Added boost header

test/external/boost/polygon/detail/boolean_op.hpp

@@ -0,0 +1,448 @@
+/*
+  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_HPP
+#define BOOST_POLYGON_BOOLEAN_OP_HPP
+namespace boost { namespace polygon{
+namespace boolean_op {
+
+  //BooleanOp is the generic boolean operation scanline algorithm that provides
+  //all the simple boolean set operations on manhattan data.  By templatizing
+  //the intersection count of the input and algorithm internals it is extensible
+  //to multi-layer scans, properties and other advanced scanline operations above
+  //and beyond simple booleans.
+  //T must cast to int
+  template <class T, typename Unit>
+  class BooleanOp {
+  public:
+    typedef std::map<Unit, T> ScanData;
+    typedef std::pair<Unit, T> ElementType;
+  protected:
+    ScanData scanData_;
+    typename ScanData::iterator nextItr_;
+    T nullT_;
+  public:
+    inline BooleanOp () : scanData_(), nextItr_(), nullT_() { nextItr_ = scanData_.end(); nullT_ = 0; }
+    inline BooleanOp (T nullT) : scanData_(), nextItr_(), nullT_(nullT) { nextItr_ = scanData_.end(); }
+    inline BooleanOp (const BooleanOp& that) : scanData_(that.scanData_), nextItr_(),
+                                               nullT_(that.nullT_) { nextItr_ = scanData_.begin(); }
+    inline BooleanOp& operator=(const BooleanOp& that); 
+   
+    //moves scanline forward
+    inline void advanceScan() { nextItr_ = scanData_.begin(); }
+
+    //proceses the given interval and T data
+    //appends output edges to cT
+    template <class cT>
+    inline void processInterval(cT& outputContainer, interval_data<Unit> ivl, T deltaCount);
+   
+  private:
+    inline typename ScanData::iterator lookup_(Unit pos){
+      if(nextItr_ != scanData_.end() && nextItr_->first >= pos) {
+        return nextItr_;
+      }
+      return nextItr_ = scanData_.lower_bound(pos);
+    }
+    inline typename ScanData::iterator insert_(Unit pos, T count){ 
+      return nextItr_ = scanData_.insert(nextItr_, ElementType(pos, count)); 
+    } 
+    template <class cT>
+    inline void evaluateInterval_(cT& outputContainer, interval_data<Unit> ivl, T beforeCount, T afterCount);
+  };
+
+  class BinaryAnd {
+  public:
+    inline BinaryAnd() {}
+    inline bool operator()(int a, int b) { return (a > 0) & (b > 0); }
+  };
+  class BinaryOr {
+  public:
+    inline BinaryOr() {}
+    inline bool operator()(int a, int b) { return (a > 0) | (b > 0); }
+  };
+  class BinaryNot {
+  public:
+    inline BinaryNot() {}
+    inline bool operator()(int a, int b) { return (a > 0) & !(b > 0); }
+  };
+  class BinaryXor {
+  public:
+    inline BinaryXor() {}
+    inline bool operator()(int a, int b) { return (a > 0) ^ (b > 0); }
+  };
+
+  //BinaryCount is an array of two deltaCounts coming from two different layers
+  //of scan event data.  It is the merged count of the two suitable for consumption
+  //as the template argument of the BooleanOp algorithm because BinaryCount casts to int.
+  //T is a binary functor object that evaluates the array of counts and returns a logical 
+  //result of some operation on those values.
+  //BinaryCount supports many of the operators that work with int, particularly the
+  //binary operators, but cannot support less than or increment.
