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).
  */
  #ifndef BOOST_POLYGON_BOOLEAN_OP_45_HPP
  #define BOOST_POLYGON_BOOLEAN_OP_45_HPP
  namespace boost { namespace polygon{
  
    template <typename Unit>
    struct boolean_op_45 {
      typedef point_data<Unit> Point;
      typedef typename coordinate_traits<Unit>::manhattan_area_type LongUnit;
  
      class Count2 {
      public:
        inline Count2()
  #ifndef BOOST_POLYGON_MSVC
        : counts()
  #endif
        { counts[0] = counts[1] = 0; }
        //inline Count2(int count) { counts[0] = counts[1] = count; }
        inline Count2(int count1, int count2)
  #ifndef BOOST_POLYGON_MSVC
        : counts()
  #endif
        { counts[0] = count1; counts[1] = count2; }
        inline Count2(const Count2& count)
  #ifndef BOOST_POLYGON_MSVC
        : counts()
  #endif
        { counts[0] = count.counts[0]; counts[1] = count.counts[1]; }
        inline bool operator==(const Count2& count) const { return counts[0] == count.counts[0] && counts[1] == count.counts[1]; }
        inline bool operator!=(const Count2& count) const { return !((*this) == count); }
        inline Count2& operator=(int count) { counts[0] = counts[1] = count; return *this; }
        inline Count2& operator=(const Count2& count) { counts[0] = count.counts[0]; counts[1] = count.counts[1]; return *this; }
        inline int& operator[](bool index) { return counts[index]; }
        inline int operator[](bool index) const {return counts[index]; }
        inline Count2& operator+=(const Count2& count){
          counts[0] += count[0];
          counts[1] += count[1];
          return *this;
        }
        inline Count2& operator-=(const Count2& count){
          counts[0] -= count[0];
          counts[1] -= count[1];
          return *this;
        }
        inline Count2 operator+(const Count2& count) const {
          return Count2(*this)+=count;
        }
        inline Count2 operator-(const Count2& count) const {
          return Count2(*this)-=count;
        }
        inline Count2 invert() const {
          return Count2(-counts[0], -counts[1]);
        }
      private:
        int counts[2];
      };
  
      class Count1 {
      public:
        inline Count1() : count_(0) { }
        inline Count1(int count) : count_(count) { }
        inline Count1(const Count1& count) : count_(count.count_) { }
        inline bool operator==(const Count1& count) const { return count_ == count.count_; }
        inline bool operator!=(const Count1& count) const { return !((*this) == count); }
        inline Count1& operator=(int count) { count_ = count; return *this; }
        inline Count1& operator=(const Count1& count) { count_ = count.count_; return *this; }
        inline Count1& operator+=(const Count1& count){
          count_ += count.count_;
          return *this;
        }
        inline Count1& operator-=(const Count1& count){
          count_ -= count.count_;
          return *this;
        }
        inline Count1 operator+(const Count1& count) const {
          return Count1(*this)+=count;
        }
        inline Count1 operator-(const Count1& count) const {
          return Count1(*this)-=count;
        }
        inline Count1 invert() const {
          return Count1(-count_);
        }
        int count_;
      };
  
      //     inline std::ostream& operator<< (std::ostream& o, const Count2& c) {
      //       o << c[0] << " " << c[1];
      //       return o;
      //     }
  
      template <typename CountType>
      class Scan45ElementT {
      public:
        Unit x;
        Unit y;
        int rise; //-1, 0, +1
        mutable CountType count;
        inline Scan45ElementT() : x(), y(), rise(), count() {}
        inline Scan45ElementT(Unit xIn, Unit yIn, int riseIn, CountType countIn = CountType()) :
          x(xIn), y(yIn), rise(riseIn), count(countIn) {}
        inline Scan45ElementT(const Scan45ElementT& that) :
          x(that.x), y(that.y), rise(that.rise), count(that.count) {}
        inline Scan45ElementT& operator=(const Scan45ElementT& that) {
          x = that.x; y = that.y; rise = that.rise; count = that.count;
          return *this;
        }
        inline Unit evalAtX(Unit xIn) const {
          return y + rise * (xIn - x);
        }
  
        inline bool cross(Point& crossPoint, const Scan45ElementT& edge, Unit currentX) const {
          Unit y1 = evalAtX(currentX);
          Unit y2 = edge.evalAtX(currentX);
          int rise1 = rise;
          int rise2 = edge.rise;
          if(rise > edge.rise){
            if(y1 > y2) return false;
          } else if(rise < edge.rise){
            if(y2 > y1) return false;
            std::swap(y1, y2);
            std::swap(rise1, rise2);
          } else { return false; }
          if(rise1 == 1) {
            if(rise2 == 0) {
              crossPoint = Point(currentX + y2 - y1, y2);
            } else {
              //rise2 == -1
              Unit delta = (y2 - y1)/2;
              crossPoint = Point(currentX + delta, y1 + delta);
            }
          } else {
            //rise1 == 0 and rise2 == -1
            crossPoint = Point(currentX + y2 - y1, y1);
          }
          return true;
        }
      };
  
      typedef Scan45ElementT<Count2> Scan45Element;
  
      //     inline std::ostream& operator<< (std::ostream& o, const Scan45Element& c) {
      //       o << c.x << " " << c.y << " " << c.rise << " " << c.count;
      //       return o;
      //     }
  
      class lessScan45ElementRise : public std::binary_function<Scan45Element, Scan45Element, bool> {
      public:
        inline lessScan45ElementRise() {} //default constructor is only constructor
        inline bool operator () (Scan45Element elm1, Scan45Element elm2) const {
          return elm1.rise < elm2.rise;
        }
      };
  
      template <typename CountType>
      class lessScan45Element {
      private:
        Unit *x_; //x value at which to apply comparison
        int *justBefore_;
      public:
        inline lessScan45Element() : x_(0), justBefore_(0) {}
        inline lessScan45Element(Unit *x, int *justBefore) : x_(x), justBefore_(justBefore) {}
        inline lessScan45Element(const lessScan45Element& that) : x_(that.x_), justBefore_(that.justBefore_) {}
        inline lessScan45Element& operator=(const lessScan45Element& that) { x_ = that.x_; justBefore_ = that.justBefore_; return *this; }
        inline bool operator () (const Scan45ElementT<CountType>& elm1,
                                 const Scan45ElementT<CountType>& elm2) const {
          Unit y1 = elm1.evalAtX(*x_);
          Unit y2 = elm2.evalAtX(*x_);
          if(y1 < y2) return true;
          if(y1 == y2) {
            //if justBefore is true we invert the result of the comparison of slopes
            if(*justBefore_) {
              return elm1.rise > elm2.rise;
            } else {
              return elm1.rise < elm2.rise;
            }
          }
          return false;
        }
      };
  
