bool can_cut(const Polygon_2& polygon, Polygon_2::Vertex_circulator p, Polygon_2::Vertex_circulator c, Polygon_2::Vertex_circulator n,
const boost::unordered_map<Point_3, boost::unordered_set<Segment_3_undirected> >& point2edges)
{
Segment_2 seg(*p, *n);
Point_2 mid((p->x()+n->x())/2.0, (p->y()+n->y())/2.0);
return (CGAL::left_turn(*p, *c, *n) &&
is_legal(*p, *c, *n, point2edges) &&
!intersects_boundary(polygon, seg, true, false) &&
polygon.has_on_bounded_side(mid));
}
static Point_2 centroid(const Polygon_2& poly)
{
assert(poly.size() >= 3);
Polygon_2::Vertex_circulator vcir = poly.vertices_circulator();
Polygon_2::Vertex_circulator vend = vcir;
Polygon_2::Vertex_circulator vnext = vcir; ++vnext;
Vector_2 centre(0, 0);
NT a(0), asum(0);
do {
a = (vcir->x() * vnext->y()) - (vnext->x() * vcir->y());
centre = centre + a * ((*vcir - CGAL::ORIGIN) + (*vnext - CGAL::ORIGIN)); // slow...
asum += a;
vcir = vnext;
++vnext;
} while(vcir != vend);
centre = centre / (asum * 3);
return CGAL::ORIGIN + centre;
}