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How can I create only the base of a cup, with no sharp edges?

I want to make something like this (image taken from this post), but rotated around the leftmost point.

The end result will look something like a bowl.

I want to use this as the background for studio lighting.

Either a manual or scripted approach is ok.

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enter image description here

Create a vertex extrude it to make an "L" (far left model)

Teke the middle vertex and bevel it using Ctrl + Shift + B or Ctrl + B and then V (middle model)

Go in object mode and apply a screw modifier, make sure your origin point is on the far left vertex, in the middle of the screwing process (far right model)

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You could also create a Bézier curve where you can control the overall shape, and convert it finally into a mesh. Then you use the Screw modifier as above.

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