Course Information

References

• G. P. T. Choi and L. M. Lui, Recent Developments of Surface Parameterization Methods Using Quasi-conformal Geometry, in Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging, pp. 1483–1523, Springer, 2023.
• M. M. S. Nasser and M. Vuorinen, On Computation of Capacities and Conformal Invariants, Journal of Mathematical Sciences, 298, pp. 638–672, 2026.
• M. Gillespie, B. Springborn, and K. Crane, Discrete Conformal Equivalence of Polyhedral Surfaces, ACM Transactions on Graphics, 40(4), Article 103, pp. 1–20, 2021.
• F. Luo, J. Sun, and T. Wu, Discrete Conformal Geometry of Polyhedral Surfaces and Its Convergence, Geometry & Topology, 26(3), pp. 937–987, 2022.
• N. Donati, E. Corman, S. Melzi, and M. Ovsjanikov, Complex Functional Maps: A Conformal Link Between Tangent Bundles, Computer Graphics Forum, 41(1), pp. 317–334, 2022.
• R. Capouellez and D. Zorin, Metric Optimization in Penner Coordinates, ACM Transactions on Graphics, 42(6), Article 234, pp. 1–19, 2023.
• K. Akalin, U. Finnendahl, O. Sorkine-Hornung, and M. Alexa, Mesh Parameterization Meets Intrinsic Triangulations, Computer Graphics Forum, 43(5), e15134, 2024.
• S.-Y. Liu and M.-H. Yueh, Energy-Based Distortion-Balancing Parameterization for Open Surfaces, SIAM Journal on Imaging Sciences, 18(4), pp. 2059–2093, 2025.

Course Topics

• Computational quasi-conformal geometry and modern surface parameterization
• Discrete conformal equivalence of polyhedral surfaces and convergence to smooth conformal maps
• Numerical capacities, conformal invariants, and boundary-integral formulations
• Variational distortion energies, Penner coordinates, and metric optimization
• Intrinsic triangulations and robust low-distortion mesh parameterization
• Complex functional maps, tangent-bundle correspondences, and conformal shape analysis