Is there a CGAL function that checks if a point is inside a linear polygon with holes?

Question

I want to check if a point lies within, or outside a polygon with holes. Specifically, I am interested if a given point would be inside the "filled area" of a polygon with holes; if the point lies within a hole, I will consider that to be outside of the polygon with holes.

I understand that there is a CGAL function check_inside that checks if a point lies inside a polygon (without holes). There is also a CGAL function connect_holes that plots a path from topmost vertex in each hole in the polygon with holes to the polygon itself. I can see two workarounds with these functions to achieve my objective, but I was wondering if there is a CGAL function that does this directly.

Answer 1

See oriented_side() member function of CGAL::General_polygon_set_2<>. Apparently, there are also a free (overloaded) functions (for some reason not documented).

#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
#include <CGAL/Boolean_set_operations_2.h>

typedef CGAL::Exact_predicates_exact_constructions_kernel Kernel;
typedef Kernel::Point_2                                   Point_2;
typedef CGAL::Polygon_2<Kernel>                           Polygon_2;
typedef CGAL::Polygon_with_holes_2<Kernel>                Polygon_with_holes_2;

# define nice(os) ((os == CGAL::ON_ORIENTED_BOUNDARY) ? "on boundary" :  \
                   (os == CGAL::POSITIVE) ? "inside" : "outside")

int main() {
  Polygon_2 hole;
  hole.push_back(Point_2(1, 1));
  hole.push_back(Point_2(1, 2));
  hole.push_back(Point_2(2, 2));
  hole.push_back(Point_2(2, 1));

  Polygon_2 out;
  out.push_back(Point_2(0, 0));
  out.push_back(Point_2(3, 0));
  out.push_back(Point_2(3, 3));
  out.push_back(Point_2(0, 3));

  Polygon_with_holes_2 pwh(out, &hole, &hole+1);
  std::cout << pwh << std::endl;

  auto os = CGAL::oriented_side(Point_2(0, 0), pwh);
  std::cout << "(0,0) is : " << nice(os) << std::endl;
  os = CGAL::oriented_side(Point_2(0.5, 0.5), pwh);
  std::cout << "(0,0) is : " << nice(os) << std::endl;
  os = CGAL::oriented_side(Point_2(1, 1), pwh);
  std::cout << "(0,0) is : " << nice(os) << std::endl;
  os = CGAL::oriented_side(Point_2(2.5, 2.5), pwh);
  std::cout << "(0,0) is : " << nice(os) << std::endl;
  os = CGAL::oriented_side(Point_2(3, 3), pwh);
  std::cout << "(0,0) is : " << nice(os) << std::endl;
  os = CGAL::oriented_side(Point_2(3.5, 3.5), pwh);
  std::cout << "(0,0) is : " << nice(os) << std::endl;
  return 0;
}