Hello all,
Looking for help in regards to unrolling/flattening this double curved parabola (pictured in red) the goal is to create a 2D version of the curve that could be fabricated and bent backwards to then resemble the dome structure in the background. Have tried a few things but they all end in deformation of the curve so any help would be appreciated!
“Unrolling” double-curved surfaces isn’t a real thing because once material has to stretch and/or compress, the pattern could be anything. There are only “rules of thumb” based on assumed material properties, whether they’re codified in some sort of tool or not.
I assume the same applies to a curve, though what is the “curve” going to actually be in reality? It’s technically easy to flatten a 3D curve, just draw a line of its length…which isn’t what you’re looking for I know.
It seems like in your case there might be some kind of single-curved surface that more-or-less passes through the 3D curve(looking at it from the side) that you could make and unroll?
Yeah, if I project a parabola on to a sphere, any symmetric curve really, then I get a 2D profile from the side that’s unrollable.
This.
“Resembles” is kind of vague. How close do you need to get?
Are you looking for a shape that can be made with a bend into a planar arch which can be subjected to another bend in a perpendicular plane to make the arch profile match the profile of the dome opening, but which creates an arch that doesn’t sit wholly on the dome surface? (which others have already solved.)
Or do you also want to curve the final result around the vertical axis of the dome so the arch sits entirely on its surface?