      template <typename CountType>
      class Scan45CountT {
      public:
        inline Scan45CountT() : counts() {} //counts[0] = counts[1] = counts[2] = counts[3] = 0; }
        inline Scan45CountT(CountType count) : counts() { counts[0] = counts[1] = counts[2] = counts[3] = count; }
        inline Scan45CountT(const CountType& count1, const CountType& count2, const CountType& count3,
                            const CountType& count4) : counts() {
          counts[0] = count1;
          counts[1] = count2;
          counts[2] = count3;
          counts[3] = count4;
        }
        inline Scan45CountT(const Scan45CountT& count) : counts() {
          (*this) = count;
        }
        inline bool operator==(const Scan45CountT& count) const {
          for(unsigned int i = 0; i < 4; ++i) {
            if(counts[i] != count.counts[i]) return false;
          }
          return true;
        }
        inline bool operator!=(const Scan45CountT& count) const { return !((*this) == count); }
        inline Scan45CountT& operator=(CountType count) {
          counts[0] = counts[1] = counts[2] = counts[3] = count; return *this; }
        inline Scan45CountT& operator=(const Scan45CountT& count) {
          for(unsigned int i = 0; i < 4; ++i) {
            counts[i] = count.counts[i];
          }
          return *this;
        }
        inline CountType& operator[](int index) { return counts[index]; }
        inline CountType operator[](int index) const {return counts[index]; }
        inline Scan45CountT& operator+=(const Scan45CountT& count){
          for(unsigned int i = 0; i < 4; ++i) {
            counts[i] += count.counts[i];
          }
          return *this;
        }
        inline Scan45CountT& operator-=(const Scan45CountT& count){
          for(unsigned int i = 0; i < 4; ++i) {
            counts[i] -= count.counts[i];
          }
          return *this;
        }
        inline Scan45CountT operator+(const Scan45CountT& count) const {
          return Scan45CountT(*this)+=count;
        }
        inline Scan45CountT operator-(const Scan45CountT& count) const {
          return Scan45CountT(*this)-=count;
        }
        inline Scan45CountT invert() const {
          return Scan45CountT(CountType())-=(*this);
        }
        inline Scan45CountT& operator+=(const Scan45ElementT<CountType>& element){
          counts[element.rise+1] += element.count; return *this;
        }
      private:
        CountType counts[4];
      };
  
      typedef Scan45CountT<Count2> Scan45Count;
  
      //     inline std::ostream& operator<< (std::ostream& o, const Scan45Count& c) {
      //       o << c[0] << ", " << c[1] << ", ";
      //       o << c[2] << ", " << c[3];
      //       return o;
      //     }
  
  
      //     inline std::ostream& operator<< (std::ostream& o, const Scan45Vertex& c) {
      //       o << c.first << ": " << c.second;
      //       return o;
      //     }
  
  
      //vetex45 is sortable
      template <typename ct>
      class Vertex45T {
      public:
        Point pt;
        int rise; // 1, 0 or -1
        ct count; //dxdydTheta
        inline Vertex45T() : pt(), rise(), count() {}
        inline Vertex45T(const Point& point, int riseIn, ct countIn) : pt(point), rise(riseIn), count(countIn) {}
        inline Vertex45T(const Vertex45T& vertex) : pt(vertex.pt), rise(vertex.rise), count(vertex.count) {}
        inline Vertex45T& operator=(const Vertex45T& vertex){
          pt = vertex.pt; rise = vertex.rise; count = vertex.count; return *this; }
        inline bool operator==(const Vertex45T& vertex) const {
          return pt == vertex.pt && rise == vertex.rise && count == vertex.count; }
        inline bool operator!=(const Vertex45T& vertex) const { return !((*this) == vertex); }
        inline bool operator<(const Vertex45T& vertex) const {
          if(pt.x() < vertex.pt.x()) return true;
          if(pt.x() == vertex.pt.x()) {
            if(pt.y() < vertex.pt.y()) return true;
            if(pt.y() == vertex.pt.y()) { return rise < vertex.rise; }
          }
          return false;
        }
        inline bool operator>(const Vertex45T& vertex) const { return vertex < (*this); }
        inline bool operator<=(const Vertex45T& vertex) const { return !((*this) > vertex); }
        inline bool operator>=(const Vertex45T& vertex) const { return !((*this) < vertex); }
        inline Unit evalAtX(Unit xIn) const { return pt.y() + rise * (xIn - pt.x()); }
      };
  
      typedef Vertex45T<int> Vertex45;
  
      //     inline std::ostream& operator<< (std::ostream& o, const Vertex45& c) {
      //       o << c.pt << " " << c.rise << " " << c.count;
      //       return o;
      //     }
  
      //when scanning Vertex45 for polygon formation we need a scanline comparator functor
      class lessVertex45 {
      private:
        Unit *x_; //x value at which to apply comparison
        int *justBefore_;
      public:
        inline lessVertex45() : x_(0), justBefore_() {}
  
        inline lessVertex45(Unit *x, int *justBefore) : x_(x), justBefore_(justBefore) {}
  
        inline lessVertex45(const lessVertex45& that) : x_(that.x_), justBefore_(that.justBefore_) {}
  
        inline lessVertex45& operator=(const lessVertex45& that) { x_ = that.x_; justBefore_ = that.justBefore_; return *this; }
  
        template <typename ct>
        inline bool operator () (const Vertex45T<ct>& elm1, const Vertex45T<ct>& elm2) const {
          Unit y1 = elm1.evalAtX(*x_);
          Unit y2 = elm2.evalAtX(*x_);
          if(y1 < y2) return true;
          if(y1 == y2) {
            //if justBefore is true we invert the result of the comparison of slopes
            if(*justBefore_) {
              return elm1.rise > elm2.rise;
            } else {
              return elm1.rise < elm2.rise;
            }
          }
          return false;
        }
      };
  
      // 0 right to left
      // 1 upper right to lower left
      // 2 high to low
      // 3 upper left to lower right
      // 4 left to right
      // 5 lower left to upper right
      // 6 low to high
      // 7 lower right to upper left
      static inline int classifyEdge45(const Point& prevPt, const Point& nextPt) {
        if(prevPt.x() == nextPt.x()) {
          //2 or 6
          return predicated_value(prevPt.y() < nextPt.y(), 6, 2);
        }
        if(prevPt.y() == nextPt.y()) {
          //0 or 4
          return predicated_value(prevPt.x() < nextPt.x(), 4, 0);
        }
        if(prevPt.x() < nextPt.x()) {
          //3 or 5
          return predicated_value(prevPt.y() < nextPt.y(), 5, 3);
        }
        //prevPt.x() > nextPt.y()
        //1 or 7
        return predicated_value(prevPt.y() < nextPt.y(), 7, 1);
      }
  
      template <int op, typename CountType>
      static int applyLogic(CountType count1, CountType count2){
        bool l1 = applyLogic<op>(count1);
        bool l2 = applyLogic<op>(count2);
        if(l1 && !l2)
          return -1; //was true before and became false like a trailing edge
        if(!l1 && l2)
          return 1; //was false before and became true like a leading edge
        return 0; //no change in logic between the two counts
      }
      template <int op>
      static bool applyLogic(Count2 count) {
  #ifdef BOOST_POLYGON_MSVC
  #pragma warning (push)
  #pragma warning (disable: 4127)
  #endif
        if(op == 0) { //apply or
          return count[0] > 0 || count[1] > 0;
        } else if(op == 1) { //apply and
          return count[0] > 0 && count[1] > 0;
        } else if(op == 2) { //apply not
          return count[0] > 0 && !(count[1] > 0);
        } else if(op == 3) { //apply xor
          return (count[0] > 0) ^ (count[1] > 0);
        } else
          return false;
  #ifdef BOOST_POLYGON_MSVC
  #pragma warning (pop)
  #endif
      }
  
      template <int op>
      struct boolean_op_45_output_functor {
        template <typename cT>
        void operator()(cT& output, const Count2& count1, const Count2& count2,
                        const Point& pt, int rise, direction_1d end) {
          int edgeType = applyLogic<op>(count1, count2);
          if(edgeType) {
            int multiplier = end == LOW ? -1 : 1;
            //std::cout << "cross logic: " << edgeType << "\n";
            output.insert(output.end(), Vertex45(pt, rise, edgeType * multiplier));
            //std::cout << "write out: " << crossPoint << " " << Point(eraseItrs[i]->x, eraseItrs[i]->y) << "\n";
          }
        }
      };
  
