How to connect curves with flat surfaces automatically?

I constantly have to connect curve surfaces to flat surfaces. So far, I don’t know how to do it automatically so I always end up choosing few sides to my circle (to reduce workload) and connecting the dots by myself, yielding a so-so result (see picture of work in progress). Isn’t there a way to do so automatically?

In this example, I’m trying to make a replacement broomstick cap which I’m gonna 3D print and i’m trying to connect the circular top (orange arrow) to the midway of the hanger stem (green arrow). I could use the follow me tool, but it would likely make a perfect circle if it followed the orange base circle, or a perfect rectangle if i made it follow the square holder stem. What I want is a mix of both… something that does its best to merge both. Does it exist? A function? a plug in?

@Box has a fantastic demo of the Curviloft plugin by Fredo6.

This variation might be helpful too.

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NOW THAT IS REALLY USEFUL . . thanks

Wow! Exactly absolutely what I needed :slight_smile: Thanks so much.

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