I'd like to be able to render flexible lines, or ropes, as below:
I thought about using a Line Renderer but it doesn't have the flexibility to render arbitrary curves.
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This effect can be easily accomplished with just hinge joints.
This above gif, was created without any code whatsoever. Each link in the chain is connected to the one above it via a Hinge Joint 2D. You can play around with the mass of the rope vs the object it is holding for better physic response
Point is, you shouldn't be using a line renderer for something like this.
Its by using SetPosition Property. Have a look at this.
Hope this helps.