      template <int op>
      static bool applyLogic(Count1 count) {
  #ifdef BOOST_POLYGON_MSVC
  #pragma warning (push)
  #pragma warning (disable: 4127)
  #endif
        if(op == 0) { //apply or
          return count.count_ > 0;
        } else if(op == 1) { //apply and
          return count.count_ > 1;
        } else if(op == 3) { //apply xor
          return (count.count_ % 2) != 0;
        } else
          return false;
  #ifdef BOOST_POLYGON_MSVC
  #pragma warning (pop)
  #endif
      }
  
      template <int op>
      struct unary_op_45_output_functor {
        template <typename cT>
        void operator()(cT& output, const Count1& count1, const Count1& count2,
                        const Point& pt, int rise, direction_1d end) {
          int edgeType = applyLogic<op>(count1, count2);
          if(edgeType) {
            int multiplier = end == LOW ? -1 : 1;
            //std::cout << "cross logic: " << edgeType << "\n";
            output.insert(output.end(), Vertex45(pt, rise, edgeType * multiplier));
            //std::cout << "write out: " << crossPoint << " " << Point(eraseItrs[i]->x, eraseItrs[i]->y) << "\n";
          }
        }
      };
  
      class lessScan45Vertex {
      public:
        inline lessScan45Vertex() {} //default constructor is only constructor
        template <typename Scan45Vertex>
        inline bool operator () (const Scan45Vertex& v1, const Scan45Vertex& v2) const {
          return (v1.first.x() < v2.first.x()) || (v1.first.x() == v2.first.x() && v1.first.y() < v2.first.y());
        }
      };
      template <typename S45V>
      static inline void sortScan45Vector(S45V& vec) {
        polygon_sort(vec.begin(), vec.end(), lessScan45Vertex());
      }
  
      template <typename CountType, typename output_functor>
      class Scan45 {
      public:
        typedef Scan45CountT<CountType> Scan45Count;
        typedef std::pair<Point, Scan45Count> Scan45Vertex;
  
        //index is the index into the vertex
        static inline Scan45Element getElement(const Scan45Vertex& vertex, int index) {
          return Scan45Element(vertex.first.x(), vertex.first.y(), index - 1, vertex.second[index]);
        }
  
        class lessScan45Point : public std::binary_function<Point, Point, bool> {
        public:
          inline lessScan45Point() {} //default constructor is only constructor
          inline bool operator () (const Point& v1, const Point& v2) const {
            return (v1.x() < v2.x()) || (v1.x() == v2.x() && v1.y() < v2.y());
          }
        };
  
        typedef std::vector<Scan45Vertex> Scan45Vector;
  
        //definitions
        typedef std::set<Scan45ElementT<CountType>, lessScan45Element<CountType> > Scan45Data;
        typedef typename Scan45Data::iterator iterator;
        typedef typename Scan45Data::const_iterator const_iterator;
        typedef std::set<Point, lessScan45Point> CrossQueue;
  
        //data
        Scan45Data scanData_;
        CrossQueue crossQueue_;
        Scan45Vector crossVector_;
        Unit x_;
        int justBefore_;
      public:
        inline Scan45() : scanData_(), crossQueue_(), crossVector_(),
                          x_((std::numeric_limits<Unit>::min)()), justBefore_(false) {
          lessScan45Element<CountType>  lessElm(&x_, &justBefore_);
          scanData_ = std::set<Scan45ElementT<CountType>, lessScan45Element<CountType> >(lessElm);
        }
        inline Scan45(const Scan45& that) : scanData_(), crossQueue_(), crossVector_(),
                                            x_((std::numeric_limits<Unit>::min)()), justBefore_(false) {
          (*this) = that; }
        inline Scan45& operator=(const Scan45& that) {
          x_ = that.x_;
          justBefore_ = that.justBefore_;
          crossQueue_ = that.crossQueue_;
          crossVector_ = that.crossVector_;
          lessScan45Element<CountType>  lessElm(&x_, &justBefore_);
          scanData_ = std::set<Scan45ElementT<CountType>, lessScan45Element<CountType> >(lessElm);
          for(const_iterator itr = that.scanData_.begin(); itr != that.scanData_.end(); ++itr){
            scanData_.insert(scanData_.end(), *itr);
          }
          return *this;
        }
  
        //cT is an output container of Vertex45
        //iT is an iterator over Scan45Vertex elements
        template <class cT, class iT>
        void scan(cT& output, iT inputBegin, iT inputEnd) {
          //std::cout << "1\n";
          while(inputBegin != inputEnd) {
            //std::cout << "2\n";
            //std::cout << "x_ = " << x_ << "\n";
            //std::cout << "scan line size: " << scanData_.size() << "\n";
            //for(iterator iter = scanData_.begin();
            //     iter != scanData_.end(); ++iter) {
            //   std::cout << "scan element\n";
            //   std::cout << *iter << " " << iter->evalAtX(x_) << "\n";
            // }
            // std::cout << "cross queue size: " << crossQueue_.size() << "\n";
            // std::cout << "cross vector size: " << crossVector_.size() << "\n";
            //for(CrossQueue::iterator cqitr = crossQueue_.begin(); cqitr != crossQueue_.end(); ++cqitr) {
            //   std::cout << *cqitr << " ";
            //} std::cout << "\n";
            Unit nextX = (*inputBegin).first.x();
            if(!crossVector_.empty() && crossVector_[0].first.x() < nextX) nextX = crossVector_[0].first.x();
            if(nextX != x_) {
              //std::cout << "3\n";
              //we need to move to the next scanline stop
              //we need to process end events then cross events
              //process end events
              if(!crossQueue_.empty() &&
                 (*crossQueue_.begin()).x() < nextX) {
                //std::cout << "4\n";
                nextX = (std::min)(nextX, (*crossQueue_.begin()).x());
              }
              //std::cout << "6\n";
              justBefore_ = true;
              x_ = nextX;
              advance_(output);
              justBefore_ = false;
              if(!crossVector_.empty() &&
                 nextX == (*inputBegin).first.x()) {
                inputBegin = mergeCross_(inputBegin, inputEnd);
              }
              processEvent_(output, crossVector_.begin(), crossVector_.end());
              crossVector_.clear();
            } else {
              //std::cout << "7\n";
              //our scanline has progressed to the event that is next in the queue
              inputBegin = processEvent_(output, inputBegin, inputEnd);
            }
          }
          //std::cout << "done scanning\n";
        }
  
