text: /*
    Copyright 2008 Intel Corporation
  
    Use, modification and distribution are subject to the Boost Software License,
    Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
    http://www.boost.org/LICENSE_1_0.txt).
  */
  #include <iostream>
  #define BOOST_POLYGON_NO_DEPS
  #include <boost/polygon/polygon.hpp>
  
  namespace gtl = boost::polygon;
  using namespace boost::polygon::operators;
  #include <time.h>
  #include <stdlib.h>
  
  void assert_s(bool c, std::string msg) {
    if(!c) {
      std::cout << msg << std::endl;
      exit( 1);
    }
  }
  
  namespace boost { namespace polygon{
    void addpoly(polygon_45_set_data<int>& pset,
                 int* pts, unsigned int numpts) {
      std::vector<point_data<int> > mppts;
      for(unsigned int i = 0; i < numpts*2; i += 2) {
        point_data<int>  pt(pts[i], pts[i+1]);
        mppts.push_back(pt);
      }
      polygon_45_data<int> poly;
      poly.set(mppts.begin(), mppts.end());
      pset += poly;
    }
  
    template <class T>
    std::ostream& operator << (std::ostream& o, const interval_data<T>& i)
    {
      return o << i.get(LOW) << ' ' << i.get(HIGH);
    }
    template <class T>
    std::ostream& operator << (std::ostream& o, const point_data<T>& r)
    {
      return o << r.get(HORIZONTAL) << ' ' << r.get(VERTICAL);
    }
    template <typename T>
    std::ostream& operator<<(std::ostream& o, const polygon_45_data<T>& poly) {
      o << "Polygon { ";
      for(typename polygon_45_data<T>::iterator_type itr = poly.begin();
          itr != poly.end(); ++itr) {
        if(itr != poly.begin()) o << ", ";
        o << (*itr).get(HORIZONTAL) << " " << (*itr).get(VERTICAL);
      }
      o << " } ";
      return o;
    }
    template <typename Unit>
    inline std::ostream& operator<< (std::ostream& o, const polygon_45_set_data<Unit>& p) {
      o << "Polygon45Set ";
      o << " " << !p.sorted() << " " << p.dirty() << " { ";
      for(typename polygon_45_set_data<Unit>::iterator_type itr = p.begin();
          itr != p.end(); ++itr) {
        o << (*itr).pt << ":";
        for(unsigned int i = 0; i < 4; ++i) {
          o << (*itr).count[i] << ",";
        } o << " ";
        //o << (*itr).first << ":" <<  (*itr).second << "; ";
      }
      o << "} ";
      return o;
    }
  
    template <typename Unit>
    inline std::istream& operator>> (std::istream& i, polygon_45_set_data<Unit>& p) {
      //TODO
      return i;
    }
    template <typename T>
    std::ostream& operator << (std::ostream& o, const polygon_90_data<T>& r)
    {
      o << "Polygon { ";
      for(typename polygon_90_data<T>::iterator_type itr = r.begin(); itr != r.end(); ++itr) {
        o << *itr << ", ";
      }
      return o << "} ";
    }
  
    template <typename T>
    std::istream& operator >> (std::istream& i, polygon_90_data<T>& r)
    {
      std::size_t size;
      i >> size;
      std::vector<T> vec;
      vec.reserve(size);
      for(std::size_t ii = 0; ii < size; ++ii) {
        T coord;
        i >> coord;
        vec.push_back(coord);
      }
      r.set_compact(vec.begin(), vec.end());
      return i;
    }
  
    template <typename T>
    std::ostream& operator << (std::ostream& o, const std::vector<polygon_90_data<T> >& r) {
      o << r.size() << ' ';
      for(std::size_t ii = 0; ii < r.size(); ++ii) {
        o << (r[ii]);
      }
      return o;
    }
    template <typename T>
    std::istream& operator >> (std::istream& i, std::vector<polygon_90_data<T> >& r) {
      std::size_t size;
      i >> size;
      r.clear();
      r.reserve(size);
      for(std::size_t ii = 0; ii < size; ++ii) {
        polygon_90_data<T> tmp;
        i >> tmp;
        r.push_back(tmp);
      }
      return i;
    }
    template <typename T>
    std::ostream& operator<<(std::ostream& o, const polygon_data<T>& poly) {
      o << "Polygon { ";
      for(typename polygon_data<T>::iterator_type itr = poly.begin();
          itr != poly.end(); ++itr) {
        if(itr != poly.begin()) o << ", ";
        o << (*itr).get(HORIZONTAL) << " " << (*itr).get(VERTICAL);
      }
      o << " } ";
      return o;
    }
    template <typename T>
    std::ostream& operator << (std::ostream& o, const polygon_set_data<T>& r)
    {
      o << "Polygon Set Data { ";
      for(typename polygon_set_data<T>::iterator_type itr = r.begin(); itr != r.end(); ++itr) {
        o << "<" << (*itr).first.first << ", " << (*itr).first.second << ">:" << (*itr).second << " ";
      }
      o << "} ";
      return o;
    }
    template <typename T>
    std::ostream& operator<<(std::ostream& o, const polygon_90_with_holes_data<T>& poly) {
      o << "Polygon With Holes { ";
      for(typename polygon_90_with_holes_data<T>::iterator_type itr = poly.begin();
          itr != poly.end(); ++itr) {
        if(itr != poly.begin()) o << ", ";
        o << (*itr).get(HORIZONTAL) << " " << (*itr).get(VERTICAL);
      } o << " { ";
      for(typename polygon_90_with_holes_data<T>::iterator_holes_type itr = poly.begin_holes();
          itr != poly.end_holes(); ++itr) {
        o << (*itr);
      }
      o << " } } ";
      return o;
    }
    template <typename T>
    std::ostream& operator<<(std::ostream& o, const polygon_45_with_holes_data<T>& poly) {
      o << "Polygon With Holes { ";
      for(typename polygon_45_with_holes_data<T>::iterator_type itr = poly.begin();
          itr != poly.end(); ++itr) {
        if(itr != poly.begin()) o << ", ";
        o << (*itr).get(HORIZONTAL) << " " << (*itr).get(VERTICAL);
      } o << " { ";
      for(typename polygon_45_with_holes_data<T>::iterator_holes_type itr = poly.begin_holes();
          itr != poly.end_holes(); ++itr) {
        o << (*itr);
      }
      o << " } } ";
      return o;
    }
    template <typename T>
    std::ostream& operator<<(std::ostream& o, const polygon_with_holes_data<T>& poly) {
      o << "Polygon With Holes { ";
      for(typename polygon_with_holes_data<T>::iterator_type itr = poly.begin();
          itr != poly.end(); ++itr) {
        if(itr != poly.begin()) o << ", ";
        o << (*itr).get(HORIZONTAL) << " " << (*itr).get(VERTICAL);
      } o << " { ";
      for(typename polygon_with_holes_data<T>::iterator_holes_type itr = poly.begin_holes();
          itr != poly.end_holes(); ++itr) {
        o << (*itr);
      }
      o << " } } ";
      return o;
    }
    template <class T>
    std::ostream& operator << (std::ostream& o, const rectangle_data<T>& r)
    {
      return o << r.get(HORIZONTAL) << ' ' << r.get(VERTICAL);
    }
    template <class T>
    std::ostream& operator << (std::ostream& o, const segment_data<T>& r)
    {
      return o << r.get(LOW) << ' ' << r.get(HIGH);
    }
  
  
    template <typename T>
    typename enable_if<typename is_polygon_90_set_type<T>::type, void>::type
    print_is_polygon_90_set_concept(const T& ) { std::cout << "is polygon 90 set concept\n"; }
    template <typename T>
    typename enable_if<typename is_mutable_polygon_90_set_type<T>::type, void>::type
    print_is_mutable_polygon_90_set_concept(const T& ) { std::cout << "is mutable polygon 90 set concept\n"; }
    namespace boolean_op {
      //self contained unit test for BooleanOr algorithm
      template <typename Unit>
      inline bool testBooleanOr() {
        BooleanOp<int, Unit> booleanOr;
        //test one rectangle
        std::vector<std::pair<interval_data<Unit>, int> > container;
        booleanOr.processInterval(container, interval_data<Unit>(0, 10), 1);
        booleanOr.advanceScan();
        booleanOr.processInterval(container, interval_data<Unit>(0, 10), -1);
        if(container.size() != 2) {
          std::cout << "Test one rectangle, wrong output size\n";
          return false;
        }
        if(container[0] != std::pair<interval_data<Unit>, int>(interval_data<Unit>(0, 10), 1)) {
          std::cout << "Test one rectangle, first output wrong: Interval(" <<
            container[0].first << "), " << container[0].second << std::endl;
        }
        if(container[1] != std::pair<interval_data<Unit>, int>(interval_data<Unit>(0, 10), -1)) {
          std::cout << "Test one rectangle, second output wrong: Interval(" <<
            container[1].first << "), " << container[1].second << std::endl;
        }
  
        //test two rectangles
        container.clear();
        booleanOr = BooleanOp<int, Unit>();
        booleanOr.processInterval(container, interval_data<Unit>(0, 10), 1);
        booleanOr.advanceScan();
        booleanOr.processInterval(container, interval_data<Unit>(5, 15), 1);
        booleanOr.advanceScan();
        booleanOr.processInterval(container, interval_data<Unit>(0, 10), -1);
        booleanOr.advanceScan();
        booleanOr.processInterval(container, interval_data<Unit>(5, 15), -1);
        if(container.size() != 4) {
          std::cout << "Test two rectangles, wrong output size\n";
          for(std::size_t i = 0; i < container.size(); ++i){
            std::cout << container[i].first << "), " << container[i].second << std::endl;
          }
          return false;
        }
        if(container[0] != std::pair<interval_data<Unit>, int>(interval_data<Unit>(0, 10), 1)) {
          std::cout << "Test two rectangles, first output wrong: Interval(" <<
            container[0].first << "), " << container[0].second << std::endl;
        }
        if(container[1] != std::pair<interval_data<Unit>, int>(interval_data<Unit>(10, 15), 1)) {
          std::cout << "Test two rectangles, second output wrong: Interval(" <<
            container[1].first << "), " << container[1].second << std::endl;
        }
        if(container[2] != std::pair<interval_data<Unit>, int>(interval_data<Unit>(0, 5), -1)) {
          std::cout << "Test two rectangles, third output wrong: Interval(" <<
            container[2].first << "), " << container[2].second << std::endl;
        }
        if(container[3] != std::pair<interval_data<Unit>, int>(interval_data<Unit>(5, 15), -1)) {
          std::cout << "Test two rectangles, fourth output wrong: Interval(" <<
            container[3].first << "), " << container[3].second << std::endl;
        }
  
        //test two rectangles
        container.clear();
        booleanOr = BooleanOp<int, Unit>();
        booleanOr.processInterval(container, interval_data<Unit>(5, 15), 1);
        booleanOr.advanceScan();
        booleanOr.processInterval(container, interval_data<Unit>(0, 10), 1);
        booleanOr.advanceScan();
        booleanOr.processInterval(container, interval_data<Unit>(5, 15), -1);
        booleanOr.advanceScan();
        booleanOr.processInterval(container, interval_data<Unit>(0, 10), -1);
        if(container.size() != 4) {
          std::cout << "Test other two rectangles, wrong output size\n";
          for(std::size_t i = 0; i < container.size(); ++i){
            std::cout << container[i].first << "), " << container[i].second << std::endl;
          }
          return false;
        }
        if(container[0] != std::pair<interval_data<Unit>, int>(interval_data<Unit>(5, 15), 1)) {
          std::cout << "Test other two rectangles, first output wrong: Interval(" <<
            container[0].first << "), " << container[0].second << std::endl;
        }
        if(container[1] != std::pair<interval_data<Unit>, int>(interval_data<Unit>(0, 5), 1)) {
          std::cout << "Test other two rectangles, second output wrong: Interval(" <<
            container[1].first << "), " << container[1].second << std::endl;
        }
        if(container[2] != std::pair<interval_data<Unit>, int>(interval_data<Unit>(10, 15), -1)) {
          std::cout << "Test other two rectangles, third output wrong: Interval(" <<
            container[2].first << "), " << container[2].second << std::endl;
        }
        if(container[3] != std::pair<interval_data<Unit>, int>(interval_data<Unit>(0, 10), -1)) {
          std::cout << "Test other two rectangles, fourth output wrong: Interval(" <<
            container[3].first << "), " << container[3].second << std::endl;
        }
  
        //test two nonoverlapping rectangles
        container.clear();
        booleanOr = BooleanOp<int, Unit>();
        booleanOr.processInterval(container, interval_data<Unit>(0, 10), 1);
        booleanOr.advanceScan();
        booleanOr.processInterval(container, interval_data<Unit>(15, 25), 1);
        booleanOr.advanceScan();
        booleanOr.processInterval(container, interval_data<Unit>(0, 10), -1);
        booleanOr.advanceScan();
        booleanOr.processInterval(container, interval_data<Unit>(15, 25), -1);
        if(container.size() != 4) {
          std::cout << "Test two nonoverlapping rectangles, wrong output size\n";
          return false;
        }
        if(container[0] != std::pair<interval_data<Unit>, int>(interval_data<Unit>(0, 10), 1)) {
          std::cout << "Test two nonoverlapping rectangles, first output wrong: Interval(" <<
            container[0].first << "), " << container[0].second << std::endl;
        }
        if(container[1] != std::pair<interval_data<Unit>, int>(interval_data<Unit>(15, 25), 1)) {
          std::cout << "Test two nonoverlapping rectangles, second output wrong: Interval(" <<
            container[1].first << "), " << container[1].second << std::endl;
        }
        if(container[2] != std::pair<interval_data<Unit>, int>(interval_data<Unit>(0, 10), -1)) {
          std::cout << "Test two nonoverlapping rectangles, third output wrong: Interval(" <<
            container[2].first << "), " << container[2].second << std::endl;
        }
        if(container[3] != std::pair<interval_data<Unit>, int>(interval_data<Unit>(15, 25), -1)) {
          std::cout << "Test two nonoverlapping rectangles, fourth output wrong: Interval(" <<
            container[3].first << "), " << container[3].second << std::endl;
        }
        return true;
      }
    }
  
    void test_assign() {
      using namespace gtl;
      std::vector<polygon_data<int> > ps;
      polygon_90_set_data<int> ps90;
      assign(ps, ps90);
    }
  
    //this is a compile time test, if it compiles it passes
    void test_view_as() {
      using namespace gtl;
      polygon_data<int> p;
      polygon_45_data<int> p45;
      polygon_90_data<int> p90;
      polygon_with_holes_data<int> pwh;
      polygon_45_with_holes_data<int> p45wh;
      polygon_90_with_holes_data<int> p90wh;
      rectangle_data<int> rect(0, 1, 10, 11);
      polygon_90_set_data<int> ps90;
      polygon_45_set_data<int> ps45;
      polygon_set_data<int> ps;
  
      assign(p, rect);
      assign(p90, view_as<polygon_90_concept>(p));
      if(!equivalence(p90, rect))
        std::cout << "fail 1\n";
      assign(p45, view_as<polygon_45_concept>(p));
      if(!equivalence(p45, rect))
        std::cout << "fail 2\n";
      assign(p90, view_as<polygon_90_concept>(p45));
      if(!equivalence(p90, rect))
        std::cout << "fail 3\n";
      if(!equivalence(rect, view_as<rectangle_concept>(p)))
        std::cout << "fail 4\n";
      if(!equivalence(rect, view_as<rectangle_concept>(p45)))
        std::cout << "fail 5\n";
      if(!equivalence(rect, view_as<rectangle_concept>(p90)))
        std::cout << "fail 6\n";
      assign(pwh, rect);
      assign(p90wh, rect);
      assign(p45wh, rect);
      if(!equivalence(rect, view_as<rectangle_concept>(pwh)))
        std::cout << "fail 7\n";
      if(!equivalence(rect, view_as<rectangle_concept>(p45wh)))
        std::cout << "fail 8\n";
      if(!equivalence(rect, view_as<rectangle_concept>(p90wh)))
        std::cout << "fail 9\n";
      assign(p90wh, view_as<polygon_90_with_holes_concept>(pwh));
      if(!equivalence(p90wh, rect))
        std::cout << "fail 10\n";
      assign(p45wh, view_as<polygon_45_with_holes_concept>(pwh));
      if(!equivalence(p45wh, rect))
        std::cout << "fail 11\n";
      assign(p90wh, view_as<polygon_90_with_holes_concept>(p45wh));
      if(!equivalence(p90wh, rect))
        std::cout << "fail 12\n";
      assign(p90, view_as<polygon_90_concept>(pwh));
      if(!equivalence(p90, rect))
        std::cout << "fail 13\n";
      assign(p45, view_as<polygon_45_concept>(pwh));
      if(!equivalence(p45, rect))
        std::cout << "fail 14\n";
      assign(p90, view_as<polygon_90_concept>(p45wh));
      if(!equivalence(p90, rect))
        std::cout << "fail 15\n";
      assign(ps, rect);
      assign(ps90, view_as<polygon_90_set_concept>(ps));
      if(!equivalence(ps90, rect))
        std::cout << "fail 16\n";
      assign(ps45, view_as<polygon_45_set_concept>(ps));
      if(!equivalence(ps45, rect))
        std::cout << "fail 17\n";
      assign(ps90, view_as<polygon_90_set_concept>(ps45));
      if(!equivalence(ps90, rect))
        std::cout << "fail 18\n";
    }
  
    inline bool testPolygon45SetRect() {
      std::vector<point_data<int> > points;
      points.push_back(point_data<int>(0,0));
      points.push_back(point_data<int>(0,10));
      points.push_back(point_data<int>(10,10));
      points.push_back(point_data<int>(10,0));
      polygon_45_data<int> poly;
      poly.set(points.begin(), points.end());
      polygon_45_set_data<int> ps;
      ps.insert(poly);
      std::vector<polygon_45_data<int> > polys;
      ps.get_polygons(polys);
      std::cout << polys.size() << std::endl;
      for(unsigned int i = 0; i < polys.size(); ++i) {
        std::cout << polys[i] << std::endl;
      }
      return true;
    }
  
    inline bool testPolygon45Set() {
      polygon_45_formation<int>::Polygon45Formation pf(true);
      typedef boolean_op_45<int>::Vertex45 Vertex45;
      std::vector<Vertex45> data;
      // result == 0 8 -1 1
      data.push_back(Vertex45(point_data<int>(0, 8), -1, 1));
      // result == 0 8 1 -1
      data.push_back(Vertex45(point_data<int>(0, 8), 1, -1));
      // result == 4 0 1 1
      data.push_back(Vertex45(point_data<int>(4, 0), 1, 1));
      // result == 4 0 2 1
      data.push_back(Vertex45(point_data<int>(4, 0), 2, 1));
      // result == 4 4 2 -1
      data.push_back(Vertex45(point_data<int>(4, 4), 2, -1));
      // result == 4 4 -1 -1
      data.push_back(Vertex45(point_data<int>(4, 4), -1, -1));
      // result == 4 12 1 1
      data.push_back(Vertex45(point_data<int>(4, 12), 1, 1));
      // result == 4 12 2 1
      data.push_back(Vertex45(point_data<int>(4, 12), 2, 1));
      // result == 4 16 2 -1
      data.push_back(Vertex45(point_data<int>(4, 16), 2, 1));
      // result == 4 16 -1 -1
      data.push_back(Vertex45(point_data<int>(4, 16), -1, -1));
      // result == 6 2 1 -1
      data.push_back(Vertex45(point_data<int>(6, 2), 1, -1));
      // result == 6 14 -1 1
      data.push_back(Vertex45(point_data<int>(6, 14), -1, 1));
      // result == 6 2 -1 1
      data.push_back(Vertex45(point_data<int>(6, 2), -1, 1));
      // result == 6 14 1 -1
      data.push_back(Vertex45(point_data<int>(6, 14), 1, -1));
      // result == 8 0 -1 -1
      data.push_back(Vertex45(point_data<int>(8, 0), -1, -1));
      // result == 8 0 2 -1
      data.push_back(Vertex45(point_data<int>(8, 0), 2, -1));
      // result == 8 4 2 1
      data.push_back(Vertex45(point_data<int>(8, 4), 2, 1));
      // result == 8 4 1 1
      data.push_back(Vertex45(point_data<int>(8, 4), 1, 1));
      // result == 8 12 -1 -1
      data.push_back(Vertex45(point_data<int>(8, 12), -1, -1));
      // result == 8 12 2 -1
      data.push_back(Vertex45(point_data<int>(8, 12), 2, -1));
      // result == 8 16 2 1
      data.push_back(Vertex45(point_data<int>(8, 16), 2, 1));
      // result == 8 16 1 1
      data.push_back(Vertex45(point_data<int>(8, 16), 1, 1));
      // result == 12 8 1 -1
      data.push_back(Vertex45(point_data<int>(12, 8), 1, -1));
      // result == 12 8 -1 1
      data.push_back(Vertex45(point_data<int>(12, 8), -1, 1));
  
      data.push_back(Vertex45(point_data<int>(6, 4), 1, -1));
      data.push_back(Vertex45(point_data<int>(6, 4), 2, -1));
      data.push_back(Vertex45(point_data<int>(6, 12), -1, 1));
      data.push_back(Vertex45(point_data<int>(6, 12), 2, 1));
      data.push_back(Vertex45(point_data<int>(10, 8), -1, -1));
      data.push_back(Vertex45(point_data<int>(10, 8), 1, 1));
  
