A survey of global conformal parameterization

This paper mainly introduces several kinds of global conformal parameterization theories and algorithms, which can deal with complex surfaces under different genus. Pure first-order differential algorithm and pure second-order differential algorithm are based on the contents of global differential geometry, whose core ideas come from Riemann’s single-valued theorem and Teichmuller theory. Ricci flow algorithm and quasi-conformal mapping algorithm are based on the contents of the field of geometric partial differential equations, which can be optimized by minimizing energy to get results. The optimal transport algorithm is based on convex differential geometry and geometric variational principle, which can be transformed into computational geometry algorithm to find the solution.