Get vertex numbers of CGAL polygon intersection - c++

Question

I want to efficiently create a list of the vertex number of a polygon that intersects. This in order to check if I move the polygons slightly I can check whether it is the same intersection or a completely different one. Presumably if at least one vertex number remains in the list it is the same intersection.
So I have polygon P and Q at t=0 intersecting, this should give me vertex number [1,2,3] for P and [2] for polygon Q, see image for clarification. At t=1 I would get [1,2] for P and [2] for Q.
Currently I first retrieve the intersection and than for both polygons loop through the vertices and use the has_on_boundary function to determine if it is part of the intersection and store the vertex number. See code:
//Standard Includes
#include <iostream>
using std::cout;
using std::endl;
//Include CGAL options
#define CGAL_HEADER_ONLY 1 //Defining to use the CGAL library as header only
#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
#include <CGAL/Boolean_set_operations_2.h>
#include <CGAL/Constrained_Delaunay_triangulation_2.h>
//Typedefs for CGAL Uses.
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;
typedef std::vector<Polygon_with_holes_2> Pwh_list_2;
int main() {
Polygon_2 P;
P.push_back(Point_2(-1, 1));
P.push_back(Point_2(-0.01, -1));
P.push_back(Point_2(0, -1));
P.push_back(Point_2(0.01, -1));
P.push_back(Point_2(1, 1));
Polygon_2 Q;
Q.push_back(Point_2(-1, -1));
Q.push_back(Point_2(1, -1));
Q.push_back(Point_2(0, 1));
Pwh_list_2 polygon_intersections;
CGAL::intersection(P, Q, std::back_inserter(polygon_intersections));
//For ease now only assume one intersection
Polygon_2 intersection = polygon_intersections[0].outer_boundary();
//Get vertex number of P in intersection
int vertex_nr = 0;
std::set<int> overlapping_vertices_P;
cout << "Find intersection vertices of Polygon P" << endl;
for (auto it = P.vertices_begin(); it != P.vertices_end(); ++it, ++vertex_nr) {
if (intersection.has_on_boundary(*it)) {
overlapping_vertices_P.insert(vertex_nr);
cout << vertex_nr << endl;
}
}
//Get vertex number of Q in intersection
vertex_nr = 0;
std::set<int> overlapping_vertices_Q;
cout << "Find intersection vertices of Polygon Q" << endl;
for (auto it = Q.vertices_begin(); it != Q.vertices_end(); ++it, ++vertex_nr) {
if (intersection.has_on_boundary(*it)) {
overlapping_vertices_Q.insert(vertex_nr);
cout << vertex_nr << endl;
}
}
return 0;
}
Question: It works but seems very inefficient to me. Is there a better way to do this?
Any help or suggestions are highly appreciated.