problem, guaranteeing a valid solution which also outperforms previous parameterization methods, especially in cases with a large number of singularities or large target edge lengths. This enables them finally to extract a coarse quad mesh. Razafindrazaka et al. [@razafindrazaka_perfect_2015] trace out separatrices of a seamless parameterization to generate a graph of possible matchings between separatrices and singularities. They then formulate the problem of connecting singularities together as a minimum weight perfect matching problem. In a second paper [@razafindrazaka_optimal_2017] they extend their perfect matching method to work on an input quad mesh rather than a seamless parameterization. Zhang et al. [@zhang_automatic_2016] employ a similar strategy to [@razafindrazaka_perfect_2015], from an input seamless parameterization they identify candidate separatrices as monotone isolines of the parameterization in areas they call *safety turning areas* which are rectangular parameterizations between opposite singularities. From these candidate separatrices they choose an optimal set via a binary optimization problem. Pietroni et al. [@pietroni_tracing_2016] trace out candidate curves connecting either two singularities or a singularity to a boundary which they call *field-coherent* streamlines, which can deviate from the cross field but never switch to a different direction of the field. They then select a valid subset of these candidate streamlines to 