Recent development of computational conformal geometry
This survey article about numerical conformal geometry presents state-of-the-art techniques for computing conformal mappings and conformal structures with particular emphasis on surfaces of complicated topology.NEWLINENEWLINESection~2 describes relevant literature, Section~3 introduces the necessary theoretical background from algebraic topology, Riemannian geometry, (quasi)-conformal geometry, and Teichmüller theory. The main computational techniques for computing conformal maps are introduced in Section~4. They are harmonic maps, holomorphic differential, and discrete Ricci flow. Methods for computing conformal moduli and canonical conformal mappings are described in Section~5, quasi-conformal mappings are the topic of Section~6, and Section~7 presents applications from computer graphics, geometric modeling, medical imaging, computer vision, computational geometry, and wireless sensor networks.NEWLINENEWLINEThe text is interspersed with a 32 attractive figures and numerous references for further reading.NEWLINENEWLINEFor the entire collection see [Zbl 1235.00046].
scientific article; zbMATH DE number 6059327