      std::sort(data.begin(), data.end());
      std::vector<polygon_45_data<int> > polys;
      pf.scan(polys, data.begin(), data.end());
      polygon_45_set_data<int> ps;
      std::cout << "inserting1\n";
      //std::vector<point_data<int> > points;
      //points.push_back(point_data<int>(0,0));
      //points.push_back(point_data<int>(0,10));
      //points.push_back(point_data<int>(10,10));
      //points.push_back(point_data<int>(10,0));
      //Polygon45 poly;
      //poly.set(points.begin(), points.end());
      //ps.insert(poly);
      ps.insert(polys[0]);
  
      polygon_45_set_data<int> ps2;
      std::cout << "inserting2\n";
      ps2.insert(polys[0]);
      std::cout << "applying boolean\n";
      ps |= ps2;
      std::vector<polygon_45_data<int> > polys2;
      std::cout << "getting result\n";
      ps.get_polygons(polys2);
      std::cout << ps2 << std::endl;
      std::cout << ps << std::endl;
      std::cout << polys[0] << std::endl;
      std::cout << polys2[0] << std::endl;
      if(polys != polys2) std::cout << "test Polygon45Set failed\n";
      return polys == polys2;
    }
  
    inline bool testPolygon45SetPerterbation() {
      polygon_45_formation<int>::Polygon45Formation pf(true);
      typedef boolean_op_45<int>::Vertex45 Vertex45;
      std::vector<Vertex45> data;
      // result == 0 8 -1 1
      data.push_back(Vertex45(point_data<int>(0, 80), -1, 1));
      // result == 0 8 1 -1
      data.push_back(Vertex45(point_data<int>(0, 80), 1, -1));
      // result == 4 0 1 1
      data.push_back(Vertex45(point_data<int>(40, 0), 1, 1));
      // result == 4 0 2 1
      data.push_back(Vertex45(point_data<int>(40, 0), 2, 1));
      // result == 4 4 2 -1
      data.push_back(Vertex45(point_data<int>(40, 40), 2, -1));
      // result == 4 4 -1 -1
      data.push_back(Vertex45(point_data<int>(40, 40), -1, -1));
      // result == 4 12 1 1
      data.push_back(Vertex45(point_data<int>(40, 120), 1, 1));
      // result == 4 12 2 1
      data.push_back(Vertex45(point_data<int>(40, 120), 2, 1));
      // result == 4 16 2 -1
      data.push_back(Vertex45(point_data<int>(40, 160), 2, 1));
      // result == 4 16 -1 -1
      data.push_back(Vertex45(point_data<int>(40, 160), -1, -1));
      // result == 6 2 1 -1
      data.push_back(Vertex45(point_data<int>(60, 20), 1, -1));
      // result == 6 14 -1 1
      data.push_back(Vertex45(point_data<int>(60, 140), -1, 1));
      // result == 6 2 -1 1
      data.push_back(Vertex45(point_data<int>(60, 20), -1, 1));
      // result == 6 14 1 -1
      data.push_back(Vertex45(point_data<int>(60, 140), 1, -1));
      // result == 8 0 -1 -1
      data.push_back(Vertex45(point_data<int>(80, 0), -1, -1));
      // result == 8 0 2 -1
      data.push_back(Vertex45(point_data<int>(80, 0), 2, -1));
      // result == 8 4 2 1
      data.push_back(Vertex45(point_data<int>(80, 40), 2, 1));
      // result == 8 4 1 1
      data.push_back(Vertex45(point_data<int>(80, 40), 1, 1));
      // result == 8 12 -1 -1
      data.push_back(Vertex45(point_data<int>(80, 120), -1, -1));
      // result == 8 12 2 -1
      data.push_back(Vertex45(point_data<int>(80, 120), 2, -1));
      // result == 8 16 2 1
      data.push_back(Vertex45(point_data<int>(80, 160), 2, 1));
      // result == 8 16 1 1
      data.push_back(Vertex45(point_data<int>(80, 160), 1, 1));
      // result == 12 8 1 -1
      data.push_back(Vertex45(point_data<int>(120, 80), 1, -1));
      // result == 12 8 -1 1
      data.push_back(Vertex45(point_data<int>(120, 80), -1, 1));
  
      data.push_back(Vertex45(point_data<int>(60, 40), 1, -1));
      data.push_back(Vertex45(point_data<int>(60, 40), 2, -1));
      data.push_back(Vertex45(point_data<int>(60, 120), -1, 1));
      data.push_back(Vertex45(point_data<int>(60, 120), 2, 1));
      data.push_back(Vertex45(point_data<int>(100, 80), -1, -1));
      data.push_back(Vertex45(point_data<int>(100, 80), 1, 1));
  
      std::sort(data.begin(), data.end());
      std::vector<polygon_45_data<int> > polys;
      pf.scan(polys, data.begin(), data.end());
      polygon_45_set_data<int> ps;
      std::cout << "inserting1\n";
      //std::vector<point_data<int> > points;
      //points.push_back(point_data<int>(0,0));
      //points.push_back(point_data<int>(0,10));
      //points.push_back(point_data<int>(10,10));
      //points.push_back(point_data<int>(10,0));
      //Polygon45 poly;
      //poly.set(points.begin(), points.end());
      //ps.insert(poly);
      polygon_45_set_data<int> preps(polys[0]);
  
      ps.insert(polys[0]);
      convolve(polys[0], point_data<int>(0, 1) );
  
      polygon_45_set_data<int> ps2;
      std::cout << "inserting2\n";
      ps2.insert(polys[0]);
      std::cout << "applying boolean\n";
      ps |= ps2;
      std::vector<polygon_45_data<int> > polys2;
      std::cout << "getting result\n";
      ps.get_polygons(polys2);
      std::cout << preps << std::endl;
      std::cout << ps2 << std::endl;
      std::cout << ps << std::endl;
      std::cout << polys[0] << std::endl;
      std::cout << polys2[0] << std::endl;
      if(polys != polys2) std::cout << "test Polygon45Set failed\n";
      return polys == polys2;
      //return true;
    }
  
    inline int testPolygon45SetDORA() {
      std::cout << "testPolygon45SetDORA" << std::endl;
      std::vector<point_data<int> > pts;
      pts.push_back(point_data<int>(0, 0));
      pts.push_back(point_data<int>(10, 0));
      pts.push_back(point_data<int>(10, 10));
      pts.push_back(point_data<int>(0, 10));
      polygon_45_data<int> apoly;
      apoly.set(pts.begin(), pts.end());
      polygon_45_set_data<int> ps(apoly);
      polygon_45_set_data<int> ps2(ps);
      ps2 = apoly;
      std::vector<polygon_45_data<int> > apolys;
      apolys.push_back(apoly);
      ps2.insert(apolys.begin(), apolys.end());
      apolys.clear();
      ps2.get(apolys);
      std::cout << apolys.size() << std::endl;
      std::cout << (ps == ps2) << std::endl;
      std::cout << !(ps != ps2) << std::endl;
      ps2.clear();
      std::cout << (ps2.value().empty()) << std::endl;
      ps2.set(apolys.begin(), apolys.end());
      ps2.set(ps.value());
      ps.clean();
      ps2.set_clean(ps.value());
      ps2.insert(ps.value().begin(), ps.value().end());
      ps2.clear();
      for(polygon_45_set_data<int>::iterator_type itr = ps.begin();
          itr != ps.end(); ++itr) {
        ps2.insert(*itr);
      }
      std::vector<polygon_45_with_holes_data<int> > apolywhs;
      ps2.get_polygons_with_holes(apolywhs);
      std::cout << apolywhs.size() << std::endl;
      ps2 += 1;
      apolywhs.clear();
      ps2.get_polygons_with_holes(apolywhs);
      if(apolywhs.size()) std::cout << apolywhs[0] << std::endl;
      ps2 -= 1;
      apolywhs.clear();
      ps2.get_polygons_with_holes(apolywhs);
      if(apolywhs.size()) std::cout << apolywhs[0] << std::endl;
      else {
        std::cout << "test failed\n";
        return 1;
      }
      rectangle_data<int> rect;
      extents(rect, apolywhs[0]);
      ps2.clear();
      ps2.insert(rect);
      ps2.extents(rect);
      ps2.clear();
      ps2.insert(rect);
      ps2.clear();
      ps2.insert(apolywhs[0]);
      apolywhs.clear();
      ps2.get_trapezoids(apolywhs);
      if(apolywhs.size()) std::cout << apolywhs[0] << std::endl;
      else {
        std::cout << "test failed\n";
        return 1;
      }
      ps2 *= ps;
      std::cout << (ps2 == ps) << std::endl;
      ps2 ^= ps;
      std::cout << ps2.empty() << std::endl;
      axis_transformation atr(axis_transformation::WS);
      ps2 = ps;
      ps.transform(atr);
      transformation<int> tr(atr);
      tr.invert();
      ps.transform(tr);
      ps.scale_up(2);
      ps.scale_down(2);
      std::cout << (ps2 == ps) << std::endl;
      pts.clear();
      pts.push_back(point_data<int>(0,0));
      pts.push_back(point_data<int>(10,10));
      pts.push_back(point_data<int>(10,11));
      pts.push_back(point_data<int>(0,21));
      apoly.set(pts.begin(), pts.end());
      ps2.clear();
      ps2.insert(apoly);
      ps2 -= 1;
      apolywhs.clear();
      ps2.get_polygons_with_holes(apolywhs);
      if(apolywhs.size()) std::cout << apolywhs[0] << std::endl;
      else {
        std::cout << "test failed\n";
        return 1;
      }
      pts.clear();
      pts.push_back(point_data<int>(0, 0));
      pts.push_back(point_data<int>(10, 10));
      pts.push_back(point_data<int>(0, 20));
      apoly.set(pts.begin(), pts.end());
      ps2.clear();
      ps2.insert(apoly);
      pts.clear();
      pts.push_back(point_data<int>(0, 5));
      pts.push_back(point_data<int>(10, 15));
      pts.push_back(point_data<int>(0, 25));
      apoly.set(pts.begin(), pts.end());
      ps2.insert(apoly);
      apolywhs.clear();
      ps2.get_polygons_with_holes(apolywhs);
      if(apolywhs.size()) std::cout << apolywhs[0] << std::endl;
      else {
        std::cout << "test failed\n";
        return 1;
      }
      return 0;
  
    }
  }
  }
  using namespace gtl;
  
  bool testRectangle() {
    rectangle_data<int> rect, rect2;
  #ifdef BOOST_POLYGON_MSVC
    horizontal(rect, interval_data<int>(0, 10));
    vertical(rect, interval_data<int>(20, 30));
  #else
    horizontal(rect, interval_data<polygon_long_long_type>(0, 10));
    vertical(rect, interval_data<polygon_long_long_type>(20, 30));
  #endif
    xl(rect2, 0);
    xh(rect2, 10);
    yl(rect2, 20);
    yh(rect2, 30);
    if(euclidean_distance(rect, rect2) != 0) return false;
    if(euclidean_distance(rect2, rect) != 0) return false;
  #ifdef BOOST_POLYGON_MSVC
    set(rect, HORIZONTAL, interval_data<int>(0, 10));
    if(!equivalence(horizontal(rect), interval_data<int>(0, 10))) return false;
    if(!equivalence(vertical(rect2), interval_data<int>(20, 30))) return false;
  #else
    set(rect, HORIZONTAL, interval_data<polygon_long_long_type>(0, 10));
    if(!equivalence(horizontal(rect), interval_data<polygon_long_long_type>(0, 10))) return false;
    if(!equivalence(vertical(rect2), interval_data<polygon_long_long_type>(20, 30))) return false;
  #endif
    if(xl(rect) != 0) return false;
    if(xh(rect) != 10) return false;
    if(yl(rect) != 20) return false;
    if(yh(rect) != 30) return false;
    move(rect, HORIZONTAL, 10);
    if(xl(rect) != 10) return false;
  #ifdef BOOST_POLYGON_MSVC
    set_points(rect, point_data<int>(0, 20), point_data<int>(10, 30));
  #else
    set_points(rect, point_data<int>(0, 20), point_data<polygon_long_long_type>(10, 30));
  #endif
    if(xl(rect) != 0) return false;
    convolve(rect, rect2);
    if(xh(rect) != 20) return false;
    deconvolve(rect, rect2);
    if(xh(rect) != 10) return false;
    reflected_convolve(rect, rect2);
    reflected_deconvolve(rect, rect2);
    if(!equivalence(rect, rect2)) return false;
  #ifdef BOOST_POLYGON_MSVC
    convolve(rect, point_data<int>(100, 200));
  #else
    convolve(rect, point_data<polygon_long_long_type>(100, 200));
  #endif
    if(xh(rect) != 110) return false;
    deconvolve(rect, point_data<int>(100, 200));
    if(!equivalence(rect, rect2)) return false;
    xh(rect, 100);
    if(delta(rect, HORIZONTAL) != 100) return false;
    if(area(rect) != 1000) return false;
    if(half_perimeter(rect) != 110) return false;
    if(perimeter(rect) != 220) return false;
    if(guess_orientation(rect) != HORIZONTAL) return false;
    return true;
  }
  
  
  bool testPolygon() {
    int rect[4] = {0, 10, 20, 30};
    iterator_compact_to_points<int*, point_data<int> > itr(rect, rect+4);
    iterator_compact_to_points<int*, point_data<int> > itr_end(rect, rect+4);
    std::vector<point_data<int> > points;
    points.insert(points.end(), itr, itr_end);
    polygon_90_data<int> p90;
    assign(p90, rectangle_data<int>(interval_data<int>(0, 10), interval_data<int>(20, 30)));
    if(winding(p90) != COUNTERCLOCKWISE) return false;
    polygon_45_data<int> p45;
    assign(p45, rectangle_data<int>(interval_data<int>(0, 10), interval_data<int>(20, 30)));
    if(winding(p45) != COUNTERCLOCKWISE) return false;
    polygon_data<int> p;
    assign(p, rectangle_data<int>(interval_data<int>(0, 10), interval_data<int>(20, 30)));
    if(winding(p) != COUNTERCLOCKWISE) return false;
    set_compact(p90, rect, rect+4);
    if(winding(p90) != COUNTERCLOCKWISE) return false;
    points.clear();
    points.push_back(point_data<int>(0, 0));
    points.push_back(point_data<int>(10, 10));
    points.push_back(point_data<int>(0, 20));
    points.push_back(point_data<int>(-10, 10));
    set_points(p45, points.begin(), points.end());
    if(winding(p45) != COUNTERCLOCKWISE) return false;
    std::swap(points[1], points[3]);
    set_points(p, points.begin(), points.end());
    if(winding(p) == COUNTERCLOCKWISE) return false;
    point_data<int> cp;
    center(cp, p);
    if(cp != point_data<int>(0, 10)) return false;
    move(p, HORIZONTAL, 3);
    rectangle_data<int> bounding_box;
    extents(bounding_box, p);
    if(bounding_box != rectangle_data<int>(interval_data<int>(-7, 13), interval_data<int>(0, 20))) return false;
    if(area(p90) != 400) return false;
    if(area(p45) != 200) return false;
    if(perimeter(p90) != 80) return false;
    return true;
  }
  
  bool testPolygonAssign() {
    polygon_data<int> p;
    polygon_data<int> p1;
    polygon_45_data<int> p_45;
    polygon_45_data<int> p_451;
    polygon_90_data<int> p_90;
    polygon_90_data<int> p_901;
    polygon_with_holes_data<int> p_wh;
    polygon_with_holes_data<int> p_wh1;
    polygon_45_with_holes_data<int> p_45_wh;
    polygon_45_with_holes_data<int> p_45_wh1;
    polygon_90_with_holes_data<int> p_90_wh;
    polygon_90_with_holes_data<int> p_90_wh1;
    assign(p, p1);
    assign(p, p_45);
    assign(p, p_90);
    //assign(p, p_wh);
    //assign(p, p_45_wh);
    //assign(p, p_90_wh);
    //assign(p_45, p);
    assign(p_451, p_45);
    assign(p_45, p_90);
    //assign(p_45, p_wh);
    //assign(p_45, p_45_wh);
    //assign(p_45, p_90_wh);
    //assign(p_90, p);
    //assign(p_90, p_45);
    assign(p_901, p_90);
    //assign(p_90, p_wh);
    //assign(p_90, p_45_wh);
    //assign(p_90, p_90_wh);
    assign(p_wh, p);
    assign(p_wh, p_45);
    assign(p_wh, p_90);
    assign(p_wh1, p_wh);
    assign(p_wh, p_45_wh);
    assign(p_wh, p_90_wh);
    //assign(p_45_wh, p);
    assign(p_45_wh, p_45);
    assign(p_45_wh, p_90);
    //assign(p_45_wh, p_wh);
    assign(p_45_wh1, p_45_wh);
    //assign(p_90_wh, p);
    //assign(p_90_wh, p_45);
    assign(p_90_wh, p_90);
    assign(p_90_wh1, p_90_wh);
    return true;
  }
  
  int testPropertyMerge() {
    rectangle_data<int> rect1 = construct<rectangle_data<int> >(0, 1, 10, 11);
    rectangle_data<int> rect2 = construct<rectangle_data<int> >(5, 6, 17, 18);
    property_merge_90<int, int> pm;
    pm.insert(rect1, 0);
    pm.insert(rect2, 1);
    std::map<std::set<int>, polygon_90_set_data<int> > result;
    pm.merge(result);
    std::vector<rectangle_data<int> > rects;
    std::set<int> key;
    key.insert(0);
    result[key].get(rects);
    std::cout << rects.size() << std::endl;
    std::vector<polygon_data<int> > polys;
    result[key].get(polys);
    std::cout << polys.size() << std::endl;
    std::vector<polygon_90_with_holes_data<int> > polywhs;
    result[key].get(polywhs);
    std::cout << polys.size() << std::endl;
    return result.size();
  }
  
  bool testPolygonWithHoles() {
    int rect[4] = {0, 10, 20, 30};
    iterator_compact_to_points<int*, point_data<int> > itr(rect, rect+4);
    iterator_compact_to_points<int*, point_data<int> > itr_end(rect, rect+4);
    std::vector<point_data<int> > points;
    points.insert(points.end(), itr, itr_end);
    polygon_45_with_holes_data<int> p45wh;
    assign(p45wh, rectangle_data<int>(interval_data<int>(0, 10), interval_data<int>(20, 30)));
    if(winding(p45wh) != COUNTERCLOCKWISE) return false;
    polygon_45_with_holes_data<int> p45;
    assign(p45, rectangle_data<int>(interval_data<int>(0, 10), interval_data<int>(20, 30)));
    if(winding(p45) != COUNTERCLOCKWISE) return false;
    polygon_45_with_holes_data<int> p;
    assign(p, rectangle_data<int>(interval_data<int>(0, 10), interval_data<int>(20, 30)));
    if(winding(p) != COUNTERCLOCKWISE) return false;
    set_compact(p45wh, rect, rect+4);
    if(winding(p45wh) != COUNTERCLOCKWISE) return false;
    points.clear();
    points.push_back(point_data<int>(0, 0));
    points.push_back(point_data<int>(10, 10));
    points.push_back(point_data<int>(0, 20));
    points.push_back(point_data<int>(-10, 10));
    set_points(p45, points.begin(), points.end());
    if(winding(p45) != COUNTERCLOCKWISE) return false;
    std::swap(points[1], points[3]);
    set_points(p, points.begin(), points.end());
    if(winding(p) == COUNTERCLOCKWISE) return false;
    point_data<int> cp;
    center(cp, p);
    if(cp != point_data<int>(0, 10)) return false;
    move(p, HORIZONTAL, 3);
    rectangle_data<int> bounding_box;
    extents(bounding_box, p);
    if(bounding_box != rectangle_data<int>(interval_data<int>(-7, 13), interval_data<int>(0, 20))) return false;
    if(area(p45wh) != 400) return false;
    if(area(p45) != 200) return false;
    if(perimeter(p45wh) != 80) return false;
    return true;
  }
  
  using namespace gtl;
  
  typedef int Unit;
  typedef point_data<int> Point;
  typedef interval_data<int> Interval;
  typedef rectangle_data<int> Rectangle;
  typedef polygon_90_data<int> Polygon;
  typedef polygon_90_with_holes_data<int> PolygonWithHoles;
  typedef polygon_45_data<int> Polygon45;
  typedef polygon_45_with_holes_data<int> Polygon45WithHoles;
  typedef polygon_90_set_data<int> PolygonSet;
  typedef polygon_45_set_data<int> Polygon45Set;
  typedef axis_transformation AxisTransform;
  typedef transformation<int> Transform;
  
  bool getRandomBool() {
    return rand()%2 != 0;
  }
  int getRandomInt() {
    return rand()%6-2;
  }
  Point getRandomPoint() {
    int x = rand()%8;
    int y = rand()%8;
    return Point(x, y);
  }
  Polygon45 getRandomTriangle() {
    Point pts[3];
    pts[0] = getRandomPoint();
    pts[1] = pts[2] = pts[0];
    int disp = getRandomInt();
    bool dir = getRandomBool();
    x(pts[2], x(pts[2]) + disp);
    x(pts[1], x(pts[1]) + disp);
    if(dir)
      y(pts[1], y(pts[1]) + disp);
    else
      y(pts[1], y(pts[1]) - disp);
    return Polygon45(pts, pts+3);
  }
  
