Convert region between ellipses to bezier path

Question

In an Inkscape file I got from somebody I found the following:

On the right there are arcs of ellipses (not paths), and on the left there are 4-node bezier paths each perfectly corresponding to the inside of the set of four ellipses next to it. I have been trying to do the same: I create four arcs of ellipses and try to convert the inside region to a single path. Given the above examples I guess there must be a very quick way to do it, but I can't figure it out.

Answer 1

You can do it in the following steps:

1. Make full ellipses (e.g. 3 ellipses)
2. Take the complement for the green and red ellipses (Ctrl -). It will automatically produce a path.
3. Break apart the result and delete the bottom part if you don't need it (Ctrl Shift K).
4. Take the union (Ctrl *)

Answer 2

A very fast method to get an object of an inner area of several overlapping objects is the bucket fill tool..

This is how it works:

1. Draw overlapping objects:

   

2. Apply Bucket Fill:

   

3. Move new object from bucket-fill or apply custom stroke and fill: