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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).
 */
 #include<iostream>
 #include<cassert>
 #ifndef BOOST_POLYGON_POLYGON_FORMATION_HPP
 #define BOOST_POLYGON_POLYGON_FORMATION_HPP
 namespace boost { namespace polygon{
 
 namespace polygon_formation {
 
   /*
    * End has two states, HEAD and TAIL as is represented by a bool
    */
   typedef bool End;
 
   /*
    * HEAD End is represented as false because it is the lesser state
    */
   const End HEAD = false;
 
   /*
    * TAIL End is represented by true because TAIL comes after head and 1 after 0
    */
   const End TAIL = true;
 
   /*
    * 2D turning direction, left and right sides (is a boolean value since it has two states.)
    */
   typedef bool Side;
 
   /*
    * LEFT Side is 0 because we inuitively think left to right; left < right
    */
   const Side LEFT = false;
 
   /*
    * RIGHT Side is 1 so that right > left
    */
   const Side RIGHT = true;
 
   /*
    * The PolyLine class is data storage and services for building and representing partial polygons.
    * As the polyline is added to it extends its storage to accomodate the data.
    * PolyLines can be joined head-to-head/head-to-tail when it is determined that two polylines are
    * part of the same polygon.
    * PolyLines keep state information about what orientation their incomplete head and tail geometry have,
    * which side of the polyline is solid and whether the polyline is joined head-to-head and tail-to-head.
    * PolyLines have nothing whatsoever to do with holes.
    * It may be valuable to collect a histogram of PolyLine lengths used by an algorithm on its typical data
    * sets and tune the allocation of the initial vector of coordinate data to be greater than or equal to
    * the mean, median, mode, or mean plus some number of standard deviation, or just generally large enough
    * to prevent too much unnecesary reallocations, but not too big that it wastes a lot of memory and degrades cache
    * performance.
    */
   template <typename Unit>
   class PolyLine {
   private:
     //data
 
     /*
      * ptdata_ a vector of coordiantes
      * if VERTICAL_HEAD, first coordiante is an X
      * else first coordinate is a Y
      */
     std::vector<Unit> ptdata_;
 
     /*
      * head and tail points to other polylines before and after this in a chain
      */
     PolyLine* headp_;
     PolyLine* tailp_;
 
     /*
      * state bitmask
      * bit zero is orientation, 0 H, 1 V
      * bit 1 is head connectivity, 0 for head, 1 for tail
      * bit 2 is tail connectivity, 0 for head, 1 for tail
      * bit 3 is solid to left of PolyLine when 1, right when 0
      */
     int state_;
 
   public:
     /*
      * default constructor (for preallocation)
      */
     PolyLine();
 
     /*
      * constructor that takes the orientation, coordiante and side to which there is solid
      */
     PolyLine(orientation_2d orient, Unit coord, Side side);
 
     //copy constructor
     PolyLine(const PolyLine& pline);
 
     //destructor
     ~PolyLine();
 
     //assignment operator
     PolyLine& operator=(const PolyLine& that);
 
     //equivalence operator
     bool operator==(const PolyLine& b) const;
 
     /*
      * valid PolyLine (only default constructed polylines are invalid.)
      */
     bool isValid() const;
 
     /*
      * Orientation of Head
      */
     orientation_2d headOrient() const;
 
     /*
      * returns true if first coordinate is an X value (first segment is vertical)
      */
     bool verticalHead() const;
 
     /*
      * returns the orientation_2d fo the tail
      */
     orientation_2d tailOrient() const;
 
     /*
      * returns true if last coordinate is an X value (last segment is vertical)
      */
     bool verticalTail() const;
 
     /*
      * retrun true if PolyLine has odd number of coordiantes
      */
     bool oddLength() const;
 
     /*
      * retrun the End of the other polyline that the specified end of this polyline is connected to
      */
     End endConnectivity(End end) const;
 
     /*
      * retrun true if the head of this polyline is connect to the tail of a polyline
      */
     bool headToTail() const;
     /*
      * retrun true if the head of this polyline is connect to the head of a polyline
      */
     bool headToHead() const;
 
     /*
      * retrun true if the tail of this polyline is connect to the tail of a polyline
      */
     bool tailToTail() const;
     /*
      * retrun true if the tail of this polyline is connect to the head of a polyline
      */
     bool tailToHead() const;
 
     /*
      * retrun the side on which there is solid for this polyline
      */
     Side solidSide() const;
 
     /*
      * retrun true if there is solid to the right of this polyline
      */
     bool solidToRight() const;
 
     /*
      * returns true if the polyline tail is not connected
      */
     bool active() const;
 
     /*
      * adds a coordinate value to the end of the polyline changing the tail orientation
      */
     PolyLine& pushCoordinate(Unit coord);
 
     /*
      * removes a coordinate value at the end of the polyline changing the tail orientation
      */
     PolyLine& popCoordinate();
 
     /*
      * extends the tail of the polyline to include the point, changing orientation if needed
      */
     PolyLine& pushPoint(const point_data<Unit>& point);
 
     /*
      * changes the last coordinate of the tail of the polyline by the amount of the delta
      */
     PolyLine& extendTail(Unit delta);
 
     /*
      * join thisEnd of this polyline to that polyline's end
      */
     PolyLine& joinTo(End thisEnd, PolyLine& that, End end);
 
     /*
      * join an end of this polyline to the tail of that polyline
      */
     PolyLine& joinToTail(PolyLine& that, End end);
 
     /*
      * join an end of this polyline to the head of that polyline
      */
     PolyLine& joinToHead(PolyLine& that, End end);
 
     /*
      * join the head of this polyline to the head of that polyline
      */
     //join this to that in the given way
     PolyLine& joinHeadToHead(PolyLine& that);
 
     /*
      * join the head of this polyline to the tail of that polyline
      */
     PolyLine& joinHeadToTail(PolyLine& that);
 
     /*
      * join the tail of this polyline to the head of that polyline
      */
     PolyLine& joinTailToHead(PolyLine& that);
 
     /*
      * join the tail of this polyline to the tail of that polyline
      */
     PolyLine& joinTailToTail(PolyLine& that);
 
     /*
      * dissconnect the tail at the end of the polygon
      */
     PolyLine& disconnectTails();
 
     /*
      * get the coordinate at one end of this polyline, by default the tail end
      */
     Unit getEndCoord(End end = TAIL) const;
 
     /*
      * get the point on the polyline at the given index (polylines have the same number of coordinates as points
      */
     point_data<Unit> getPoint(unsigned int index) const;
 
     /*
      * get the point on one end of the polyline, by default the tail
      */
     point_data<Unit> getEndPoint(End end = TAIL) const;
 
     /*
      * get the orientation of a segment by index
      */
     orientation_2d segmentOrient(unsigned int index = 0) const;
 
     /*
      * get a coordinate by index using the square bracket operator
      */
     Unit operator[] (unsigned int index) const;
 
     /*
      * get the number of segments/points/coordinates in the polyline
      */
     unsigned int numSegments() const;
 
     /*
      * get the pointer to the next polyline at one end of this
      */
     PolyLine* next(End end) const;
 
     /*
      * write out coordinates of this and all attached polylines to a single vector
      */
     PolyLine* writeOut(std::vector<Unit>& outVec, End startEnd = TAIL) const;
 
   private:
     //methods
     PolyLine& joinTo_(End thisEnd, PolyLine& that, End end);
   };
 
   //forward declaration
   template<bool orientT, typename Unit>
   class PolyLinePolygonData;
 
   //forward declaration
   template<bool orientT, typename Unit>
   class PolyLinePolygonWithHolesData;
 
   /*
    * ActiveTail represents an edge of an incomplete polygon.
    *
    * An ActiveTail object is the active tail end of a polyline object, which may (should) be the attached to
    * a chain of polyline objects through a pointer.  The ActiveTail class provides an abstraction between
    * and algorithm that builds polygons and the PolyLine data representation of incomplete polygons that are
    * being built.  It does this by providing an iterface to access the information about the last edge at the
    * tail of the PolyLine it is associated with.  To a polygon constructing algorithm, an ActiveTail is a floating
    * edge of an incomplete polygon and has an orientation and coordinate value, as well as knowing which side of
    * that edge is supposed to be solid or space.  Any incomplete polygon will have two active tails.  Active tails
    * may be joined together to merge two incomplete polygons into a larger incomplete polygon.  If two active tails
    * that are to be merged are the oppositve ends of the same incomplete polygon that indicates that the polygon
    * has been closed and is complete.  The active tail keeps a pointer to the other active tail of its incomplete
    * polygon so that it is easy to check this condition.  These pointers are updated when active tails are joined.
    * The active tail also keeps a list of pointers to active tail objects that serve as handles to closed holes.  In
    * this way a hole can be associated to another incomplete polygon, which will eventually be its enclosing shell,
    * or reassociate the hole to another incomplete polygon in the case that it become a hole itself.  Alternately,
    * the active tail may add a filiment to stitch a hole into a shell and "fracture" the hole out of the interior
    * of a polygon.  The active tail maintains a static output buffer to temporarily write polygon data to when
    * it outputs a figure so that outputting a polygon does not require the allocation of a temporary buffer.  This
    * static buffer should be destroyed whenever the program determines that it won't need it anymore and would prefer to
    * release the memory it has allocated back to the system.
    */
   template <typename Unit>
   class ActiveTail {
   private:
     //data
     PolyLine<Unit>* tailp_;
     ActiveTail *otherTailp_;
     std::list<ActiveTail*> holesList_;
     //Sum of all the polylines which constitute the active tail (including holes)//
     size_t polyLineSize_;
   public:
 
     inline size_t getPolyLineSize(){
        return polyLineSize_;
     }
 
     inline void setPolyLineSize(int delta){
        polyLineSize_ = delta;
     }
 
     inline void addPolyLineSize(int delta){
        polyLineSize_ += delta;
     }
 
     /*
      * iterator over coordinates of the figure
      */
     class iterator {
     private:
       const PolyLine<Unit>* pLine_;
       const PolyLine<Unit>* pLineEnd_;
       unsigned int index_;
       unsigned int indexEnd_;
       End startEnd_;
     public:
       inline iterator() : pLine_(), pLineEnd_(), index_(), indexEnd_(), startEnd_() {}
       inline iterator(const ActiveTail* at, bool isHole, orientation_2d orient) :
         pLine_(), pLineEnd_(), index_(), indexEnd_(), startEnd_() {
         //if it is a hole and orientation is vertical or it is not a hole and orientation is horizontal
         //we want to use this active tail, otherwise we want to use the other active tail
         startEnd_ = TAIL;
         if(!isHole ^ (orient == HORIZONTAL)) {
           //switch winding direction
           at = at->getOtherActiveTail();
         }
         //now we have the right winding direction
         //if it is horizontal we need to skip the first element
         pLine_ = at->getTail();
 
         if(at->getTail()->numSegments() > 0)
          index_ = at->getTail()->numSegments() - 1;
 
         if((at->getOrient() == HORIZONTAL) ^ (orient == HORIZONTAL)) {
           pLineEnd_ = at->getTail();
           indexEnd_ = pLineEnd_->numSegments() - 1;
           if(index_ == 0) {
             pLine_ = at->getTail()->next(HEAD);
             if(at->getTail()->endConnectivity(HEAD) == TAIL) {
               index_ = pLine_->numSegments() -1;
             } else {
               startEnd_ = HEAD;
               index_ = 0;
             }
           } else { --index_; }
         } else {
           pLineEnd_ = at->getOtherActiveTail()->getTail();
           if(pLineEnd_->numSegments() > 0)
           indexEnd_ = pLineEnd_->numSegments() - 1;
         }
         at->getTail()->joinTailToTail(*(at->getOtherActiveTail()->getTail()));
       }
 
       inline size_t size(void){
         size_t count = 0;
         End dir = startEnd_;
         PolyLine<Unit> const * currLine = pLine_;
         size_t ops = 0;
         while(currLine != pLineEnd_){
            ops++;
            count += currLine->numSegments();
            currLine = currLine->next(dir == HEAD ? TAIL : HEAD);
            dir = currLine->endConnectivity(dir == HEAD ? TAIL : HEAD);
         }
         count += pLineEnd_->numSegments();
         return count; //no. of vertices
       }
 
