We introduce a new algorithm for the automatic computation of a global parameterization of arbitrary simplicial 2-manifolds. The parameter lines are guided by a given frame field, for example, by principal curvature frames. The parametrization is globally continuous and allows a remeshing of triangle-based surfaces into quadrilaterals. The algorithm has applications in finite element numerics, computation of minimal surfaces, and surface processing in computer aided geometric design. The talk we will introduce the necessary ingredients from discrete differential geometry, homology computation, covering spaces and integrable frame fields. We will also show a short excerpt of the new video MESH - A journey through discrete geometry.