Numerical computation of surface conformal mappings (Q766042)

In this survey article, the authors present methods for numerically computing conformal mappings between surfaces. The main tools are Ricci flow, Hodge theory (computation of the group of holomorphic 1-forms), and harmonic maps. The authors describe the classical smooth theory and then pass on to the modern discrete setting which lends itself better to numerical computations. Particular emphasis is put on applicability to surfaces of different topology. The article concludes with a section on applications of the theory. The examples are from the authors' own works cover the fields of computer graphics, geometric modeling, medical imaging, and wireless sensor networks. The numerous figures to illustrate the presented theory are quite remarkable, the list of references is exhaustive.