       //use bitwise copy and assign provided by the compiler
       inline iterator& operator++() {
         if(pLine_ == pLineEnd_ && index_ == indexEnd_) {
           pLine_ = 0;
           index_ = 0;
           return *this;
         }
         if(startEnd_ == HEAD) {
           ++index_;
           if(index_ == pLine_->numSegments()) {
             End end = pLine_->endConnectivity(TAIL);
             pLine_ = pLine_->next(TAIL);
             if(end == TAIL) {
               startEnd_ = TAIL;
               index_ = pLine_->numSegments() -1;
             } else {
               index_ = 0;
             }
           }
         } else {
           if(index_ == 0) {
             End end = pLine_->endConnectivity(HEAD);
             pLine_ = pLine_->next(HEAD);
             if(end == TAIL) {
               index_ = pLine_->numSegments() -1;
             } else {
               startEnd_ = HEAD;
               index_ = 0;
             }
           } else {
             --index_;
           }
         }
         return *this;
       }
       inline const iterator operator++(int) {
         iterator tmp(*this);
         ++(*this);
         return tmp;
       }
       inline bool operator==(const iterator& that) const {
         return pLine_ == that.pLine_ && index_ == that.index_;
       }
       inline bool operator!=(const iterator& that) const {
         return pLine_ != that.pLine_ || index_ != that.index_;
       }
       inline Unit operator*() { return (*pLine_)[index_]; }
     };
 
     /*
      * iterator over holes contained within the figure
      */
     typedef typename std::list<ActiveTail*>::const_iterator iteratorHoles;
 
     //default constructor
     ActiveTail();
 
     //constructor
     ActiveTail(orientation_2d orient, Unit coord, Side solidToRight, ActiveTail* otherTailp);
 
     //constructor
     ActiveTail(PolyLine<Unit>* active, ActiveTail* otherTailp);
 
     //copy constructor
     ActiveTail(const ActiveTail& that);
 
     //destructor
     ~ActiveTail();
 
     //assignment operator
     ActiveTail& operator=(const ActiveTail& that);
 
     //equivalence operator
     bool operator==(const ActiveTail& b) const;
 
     /*
      * comparison operators, ActiveTail objects are sortable by geometry
      */
     bool operator<(const ActiveTail& b) const;
     bool operator<=(const ActiveTail& b) const;
     bool operator>(const ActiveTail& b) const;
     bool operator>=(const ActiveTail& b) const;
 
     /*
      * get the pointer to the polyline that this is an active tail of
      */
     PolyLine<Unit>* getTail() const;
 
     /*
      * get the pointer to the polyline at the other end of the chain
      */
     PolyLine<Unit>* getOtherTail() const;
 
     /*
      * get the pointer to the activetail at the other end of the chain
      */
     ActiveTail* getOtherActiveTail() const;
 
     /*
      * test if another active tail is the other end of the chain
      */
     bool isOtherTail(const ActiveTail& b);
 
     /*
      * update this end of chain pointer to new polyline
      */
     ActiveTail& updateTail(PolyLine<Unit>* newTail);
 
     /*
      * associate a hole to this active tail by the specified policy
      */
     ActiveTail* addHole(ActiveTail* hole, bool fractureHoles);
 
     /*
      * get the list of holes
      */
     const std::list<ActiveTail*>& getHoles() const;
 
     /*
      * copy holes from that to this
      */
     void copyHoles(ActiveTail& that);
 
     /*
      * find out if solid to right
      */
     bool solidToRight() const;
 
     /*
      * get coordinate (getCoord and getCoordinate are aliases for eachother)
      */
     Unit getCoord() const;
     Unit getCoordinate() const;
 
     /*
      * get the tail orientation
      */
     orientation_2d getOrient() const;
 
     /*
      * add a coordinate to the polygon at this active tail end, properly handle degenerate edges by removing redundant coordinate
      */
     void pushCoordinate(Unit coord);
 
     /*
      * write the figure that this active tail points to out to the temp buffer
      */
     void writeOutFigure(std::vector<Unit>& outVec, bool isHole = false) const;
 
     /*
      * write the figure that this active tail points to out through iterators
      */
     void writeOutFigureItrs(iterator& beginOut, iterator& endOut, bool isHole = false, orientation_2d orient = VERTICAL) const;
     iterator begin(bool isHole, orientation_2d orient) const;
     iterator end() const;
 
     /*
      * write the holes that this active tail points to out through iterators
      */
     void writeOutFigureHoleItrs(iteratorHoles& beginOut, iteratorHoles& endOut) const;
     iteratorHoles beginHoles() const;
     iteratorHoles endHoles() const;
 
     /*
      * joins the two chains that the two active tail tails are ends of
      * checks for closure of figure and writes out polygons appropriately
      * returns a handle to a hole if one is closed
      */
     static ActiveTail* joinChains(ActiveTail* at1, ActiveTail* at2, bool solid, std::vector<Unit>& outBufferTmp);
     template <typename PolygonT>
     static ActiveTail* joinChains(ActiveTail* at1, ActiveTail* at2, bool solid, typename std::vector<PolygonT>& outBufferTmp);
 
     /*
      * deallocate temp buffer
      */
     static void destroyOutBuffer();
 
     /*
      * deallocate all polygon data this active tail points to (deep delete, call only from one of a pair of active tails)
      */
     void destroyContents();
   };
 
   /* allocate a polyline object */
   template <typename Unit>
   PolyLine<Unit>* createPolyLine(orientation_2d orient, Unit coord, Side side);
 
   /* deallocate a polyline object */
   template <typename Unit>
   void destroyPolyLine(PolyLine<Unit>* pLine);
 
   /* allocate an activetail object */
   template <typename Unit>
   ActiveTail<Unit>* createActiveTail();
 
   /* deallocate an activetail object */
   template <typename Unit>
   void destroyActiveTail(ActiveTail<Unit>* aTail);
 
   template<bool orientT, typename Unit>
   class PolyLineHoleData {
   private:
     ActiveTail<Unit>* p_;
   public:
     typedef Unit coordinate_type;
     typedef typename ActiveTail<Unit>::iterator compact_iterator_type;
     typedef iterator_compact_to_points<compact_iterator_type, point_data<coordinate_type> > iterator_type;
     inline PolyLineHoleData() : p_(0) {}
     inline PolyLineHoleData(ActiveTail<Unit>* p) : p_(p) {}
     //use default copy and assign
     inline compact_iterator_type begin_compact() const { return p_->begin(true, (orientT ? VERTICAL : HORIZONTAL)); }
     inline compact_iterator_type end_compact() const { return p_->end(); }
     inline iterator_type begin() const { return iterator_type(begin_compact(), end_compact()); }
     inline iterator_type end() const { return iterator_type(end_compact(), end_compact()); }
     inline std::size_t size() const {
        return p_->getPolyLineSize();
     }
     inline ActiveTail<Unit>* yield() { return p_; }
   };
 
   template<bool orientT, typename Unit>
   class PolyLinePolygonWithHolesData {
   private:
     ActiveTail<Unit>* p_;
   public:
     typedef Unit coordinate_type;
     typedef typename ActiveTail<Unit>::iterator compact_iterator_type;
     typedef iterator_compact_to_points<compact_iterator_type, point_data<coordinate_type> > iterator_type;
     typedef PolyLineHoleData<orientT, Unit> hole_type;
     typedef typename coordinate_traits<Unit>::area_type area_type;
     class iteratorHoles {
     private:
       typename ActiveTail<Unit>::iteratorHoles itr_;
     public:
       inline iteratorHoles() : itr_() {}
       inline iteratorHoles(typename ActiveTail<Unit>::iteratorHoles itr) : itr_(itr) {}
       //use bitwise copy and assign provided by the compiler
       inline iteratorHoles& operator++() {
         ++itr_;
         return *this;
       }
       inline const iteratorHoles operator++(int) {
         iteratorHoles tmp(*this);
         ++(*this);
         return tmp;
       }
       inline bool operator==(const iteratorHoles& that) const {
         return itr_ == that.itr_;
       }
       inline bool operator!=(const iteratorHoles& that) const {
         return itr_ != that.itr_;
       }
       inline PolyLineHoleData<orientT, Unit> operator*() { return PolyLineHoleData<orientT, Unit>(*itr_);}
     };
     typedef iteratorHoles iterator_holes_type;
 
     inline PolyLinePolygonWithHolesData() : p_(0) {}
     inline PolyLinePolygonWithHolesData(ActiveTail<Unit>* p) : p_(p) {}
     //use default copy and assign
     inline compact_iterator_type begin_compact() const { return p_->begin(false, (orientT ? VERTICAL : HORIZONTAL)); }
     inline compact_iterator_type end_compact() const { return p_->end(); }
     inline iterator_type begin() const { return iterator_type(begin_compact(), end_compact()); }
     inline iterator_type end() const { return iterator_type(end_compact(), end_compact()); }
     inline iteratorHoles begin_holes() const { return iteratorHoles(p_->beginHoles()); }
     inline iteratorHoles end_holes() const { return iteratorHoles(p_->endHoles()); }
     inline ActiveTail<Unit>* yield() { return p_; }
     //stub out these four required functions that will not be used but are needed for the interface
     inline std::size_t size_holes() const { return 0; }
     inline std::size_t size() const { return 0; }
   };
 
 
   template <bool orientT, typename Unit, typename polygon_concept_type>
   struct PolyLineType { };
   template <bool orientT, typename Unit>
   struct PolyLineType<orientT, Unit, polygon_90_with_holes_concept> { typedef PolyLinePolygonWithHolesData<orientT, Unit> type; };
   template <bool orientT, typename Unit>
   struct PolyLineType<orientT, Unit, polygon_45_with_holes_concept> { typedef PolyLinePolygonWithHolesData<orientT, Unit> type; };
   template <bool orientT, typename Unit>
   struct PolyLineType<orientT, Unit, polygon_with_holes_concept> { typedef PolyLinePolygonWithHolesData<orientT, Unit> type; };
   template <bool orientT, typename Unit>
   struct PolyLineType<orientT, Unit, polygon_90_concept> { typedef PolyLineHoleData<orientT, Unit> type; };
   template <bool orientT, typename Unit>
   struct PolyLineType<orientT, Unit, polygon_45_concept> { typedef PolyLineHoleData<orientT, Unit> type; };
   template <bool orientT, typename Unit>
   struct PolyLineType<orientT, Unit, polygon_concept> { typedef PolyLineHoleData<orientT, Unit> type; };
 
   template <bool orientT, typename Unit, typename polygon_concept_type>
   class ScanLineToPolygonItrs {
   private:
     std::map<Unit, ActiveTail<Unit>*> tailMap_;
     typedef typename PolyLineType<orientT, Unit, polygon_concept_type>::type PolyLinePolygonData;
     std::vector<PolyLinePolygonData> outputPolygons_;
     bool fractureHoles_;
   public:
     typedef typename std::vector<PolyLinePolygonData>::iterator iterator;
     inline ScanLineToPolygonItrs() : tailMap_(), outputPolygons_(), fractureHoles_(false)  {}
     /* construct a scanline with the proper offsets, protocol and options */
     inline ScanLineToPolygonItrs(bool fractureHoles) : tailMap_(), outputPolygons_(), fractureHoles_(fractureHoles) {}
 