  bool nonInteger45StessTest() {
    for(unsigned int tests = 0; tests < 10; ++tests) {
      Polygon45Set ps1, ps2;
      std::vector<Polygon45> p45s;
      for(unsigned int i = 0; i < 10; ++i) {
        Polygon45 p45 = getRandomTriangle();
        p45s.push_back(p45);
        ps1.insert(p45);
        scale_up(p45, 2);
        ps2.insert(p45);
      }
      std::vector<Polygon45> polys;
      ps1.get(polys);
      Polygon45Set ps3;
      for(unsigned int i = 0; i < polys.size(); ++i) {
        scale_up(polys[i], 2);
        ps3.insert(polys[i]);
      }
      Polygon45Set ps4 = ps3 ^ ps2;
      std::vector<Polygon45> polys_error;
      ps4.get(polys_error);
      for(unsigned int i = 0; i < polys_error.size(); ++i) {
        //if(polys_error[i].size() > 3) return false;
        if(area(polys_error[i]) != 1) {
          if(area(polys_error[i]) == 2) {
            //if two area 1 errors merge it will have area 2
            continue;
          }
          std::cout << "test failed\n";
          for(unsigned int j =0; j < p45s.size(); ++j) {
            std::cout << p45s[j] << std::endl;
          }
          return false;
        }
      }
    }
    return true;
  }
  
  bool validate_polygon_set_op(Polygon45Set& ps45_o,
                               const Polygon45Set& ps45_1,
                               const Polygon45Set& ps45_2,
                               int op_type) {
    Polygon45Set s_ps_45_o(ps45_o);
    Polygon45Set s_ps_45_1(ps45_1);
    Polygon45Set s_ps_45_2(ps45_2);
    s_ps_45_o.scale_up(2);
    s_ps_45_1.scale_up(2);
    s_ps_45_2.scale_up(2);
    Polygon45Set s_ps_45_validate;
    if(op_type == 0) {
      s_ps_45_validate = s_ps_45_1 + s_ps_45_2;
      s_ps_45_validate += Rectangle(4, 4, 6, 6);
    } else if(op_type == 1) {
      s_ps_45_validate = s_ps_45_1 * s_ps_45_2;
      s_ps_45_validate -= Rectangle(4, 4, 6, 6);
    } else if(op_type == 2) {
      s_ps_45_validate = s_ps_45_1 ^ s_ps_45_2;
      s_ps_45_validate -= Rectangle(4, 4, 6, 6);
    } else {
      s_ps_45_validate = s_ps_45_1 - s_ps_45_2;
      s_ps_45_validate -= Rectangle(4, 4, 6, 6);
    }
    if(s_ps_45_validate != s_ps_45_o) {
      std::cout << "TEST FAILED\n";
      std::vector<Polygon45> polys;
      s_ps_45_o.get(polys);
      std::cout << "Result:\n";
      for(unsigned int i = 0; i < polys.size(); ++i) {
        std::cout << polys[i] << std::endl;
      }
      polys.clear();
      s_ps_45_validate.get(polys);
      std::cout << "Expected Result:\n";
      for(unsigned int i = 0; i < polys.size(); ++i) {
        std::cout << polys[i] << std::endl;
      }
      //redo the operation, set breakpoints here
      switch (op_type) {
      case 0:
        ps45_o = ps45_1 + ps45_2;
        ps45_o.get(polys);//needed to force clean
        break;
      case 1:
        ps45_o = ps45_1 * ps45_2;
        break;
      case 2:
        ps45_o = ps45_1 ^ ps45_2;
        break;
      default:
        ps45_o = ps45_1 - ps45_2;
      };
      //redo the check, set breakpoints here
      if(op_type == 0) {
        s_ps_45_validate = s_ps_45_1 + s_ps_45_2;
        s_ps_45_validate += Rectangle(4, 4, 6, 6);
        s_ps_45_validate.get(polys);
      } else if(op_type == 1) {
        s_ps_45_validate = s_ps_45_1 * s_ps_45_2;
        s_ps_45_validate -= Rectangle(4, 4, 6, 6);
      } else if(op_type == 2) {
        s_ps_45_validate = s_ps_45_1 ^ s_ps_45_2;
        s_ps_45_validate -= Rectangle(4, 4, 6, 6);
      } else {
        s_ps_45_validate = s_ps_45_1 - s_ps_45_2;
        s_ps_45_validate -= Rectangle(4, 4, 6, 6);
      }
      return false;
    }
    return true;
  }
  
  bool test_two_polygon_sets(const Polygon45Set& ps45_1,
                             const Polygon45Set& ps45_2) {
    std::cout << "test two polygon sets \n";
    std::vector<Polygon45> polys;
    ps45_1.get(polys);
    std::cout << "LVALUE:\n";
    for(unsigned int i = 0; i < polys.size(); ++i) {
      std::cout << polys[i] << std::endl;
    }
    polys.clear();
    ps45_2.get(polys);
    std::cout << "RVALUE:\n";
    for(unsigned int i = 0; i < polys.size(); ++i) {
      std::cout << polys[i] << std::endl;
    }
    Polygon45Set ps45_o;
    std::cout << "OR\n";
    ps45_o = ps45_1 + ps45_2;
    polys.clear();
    ps45_o.get(polys);
    for(unsigned int i = 0; i < polys.size(); ++i) {
      std::cout << polys[i] << std::endl;
    }
    if(!validate_polygon_set_op(ps45_o, ps45_1, ps45_2, 0)) return false;
    std::cout << "AND\n";
    ps45_o = ps45_1 * ps45_2;
    polys.clear();
    ps45_o.get(polys);
    for(unsigned int i = 0; i < polys.size(); ++i) {
      std::cout << polys[i] << std::endl;
    }
    if(!validate_polygon_set_op(ps45_o, ps45_1, ps45_2, 1)) return false;
    std::cout << "XOR\n";
    ps45_o = ps45_1 ^ ps45_2;
    polys.clear();
    ps45_o.get(polys);
    for(unsigned int i = 0; i < polys.size(); ++i) {
      std::cout << polys[i] << std::endl;
    }
    if(!validate_polygon_set_op(ps45_o, ps45_1, ps45_2, 2)) return false;
    std::cout << "SUBTRACT\n";
    ps45_o = ps45_1 - ps45_2;
    polys.clear();
    ps45_o.get(polys);
    for(unsigned int i = 0; i < polys.size(); ++i) {
      std::cout << polys[i] << std::endl;
    }
    if(!validate_polygon_set_op(ps45_o, ps45_1, ps45_2, 3)) return false;
    return true;
  }
  
  bool test_two_polygons(const Polygon45& p45_1,
                         const Polygon45& p45_2) {
    Polygon45Set ps45_1, ps45_2;
    ps45_1.insert(p45_1);
    ps45_2.insert(p45_2);
    ps45_1.insert(rectangle_data<int>(10, -100, 20, 100));
    ps45_2.insert(rectangle_data<int>(0, 10, 100, 20));
    if(!test_two_polygon_sets(ps45_1, ps45_2)) return false;
    Polygon45Set ps45_1_c = ps45_1 - Rectangle(0, 0, 2, 5);
    Polygon45Set ps45_2_c = ps45_2 - Rectangle(0, 0, 2, 5);
    if(!test_two_polygon_sets(ps45_1_c, ps45_2_c)) return false;
    if(!test_two_polygon_sets(ps45_1_c, ps45_2)) return false;
    if(!test_two_polygon_sets(ps45_1, ps45_2_c)) return false;
    return true;
  }
  
  bool test_45_touch() {
    using namespace gtl;
    connectivity_extraction_45<int> ce;
    rectangle_data<int> rect1(0, 0, 10, 10);
    rectangle_data<int> rect2(5, 5, 15, 15);
    rectangle_data<int> rect3(5, 20, 15, 25);
    ce.insert(rect1);
    ce.insert(rect2);
    ce.insert(rect3);
    std::vector<std::set<int> > graph(3);
    ce.extract(graph);
    if(graph[0].size() == 1 && graph[1].size() == 1 && graph[2].size() == 0) {
      std::set<int>::iterator itr = graph[0].begin();
      std::cout << *itr << std::endl;
      std::set<int>::iterator itr1 = graph[1].begin();
      std::cout << *itr1 << std::endl;
      return true;
    }
    std::cout << "test failed\n";
    return false;
  }
  
  bool test_45_touch_ur() {
    using namespace gtl;
    connectivity_extraction_45<int> ce;
    rectangle_data<int> rect1(0, 0, 5, 5);
    rectangle_data<int> rect2(5, 5, 10, 10);
    ce.insert(rect1);
    ce.insert(rect2);
    std::vector<std::set<int> > graph(2);
    ce.extract(graph);
    if(graph[0].size() == 1 && graph[1].size() == 1) {
      std::set<int>::iterator itr = graph[0].begin();
      std::cout << *itr << std::endl;
      std::set<int>::iterator itr1 = graph[1].begin();
      std::cout << *itr1 << std::endl;
      return true;
    }
    std::cout << "test failed\n";
    return false;
  }
  
  bool test_45_touch_r() {
    using namespace gtl;
    connectivity_extraction_45<int> ce;
    rectangle_data<int> rect1(0, 0, 5, 5);
    rectangle_data<int> rect2(5, 0, 10, 5);
    ce.insert(rect1);
    ce.insert(rect2);
    std::vector<std::set<int> > graph(2);
    ce.extract(graph);
    if(graph[0].size() == 1 && graph[1].size() == 1) {
      std::set<int>::iterator itr = graph[0].begin();
      std::cout << *itr << std::endl;
      std::set<int>::iterator itr1 = graph[1].begin();
      std::cout << *itr1 << std::endl;
      return true;
    }
    std::cout << "test failed\n";
    return false;
  }
  
  bool test_45_touch_boundaries() {
    using namespace gtl;
    connectivity_extraction_45<int> ce;
    rectangle_data<int> rect1(0, 0, 10, 10);
    rectangle_data<int> rect2(10, 0, 20, 10);
    rectangle_data<int> rect3(20, 0, 30, 10);
    rectangle_data<int> rect4(0, 10, 10, 20);
    rectangle_data<int> rect5(10, 10, 20, 20);
    rectangle_data<int> rect6(20, 10, 30, 20);
    rectangle_data<int> rect7(0, 20, 10, 30);
    rectangle_data<int> rect8(10, 20, 20, 30);
    rectangle_data<int> rect9(20, 20, 30, 30);
    ce.insert(rect1);
    ce.insert(rect2);
    ce.insert(rect3);
    ce.insert(rect4);
    ce.insert(rect5);
    ce.insert(rect6);
    ce.insert(rect7);
    ce.insert(rect8);
    ce.insert(rect9);
    std::vector<std::set<int> > graph(9);
    ce.extract(graph);
    for(unsigned int i = 0; i < 9; ++i) {
      std::cout << i << ": ";
      for(std::set<int>::iterator itr = graph[i].begin(); itr != graph[i].end(); ++itr) {
        std::cout << *itr << " ";
      } std::cout << std::endl;
    }
    if(graph[0].size() == 3 && graph[1].size() == 5 && graph[2].size() == 3 &&
       graph[3].size() == 5 && graph[4].size() == 8 && graph[5].size() == 5 &&
       graph[6].size() == 3 && graph[7].size() == 5 && graph[8].size() == 3) {
      return true;
    }
    std::cout << "test failed\n";
    return false;
  }
  
  bool test_45_concept_interact() {
    using namespace gtl;
    std::vector<polygon_45_data<int> > polys;
    polys += rectangle_data<int>(10, 10, 20, 20);
    polys += rectangle_data<int>(15, 15, 25, 25);
    polys += rectangle_data<int>(5, 25, 10, 35);
    interact(polys, rectangle_data<int>(0, 0, 13, 13));
    if(polys.size() != 1) return false;
    return true;
  }
  
  bool test_aa_touch() {
    using namespace gtl;
    connectivity_extraction<int> ce;
    rectangle_data<int> rect1(0, 0, 10, 10);
    rectangle_data<int> rect2(5, 5, 15, 15);
    rectangle_data<int> rect3(5, 20, 15, 25);
    ce.insert(rect1);
    ce.insert(rect2);
    ce.insert(rect3);
    std::vector<std::set<int> > graph(3);
    ce.extract(graph);
    if(graph[0].size() == 1 && graph[1].size() == 1 && graph[2].size() == 0) {
      std::set<int>::iterator itr = graph[0].begin();
      std::cout << *itr << std::endl;
      std::set<int>::iterator itr1 = graph[1].begin();
      std::cout << *itr1 << std::endl;
      return true;
    }
    std::cout << "test failed\n";
    return false;
  }
  
  bool test_aa_touch_ur() {
    using namespace gtl;
    connectivity_extraction<int> ce;
    rectangle_data<int> rect1(0, 0, 5, 5);
    rectangle_data<int> rect2(5, 5, 10, 10);
    ce.insert(rect1);
    ce.insert(rect2);
    std::vector<std::set<int> > graph(2);
    ce.extract(graph);
    if(graph[0].size() == 1 && graph[1].size() == 1) {
      std::set<int>::iterator itr = graph[0].begin();
      std::cout << *itr << std::endl;
      std::set<int>::iterator itr1 = graph[1].begin();
      std::cout << *itr1 << std::endl;
      return true;
    }
    std::cout << "test failed\n";
    return false;
  }
  
  bool test_aa_touch_ur2() {
    using namespace gtl;
    connectivity_extraction<int> ce;
    rectangle_data<int> rect2(5, 5, 10, 10);
    point_data<int> pts[3] = {
      point_data<int>(0, 0),
      point_data<int>(5, 5),
      point_data<int>(0, 5)
    };
    polygon_data<int> poly;
    poly.set(pts, pts+3);
    ce.insert(poly);
    ce.insert(rect2);
    std::vector<std::set<int> > graph(2);
    ce.extract(graph);
    if(graph[0].size() == 1 && graph[1].size() == 1) {
      std::set<int>::iterator itr = graph[0].begin();
      std::cout << *itr << std::endl;
      std::set<int>::iterator itr1 = graph[1].begin();
      std::cout << *itr1 << std::endl;
      return true;
    }
    std::cout << "test failed\n";
    return false;
  }
  
  bool test_aa_touch_r() {
    using namespace gtl;
    connectivity_extraction<int> ce;
    rectangle_data<int> rect1(0, 0, 5, 5);
    rectangle_data<int> rect2(5, 0, 10, 5);
    ce.insert(rect1);
    ce.insert(rect2);
    std::vector<std::set<int> > graph(2);
    ce.extract(graph);
    if(graph[0].size() == 1 && graph[1].size() == 1) {
      std::set<int>::iterator itr = graph[0].begin();
      std::cout << *itr << std::endl;
      std::set<int>::iterator itr1 = graph[1].begin();
      std::cout << *itr1 << std::endl;
      return true;
    }
    std::cout << "test failed\n";
    return false;
  }
  
  bool test_aa_touch_boundaries() {
    using namespace gtl;
    connectivity_extraction<int> ce;
    rectangle_data<int> rect1(0, 0, 10, 10);
    rectangle_data<int> rect2(10, 0, 20, 10);
    rectangle_data<int> rect3(20, 0, 30, 10);
    rectangle_data<int> rect4(0, 10, 10, 20);
    rectangle_data<int> rect5(10, 10, 20, 20);
    rectangle_data<int> rect6(20, 10, 30, 20);
    rectangle_data<int> rect7(0, 20, 10, 30);
    rectangle_data<int> rect8(10, 20, 20, 30);
    rectangle_data<int> rect9(20, 20, 30, 30);
    ce.insert(rect1);
    ce.insert(rect2);
    ce.insert(rect3);
    ce.insert(rect4);
    ce.insert(rect5);
    ce.insert(rect6);
    ce.insert(rect7);
    ce.insert(rect8);
    ce.insert(rect9);
    std::vector<std::set<int> > graph(9);
    ce.extract(graph);
    for(unsigned int i = 0; i < 9; ++i) {
      std::cout << i << ": ";
      for(std::set<int>::iterator itr = graph[i].begin(); itr != graph[i].end(); ++itr) {
        std::cout << *itr << " ";
      } std::cout << std::endl;
    }
    if(graph[0].size() == 3 && graph[1].size() == 5 && graph[2].size() == 3 &&
       graph[3].size() == 5 && graph[4].size() == 8 && graph[5].size() == 5 &&
       graph[6].size() == 3 && graph[7].size() == 5 && graph[8].size() == 3) {
      return true;
    }
    std::cout << "test failed\n";
    return false;
  }
  
  bool test_aa_concept_interact() {
    using namespace gtl;
    std::vector<polygon_data<int> > polys;
    polys += rectangle_data<int>(10, 10, 20, 20);
    polys += rectangle_data<int>(15, 15, 25, 25);
    polys += rectangle_data<int>(5, 25, 10, 35);
    interact(polys, rectangle_data<int>(0, 0, 13, 13));
    if(polys.size() != 1) return false;
    return true;
  }
  
  bool test_get_rectangles() {
    using namespace gtl;
    polygon_90_set_data<int> ps(VERTICAL);
    ps += rectangle_data<int>(0, 0, 10, 10);
    ps += rectangle_data<int>(5, 5, 15, 15);
    std::vector<polygon_90_data<int> > polys;
    ps.get_rectangles(polys, HORIZONTAL);
    for(unsigned int i = 0; i < polys.size(); ++i) {
      std::cout << polys[i] << std::endl;
    }
    if(polys.size() != 3) return false;
    std::vector<rectangle_data<int> > rects;
    ps.get_rectangles(rects, HORIZONTAL);
    for(unsigned int i = 0; i < rects.size(); ++i) {
      std::cout << rects[i] << std::endl;
    }
    if(rects.size() != 3) return false;
    if(!equivalence(rects[2], rectangle_data<int>(5,10,15,15))) return false;
  
    get_rectangles(polys, rects, VERTICAL);
    get_rectangles(rects, polys, HORIZONTAL);
    return equivalence(rects, polys);
  }
  
  bool test_get_trapezoids() {
    using namespace gtl;
    polygon_45_set_data<int> ps;
    ps += rectangle_data<int>(0, 0, 10, 10);
    ps += rectangle_data<int>(5, 5, 15, 15);
    std::vector<polygon_45_data<int> > polys;
    ps.get_trapezoids(polys, HORIZONTAL);
    for(unsigned int i = 0; i < polys.size(); ++i) {
      std::cout << polys[i] << std::endl;
    }
    if(polys.size() != 3) return false;
    std::vector<polygon_45_data<int> > rects;
    ps.get_trapezoids(rects, HORIZONTAL);
    for(unsigned int i = 0; i < rects.size(); ++i) {
      std::cout << rects[i] << std::endl;
    }
    if(rects.size() != 3) return false;
    if(!equivalence(rects[2], rectangle_data<int>(5,10,15,15))) return false;
    get_trapezoids(polys, rects, VERTICAL);
    get_trapezoids(rects, polys, HORIZONTAL);
    return equivalence(rects, polys);
  }
  
  bool test_SQRT1OVER2() {
    Point pts[] = {
      Point(100, 100),
      Point(0, 100),
      Point(100, 200),
      Point(0, 300),
      Point(100, 400),
      Point(0, 500),
      Point(100, 500),
      Point(100, 600),
      Point(200, 500),
      Point(300, 600),
      Point(400, 500),
      Point(500, 600),
      Point(500, 500),
      Point(600, 500),
      Point(500, 400),
      Point(600, 300),
      Point(500, 200),
      Point(600, 100),
      Point(500, 100),
      Point(500, 0),
      Point(400, 100),
      Point(300, 0),
      Point(200, 100),
      Point(100, 0),
      Point(100, 100)
    };
    Polygon45 p45(pts, pts+25);
    std::cout << is_45(p45) << std::endl;
    std::cout << p45 << std::endl;
    Polygon45Set ps45;
    ps45 += p45;
    ps45.resize(10, SQRT1OVER2, ORTHOGONAL);
    std::vector<Polygon45> polys;
    ps45.get(polys);
    if(polys.size() != 1) return false;
    Point pts2[] = {
      Point(90, 90),
      Point(-10, 90),
      Point(-10, 100),
      Point(90, 200),
      Point(-10, 300),
      Point(90, 400),
      Point(-10, 500),
      Point(-10, 510),
      Point(90, 510),
      Point(90, 610),
      Point(100, 610),
      Point(200, 510),
      Point(300, 610),
      Point(400, 510),
      Point(500, 610),
      Point(510, 610),
      Point(510, 510),
      Point(610, 510),
      Point(610, 500),
      Point(510, 400),
      Point(610, 300),
      Point(510, 200),
      Point(610, 100),
      Point(610, 90),
      Point(510, 90),
      Point(510, -10),
      Point(500, -10),
      Point(400, 90),
      Point(300, -10),
      Point(200, 90),
      Point(100, -10),
      Point(90, -10),
      Point(90, 90)
    };
    Polygon45 p45reference(pts2, pts2+33);
    std::cout << is_45(polys[0]) << std::endl;
    std::cout << polys[0] << std::endl;
    std::cout << p45reference << std::endl;
    std::cout << is_45(p45reference) << std::endl;
    if(!equivalence(polys[0], p45reference)) {
      std::cout << "polys don't match\n";
      return false;
    }
    ps45.resize(-10, SQRT1OVER2, ORTHOGONAL);
    polys.clear();
    ps45.get(polys);
    if(polys.size() != 1) return false;
    std::cout << is_45(polys[0]) << std::endl;
    std::cout << polys[0] << std::endl;
    if(!equivalence(polys[0], p45)) {
      std::cout << "polys don't match\n";
      return false;
    }
    ps45.resize(11, SQRT1OVER2, UNFILLED);
    polys.clear();
    ps45.get(polys);
    if(polys.size() != 1) return false;
    std::cout << is_45(polys[0]) << std::endl;
    std::cout << polys[0] << std::endl;
    return true;
  }
  