+  template <class T>
+  class BinaryCount {
+  public:
+    inline BinaryCount() 
+#ifndef BOOST_POLYGON_MSVC  
+      : counts_() 
+#endif
+    { counts_[0] = counts_[1] = 0; }
+    // constructs from two integers
+    inline BinaryCount(int countL, int countR) 
+#ifndef BOOST_POLYGON_MSVC  
+      : counts_() 
+#endif
+    { counts_[0] = countL, counts_[1] = countR; }
+    inline BinaryCount& operator=(int count) { counts_[0] = count, counts_[1] = count; return *this; }
+    inline BinaryCount& operator=(const BinaryCount& that); 
+    inline BinaryCount(const BinaryCount& that)
+#ifndef BOOST_POLYGON_MSVC
+      : counts_() 
+#endif
+    { *this = that; }
+    inline bool operator==(const BinaryCount& that) const;
+    inline bool operator!=(const BinaryCount& that) const { return !((*this) == that);}
+    inline BinaryCount& operator+=(const BinaryCount& that);
+    inline BinaryCount& operator-=(const BinaryCount& that);
+    inline BinaryCount operator+(const BinaryCount& that) const;
+    inline BinaryCount operator-(const BinaryCount& that) const;
+    inline BinaryCount operator-() const;
+    inline int& operator[](bool index) { return counts_[index]; }
+
+    //cast to int operator evaluates data using T binary functor
+    inline operator int() const { return T()(counts_[0], counts_[1]); }
+  private:
+    int counts_[2];
+  };
+
+  class UnaryCount {
+  public:
+    inline UnaryCount() : count_(0) {}
+    // constructs from two integers
+    inline explicit UnaryCount(int count) : count_(count) {}
+    inline UnaryCount& operator=(int count) { count_ = count; return *this; }
+    inline UnaryCount& operator=(const UnaryCount& that) { count_ = that.count_; return *this; }
+    inline UnaryCount(const UnaryCount& that) : count_(that.count_) {}
+    inline bool operator==(const UnaryCount& that) const { return count_ == that.count_; }
+    inline bool operator!=(const UnaryCount& that) const { return !((*this) == that);}
+    inline UnaryCount& operator+=(const UnaryCount& that) { count_ += that.count_; return *this; }
+    inline UnaryCount& operator-=(const UnaryCount& that) { count_ -= that.count_; return *this; }
+    inline UnaryCount operator+(const UnaryCount& that) const { UnaryCount tmp(*this); tmp += that; return tmp; }
+    inline UnaryCount operator-(const UnaryCount& that) const { UnaryCount tmp(*this); tmp -= that; return tmp; }
+    inline UnaryCount operator-() const { UnaryCount tmp; return tmp - *this; }
+
+    //cast to int operator evaluates data using T binary functor
+    inline operator int() const { return count_ % 2; }
+  private:
+    int count_;
+  };
+
+  template <class T, typename Unit>
+  inline BooleanOp<T, Unit>& BooleanOp<T, Unit>::operator=(const BooleanOp& that) { 
+    scanData_ = that.scanData_; 
+    nextItr_ = scanData_.begin();
+    nullT_ = that.nullT_;
+    return *this;
+  }
+   
+  //appends output edges to cT
+  template <class T, typename Unit>
+  template <class cT>
+  inline void BooleanOp<T, Unit>::processInterval(cT& outputContainer, interval_data<Unit> ivl, T deltaCount) {
+    typename ScanData::iterator lowItr = lookup_(ivl.low());
+    typename ScanData::iterator highItr = lookup_(ivl.high());
+    //add interval to scan data if it is past the end
+    if(lowItr == scanData_.end()) {
+      lowItr = insert_(ivl.low(), deltaCount);
+      highItr = insert_(ivl.high(), nullT_);
+      evaluateInterval_(outputContainer, ivl, nullT_, deltaCount);
+      return;
+    }
+    //ensure that highItr points to the end of the ivl
+    if(highItr == scanData_.end() || (*highItr).first > ivl.high()) {
+      T value = nullT_;
+      if(highItr != scanData_.begin()) {
+        --highItr;
+        value = highItr->second;
+      }
+      nextItr_ = highItr;
+      highItr = insert_(ivl.high(), value);
+    }
+    //split the low interval if needed
+    if(lowItr->first > ivl.low()) {
