Smooth Corner?

How would i go about smoothing a corner like the picture shows.

The yellow 1 and 2 is locatons and the red cricle is the corner between those two location
The blue line is the curve i want to archive, and the green circles is the points/location i want to get in order to make the curved line

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With a spline, would be my immediate reaction. But, smooth the corner of what? What are you trying to do?

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If you take a look at the image, you can see somethings

The 1 and 2 numbers er locations/vectors
The red cricle is the corner i have in location that i already calculated

Now, what i am looking for is how i would go about smoothing the corners so it would match the blue line with the black
For visual purposes, imagine a line would go for vector 1 to vector 2 but with a smooth curve like that image shows

In my case i would love to know how i would go about calculating the green points showen in the image

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Yes, I totally understand the concept. But is this just an ethereal vector calculation, or does it have a purpose, like a projectile path, or are you going to move something along the path, etc?

Why bother doing this calculation?

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If you are asking what its for, its for nothing other then learnings purpose. Trying to recreate some sort of spline system that isn’t from unreal engine inhouse spline

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It would be cool to use with procedural pipes and conveyor belts, maybe you can obtain it creating a regular spline with three points (start, corner, end), than adding two points at a fixed distance from the corner and at last remove the corner point (it should smooth the curve automatically), if you need other spline points you can add them later