      private:
        //functions
  
        template <class cT>
        inline void advance_(cT& output) {
          //process all cross points on the cross queue at the current x_
          //std::cout << "advance_\n";
          std::vector<iterator> eraseVec;
          while(!crossQueue_.empty() &&
                (*crossQueue_.begin()).x() == x_){
            //std::cout << "loop\n";
            //pop point off the cross queue
            Point crossPoint = *(crossQueue_.begin());
            //std::cout << crossPoint << "\n";
            //for(iterator iter = scanData_.begin();
            //    iter != scanData_.end(); ++iter) {
            //  std::cout << "scan element\n";
            //  std::cout << *iter << " " << iter->evalAtX(x_) << "\n";
            //}
            crossQueue_.erase(crossQueue_.begin());
            Scan45Vertex vertex(crossPoint, Scan45Count());
            iterator lowIter = lookUp_(vertex.first.y());
            //std::cout << "searching at: " << vertex.first.y() << "\n";
            //if(lowIter == scanData_.end()) std::cout << "could not find\n";
            //else std::cout << "found: " << *lowIter << "\n";
            if(lowIter == scanData_.end() ||
               lowIter->evalAtX(x_) != vertex.first.y()) {
              //   std::cout << "skipping\n";
              //there weren't any edges at this potential cross point
              continue;
            }
            CountType countBelow;
            iterator searchDownItr = lowIter;
            while(searchDownItr != scanData_.begin()
                  && searchDownItr->evalAtX(x_) == vertex.first.y()) {
              //get count from below
              --searchDownItr;
              countBelow = searchDownItr->count;
            }
            //std::cout << "Below Count: " << countBelow << "\n";
            Scan45Count count(countBelow);
            std::size_t numEdges = 0;
            iterator eraseItrs[3];
            while(lowIter != scanData_.end() &&
                  lowIter->evalAtX(x_) == vertex.first.y()) {
              for(int index = lowIter->rise +1; index >= 0; --index)
                count[index] = lowIter->count;
              //std::cout << count << "\n";
              eraseItrs[numEdges] = lowIter;
              ++numEdges;
              ++lowIter;
            }
            if(numEdges == 1) {
              //look for the next crossing point and continue
              //std::cout << "found only one edge\n";
              findCross_(eraseItrs[0]);
              continue;
            }
            //before we erase the elements we need to decide if they should be written out
            CountType currentCount = countBelow;
            for(std::size_t i = 0; i < numEdges; ++i) {
              output_functor f;
              f(output, currentCount, eraseItrs[i]->count, crossPoint, eraseItrs[i]->rise, LOW);
              currentCount = eraseItrs[i]->count;
            }
            //schedule erase of the elements
            for(std::size_t i = 0; i < numEdges; ++i) {
              eraseVec.push_back(eraseItrs[i]);
            }
  
            //take the derivative wrt theta of the count at the crossing point
            vertex.second[2] = count[2] - countBelow;
            vertex.second[1] = count[1] - count[2];
            vertex.second[0] = count[0] - count[1];
            //add the point, deriviative pair into the cross vector
            //std::cout << "LOOK HERE!\n";
            //std::cout << count << "\n";
            //std::cout << vertex << "\n";
            crossVector_.push_back(vertex);
          }
          //erase crossing elements
          std::vector<iterator> searchVec;
          for(std::size_t i = 0; i < eraseVec.size(); ++i) {
            if(eraseVec[i] != scanData_.begin()) {
              iterator searchItr = eraseVec[i];
              --searchItr;
              if(searchVec.empty() ||
                 searchVec.back() != searchItr)
                searchVec.push_back(searchItr);
            }
            scanData_.erase(eraseVec[i]);
          }
          for(std::size_t i = 0; i < searchVec.size(); ++i) {
            findCross_(searchVec[i]);
          }
        }
  
        template <class iT>
        inline iT mergeCross_(iT inputBegin, iT inputEnd) {
          Scan45Vector vec;
          swap(vec, crossVector_);
          iT mergeEnd = inputBegin;
          std::size_t mergeCount = 0;
          while(mergeEnd != inputEnd &&
                (*mergeEnd).first.x() == x_) {
            ++mergeCount;
            ++mergeEnd;
          }
          crossVector_.reserve((std::max)(vec.capacity(), vec.size() + mergeCount));
          for(std::size_t i = 0; i < vec.size(); ++i){
            while(inputBegin != mergeEnd &&
                  (*inputBegin).first.y() < vec[i].first.y()) {
              crossVector_.push_back(*inputBegin);
              ++inputBegin;
            }
            crossVector_.push_back(vec[i]);
          }
          while(inputBegin != mergeEnd){
            crossVector_.push_back(*inputBegin);
            ++inputBegin;
          }
          return inputBegin;
        }
  
        template <class cT, class iT>
        inline iT processEvent_(cT& output, iT inputBegin, iT inputEnd) {
          //std::cout << "processEvent_\n";
          CountType verticalCount = CountType();
          Point prevPoint;
          iterator prevIter = scanData_.end();
          while(inputBegin != inputEnd &&
                (*inputBegin).first.x() == x_) {
            //std::cout << (*inputBegin) << "\n";
            //std::cout << "loop\n";
            Scan45Vertex vertex = *inputBegin;
            //std::cout << vertex.first << "\n";
            //if vertical count propigating up fake a null event at the next element
            if(verticalCount != CountType() && (prevIter != scanData_.end() &&
                                                prevIter->evalAtX(x_) < vertex.first.y())) {
              //std::cout << "faking null event\n";
              vertex = Scan45Vertex(Point(x_, prevIter->evalAtX(x_)), Scan45Count());
            } else {
              ++inputBegin;
              //std::cout << "after increment\n";
              //accumulate overlapping changes in Scan45Count
              while(inputBegin != inputEnd &&
                    (*inputBegin).first.x() == x_ &&
                    (*inputBegin).first.y() == vertex.first.y()) {
                //std::cout << "accumulate\n";
                vertex.second += (*inputBegin).second;
                ++inputBegin;
              }
            }
            //std::cout << vertex.second << "\n";
            //integrate vertex
            CountType currentCount = verticalCount;// + vertex.second[0];
            for(unsigned int i = 0; i < 3; ++i) {
              vertex.second[i] = currentCount += vertex.second[i];
            }
            //std::cout << vertex.second << "\n";
            //vertex represents the change in state at this point
  
            //get counts at current vertex
            CountType countBelow;
            iterator lowIter = lookUp_(vertex.first.y());
            if(lowIter != scanData_.begin()) {
              //get count from below
              --lowIter;
              countBelow = lowIter->count;
              ++lowIter;
            }
            //std::cout << "Count Below: " << countBelow[0] << " " << countBelow[1] << "\n";
            //std::cout << "vertical count: " << verticalCount[0] << " " << verticalCount[1] << "\n";
            Scan45Count countAt(countBelow - verticalCount);
            //check if the vertical edge should be written out
            if(verticalCount != CountType()) {
              output_functor f;
              f(output, countBelow - verticalCount, countBelow, prevPoint, 2, HIGH);
              f(output, countBelow - verticalCount, countBelow, vertex.first, 2, LOW);
            }
            currentCount = countBelow - verticalCount;
            while(lowIter != scanData_.end() &&
                  lowIter->evalAtX(x_) == vertex.first.y()) {
              for(unsigned int i = lowIter->rise + 1; i < 3; ++i) {
                countAt[i] = lowIter->count;
              }
              Point lp(lowIter->x, lowIter->y);
              if(lp != vertex.first) {
                output_functor f;
                f(output, currentCount, lowIter->count, vertex.first, lowIter->rise, LOW);
              }
              currentCount = lowIter->count;
              iterator nextIter = lowIter;
              ++nextIter;
              //std::cout << "erase\n";
              scanData_.erase(lowIter);
              if(nextIter != scanData_.end())
                findCross_(nextIter);
              lowIter = nextIter;
            }
            verticalCount += vertex.second[3];
            prevPoint = vertex.first;
            //std::cout << "new vertical count: " << verticalCount[0] << " " << verticalCount[1] << "\n";
            prevIter = lowIter;
            //count represents the current state at this point
            //std::cout << vertex.second << "\n";
            //std::cout << countAt << "\n";
            //std::cout << "ADD\n";
            vertex.second += countAt;
            //std::cout << vertex.second << "\n";
  
            //add elements to the scanline
            for(int i = 0; i < 3; ++i) {
              if(vertex.second[i] != countBelow) {
                //std::cout << "insert: " << vertex.first.x() << " " << vertex.first.y() << " " << i-1 <<
                //  " " << vertex.second[i][0] << " " << vertex.second[i][1] << "\n";
                iterator insertIter = scanData_.insert(scanData_.end(),
                                                       Scan45ElementT<CountType>(vertex.first.x(),
                                                                                 vertex.first.y(),
                                                                                 i - 1, vertex.second[i]));
                findCross_(insertIter);
                output_functor f;
                f(output, countBelow, vertex.second[i], vertex.first, i - 1, HIGH);
              }
              countBelow = vertex.second[i];
            }
          }
          //std::cout << "end processEvent\n";
          return inputBegin;
        }
  
