Smooth transition from straight to a curve? What is the methodology?

This isn’t related to SU specifically, although I am doing it in SU.

I have a shape outline that I need to give a height and then put a rounded corner along the top face of. I’ll do that with Follow Me. The thing is, I would like to know if anyone has a method (or there’s a plug in) for working out the best (as in the least apparent) transition from the straight line to the curve. Here’s a pic, with circles showing where the transitions are. As expected, the transition is noticeable. Is there a formula/secret sauce to make it the least abrupt possible?

Also, should I use more sides than the default if this file ends up being used to make a physical form?

Sorry if I sound like I don’t know what I’m talking about, There’s a good reason – I don’t know what I’m talking about.

Thanks in advance!

Using a two point arc, the arc will turn magenta in color when it is quarter circle. After clicking to set the arc while magenta, move the mouse back along the straight edge toward the corner until the arc becomes magenta again and you can let go to the mouse and enter a radius number in the keyboard.

The more sides you use the smoother the final curve will be, but also the more polygons will be used. Try to use a multiple of 12 (24,48,96), they are easier to work with. At some point you may need to size up your object if the faces get too small to work with.

Thanks, the added factor here though is that the curve originates and terminates at specific points that are the ends of straight lines (the circled endpoints). It’s based off a shape I’ve been given to recreate, so I don’t have control of the dimensions or the arc of the curve that much.

I ~think~ this is the same sort of issue that railway track designers face when going from straight sections to curves, but I have no idea how to do it the mathematically correct way, if that makes sense.

It works with specific start and stop points, teal means it is tangent to the start point and magenta means it is tangent to both ends.
The more segments the smoother the transition. Here I have used 24

In that case, another couple of options. An extension to draw bezier curves, or start with a quarter circle and scale it after.

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Great, thanks for the tips, I’ll mess around and see what I come up with!

Again, thanks to both.