Add deflection in middle of edge (catenary curve) I'm very new to Blender and trying to use it to design cut patterns for a tent I plan to sew. In tent design, you need to add catenary curves to edges so they tension the panels nicely. For instance, you can see the curvature where the panels join in this image

In modeling terms, I need to create a 3-point arc edge. I'd like to specify the deflection at the midpoint to accomplish this

I have a feeling the solution is something related to beveling. However, the answer here does not work if I add a vertex to the middle of my edge - the bevel just adds additional vertices without introducing any curvature. Another answer shows beveling for faces, but I need to bevel the edge connecting two faces.
I guess somebody has to suggest a cloth simulation, although I'm not sure it will meet your specifications. The curves resulting from pinning and tension don't appear to be catenaries, until the tension is wound up to an unrealistic level.
The topology is as shown, with the selected vertex-groups pinned in the simulation:

The edges between planes have also been given some damping in tension.. there may be more accurate settings, depending on the real-life constraints. The cloth settings are a slight variation on the 'Rubber' preset, supplied in the .blend as 'Tent', with a Shape &gt; Shrink Factor providing the forces.
The result after running the simulation for ~75 frames: