the cross field. 3. Simplify the quad layout with T-junctions.

To demonstrate these contributions, we include them in the pipeline described in algorithm \[alg:ps-overview\], which takes as input a triangle mesh, and outputs a coarse quad layout, possibly with T-junctions.

Related Work
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Several researchers have taken an approach to generating quad layouts that is similar to the pipeline in algorithm \[alg:ps-overview\]. Kowalski et al. [@kowalski_pde_2013] design a cross field by solving a PDE with a constraint applied via Lagrange multipliers. They numerically integrate streamlines from each interior singularity and boundary corner, and snap streamlines to singularities when they pass within a certain tolerance of the singularity in order to obtain a coarser quad layout. While streamline snapping works well on some examples, it is not robust in general because it can introduce tangential crossings when more than one streamline passes nearby a singularity. Fogg et al. [@fogg_automatic_2015] take a similar approach, but initialize the cross field by an advancing front method and then smooth it with the energy functional introduced by Hertzmann and Zorin [@hertzmann_illustrating_2000]. Rather than snapping separatrices to singularities, they allow them to pass by singularities, resulting in thin regions throughout the partition. Ray and Sokolov [@ray_robust_2014] 