and Myles et al. [@myles_robust_2014] both implement robust streamline tracing algorithms based on edge maps [@jadhav_consistent_2012], and then trace out streamlines in parallel until their first crossing with another streamline, forming a motorcycle graph [@eppstein_motorcycle_2008]. This approach yields coarse quad patches because of the large number of T-junctions that appear in the decomposition. Because of the T-junctions, it is a non-trivial matter to assign globally consistent parametric lengths to each edge. Myles et al. [@myles_robust_2014] are able to achieve this via a heuristic method, which includes a collapse operation, similar to the one we describe in \[sec:partition-simplification\], used to remove edges with zero parametric length, and 2-6 cone insertion to remove zero edges which cannot be collapsed. They subsequently generate a globally consistent seamless parameterization on each quad region. This method differs from our goal in that the parameterization is not *quantized* (cf. [@campen_quantized_2015]) and so does not correspond to a quad mesh let alone a coarse quad decomposition. Campen et al. [@campen_quantized_2015] compute quantized parameterizations on surfaces by solving a combinatorial optimization problem similar to [@bommes_integer-grid_2013] but leverage the structure of a motorcycle graph to determine a set of linear equality constraints which are applied to the final optimization 