonoscopy Supine-Prone Colon Registration
　

APPLICATIONS IN COMPUTER VISION


Dynamic Conformal Mapping

 Non-Rigid Surface Registration Ricci Flow for Shape Analysis
　

APPLICATIONS IN GRAPHICS

Scientific Computation Texture Mapping

   

Geometry Image Stanford Bunny - Texture Mapping
　

APPLICATIONS IN GEOMETRIC MODELING

            

Manifold Spline (Bird - Buddha - David_Head) for Inverse Engineering
　

APPLICATIONS IN WIRELESS SENSOR NETWORKING

Greedy Routing by Euclidean Ricci Flow Resilient Routing in Hyperbolic Universal Covering Space Routing by Schottky Group
　

The materials published on this site are for non-commercial use such as research and teaching.

If you need higher resolution version, please contact gu AT cs.sunysb.edu.

©2003-2010 Xianfeng David Gu    http://www.cs.sunysb.edu/~gu
Wei Zeng   http://www.cs.sunysb.edu/~zengwei
Last Updated: 12/15/2010