How to merge multiple shapes leaving only outer borders?

Question

Algorithms

How to merge multiple intersecting polygons?

Answer 1

Fill each polygon separately with the fill algorithm, combine by OR, getting the combined figure, and then go through any boundary selection algorithm.
Or are you interested in faster algorithms?

Answer 2

You don't need to fill anything, there are special libraries for working with polygons :
www.angusj.com/delphi/clipper.php
circles, and don't draw them.