  bool test_scaling_by_floating(){
    Point pts[] = {
      Point(1, 1),
      Point(10, 1),
      Point(1, 10)
    };
    Polygon45 poly(pts, pts+3);
    Polygon45Set ps45;
    ps45 += poly;
    ps45.scale(double(2.5));
    std::vector<Polygon45> polys;
    ps45.get(polys);
    for(unsigned int i = 0; i < polys.size(); ++i) {
      std::cout << polys[i] << std::endl;
      std::cout << area(polys[i]) << std::endl;
    }
    if(polys.size() != 1) return false;
    if(area(polys[0]) != 242) return false;
    scale(ps45, double(1)/double(2.5));
    polys.clear();
    ps45.get(polys);
    for(unsigned int i = 0; i < polys.size(); ++i) {
      std::cout << polys[i] << std::endl;
    }
    return equivalence(polys, poly);
  }
  
  bool test_directional_resize() {
    std::vector<Rectangle> rects;
    rects.push_back(Rectangle(0, 0, 100, 100));
    resize(rects, -10, 10, -10, 10);
    for(unsigned int i = 0; i < rects.size(); ++i) {
      std::cout << rects[i] << std::endl;
    }
    if(rects.size() != 1) return false;
    if(rects[0] != Rectangle(10, 10, 110, 110)) return false;
  
    return true;
  }
  
  bool test_self_xor() {
    std::vector<Rectangle> rects;
    rects.push_back(Rectangle(0, 0, 10, 10));
    rects.push_back(Rectangle(5, 5, 15, 15));
    self_xor(rects);
    for(unsigned int i = 0; i < rects.size(); ++i) {
      std::cout << rects[i] << std::endl;
    }
    if(rects.size() == 4) return true;
    else return false;
  }
  
  bool test_grow_and_45() {
    polygon_45_set_data<int> ps;
    ps.insert(Rectangle(0, 0, 5, 5));
    ps.insert(Rectangle(5, 5, 15, 15));
    grow_and(ps, 2);
    std::vector<polygon_45_data<int> > rects;
    ps.get_trapezoids(rects);
    for(unsigned int i = 0; i < rects.size(); ++i) {
      std::cout << rects[i] << std::endl;
    }
    if(rects.size() != 1) return false;
    return equivalence(rects, Rectangle(3, 3, 7, 7));
  }
  
  bool test_self_xor_45() {
    polygon_45_set_data<int> ps;
    ps.insert(Rectangle(0, 0, 10, 10));
    ps.insert(Rectangle(5, 5, 15, 15));
    self_xor(ps);
    std::vector<polygon_45_data<int> > rects;
    ps.get_trapezoids(rects);
    for(unsigned int i = 0; i < rects.size(); ++i) {
      std::cout << rects[i] << std::endl;
    }
    if(rects.size() == 4) return true;
    else return false;
  }
  
  bool testViewCopyConstruct() {
    PolygonSet ps1, ps2;
    ps1.insert(Rectangle(0, 0, 10, 10));
    ps2.insert(Rectangle(5, 5, 15, 15));
    PolygonSet psr = ps1 - ps2;
    std::vector<Rectangle> rects;
    rects += psr;
    for(unsigned int i = 0; i < rects.size(); ++i)
      std::cout << rects[i] << std::endl;
    if( rects.size() != 2) return false;
    Polygon45Set ps45_1, ps45_2;
    ps45_1.insert(Rectangle(0, 0, 10, 10));
    ps45_2.insert(Rectangle(5, 5, 15, 15));
    Polygon45Set ps45_r = ps45_1 - ps45_2;
    std::vector<Polygon45> polys;
    ps45_r.get_trapezoids(polys);
    for(unsigned int i = 0; i < polys.size(); ++i)
      std::cout << polys[i] << std::endl;
    if( polys.size() != 2) return false;
    return true;
  }
  
  bool testpip() {
    std::vector<Point> pts;
    pts.push_back(Point(0, 0));
    pts.push_back(Point(10, 0));
    pts.push_back(Point(20, 10));
    pts.push_back(Point(0, 20));
    pts.push_back(Point(30, 40));
    pts.push_back(Point(-10, 50));
    pts.push_back(Point(-20, -20));
    pts.push_back(Point(0, 0));
    polygon_data<int> poly;
    polygon_with_holes_data<int> poly2;
    polygon_45_data<int> poly45;
    polygon_45_with_holes_data<int> poly245;
    polygon_90_data<int> poly90;
    polygon_90_with_holes_data<int> poly290;
    poly.set(pts.begin(), pts.end());
    poly2.set(pts.begin(), pts.end());
    assign(poly45, Rectangle(0, 0, 100, 100));
    assign(poly245, Rectangle(0, 0, 100, 100));
    assign(poly90, Rectangle(0, 0, 100, 100));
    assign(poly290, Rectangle(0, 0, 100, 100));
    for(unsigned int i = 0; i < pts.size(); ++i) {
      if(!contains(poly, pts[i], true)) return false;
      if(contains(poly, pts[i], false)) return false;
      if(!contains(poly2, pts[i], true)) return false;
      if(contains(poly2, pts[i], false)) return false;
    }
    if(!contains(poly45, pts[0], true)) return false;
    if(contains(poly245, pts[0], false)) return false;
    if(!contains(poly90, pts[0], true)) return false;
    if(contains(poly290, pts[0], false)) return false;
    Point pt(0, -10);
    if(contains(poly, pt)) return false;
    Point p2(0, 1);
    if(!contains(poly, p2)) return false;
    return true;
  }
  
  void testHand() {
    using namespace gtl;
    int handcoords[] = {
  12375, 11050, 13175, 10200, 15825, 9275, 18750, 8525, 24150, 8300, 27575, 8400, 31775, 7800,
  35975, 7200, 41375, 4800, 42575, 4200, 43175, 4200, 47375, 2400, 49175, 1800, 51150, 2200,
  52275, 2825, 52625, 4150, 52375, 4975, 51575, 6000, 49275, 6850, 45700, 7950, 43175, 9600,
  39575, 10800, 37775, 12000, 37775, 12600, 37775, 13800, 38975, 14400, 41375, 14400, 45575, 13200,
  48600, 13000, 51575, 13200, 55175, 12600, 58775, 12600, 61175, 13200, 62375, 14400, 62550, 15700,
  61975, 16875, 60775, 17600, 60100, 17675, 58525, 17675, 56150, 17575, 52175, 18000, 47975, 18600,
  45575, 19200, 44375, 19200, 42675, 19325, 41600, 19775, 41600, 20500, 42100, 20825, 44975, 20400,
  48575, 20400, 52775, 21000, 53975, 21000, 57575, 21000, 62375, 21000, 65450, 22000, 66300, 23100,
  66100, 24550, 64750, 25925, 62975, 26400, 61175, 26400, 58775, 26400, 56025, 26050, 53450, 26025,
  50975, 26400, 48575, 26400, 46775, 26400, 43650, 26075, 41375, 26400, 40775, 27000, 40775, 27600,
  42225, 28650, 44375, 29400, 48575, 30000, 50975, 31200, 53975, 31800, 58775, 33000, 61200, 34300,
  62375, 35400, 62375, 37200, 61175, 38400, 60000, 38700, 57575, 38400, 54550, 37575, 50975, 36600,
  49075, 36125, 47750, 36125, 45700, 35425, 42350, 34350, 38900, 33775, 30575, 33000, 26975, 33600,
  25975, 34900, 26375, 36600, 28175, 38400, 30575, 40800, 32375, 43800, 33200, 46200, 33200, 48000,
  32650, 49300, 31425, 50000, 29950, 50125, 28825, 49375, 27575, 48000, 25825, 46000, 23975, 44100,
  22175, 42600, 19775, 39600, 17325, 37300, 14975, 34800, 13175, 31800, 10775, 29400, 9600, 27400,
  10175, 27000, 11375, 27600, 12575, 28800, 14375, 31800, 16175, 34800, 18575, 37200, 21575, 39000,
  22775, 40200, 23975, 41400, 24575, 42600, 26375, 44400, 28325, 46000, 29850, 46775, 31175, 46200,
  31550, 44575, 30575, 43200, 28775, 40800, 25775, 38400, 24575, 34800, 24750, 33175, 26975, 31800,
  29975, 31800, 33575, 31800, 37775, 32400, 39575, 33000, 41975, 33600, 45150, 34175, 46975, 34750,
  48575, 35400, 50975, 35400, 51575, 34800, 51875, 33725, 50775, 32575, 48575, 31800, 45750, 30875,
  43775, 30600, 41375, 29400, 38975, 28800, 35975, 28200, 34775, 27600, 34175, 27000, 34775, 25800,
  37175, 25200, 40175, 25200, 43175, 25200, 46775, 25200, 50975, 25425, 53375, 25200, 55175, 24600,
  55525, 23450, 53975, 22200, 52775, 22200, 49075, 21850, 45950, 21925, 40775, 21600, 37775, 21600,
  35150, 21350, 34325, 20950, 34175, 19800, 35975, 19200, 38375, 19200, 40750, 18900, 42575, 18600,
  44375, 18000, 47975, 17400, 50375, 17125, 52025, 16625, 52775, 15600, 52100, 14625, 49675, 14125,
  48625, 14125, 46775, 14400, 44375, 15000, 41375, 15150, 37700, 15275, 34775, 15600, 32850, 15925,
  31775, 15600, 31425, 14875, 32375, 13800, 36575, 11400, 38975, 10200, 41375, 9000, 43075, 8150,
  43650, 7200, 43325, 6250, 42225, 5825, 40800, 6275, 38900, 6925, 35375, 8400, 32375, 10200,
  27575, 11400, 22775, 12600, 19775, 13225, 16775, 13800, 14975, 14400, 13050, 14000, 11975, 12600,
      0, 0 };
    std::vector<Point> handpoints;
    for(unsigned int i = 0; i < 100000; i += 2) {
      Point pt(handcoords[i], handcoords[i+1]);
      if(pt == Point(0, 0)) break;
      handpoints.push_back(pt);
    }
    polygon_data<int> handpoly;
    handpoly.set(handpoints.begin(), handpoints.end());
    int spiralcoords [] = {
  37200, 3600, 42075, 4025, 47475, 5875, 51000, 7800, 55800, 12300, 59000, 17075, 60000, 20400,
  61200, 25800, 61200, 29400, 60600, 33600, 58800, 38400, 55800, 42600, 53200, 45625,
  49200, 48600, 43200, 51000, 35400, 51600, 29400, 50400, 23400, 47400, 19200, 43800,
  16200, 39600, 14400, 35400, 13200, 29400, 13200, 24000, 15000, 18600, 17400, 13800,
  20525, 10300, 24600, 7200, 29400, 4800, 32450, 4000, 34825, 3675, 35625, 3625,
  35825, 7275, 39600, 7200, 43800, 8400, 46800, 9600, 50400, 12000, 53400, 15000,
  55800, 18600, 57000, 23400, 57600, 27000, 57000, 32400, 55200, 37200, 52200, 41400,
  48000, 45000, 42000, 47400, 35400, 48000, 30000, 46800, 24600, 43800, 20325, 39100,
  17850, 34275, 16800, 27600, 17400, 22200, 20400, 16200, 24600, 11400, 28800, 9000,
  32400, 7800, 33200, 7575, 33925, 11050, 35400, 10800, 37200, 10800, 41400, 11400,
  46200, 13200, 49800, 16200, 51600, 19200, 53400, 23400, 54000, 29400, 52800, 33600,
  49800, 39000, 45000, 42600, 39000, 44400, 33600, 43800, 28200, 42000, 24000, 37800,
  21000, 33000, 20400, 26400, 21600, 21000, 24600, 16200, 28200, 13200, 31875, 11625,
  33200, 15625, 36000, 15000, 39000, 15000, 43800, 16800, 46800, 19200, 49200, 23400,
  49800, 27600, 48750, 32700, 46350, 36275, 42600, 39000, 38400, 40200, 31800, 39000,
  28200, 36600, 25200, 31200, 24600, 26400, 26025, 21800, 28200, 18600, 30600, 16800,
  32575, 19875, 34200, 19200, 36000, 18600, 37200, 18600, 40375, 19125, 43200, 21000,
  45600, 24000, 46200, 27600, 45600, 30600, 43800, 33600, 41475, 35625, 37800, 36600,
  33600, 36000, 30000, 33600, 28200, 28800, 28800, 24600, 30000, 22200, 31200, 23400,
  30600, 25200, 30000, 27000, 30600, 30000, 31800, 32400, 34200, 34200, 38400, 34800,
  41400, 33000, 44025, 30225, 44400, 26400, 43200, 23400, 40900, 21200, 37800, 20400,
  34950, 20675, 32400, 22200, 30175, 19475, 28425, 21300, 27000, 24000, 26400, 27600,
  27000, 31800, 31200, 36600, 36600, 38400, 42600, 37200, 46200, 33600, 48000, 30000,
  47650, 24425, 45600, 20400, 42650, 18200, 39000, 16800, 35400, 16800, 33600, 17400,
  32875, 17675, 31100, 13850, 28200, 15600, 25200, 18600, 22800, 22800, 22200, 27000,
  23400, 33600, 26400, 38400, 31675, 41575, 37800, 42600, 40850, 42150, 42800, 41550,
  47050, 39025, 50100, 35375, 52200, 29400, 51675, 23950, 49800, 19200, 46200, 15600,
  41400, 13200, 37800, 12600, 35025, 12750, 33350, 13050, 32400, 9600, 30025, 10325,
  25925, 12725, 22200, 16800, 19800, 21000, 18600, 25800, 18600, 30000, 20400, 35400,
  22575, 39250, 25225, 41825, 28200, 43800, 33600, 46200, 39000, 46200, 44400, 45000,
  48650, 42350, 52800, 37800, 55200, 32400, 55800, 26400, 54600, 21000, 53400, 18000,
  50400, 14400, 47400, 12000, 42600, 9600, 39000, 9000, 36000, 9000, 34775, 9125,
  34300, 5600, 30000, 6600, 25800, 8400, 22025, 11350, 18725, 15125, 16200, 20400,
  15000, 24600, 15000, 30600, 16800, 36600, 20400, 42600, 25800, 46800, 31200, 49200,
  38400, 49800, 45000, 48600, 51000, 45000, 55475, 40225, 58200, 34800, 59400, 30000,
  59400, 25200, 58200, 19800, 55200, 14400, 52225, 11150, 47400, 7800, 44175, 6500,
  40200, 5400, 38400, 5400, 37200, 5400, 0, 0 };
    std::vector<Point> spiralpoints;
    for(unsigned int i = 0; i < 100000; i += 2) {
      Point pt(spiralcoords[i], spiralcoords[i+1]);
      if(pt == Point(0, 0)) break;
      spiralpoints.push_back(pt);
    }
    polygon_data<int> spiralpoly;
    spiralpoly.set(spiralpoints.begin(), spiralpoints.end());
    polygon_set_data<int> handset;
    handset += handpoly;
    polygon_set_data<int> spiralset;
    spiralset += spiralpoly;
    polygon_set_data<int> xorset = handset ^ spiralset;
    std::vector<polygon_data<int> > polys;
    polys += xorset;
    std::cout << polys.size() << std::endl;
    for(unsigned int i = 0; i < polys.size(); ++i)
      std::cout << polys[i] << std::endl;
  }
  
  //void testHandFloat() {
  //  using namespace gtl;
  //  double handcoords[] = {
  //12375, 11050, 13175, 10200, 15825, 9275, 18750, 8525, 24150, 8300, 27575, 8400, 31775, 7800,
  //35975, 7200, 41375, 4800, 42575, 4200, 43175, 4200, 47375, 2400, 49175, 1800, 51150, 2200,
  //52275, 2825, 52625, 4150, 52375, 4975, 51575, 6000, 49275, 6850, 45700, 7950, 43175, 9600,
  //39575, 10800, 37775, 12000, 37775, 12600, 37775, 13800, 38975, 14400, 41375, 14400, 45575, 13200,
  //48600, 13000, 51575, 13200, 55175, 12600, 58775, 12600, 61175, 13200, 62375, 14400, 62550, 15700,
  //61975, 16875, 60775, 17600, 60100, 17675, 58525, 17675, 56150, 17575, 52175, 18000, 47975, 18600,
  //45575, 19200, 44375, 19200, 42675, 19325, 41600, 19775, 41600, 20500, 42100, 20825, 44975, 20400,
  //48575, 20400, 52775, 21000, 53975, 21000, 57575, 21000, 62375, 21000, 65450, 22000, 66300, 23100,
  //66100, 24550, 64750, 25925, 62975, 26400, 61175, 26400, 58775, 26400, 56025, 26050, 53450, 26025,
  //50975, 26400, 48575, 26400, 46775, 26400, 43650, 26075, 41375, 26400, 40775, 27000, 40775, 27600,
  //42225, 28650, 44375, 29400, 48575, 30000, 50975, 31200, 53975, 31800, 58775, 33000, 61200, 34300,
  //62375, 35400, 62375, 37200, 61175, 38400, 60000, 38700, 57575, 38400, 54550, 37575, 50975, 36600,
  //49075, 36125, 47750, 36125, 45700, 35425, 42350, 34350, 38900, 33775, 30575, 33000, 26975, 33600,
  //25975, 34900, 26375, 36600, 28175, 38400, 30575, 40800, 32375, 43800, 33200, 46200, 33200, 48000,
  //32650, 49300, 31425, 50000, 29950, 50125, 28825, 49375, 27575, 48000, 25825, 46000, 23975, 44100,
  //22175, 42600, 19775, 39600, 17325, 37300, 14975, 34800, 13175, 31800, 10775, 29400, 9600, 27400,
  //10175, 27000, 11375, 27600, 12575, 28800, 14375, 31800, 16175, 34800, 18575, 37200, 21575, 39000,
  //22775, 40200, 23975, 41400, 24575, 42600, 26375, 44400, 28325, 46000, 29850, 46775, 31175, 46200,
  //31550, 44575, 30575, 43200, 28775, 40800, 25775, 38400, 24575, 34800, 24750, 33175, 26975, 31800,
  //29975, 31800, 33575, 31800, 37775, 32400, 39575, 33000, 41975, 33600, 45150, 34175, 46975, 34750,
  //48575, 35400, 50975, 35400, 51575, 34800, 51875, 33725, 50775, 32575, 48575, 31800, 45750, 30875,
  //43775, 30600, 41375, 29400, 38975, 28800, 35975, 28200, 34775, 27600, 34175, 27000, 34775, 25800,
  //37175, 25200, 40175, 25200, 43175, 25200, 46775, 25200, 50975, 25425, 53375, 25200, 55175, 24600,
  //55525, 23450, 53975, 22200, 52775, 22200, 49075, 21850, 45950, 21925, 40775, 21600, 37775, 21600,
  //35150, 21350, 34325, 20950, 34175, 19800, 35975, 19200, 38375, 19200, 40750, 18900, 42575, 18600,
  //44375, 18000, 47975, 17400, 50375, 17125, 52025, 16625, 52775, 15600, 52100, 14625, 49675, 14125,
  //48625, 14125, 46775, 14400, 44375, 15000, 41375, 15150, 37700, 15275, 34775, 15600, 32850, 15925,
  //31775, 15600, 31425, 14875, 32375, 13800, 36575, 11400, 38975, 10200, 41375, 9000, 43075, 8150,
  //43650, 7200, 43325, 6250, 42225, 5825, 40800, 6275, 38900, 6925, 35375, 8400, 32375, 10200,
  //27575, 11400, 22775, 12600, 19775, 13225, 16775, 13800, 14975, 14400, 13050, 14000, 11975, 12600,
  //    0, 0 };
  //  std::vector<point_data<double> > handpoints;
  //  for(unsigned int i = 0; i < 100000; i += 2) {
  //    point_data<double>  pt(handcoords[i], handcoords[i+1]);
  //    if(pt == point_data<double> (0, 0)) break;
  //    handpoints.push_back(pt);
  //  }
  //  polygon_data<double> handpoly;
  //  handpoly.set(handpoints.begin(), handpoints.end());
  //  double spiralcoords [] = {
  //37200, 3600, 42075, 4025, 47475, 5875, 51000, 7800, 55800, 12300, 59000, 17075, 60000, 20400,
  //61200, 25800, 61200, 29400, 60600, 33600, 58800, 38400, 55800, 42600, 53200, 45625,
  //49200, 48600, 43200, 51000, 35400, 51600, 29400, 50400, 23400, 47400, 19200, 43800,
  //16200, 39600, 14400, 35400, 13200, 29400, 13200, 24000, 15000, 18600, 17400, 13800,
  //20525, 10300, 24600, 7200, 29400, 4800, 32450, 4000, 34825, 3675, 35625, 3625,
  //35825, 7275, 39600, 7200, 43800, 8400, 46800, 9600, 50400, 12000, 53400, 15000,
  //55800, 18600, 57000, 23400, 57600, 27000, 57000, 32400, 55200, 37200, 52200, 41400,
  //48000, 45000, 42000, 47400, 35400, 48000, 30000, 46800, 24600, 43800, 20325, 39100,
  //17850, 34275, 16800, 27600, 17400, 22200, 20400, 16200, 24600, 11400, 28800, 9000,
  //32400, 7800, 33200, 7575, 33925, 11050, 35400, 10800, 37200, 10800, 41400, 11400,
  //46200, 13200, 49800, 16200, 51600, 19200, 53400, 23400, 54000, 29400, 52800, 33600,
  //49800, 39000, 45000, 42600, 39000, 44400, 33600, 43800, 28200, 42000, 24000, 37800,
  //21000, 33000, 20400, 26400, 21600, 21000, 24600, 16200, 28200, 13200, 31875, 11625,
  //33200, 15625, 36000, 15000, 39000, 15000, 43800, 16800, 46800, 19200, 49200, 23400,
  //49800, 27600, 48750, 32700, 46350, 36275, 42600, 39000, 38400, 40200, 31800, 39000,
  //28200, 36600, 25200, 31200, 24600, 26400, 26025, 21800, 28200, 18600, 30600, 16800,
  //32575, 19875, 34200, 19200, 36000, 18600, 37200, 18600, 40375, 19125, 43200, 21000,
  //45600, 24000, 46200, 27600, 45600, 30600, 43800, 33600, 41475, 35625, 37800, 36600,
  //33600, 36000, 30000, 33600, 28200, 28800, 28800, 24600, 30000, 22200, 31200, 23400,
  //30600, 25200, 30000, 27000, 30600, 30000, 31800, 32400, 34200, 34200, 38400, 34800,
  //41400, 33000, 44025, 30225, 44400, 26400, 43200, 23400, 40900, 21200, 37800, 20400,
  //34950, 20675, 32400, 22200, 30175, 19475, 28425, 21300, 27000, 24000, 26400, 27600,
  //27000, 31800, 31200, 36600, 36600, 38400, 42600, 37200, 46200, 33600, 48000, 30000,
  //47650, 24425, 45600, 20400, 42650, 18200, 39000, 16800, 35400, 16800, 33600, 17400,
  //32875, 17675, 31100, 13850, 28200, 15600, 25200, 18600, 22800, 22800, 22200, 27000,
  //23400, 33600, 26400, 38400, 31675, 41575, 37800, 42600, 40850, 42150, 42800, 41550,
  //47050, 39025, 50100, 35375, 52200, 29400, 51675, 23950, 49800, 19200, 46200, 15600,
  //41400, 13200, 37800, 12600, 35025, 12750, 33350, 13050, 32400, 9600, 30025, 10325,
  //25925, 12725, 22200, 16800, 19800, 21000, 18600, 25800, 18600, 30000, 20400, 35400,
  //22575, 39250, 25225, 41825, 28200, 43800, 33600, 46200, 39000, 46200, 44400, 45000,
  //48650, 42350, 52800, 37800, 55200, 32400, 55800, 26400, 54600, 21000, 53400, 18000,
  //50400, 14400, 47400, 12000, 42600, 9600, 39000, 9000, 36000, 9000, 34775, 9125,
  //34300, 5600, 30000, 6600, 25800, 8400, 22025, 11350, 18725, 15125, 16200, 20400,
  //15000, 24600, 15000, 30600, 16800, 36600, 20400, 42600, 25800, 46800, 31200, 49200,
  //38400, 49800, 45000, 48600, 51000, 45000, 55475, 40225, 58200, 34800, 59400, 30000,
  //59400, 25200, 58200, 19800, 55200, 14400, 52225, 11150, 47400, 7800, 44175, 6500,
  //40200, 5400, 38400, 5400, 37200, 5400, 0, 0 };
  //  std::vector<point_data<double> > spiralpoints;
  //  for(unsigned int i = 0; i < 100000; i += 2) {
  //    point_data<double>  pt(spiralcoords[i], spiralcoords[i+1]);
  //    if(pt == point_data<double> (0, 0)) break;
  //    spiralpoints.push_back(pt);
  //  }
  //  polygon_data<double> spiralpoly;
  //  spiralpoly.set(spiralpoints.begin(), spiralpoints.end());
  //  polygon_set_data<double> handset;
  //  handset += handpoly;
  //  polygon_set_data<double> spiralset;
  //  spiralset += spiralpoly;
  //  polygon_set_data<double> xorset = handset ^ spiralset;
  //  std::vector<polygon_data<double> > polys;
  //  polys += xorset;
  //  std::cout << polys.size() << std::endl;
  //  for(unsigned int i = 0; i < polys.size(); ++i)
  //    std::cout << polys[i] << std::endl;
  //}
  
