計算共形幾何（二）

Spring 2024

樂美亨

Course Information

課程名稱：計算共形幾何（二）
英文課名：Computational Conformal Geometry (II)
課程時間：週五 13:20～16:20
課程地點：數學館 M210 教室

Course Topics

• Theories
• Differential Geometry (Chapter 5)
• Riemann Surface (Chapter 6)
• Optimal Mass Transportation


• Algorithms
• Harmonic and Holomorphic Froms (Chapter 11)
• Quasi-Conformal Mappings
• Volume-Preserving Parameterizations of Discrete 3-Manifolds


• Applications
• Manifold Registration
• 3D Image Visualization

Textbooks and References

• Computational Conformal Geometry, Xianfeng David Gu and Shing-Tung Yau, Higher Education Press (2008)


• Conformal Geometry - Computational Algorithms and Engineering Applications, Miao Jin, Xianfeng Gu, Ying He, and Yalin Wang, Springer (2018)


• Recent Developments of Surface Parameterization Methods Using Quasi-conformal Geometry, Gary P. T. Choi and Lok Ming Lui, Springer (2022)


• Computational Conformal Geometric Methods for Vision, Na Lei, Feng Luo, Shing-Tung Yau, and Xianfeng Gu, Springer (2023)

Resources

• MATLAB程式設計《入門篇》


• MATLAB程式設計《進階篇》


• Tutorialspoint - MATLAB Tutorial


• File Exchange - MATLAB Central


• Octave Online


• Software - Xianfeng David Gu's Homepage

Application Demonstrations

▲Brain Tumor Visualization




▲Optimal Mass Transportation Path between Brains