I don't completely understand the process in the pictures. It appears to me the carpenter has made a template to use as a basis for transferring dimensions from one timber to another. I have never done this, so I could only speculate on how it works.
I don't like joining logs together in the round, with contrary grain (that is, perpendicular or at an angle as shown). This is because of the way the wood will work in a round log so joined. I always prefer to reduce the wood around the joint in some way, even if the rest of the log is left round. This can be done to be very attractive and in keeping with the nature of the wood.
It's kind of like Tim says, convert it to square, only here it is only squared at the point of the joint. Study Norwegian log building, and you will see this is how they do it. I'd recommend you get the Book, The Craft of Log Building, by Hermann Phlepps, if you can find it. That will teach you a lot about working with logs as a building material.
Like Tim, I like things to be square. Even log walls, I like the wood to be square timber!