  bool testDirectionalSize() {
    {
      PolygonSet ps(VERTICAL);
      ps += Rectangle(0, 0, 100, 100);
      ps.resize(0, -10, 0, -10);
      std::vector<Rectangle> rects;
      ps.get(rects);
      if(rects.size() != 1) return false;
      std::cout << rects[0] << std::endl;
      std::cout << Rectangle(0, 0, 90, 90) << std::endl;
      if(rects[0] != Rectangle(0, 0, 90, 90)) return false;
    }
    {
      PolygonSet ps(VERTICAL);
      ps += Rectangle(0, 0, 100, 100);
      ps.resize(0, 0, 0, -10);
      std::vector<Rectangle> rects;
      ps.get(rects);
      if(rects.size() != 1) return false;
      std::cout << rects[0] << std::endl;
      std::cout << Rectangle(0, 0, 100, 90) << std::endl;
      if(rects[0] != Rectangle(0, 0, 100, 90)) return false;
    }
    {
      PolygonSet ps;
      ps += Rectangle(0, 0, 100, 100);
      ps.resize(0, -10, 0, 0);
      std::vector<Rectangle> rects;
      ps.get(rects);
      if(rects.size() != 1) return false;
      std::cout << rects[0] << std::endl;
      std::cout << Rectangle(0, 0, 90, 100) << std::endl;
      if(rects[0] != Rectangle(0, 0, 90, 100)) return false;
    }
    {
      PolygonSet ps;
      ps += Rectangle(0, 0, 100, 100);
      ps.resize(0, 0, -10, 0);
      std::vector<Rectangle> rects;
      ps.get(rects);
      if(rects.size() != 1) return false;
      std::cout << rects[0] << std::endl;
      std::cout << Rectangle(0, 10, 100, 100) << std::endl;
      if(rects[0] != Rectangle(0, 10, 100, 100)) return false;
    }
    {
      PolygonSet ps;
      ps += Rectangle(0, 0, 100, 100);
      ps.resize(-10, 0, 0, 0);
      std::vector<Rectangle> rects;
      ps.get(rects);
      if(rects.size() != 1) return false;
      std::cout << rects[0] << std::endl;
      std::cout << Rectangle(10, 0, 100, 100) << std::endl;
      if(rects[0] != Rectangle(10, 0, 100, 100)) return false;
    }
    {
      PolygonSet ps;
      ps += Rectangle(0, 0, 100, 100);
      ps.resize(-10, 10, 0, 0);
      std::vector<Rectangle> rects;
      ps.get(rects);
      if(rects.size() != 1) return false;
      std::cout << rects[0] << std::endl;
      std::cout << Rectangle(10, 0, 110, 100) << std::endl;
      if(rects[0] != Rectangle(10, 0, 110, 100)) return false;
    }
    {
      PolygonSet ps;
      ps += Rectangle(0, 0, 100, 100);
      ps.resize(-10, 10, 10, -10);
      std::vector<Rectangle> rects;
      ps.get(rects);
      if(rects.size() != 1) return false;
      std::cout << rects[0] << std::endl;
      std::cout << Rectangle(10, -10, 110, 90) << std::endl;
      if(rects[0] != Rectangle(10, -10, 110, 90)) return false;
    }
    {
      PolygonSet ps;
      ps += Rectangle(0, 0, 100, 100);
      ps.resize(10, 10, -10, -10);
      std::vector<Rectangle> rects;
      ps.get(rects);
      if(rects.size() != 1) return false;
      std::cout << rects[0] << std::endl;
      std::cout << Rectangle(-10, 10, 110, 90) << std::endl;
      if(rects[0] != Rectangle(-10, 10, 110, 90)) return false;
    }
    return true;
  }
  
  bool testMaxCover() {
    std::vector<Rectangle> rects;
    rects.push_back(Rectangle(Interval(60, 124), Interval( 1, 3)));
    rects.push_back(Rectangle(Interval(59, 83), Interval( 9, 28)));
    rects.push_back(Rectangle(Interval(90, 124), Interval( 3, 29)));
    rects.push_back(Rectangle(Interval(64, 124), Interval( 29, 35)));
    rects.push_back(Rectangle(Interval(64, 102), Interval( 35, 49)));
    rects.push_back(Rectangle(Interval(1, 20), Interval( 44, 60)));
    rects.push_back(Rectangle(Interval(50, 102), Interval( 49, 71)));
    rects.push_back(Rectangle(Interval(49, 102), Interval( 71, 72)));
    rects.push_back(Rectangle(Interval(49, 94), Interval( 72, 75)));
    rects.push_back(Rectangle(Interval(50, 74), Interval( 75, 81)));
    rects.push_back(Rectangle(Interval(90, 127), Interval( 75, 81)));
    rects.push_back(Rectangle(Interval(50, 127), Interval( 81, 82)));
    rects.push_back(Rectangle(Interval(3, 7), Interval( 60, 88)));
    rects.push_back(Rectangle(Interval(50, 92), Interval( 82, 94)));
    rects.push_back(Rectangle(Interval(58, 92), Interval( 94, 111)));
    std::vector<Rectangle> expected_result;
    expected_result.push_back(Rectangle(Interval(60, 124), Interval( 1, 3)));
    expected_result.push_back(Rectangle(Interval(90, 124), Interval( 1, 35)));
    expected_result.push_back(Rectangle(Interval(90, 102), Interval( 1, 72)));
    expected_result.push_back(Rectangle(Interval(90, 94 ), Interval(1 ,82)));
    expected_result.push_back(Rectangle(Interval(90, 92), Interval( 1, 111)));
    expected_result.push_back(Rectangle(Interval(59, 83 ), Interval(9, 28)));
    expected_result.push_back(Rectangle(Interval(64, 124), Interval( 29, 35)));
    expected_result.push_back(Rectangle(Interval(64, 102), Interval( 29, 72)));
    expected_result.push_back(Rectangle(Interval(64, 94), Interval( 29, 75)));
    expected_result.push_back(Rectangle(Interval(64, 74), Interval( 29, 111)));
    expected_result.push_back(Rectangle(Interval(1, 20), Interval( 44, 60)));
    expected_result.push_back(Rectangle(Interval(3, 7), Interval( 44, 88)));
    expected_result.push_back(Rectangle(Interval(50, 102 ), Interval(49, 72)));
    expected_result.push_back(Rectangle(Interval(50, 94), Interval( 49, 75)));
    expected_result.push_back(Rectangle(Interval(50, 74), Interval( 49, 94)));
    expected_result.push_back(Rectangle(Interval(58, 74), Interval( 49, 111)));
    expected_result.push_back(Rectangle(Interval(49, 102 ), Interval(71, 72)));
    expected_result.push_back(Rectangle(Interval(49, 94 ), Interval(71, 75)));
    expected_result.push_back(Rectangle(Interval(90, 127), Interval( 75, 82)));
    expected_result.push_back(Rectangle(Interval(50, 127), Interval( 81, 82)));
    expected_result.push_back(Rectangle(Interval(50, 92), Interval( 81, 94)));
    expected_result.push_back(Rectangle(Interval(58, 92), Interval( 81, 111)));
    std::vector<Rectangle> result;
    get_max_rectangles(result, rects);
    std::cout << "result XOR clean: " << equivalence(result, rects) << std::endl;
    std::cout << "expected result XOR clean: " << equivalence(expected_result, rects) << std::endl;
    std::vector<Rectangle>& output = result;
    std::vector<Rectangle>& voutput = expected_result;
    std::sort(output.begin(), output.end(), less_rectangle_concept< Rectangle, Rectangle>());
    std::sort(voutput.begin(), voutput.end(), less_rectangle_concept< Rectangle, Rectangle>());
    if(output != voutput) {
      std::cerr << "Max Rectangle TEST failed\n";
      for(unsigned int i = 0; i < output.size(); ++i) {
        std::cerr << output[i] << std::endl;
      }
      std::cerr << "Incorrect result\n";
      for(unsigned int i = 0; i < voutput.size(); ++i) {
        std::cerr << voutput[i] << std::endl;
      }
      std::cerr << "Max Rectangle TEST failed\n";
      for(unsigned int i = 0; i < rects.size(); ++i) {
        std::cout << rects[i] << std::endl;
      }
      return false;
    }
    return true;
  }
  
  void max_cover_stress_test() {
    for(unsigned int k = 3; k < 20; k++) {
      for(unsigned int i = 0; i < k * k; ++i) {
        std::vector<Rectangle> rects, result;
        //std::cout << "test " << i << std::endl;
        for(unsigned int j = 0; j < k; ++j) {
          int x1 = rand() % 100;
          int x2 = rand() % 50;
          int y1 = rand() % 100;
          int y2 = rand() % 50;
          rects.push_back(Rectangle(x1, y1, x1+x2, y1+y2));
          //std::cout << rects.back() << std::endl;
        }
        get_max_rectangles(result, rects);
      }
    }
  }
  
  // namespace boost { namespace polygon{
  //   template <typename GCT, typename T>
  //   struct view_of {};
  
  //   template <typename T>
  //   struct view_of<polygon_45_concept, T> {
  //     const T* t;
  //     view_of(const T& obj) : t(&obj) {}
  //     typedef typename polygon_traits<T>::coordinate_type coordinate_type;
  //     typedef typename polygon_traits<T>::iterator_type iterator_type;
  //     typedef typename polygon_traits<T>::point_type point_type;
  
  //     /// Get the begin iterator
  //     inline iterator_type begin() const {
  //       return polygon_traits<T>::begin_points(*t);
  //     }
  
  //     /// Get the end iterator
  //     inline iterator_type end() const {
  //       return polygon_traits<T>::end_points(*t);
  //     }
  
  //     /// Get the number of sides of the polygon
  //     inline unsigned int size() const {
  //       return polygon_traits<T>::size(*t);
  //     }
  
  //     /// Get the winding direction of the polygon
  //     inline winding_direction winding() const {
  //       return polygon_traits<T>::winding(*t);
  //     }
  //   };
  
  //   template <typename T1, typename T2>
  //   view_of<T1, T2> view_as(const T2& obj) { return view_of<T1, T2>(obj); }
  
  //   template <typename T>
  //   struct geometry_concept<view_of<polygon_45_concept, T> > {
  //     typedef polygon_45_concept type;
  //   };
  
  //   template <typename T>
  //   struct view_of<polygon_90_concept, T> {
  //     const T* t;
  //     view_of(const T& obj) : t(&obj) {}
  //     typedef typename polygon_traits<T>::coordinate_type coordinate_type;
  //     typedef typename polygon_traits<T>::iterator_type iterator_type;
  //     typedef typename polygon_traits<T>::point_type point_type;
  //     typedef iterator_points_to_compact<iterator_type, point_type> compact_iterator_type;
  
  //     /// Get the begin iterator
  //     inline compact_iterator_type begin_compact() const {
  //       return compact_iterator_type(polygon_traits<T>::begin_points(*t),
  //                                    polygon_traits<T>::end_points(*t));
  //     }
  
  //     /// Get the end iterator
  //     inline compact_iterator_type end_compact() const {
  //       return compact_iterator_type(polygon_traits<T>::end_points(*t),
  //                                    polygon_traits<T>::end_points(*t));
  //     }
  
  //     /// Get the number of sides of the polygon
  //     inline unsigned int size() const {
  //       return polygon_traits<T>::size(*t);
  //     }
  
  //     /// Get the winding direction of the polygon
  //     inline winding_direction winding() const {
  //       return polygon_traits<T>::winding(*t);
  //     }
  //   };
  
  //   template <typename T>
  //   struct geometry_concept<view_of<polygon_90_concept, T> > {
  //     typedef polygon_90_concept type;
  //   };
  // }}
  using namespace gtl;
  
  //this test fails and I'd like to get it to pass
  bool test_colinear_duplicate_points() {
    Point pts[6] = { Point(0, 10), Point(0, 0), Point(100, 0), Point(100, 100), Point(0, 100), Point(0, 10)};
    Polygon45 p1;
    p1.set(pts, pts+5);
    Polygon45 pg;
    pg.set(pts, pts+6);
    Polygon45 p2;
    p2.set(pts+1, pts+6);
    std::cout << p2 << std::endl;
    if(!equivalence(view_as<polygon_90_concept>(p2), view_as<polygon_90_concept>(pg))) return false;
    std::cout << p1 << std::endl;
    if(!equivalence(view_as<polygon_90_concept>(p1), view_as<polygon_90_concept>(pg))) return false;
    return true;
  }
  
  bool test_extents() {
    PolygonSet psT(gtl::VERTICAL);
    //int xy[] = { 126, 69, 54, 69, 54, 81, 126, 81 };
    //CPolygonQuery polygon(0, 4, xy);
    //Rectangle rectIn(54, 69, 126, 81);
    polygon_data<int> polygon;
    std::vector<Point> pts;
    pts.push_back(Point(126, 69));
    pts.push_back(Point(54, 69));
    pts.push_back(Point(54, 81));
    pts.push_back(Point(126, 81));
    set_points(polygon, pts.begin(), pts.end());
    psT.insert(view_as<polygon_90_concept>(polygon));
  
    Rectangle rect, rect2;
    psT.extents(rect2);
    gtl::extents(rect, psT);
  
    if (rect != rect2) {
      std::cout << "gtl::Rectangles differ: " << gtl::xl(rect)  << " " << gtl::xh(rect)  << " " << gtl::yl(rect)  << " " << gtl::yh(rect)  <<     std::endl;
          std::cout << "                        " << gtl::xl(rect2) << " " << gtl::xh(rect2) << " " << gtl::yl(rect2) << " " << gtl::yh(rect2) <<     std::endl;
      return false;
    }
    return true;
  }
  
  bool test_extents2() {
    Polygon45Set psT;
    Point xy[] = { Point(130, 50),   Point(50, 50),   Point(50, 100),   Point(119, 100),
                   Point(119, 59),   Point(89, 89),   Point(59, 59),   Point(119, 59),   Point(119, 100),  Point(130, 100) };
    Polygon45 polygon(xy, xy+10);
  
    psT.insert(polygon);
    psT += 2;
  
    Rectangle rect, rect2;
    psT.extents(rect2);
    gtl::extents(rect, psT);
    std::cout << "Extents: " << gtl::xl(rect)   << " " << gtl::xh(rect)   << " " << gtl::yl(rect)   << " " << gtl::yh(rect)  <<   std::endl;
      std::cout << "Extents: " << gtl::xl(rect2)  << " " << gtl::xh(rect2)  << " " << gtl::yl(rect2)  << " " << gtl::yh(rect2) <<   std::endl;
      std::vector<Polygon45WithHoles> pwhs;
      psT.get(pwhs);
      for(unsigned int i = 0; i < pwhs.size(); ++i) {
        std::cout << pwhs[i] << std::endl;
      }
    return gtl::equivalence(rect, rect2);
  }
  
  /*************New Polygon Formation Tests********************/
  /*
   *
   * Test Input:
   * +--------------------+
   * |        +-------+   |
   * |        |       |   |
   * |        |       |   |
   * +-----+  |       |   |
   *       |  |       |   |
   *       |  |       |   |
   * +-----+  |       |   |
   * |        |       |   |
   * |        |       |   |
   * |        +-------+   |
   * +--------+           |
   *          |           |
   *          |           |
   * +--------+           |
   * |                    |
   * |                    |
   * +--------+           |
   *          |           |
   *          |           |
   * +--------+           |
   * |                    |
   * |                    |
   * +--------------------+
   *
   * Test Plan: 
   * a. call 'get(out, param)' , param >=4 
   * b. check if each polygon in the container is <= param
   * c. check the area of all the pieces sum up to original piece
   */
  typedef int intDC;
  typedef boost::polygon::polygon_90_with_holes_data<intDC> GTLPolygon;
  typedef boost::polygon::polygon_90_set_data<intDC> GTLPolygonSet;
  typedef boost::polygon::polygon_90_concept GTLPolygonConcept;
  typedef boost::polygon::point_data<intDC> GTLPoint;
  inline void PrintPolygon(const GTLPolygon&);
  inline GTLPolygon CreateGTLPolygon(const int*, size_t); 
  int test_new_polygon_formation(int argc, char** argv){
     //                                               //
     // Sub-Test-1: do a Boolean and call the new get //
     //                                               //
     int coordinates[] = {0,0, 10,0, 10,10, 0,10};
     int coordinates1[] = {9,1, 20,1, 20,10, 9,10};
     std::vector<GTLPoint> pts;
     size_t count = sizeof(coordinates)/(2*sizeof(intDC)); 
     size_t count1 = sizeof(coordinates1)/(2*sizeof(intDC));
     GTLPolygon poly, poly1;
     GTLPolygonSet polySet;
     
     poly = CreateGTLPolygon(coordinates, count);
     poly1 = CreateGTLPolygon(coordinates1, count1);
  
     polySet.insert(poly);
     polySet.insert(poly1);
  
     std::vector<GTLPolygon> result;
     polySet.get(result, 100);
  
     if(result.size() > 1){
        std::cerr << "FAILED: expecting only one polygon because the"
           " threshold is 100" << std::endl;
        return 1;
     }
  
     if(result[0].size() != 6){
        std::cerr << "FAILED: expecting only 6 vertices" << std::endl;
        return 1;
     }
  
     if(area(result[0]) != 190){
        std::cerr <<"FAILED: expecting only 6 vertices" << std::endl;
        return 1;
     }
  