+      if(lowItr != scanData_.begin()) {
+        --lowItr;
+        nextItr_ = lowItr;
+        lowItr = insert_(ivl.low(), lowItr->second);
+      } else {
+        nextItr_ = lowItr;
+        lowItr = insert_(ivl.low(), nullT_);
+      }
+    }
+    //process scan data intersecting interval
+    for(typename ScanData::iterator itr = lowItr; itr != highItr; ){
+      T beforeCount = itr->second;
+      T afterCount = itr->second += deltaCount;
+      Unit low = itr->first;
+      ++itr;
+      Unit high = itr->first;
+      evaluateInterval_(outputContainer, interval_data<Unit>(low, high), beforeCount, afterCount);
+    }
+    //merge the bottom interval with the one below if they have the same count
+    if(lowItr != scanData_.begin()){
+      typename ScanData::iterator belowLowItr = lowItr;
+      --belowLowItr;
+      if(belowLowItr->second == lowItr->second) {
+        scanData_.erase(lowItr);
+      }
+    }
+    //merge the top interval with the one above if they have the same count
+    if(highItr != scanData_.begin()) {
+      typename ScanData::iterator beforeHighItr = highItr;
+      --beforeHighItr;
+      if(beforeHighItr->second == highItr->second) {
+        scanData_.erase(highItr);
+        highItr = beforeHighItr;
+        ++highItr;
+      }
+    }
+    nextItr_ = highItr;
+  }
+
+  template <class T, typename Unit>
+  template <class cT>
+  inline void BooleanOp<T, Unit>::evaluateInterval_(cT& outputContainer, interval_data<Unit> ivl, 
+                                              T beforeCount, T afterCount) {
+    bool before = (int)beforeCount > 0;
+    bool after = (int)afterCount > 0;
+    int value =  (!before & after) - (before & !after);
+    if(value) {
+      outputContainer.insert(outputContainer.end(), std::pair<interval_data<Unit>, int>(ivl, value));
+    }
+  }
+
+  template <class T>
+  inline BinaryCount<T>& BinaryCount<T>::operator=(const BinaryCount<T>& that) { 
+    counts_[0] = that.counts_[0];
+    counts_[1] = that.counts_[1];
+    return *this;
+  }
+  template <class T>
+  inline bool BinaryCount<T>::operator==(const BinaryCount<T>& that) const { 
+    return counts_[0] == that.counts_[0] &&
+      counts_[1] == that.counts_[1];
+  }
+  template <class T>
+  inline BinaryCount<T>& BinaryCount<T>::operator+=(const BinaryCount<T>& that) {
+    counts_[0] += that.counts_[0];
+    counts_[1] += that.counts_[1];
+    return *this;
+  }
+  template <class T>
+  inline BinaryCount<T>& BinaryCount<T>::operator-=(const BinaryCount<T>& that) {
+    counts_[0] += that.counts_[0];
+    counts_[1] += that.counts_[1];
+    return *this;
+  }
+  template <class T>
+  inline BinaryCount<T> BinaryCount<T>::operator+(const BinaryCount<T>& that) const {
+    BinaryCount retVal(*this);
+    retVal += that;
+    return retVal;
+  }
+  template <class T>
+  inline BinaryCount<T> BinaryCount<T>::operator-(const BinaryCount<T>& that) const {
+    BinaryCount retVal(*this);
+    retVal -= that;
+    return retVal;
+  }
+  template <class T>
+  inline BinaryCount<T> BinaryCount<T>::operator-() const {
+    return BinaryCount<T>() - *this;
+  }
+
+
+  template <class T, typename Unit, typename iterator_type_1, typename iterator_type_2>
+  inline void applyBooleanBinaryOp(std::vector<std::pair<Unit, std::pair<Unit, int> > >& output,
+                                   //const std::vector<std::pair<Unit, std::pair<Unit, int> > >& input1,
+                                   //const std::vector<std::pair<Unit, std::pair<Unit, int> > >& input2,
+                                   iterator_type_1 itr1, iterator_type_1 itr1_end,
+                                   iterator_type_2 itr2, iterator_type_2 itr2_end,
+                                   T defaultCount) {
+    BooleanOp<T, Unit> boolean(defaultCount);
+    //typename std::vector<std::pair<Unit, std::pair<Unit, int> > >::const_iterator itr1 = input1.begin();
