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I tried to make a smooth circle, but somehow its not getting smooth, like on the picture.

I made is Shade Smooth, subdivided it a few times, even tried to add a subdivision modifier and I did increase the resolution of the render output, but the result stays the same.

Does anyone know how to fix this problem?

edges are not smooth

vertices on the object

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If you subdivide with the Subdivide operation, it won't round the shape, it will just add some subdivisions, and putting the Smoothness value won't fix the problem:

enter image description here

Come back the previous version with a X > Limited Dissolve and instead use a Subdivision Surface modifier which will round the shape this time, but you'll need to bevel the top and bottom faces so that your cylinder doesn't get completely round. Then apply the modifier if you don't want any modifier:

enter image description here

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