     ~ScanLineToPolygonItrs() { clearOutput_(); }
 
     /* process all vertical edges, left and right, at a unique x coordinate, edges must be sorted low to high */
     void processEdges(iterator& beginOutput, iterator& endOutput,
                       Unit currentX, std::vector<interval_data<Unit> >& leftEdges,
                       std::vector<interval_data<Unit> >& rightEdges,
                       size_t vertexThreshold=(std::numeric_limits<size_t>::max)() );
 
    /**********************************************************************
     *methods implementing new polygon formation code
     *
     **********************************************************************/
     void updatePartialSimplePolygonsWithRightEdges(Unit currentX,
          const std::vector<interval_data<Unit> >& leftEdges, size_t threshold);
 
     void updatePartialSimplePolygonsWithLeftEdges(Unit currentX,
          const std::vector<interval_data<Unit> >& leftEdges, size_t threshold);
 
     void closePartialSimplePolygon(Unit, ActiveTail<Unit>*, ActiveTail<Unit>*);
 
     void maintainPartialSimplePolygonInvariant(iterator& ,iterator& ,Unit,
          const std::vector<interval_data<Unit> >&,
          const std::vector<interval_data<Unit> >&,
          size_t vertexThreshold=(std::numeric_limits<size_t>::max)());
 
     void insertNewLeftEdgeIntoTailMap(Unit, Unit, Unit,
       typename std::map<Unit, ActiveTail<Unit>*>::iterator &);
     /**********************************************************************/
 
     inline size_t getTailMapSize(){
        typename std::map<Unit, ActiveTail<Unit>* >::const_iterator itr;
        size_t tsize = 0;
        for(itr=tailMap_.begin(); itr!=tailMap_.end(); ++itr){
           tsize +=  (itr->second)->getPolyLineSize();
        }
        return tsize;
     }
    /*print the active tails in this map:*/
    inline void print(){
       typename std::map<Unit, ActiveTail<Unit>* >::const_iterator itr;
       printf("=========TailMap[%lu]=========\n", tailMap_.size());
       for(itr=tailMap_.begin(); itr!=tailMap_.end(); ++itr){
          std::cout<< "[" << itr->first << "] : " << std::endl;
          //print active tail//
          ActiveTail<Unit> const *t = (itr->second);
          PolyLine<Unit> const *pBegin = t->getTail();
          PolyLine<Unit> const *pEnd = t->getOtherActiveTail()->getTail();
          std::string sorient = pBegin->solidToRight() ? "RIGHT" : "LEFT";
          std::cout<< " ActiveTail.tailp_ (solid= " << sorient ;
          End dir = TAIL;
          while(pBegin!=pEnd){
             std::cout << pBegin  << "={ ";
             for(size_t i=0; i<pBegin->numSegments(); i++){
                point_data<Unit> u = pBegin->getPoint(i);
                std::cout << "(" << u.x() << "," << u.y() << ") ";
             }
             std::cout << "}  ";
             pBegin = pBegin->next(dir == HEAD ? TAIL : HEAD);
             dir = pBegin->endConnectivity(dir == HEAD ? TAIL : HEAD);
          }
          if(pEnd){
             std::cout << pEnd << "={ ";
             for(size_t i=0; i<pEnd->numSegments(); i++){
                point_data<Unit> u = pEnd->getPoint(i);
                std::cout << "(" << u.x() << "," << u.y() << ") ";
             }
             std::cout << "}  ";
          }
          std::cout << " end= " << pEnd << std::endl;
       }
    }
 
   private:
     void clearOutput_();
   };
 
   /*
    * ScanLine does all the work of stitching together polygons from incoming vertical edges
    */
 //   template <typename Unit, typename polygon_concept_type>
 //   class ScanLineToPolygons {
 //   private:
 //     ScanLineToPolygonItrs<true, Unit> scanline_;
 //   public:
 //     inline ScanLineToPolygons() : scanline_() {}
 //     /* construct a scanline with the proper offsets, protocol and options */
 //     inline ScanLineToPolygons(bool fractureHoles) : scanline_(fractureHoles) {}
 
 //     /* process all vertical edges, left and right, at a unique x coordinate, edges must be sorted low to high */
 //     inline void processEdges(std::vector<Unit>& outBufferTmp, Unit currentX, std::vector<interval_data<Unit> >& leftEdges,
 //                              std::vector<interval_data<Unit> >& rightEdges) {
 //       typename ScanLineToPolygonItrs<true, Unit>::iterator itr, endItr;
 //       scanline_.processEdges(itr, endItr, currentX, leftEdges, rightEdges);
 //       //copy data into outBufferTmp
 //       while(itr != endItr) {
 //         typename PolyLinePolygonData<true, Unit>::iterator pditr;
 //         outBufferTmp.push_back(0);
 //         unsigned int sizeIndex = outBufferTmp.size() - 1;
 //         int count = 0;
 //         for(pditr = (*itr).begin(); pditr != (*itr).end(); ++pditr) {
 //           outBufferTmp.push_back(*pditr);
 //           ++count;
 //         }
 //         outBufferTmp[sizeIndex] = count;
 //         typename PolyLinePolygonData<true, Unit>::iteratorHoles pdHoleItr;
 //         for(pdHoleItr = (*itr).beginHoles(); pdHoleItr != (*itr).endHoles(); ++pdHoleItr) {
 //           outBufferTmp.push_back(0);
 //           unsigned int sizeIndex2 = outBufferTmp.size() - 1;
 //           int count2 = 0;
 //           for(pditr = (*pdHoleItr).begin(); pditr != (*pdHoleItr).end(); ++pditr) {
 //             outBufferTmp.push_back(*pditr);
 //             ++count2;
 //           }
 //           outBufferTmp[sizeIndex2] = -count;
 //         }
 //         ++itr;
 //       }
 //     }
 //   };
 
   const int VERTICAL_HEAD = 1, HEAD_TO_TAIL = 2, TAIL_TO_TAIL = 4, SOLID_TO_RIGHT = 8;
 
   //EVERY FUNCTION in this DEF file should be explicitly defined as inline
 
   //microsoft compiler improperly warns whenever you cast an integer to bool
   //call this function on an integer to convert it to bool without a warning
   template <class T>
   inline bool to_bool(const T& val) { return val != 0; }
 
   //default constructor (for preallocation)
   template <typename Unit>
   inline PolyLine<Unit>::PolyLine() : ptdata_() ,headp_(0), tailp_(0), state_(-1) {}
 
   //constructor
   template <typename Unit>
   inline PolyLine<Unit>::PolyLine(orientation_2d orient, Unit coord, Side side) :
     ptdata_(1, coord),
     headp_(0),
     tailp_(0),
     state_(orient.to_int() +
            (side << 3)){}
 
   //copy constructor
   template <typename Unit>
   inline PolyLine<Unit>::PolyLine(const PolyLine<Unit>& pline) : ptdata_(pline.ptdata_),
                                                      headp_(pline.headp_),
                                                      tailp_(pline.tailp_),
                                                      state_(pline.state_) {}
 
   //destructor
   template <typename Unit>
   inline PolyLine<Unit>::~PolyLine() {
     //clear out data just in case it is read later
     headp_ = tailp_ = 0;
     state_ = 0;
   }
 
   template <typename Unit>
   inline PolyLine<Unit>& PolyLine<Unit>::operator=(const PolyLine<Unit>& that) {
     if(!(this == &that)) {
       headp_ = that.headp_;
       tailp_ = that.tailp_;
       ptdata_ = that.ptdata_;
       state_ = that.state_;
     }
     return *this;
   }
 
   template <typename Unit>
   inline bool PolyLine<Unit>::operator==(const PolyLine<Unit>& b) const {
     return this == &b || (state_ == b.state_ &&
                           headp_ == b.headp_ &&
                           tailp_ == b.tailp_);
   }
 
   //valid PolyLine
   template <typename Unit>
   inline bool PolyLine<Unit>::isValid() const {
     return state_ > -1; }
 
   //first coordinate is an X value
   //first segment is vertical
   template <typename Unit>
   inline bool PolyLine<Unit>::verticalHead() const {
     return state_ & VERTICAL_HEAD;
   }
 
   //retrun true is PolyLine has odd number of coordiantes
   template <typename Unit>
   inline bool PolyLine<Unit>::oddLength() const {
     return to_bool((ptdata_.size()-1) % 2);
   }
 
   //last coordiante is an X value
   //last segment is vertical
   template <typename Unit>
   inline bool PolyLine<Unit>::verticalTail() const {
     return to_bool(verticalHead() ^ oddLength());
   }
 
   template <typename Unit>
   inline orientation_2d PolyLine<Unit>::tailOrient() const {
     return (verticalTail() ? VERTICAL : HORIZONTAL);
   }
 
   template <typename Unit>
   inline orientation_2d PolyLine<Unit>::headOrient() const {
     return (verticalHead() ? VERTICAL : HORIZONTAL);
   }
 
   template <typename Unit>
   inline End PolyLine<Unit>::endConnectivity(End end) const {
     //Tail should be defined as true
     if(end) { return tailToTail(); }
     return headToTail();
   }
 
   template <typename Unit>
   inline bool PolyLine<Unit>::headToTail() const {
     return to_bool(state_ & HEAD_TO_TAIL);
   }
 
   template <typename Unit>
   inline bool PolyLine<Unit>::headToHead() const {
     return to_bool(!headToTail());
   }
 
   template <typename Unit>
   inline bool PolyLine<Unit>::tailToHead() const {
     return to_bool(!tailToTail());
   }
 
   template <typename Unit>
   inline bool PolyLine<Unit>::tailToTail() const {
     return to_bool(state_ & TAIL_TO_TAIL);
   }
 
   template <typename Unit>
   inline Side PolyLine<Unit>::solidSide() const {
     return solidToRight(); }
 
   template <typename Unit>
   inline bool PolyLine<Unit>::solidToRight() const {
     return to_bool(state_ & SOLID_TO_RIGHT) != 0;
   }
 
   template <typename Unit>
   inline bool PolyLine<Unit>::active() const {
     return !to_bool(tailp_);
   }
 
   template <typename Unit>
   inline PolyLine<Unit>& PolyLine<Unit>::pushCoordinate(Unit coord) {
     ptdata_.push_back(coord);
     return *this;
   }
 
   template <typename Unit>
   inline PolyLine<Unit>& PolyLine<Unit>::popCoordinate() {
     ptdata_.pop_back();
     return *this;
   }
 
   template <typename Unit>
   inline PolyLine<Unit>& PolyLine<Unit>::pushPoint(const point_data<Unit>& point) {
      if(numSegments()){
        point_data<Unit> endPt = getEndPoint();
        //vertical is true, horizontal is false
        if((tailOrient().to_int() ? point.get(VERTICAL) == endPt.get(VERTICAL) : point.get(HORIZONTAL) == endPt.get(HORIZONTAL))) {
          //we were pushing a colinear segment
          return popCoordinate();
        }
      }
     return pushCoordinate(tailOrient().to_int() ? point.get(VERTICAL) : point.get(HORIZONTAL));
   }
 
   template <typename Unit>
   inline PolyLine<Unit>& PolyLine<Unit>::extendTail(Unit delta) {
     ptdata_.back() += delta;
     return *this;
   }
 
