I'm trying to find information about the possibilities to map an arc (or a circle to be specific) as a straight line. Imagine a circle mapped onto a country or continent, that represents a path with a starting point 'A'. The circle has a small buffer. I'm trying to map this path into a straight line starting and ending with point 'A', so that I end up with, instead of a square map containing the circle, a very long (length of the path) and thin (height of the buffer) rectangle shaped map.
I figure that I will need to create a custom projection of some sort, and possibly splitting the circle into two or more arcs. But I have a hard time finding a grip on the subject, and think I might be overlooking a simple solution.