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+1 Daniel Simon
I wanted more pronounced curvature in the transition area, almost like a curved surface rather than just a bevel to clearly show the geometry is fused and not two separate objects. This is where the vertex group bevel comes in.
[!] it is recommended to have a ‘safe area’ around the vertex group bevel so you can increase / decrease the strength of the bevel without running into nearby vertices. It also helps to have edges radiate out like spokes in a wheel to help the bevel.
A good approach is to scale up the 2D shape in edit mode and knife project this onto the sphere.
Unfortunately there is no ‘offset’ command similar to AutoCAD or Fusion360 and simply scaling does not produce the desired result. So I used this addon instead:
Blender 2.8 addon source file: mesh_offset_edges.zip
I can now resolve any ngons to the outside perimeter edge loop and safely adjust the inner edge loop vertex bevel strength as I see fit. Increase the number of segments from 3 to 6 or 7 to smoothen the curvature. This produces a well defined curved transition between sphere and extrusion.
As the face selection assigned black material uses faces created by the bevel modifier, you unfortunately will need to apply the bevel modifier to avoid shading artefacts.