   //private member function that creates a link from this PolyLine to that
   template <typename Unit>
   inline PolyLine<Unit>& PolyLine<Unit>::joinTo_(End thisEnd, PolyLine<Unit>& that, End end) {
     if(thisEnd){
       tailp_ = &that;
       state_ &= ~TAIL_TO_TAIL; //clear any previous state_ of bit (for safety)
       state_ |= (end << 2); //place bit into mask
     } else {
       headp_ = &that;
       state_ &= ~HEAD_TO_TAIL; //clear any previous state_ of bit (for safety)
       state_ |= (end << 1); //place bit into mask
     }
     return *this;
   }
 
   //join two PolyLines (both ways of the association)
   template <typename Unit>
   inline PolyLine<Unit>& PolyLine<Unit>::joinTo(End thisEnd, PolyLine<Unit>& that, End end) {
     joinTo_(thisEnd, that, end);
     that.joinTo_(end, *this, thisEnd);
     return *this;
   }
 
   //convenience functions for joining PolyLines
   template <typename Unit>
   inline PolyLine<Unit>& PolyLine<Unit>::joinToTail(PolyLine<Unit>& that, End end) {
     return joinTo(TAIL, that, end);
   }
   template <typename Unit>
   inline PolyLine<Unit>& PolyLine<Unit>::joinToHead(PolyLine<Unit>& that, End end) {
     return joinTo(HEAD, that, end);
   }
   template <typename Unit>
   inline PolyLine<Unit>& PolyLine<Unit>::joinHeadToHead(PolyLine<Unit>& that) {
     return joinToHead(that, HEAD);
   }
   template <typename Unit>
   inline PolyLine<Unit>& PolyLine<Unit>::joinHeadToTail(PolyLine<Unit>& that) {
     return joinToHead(that, TAIL);
   }
   template <typename Unit>
   inline PolyLine<Unit>& PolyLine<Unit>::joinTailToHead(PolyLine<Unit>& that) {
     return joinToTail(that, HEAD);
   }
   template <typename Unit>
   inline PolyLine<Unit>& PolyLine<Unit>::joinTailToTail(PolyLine<Unit>& that) {
     return joinToTail(that, TAIL);
   }
 
   template <typename Unit>
   inline PolyLine<Unit>& PolyLine<Unit>::disconnectTails() {
     next(TAIL)->state_ &= !TAIL_TO_TAIL;
     next(TAIL)->tailp_ = 0;
     state_ &= !TAIL_TO_TAIL;
     tailp_ = 0;
     return *this;
   }
 
   template <typename Unit>
   inline Unit PolyLine<Unit>::getEndCoord(End end) const {
     if(end)
       return ptdata_.back();
     return ptdata_.front();
   }
 
   template <typename Unit>
   inline orientation_2d PolyLine<Unit>::segmentOrient(unsigned int index) const {
     return (to_bool((unsigned int)verticalHead() ^ (index % 2)) ? VERTICAL : HORIZONTAL);
   }
 
   template <typename Unit>
   inline point_data<Unit> PolyLine<Unit>::getPoint(unsigned int index) const {
     //assert(isValid() && headp_->isValid()) ("PolyLine: headp_ must be valid");
     point_data<Unit> pt;
     pt.set(HORIZONTAL, ptdata_[index]);
     pt.set(VERTICAL, ptdata_[index]);
     Unit prevCoord;
     if(index == 0) {
       prevCoord = headp_->getEndCoord(headToTail());
     } else {
       prevCoord = ptdata_[index-1];
     }
     pt.set(segmentOrient(index), prevCoord);
     return pt;
   }
 
   template <typename Unit>
   inline point_data<Unit> PolyLine<Unit>::getEndPoint(End end) const {
     return getPoint((end ? numSegments() - 1 : (unsigned int)0));
   }
 
   template <typename Unit>
   inline Unit PolyLine<Unit>::operator[] (unsigned int index) const {
     //assert(ptdata_.size() > index) ("PolyLine: out of bounds index");
     return ptdata_[index];
   }
 
   template <typename Unit>
   inline unsigned int PolyLine<Unit>::numSegments() const {
     return ptdata_.size();
   }
 
   template <typename Unit>
   inline PolyLine<Unit>* PolyLine<Unit>::next(End end) const {
     return (end ? tailp_ : headp_);
   }
 
   template <typename Unit>
   inline ActiveTail<Unit>::ActiveTail() : tailp_(0), otherTailp_(0), holesList_(),
    polyLineSize_(0) {}
 
   template <typename Unit>
   inline ActiveTail<Unit>::ActiveTail(orientation_2d orient, Unit coord, Side solidToRight, ActiveTail* otherTailp) :
     tailp_(0), otherTailp_(0), holesList_(), polyLineSize_(0) {
     tailp_ = createPolyLine(orient, coord, solidToRight);
     otherTailp_ = otherTailp;
     polyLineSize_ = tailp_->numSegments();
   }
 
   template <typename Unit>
   inline ActiveTail<Unit>::ActiveTail(PolyLine<Unit>* active, ActiveTail<Unit>* otherTailp) :
     tailp_(active), otherTailp_(otherTailp), holesList_(),
       polyLineSize_(0) {}
 
   //copy constructor
   template <typename Unit>
   inline ActiveTail<Unit>::ActiveTail(const ActiveTail<Unit>& that) : tailp_(that.tailp_), otherTailp_(that.otherTailp_), holesList_(), polyLineSize_(that.polyLineSize_) {}
 
   //destructor
   template <typename Unit>
   inline ActiveTail<Unit>::~ActiveTail() {
     //clear them in case the memory is read later
     tailp_ = 0; otherTailp_ = 0;
   }
 
   template <typename Unit>
   inline ActiveTail<Unit>& ActiveTail<Unit>::operator=(const ActiveTail<Unit>& that) {
     //self assignment is safe in this case
     tailp_ = that.tailp_;
     otherTailp_ = that.otherTailp_;
     polyLineSize_ = that.polyLineSize_;
     return *this;
   }
 
   template <typename Unit>
   inline bool ActiveTail<Unit>::operator==(const ActiveTail<Unit>& b) const {
     return tailp_ == b.tailp_ && otherTailp_ == b.otherTailp_;
   }
 
   template <typename Unit>
   inline bool ActiveTail<Unit>::operator<(const ActiveTail<Unit>& b) const {
     return tailp_->getEndPoint().get(VERTICAL) < b.tailp_->getEndPoint().get(VERTICAL);
   }
 
   template <typename Unit>
   inline bool ActiveTail<Unit>::operator<=(const ActiveTail<Unit>& b) const {
     return !(*this > b); }
 
   template <typename Unit>
   inline bool ActiveTail<Unit>::operator>(const ActiveTail<Unit>& b) const {
     return b < (*this); }
 
   template <typename Unit>
   inline bool ActiveTail<Unit>::operator>=(const ActiveTail<Unit>& b) const {
     return !(*this < b); }
 
   template <typename Unit>
   inline PolyLine<Unit>* ActiveTail<Unit>::getTail() const {
     return tailp_; }
 
   template <typename Unit>
   inline PolyLine<Unit>* ActiveTail<Unit>::getOtherTail() const {
     return otherTailp_->tailp_; }
 
   template <typename Unit>
   inline ActiveTail<Unit>* ActiveTail<Unit>::getOtherActiveTail() const {
     return otherTailp_; }
 
   template <typename Unit>
   inline bool ActiveTail<Unit>::isOtherTail(const ActiveTail<Unit>& b) {
     //       assert( (tailp_ == b.getOtherTail() && getOtherTail() == b.tailp_) ||
     //                     (tailp_ != b.getOtherTail() && getOtherTail() != b.tailp_))
     //         ("ActiveTail: Active tails out of sync");
     return otherTailp_ == &b;
   }
 
   template <typename Unit>
   inline ActiveTail<Unit>& ActiveTail<Unit>::updateTail(PolyLine<Unit>* newTail) {
     //subtract the old size and add new size//
     int delta = newTail->numSegments() - tailp_->numSegments();
     addPolyLineSize(delta);
     otherTailp_->addPolyLineSize(delta);
     tailp_ = newTail;
     return *this;
   }
 
   template <typename Unit>
   inline ActiveTail<Unit>* ActiveTail<Unit>::addHole(ActiveTail<Unit>* hole, bool fractureHoles) {
 
     if(!fractureHoles){
       holesList_.push_back(hole);
       copyHoles(*hole);
       copyHoles(*(hole->getOtherActiveTail()));
       return this;
     }
     ActiveTail<Unit>* h, *v;
     ActiveTail<Unit>* other = hole->getOtherActiveTail();
     if(other->getOrient() == VERTICAL) {
       //assert that hole.getOrient() == HORIZONTAL
       //this case should never happen
       h = hole;
       v = other;
     } else {
       //assert that hole.getOrient() == VERTICAL
       h = other;
       v = hole;
     }
     h->pushCoordinate(v->getCoordinate());
     //assert that h->getOrient() == VERTICAL
     //v->pushCoordinate(getCoordinate());
     //assert that v->getOrient() == VERTICAL
     //I can't close a figure by adding a hole, so pass zero for xMin and yMin
     std::vector<Unit> tmpVec;
     ActiveTail<Unit>::joinChains(this, h, false, tmpVec);
     return v;
   }
 
   template <typename Unit>
   inline const std::list<ActiveTail<Unit>*>& ActiveTail<Unit>::getHoles() const {
     return holesList_;
   }
 
   template <typename Unit>
   inline void ActiveTail<Unit>::copyHoles(ActiveTail<Unit>& that) {
     holesList_.splice(holesList_.end(), that.holesList_); //splice the two lists together
   }
 
   template <typename Unit>
   inline bool ActiveTail<Unit>::solidToRight() const {
     return getTail()->solidToRight(); }
 
   template <typename Unit>
   inline Unit ActiveTail<Unit>::getCoord() const {
     return getTail()->getEndCoord(); }
 
   template <typename Unit>
   inline Unit ActiveTail<Unit>::getCoordinate() const {
     return getCoord(); }
 
   template <typename Unit>
   inline orientation_2d ActiveTail<Unit>::getOrient() const {
     return getTail()->tailOrient(); }
 
   template <typename Unit>
   inline void ActiveTail<Unit>::pushCoordinate(Unit coord) {
     //appropriately handle any co-linear polyline segments by calling push point internally
     point_data<Unit> p;
     p.set(HORIZONTAL, coord);
     p.set(VERTICAL, coord);
     //if we are vertical assign the last coordinate (an X) to p.x, else to p.y
     p.set(getOrient().get_perpendicular(), getCoordinate());
     int oldSegments = tailp_->numSegments();
     tailp_->pushPoint(p);
     int delta = tailp_->numSegments() - oldSegments;
     addPolyLineSize(delta);
     otherTailp_->addPolyLineSize(delta);
   }
 
