Compute intersection area of two polygons with cgal - c++

Question

Given the vertices of two convex polygons, what is the simplest way of computing the area of their intersection using cgal?

Answer 1

Because you are working with convex polygons, there is no need to worry about holes. So the simplest code that I can think of is basically construct the polygons, call intersection, loop over intersection and total up the area::
#include <iostream>
#include <CGAL/Simple_cartesian.h>
#include <CGAL/Polygon_2.h>
#include <CGAL/Polygon_with_holes_2.h>
#include <CGAL/Boolean_set_operations_2.h>
#include <CGAL/Polygon_2_algorithms.h>
typedef CGAL::Simple_cartesian<double> K;
typedef K::Point_2 Point;
typedef CGAL::Polygon_2<K> Polygon_2;
typedef CGAL::Polygon_with_holes_2<K> Polygon_with_holes_2;
using std::cout; using std::endl;
int main(){
Point points[] = { Point(0,0), Point(1,0), Point(1,1), Point(0,1)};
Point points2[] = { Point(0.5,0.5), Point(1.5,0.5), Point(1.5,1.5), Point(0.5,1.5)};
Polygon_2 poly1(points, points+4);
Polygon_2 poly2(points2, points2+4);
//CGAL::General_polygon_with_holes_2<K> poly3;
std::list<Polygon_with_holes_2> polyI;
CGAL::intersection(poly1, poly2, std::back_inserter(polyI));
double totalArea = 0;
typedef std::list<Polygon_with_holes_2>::iterator LIT;
for(LIT lit = polyI.begin(); lit!=polyI.end(); lit++){
totalArea+=lit->outer_boundary().area();
}
cout << "TotalArea::" << totalArea;
}