Tired of unsightly lines ruining the display of your finely crafted meshes in Floor Plan view? Well, worry no more! With the judicious application of a single setting in the Mesh tool, you can change your spider-web meshes from this:
to this: 
Too good to be true, you say? Don’t take my word for it, try it yourself! Just select the problem mesh and go into it’s settings. In the Floor Plan and Section area, under Outlines, set the Ridge Selection to Show User Defined Ridges, instead of showing all. This will make it only display the actual contours you traced onto the mesh.
BAM!