 
   //global utility functions
   template <typename Unit>
   inline PolyLine<Unit>* createPolyLine(orientation_2d orient, Unit coord, Side side) {
     return new PolyLine<Unit>(orient, coord, side);
   }
 
   template <typename Unit>
   inline void destroyPolyLine(PolyLine<Unit>* pLine) {
     delete pLine;
   }
 
   template <typename Unit>
   inline ActiveTail<Unit>* createActiveTail() {
     //consider replacing system allocator with ActiveTail memory pool
     return new ActiveTail<Unit>();
   }
 
   template <typename Unit>
   inline void destroyActiveTail(ActiveTail<Unit>* aTail) {
     delete aTail;
   }
 
 
   //no recursion, to prevent max recursion depth errors
   template <typename Unit>
   inline void ActiveTail<Unit>::destroyContents() {
     tailp_->disconnectTails();
     PolyLine<Unit>* nextPolyLinep = tailp_->next(HEAD);
     End end = tailp_->endConnectivity(HEAD);
     destroyPolyLine(tailp_);
     while(nextPolyLinep) {
       End nextEnd = nextPolyLinep->endConnectivity(!end); //get the direction of next polyLine
       PolyLine<Unit>* nextNextPolyLinep = nextPolyLinep->next(!end); //get the next polyline
       destroyPolyLine(nextPolyLinep); //destroy the current polyline
       end = nextEnd;
       nextPolyLinep = nextNextPolyLinep;
     }
   }
 
   template <typename Unit>
   inline typename ActiveTail<Unit>::iterator ActiveTail<Unit>::begin(bool isHole, orientation_2d orient) const {
     return iterator(this, isHole, orient);
   }
 
   template <typename Unit>
   inline typename ActiveTail<Unit>::iterator ActiveTail<Unit>::end() const {
     return iterator();
   }
 
   template <typename Unit>
   inline typename ActiveTail<Unit>::iteratorHoles ActiveTail<Unit>::beginHoles() const {
     return holesList_.begin();
   }
 
   template <typename Unit>
   inline typename ActiveTail<Unit>::iteratorHoles ActiveTail<Unit>::endHoles() const {
     return holesList_.end();
   }
 
   template <typename Unit>
   inline void ActiveTail<Unit>::writeOutFigureItrs(iterator& beginOut, iterator& endOut, bool isHole, orientation_2d orient) const {
     beginOut = begin(isHole, orient);
     endOut = end();
   }
 
   template <typename Unit>
   inline void ActiveTail<Unit>::writeOutFigureHoleItrs(iteratorHoles& beginOut, iteratorHoles& endOut) const {
     beginOut = beginHoles();
     endOut = endHoles();
   }
 
   template <typename Unit>
   inline void ActiveTail<Unit>::writeOutFigure(std::vector<Unit>& outVec, bool isHole) const {
     //we start writing out the polyLine that this active tail points to at its tail
     std::size_t size = outVec.size();
     outVec.push_back(0); //place holder for size
     PolyLine<Unit>* nextPolyLinep = 0;
     if(!isHole){
       nextPolyLinep = otherTailp_->tailp_->writeOut(outVec);
     } else {
       nextPolyLinep = tailp_->writeOut(outVec);
     }
     Unit firsty = outVec[size + 1];
     if((getOrient() == HORIZONTAL) ^ !isHole) {
       //our first coordinate is a y value, so we need to rotate it to the end
       typename std::vector<Unit>::iterator tmpItr = outVec.begin();
       tmpItr += size;
       outVec.erase(++tmpItr); //erase the 2nd element
     }
     End startEnd = tailp_->endConnectivity(HEAD);
     if(isHole) startEnd = otherTailp_->tailp_->endConnectivity(HEAD);
     while(nextPolyLinep) {
       bool nextStartEnd = nextPolyLinep->endConnectivity(!startEnd);
       nextPolyLinep = nextPolyLinep->writeOut(outVec, startEnd);
       startEnd = nextStartEnd;
     }
     if((getOrient() == HORIZONTAL) ^ !isHole) {
       //we want to push the y value onto the end since we ought to have ended with an x
       outVec.push_back(firsty); //should never be executed because we want first value to be an x
     }
     //the vector contains the coordinates of the linked list of PolyLines in the correct order
     //first element is supposed to be the size
     outVec[size] = outVec.size() - 1 - size;  //number of coordinates in vector
     //assert outVec[size] % 2 == 0 //it should be even
     //make the size negative for holes
     outVec[size] *= (isHole ? -1 : 1);
   }
 
   //no recursion to prevent max recursion depth errors
   template <typename Unit>
   inline PolyLine<Unit>* PolyLine<Unit>::writeOut(std::vector<Unit>& outVec, End startEnd) const {
     if(startEnd == HEAD){
       //forward order
       outVec.insert(outVec.end(), ptdata_.begin(), ptdata_.end());
       return tailp_;
     }else{
       //reverse order
       //do not reserve because we expect outVec to be large enough already
       for(int i = ptdata_.size() - 1; i >= 0; --i){
         outVec.push_back(ptdata_[i]);
       }
       //NT didn't know about this version of the API....
       //outVec.insert(outVec.end(), ptdata_.rbegin(), ptdata_.rend());
       return headp_;
     }
   }
 
   //solid indicates if it was joined by a solit or a space
   template <typename Unit>
   inline ActiveTail<Unit>* ActiveTail<Unit>::joinChains(ActiveTail<Unit>* at1, ActiveTail<Unit>* at2, bool solid, std::vector<Unit>& outBufferTmp)
   {
     //checks to see if we closed a figure
     if(at1->isOtherTail(*at2)){
       //value of solid tells us if we closed solid or hole
       //and output the solid or handle the hole appropriately
       //if the hole needs to fracture across horizontal partition boundary we need to notify
       //the calling context to do so
       if(solid) {
         //the chains are being joined because there is solid to the right
         //this means that if the figure is closed at this point it must be a hole
         //because otherwise it would have to have another vertex to the right of this one
         //and would not be closed at this point
         return at1;
       } else {
         //assert pG != 0
         //the figure that was closed is a shell
         at1->writeOutFigure(outBufferTmp);
         //process holes of the polygon
         at1->copyHoles(*at2); //there should not be holes on at2, but if there are, copy them over
         const std::list<ActiveTail<Unit>*>& holes = at1->getHoles();
         for(typename std::list<ActiveTail<Unit>*>::const_iterator litr = holes.begin(); litr != holes.end(); ++litr) {
           (*litr)->writeOutFigure(outBufferTmp, true);
           //delete the hole
           (*litr)->destroyContents();
           destroyActiveTail((*litr)->getOtherActiveTail());
           destroyActiveTail((*litr));
         }
         //delete the polygon
         at1->destroyContents();
         //at2 contents are the same as at1, so it should not destroy them
         destroyActiveTail(at1);
         destroyActiveTail(at2);
       }
       return 0;
     }
     //join the two partial polygons into one large partial polygon
     at1->getTail()->joinTailToTail(*(at2->getTail()));
     *(at1->getOtherActiveTail()) = ActiveTail(at1->getOtherTail(), at2->getOtherActiveTail());
     *(at2->getOtherActiveTail()) = ActiveTail(at2->getOtherTail(), at1->getOtherActiveTail());
 
     int accumulate = at2->getPolyLineSize() + at1->getPolyLineSize();
     (at1->getOtherActiveTail())->setPolyLineSize(accumulate);
     (at2->getOtherActiveTail())->setPolyLineSize(accumulate);
 
     at1->getOtherActiveTail()->copyHoles(*at1);
     at1->getOtherActiveTail()->copyHoles(*at2);
     destroyActiveTail(at1);
     destroyActiveTail(at2);
     return 0;
   }
 
   //solid indicates if it was joined by a solit or a space
   template <typename Unit>
   template <typename PolygonT>
   inline ActiveTail<Unit>* ActiveTail<Unit>::joinChains(ActiveTail<Unit>* at1, ActiveTail<Unit>* at2, bool solid,
                                                         std::vector<PolygonT>& outBufferTmp) {
     //checks to see if we closed a figure
     if(at1->isOtherTail(*at2)){
       //value of solid tells us if we closed solid or hole
       //and output the solid or handle the hole appropriately
       //if the hole needs to fracture across horizontal partition boundary we need to notify
       //the calling context to do so
       if(solid) {
         //the chains are being joined because there is solid to the right
         //this means that if the figure is closed at this point it must be a hole
         //because otherwise it would have to have another vertex to the right of this one
         //and would not be closed at this point
         return at1;
       } else {
         //assert pG != 0
         //the figure that was closed is a shell
         outBufferTmp.push_back(at1);
         at1->copyHoles(*at2); //there should not be holes on at2, but if there are, copy them over
       }
       return 0;
     }
     //join the two partial polygons into one large partial polygon
     at1->getTail()->joinTailToTail(*(at2->getTail()));
     *(at1->getOtherActiveTail()) = ActiveTail<Unit>(at1->getOtherTail(), at2->getOtherActiveTail());
     *(at2->getOtherActiveTail()) = ActiveTail<Unit>(at2->getOtherTail(), at1->getOtherActiveTail());
 
     int accumulate = at2->getPolyLineSize() + at1->getPolyLineSize();
     (at1->getOtherActiveTail())->setPolyLineSize(accumulate);
     (at2->getOtherActiveTail())->setPolyLineSize(accumulate);
 
     at1->getOtherActiveTail()->copyHoles(*at1);
     at1->getOtherActiveTail()->copyHoles(*at2);
     destroyActiveTail(at1);
     destroyActiveTail(at2);
     return 0;
   }
 
   template <class TKey, class T> inline typename std::map<TKey, T>::iterator findAtNext(std::map<TKey, T>& theMap,
                                                                                         typename std::map<TKey, T>::iterator pos, const TKey& key)
   {
     if(pos == theMap.end()) return theMap.find(key);
     //if they match the mapItr is pointing to the correct position
     if(pos->first < key) {
       return theMap.find(key);
     }
     if(pos->first > key) {
       return theMap.end();
     }
     //else they are equal and no need to do anything to the iterator
     return pos;
   }
 
