The Bentley-Ottoman algorithm finds all crossings in a set of line segments. For a well known and important algorithm, it seems quite weird that a C++ implementation of Bentley-Ottmann algorithm — the implementation that can handle all the degenerated cases (i.e., no special assumption on the sweeping line and the number of intersection points, and so on) — is simply not available. The only code I can found is here, but it doesn't seem to handle the generalized case.
Is Bentley-Ottmann algorithm already implemented in any well-tested library, such as Boost or LEDA? If yes, may I have the reference to it?
CGAL has something in there with the same complexity as Bentley-Ottmann, O((n + k)*log(n)) where n is the number of segments and k is the number of intersections (not sure which algorithm they used):
//! \file examples/Arrangement_on_surface_2/sweep_line.cpp
// Computing intersection points among curves using the sweep line.
#include <CGAL/Cartesian.h>
#include <CGAL/MP_Float.h>
#include <CGAL/Quotient.h>
#include <CGAL/Arr_segment_traits_2.h>
#include <CGAL/Sweep_line_2_algorithms.h>
#include <list>
typedef CGAL::Quotient<CGAL::MP_Float> NT;
typedef CGAL::Cartesian<NT> Kernel;
typedef Kernel::Point_2 Point_2;
typedef CGAL::Arr_segment_traits_2<Kernel> Traits_2;
typedef Traits_2::Curve_2 Segment_2;
int main()
{
// Construct the input segments.
Segment_2 segments[] = {Segment_2 (Point_2 (1, 5), Point_2 (8, 5)),
Segment_2 (Point_2 (1, 1), Point_2 (8, 8)),
Segment_2 (Point_2 (3, 1), Point_2 (3, 8)),
Segment_2 (Point_2 (8, 5), Point_2 (8, 8))};
// Compute all intersection points.
std::list<Point_2> pts;
CGAL::compute_intersection_points (segments, segments + 4,
std::back_inserter (pts));
// Print the result.
std::cout << "Found " << pts.size() << " intersection points: " << std::endl;
std::copy (pts.begin(), pts.end(),
std::ostream_iterator<Point_2>(std::cout, "\n"));
// Compute the non-intersecting sub-segments induced by the input segments.
std::list<Segment_2> sub_segs;
CGAL::compute_subcurves(segments, segments + 4, std::back_inserter(sub_segs));
std::cout << "Found " << sub_segs.size()
<< " interior-disjoint sub-segments." << std::endl;
CGAL_assertion (CGAL::do_curves_intersect (segments, segments + 4));
return 0;
}