| 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. |