     //expect no more than 1 polygon
     std::cout << "Found " << result.size() << "polygons after union" 
        << std::endl;
     for(size_t i=0; i<result.size(); i++){
        PrintPolygon(result[i]);
     }
  
     intDC shell_coords[] = {0,0, 10,0, 10,21, 0,21, 0,15, 3,15, 3,13,
        0,13, 0,10, 5,10, 5,8, 0,8, 0,5, 5,5, 5,3, 0,3};
     intDC hole_coords[] = {4,11, 7,11, 7,19, 4,19};
     GTLPolygon slice_polygon, slice_hole;
     count = sizeof(shell_coords)/(2*sizeof(intDC));
     count1 = sizeof(hole_coords)/(2*sizeof(intDC));
  
     slice_polygon = CreateGTLPolygon(shell_coords, count);
     slice_hole = CreateGTLPolygon(hole_coords, count1);
  
     result.clear();
     polySet.clear();
     polySet.insert(slice_polygon);
     polySet.insert(slice_hole, true);
  
     polySet.get(result);
     double gold_area = 0;
     std::cout << "Found " << result.size() << " slices" << std::endl;
     for(size_t i=0; i<result.size(); i++){
        PrintPolygon(result[i]);
        gold_area += area(result[i]); 
     }
  
     result.clear();
     polySet.get(result, 6);
     double platinum_area = 0;
     std::cout << "Found " << result.size() << " slices" << std::endl;
     for(size_t i=0; i<result.size(); i++){
        PrintPolygon(result[i]);
        platinum_area += area(result[i]); 
        if(result[i].size() > 6){
           std::cerr << "FAILED: expecting size to be less than 6" << std::endl;
           return 1;
        }
     }
  
     std::cout << "platinum_area = " << platinum_area << " , gold_area=" 
        << gold_area << std::endl;
     if( platinum_area != gold_area){
        std::cerr << "FAILED: Area mismatch" << std::endl;
        return 1;
     }
     std::cout << "[SUB-TEST-1] PASSED\n";
  
     result.clear();
     polySet.get(result, 4);
     platinum_area = 0;
     std::cout << "Found " << result.size() << " slices" << std::endl;
     for(size_t i=0; i<result.size(); i++){
        PrintPolygon(result[i]);
        platinum_area += area(result[i]); 
        if(result[i].size() > 4){ 
           std::cerr << "FAILED: expecting size to be < 4" << std::endl;
           return 1;
        }
     }
  
     std::cout << "platinum_area=" << platinum_area << ", gold_area=" 
        << gold_area << std::endl;
  
     if( platinum_area != gold_area){
        std::cerr << "FAILED: Area mismatch" << std::endl;
        return 1;
     }
  
     std::cout << "[SUB-TEST-1] PASSED" << std::endl;
     return 0;
  }
  
  /* 
   * INPUT:
   *   +--------+
   *   |        |
   *   |        |
   *   |        +---+
   *   |            |
   *   |        +---+
   *   |        |
   *   +--------+
   *            X 
   *            
   * TEST PLAN: as the sweepline moves and reaches
   * X the number of vertices in the solid jumps by 4
   * instead of 2. So make sure we don't get a 6 vertex
   * polygon when the threshold is 4 and 6.
   */
  int test_new_polygon_formation_marginal_threshold(int argc, char**){
     std::vector<GTLPoint> pts;
     GTLPolygon polygon;
     GTLPolygonSet pset;
     std::vector<GTLPolygon> result;
     intDC coords[] = {0,0, 15,0, 15,10, 10,10, 10,15, 5,15, 5,10, 0,10};
     size_t count = sizeof(coords)/(2*sizeof(intDC));
  
     polygon = CreateGTLPolygon(coords, count);
     pset.insert(polygon);
  
     for(size_t i=0; i<1; i++){
        pset.get(result, i ? 4 : 6);
        double gold_area = 175, plat_area = 0;
        for(size_t i=0; i<result.size(); i++){
           if(result[i].size() > (i ? 4 : 6) ){
              size_t expected = i ? 4 : 6;
              std::cerr << "FAILED: Expecting no more than " <<
                 expected << " vertices" << std::endl;
              return 1;
           }
           PrintPolygon(result[i]);
           plat_area += area(result[i]); 
        }
  
        if(plat_area != gold_area){
           std::cerr << "FAILED area mismatch gold=" << gold_area <<
              " plat=" << plat_area << std::endl;
           return 1;
        }
     }
     std::cout << "Test Passed" << std::endl;
     return 0;
  }
  
  inline void PrintPolygon(const GTLPolygon& p){
     //get an iterator of the point_data<int>
     boost::polygon::point_data<int> pt;
     boost::polygon::polygon_90_data<int>::iterator_type itr;
  
     size_t vertex_id = 0;
     for(itr = p.begin(); itr != p.end(); ++itr){
        pt = *itr;
        std::cout << "Vertex-" << ++vertex_id << "(" << pt.x() <<
           "," << pt.y() << ")" << std::endl;
     }
  }
  
  // size: is the number of vertices //
  inline GTLPolygon CreateGTLPolygon(const int *coords, size_t size){
     GTLPolygon r;
     std::vector<GTLPoint> pts;
  
     for(size_t i=0; i<size; i++){
        pts.push_back( GTLPoint(coords[2*i], coords[2*i+1]) );
     }
     boost::polygon::set_points(r, pts.begin(), pts.end());
     return r;
  }
  
  /************************************************************/
  
  int main() {
    test_view_as();
    //this test fails and I'd like to get it to pass
    //if(!test_colinear_duplicate_points()) return 1;
    if(!test_extents2()) return 1;
    if(!test_extents()) return 1;
    if(!testMaxCover()) return 1;
    //max_cover_stress_test(); //does not include functional testing
    if(!testDirectionalSize()) return 1;
    testHand();
    //testHandFloat();
    if(!testpip()) return 1;
    {
      PolygonSet ps;
      Polygon p;
      assign(ps, p);
    }
    if(!testViewCopyConstruct()) return 1;
    if(!test_grow_and_45()) return 1;
    if(!test_self_xor_45()) return 1;
    if(!test_self_xor()) return 1;
    if(!test_directional_resize()) return 1;
    if(!test_scaling_by_floating()) return 1;
    if(!test_SQRT1OVER2()) return 1;
    if(!test_get_trapezoids()) return 1;
    if(!test_get_rectangles()) return 1;
    if(!test_45_concept_interact()) return 1;
    if(!test_45_touch_r()) return 1;
    if(!test_45_touch_ur()) return 1;
    if(!test_45_touch()) return 1;
    if(!test_45_touch_boundaries()) return 1;
    {
    Point pts[] = {Point(0,0), Point(5, 5), Point(5, 0)};
    Polygon45 p45(pts, pts+3);
    pts[1] = Point(0, 5);
    Polygon45 p452(pts, pts+3);
    if(!test_two_polygons(p45,p452)) return 1;
    pts[2] = Point(5,5);
    p45.set(pts, pts+3);
    if(!test_two_polygons(p45,p452)) return 1;
    pts[0] = Point(5,0);
    p452.set(pts, pts+3);
    if(!test_two_polygons(p45, p452)) return 1;
    Point pts2[] = {Point(0,5), Point(5, 5), Point(5, 0)};
    Point pts3[] = {Point(0,0), Point(5, 5), Point(5, 0)};
    p45.set(pts2, pts2 + 3);
    p452.set(pts3, pts3+3);
    if(!test_two_polygons(p45, p452)) return 1;
    Point pts4[] = {Point(0, 5), Point(3, 2), Point(3,5)};
    Point pts5[] = {Point(0,0), Point(5, 5), Point(5, 0)};
    p45.set(pts4, pts4+3);
    p452.set(pts5, pts5+3);
    if(!test_two_polygons(p45, p452)) return 1;
    }
    {
    std::vector<point_data<int> > pts;
    pts.push_back(point_data<int>(0, 0));
    pts.push_back(point_data<int>(10, 0));
    pts.push_back(point_data<int>(10, 10));
    pts.push_back(point_data<int>(0, 10));
    std::vector<point_data<int> > pts2;
    pts2.push_back(point_data<int>(0, 0));
    pts2.push_back(point_data<int>(10, 10));
    pts2.push_back(point_data<int>(0, 20));
    pts2.push_back(point_data<int>(-10, 10));
    std::vector<point_data<int> > pts3;
    pts3.push_back(point_data<int>(0, 0));
    pts3.push_back(point_data<int>(10, 11));
    pts3.push_back(point_data<int>(0, 20));
    pts3.push_back(point_data<int>(-100, 8));
    polygon_data<int> p, p1; p.set(pts3.begin(), pts3.end());
    polygon_45_data<int> p45, p451; p45.set(pts2.begin(), pts2.end());
    polygon_90_data<int> p90, p901; p90.set(pts.begin(), pts.end());
    polygon_with_holes_data<int> pwh, pwh1; pwh.set(pts3.begin(), pts3.end());
    polygon_45_with_holes_data<int> p45wh, p45wh1; p45wh.set(pts2.begin(), pts2.end());
    polygon_90_with_holes_data<int> p90wh, p90wh1; p90wh.set(pts.begin(), pts.end());
    assign(p, p90);
    assign(p, p45);
    assign(p1, p);
    //illegal: assign(p, p90wh);
    //illegal: assign(p, p45wh);
    //illegal: assign(p, pwh);
  
    assign(p45, p90);
    assign(p451, p45);
    //illegal: assign(p45, p);
    //illegal: assign(p45, p90wh);
    //illegal: assign(p45, p45wh);
    //illegal: assign(p45, pwh);
  
    assign(p901, p90);
    //illegal: assign(p90, p45);
    //illegal: assign(p90, p);
    //illegal: assign(p90, p90wh);
    //illegal: assign(p90, p45wh);
    //illegal: assign(p90, pwh);
  
    assign(pwh, p90);
    assign(pwh, p45);
    assign(pwh, p);
    assign(pwh, p90wh);
    assign(pwh, p45wh);
    assign(pwh1, pwh);
  
    assign(p45wh, p90);
    assign(p45wh, p45);
    //illegal: assign(p45wh, p);
    assign(p45wh, p90wh);
    assign(p45wh1, p45wh);
    //illegal: assign(p45wh, pwh);
  
    assign(p90wh, p90);
    //illegal: assign(p90wh, p45);
    //illegal: assign(p90wh, p);
    assign(p90wh1, p90wh);
    //illegal: assign(p90wh, p45wh);
    //illegal: assign(p90wh, pwh);
    pts.clear();
    pts.push_back(point_data<int>(0, 0));
    pts.push_back(point_data<int>(3, 0));
    pts.push_back(point_data<int>(0, 1));
    p.set(pts.begin(), pts.end());
    std::cout << std::endl; std::cout << (area(p90));
    std::cout << std::endl; std::cout << (area(p45));
    std::cout << std::endl; std::cout << (area(p));
    std::cout << std::endl; std::cout << (area(p90wh));
    std::cout << std::endl; std::cout << (area(p45wh));
    std::cout << std::endl; std::cout << (area(pwh));
    std::cout << std::endl;
    point_data<int> pt(1, 1);
    std::cout << contains(p, pt) << std::endl;
    std::cout << contains(p90, pt) << std::endl;
  
    interval_data<int> ivl = construct<interval_data<int> >(0, 10);
    std::cout << get(ivl, LOW) << std::endl;
    set(ivl, HIGH, 20);
  
    std::cout << perimeter(p) << std::endl;
    if(winding(p) == LOW) std::cout << "LOW" << std::endl;
    if(winding(p) == HIGH) std::cout << "HIGH" << std::endl;
    rectangle_data<polygon_long_long_type> rd;
    std::cout << extents(rd, p) << std::endl;
    std::cout << rd << std::endl;
  
    boolean_op::testBooleanOr<int>();
  
    std::vector<rectangle_data<int> > rects1, rects2;
    rects2.push_back(rectangle_data<int>(0, 0, 10, 10));
    print_is_polygon_90_set_concept((polygon_90_set_data<int>()));
    print_is_mutable_polygon_90_set_concept((polygon_90_set_data<int>()));
    print_is_polygon_90_set_concept((polygon_90_data<int>()));
    print_is_polygon_90_set_concept((std::vector<polygon_90_data<int> >()));
    assign(rects1, rects2);
    polygon_90_set_data<int> ps90;
    assign(ps90, rects2);
    assign(rects2, ps90);
    assign(ps90, p90);
    assign(rects2, p90);
    std::cout << p90 << std::endl;
    for(unsigned int i = 0; i < rects2.size(); ++i) {
      std::cout << rects2[i] << std::endl;
    }
    bloat(rects2, 10);
    shrink(rects2[0], 10);
    for(unsigned int i = 0; i < rects2.size(); ++i) {
      std::cout << rects2[i] << std::endl;
    }
    move(rects2[0], HORIZONTAL, 30);
    assign(rects1, rects2 + p90);
    std::cout << "result of boolean or\n";
    for(unsigned int i = 0; i < rects1.size(); ++i) {
      std::cout << rects1[i] << std::endl;
    }
    rects1 -= p90;
    std::cout << "result of boolean not\n";
    for(unsigned int i = 0; i < rects1.size(); ++i) {
      std::cout << rects1[i] << std::endl;
    }
    rects1 += p90;
    std::cout << "result of boolean OR\n";
    for(unsigned int i = 0; i < rects1.size(); ++i) {
      std::cout << rects1[i] << std::endl;
    }
    rects1 *= p90;
    std::cout << "result of boolean AND\n";
    for(unsigned int i = 0; i < rects1.size(); ++i) {
      std::cout << rects1[i] << std::endl;
    }
    rects1 ^= rects2;
    std::cout << "result of boolean XOR\n";
    for(unsigned int i = 0; i < rects1.size(); ++i) {
      std::cout << rects1[i] << std::endl;
    }
    rects2.clear();
    get_max_rectangles(rects2, p90);
    std::cout << "result of max rectangles\n";
    for(unsigned int i = 0; i < rects2.size(); ++i) {
      std::cout << rects2[i] << std::endl;
    }
    rects2.clear();
    //operator += and -= don't support polygons, so + and - should not exist
  //   rects2 += p90 + 6;
  //   std::cout << "result of resize\n";
  //   for(unsigned int i = 0; i < rects2.size(); ++i) {
  //     std::cout << rects2[i] << std::endl;
  //   }
  //   std::cout << "result of resize\n";
     std::vector<polygon_90_with_holes_data<int> > polyswh1, polyswh2;
  //   polyswh1 += p90 -2;
  //   for(unsigned int i = 0; i < polyswh1.size(); ++i) {
  //     std::cout << polyswh1[i] << std::endl;
  //   }
  //   std::cout << "result of resize\n";
     std::vector<polygon_90_data<int> > polys1, polys2;
     polys1 += p90;
     polys1 -= 2;
  //   polys1 += p90 -2;
     for(unsigned int i = 0; i < polys1.size(); ++i) {
       std::cout << polys1[i] << std::endl;
     }
  
     boolean_op_45<int>::testScan45(std::cout);
     polygon_45_formation<int>::testPolygon45Formation(std::cout);
    polygon_45_formation<int>::testPolygon45Tiling(std::cout);
  
    axis_transformation atr;
    transform(p, atr);
    transform(p45, atr);
    transform(p90, atr);
    transform(pwh, atr);
    transform(p45wh, atr);
    transform(p90wh, atr);
    scale_up(p, 2);
    scale_up(p45, 2);
    scale_up(p90, 2);
    scale_up(pwh, 2);
    scale_up(p45wh, 2);
    scale_up(p90wh, 2);
    scale_down(p, 2);
    scale_down(p45, 2);
    scale_down(p90, 2);
    scale_down(pwh, 2);
    scale_down(p45wh, 2);
    scale_down(p90wh, 2);
    std::vector<polygon_45_data<int> > p45s1, p45s2;
    std::cout << equivalence(p45s1, p45s2) << std::endl;
    std::cout << equivalence(p45, p45wh) << std::endl;
    std::cout << equivalence(p90, p45wh) << std::endl;
    gtl::assign(p45s1, p90);
    p90 = polys1[0];
    move(p90, orientation_2d(HORIZONTAL), 8);
    std::cout << p90 << std::endl << p45wh << std::endl;
    polygon_45_set_data<int> ps45 = p90 + p45wh;
    assign(p45s1, ps45);
    std::cout << "result\n";
    for(unsigned int i = 0; i < p45s1.size(); ++i) {
      std::cout << p45s1[i] << std::endl;
    }
    std::cout << equivalence(p, pwh) << std::endl;
    std::cout << equivalence(p90, pwh) << std::endl;
    std::cout << equivalence(p45, pwh) << std::endl;
    std::cout << equivalence(pwh, pwh) << std::endl;
    p + pwh;
    p90 + pwh;
    p45 + pwh;
    std::cout << testRectangle() << std::endl;
    std::cout << testPolygon() << std::endl;
    std::cout << testPropertyMerge() << std::endl;
    std::cout << testPolygonAssign() << std::endl;
    std::cout << testPolygonWithHoles() << std::endl;
    std::cout << (polygon_arbitrary_formation<int>::testPolygonArbitraryFormationRect(std::cout)) << std::endl;
    std::cout << (polygon_arbitrary_formation<int>::testPolygonArbitraryFormationP1(std::cout)) << std::endl;
    std::cout << (polygon_arbitrary_formation<int>::testPolygonArbitraryFormationP2(std::cout)) << std::endl;
    std::cout << (polygon_arbitrary_formation<int>::testPolygonArbitraryFormationPolys(std::cout)) << std::endl;
    std::cout << (polygon_arbitrary_formation<int>::testPolygonArbitraryFormationSelfTouch1(std::cout)) << std::endl;
    std::cout << (polygon_arbitrary_formation<int>::testPolygonArbitraryFormationSelfTouch2(std::cout)) << std::endl;
    std::cout << (polygon_arbitrary_formation<int>::testPolygonArbitraryFormationSelfTouch3(std::cout)) << std::endl;
    std::cout << (polygon_arbitrary_formation<int>::testSegmentIntersection(std::cout)) << std::endl;
    std::cout << (property_merge<int, int>::test_insertion(std::cout)) << std::endl;
    std::cout << (line_intersection<int>::test_verify_scan(std::cout)) << std::endl;
    std::cout << (line_intersection<int>::test_validate_scan(std::cout)) << std::endl;
    std::cout << (scanline<int, int>::test_scanline(std::cout)) << std::endl;
    std::cout << (property_merge<int, int>::test_merge(std::cout)) << std::endl;
    std::cout << (property_merge<int, int>::test_intersection(std::cout)) << std::endl;
    std::cout << (polygon_arbitrary_formation<int>::testPolygonArbitraryFormationColinear(std::cout)) << std::endl;
    std::cout << (property_merge<int, int>::test_manhattan_intersection(std::cout)) << std::endl;
    std::cout << (test_arbitrary_boolean_op<int>(std::cout)) << std::endl;
    }
    {
      polygon_set_data<int> psd;
      rectangle_data<int> rect;
      set_points(rect, point_data<int>(0, 0), point_data<int>(10, 10));
      psd.insert(rect);
      polygon_set_data<int> psd2;
      set_points(rect, point_data<int>(5, 5), point_data<int>(15, 15));
      psd2.insert(rect);
      std::vector<polygon_data<int> > pv;
      polygon_set_data<int> psd3;
      psd3 = psd + psd2;
      psd3.get(pv);
      for(unsigned int i = 0; i < pv.size(); ++i) {
        std::cout << pv[i] << std::endl;
      }
      psd += psd2;
      pv.clear();
      psd3.get(pv);
      for(unsigned int i = 0; i < pv.size(); ++i) {
        std::cout << pv[i] << std::endl;
      }
    }
    {
      polygon_90_set_data<int> psd;
      rectangle_data<int> rect;
      set_points(rect, point_data<int>(0, 0), point_data<int>(10, 10));
      psd.insert(rect);
      polygon_90_set_data<int> psd2;
      set_points(rect, point_data<int>(5, 5), point_data<int>(15, 15));
      psd2.insert(rect);
      std::vector<polygon_90_data<int> > pv;
      interact(psd, psd2);
      assign(pv, psd);
      for(unsigned int i = 0; i < pv.size(); ++i) {
        std::cout << pv[i] << std::endl;
      }
  
      connectivity_extraction_90<int> ce;
      ce.insert(pv[0]);
      ce.insert(psd2);
      std::vector<std::set<int> > graph(2);
      ce.extract(graph);
      if(graph[0].size() == 1) std::cout << "connectivity extraction is alive\n";
  