   // createActiveTailsAsPair is called in these two end cases of geometry
   // 1. lower left concave corner
   //         ###|
   //         ###|
   //         ###|###
   //         ###|###
   // 2. lower left convex corner
   //            |###
   //            |###
   //            |
   //            |
   // In case 1 there may be a hole propigated up from the bottom.  If the fracture option is enabled
   // the two active tails that form the filament fracture line edges can become the new active tail pair
   // by pushing x and y onto them.  Otherwise the hole simply needs to be associated to one of the new active tails
   // with add hole
   template <typename Unit>
   inline std::pair<ActiveTail<Unit>*, ActiveTail<Unit>*> createActiveTailsAsPair(Unit x, Unit y, bool solid, ActiveTail<Unit>* phole, bool fractureHoles) {
     ActiveTail<Unit>* at1 = 0;
     ActiveTail<Unit>* at2 = 0;
     if(!phole || !fractureHoles){
       at1 = createActiveTail<Unit>();
       at2 = createActiveTail<Unit>();
       (*at1) = ActiveTail<Unit>(VERTICAL, x, solid, at2);
       (*at2) = ActiveTail<Unit>(HORIZONTAL, y, !solid, at1);
       //provide a function through activeTail class to provide this
       at1->getTail()->joinHeadToHead(*(at2->getTail()));
 
       at1->addPolyLineSize(1);
       at2->addPolyLineSize(1);
 
       if(phole)
         at1->addHole(phole, fractureHoles); //assert fractureHoles == false
       return std::pair<ActiveTail<Unit>*, ActiveTail<Unit>*>(at1, at2);
     }
     //assert phole is not null
     //assert fractureHoles is true
     if(phole->getOrient() == VERTICAL) {
       at2 = phole;
     } else {
       at2 = phole->getOtherActiveTail(); //should never be executed since orientation is expected to be vertical
     }
     //assert solid == false, we should be creating a corner with solid below and to the left if there was a hole
     at1 = at2->getOtherActiveTail();
     //assert at1 is horizontal
     at1->pushCoordinate(x);
     //assert at2 is vertical
     at2->pushCoordinate(y);
 
     return std::pair<ActiveTail<Unit>*, ActiveTail<Unit>*>(at1, at2);
   }
 
   /*
    *     |
    *     |
    *     =
    *     |########
    *     |########  (add a new ActiveTail in the tailMap_).
    *     |########
    *     |########
    *     |########
    *     =
    *     |
    *     |
    *
    * NOTE: Call this only if you are sure that the $ledege$ is not in the tailMap_
    */
   template<bool orientT, typename Unit, typename polygon_concept_type>
   inline void ScanLineToPolygonItrs<orientT, Unit, polygon_concept_type>::
   insertNewLeftEdgeIntoTailMap(Unit currentX, Unit yBegin, Unit yEnd,
    typename std::map<Unit, ActiveTail<Unit> *>::iterator &hint){
      ActiveTail<Unit> *currentTail = NULL;
      std::pair<ActiveTail<Unit>*, ActiveTail<Unit>*> tailPair =
       createActiveTailsAsPair(currentX, yBegin, true, currentTail,
          fractureHoles_);
      currentTail = tailPair.first;
      if(!tailMap_.empty()){
         ++hint;
      }
      hint = tailMap_.insert(hint, std::make_pair(yBegin, tailPair.second));
      currentTail->pushCoordinate(yEnd); ++hint;
      hint = tailMap_.insert(hint, std::make_pair(yEnd, currentTail));
   }
 
   template<bool orientT, typename Unit, typename polygon_concept_type>
   inline void ScanLineToPolygonItrs<orientT, Unit, polygon_concept_type>::
   closePartialSimplePolygon(Unit currentX, ActiveTail<Unit>*pfig,
       ActiveTail<Unit>*ppfig){
      pfig->pushCoordinate(currentX);
      ActiveTail<Unit>::joinChains(pfig, ppfig, false, outputPolygons_);
   }
   /*
    * If the invariant is maintained correctly then left edges can do the
    * following.
    *
    *               =###
    *            #######
    *            #######
    *            #######
    *            #######
    *               =###
    *               |### (input left edge)
    *               |###
    *               =###
    *            #######
    *            #######
    *               =###
    */
   template<bool orientT, typename Unit, typename polygon_concept_type>
   inline void ScanLineToPolygonItrs<orientT, Unit, polygon_concept_type>::
   updatePartialSimplePolygonsWithLeftEdges(Unit currentX,
    const std::vector<interval_data<Unit> > &leftEdges, size_t vertexThreshold){
      typename std::map<Unit, ActiveTail<Unit>* >::iterator succ, succ1;
      typename std::map<Unit, ActiveTail<Unit>* >::iterator pred, pred1, hint;
      Unit begin, end;
      ActiveTail<Unit> *pfig, *ppfig;
      std::pair<ActiveTail<Unit>*, ActiveTail<Unit>*> tailPair;
      size_t pfig_size = 0;
 
      hint = tailMap_.begin();
      for(size_t i=0; i < leftEdges.size(); i++){
         begin = leftEdges[i].get(LOW); end = leftEdges[i].get(HIGH);
         succ = findAtNext(tailMap_, hint, begin);
         pred = findAtNext(tailMap_, hint, end);
 
         if(succ != tailMap_.end() && pred != tailMap_.end()){ //CASE-1//
            //join the corresponding active tails//
            pfig = succ->second; ppfig = pred->second;
            pfig_size = pfig->getPolyLineSize() + ppfig->getPolyLineSize();
 
            if(pfig_size >= vertexThreshold){
               size_t bsize = pfig->getPolyLineSize();
               size_t usize = ppfig->getPolyLineSize();
 
               if(usize+2 < vertexThreshold){
                  //cut-off the lower piece (succ1, succ) join (succ1, pred)//
                  succ1 = succ; --succ1;
                  assert((succ1 != tailMap_.end()) &&
                   ((succ->second)->getOtherActiveTail() == succ1->second));
                  closePartialSimplePolygon(currentX, succ1->second, succ->second);
                  tailPair = createActiveTailsAsPair<Unit>(currentX, succ1->first,
                      true, NULL, fractureHoles_);
 
                  //just update the succ1 with new ActiveTail<Unit>*//
                  succ1->second = tailPair.second;
                  ActiveTail<Unit>::joinChains(tailPair.first, pred->second, true,
                      outputPolygons_);
               }else if(bsize+2 < vertexThreshold){
                  //cut-off the upper piece () join ()//
                  pred1 = pred; ++pred1;
                  assert(pred1 != tailMap_.end() &&
                   ((pred1->second)->getOtherActiveTail() == pred->second));
                  closePartialSimplePolygon(currentX, pred->second, pred1->second);
 
                  //just update the pred1 with ActiveTail<Unit>* = pfig//
                  pred1->second = pfig;
                  pfig->pushCoordinate(currentX);
                  pfig->pushCoordinate(pred1->first);
               }else{
                  //cut both and create an left edge between (pred->first, succ1)//
                  succ1 = succ; --succ1;
                  pred1 = pred; ++pred1;
                  assert(pred1 != tailMap_.end() && succ1 != tailMap_.end());
                  assert((pred1->second)->getOtherActiveTail() == pred->second);
                  assert((succ1->second)->getOtherActiveTail() == succ->second);
 
                  closePartialSimplePolygon(currentX, succ1->second, succ->second);
                  closePartialSimplePolygon(currentX, pred->second, pred1->second);
 
                  tailPair = createActiveTailsAsPair<Unit>(currentX, succ1->first,
                      true, NULL, fractureHoles_);
                  succ1->second = tailPair.second;
                  pred1->second = tailPair.first;
                  (tailPair.first)->pushCoordinate(pred1->first);
               }
            }else{
               //just join them with closing//
               pfig->pushCoordinate(currentX);
               ActiveTail<Unit>::joinChains(pfig, ppfig, true, outputPolygons_);
            }
            hint = pred; ++hint;
            tailMap_.erase(succ); tailMap_.erase(pred);
         }else if(succ == tailMap_.end() && pred != tailMap_.end()){ //CASE-2//
            //succ is missing in the map, first insert it into the map//
            tailPair = createActiveTailsAsPair<Unit>(currentX, begin, true, NULL,
                fractureHoles_);
            hint = pred; ++hint;
            hint = tailMap_.insert(hint, std::make_pair(begin, tailPair.second));
 
            pfig = pred->second;
            pfig_size = pfig->getPolyLineSize() + 2;
            if(pfig_size >= vertexThreshold){
               //cut-off piece from [pred, pred1] , add [begin, pred1]//
               pred1 = pred; ++pred1;
               assert((pred1 != tailMap_.end()) &&
                ((pred1->second)->getOtherActiveTail() == pred->second));
               closePartialSimplePolygon(currentX, pred->second, pred1->second);
 
               //update: we need left edge between (begin, pred1->first)//
               pred1->second = tailPair.first;
               (tailPair.first)->pushCoordinate(pred1->first);
            }else{
               //just join//
               ActiveTail<Unit>::joinChains(tailPair.first, pfig,
                   true, outputPolygons_);
            }
            tailMap_.erase(pred);
         }else if(succ != tailMap_.end() && pred == tailMap_.end()){ //CASE-3//
             //pred is missing in the map, first insert it into the map//
             hint = succ; ++hint;
             hint = tailMap_.insert(hint, std::make_pair(end, (ActiveTail<Unit> *) NULL));
             pfig = succ->second;
             pfig_size = pfig->getPolyLineSize() + 2;
             if(pfig_size >= vertexThreshold){
                //this figure needs cutting here//
                succ1 = succ; --succ1;
                assert((succ1 != tailMap_.end()) &&
                   (succ1->second == pfig->getOtherActiveTail()));
                ppfig = succ1->second;
                closePartialSimplePolygon(currentX, ppfig, pfig);
 
                //update: we need a left edge between (succ1->first, end)//
                tailPair = createActiveTailsAsPair<Unit>(currentX, succ1->first,
                   true, NULL, fractureHoles_);
                succ1->second = tailPair.second;
                hint->second = tailPair.first;
                (tailPair.first)->pushCoordinate(end);
             }else{
                //no cutting needed//
                hint->second = pfig;
                pfig->pushCoordinate(currentX);
                pfig->pushCoordinate(end);
             }
             tailMap_.erase(succ);
         }else{
            //insert both pred and succ//
            insertNewLeftEdgeIntoTailMap(currentX, begin, end, hint);
         }
      }
   }
 
   template<bool orientT, typename Unit, typename polygon_concept_type>
   inline void ScanLineToPolygonItrs<orientT, Unit, polygon_concept_type>::
   updatePartialSimplePolygonsWithRightEdges(Unit currentX,
    const std::vector<interval_data<Unit> > &rightEdges, size_t vertexThreshold)
    {
 
      typename std::map<Unit, ActiveTail<Unit>* >::iterator succ, pred, hint;
      std::pair<ActiveTail<Unit>*, ActiveTail<Unit>*> tailPair;
      Unit begin, end;
      size_t i = 0;
      //If rightEdges is non-empty Then tailMap_ is non-empty //
      assert(rightEdges.empty() || !tailMap_.empty() );
 
      while( i < rightEdges.size() ){
         //find the interval in the tailMap which contains this interval//
         pred = tailMap_.lower_bound(rightEdges[i].get(HIGH));
         assert(pred != tailMap_.end());
         succ = pred; --succ;
         assert(pred != succ);
         end =  pred->first; begin = succ->first;
 