+    //typename std::vector<std::pair<Unit, std::pair<Unit, int> > >::const_iterator itr2 = input2.begin();
+    std::vector<std::pair<interval_data<Unit>, int> > container;
+    //output.reserve((std::max)(input1.size(), input2.size()));
+
+    //consider eliminating dependecy on limits with bool flag for initial state
+    Unit UnitMax = (std::numeric_limits<Unit>::max)();
+    Unit prevCoord = UnitMax;
+    Unit prevPosition = UnitMax;
+    T count(defaultCount);
+    //define the starting point
+    if(itr1 != itr1_end) {
+      prevCoord = (*itr1).first;
+      prevPosition = (*itr1).second.first;
+      count[0] += (*itr1).second.second;
+    }
+    if(itr2 != itr2_end) {
+      if((*itr2).first < prevCoord || 
+         ((*itr2).first == prevCoord && (*itr2).second.first < prevPosition)) {
+        prevCoord = (*itr2).first;
+        prevPosition = (*itr2).second.first;
+        count = defaultCount;
+        count[1] += (*itr2).second.second;
+        ++itr2;
+      } else if((*itr2).first == prevCoord && (*itr2).second.first == prevPosition) {
+        count[1] += (*itr2).second.second;
+        ++itr2;
+        if(itr1 != itr1_end) ++itr1;
+      } else {
+        if(itr1 != itr1_end) ++itr1;
+      }
+    } else {
+      if(itr1 != itr1_end) ++itr1;
+    }
+    
+    while(itr1 != itr1_end || itr2 != itr2_end) {
+      Unit curCoord = UnitMax;
+      Unit curPosition = UnitMax;
+      T curCount(defaultCount);
+      if(itr1 != itr1_end) {
+        curCoord = (*itr1).first;
+        curPosition = (*itr1).second.first;
+        curCount[0] += (*itr1).second.second;
+      }
+      if(itr2 != itr2_end) {
+        if((*itr2).first < curCoord || 
+           ((*itr2).first == curCoord && (*itr2).second.first < curPosition)) {
+          curCoord = (*itr2).first;
+          curPosition = (*itr2).second.first;
+          curCount = defaultCount;
+          curCount[1] += (*itr2).second.second;
+          ++itr2;
+        } else if((*itr2).first == curCoord && (*itr2).second.first == curPosition) {
+          curCount[1] += (*itr2).second.second;
+          ++itr2;
+          if(itr1 != itr1_end) ++itr1;
+        } else {
+          if(itr1 != itr1_end) ++itr1;
+        }
+      } else {
+        ++itr1;
+      }
+
+      if(prevCoord != curCoord) {
+        boolean.advanceScan();
+        prevCoord = curCoord;
+        prevPosition = curPosition;
+        count = curCount;
+        continue;
+      }
+      if(curPosition != prevPosition && count != defaultCount) {
+        interval_data<Unit> ivl(prevPosition, curPosition);
+        container.clear();
+        boolean.processInterval(container, ivl, count);
+        for(std::size_t i = 0; i < container.size(); ++i) {
+          std::pair<interval_data<Unit>, int>& element = container[i];
+          if(!output.empty() && output.back().first == prevCoord && 
+             output.back().second.first == element.first.low() &&
+             output.back().second.second == element.second * -1) {
+            output.pop_back();
+          } else {
+            output.push_back(std::pair<Unit, std::pair<Unit, int> >(prevCoord, std::pair<Unit, int>(element.first.low(), 
+                                                                                                    element.second)));
+          }
+          output.push_back(std::pair<Unit, std::pair<Unit, int> >(prevCoord, std::pair<Unit, int>(element.first.high(), 
+                                                                                                  element.second * -1)));
+        }
+      }
+      prevPosition = curPosition;
+      count += curCount;
+    }
+  }
+
+  template <class T, typename Unit>
+  inline void applyBooleanBinaryOp(std::vector<std::pair<Unit, std::pair<Unit, int> > >& inputOutput,
+                                   const std::vector<std::pair<Unit, std::pair<Unit, int> > >& input2,
+                                   T defaultCount) {
