MATH6212A - Topics in Applied Mathematics II - 2020/21

Announcement

• Reading for presentation:

  1. Discrete Surface Ricci Flow - Computation of surface conformal map using Ricci flow idea (Download)

  2. An Efficient Energy Minimization for Conformal Parameterizations (Download)

  3. Folding-Free Global Conformal Mapping for Genus-0 Surfaces by Harmonic Energy Minimization (Download)

  4. Efficient conformal parameterization of multiply-connected surfaces using quasi-conformal theory (Download)

  5. Spherical Conformal Parameterization of Genus-0 Point Clouds for Meshing(Download)

  6. TEMPO: Feature-Endowed Teichmuller Extremal Mappings of Point Clouds (Download)

  7. Parallelizable Global Conformal Parameterization of Simply-Connected Surfaces via Partial Welding (Download) 

General Information

Lecturer

• Ronald Lok Ming LUI
  • Office: LSB 207
  • Tel: 3943-7975
  • Email:

Time and Venue

• Lecture:

  Mon 1:30pm-4:00pm (Zoom link:https://cuhk.zoom.us/j/98652025264)

   

Course Description

Computational Quasiconformal Geometry (CQC) studies the deformation pattern between shapes. It has been widely used in various applications, such as image processing, medical image analysis, computer graphics and so on. This course gives an overview of CQC from fundamental concepts, theoretical aspects, computational aspects as well as real-world applications. It is expected that students will get a better idea of this fascinating topic after taking the course.

Lecture Notes

• Lecture 1: Introduction (Powerpoint)

• Lecture 2: Basic mathematical concepts of topological & Riemannian manifolds
• Lecture 3: Basic theories of Riemann surface and conformal structures
• Lecture 4: Surface harmonic map: theories and computation
• Lecture 5: Computation of surface harmonic and conformal maps
• Lecture 6: Fast algorithm for optimized harmonic map and Introduction to Quasiconformal Geometry
• Lecture 7: Some more computational algorithms for Quasiconformal maps
• Lecture 8: Beltrami Holomorphic Flow
• Lecture 8: Power Point illustration
• Lecture 9: Splitting method for Diffeomorphism Optimization Problem & Beltrami differentials

Useful Links

• Lecture 1 recording
• Lecture 2 recording
• Lecture 3 recording fixing
• Lecture 4 recording
• Lecture 5 recording
• Lecture 6 recording
• Lecture 7 recording
• Lecture 8 recording
• Lecture 9 recording

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