         //we now have a [begin, end] //
         bool found_solid_opening = false;
         bool erase_succ = true, erase_pred = true;
         Unit solid_opening_begin = 0;
         Unit solid_opening_end = 0;
         size_t j = i+1;
         ActiveTail<Unit> *pfig = succ->second;
         ActiveTail<Unit> *ppfig = pred->second;
         size_t partial_fig_size = pfig->getPolyLineSize();
         //Invariant://
         assert(succ->second && (pfig)->getOtherActiveTail() == ppfig);
 
         hint = succ;
         Unit key = rightEdges[i].get(LOW);
         if(begin != key){
            found_solid_opening = true;
            solid_opening_begin = begin; solid_opening_end = key;
         }
 
         while(j < rightEdges.size() && rightEdges[j].get(HIGH) <= end){
            if(rightEdges[j-1].get(HIGH) != rightEdges[j].get(LOW)){
               if(!found_solid_opening){
                  found_solid_opening = true;
                  solid_opening_begin = rightEdges[j-1].get(HIGH);
                  solid_opening_end = rightEdges[j].get(LOW);
               }else{
                  ++hint;
                  insertNewLeftEdgeIntoTailMap(currentX,
                      rightEdges[j-1].get(HIGH), rightEdges[j].get(LOW), hint);
               }
            }
            j++;
         }
 
         //trailing edge//
         if(end != rightEdges[j-1].get(HIGH)){
            if(!found_solid_opening){
               found_solid_opening = true;
               solid_opening_begin = rightEdges[j-1].get(HIGH); solid_opening_end = end;
            }else{
               // a solid opening has been found already, we need to insert a new left
               // between [rightEdges[j-1].get(HIGH), end]
               Unit lbegin = rightEdges[j-1].get(HIGH);
               tailPair = createActiveTailsAsPair<Unit>(currentX, lbegin, true, NULL,
                   fractureHoles_);
               hint = tailMap_.insert(pred, std::make_pair(lbegin, tailPair.second));
               pred->second = tailPair.first;
               (tailPair.first)->pushCoordinate(end);
               erase_pred = false;
            }
         }
 
         size_t vertex_delta = ((begin != solid_opening_begin) &&
                (end != solid_opening_end)) ? 4 : 2;
 
         if(!found_solid_opening){
            //just close the figure, TODO: call closePartialPolygon//
            pfig->pushCoordinate(currentX);
            ActiveTail<Unit>::joinChains(pfig, ppfig, false, outputPolygons_);
            hint = pred; ++hint;
         }else if(partial_fig_size+vertex_delta >= vertexThreshold){
            //close the figure and add a pseudo left-edge//
            closePartialSimplePolygon(currentX, pfig, ppfig);
            assert(begin != solid_opening_begin || end != solid_opening_end);
 
            if(begin != solid_opening_begin && end != solid_opening_end){
                insertNewLeftEdgeIntoTailMap(currentX, solid_opening_begin,
                      solid_opening_end, hint);
            }else if(begin == solid_opening_begin){
               //we just need to update the succ in the tailMap_//
               tailPair = createActiveTailsAsPair<Unit>(currentX, solid_opening_begin,
                   true, NULL, fractureHoles_);
               succ->second = tailPair.second;
               hint = succ; ++hint;
               hint = tailMap_.insert(pred, std::make_pair(solid_opening_end,
                   tailPair.first));
               (tailPair.first)->pushCoordinate(solid_opening_end);
               erase_succ = false;
            }else{
               //we just need to update the pred in the tailMap_//
               tailPair = createActiveTailsAsPair<Unit>(currentX, solid_opening_begin,
                   true, NULL, fractureHoles_);
               hint = tailMap_.insert(pred, std::make_pair(solid_opening_begin,
                   tailPair.second));
               pred->second = tailPair.first;
               (tailPair.first)->pushCoordinate(solid_opening_end);
               erase_pred = false;
            }
         }else{
            //continue the figure (by adding at-most two new vertices)//
            if(begin != solid_opening_begin){
               pfig->pushCoordinate(currentX);
               pfig->pushCoordinate(solid_opening_begin);
               //insert solid_opening_begin//
               hint = succ; ++hint;
               hint = tailMap_.insert(hint, std::make_pair(solid_opening_begin, pfig));
            }else{
               erase_succ = false;
            }
 
            if(end != solid_opening_end){
               std::pair<ActiveTail<Unit>*, ActiveTail<Unit>*> tailPair =
                createActiveTailsAsPair<Unit>(currentX, solid_opening_end, false,
                      NULL, fractureHoles_);
               hint = pred; ++hint;
               hint = tailMap_.insert(hint, std::make_pair(solid_opening_end,
                   tailPair.second));
               ActiveTail<Unit>::joinChains(tailPair.first, ppfig, false,
                   outputPolygons_);
            }else{
               erase_pred = false;
            }
         }
 
         //Remove the pred and succ if necessary//
         if(erase_succ){
            tailMap_.erase(succ);
         }
         if(erase_pred){
            tailMap_.erase(pred);
         }
         i = j;
      }
  }
 
  // Maintains the following invariant:
  // a. All the partial polygons formed at any state can be closed
  //    by a single edge.
  template<bool orientT, typename Unit, typename polygon_concept_type>
  inline void ScanLineToPolygonItrs<orientT, Unit, polygon_concept_type>::
  maintainPartialSimplePolygonInvariant(iterator& beginOutput,
    iterator& endOutput, Unit currentX, const std::vector<interval_data<Unit> >& l,
       const std::vector<interval_data<Unit> >& r, size_t vertexThreshold) {
 
       clearOutput_();
       if(!l.empty()){
          updatePartialSimplePolygonsWithLeftEdges(currentX, l, vertexThreshold);
       }
 
       if(!r.empty()){
          updatePartialSimplePolygonsWithRightEdges(currentX, r, vertexThreshold);
       }
       beginOutput = outputPolygons_.begin();
       endOutput = outputPolygons_.end();
 
   }
 
   //Process edges connects vertical input edges (right or left edges of figures) to horizontal edges stored as member
   //data of the scanline object.  It also creates now horizontal edges as needed to construct figures from edge data.
   //
   //There are only 12 geometric end cases where the scanline intersects a horizontal edge and even fewer unique
   //actions to take:
   // 1. Solid on both sides of the vertical partition after the current position and space on both sides before
   //         ###|###
   //         ###|###
   //            |
   //            |
   //    This case does not need to be handled because there is no vertical edge at the current x coordinate.
   //
   // 2. Solid on both sides of the vertical partition before the current position and space on both sides after
   //            |
   //            |
   //         ###|###
   //         ###|###
   //    This case does not need to be handled because there is no vertical edge at the current x coordinate.
   //
   // 3. Solid on the left of the vertical partition after the current position and space elsewhere
   //         ###|
   //         ###|
   //            |
   //            |
   //    The horizontal edge from the left is found and turns upward because of the vertical right edge to become
   //    the currently active vertical edge.
   //
   // 4. Solid on the left of the vertical partion before the current position and space elsewhere
   //            |
   //            |
   //         ###|
   //         ###|
   //    The horizontal edge from the left is found and joined to the currently active vertical edge.
   //
   // 5. Solid to the right above and below and solid to the left above current position.
   //         ###|###
   //         ###|###
   //            |###
   //            |###
   //    The horizontal edge from the left is found and joined to the currently active vertical edge,
   //    potentially closing a hole.
   //
   // 6. Solid on the left of the vertical partion before the current position and solid to the right above and below
   //            |###
   //            |###
   //         ###|###
   //         ###|###
   //    The horizontal edge from the left is found and turns upward because of the vertical right edge to become
   //    the currently active vertical edge.
   //
   // 7. Solid on the right of the vertical partition after the current position and space elsewhere
   //            |###
   //            |###
   //            |
   //            |
   //    Create two new ActiveTails, one is added to the horizontal edges and the other becomes the vertical currentTail
   //
   // 8. Solid on the right of the vertical partion before the current position and space elsewhere
   //            |
   //            |
   //            |###
   //            |###
   //    The currentTail vertical edge turns right and is added to the horizontal edges data
   //
   // 9. Solid to the right above and solid to the left above and below current position.
   //         ###|###
   //         ###|###
   //         ###|
   //         ###|
   //    The currentTail vertical edge turns right and is added to the horizontal edges data
   //
   // 10. Solid on the left of the vertical partion above and below the current position and solid to the right below
   //         ###|
   //         ###|
   //         ###|###
   //         ###|###
   //    Create two new ActiveTails, one is added to the horizontal edges data and the other becomes the vertical currentTail
   //
   // 11. Solid to the right above and solid to the left below current position.
   //            |###
   //            |###
   //         ###|
   //         ###|
   //    The currentTail vertical edge joins the horizontal edge from the left (may close a polygon)
   //    Create two new ActiveTails, one is added to the horizontal edges data and the other becomes the vertical currentTail
   //
   // 12. Solid on the left of the vertical partion above the current position and solid to the right below
   //         ###|
   //         ###|
   //            |###
   //            |###
   //    The currentTail vertical edge turns right and is added to the horizontal edges data.
   //    The horizontal edge from the left turns upward and becomes the currentTail vertical edge
   //
   template <bool orientT, typename Unit, typename polygon_concept_type>
   inline void ScanLineToPolygonItrs<orientT, Unit, polygon_concept_type>::
   processEdges(iterator& beginOutput, iterator& endOutput,
                Unit currentX, std::vector<interval_data<Unit> >& leftEdges,
                std::vector<interval_data<Unit> >& rightEdges,
                size_t vertexThreshold) {
     clearOutput_();
     typename std::map<Unit, ActiveTail<Unit>*>::iterator nextMapItr;
     //foreach edge
     unsigned int leftIndex = 0;
     unsigned int rightIndex = 0;
     bool bottomAlreadyProcessed = false;
     ActiveTail<Unit>* currentTail = 0;
     const Unit UnitMax = (std::numeric_limits<Unit>::max)();
 
     if(vertexThreshold < (std::numeric_limits<size_t>::max)()){
       maintainPartialSimplePolygonInvariant(beginOutput, endOutput, currentX,
          leftEdges, rightEdges, vertexThreshold);
       return;
     }
 
     nextMapItr = tailMap_.begin();
     while(leftIndex < leftEdges.size() || rightIndex < rightEdges.size()) {
       interval_data<Unit>  edges[2] = {interval_data<Unit> (UnitMax, UnitMax),
          interval_data<Unit> (UnitMax, UnitMax)};
       bool haveNextEdge = true;
       if(leftIndex < leftEdges.size())
         edges[0] = leftEdges[leftIndex];
       else
         haveNextEdge = false;
       if(rightIndex < rightEdges.size())
         edges[1] = rightEdges[rightIndex];
       else
         haveNextEdge = false;
       bool trailingEdge = edges[1].get(LOW) < edges[0].get(LOW);
       interval_data<Unit> & edge = edges[trailingEdge];
       interval_data<Unit> & nextEdge = edges[!trailingEdge];
       //process this edge
       if(!bottomAlreadyProcessed) {
         //assert currentTail = 0
 
