【115/10/29】15:20-16:10 劉書詠 先生(國立臺灣師範大學數學系博士候選人)
發佈日期 :
2026-10-27
| Colloquium | |
|---|---|
|
|
|
| Time | 2026-10-29 15:20-16:10 |
| Venue | 數學館1樓 31106 教室 |
| Speaker | 劉書詠 先生(國立臺灣師範大學數學系博士候選人) |
| Title | Area-Preserving Parameterization: Stretch Energy, Variational Theory, and Convergent Algorithms |
| Abstract | Surface parameterization is an essential tool in geometry processing, with applications to texture mapping, surface registration, and shape analysis. In this talk, we present a complete framework for computing area-preserving parameterizations of surfaces. We first review prior approaches, including optimal transport, density-equalizing maps, and stretch energy minimization, together with their limitations. We then develop a variational theory that connects smooth surfaces and triangular meshes: area-preserving maps are exactly the critical points of the stretch energy, and its discrete minimization recovers area preservation as the mesh is refined. Finally, we derive the discrete authalic flow, an efficient and globally convergent algorithm for surfaces of various topologies. |
|
|
|