        //iter1 is horizontal
        inline void scheduleCross0_(iterator iter1, iterator iter2) {
          //std::cout << "0, ";
          Unit y1 = iter1->evalAtX(x_);
          Unit y2 = iter2->evalAtX(x_);
          LongUnit delta = local_abs(LongUnit(y1) - LongUnit(y2));
          if(delta + static_cast<LongUnit>(x_) <= (std::numeric_limits<Unit>::max)())
            crossQueue_.insert(crossQueue_.end(), Point(x_ + static_cast<Unit>(delta), y1));
          //std::cout <<  Point(x_ + delta, y1);
        }
  
        //neither iter is horizontal
        inline void scheduleCross1_(iterator iter1, iterator iter2) {
          //std::cout << "1, ";
          Unit y1 = iter1->evalAtX(x_);
          Unit y2 = iter2->evalAtX(x_);
          //std::cout << y1 << " " << y2 << ": ";
          //note that half the delta cannot exceed the positive inter range
          LongUnit delta = y1;
          delta -= y2;
          Unit UnitMax = (std::numeric_limits<Unit>::max)();
          if((delta & 1) == 1) {
            //delta is odd, division by 2 will result in integer trunctaion
            if(delta == 1) {
              //the cross point is not on the integer grid and cannot be represented
              //we must throw an exception
              std::string msg = "GTL 45 Boolean error, precision insufficient to represent edge intersection coordinate value.";
              throw(msg);
            } else {
              //note that result of this subtraction is always positive because itr1 is above itr2 in scanline
              LongUnit halfDelta2 = (LongUnit)((((LongUnit)y1) - y2)/2);
              //note that halfDelta2 has been truncated
              if(halfDelta2 + x_ <= UnitMax && halfDelta2 + y2 <= UnitMax) {
                crossQueue_.insert(crossQueue_.end(), Point(x_+static_cast<Unit>(halfDelta2), y2+static_cast<Unit>(halfDelta2)));
                crossQueue_.insert(crossQueue_.end(), Point(x_+static_cast<Unit>(halfDelta2), y2+static_cast<Unit>(halfDelta2)+1));
              }
            }
          } else {
            LongUnit halfDelta = (LongUnit)((((LongUnit)y1) - y2)/2);
            if(halfDelta + x_ <= UnitMax && halfDelta + y2 <= UnitMax)
              crossQueue_.insert(crossQueue_.end(), Point(x_+static_cast<Unit>(halfDelta), y2+static_cast<Unit>(halfDelta)));
            //std::cout << Point(x_+halfDelta, y2+halfDelta);
          }
        }
  
        inline void findCross_(iterator iter) {
          //std::cout << "find cross ";
          iterator iteratorBelow = iter;
          iterator iteratorAbove = iter;
          if(iter != scanData_.begin() && iter->rise < 1) {
            --iteratorBelow;
            if(iter->rise == 0){
              if(iteratorBelow->rise == 1) {
                scheduleCross0_(iter, iteratorBelow);
              }
            } else {
              //iter->rise == -1
              if(iteratorBelow->rise == 1) {
                scheduleCross1_(iter, iteratorBelow);
              } else if(iteratorBelow->rise == 0) {
                scheduleCross0_(iteratorBelow, iter);
              }
            }
          }
          ++iteratorAbove;
          if(iteratorAbove != scanData_.end() && iter->rise > -1) {
            if(iter->rise == 0) {
              if(iteratorAbove->rise == -1) {
                scheduleCross0_(iter, iteratorAbove);
              }
            } else {
              //iter->rise == 1
              if(iteratorAbove->rise == -1) {
                scheduleCross1_(iteratorAbove, iter);
              } else if(iteratorAbove->rise == 0) {
                scheduleCross0_(iteratorAbove, iter);
              }
            }
          }
          //std::cout << "\n";
        }
  
        inline iterator lookUp_(Unit y){
          //if just before then we need to look from 1 not -1
          return scanData_.lower_bound(Scan45ElementT<CountType>(x_, y, -1+2*justBefore_));
        }
      };
  
      //template <typename CountType>
      //static inline void print45Data(const std::set<Scan45ElementT<CountType>,
      //                               lessScan45Element<CountType> >& data) {
      //  typename std::set<Scan45ElementT<CountType>, lessScan45Element<CountType> >::const_iterator iter;
      //  for(iter = data.begin(); iter != data.end(); ++iter) {
      //    std::cout << iter->x << " " << iter->y << " " << iter->rise << "\n";
      //  }
      //}
  
      template <typename streamtype>
      static inline bool testScan45Data(streamtype& stdcout) {
        Unit x = 0;
        int justBefore = false;
        lessScan45Element<Count2> lessElm(&x, &justBefore);
        std::set<Scan45ElementT<Count2>, lessScan45Element<Count2> > testData(lessElm);
        //Unit size = testData.size();
        typedef std::set<Scan45ElementT<Count2>, lessScan45Element<Count2> > Scan45Data;
        typename Scan45Data::iterator itr10 = testData.insert(testData.end(), Scan45Element(0, 10, 1));
        typename Scan45Data::iterator itr20 = testData.insert(testData.end(), Scan45Element(0, 20, 1));
        typename Scan45Data::iterator itr30 = testData.insert(testData.end(), Scan45Element(0, 30, -1));
        typename Scan45Data::iterator itr40 = testData.insert(testData.end(), Scan45Element(0, 40, -1));
        typename Scan45Data::iterator itrA = testData.lower_bound(Scan45Element(0, 29, -1));
        typename Scan45Data::iterator itr1 = testData.lower_bound(Scan45Element(0, 10, -1));
        x = 4;
        //now at 14 24 26 36
        typename Scan45Data::iterator itrB = testData.lower_bound(Scan45Element(4, 29, -1));
        typename Scan45Data::iterator itr2 = testData.lower_bound(Scan45Element(4, 14, -1));
        if(itr1 != itr2) stdcout << "test1 failed\n";
        if(itrA == itrB) stdcout << "test2 failed\n";
        //remove crossing elements
        testData.erase(itr20);
        testData.erase(itr30);
        x = 5;
        itr20 = testData.insert(testData.end(), Scan45Element(0, 20, 1));
        itr30 = testData.insert(testData.end(), Scan45Element(0, 30, -1));
        //now at 15 25 25 35
        typename Scan45Data::iterator itr = testData.begin();
        if(itr != itr10) stdcout << "test3 failed\n";
        ++itr;
        if(itr != itr30) stdcout << "test4 failed\n";
        ++itr;
        if(itr != itr20) stdcout << "test5 failed\n";
        ++itr;
        if(itr != itr40) stdcout << "test6 failed\n";
        stdcout << "done testing Scan45Data\n";
        return true;
      }
  
