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Geometry and Computer

Computational Conformal **Geometry**: Theories **and** Applications Xianfeng Gu, Gu Gu, Shing-Tung Shing Shing-Tung Tung Yau UFL, Harvard University

- Page 2 and 3: An important important goal of clas
- Page 4 and 5: The basic technique involves solvin
- Page 6 and 7: Definition: Conformal Mapping Sca
- Page 8 and 9: Motivation
- Page 10 and 11: Texture Mapping - Nondistortion
- Page 12 and 13: Construct conformal geometry image
- Page 14 and 15: Brain Conformal Mapping Alzheimer
- Page 16 and 17: Geometry Matching-brain Matching Ma
- Page 18 and 19: Geometric Matching-brain Matching M
- Page 20 and 21: Solution
- Page 22 and 23: Theoretic background - Riemann surf
- Page 24 and 25: Novel view Treat surfaces as Riem
- Page 26 and 27: Genus 0 surfaces All conformally
- Page 28 and 29: Global conformal parameterization a
- Page 30 and 31: Mobius Transformation Linear rati
- Page 32 and 33: Genus zero Gargoyle example Spher
- Page 34 and 35: Example:Sculpture
- Page 36 and 37: Topology: Homology group Curve sp
- Page 38 and 39: Holomorphic one-form one one-form f
- Page 40 and 41: Linear system for holomorphic 1-for
- Page 42 and 43: Holomorphic one-form one one-form f
- Page 44 and 45: Linear combination Linearly combi
- Page 46 and 47: Global Conformal Parametrization
- Page 48 and 49: Zero points Different holomorphic
- Page 50 and 51: Global conformal atlas demo
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Properties: Homology Basis Independ

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Properties:Triangulation & Resoluti

- Page 56 and 57:
Progressive Mesh

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Results: Knot

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Example:Rocker

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Surfaces with boundaries

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Example:Minimal Surface Genus one

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Non-uniformity Non Non-uniformity u

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Conformal factor Denser for high

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Facial Recognition using Conformal

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Hand Model

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David demo

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Geometry classification

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Conformal invariants - periods To

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Conformal invariants - period matri

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Embedding in Hyperbolic Space Canon

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Matching Landmarks

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Future Research Surface classific