         //process the bottom end of this edge
         typename std::map<Unit, ActiveTail<Unit>*>::iterator thisMapItr = findAtNext(tailMap_, nextMapItr, edge.get(LOW));
         if(thisMapItr != tailMap_.end()) {
           //there is an edge in the map at the low end of this edge
           //it needs to turn upward and become the current tail
           ActiveTail<Unit>* tail = thisMapItr->second;
           if(currentTail) {
             //stitch currentTail into this tail
             currentTail = tail->addHole(currentTail, fractureHoles_);
             if(!fractureHoles_)
               currentTail->pushCoordinate(currentX);
           } else {
             currentTail = tail;
             currentTail->pushCoordinate(currentX);
           }
           //assert currentTail->getOrient() == VERTICAL
           nextMapItr = thisMapItr; //set nextMapItr to the next position after this one
           ++nextMapItr;
           //remove thisMapItr from the map
           tailMap_.erase(thisMapItr);
         } else {
           //there is no edge in the map at the low end of this edge
           //we need to create one and another one to be the current vertical tail
           //if this is a trailing edge then there is space to the right of the vertical edge
           //so pass the inverse of trailingEdge to indicate solid to the right
           std::pair<ActiveTail<Unit>*, ActiveTail<Unit>*> tailPair =
             createActiveTailsAsPair(currentX, edge.get(LOW), !trailingEdge, currentTail, fractureHoles_);
           currentTail = tailPair.first;
           tailMap_.insert(nextMapItr, std::pair<Unit, ActiveTail<Unit>*>(edge.get(LOW), tailPair.second));
           // leave nextMapItr unchanged
         }
 
       }
       if(haveNextEdge && edge.get(HIGH) == nextEdge.get(LOW)) {
         //the top of this edge is equal to the bottom of the next edge, process them both
         bottomAlreadyProcessed = true;
         typename std::map<Unit, ActiveTail<Unit>*>::iterator thisMapItr = findAtNext(tailMap_, nextMapItr, edge.get(HIGH));
         if(thisMapItr == tailMap_.end()) //assert this should never happen
           return;
         if(trailingEdge) {
           //geometry at this position
           //   |##
           //   |##
           // -----
           // ##|
           // ##|
           //current tail should join thisMapItr tail
           ActiveTail<Unit>* tail = thisMapItr->second;
           //pass false because they are being joined because space is to the right and it will close a solid figure
           ActiveTail<Unit>::joinChains(currentTail, tail, false, outputPolygons_);
           //two new tails are created, the vertical becomes current tail, the horizontal becomes thisMapItr tail
           //pass true becuase they are created at the lower left corner of some solid
           //pass null because there is no hole pointer possible
           std::pair<ActiveTail<Unit>*, ActiveTail<Unit>*> tailPair =
             createActiveTailsAsPair<Unit>(currentX, edge.get(HIGH), true, 0, fractureHoles_);
           currentTail = tailPair.first;
           thisMapItr->second = tailPair.second;
         } else {
           //geometry at this position
           // ##|
           // ##|
           // -----
           //   |##
           //   |##
           //current tail should turn right
           currentTail->pushCoordinate(edge.get(HIGH));
           //thisMapItr tail should turn up
           thisMapItr->second->pushCoordinate(currentX);
           //thisMapItr tail becomes current tail and current tail becomes thisMapItr tail
           std::swap(currentTail, thisMapItr->second);
         }
         nextMapItr = thisMapItr; //set nextMapItr to the next position after this one
         ++nextMapItr;
       } else {
         //there is a gap between the top of this edge and the bottom of the next, process the top of this edge
         bottomAlreadyProcessed = false;
         //process the top of this edge
         typename std::map<Unit, ActiveTail<Unit>*>::iterator thisMapItr = findAtNext(tailMap_, nextMapItr, edge.get(HIGH));
         if(thisMapItr != tailMap_.end()) {
           //thisMapItr is pointing to a horizontal edge in the map at the top of this vertical edge
           //we need to join them and potentially close a figure
           //assert currentTail != 0
           ActiveTail<Unit>* tail = thisMapItr->second;
           //pass the opositve of trailing edge to mean that they are joined because of solid to the right
           currentTail = ActiveTail<Unit>::joinChains(currentTail, tail, !trailingEdge, outputPolygons_);
           nextMapItr = thisMapItr; //set nextMapItr to the next position after this one
           ++nextMapItr;
           if(currentTail) { //figure is not closed//
             Unit nextItrY = UnitMax;
             if(nextMapItr != tailMap_.end()) {
               nextItrY = nextMapItr->first;
             }
             //for it to be a hole this must have been a left edge
             Unit leftY = UnitMax;
             if(leftIndex + 1 < leftEdges.size())
               leftY = leftEdges[leftIndex+1].get(LOW);
             Unit rightY = nextEdge.get(LOW);
             if(!haveNextEdge || (nextItrY < leftY && nextItrY < rightY)) {
               //we need to add it to the next edge above it in the map
               tail = nextMapItr->second;
               tail = tail->addHole(currentTail, fractureHoles_);
               if(fractureHoles_) {
                 //some small additional work stitching in the filament
                 tail->pushCoordinate(nextItrY);
                 nextMapItr->second = tail;
               }
               //set current tail to null
               currentTail = 0;
             }
           }
           //delete thisMapItr from the map
           tailMap_.erase(thisMapItr);
         } else {
           //currentTail must turn right and be added into the map
           currentTail->pushCoordinate(edge.get(HIGH));
           //assert currentTail->getOrient() == HORIZONTAL
           tailMap_.insert(nextMapItr, std::pair<Unit, ActiveTail<Unit>*>(edge.get(HIGH), currentTail));
           //set currentTail to null
           currentTail = 0;
           //leave nextMapItr unchanged, it is still next
         }
       }
 
       //increment index
       leftIndex += !trailingEdge;
       rightIndex += trailingEdge;
     } //end while
     beginOutput = outputPolygons_.begin();
     endOutput = outputPolygons_.end();
   } //end function
 
   template<bool orientT, typename Unit, typename polygon_concept_type>
   inline void ScanLineToPolygonItrs<orientT, Unit, polygon_concept_type>::clearOutput_() {
     for(std::size_t i = 0; i < outputPolygons_.size(); ++i) {
       ActiveTail<Unit>* at1 = outputPolygons_[i].yield();
       const std::list<ActiveTail<Unit>*>& holes = at1->getHoles();
       for(typename std::list<ActiveTail<Unit>*>::const_iterator litr = holes.begin(); litr != holes.end(); ++litr) {
         //delete the hole
         (*litr)->destroyContents();
         destroyActiveTail((*litr)->getOtherActiveTail());
         destroyActiveTail((*litr));
       }
       //delete the polygon
       at1->destroyContents();
       //at2 contents are the same as at1, so it should not destroy them
       destroyActiveTail((at1)->getOtherActiveTail());
       destroyActiveTail(at1);
     }
     outputPolygons_.clear();
   }
 
 } //polygon_formation namespace
 
   template <bool orientT, typename Unit>
   struct geometry_concept<polygon_formation::PolyLinePolygonWithHolesData<orientT, Unit> > {
     typedef polygon_90_with_holes_concept type;
   };
 
   template <bool orientT, typename Unit>
   struct geometry_concept<polygon_formation::PolyLineHoleData<orientT, Unit> > {
     typedef polygon_90_concept type;
   };
 
   //public API to access polygon formation algorithm
   template <typename output_container, typename iterator_type, typename concept_type>
   unsigned int get_polygons(output_container& container,
       iterator_type begin, iterator_type end, orientation_2d orient,
       bool fracture_holes, concept_type,
       size_t sliceThreshold = (std::numeric_limits<size_t>::max)() ) {
     typedef typename output_container::value_type polygon_type;
     typedef typename std::iterator_traits<iterator_type>::value_type::first_type coordinate_type;
     polygon_type poly;
     unsigned int countPolygons = 0;
     typedef typename geometry_concept<polygon_type>::type polygon_concept_type;
     polygon_formation::ScanLineToPolygonItrs<true, coordinate_type, polygon_concept_type> scanlineToPolygonItrsV(fracture_holes);
     polygon_formation::ScanLineToPolygonItrs<false, coordinate_type, polygon_concept_type> scanlineToPolygonItrsH(fracture_holes);
     std::vector<interval_data<coordinate_type> > leftEdges;
     std::vector<interval_data<coordinate_type> > rightEdges;
     coordinate_type prevPos = (std::numeric_limits<coordinate_type>::max)();
     coordinate_type prevY = (std::numeric_limits<coordinate_type>::max)();
     int count = 0;
     for(iterator_type itr = begin;
         itr != end; ++ itr) {
       coordinate_type pos = (*itr).first;
       if(pos != prevPos) {
         if(orient == VERTICAL) {
           typename polygon_formation::ScanLineToPolygonItrs<true, coordinate_type, polygon_concept_type>::iterator itrPoly, itrPolyEnd;
            scanlineToPolygonItrsV.processEdges(itrPoly, itrPolyEnd, prevPos,
                leftEdges, rightEdges, sliceThreshold);
           for( ; itrPoly != itrPolyEnd; ++ itrPoly) {
             ++countPolygons;
             assign(poly, *itrPoly);
             container.insert(container.end(), poly);
           }
         } else {
           typename polygon_formation::ScanLineToPolygonItrs<false, coordinate_type, polygon_concept_type>::iterator itrPoly, itrPolyEnd;
           scanlineToPolygonItrsH.processEdges(itrPoly, itrPolyEnd, prevPos,
                leftEdges, rightEdges, sliceThreshold);
           for( ; itrPoly != itrPolyEnd; ++ itrPoly) {
             ++countPolygons;
             assign(poly, *itrPoly);
             container.insert(container.end(), poly);
           }
         }
         leftEdges.clear();
         rightEdges.clear();
         prevPos = pos;
         prevY = (*itr).second.first;
         count = (*itr).second.second;
         continue;
       }
       coordinate_type y = (*itr).second.first;
       if(count != 0 && y != prevY) {
         std::pair<interval_data<coordinate_type>, int> element(interval_data<coordinate_type>(prevY, y), count);
         if(element.second == 1) {
           if(leftEdges.size() && leftEdges.back().high() == element.first.low()) {
             encompass(leftEdges.back(), element.first);
           } else {
             leftEdges.push_back(element.first);
           }
         } else {
           if(rightEdges.size() && rightEdges.back().high() == element.first.low()) {
             encompass(rightEdges.back(), element.first);
           } else {
             rightEdges.push_back(element.first);
           }
         }
 
       }
       prevY = y;
       count += (*itr).second.second;
     }
     if(orient == VERTICAL) {
       typename polygon_formation::ScanLineToPolygonItrs<true, coordinate_type, polygon_concept_type>::iterator itrPoly, itrPolyEnd;
       scanlineToPolygonItrsV.processEdges(itrPoly, itrPolyEnd, prevPos, leftEdges, rightEdges, sliceThreshold);
       for( ; itrPoly != itrPolyEnd; ++ itrPoly) {
         ++countPolygons;
         assign(poly, *itrPoly);
         container.insert(container.end(), poly);
       }
     } else {
       typename polygon_formation::ScanLineToPolygonItrs<false, coordinate_type, polygon_concept_type>::iterator itrPoly, itrPolyEnd;
       scanlineToPolygonItrsH.processEdges(itrPoly, itrPolyEnd, prevPos, leftEdges, rightEdges,  sliceThreshold);
 
       for( ; itrPoly != itrPolyEnd; ++ itrPoly) {
         ++countPolygons;
         assign(poly, *itrPoly);
         container.insert(container.end(), poly);
       }
     }
     return countPolygons;
   }
 
 }
 }
 #endif