      template <typename stream_type>
      static inline bool testScan45Rect(stream_type& stdcout) {
        stdcout << "testing Scan45Rect\n";
        Scan45<Count2, boolean_op_45_output_functor<0> > scan45;
        std::vector<Vertex45 > result;
        typedef std::pair<Point, Scan45Count> Scan45Vertex;
        std::vector<Scan45Vertex> vertices;
        //is a Rectnagle(0, 0, 10, 10);
        Count2 count(1, 0);
        Count2 ncount(-1, 0);
        vertices.push_back(Scan45Vertex(Point(0,0), Scan45Count(Count2(0, 0), count, Count2(0, 0), count)));
        vertices.push_back(Scan45Vertex(Point(0,10), Scan45Count(Count2(0, 0), ncount, Count2(0, 0), ncount)));
        vertices.push_back(Scan45Vertex(Point(10,0), Scan45Count(Count2(0, 0), ncount, Count2(0, 0), ncount)));
        vertices.push_back(Scan45Vertex(Point(10,10), Scan45Count(Count2(0, 0), count, Count2(0, 0), count)));
        stdcout << "scanning\n";
        scan45.scan(result, vertices.begin(), vertices.end());
        stdcout << "done scanning\n";
        // result size == 8
        // result == 0 0 0 1
        // result == 0 0 2 1
        // result == 0 10 2 -1
        // result == 0 10 0 -1
        // result == 10 0 0 -1
        // result == 10 0 2 -1
        // result == 10 10 2 1
        // result == 10 10 0 1
        std::vector<Vertex45> reference;
        reference.push_back(Vertex45(Point(0, 0), 0, 1));
        reference.push_back(Vertex45(Point(0, 0), 2, 1));
        reference.push_back(Vertex45(Point(0, 10), 2, -1));
        reference.push_back(Vertex45(Point(0, 10), 0, -1));
        reference.push_back(Vertex45(Point(10, 0), 0, -1));
        reference.push_back(Vertex45(Point(10, 0), 2, -1));
        reference.push_back(Vertex45(Point(10, 10), 2, 1));
        reference.push_back(Vertex45(Point(10, 10), 0, 1));
        if(result != reference) {
          stdcout << "result size == " << result.size() << "\n";
          for(std::size_t i = 0; i < result.size(); ++i) {
            //std::cout << "result == " << result[i]<< "\n";
          }
          stdcout << "reference size == " << reference.size() << "\n";
          for(std::size_t i = 0; i < reference.size(); ++i) {
            //std::cout << "reference == " << reference[i]<< "\n";
          }
          return false;
        }
        stdcout << "done testing Scan45Rect\n";
        return true;
      }
  
      template <typename stream_type>
      static inline bool testScan45P1(stream_type& stdcout) {
        stdcout << "testing Scan45P1\n";
        Scan45<Count2, boolean_op_45_output_functor<0> > scan45;
        std::vector<Vertex45 > result;
        typedef std::pair<Point, Scan45Count> Scan45Vertex;
        std::vector<Scan45Vertex> vertices;
        //is a Rectnagle(0, 0, 10, 10);
        Count2 count(1, 0);
        Count2 ncount(-1, 0);
        vertices.push_back(Scan45Vertex(Point(0,0), Scan45Count(Count2(0, 0), Count2(0, 0), count, count)));
        vertices.push_back(Scan45Vertex(Point(0,10), Scan45Count(Count2(0, 0), Count2(0, 0), ncount, ncount)));
        vertices.push_back(Scan45Vertex(Point(10,10), Scan45Count(Count2(0, 0), Count2(0, 0), ncount, ncount)));
        vertices.push_back(Scan45Vertex(Point(10,20), Scan45Count(Count2(0, 0), Count2(0, 0), count, count)));
        stdcout << "scanning\n";
        scan45.scan(result, vertices.begin(), vertices.end());
        stdcout << "done scanning\n";
        // result size == 8
        // result == 0 0 1 1
        // result == 0 0 2 1
        // result == 0 10 2 -1
        // result == 0 10 1 -1
        // result == 10 10 1 -1
        // result == 10 10 2 -1
        // result == 10 20 2 1
        // result == 10 20 1 1
        std::vector<Vertex45> reference;
        reference.push_back(Vertex45(Point(0, 0), 1, 1));
        reference.push_back(Vertex45(Point(0, 0), 2, 1));
        reference.push_back(Vertex45(Point(0, 10), 2, -1));
        reference.push_back(Vertex45(Point(0, 10), 1, -1));
        reference.push_back(Vertex45(Point(10, 10), 1, -1));
        reference.push_back(Vertex45(Point(10, 10), 2, -1));
        reference.push_back(Vertex45(Point(10, 20), 2, 1));
        reference.push_back(Vertex45(Point(10, 20), 1, 1));
        if(result != reference) {
          stdcout << "result size == " << result.size() << "\n";
          for(std::size_t i = 0; i < result.size(); ++i) {
            //std::cout << "result == " << result[i]<< "\n";
          }
          stdcout << "reference size == " << reference.size() << "\n";
          for(std::size_t i = 0; i < reference.size(); ++i) {
            //std::cout << "reference == " << reference[i]<< "\n";
          }
          return false;
        }
        stdcout << "done testing Scan45P1\n";
        return true;
      }
  
      template <typename stream_type>
      static inline bool testScan45P2(stream_type& stdcout) {
        stdcout << "testing Scan45P2\n";
        Scan45<Count2, boolean_op_45_output_functor<0> > scan45;
        std::vector<Vertex45 > result;
        typedef std::pair<Point, Scan45Count> Scan45Vertex;
        std::vector<Scan45Vertex> vertices;
        //is a Rectnagle(0, 0, 10, 10);
        Count2 count(1, 0);
        Count2 ncount(-1, 0);
        vertices.push_back(Scan45Vertex(Point(0,0), Scan45Count(Count2(0, 0), count, ncount, Count2(0, 0))));
        vertices.push_back(Scan45Vertex(Point(10,0), Scan45Count(Count2(0, 0), ncount, count, Count2(0, 0))));
        vertices.push_back(Scan45Vertex(Point(10,10), Scan45Count(Count2(0, 0), ncount, count, Count2(0, 0))));
        vertices.push_back(Scan45Vertex(Point(20,10), Scan45Count(Count2(0, 0), count, ncount, Count2(0, 0))));
        stdcout << "scanning\n";
        scan45.scan(result, vertices.begin(), vertices.end());
        stdcout << "done scanning\n";
        // result size == 8
        // result == 0 0 0 1
        // result == 0 0 1 -1
        // result == 10 0 0 -1
        // result == 10 0 1 1
        // result == 10 10 1 1
        // result == 10 10 0 -1
        // result == 20 10 1 -1
        // result == 20 10 0 1
        std::vector<Vertex45> reference;
        reference.push_back(Vertex45(Point(0, 0), 0, 1));
        reference.push_back(Vertex45(Point(0, 0), 1, -1));
        reference.push_back(Vertex45(Point(10, 0), 0, -1));
        reference.push_back(Vertex45(Point(10, 0), 1, 1));
        reference.push_back(Vertex45(Point(10, 10), 1, 1));
        reference.push_back(Vertex45(Point(10, 10), 0, -1));
        reference.push_back(Vertex45(Point(20, 10), 1, -1));
        reference.push_back(Vertex45(Point(20, 10), 0, 1));
        if(result != reference) {
          stdcout << "result size == " << result.size() << "\n";
          for(std::size_t i = 0; i < result.size(); ++i) {
            //stdcout << "result == " << result[i]<< "\n";
          }
          stdcout << "reference size == " << reference.size() << "\n";
          for(std::size_t i = 0; i < reference.size(); ++i) {
            //stdcout << "reference == " << reference[i]<< "\n";
          }
          return false;
        }
        stdcout << "done testing Scan45P2\n";
        return true;
      }
  
