Geometry Boost List: [ggl] Any way to simplify polyline in following way with GGL?

Subject: [ggl] Any way to simplify polyline in following way with GGL?
From: Denis Pesotsky (obey)
Date: 2011-02-10 23:11:48

I need to simplify self-intersecting polyline. I have no ides on how
to describe this action, just look at attacked animated picture
(animation.png).

Actually, I already have implementation of this stuff using graphs
(look at attached impl1.png and impl2.png), but just wondering:
Boost.Geometry can do same?
-------------- next part --------------
A non-text attachment was scrubbed...
Name: animation.png
Type: image/png
Size: 15985 bytes
Desc: not available
Url : http://lists.osgeo.org/pipermail/ggl/attachments/20110211/e25d72b4/animation-0001.png
-------------- next part --------------
A non-text attachment was scrubbed...
Name: impl1.png
Type: image/png
Size: 5312 bytes
Desc: not available
Url : http://lists.osgeo.org/pipermail/ggl/attachments/20110211/e25d72b4/impl1-0001.png
-------------- next part --------------
A non-text attachment was scrubbed...
Name: impl2.png
Type: image/png
Size: 6367 bytes
Desc: not available
Url : http://lists.osgeo.org/pipermail/ggl/attachments/20110211/e25d72b4/impl2-0001.png