Building fabrics in traveling salesman (TSP) order

It's real simple. Choose a map of the surface. Choose a subset of map's edges that constitutes a spanning tree. Place the quadrilateral truchet tiles of the previous post so that the dashed line coincides with the map edge if that edge is in the spanning tree; otherwise, orient the tile so that the dashed line coincides with the dual edge. Choose a place to start the knitting, and the tiles do the rest. Every shape: no increases or decreases.