Take a look at Geometric Tools for Computer Graphics.
- Refined over a decade
- Unbelievably good documentation, both in hard bound and extensively in PDF form
- Boost license
It meets all your requirements:
- Exact precision 2D euclidean space: Yes
- Complex polygons : Yes
- Polygons able to have curved line (arc) segments : Nonsensical. By
definition, polygons are composed of line segments. If you are
looking for splines and NURBS, the library has them.
- Boolean operations on those polygons : Yes
- Polygon offsetting : Unclear what you mean. The library certainly supports translation.
- Polygon partitioning or effective triangulation: Yes, Delaunay triangulation
and Voronoi regions
- Inscribed area and polygon fitting algorithms :Yes
- Possibly some spatial sorting structures with circular range searches : Yes, spatial sorting and a whole bushel of intersection functions.
All this comes from the book Geomtric Tools for Computer Graphics by Schneider and Eberly. The book is outstanding, with clear presentation of how the algorithms work and what their limitations are. The authors have made the code available online under the Boost license and include most (all?) of the book online as a PDF to accompany each code module. They maintain an very useful website that is indexed in various ways.
I have no connection to the authors nor any monetary interest. I used their book in my thesis and it was extremely pleased with it as an easy to use reference and a powerful library.
