# 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 > Shrink Factor providing the forces.

The result after running the simulation for ~75 frames:

• Looked up solving for sag and found link (added to answer) which would require some numerical method to solve. Let the cloth sim work it out. (aside) Wonder do modified meshes (eg mirror above) perform better in cloth sim? Came across draw a catenary by mapping a parabolas focus point as parabola is rotated about a line. (Bernoulli IIRC) Did you forget the capital D?. – batFINGER Dec 18 '20 at 10:41
• @batFINGER Hmm! Mirror? Dunno! I don't think cloth deals with tension across mirror-plane, if mirror is below, and if mirror is above, then has to simulate the lot anyway? Catenaries.. does a 2D stretch follow a catenary, anyway? is it not more like a minimal surface .. which may be the same thing.. Interested in how you would flatten the surface after simulation for use as a cutting-pattern. .. Capital D? Still decyphering that remark :) – Robin Betts Dec 18 '20 at 11:05
• Begs the question re elastic material. Came up here as well mathworld.wolfram.com/Catenary.html D re hair comment, keep small d for the hoi polloi. – batFINGER Dec 18 '20 at 11:44

Another curve based option is to use the the catenary curve provided. It has an option to "hang" a catenary curve between two objects. Powerlines, cables, etc

Enable the add curve extra objects addon. In demo below have two cubes at x = +/- 4. With them both selected Add Curve > Knots > Catenary

The "dangle" of the curve is defined using the parameter a as described in

To calculate the sag given seam length and end points is demonstrated here

https://physics.stackexchange.com/questions/481379/catenary-equations-solving-for-sag-given-distance-and-cable-length

Somewhat related.

How can I create a mathematically correct arc/circular segment?

Use curves.