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 /*
   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:
       typedef Scan45Element first_argument_type;
       typedef Scan45Element second_argument_type;
       typedef bool result_type;
       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:
       typedef Point first_argument_type;
       typedef Point second_argument_type;
       typedef bool result_type;
         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

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