Edit:
The main repository is here in case you’re interested in the math/code:
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This has got to be one of the most concise first-time posts ever! 
Presets 1, 3 and 4 even contain mathematically and physically correct (at least so it seems) catenary curve simulations.
Well done and worth a look! 
As an extension, I would like to see a toggle switch between mouse events processed either as acting on control points (as is) or as orbit controls …
[Edit:] the horizontal movement of a control point once it rests on the floor would benefit from speed attenuation (friction) and/or some more (fluid) damping, to make it more realistic looking in comparison to the “dangling” of thread/cable/chain segments fully suspended
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Interesting!
I somehow got the Gordian Knot to untangle.