      template <typename streamtype>
      static inline bool testScan45And(streamtype& stdcout) {
        stdcout << "testing Scan45And\n";
        Scan45<Count2, boolean_op_45_output_functor<1> > scan45;
        std::vector<Vertex45 > result;
        typedef std::pair<Point, Scan45Count> Scan45Vertex;
        std::vector<Scan45Vertex> vertices;
        //is a Rectnagle(0, 0, 10, 10);
        Count2 count(1, 0);
        Count2 ncount(-1, 0);
        vertices.push_back(Scan45Vertex(Point(0,0), Scan45Count(Count2(0, 0), count, Count2(0, 0), count)));
        vertices.push_back(Scan45Vertex(Point(0,10), Scan45Count(Count2(0, 0), ncount, Count2(0, 0), ncount)));
        vertices.push_back(Scan45Vertex(Point(10,0), Scan45Count(Count2(0, 0), ncount, Count2(0, 0), ncount)));
        vertices.push_back(Scan45Vertex(Point(10,10), Scan45Count(Count2(0, 0), count, Count2(0, 0), count)));
        count = Count2(0, 1);
        ncount = count.invert();
        vertices.push_back(Scan45Vertex(Point(2,2), Scan45Count(Count2(0, 0), count, Count2(0, 0), count)));
        vertices.push_back(Scan45Vertex(Point(2,12), Scan45Count(Count2(0, 0), ncount, Count2(0, 0), ncount)));
        vertices.push_back(Scan45Vertex(Point(12,2), Scan45Count(Count2(0, 0), ncount, Count2(0, 0), ncount)));
        vertices.push_back(Scan45Vertex(Point(12,12), Scan45Count(Count2(0, 0), count, Count2(0, 0), count)));
        sortScan45Vector(vertices);
        stdcout << "scanning\n";
        scan45.scan(result, vertices.begin(), vertices.end());
        stdcout << "done scanning\n";
        //result size == 8
        //result == 2 2 0 1
        //result == 2 2 2 1
        //result == 2 10 2 -1
        //result == 2 10 0 -1
        //result == 10 2 0 -1
        //result == 10 2 2 -1
        //result == 10 10 2 1
        //result == 10 10 0 1
        std::vector<Vertex45> reference;
        reference.push_back(Vertex45(Point(2, 2), 0, 1));
        reference.push_back(Vertex45(Point(2, 2), 2, 1));
        reference.push_back(Vertex45(Point(2, 10), 2, -1));
        reference.push_back(Vertex45(Point(2, 10), 0, -1));
        reference.push_back(Vertex45(Point(10, 2), 0, -1));
        reference.push_back(Vertex45(Point(10, 2), 2, -1));
        reference.push_back(Vertex45(Point(10, 10), 2, 1));
        reference.push_back(Vertex45(Point(10, 10), 0, 1));
        if(result != reference) {
          stdcout << "result size == " << result.size() << "\n";
          for(std::size_t i = 0; i < result.size(); ++i) {
            //stdcout << "result == " << result[i]<< "\n";
          }
          stdcout << "reference size == " << reference.size() << "\n";
          for(std::size_t i = 0; i < reference.size(); ++i) {
            //stdcout << "reference == " << reference[i]<< "\n";
          }
          return false;
        }
        stdcout << "done testing Scan45And\n";
        return true;
      }
  
      template <typename stream_type>
      static inline bool testScan45Star1(stream_type& stdcout) {
        stdcout << "testing Scan45Star1\n";
        Scan45<Count2, boolean_op_45_output_functor<0> > scan45;
        std::vector<Vertex45 > result;
        typedef std::pair<Point, Scan45Count> Scan45Vertex;
        std::vector<Scan45Vertex> vertices;
        //is a Rectnagle(0, 0, 10, 10);
        Count2 count(1, 0);
        Count2 ncount(-1, 0);
        vertices.push_back(Scan45Vertex(Point(0,8), Scan45Count(count, Count2(0, 0), ncount, Count2(0, 0))));
        vertices.push_back(Scan45Vertex(Point(8,0), Scan45Count(ncount, Count2(0, 0), Count2(0, 0), ncount)));
        vertices.push_back(Scan45Vertex(Point(8,16), Scan45Count(Count2(0, 0), Count2(0, 0), count, count)));
        count = Count2(0, 1);
        ncount = count.invert();
        vertices.push_back(Scan45Vertex(Point(12,8), Scan45Count(count, Count2(0, 0), ncount, Count2(0, 0))));
        vertices.push_back(Scan45Vertex(Point(4,0), Scan45Count(Count2(0, 0), Count2(0, 0), count, count)));
        vertices.push_back(Scan45Vertex(Point(4,16), Scan45Count(ncount, Count2(0, 0), Count2(0, 0), ncount)));
        sortScan45Vector(vertices);
        stdcout << "scanning\n";
        scan45.scan(result, vertices.begin(), vertices.end());
        stdcout << "done scanning\n";
        // result size == 24
        // result == 0 8 -1 1
        // result == 0 8 1 -1
        // result == 4 0 1 1
        // result == 4 0 2 1
        // result == 4 4 2 -1
        // result == 4 4 -1 -1
        // result == 4 12 1 1
        // result == 4 12 2 1
        // result == 4 16 2 -1
        // result == 4 16 -1 -1
        // result == 6 2 1 -1
        // result == 6 14 -1 1
        // result == 6 2 -1 1
        // result == 6 14 1 -1
        // result == 8 0 -1 -1
        // result == 8 0 2 -1
        // result == 8 4 2 1
        // result == 8 4 1 1
        // result == 8 12 -1 -1
        // result == 8 12 2 -1
        // result == 8 16 2 1
        // result == 8 16 1 1
        // result == 12 8 1 -1
        // result == 12 8 -1 1
        if(result.size() != 24) {
          //stdcout << "result size == " << result.size() << "\n";
          //stdcout << "reference size == " << 24 << "\n";
          return false;
        }
        stdcout << "done testing Scan45Star1\n";
        return true;
      }
  
      template <typename stream_type>
      static inline bool testScan45Star2(stream_type& stdcout) {
        stdcout << "testing Scan45Star2\n";
        Scan45<Count2, boolean_op_45_output_functor<0> > scan45;
        std::vector<Vertex45 > result;
        typedef std::pair<Point, Scan45Count> Scan45Vertex;
        std::vector<Scan45Vertex> vertices;
        //is a Rectnagle(0, 0, 10, 10);
        Count2 count(1, 0);
        Count2 ncount(-1, 0);
        vertices.push_back(Scan45Vertex(Point(0,4), Scan45Count(Count2(0, 0), count, ncount, Count2(0, 0))));
        vertices.push_back(Scan45Vertex(Point(16,4), Scan45Count(count, ncount, Count2(0, 0), Count2(0, 0))));
        vertices.push_back(Scan45Vertex(Point(8,12), Scan45Count(ncount, Count2(0, 0), count, Count2(0, 0))));
        count = Count2(0, 1);
        ncount = count.invert();
        vertices.push_back(Scan45Vertex(Point(0,8), Scan45Count(count, ncount, Count2(0, 0), Count2(0, 0))));
        vertices.push_back(Scan45Vertex(Point(16,8), Scan45Count(Count2(0, 0), count, ncount, Count2(0, 0))));
        vertices.push_back(Scan45Vertex(Point(8,0), Scan45Count(ncount, Count2(0, 0), count, Count2(0, 0))));
        sortScan45Vector(vertices);
        stdcout << "scanning\n";
        scan45.scan(result, vertices.begin(), vertices.end());
        stdcout << "done scanning\n";
        // result size == 24
        // result == 0 4 0 1
        // result == 0 4 1 -1
        // result == 0 8 -1 1
        // result == 0 8 0 -1
        // result == 2 6 1 1
        // result == 2 6 -1 -1
        // result == 4 4 0 -1
        // result == 4 8 0 1
        // result == 4 4 -1 1
        // result == 4 8 1 -1
        // result == 8 0 -1 -1
        // result == 8 0 1 1
        // result == 8 12 1 1
        // result == 8 12 -1 -1
        // result == 12 4 1 -1
        // result == 12 8 -1 1
        // result == 12 4 0 1
        // result == 12 8 0 -1
        // result == 14 6 -1 -1
        // result == 14 6 1 1
        // result == 16 4 0 -1
        // result == 16 4 -1 1
        // result == 16 8 1 -1
        // result == 16 8 0 1
        if(result.size() != 24) {
          //std::cout << "result size == " << result.size() << "\n";
          //std::cout << "reference size == " << 24 << "\n";
          return false;
        }
        stdcout << "done testing Scan45Star2\n";
        return true;
      }
  
