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I'm trying to make an object consisting of a curved flat shape transitioning to an upright circle. I already made some edges for the transition profile using curves.

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If I convert those curves to a mesh, it kind of gives a feeling of how it should look, but the mesh is interpolated linear and not actually transitioning into the circle.

enter image description here

What can I do tho make it a smooth transition? I had considered adding more curves and doing the transition by hand, but it kind of feels like I'm missing some tools that could make this a lot easier.

Any help is appreciated!

.blend file

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enter image description here

I prepared a rectangle with evenly spaced vertices using the snap to vertex option, it resulted maden of 38 vertices, so i added a circle of 38 vertices in the appropriate location, and I used Bridge edge loops function to connect them.

Then I added a loopcut in the middle and adjusted scaling based on your curve, and added similarily other 2 edge loops.

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