      //std::vector<rectangle_data<polygon_long_long_type> > lobs;
      //get_max_rectangles(lobs, psd);
      //if(lobs.size() == 1) std::cout << "max rectangles is alive\n";
  
      std::vector<rectangle_data<int> > rv;
      rv.push_back(rect);
      set_points(rect, point_data<int>(0, 0), point_data<int>(10, 10));
      rv.push_back(rect);
      self_intersect(rv);
      if(rv.size() == 1) {
        assign(rect, rv.back());
        std::cout << rect << std::endl;
      }
  
      assign(rv, rv + 1);
      std::cout << rv.size() << std::endl;
      if(rv.size() == 1) {
        assign(rect, rv.back());
        std::cout << rect << std::endl;
      }
      assign(rv, rv - 1);
      if(rv.size() == 1) {
        assign(rect, rv.back());
        std::cout << rect << std::endl;
      }
      rv += 1;
      if(rv.size() == 1) {
        assign(rect, rv.back());
        std::cout << rect << std::endl;
      }
      rv -= 1;
      if(rv.size() == 1) {
        assign(rect, rv.back());
        std::cout << rect << std::endl;
      }
      rv.clear();
      set_points(rect, point_data<int>(0, 0), point_data<int>(10, 10));
      rv.push_back(rect);
      set_points(rect, point_data<int>(12, 12), point_data<int>(20, 20));
      rv.push_back(rect);
      grow_and(rv, 7);
      if(rv.size() == 1) {
        assign(rect, rv.back());
        std::cout << rect << std::endl;
      }
      std::cout << area(rv) << std::endl;
      std::cout << area(rv) << std::endl;
  
      scale_up(rv, 10);
      std::cout << area(rv) << std::endl;
      scale_down(rv, 7);
      std::cout << area(rv) << std::endl;
      if(rv.size() == 1) {
        assign(rect, rv.back());
        std::cout << rect << std::endl;
      }
      keep(rv, 290, 300, 7, 24, 7, 24);
      if(rv.size() == 1) {
        assign(rect, rv.back());
        std::cout << rect << std::endl;
      }
      keep(rv, 300, 310, 7, 24, 7, 24);
      if(rv.empty()) std::cout << "keep is alive\n";
    }
    {
  //     typedef int Unit;
  //     typedef point_data<int> Point;
  //     typedef interval_data<int> Interval;
  //     typedef rectangle_data<int> Rectangle;
  //     typedef polygon_90_data<int> Polygon;
  //     typedef polygon_90_with_holes_data<int> PolygonWithHoles;
  //     typedef polygon_45_data<int> Polygon45;
  //     typedef polygon_45_with_holes_data<int> Polygon45WithHoles;
  //     typedef polygon_90_set_data<int> PolygonSet;
  //     //typedef polygon_45_set_data<int> Polygon45Set;
  //     typedef axis_transformation AxisTransform;
  //     typedef transformation<int> Transform;
      //test polygon45 area, polygon45 with holes area
      std::vector<Point> pts;
      pts.clear();
      pts.push_back(Point(10, 10));
      pts.push_back(Point(15, 10));
      pts.push_back(Point(10, 15));
      Polygon45 polyHole;
      polyHole.set(pts.begin(), pts.end());
      pts.clear();
      pts.push_back(Point(10, 0));
      pts.push_back(Point(20, 10));
      pts.push_back(Point(20, 30));
      pts.push_back(Point(0, 50));
      pts.push_back(Point(0, 10));
      Polygon45WithHoles polyWHoles;
      polyWHoles.set(pts.begin(), pts.end());
      polyWHoles.set_holes(&polyHole, (&polyHole)+1);
       std::cout << polyWHoles << std::endl;
      std::cout << area(polyWHoles) << std::endl;
      std::cout << area(polyWHoles) << std::endl;
       //test polygon45, polygon45with holes transform
       AxisTransform atr(AxisTransform::EAST_SOUTH);
       Polygon45WithHoles p45wh(polyWHoles);
       transform(polyWHoles, atr);
       std::cout << polyWHoles << std::endl;
       Transform tr(atr);
       tr.invert();
       transform(polyWHoles, tr);
       std::cout << polyWHoles << std::endl;
       if(area(polyWHoles) != 687.5) return 1;
       //test polygon, polygon with holes transform
       Polygon ph;
       assign(ph, Rectangle(10, 10, 20, 20));
       PolygonWithHoles pwh;
       assign(pwh, Rectangle(0, 0, 100, 100));
       pwh.set_holes(&ph, (&ph)+1);
       std::cout << area(pwh) << std::endl;
       transform(pwh, atr);
       std::cout << pwh << std::endl;
       std::cout << area(pwh) << std::endl;
       transform(pwh, tr);
       std::cout << pwh << std::endl;
       std::cout << area(pwh) << std::endl;
       if(area(pwh) != 9900) return 1;
  
      //test point scale up / down
      Point pt(10, 10);
      scale_up(pt, 25);
      if(pt != Point(250, 250)) return 1;
      std::cout << pt << std::endl;
      scale_down(pt, 25);
      if(pt != Point(10, 10)) return 1;
      std::cout << pt << std::endl;
      scale_down(pt, 25);
      if(pt != Point(0, 0)) return 1;
      std::cout << pt << std::endl;
  
      //test polygon, polygon with holes scale up down
      PolygonWithHoles tmpPwh(pwh);
      scale_up(pwh, 25);
      std::cout << pwh << std::endl;
      scale_down(pwh, 25);
      if(area(pwh) != area(tmpPwh)) return 1;
      std::cout << pwh << std::endl;
      scale_down(pwh, 25);
      std::cout << pwh << std::endl;
      //test polygon45, polygon45 with holes is45
      std::cout << is_45(polyHole) << std::endl;
      if(is_45(polyHole) != true) return 1;
      pts.clear();
      pts.push_back(Point(10, 10));
      pts.push_back(Point(15, 10));
      pts.push_back(Point(10, 16));
      polyHole.set(pts.begin(), pts.end());
      std::cout << is_45(polyHole) << std::endl;
      if(is_45(polyHole) != false) return 1;
      //test polygon45, polygon45 with holes snap 45
      snap_to_45(polyHole);
      std::cout << is_45(polyHole) << std::endl;
      if(is_45(polyHole) != true) return 1;
      std::cout << polyHole << std::endl;
      //test polygon45, polygon45 with holes scalue up down
      scale_up(polyHole, 10000);
      std::cout << polyHole << std::endl;
      scale_down(polyHole, 3);
      std::cout << is_45(polyHole) << " " << polyHole << std::endl;
      if(is_45(polyHole) != true) return 1;
      scale_down(polyHole, 5);
      std::cout << is_45(polyHole) << " " << polyHole << std::endl;
      if(is_45(polyHole) != true) return 1;
      scale_down(polyHole, 7);
      std::cout << is_45(polyHole) << " " << polyHole << std::endl;
      if(is_45(polyHole) != true) return 1;
      scale_down(polyHole, 13);
      std::cout << is_45(polyHole) << " " << polyHole << std::endl;
      if(is_45(polyHole) != true) return 1;
      scale_down(polyHole, 2);
      std::cout << is_45(polyHole) << " " << polyHole << std::endl;
      if(is_45(polyHole) != true) return 1;
      scale_down(polyHole, 2);
      std::cout << is_45(polyHole) << " " << polyHole << std::endl;
      if(is_45(polyHole) != true) return 1;
      scale_down(polyHole, 2);
      std::cout << is_45(polyHole) << " " << polyHole << std::endl;
      if(is_45(polyHole) != true) return 1;
      scale_down(polyHole, 2);
      std::cout << is_45(polyHole) << " " << polyHole << std::endl;
      if(is_45(polyHole) != true) return 1;
      scale_down(polyHole, 2);
      std::cout << is_45(polyHole) << " " << polyHole << std::endl;
      if(is_45(polyHole) != true) return 1;
      scale_up(polyHole, 3);
      std::cout << is_45(polyHole) << " " << polyHole << std::endl;
      if(is_45(polyHole) != true) return 1;
      scale_down(polyHole, 2);
      std::cout << is_45(polyHole) << " " << polyHole << std::endl;
      if(is_45(polyHole) != true) return 1;
      scale_down(polyHole, 2);
      std::cout << is_45(polyHole) << " " << polyHole << std::endl;
      if(is_45(polyHole) != true) return 1;
      scale_down(polyHole, 2);
      std::cout << is_45(polyHole) << " " << polyHole << std::endl;
      if(is_45(polyHole) != true) return 1;
      scale_down(polyHole, 2);
      std::cout << is_45(polyHole) << " " << polyHole << std::endl;
      if(is_45(polyHole) != true) return 1;
      pts.clear();
      pts.push_back(Point(11, 1));
      pts.push_back(Point(21, 11));
      pts.push_back(Point(11, 21));
      pts.push_back(Point(1, 11));
      polyHole.set(pts.begin(), pts.end());
      std::cout << is_45(polyHole) << " " << polyHole << std::endl;
      if(is_45(polyHole) != true) return 1;
      scale_down(polyHole, 3);
      std::cout << is_45(polyHole) << " " << polyHole << std::endl;
      if(is_45(polyHole) != true) return 1;
      scale_up(polyHole, 10000);
      std::cout << polyHole << std::endl;
      scale_down(polyHole, 3);
      std::cout << is_45(polyHole) << " " << polyHole << std::endl;
      if(is_45(polyHole) != true) return 1;
      scale_down(polyHole, 5);
      std::cout << is_45(polyHole) << " " << polyHole << std::endl;
      if(is_45(polyHole) != true) return 1;
      scale_down(polyHole, 7);
      std::cout << is_45(polyHole) << " " << polyHole << std::endl;
      if(is_45(polyHole) != true) return 1;
      scale_down(polyHole, 13);
      std::cout << is_45(polyHole) << " " << polyHole << std::endl;
      if(is_45(polyHole) != true) return 1;
      scale_down(polyHole, 2);
      std::cout << is_45(polyHole) << " " << polyHole << std::endl;
      if(is_45(polyHole) != true) return 1;
      scale_down(polyHole, 2);
      std::cout << is_45(polyHole) << " " << polyHole << std::endl;
      if(is_45(polyHole) != true) return 1;
      scale_down(polyHole, 2);
      std::cout << is_45(polyHole) << " " << polyHole << std::endl;
      if(is_45(polyHole) != true) return 1;
      scale_down(polyHole, 2);
      std::cout << is_45(polyHole) << " " << polyHole << std::endl;
      if(is_45(polyHole) != true) return 1;
      scale_down(polyHole, 2);
      std::cout << is_45(polyHole) << " " << polyHole << std::endl;
      if(is_45(polyHole) != true) return 1;
      scale_up(polyHole, 3);
      std::cout << is_45(polyHole) << " " << polyHole << std::endl;
      if(is_45(polyHole) != true) return 1;
      scale_down(polyHole, 2);
      std::cout << is_45(polyHole) << " " << polyHole << std::endl;
      if(is_45(polyHole) != true) return 1;
      scale_down(polyHole, 2);
      std::cout << is_45(polyHole) << " " << polyHole << std::endl;
      if(is_45(polyHole) != true) return 1;
      scale_down(polyHole, 2);
      std::cout << is_45(polyHole) << " " << polyHole << std::endl;
      if(is_45(polyHole) != true) return 1;
      scale_down(polyHole, 2);
      std::cout << is_45(polyHole) << " " << polyHole << std::endl;
      if(is_45(polyHole) != true) return 1;
  
      std::cout << is_45(polyWHoles) << " " << polyWHoles << std::endl;
      if(is_45(polyWHoles) != true) return 1;
      scale_up(polyWHoles, 100013);
      std::cout << polyWHoles << std::endl;
      scale_down(polyWHoles, 3);
      std::cout << is_45(polyWHoles) << " " << polyWHoles << std::endl;
      if(is_45(polyWHoles) != true) return 1;
      scale_down(polyWHoles, 2);
      std::cout << is_45(polyWHoles) << " " << polyWHoles << std::endl;
      if(is_45(polyWHoles) != true) return 1;
      scale_down(polyWHoles, 3);
      std::cout << is_45(polyWHoles) << " " << polyWHoles << std::endl;
      if(is_45(polyWHoles) != true) return 1;
      scale_down(polyWHoles, 2);
      std::cout << is_45(polyWHoles) << " " << polyWHoles << std::endl;
      if(is_45(polyWHoles) != true) return 1;
      scale_down(polyWHoles, 3);
      std::cout << is_45(polyWHoles) << " " << polyWHoles << std::endl;
      if(is_45(polyWHoles) != true) return 1;
      scale_down(polyWHoles, 2);
      std::cout << is_45(polyWHoles) << " " << polyWHoles << std::endl;
      if(is_45(polyWHoles) != true) return 1;
      scale_down(polyWHoles, 3);
      std::cout << is_45(polyWHoles) << " " << polyWHoles << std::endl;
      if(is_45(polyWHoles) != true) return 1;
      scale_down(polyWHoles, 2);
      std::cout << is_45(polyWHoles) << " " << polyWHoles << std::endl;
      if(is_45(polyWHoles) != true) return 1;
      scale_down(polyWHoles, 3);
      std::cout << is_45(polyWHoles) << " " << polyWHoles << std::endl;
      if(is_45(polyWHoles) != true) return 1;
      scale_down(polyWHoles, 2);
      std::cout << is_45(polyWHoles) << " " << polyWHoles << std::endl;
      if(is_45(polyWHoles) != true) return 1;
      scale_down(polyWHoles, 3);
      std::cout << is_45(polyWHoles) << " " << polyWHoles << std::endl;
      if(is_45(polyWHoles) != true) return 1;
      scale_down(polyWHoles, 3);
      std::cout << is_45(polyWHoles) << " " << polyWHoles << std::endl;
      if(is_45(polyWHoles) != true) return 1;
      scale_down(polyWHoles, 2);
      std::cout << is_45(polyWHoles) << " " << polyWHoles << std::endl;
      if(is_45(polyWHoles) != true) return 1;
      scale_down(polyWHoles, 3);
      std::cout << is_45(polyWHoles) << " " << polyWHoles << std::endl;
      if(is_45(polyWHoles) != true) return 1;
      scale_down(polyWHoles, 2);
      std::cout << is_45(polyWHoles) << " " << polyWHoles << std::endl;
      if(is_45(polyWHoles) != true) return 1;
      scale_down(polyWHoles, 3);
      std::cout << is_45(polyWHoles) << " " << polyWHoles << std::endl;
      if(is_45(polyWHoles) != true) return 1;
      scale_down(polyWHoles, 2);
      std::cout << is_45(polyWHoles) << " " << polyWHoles << std::endl;
      if(is_45(polyWHoles) != true) return 1;
  
      std::cout << (boolean_op_45<Unit>::testScan45(std::cout)) << std::endl;
      std::cout << (polygon_45_formation<Unit>::testPolygon45Formation(std::cout)) << std::endl;
      std::cout << (polygon_45_formation<Unit>::testPolygon45Tiling(std::cout)) << std::endl;
  
  
      {
        PolygonSet ps;
        Rectangle rect;
        ps.insert(Rectangle(0, 0, 10, 10));
        std::cout << area(ps) << std::endl;
        if(area(ps) != 100) return 1;
        scale_up(ps, 3);
        std::cout << area(ps) << std::endl;
        if(area(ps) != 900) return 1;
        scale_down(ps, 2);
        std::cout << area(ps) << std::endl;
        if(area(ps) != 225) return 1;
        transform(ps, atr);
        std::vector<Rectangle> rv;
        rv.clear();
        ps.get(rv);
        if(rv.size() == 1) {
          assign(rect, rv.back());
          std::cout << rect << std::endl;
        }
        transform(ps, tr);
        rv.clear();
        ps.get(rv);
        if(rv.size() == 1) {
          assign(rect, rv.back());
          std::cout << rect << std::endl;
        }
      }
      //test polygon45set transform
      pts.clear();
      pts.push_back(Point(10, 10));
      pts.push_back(Point(15, 10));
      pts.push_back(Point(10, 15));
      polyHole.set(pts.begin(), pts.end());
      Polygon45Set ps451, ps452;
      ps451.insert(polyHole);
      ps452 = ps451;
      std::cout << (ps451 == ps452) << std::endl;
      if(ps451 != ps452) return 1;
      ps451.transform(atr);
      std::cout << (ps451 == ps452) << std::endl;
      if(ps451 == ps452) return 1;
      ps451.transform(tr);
      std::cout << (ps451 == ps452) << std::endl;
      if(ps451 != ps452) return 1;
  
      //test polygon45set area
      std::cout << area(ps451) << std::endl;
      if(area(ps451) != 12.5) return 1;
      //test polygon45set scale up down
      ps451.scale_up(3);
      std::cout << area(ps451) << std::endl;
      if(area(ps451) != 112.5) return 1;
      ps451.scale_down(2);
      std::cout << area(ps451) << std::endl;
      if(area(ps451) != 32) return 1;
      //test polygonset scalue up down
    }
    {
      std::cout << (testPolygon45SetRect()) << std::endl;
      testPolygon45SetPerterbation(); //re-enable after non-intersection fix
      testPolygon45Set();
      testPolygon45SetDORA();  //re-enable after non-intersection fix
      polygon_45_set_data<int> ps45_1, ps45_2, ps45_3;
      ps45_1.insert(rectangle_data<int>(0, 0, 10, 10));
      ps45_2.insert(rectangle_data<int>(5, 5, 15, 15));
      std::vector<polygon_45_data<int> > p45s;
      ps45_3 = ps45_1 | ps45_2;
      ps45_3.get(p45s);
      if(p45s.size()) std::cout << p45s[0] << std::endl;
      else {
        std::cout << "test failed\n";
        return 1;
      }
      p45s.clear();
      ps45_3 = ps45_1 + ps45_2;
      ps45_3.get(p45s);
      if(p45s.size()) std::cout << p45s[0] << std::endl;
      else {
        std::cout << "test failed\n";
        return 1;
      }
      p45s.clear();
      ps45_3 = ps45_1 * ps45_2;
      ps45_3.get(p45s);
      if(p45s.size()) std::cout << p45s[0] << std::endl;
      else {
        std::cout << "test failed\n";
        return 1;
      }
      p45s.clear();
      ps45_3 = ps45_1 - ps45_2;
      ps45_3.get(p45s);
      if(p45s.size()) std::cout << p45s[0] << std::endl;
      else {
        std::cout << "test failed\n";
        return 1;
      }
      p45s.clear();
      ps45_3 = ps45_1 ^ ps45_2;
      ps45_3.get(p45s);
      if(p45s.size() == 2) std::cout << p45s[0] << " " << p45s[1] << std::endl;
      else {
        std::cout << "test failed\n";
        return 1;
      }
      std::vector<point_data<int> > pts;
      pts.clear();
      pts.push_back(point_data<int>(7, 0));
      pts.push_back(point_data<int>(20, 13));
      pts.push_back(point_data<int>(0, 13));
      pts.push_back(point_data<int>(0, 0));
      polygon_45_data<int> p45_1(pts.begin(), pts.end());
      ps45_3.clear();
      ps45_3.insert(p45_1);
      p45s.clear();
      ps45_3.get(p45s);
      if(p45s.size()) std::cout << p45s[0] << std::endl;
      else {
        std::cout << "test failed\n";
        return 1;
      }
      ps45_3 += 1;
      p45s.clear();
      ps45_3.get(p45s);
      if(p45s.size()) std::cout << p45s[0] << std::endl;
      else {
        std::cout << "test failed\n";
        return 1;
      }
      ps45_3 -= 1;
      p45s.clear();
      ps45_3.get(p45s);
      if(p45s.size()) std::cout << p45s[0] << std::endl;
      else {
        std::cout << "test failed\n";
        return 1;
      }
    }
    {
      polygon_90_set_data<int> p90sd;
      p90sd.insert(rectangle_data<int>(0, 0, 10, 10));
      std::vector<rectangle_data<int> > rects;
      std::vector<polygon_90_data<int> > polys90;
      std::vector<polygon_90_with_holes_data<int> > pwhs90;
      assign(rects, p90sd);
      assign(polys90, p90sd);
      assign(pwhs90, p90sd);
      std::cout << equivalence(rects, polys90) << std::endl;
      std::cout << equivalence(pwhs90, polys90) << std::endl;
      pwhs90.clear();
      assign(pwhs90, polys90);
      std::cout << equivalence(pwhs90, polys90) << std::endl;
    }
    {
      polygon_45_set_data<int> p45sd;
      p45sd.insert(rectangle_data<int>(0, 0, 10, 10));
      std::vector<rectangle_data<int> > rects;
      std::vector<polygon_45_data<int> > polys45;
      std::vector<polygon_45_with_holes_data<int> > pwhs45;
      get_trapezoids(polys45, p45sd);
      assign(polys45, p45sd);
      assign(pwhs45, p45sd);
      std::cout << equivalence(pwhs45, polys45) << std::endl;
      pwhs45.clear();
      assign(pwhs45, polys45);
      std::cout << equivalence(pwhs45, polys45) << std::endl;
    }
    {
      polygon_set_data<int> psd;
      psd.insert(rectangle_data<int>(0, 0, 10, 10));
      std::vector<polygon_data<int> > polys;
      std::vector<polygon_with_holes_data<int> > pwhs;
      assign(polys, psd);
      assign(pwhs, psd);
      std::cout << equivalence(pwhs, polys) << std::endl;
      pwhs.clear();
      assign(pwhs, polys);
      std::cout << equivalence(pwhs, polys) << std::endl;
    }
    {
      polygon_90_set_data<int> ps1(HORIZONTAL), ps2(VERTICAL);
      ps1 += rectangle_data<int>(0, 0, 10, 120);
      assign(ps1, ps2);
      std::cout << equivalence(ps1, ps2) << std::endl;
    }
    {
      std::vector<rectangle_data<polygon_long_long_type> > lobs, input;
      input.push_back(rectangle_data<polygon_long_long_type>(0, 0, 10, 10));
      input.push_back(rectangle_data<polygon_long_long_type>(10, 5, 15, 15));
      get_max_rectangles(lobs, input);
      if(lobs.size() == 3) std::cout << "max rectangles is correct\n";
    }
    {
      polygon_set_data<int> ps1, ps2, ps3;
      ps1.insert(rectangle_data<int>(0, 0, 10, 10));
      ps2.insert(rectangle_data<int>(0, 0, 15, 5));
      ps3.insert(rectangle_data<int>(0, 0, 20, 2));
      std::cout << area(ps1 + ps2) << std::endl;
      keep(ps1, 0, 100, 0, 100, 0, 100);
      if(empty(ps1)) return 1;
      rectangle_data<int> bbox;
      extents(bbox, ps1);
      std::cout << bbox << std::endl;
      //resize(ps1, 1);
      //shrink(ps1, 1);
      //bloat(ps1, 1);
      scale_up(ps1, 2);
      scale_down(ps1, 2);
      axis_transformation atr;
      transform(ps1, atr);
      std::cout << area(ps1) << std::endl;
      if(area(ps1) != 100) return 1;
      clear(ps1);
      if(!empty(ps1)) return 1;
      ps1 = ps2 * ps3;
      ps1 *= ps2;
      ps1 - ps2;
      ps1 -= ps2;
      ps1 ^ ps2;
      ps1 ^= ps2;
      ps1 | ps2;
      ps1 |= ps2;
    }
    {
      polygon_45_set_data<int> ps45_1, ps45_2;
      ps45_1.insert(rectangle_data<int>(0, 0, 10, 10));
      keep(ps45_1, 0, 1000, 0, 1000, 0, 1000);
      std::cout << area(ps45_1) << std::endl;
      std::cout << empty(ps45_1) << std::endl;
      rectangle_data<int> bbox;
      extents(bbox, ps45_1);
      std::cout << bbox << std::endl;
      resize(ps45_1, 1);
      shrink(ps45_1, 1);
      bloat(ps45_1, 1);
      scale_up(ps45_1, 2);
      scale_down(ps45_1, 2);
      axis_transformation atr;
      transform(ps45_1, atr);
      std::cout << area(ps45_1) << std::endl;
      if(area(ps45_1) != 144) return 1;
      clear(ps45_1);
      if(!empty(ps45_1)) return 1;
    }
    {
      std::vector<polygon_45_data<int> > p45v;
      p45v + p45v;
      p45v *= p45v;
      p45v += p45v;
      p45v - p45v;
      p45v -= p45v;
      p45v ^ p45v;
      p45v ^= p45v;
      p45v | p45v;
      p45v |= p45v;
      p45v + 1;
      p45v += 1;
      p45v - 1;
      p45v -= 1;
      p45v + (p45v + p45v);
    }
    {
      polygon_45_set_data<int> ps45;
      polygon_90_set_data<int> ps90;
      std::vector<polygon_90_with_holes_data<int> > p90whv;
      ps45.insert(ps90);
      ps45.insert(p90whv);
      ps45.insert(p90whv + p90whv);
  
