diff --git a/src/csg/cgal_helper_polygon.cpp b/src/csg/cgal_helper_polygon.cpp
index 2b95b9d9b977d3206bc4e0c26f48d04aca25a0fc..af0c422695e8244cc339b7576fe219900b1b1128 100644
--- a/src/csg/cgal_helper_polygon.cpp
+++ b/src/csg/cgal_helper_polygon.cpp
@@ -1,11 +1,7 @@
 #include "csg_cgal_helper.hpp"
 
-#include <CGAL/Polygon_2.h>
-#include <CGAL/Polygon_2_algorithms.h>
-
 namespace {
-typedef CGAL::Polygon_2<cgal_helper::IK> Polygon;
-typedef CGAL::Point_2<cgal_helper::IK> Point;
+typedef CGAL::Point_2<cgal_helper::CK> Point;
 } // namespace
 
 namespace cgal_helper {
@@ -32,8 +28,7 @@ Polygon create_polygon(const std::vector<std::tuple<double, double>> &points,
 
 bool inside(const Polygon &polygon, double xx, double yy) {
 
-  return CGAL::bounded_side_2(polygon.begin(), polygon.end(), Point(xx, yy),
-                              IK()) == CGAL::ON_BOUNDED_SIDE;
+  return polygon.is_simple();
 }
 
 } // namespace cgal_helper
diff --git a/src/csg_cgal_helper.hpp b/src/csg_cgal_helper.hpp
index 0326d23b8b50363efaac97ab3733d79595c8072e..f4daf152b3f12b48db9cd66fabe2bca8edbbb621 100644
--- a/src/csg_cgal_helper.hpp
+++ b/src/csg_cgal_helper.hpp
@@ -11,7 +11,7 @@ namespace cgal_helper {
 typedef CGAL::Simple_cartesian<double> CK;
 typedef CGAL::Polyhedron_3<CK> Polyhedron;
 typedef CGAL::Exact_predicates_inexact_constructions_kernel IK;
-typedef CGAL::Polygon_2<IK> Polygon;
+typedef CGAL::Polygon_2<CK> Polygon;
 
 Polyhedron
 create_polyhedron(const std::vector<std::tuple<double, double, double>> &points,