+    std::vector<std::pair<Unit, std::pair<Unit, int> > > output;
+    applyBooleanBinaryOp(output, inputOutput, input2, defaultCount);
+    if(output.size() < inputOutput.size() / 2) {
+      inputOutput = std::vector<std::pair<Unit, std::pair<Unit, int> > >();
+    } else {
+      inputOutput.clear();
+    }
+    inputOutput.insert(inputOutput.end(), output.begin(), output.end());
+  }
+ 
+  template <typename Unit>
+  inline void applyUnaryXOr(std::vector<std::pair<Unit, std::pair<Unit, int> > >& input) {
+    BooleanOp<UnaryCount, Unit> booleanXOr;
+    
+  }
+
+  template <typename count_type = int>
+  struct default_arg_workaround {
+    template <typename Unit>
+    static inline void applyBooleanOr(std::vector<std::pair<Unit, std::pair<Unit, int> > >& input) {
+      BooleanOp<count_type, Unit> booleanOr;
+      std::vector<std::pair<interval_data<Unit>, int> > container;
+      std::vector<std::pair<Unit, std::pair<Unit, int> > > output;
+      output.reserve(input.size());
+      //consider eliminating dependecy on limits with bool flag for initial state
+      Unit UnitMax = (std::numeric_limits<Unit>::max)();
+      Unit prevPos = UnitMax;
+      Unit prevY = UnitMax;
+      int count = 0;
+      for(typename std::vector<std::pair<Unit, std::pair<Unit, int> > >::iterator itr = input.begin();
+          itr != input.end(); ++itr) {
+        Unit pos = (*itr).first;
+        Unit y = (*itr).second.first;
+        if(pos != prevPos) {
+          booleanOr.advanceScan();
+          prevPos = pos;
+          prevY = y;
+          count = (*itr).second.second;
+          continue;
+        }
+        if(y != prevY && count != 0) {
+          interval_data<Unit> ivl(prevY, y);
+          container.clear();
+          booleanOr.processInterval(container, ivl, count_type(count));
+          for(std::size_t i = 0; i < container.size(); ++i) {
+            std::pair<interval_data<Unit>, int>& element = container[i];
+            if(!output.empty() && output.back().first == prevPos && 
+               output.back().second.first == element.first.low() &&
+               output.back().second.second == element.second * -1) {
+              output.pop_back();
+            } else {
+              output.push_back(std::pair<Unit, std::pair<Unit, int> >(prevPos, std::pair<Unit, int>(element.first.low(), 
+                                                                                                    element.second)));
+            }
+            output.push_back(std::pair<Unit, std::pair<Unit, int> >(prevPos, std::pair<Unit, int>(element.first.high(), 
+                                                                                                  element.second * -1)));
+          }
+        }
+        prevY = y;
+        count += (*itr).second.second;
+      }
+      if(output.size() < input.size() / 2) {
+        input = std::vector<std::pair<Unit, std::pair<Unit, int> > >();
+      } else {
+      input.clear();
+      } 
+      input.insert(input.end(), output.begin(), output.end());
+    }
+  };
+
+}
+
+}
+
+}
+#endif

test/external/boost/polygon/detail/iterator_compact_to_points.hpp

@@ -0,0 +1,69 @@
+/*
+  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_ITERATOR_COMPACT_TO_POINTS_HPP
+#define BOOST_POLYGON_ITERATOR_COMPACT_TO_POINTS_HPP
+namespace boost { namespace polygon{
+template <typename iterator_type, typename point_type>
+class iterator_compact_to_points {
+private:
+  iterator_type iter_;
+  iterator_type iter_end_;
+  point_type pt_;
+  typename point_traits<point_type>::coordinate_type firstX_;
+  orientation_2d orient_;
+public:
+  typedef std::forward_iterator_tag iterator_category;
+  typedef point_type value_type;
+  typedef std::ptrdiff_t difference_type;
+  typedef const point_type* pointer; //immutable
+  typedef const point_type& reference; //immutable
+
+  inline iterator_compact_to_points() : iter_(), iter_end_(), pt_(), firstX_(), orient_() {}
