Plane or saw (circular or jigsaw) or a router
 
I tested with a jigsaw and a circular saw, it became j,..igt tricky, as it should not be beveled along the entire length of the post.
 
You get to measure where it should start and end and phase in.
 
I will do exactly the same thing. I think the given choice is a router. How else do you get the rounded ends on the chamfers?

I would be really happy if I were wrong because I have both a plunge saw and a circular saw but no router.
 
You can cut the longer stretches with a circular saw/plunge saw and then do the beginning and end with a jigsaw. You will need to sand it afterward.

I have done it this way myself.
 
If you want it to look nice, buy ready-made. If you want a "do it yourself" project, get a vertical milling machine with a tiltable spindle and a round cutter, with a diameter suitable for the finishing radius. If you need custom measurements without major investments, leave it to a carpenter's workshop.

You can't use a 45-degree cutter in a hand router since the radii are different at the outermost and innermost parts of the cutter steel.

A circular saw and jigsaw will look terrible, and after lots of sanding, each post will have four different bevels.

Pessimist Protte
 
If you just draw properly on the pole, it becomes uniform
 
protte: Shouldn't something like this work? http://www.jula.se/fasfras-45-25-4mm-186128

The circular saw and jigsaw didn't give a good result, way too cumbersome. Another option I'm considering is a chisel for the transitions and then a hand plane, followed by a "hand plane with a small nose" to get close to the transition.
 
It will look a bit strange, the beginning and the end will look slanted.
Possibly if you work from both sides and leave the back intact or grind it down.

The tool for doing it by hand might be one with two handles, the name of which I've forgotten.

Protte
 
Regarding the beginning and end looking strange, I was thinking of using a chisel in such cases to fix it.
 
I would probably have checked how it would look if someone had turned it.
But finding someone with a lathe might be difficult?

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