      template <typename stream_type>
      static inline bool testScan45Star3(stream_type& stdcout) {
        stdcout << "testing Scan45Star3\n";
        Scan45<Count2, boolean_op_45_output_functor<0> > scan45;
        std::vector<Vertex45 > result;
        typedef std::pair<Point, Scan45Count> Scan45Vertex;
        std::vector<Scan45Vertex> vertices;
        //is a Rectnagle(0, 0, 10, 10);
        Count2 count(1, 0);
        Count2 ncount(-1, 0);
        vertices.push_back(Scan45Vertex(Point(0,8), Scan45Count(count, Count2(0, 0), ncount, Count2(0, 0))));
        vertices.push_back(Scan45Vertex(Point(8,0), Scan45Count(ncount, Count2(0, 0), Count2(0, 0), ncount)));
        vertices.push_back(Scan45Vertex(Point(8,16), Scan45Count(Count2(0, 0), Count2(0, 0), count, count)));
  
        vertices.push_back(Scan45Vertex(Point(6,0), Scan45Count(Count2(0, 0), count, Count2(0, 0), count)));
        vertices.push_back(Scan45Vertex(Point(6,14), Scan45Count(Count2(0, 0), ncount, Count2(0, 0), ncount)));
        vertices.push_back(Scan45Vertex(Point(12,0), Scan45Count(Count2(0, 0), ncount, Count2(0, 0), ncount)));
        vertices.push_back(Scan45Vertex(Point(12,14), Scan45Count(Count2(0, 0), count, Count2(0, 0), count)));
        count = Count2(0, 1);
        ncount = count.invert();
        vertices.push_back(Scan45Vertex(Point(12,8), Scan45Count(count, Count2(0, 0), ncount, Count2(0, 0))));
        vertices.push_back(Scan45Vertex(Point(4,0), Scan45Count(Count2(0, 0), Count2(0, 0), count, count)));
        vertices.push_back(Scan45Vertex(Point(4,16), Scan45Count(ncount, Count2(0, 0), Count2(0, 0), ncount)));
        sortScan45Vector(vertices);
        stdcout << "scanning\n";
        scan45.scan(result, vertices.begin(), vertices.end());
        stdcout << "done scanning\n";
        // result size == 28
        // result == 0 8 -1 1
        // result == 0 8 1 -1
        // result == 4 0 1 1
        // result == 4 0 2 1
        // result == 4 4 2 -1
        // result == 4 4 -1 -1
        // result == 4 12 1 1
        // result == 4 12 2 1
        // result == 4 16 2 -1
        // result == 4 16 -1 -1
        // result == 6 2 1 -1
        // result == 6 14 -1 1
        // result == 6 0 0 1
        // result == 6 0 2 1
        // result == 6 2 2 -1
        // result == 6 14 1 -1
        // result == 8 0 0 -1
        // result == 8 0 0 1
        // result == 8 14 0 -1
        // result == 8 14 2 -1
        // result == 8 16 2 1
        // result == 8 16 1 1
        // result == 12 0 0 -1
        // result == 12 0 2 -1
        // result == 12 8 2 1
        // result == 12 8 2 -1
        // result == 12 14 2 1
        // result == 12 14 0 1
        if(result.size() != 28) {
          //std::cout << "result size == " << result.size() << "\n";
          //std::cout << "reference size == " << 28 << "\n";
          return false;
        }
  
        stdcout << "done testing Scan45Star3\n";
        return true;
      }
  
  
      template <typename stream_type>
      static inline bool testScan45Star4(stream_type& stdcout) {
        stdcout << "testing Scan45Star4\n";
        Scan45<Count2, boolean_op_45_output_functor<0> > scan45;
        std::vector<Vertex45 > result;
        typedef std::pair<Point, Scan45Count> Scan45Vertex;
        std::vector<Scan45Vertex> vertices;
        //is a Rectnagle(0, 0, 10, 10);
        Count2 count(1, 0);
        Count2 ncount(-1, 0);
        vertices.push_back(Scan45Vertex(Point(0,4), Scan45Count(Count2(0, 0), count, ncount, Count2(0, 0))));
        vertices.push_back(Scan45Vertex(Point(16,4), Scan45Count(count, ncount, Count2(0, 0), Count2(0, 0))));
        vertices.push_back(Scan45Vertex(Point(8,12), Scan45Count(ncount, Count2(0, 0), count, Count2(0, 0))));
  
        vertices.push_back(Scan45Vertex(Point(0,6), Scan45Count(Count2(0, 0), count, Count2(0, 0), count)));
        vertices.push_back(Scan45Vertex(Point(0,12), Scan45Count(Count2(0, 0), ncount, Count2(0, 0), ncount)));
        vertices.push_back(Scan45Vertex(Point(16,6), Scan45Count(Count2(0, 0), ncount, Count2(0, 0), ncount)));
        vertices.push_back(Scan45Vertex(Point(16,12), Scan45Count(Count2(0, 0), count, Count2(0, 0), count)));
        count = Count2(0, 1);
        ncount = count.invert();
        vertices.push_back(Scan45Vertex(Point(0,8), Scan45Count(count, ncount, Count2(0, 0), Count2(0, 0))));
        vertices.push_back(Scan45Vertex(Point(16,8), Scan45Count(Count2(0, 0), count, ncount, Count2(0, 0))));
        vertices.push_back(Scan45Vertex(Point(8,0), Scan45Count(ncount, Count2(0, 0), count, Count2(0, 0))));
        sortScan45Vector(vertices);
        stdcout << "scanning\n";
        scan45.scan(result, vertices.begin(), vertices.end());
        stdcout << "done scanning\n";
        // result size == 28
        // result == 0 4 0 1
        // result == 0 4 1 -1
        // result == 0 6 0 1
        // result == 0 6 2 1
        // result == 0 8 2 -1
        // result == 0 8 2 1
        // result == 0 12 2 -1
        // result == 0 12 0 -1
        // result == 2 6 1 1
        // result == 2 6 0 -1
        // result == 4 4 0 -1
        // result == 4 4 -1 1
        // result == 8 12 0 1
        // result == 8 0 -1 -1
        // result == 8 0 1 1
        // result == 8 12 0 -1
        // result == 12 4 1 -1
        // result == 12 4 0 1
        // result == 14 6 -1 -1
        // result == 14 6 0 1
        // result == 16 4 0 -1
        // result == 16 4 -1 1
        // result == 16 6 0 -1
        // result == 16 6 2 -1
        // result == 16 8 2 1
        // result == 16 8 2 -1
        // result == 16 12 2 1
        // result == 16 12 0 1
        if(result.size() != 28) {
          //stdcout << "result size == " << result.size() << "\n";
          //stdcout << "reference size == " << 28 << "\n";
          return false;
        }
  
        stdcout << "done testing Scan45Star4\n";
        return true;
      }
  
      template <typename stream_type>
      static inline bool testScan45(stream_type& stdcout) {
        if(!testScan45Rect(stdcout)) return false;
        if(!testScan45P1(stdcout)) return false;
        if(!testScan45P2(stdcout)) return false;
        if(!testScan45And(stdcout)) return false;
        if(!testScan45Star1(stdcout)) return false;
        if(!testScan45Star2(stdcout)) return false;
        if(!testScan45Star3(stdcout)) return false;
        if(!testScan45Star4(stdcout)) return false;
        return true;
      }
  
    };
  
  }
  
  }
  #endif
  