form a quad layout with T-junctions by solving a binary optimization problem.

The pipeline we implement is most similar to [@razafindrazaka_perfect_2015; @zhang_automatic_2016] and [@pietroni_tracing_2016] because it attempts to generate a quad layout by directly manipulating the streamlines of an underlying cross field. It also shares similarities with the methods of Tarini et al. [@tarini_simple_2011] and Bommes et al. [@bommes_global_2011], which attempt to simplify the base complex of an unstructured quad mesh via greedy application of grid preserving operators, the difference being that our simplification method is applied directly to the separatrices of a cross field rather than an input quad mesh.

Cross Field Design {#sec:cross-fields}
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Many different methods exist to design a smooth cross field on a curved surface [@hertzmann_illustrating_2000; @palacios_rotational_2007; @ray_n-symmetry_2008; @ray_geometry-aware_2009; @bommes_mixed-integer_2009; @crane_trivial_2010; @knoppel_globally_2013; @panozzo_frame_2014; @jakob_instant_2015; @vaxman_directional_2016; @huang_extrinsically_2016; @beaufort_computing_2017], any of which might be used in algorithm \[alg:ps-overview\]. In the interest of brevity, we will not offer a full review of the literature here but instead refer the reader to [@vaxman_directional_2016]. The diffusion generated method introduced in Viertel and Osting [@viertel_approach_2019] is appealing in the context of meshing CAD surfaces because it is comparable in speed to the fastest methods such as those described in Knöppel et 