How can I have a shape smoothly attached to another shape?

As an example, see how the shape sitting on top of the sphere has an edge and is clearly separate? I used shrink wrap and solidify to do this. I want the shape to have a smooth edge that perfectly blends into the sphere. I tried joining these two shapes and retopologizing and its ok but not as precise as I want.

May this helps you:

Yeah, this is also what I had in mind. Something you can play around with:

  1. create and inset loop and the boundary of your shape

  2. add all vertices to a vertex group, assign 0 to everything, and 1 to the outermost loop

  3. add more loops (the vertex weights will automatically be interpolated)

4)add some modifiers:

shrinwrap_smoothing.blend (398.1 KB)

I would try knife project + extrude + edge crease.