      ps45.insert(polygon_90_with_holes_data<int>());
      polygon_with_holes_data<int> pwh;
      snap_to_45(pwh);
    }
    {
      polygon_90_set_data<int> ps90_1, ps90_2;
      ps90_1.insert(rectangle_data<int>(0, 0, 10, 10));
      keep(ps90_1, 0, 1000, 0, 1000, 0, 1000);
      std::cout << area(ps90_1) << std::endl;
      std::cout << empty(ps90_1) << std::endl;
      rectangle_data<int> bbox;
      extents(bbox, ps90_1);
      std::cout << bbox << std::endl;
      resize(ps90_1, 1);
      shrink(ps90_1, 1);
      bloat(ps90_1, 1);
      scale_up(ps90_1, 2);
      scale_down(ps90_1, 2);
      scale(ps90_1, anisotropic_scale_factor<double>(2, 2));
      scale(ps90_1, anisotropic_scale_factor<double>(0.5, 0.5));
      axis_transformation atr;
      transform(ps90_1, atr);
      std::cout << area(ps90_1) << std::endl;
      if(area(ps90_1) != 144) return 1;
      clear(ps90_1);
      if(!empty(ps90_1)) return 1;
    }
    if(!nonInteger45StessTest()) return 1;
    {
    using namespace gtl;
    typedef polygon_45_property_merge<int, int> p45pm;
    p45pm::MergeSetData msd;
    polygon_45_set_data<int> ps;
    ps += rectangle_data<int>(0, 0, 10, 10);
    p45pm::populateMergeSetData(msd, ps.begin(), ps.end(), 444);
    ps.clear();
    ps += rectangle_data<int>(5, 5, 15, 15);
    p45pm::populateMergeSetData(msd, ps.begin(), ps.end(), 333);
    std::map<std::set<int>, polygon_45_set_data<int> > result;
    p45pm::performMerge(result, msd);
    int i = 0;
    for(std::map<std::set<int>, polygon_45_set_data<int> >::iterator itr = result.begin();
        itr != result.end(); ++itr) {
      for(std::set<int>::const_iterator itr2 = (*itr).first.begin();
          itr2 != (*itr).first.end(); ++itr2) {
        std::cout << *itr2 << " ";
      } std::cout << " : ";
      std::cout << area((*itr).second) << std::endl;
      if(i == 1) {
        if(area((*itr).second) != 100) return 1;
      } else
        if(area((*itr).second) != 300) return 1;
      ++i;
    }
  
  
    property_merge_45<int, int> pm;
    pm.insert(rectangle_data<int>(0, 0, 10, 10), 444);
    pm.insert(rectangle_data<int>(5, 5, 15, 15), 333);
    std::map<std::set<int>, polygon_45_set_data<int> > mp;
    pm.merge(mp);
    i = 0;
    for(std::map<std::set<int>, polygon_45_set_data<int> >::iterator itr = mp.begin();
        itr != mp.end(); ++itr) {
      for(std::set<int>::const_iterator itr2 = (*itr).first.begin();
          itr2 != (*itr).first.end(); ++itr2) {
        std::cout << *itr2 << " ";
      } std::cout << " : ";
      std::cout << area((*itr).second) << std::endl;
      if(i == 1) {
        if(area((*itr).second) != 25) return 1;
      } else
        if(area((*itr).second) != 75) return 1;
      ++i;
    }
    std::map<std::vector<int>, polygon_45_set_data<int> > mp2;
    pm.merge(mp2);
    i = 0;
    for(std::map<std::vector<int>, polygon_45_set_data<int> >::iterator itr = mp2.begin();
        itr != mp2.end(); ++itr) {
      for(std::vector<int>::const_iterator itr2 = (*itr).first.begin();
          itr2 != (*itr).first.end(); ++itr2) {
        std::cout << *itr2 << " ";
      } std::cout << " : ";
      std::cout << area((*itr).second) << std::endl;
      if(i == 1) {
        if(area((*itr).second) != 25) return 1;
      } else
        if(area((*itr).second) != 75) return 1;
      ++i;
    }
    }
    {
    std::cout << trapezoid_arbitrary_formation<int>::testTrapezoidArbitraryFormationRect(std::cout) << std::endl;
    std::cout << trapezoid_arbitrary_formation<int>::testTrapezoidArbitraryFormationP1(std::cout) << std::endl;
    std::cout << trapezoid_arbitrary_formation<int>::testTrapezoidArbitraryFormationP2(std::cout) << std::endl;
    std::cout << trapezoid_arbitrary_formation<int>::testTrapezoidArbitraryFormationPolys(std::cout) << std::endl;
    std::cout << polygon_arbitrary_formation<int>::testPolygonArbitraryFormationSelfTouch1(std::cout) << std::endl;
    std::cout << trapezoid_arbitrary_formation<int>::testTrapezoidArbitraryFormationSelfTouch1(std::cout) << std::endl;
    typedef rectangle_data<int> Rectangle;
    polygon_set_data<int> ps;
    ps += Rectangle(0, 1, 10, 11);
    ps += Rectangle(5, 6, 15, 16);
    std::vector<polygon_data<int> > polys;
    ps.get_trapezoids(polys);
    for(unsigned int i = 0; i < polys.size(); ++i) {
      std::cout << polys[i] << std::endl;
    }
    ps.transform(axis_transformation(axis_transformation::FLIP_X));
    polys.clear();
    ps.get_trapezoids(polys);
    for(unsigned int i = 0; i < polys.size(); ++i) {
      std::cout << polys[i] << std::endl;
    }
    polys.clear();
    ps.get_trapezoids(polys, HORIZONTAL);
    for(unsigned int i = 0; i < polys.size(); ++i) {
      std::cout << polys[i] << std::endl;
    }
    }
  
    if(!test_aa_touch()) {
      std::cout << "test_aa_touch failed\n";
      return 1;
    }
    if(!test_aa_touch_ur()) {
      std::cout << "test_aa_touch_ur failed\n";
      return 1;
    }
    if(!test_aa_touch_ur()) {
      std::cout << "test_aa_touch_ur failed\n";
      return 1;
    }
    if(!test_aa_touch_r()) {
      std::cout << "test_aa_touch_r failed\n";
      return 1;
    }
    if(!test_aa_touch_boundaries()) {
      std::cout << "test_aa_touch_boundaries failed\n";
      return 1;
    }
    if(!test_aa_concept_interact()) {
      std::cout << "test_aa_concept_interact failed\n";
      return 1;
    }
  
    {
      polygon_set_data<int> ps;
      polygon_90_set_data<int> ps90;
      rectangle_data<int> rect(0, 1, 10, 100);
      std::vector<polygon_data<int> > rupolys, rupolys45;
      ps.insert(rect);
      ps90.insert(rect);
      ps.bloat(10);
      ps90.bloat(10, 10, 10, 10);
      rupolys.clear();
      rupolys45.clear();
      ps.get(rupolys);
      ps90.get(rupolys45);
      std::cout << rupolys[0] << std::endl;
      std::cout << rupolys45[0] << std::endl;
      if(!equivalence(ps, ps90)) {
        std::cout << "test manhattan vs general resize up failed\n";
        return 1;
      }
      ps.shrink(10);
      ps90.shrink(10, 10, 10, 10);
      if(!equivalence(ps, rect)) {
        std::cout << "test manhattan vs general resize down failed\n";
        return 1;
      }
      rectangle_data<int> rect2(3, 4, 6, 80);
      ps -= rect2;
      ps90 -= rect2;
      ps.bloat(1);
      ps90.bloat(1, 1, 1, 1);
      if(!equivalence(ps, ps90)) {
        std::cout << "test manhattan vs general with hole resize up failed\n";
        return 1;
      }
      ps.shrink(1);
      ps90.shrink(1, 1, 1, 1);
      if(!equivalence(ps, ps90)) {
        std::cout << "test manhattan vs general with hole resize down failed\n";
        return 1;
      }
      ps.clear();
      polygon_45_data<int> poly;
      std::vector<point_data<int> > pts;
      pts.push_back(point_data<int>(0, 0));
      pts.push_back(point_data<int>(10, 0));
      pts.push_back(point_data<int>(0, 10));
      polygon_45_set_data<int> ps45;
      set_points(poly, pts.begin(), pts.end());
      ps.insert(poly);
      ps45.insert(poly);
      ps.bloat(9);
      ps45.resize(9);
      rupolys.clear();
      rupolys45.clear();
      ps.get(rupolys);
      ps45.get(rupolys45);
      std::cout << rupolys[0] << std::endl;
      std::cout << rupolys45[0] << std::endl;
      pts.clear();
      pts.push_back(point_data<int>(32, -9));
      pts.push_back(point_data<int>(-9, 32));
      pts.push_back(point_data<int>(-9, -9));
      set_points(poly, pts.begin(), pts.end());
      if(!equivalence(ps, poly)) {
        std::cout << "test general resize up failed\n";
        return 1;
      }
      // this test is waived due to rounding differences between 45 and general resizing
      // general resizing is computing floating point coordinates for the intersection
      // and rounding those to closest while 45 is computing the normal point and rounding
      // that to closest, it turns out to result in different intersection point
      // we want the general to be more accurate to avoid artifacts
      //if(!equivalence(ps, ps45)) {
      //  std::cout << "test 45 vs general resize up failed\n";
      //  return 1;
      //}
      ps.shrink(9);
      ps45.resize(-9);
      if(!equivalence(ps, ps45)) {
        std::cout << "test 45 vs general resize down failed\n";
        return 1;
      }
      pts.clear();
      pts.push_back(point_data<int>(1, 1));
      pts.push_back(point_data<int>(7, 1));
      pts.push_back(point_data<int>(1, 7));
      set_points(poly, pts.begin(), pts.end());
      ps.insert(poly, true);
      ps45.insert(poly, true);
      ps.bloat(1);
      ps45.resize(1);
      rupolys.clear();
      rupolys45.clear();
      ps.get(rupolys);
      ps45.get(rupolys45);
      std::cout << rupolys[0] << std::endl;
      std::cout << rupolys45[0] << std::endl;
      pts.clear();
      pts.push_back(point_data<int>(12, -1));
      pts.push_back(point_data<int>(5, 6));
      pts.push_back(point_data<int>(5, 2));
      pts.push_back(point_data<int>(2, 2));
      pts.push_back(point_data<int>(2, 5));
      pts.push_back(point_data<int>(5, 2));
      pts.push_back(point_data<int>(5, 6));
      pts.push_back(point_data<int>(-1, 12));
      pts.push_back(point_data<int>(-1, -1));
      pts.push_back(point_data<int>(12, -1));
      set_points(poly, pts.begin(), pts.end());
      //waived
      //if(!equivalence(ps, poly)) {
      //  std::cout << "test general resize up with holes failed\n";
      //  return 1;
      //}
      //waived
      //if(!equivalence(ps, ps45)) {
      //  std::cout << "test 45 vs general resize up with holes failed\n";
      //  return 1;
      //}
      ps.shrink(1);
      ps45.resize(-1);
      if(!equivalence(ps, ps45)) {
        std::cout << "test 45 vs general resize down with holes failed\n";
        return 1;
      }
      ps.shrink(10);
      ps45.resize(-10);
      if(!equivalence(ps, ps45)) {
        std::cout << "test 45 vs general resize down 2 with holes failed\n";
        return 1;
      }
    }
  
    {
  
      Point pts[] = {construct<Point>(1565, 5735),
                     construct<Point>(915, 5735),
                     construct<Point>(915, 7085),
                     construct<Point>(1565, 7085) };
      Polygon poly;
      set_points(poly, pts, pts+4);
      bool ret=gtl::contains(poly,gtl::construct<Point>(920, 7080));
      if(!ret) {
        std::cout << "contains failed!" << std::endl;
        return 1;
      }
      polygon_data<int> poly_aa;
      set_points(poly_aa, pts, pts+4);
      ret=gtl::contains(poly,gtl::construct<Point>(920, 7080));
      if(!ret) {
        std::cout << "contains 90 failed!" << std::endl;
        return 1;
      }
      polygon_with_holes_data<int> pwh;
      polygon_90_with_holes_data<int> p90wh;
      Point pts2[] = {construct<Point>(565, 15735),
                     construct<Point>(15, 15735),
                     construct<Point>(15, 17085),
                     construct<Point>(565, 17085) };
      set_points(pwh, pts2, pts2+4);
      set_points(p90wh, pts2, pts2+4);
      pwh.set_holes(&poly_aa, (&poly_aa)+1);
      p90wh.set_holes(&poly, (&poly)+1);
      ret=gtl::contains(pwh,gtl::construct<Point>(920, 7080));
      if(ret) {
        std::cout << "contains wh failed!" << std::endl;
        return 1;
      }
      ret=gtl::contains(p90wh,gtl::construct<Point>(920, 7080));
      if(ret) {
        std::cout << "contains 90wh failed!" << std::endl;
        return 1;
      }
      std::reverse(pts, pts+4);
      set_points(poly, pts, pts+4);
      ret=gtl::contains(poly,gtl::construct<Point>(920, 7080));
      if(!ret) {
        std::cout << "reverse contains failed!" << std::endl;
        return 1;
      }
    }
    {
  //     //MULTIPOLYGON
  //     (
  //      ((200 400,100 400,100 300,200 400)),
  //      ((300 100,200 100,200 0,300 0,300 100)),
  //      ((600 700,500 700,500 600,600 700)),
  //      ((700 300,600 300,600 200,700 300)),
  //      ((800 500,700 600,700 500,800 500)),
  //      ((900 800,800 700,900 700,900 800)),
  //      ((1000 200,900 100,1000 100,1000 200)),
  //      ((1000 800,900 900,900 800,1000 800))),
      int mp1 [7][2*4] = {
        {200,400,100,400,100,300,200,400},
        {600,700,500,700,500,600,600,700},
        {700,300,600,300,600,200,700,300},
        {800,500,700,600,700,500,800,500},
        {900,800,800,700,900,700,900,800},
        {1000,200,900,100,1000,100,1000,200},
        {1000,800,900,900,900,800,1000,800}
      };
      int mp11 [2*5] = {300,100,200,100,200,0,300,0,300,100};
      polygon_45_set_data<int> pset1;
      polygon_45_set_data<int> pset2;
      for(int i = 0; i < 7; ++i) {
        addpoly(pset1, mp1[i], 4);
      }
      addpoly(pset1, mp11, 5);
  //     //MULTIPOLYGON
  //       (
  //        ((200 800,100 800,100 700,200 700,200 800)),
  //        ((400 200,300 100,400 100,400 200)),
  //        ((400 800,300 700,400 700,400 800)),
  //        ((700 100,600 0,700 0,700 100)),
  //        ((700 200,600 200,600 100,700 200)),
  //        ((900 200,800 200,800 0,900 0,900 200)),
  //        ((1000 300,900 200,1000 200,1000 300)))
      int mp2 [5][2*4] = {
        {400,200,300,100,400,100,400,200},
        {400,800,300,700,400,700,400,800},
        {700,100,600,0,700,0,700,100},
        {700,200,600,200,600,100,700,200},
        {1000,300,900,200,1000,200,1000,300},
      };
      int mp21 [2*5] = {200,800,100,800,100,700,200,700,200,800};
      int mp22 [2*5] = {900,200,800,200,800,0,900,0,900,200};
      for(int i = 0; i < 5; ++i) {
        addpoly(pset2, mp2[i], 4);
      }
      addpoly(pset2, mp21, 5);
      addpoly(pset2, mp22, 5);
      polygon_45_set_data<int> orr = pset1 + pset2;
      polygon_45_set_data<int> inr = pset1 & pset2;
      std::cout << area(orr)<<std::endl;;
      std::cout << area(inr)<<std::endl;;
      std::vector<polygon_45_with_holes_data<int> > polys;
      assign(polys, orr);
      std::cout << area(polys) << std::endl;
      polygon_set_data<int> testbug;
      testbug.insert(orr);
      std::cout << area(testbug) << std::endl;
      polygon_set_data<int> testbug2;
      for(size_t i = 0; i < polys.size(); ++i) {
        for(size_t j = 0; j < polys.size(); ++j) {
          testbug2.clear();
          testbug2.insert(polys[i]);
          testbug2.insert(polys[j]);
          std::cout << i << " " << j << std::endl;
          std::cout << polys[i] << std::endl;
          std::cout << polys[j] << std::endl;
          if(area(testbug2) == 0.0) {
            std::cout << area(testbug2) << std::endl;
            std::cout << "Self touch 45 through general interface failed!\n";
            return 1;
          }
        }
      }
    }
  
    {
      polygon_set_data<int> t_eq;
      t_eq.insert(rectangle_data<int>(0, 0, 5, 10));
      t_eq.insert(rectangle_data<int>(0, 5, 5, 10));
      std::cout << t_eq <<std::endl;
      polygon_set_data<int> t_eq2;
      t_eq2 += rectangle_data<int>(0, 0, 5, 10);
      std::cout << area(t_eq) <<std::endl;
      std::cout << area(t_eq2) <<std::endl;   
      std::cout << t_eq <<std::endl;
      std::cout << t_eq2 <<std::endl;   
      if(t_eq != t_eq2) {
        std::cout << "equivalence failed" << std::endl;
        return 1;
      }    
    }
  
    {
      using namespace boost::polygon;
      typedef point_data<int> Point;
      typedef segment_data<int> Dls;
      Point pt1(0, 0);
      Point pt2(10, 10);
      Point pt3(20, 20);
      Point pt4(20, 0);
      Dls dls1(pt1, pt2);
      Dls dls2(pt1, pt3);
      Dls dls3(pt1, pt4);
      Dls dls4(pt2, pt1);
      typedef std::vector<segment_data<int> > Dlss;
      Dlss dlss, result;
      dlss.push_back(dls1);
      dlss.push_back(dls2);
      dlss.push_back(dls3);
      dlss.push_back(dls4);
      rectangle_data<int> rect;
      envelope_segments(rect, dlss.begin(), dlss.end());
      assert_s(area(rect) == 400.0, "envelope");
      intersect_segments(result, dlss.begin(), dlss.end());
      dlss.swap(result);
      for (Dlss::iterator itr = dlss.begin(); itr != dlss.end(); ++itr) {
        std::cout << *itr << std::endl;
      }
      assert_s(dlss.size() == 5, "intersection");
      Dls dls5(Point(0,5), Point(5,0));
      dlss.push_back(dls5);
      std::cout << std::endl;
      result.clear();
      intersect_segments(result, dlss.begin(), dlss.end());
      dlss.swap(result);
      for (Dlss::iterator itr = dlss.begin(); itr != dlss.end(); ++itr) {
        std::cout << *itr << std::endl;
      }
      assert_s(dlss.size() == 11, "intersection2");
    }
    
    {
      using namespace boost::polygon;
      std::vector<std::pair<std::size_t, segment_data<int> > > segs;
      segment_data<int> sarray[2];
      sarray[0] = segment_data<int>(point_data<int>(0,0), point_data<int>(10,10));
      sarray[1] = segment_data<int>(point_data<int>(10,0), point_data<int>(0,10));
      intersect_segments(segs, sarray, sarray+2);
      std::cout << segs.size() << std::endl;
      assert_s(segs.size() == 4, "intersection3");
    }
  
  
    /*New polygon_formation tests*/ 
    if(test_new_polygon_formation(0,NULL)){
       std::cerr << "[test_new_polygon_formation] failed" << std::endl;
       return 1;
    }
  
    if(test_new_polygon_formation_marginal_threshold(0,NULL)){
       std::cerr << "[test_new_polygon_formation_marginal_threshold] failed" 
           << std::endl;
       return 1;
    }
  
    std::cout << "ALL TESTS COMPLETE\n";
    return 0;
  }
  