+  inline iterator_compact_to_points(iterator_type iter, iterator_type iter_end) : 
+    iter_(iter), iter_end_(iter_end), pt_(), firstX_(), orient_(HORIZONTAL) {
+    if(iter_ != iter_end_) {
+      firstX_ = *iter_;
+      x(pt_, firstX_);
+      ++iter_;
+      if(iter_ != iter_end_) {
+        y(pt_, *iter_);
+      }
+    }
+  }
+  //use bitwise copy and assign provided by the compiler
+  inline iterator_compact_to_points& operator++() {
+    iterator_type prev_iter = iter_;
+    ++iter_;
+    if(iter_ == iter_end_) {
+      if(x(pt_) != firstX_) {
+        iter_ = prev_iter;
+        x(pt_, firstX_);
+      }
+    } else {
+      set(pt_, orient_, *iter_);
+      orient_.turn_90();
+    }
+    return *this;
+  }
+  inline const iterator_compact_to_points operator++(int) {
+    iterator_compact_to_points tmp(*this);
+    ++(*this);
+    return tmp;
+  }
+  inline bool operator==(const iterator_compact_to_points& that) const {
+    return (iter_ == that.iter_);
+  }
+  inline bool operator!=(const iterator_compact_to_points& that) const {
+    return (iter_ != that.iter_);
+  }
+  inline reference operator*() const { return pt_; }
+};
+}
+}
+#endif
+

test/external/boost/polygon/detail/iterator_geometry_to_set.hpp

@@ -0,0 +1,315 @@
+/*
+  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_ITERATOR_GEOMETRY_TO_SET_HPP
+#define BOOST_POLYGON_ITERATOR_GEOMETRY_TO_SET_HPP
+namespace boost { namespace polygon{
+template <typename concept_type, typename geometry_type>
+class iterator_geometry_to_set {};
+
+template <typename rectangle_type>
+class iterator_geometry_to_set<rectangle_concept, rectangle_type> {
+public:
+  typedef typename rectangle_traits<rectangle_type>::coordinate_type coordinate_type;
+  typedef std::forward_iterator_tag iterator_category;
+  typedef std::pair<coordinate_type, std::pair<coordinate_type, int> > value_type;
+  typedef std::ptrdiff_t difference_type;
+  typedef const value_type* pointer; //immutable
+  typedef const value_type& reference; //immutable
+private:
+  rectangle_data<coordinate_type> rectangle_;
+  mutable value_type vertex_;
+  unsigned int corner_;
+  orientation_2d orient_;
+  bool is_hole_;
+public:
+  iterator_geometry_to_set() : rectangle_(), vertex_(), corner_(4), orient_(), is_hole_() {}
+  iterator_geometry_to_set(const rectangle_type& rectangle, direction_1d dir, 
+                           orientation_2d orient = HORIZONTAL, bool is_hole = false, bool = false, direction_1d = CLOCKWISE) : 
+    rectangle_(), vertex_(), corner_(0), orient_(orient), is_hole_(is_hole) {
+    assign(rectangle_, rectangle);
+    if(dir == HIGH) corner_ = 4;
+  }
+  inline iterator_geometry_to_set& operator++() {
+    ++corner_;
+    return *this;
+  }
+  inline const iterator_geometry_to_set operator++(int) {
+    iterator_geometry_to_set tmp(*this);
+    ++(*this);
+    return tmp;
+  }
+  inline bool operator==(const iterator_geometry_to_set& that) const {
+    return corner_ == that.corner_;
+  }
+  inline bool operator!=(const iterator_geometry_to_set& that) const {
+    return !(*this == that);
+  }
+  inline reference operator*() const {
+    if(corner_ == 0) {
+      vertex_.first = get(get(rectangle_, orient_.get_perpendicular()), LOW);
+      vertex_.second.first = get(get(rectangle_, orient_), LOW);
+      vertex_.second.second = 1;
+      if(is_hole_) vertex_.second.second *= -1;
+    } else if(corner_ == 1) {
+      vertex_.second.first = get(get(rectangle_, orient_), HIGH);
+      vertex_.second.second = -1;
+      if(is_hole_) vertex_.second.second *= -1;
+    } else if(corner_ == 2) {
+      vertex_.first = get(get(rectangle_, orient_.get_perpendicular()), HIGH);
+      vertex_.second.first = get(get(rectangle_, orient_), LOW);
+    } else {
+      vertex_.second.first = get(get(rectangle_, orient_), HIGH);
+      vertex_.second.second = 1;
+      if(is_hole_) vertex_.second.second *= -1;
+    }
+    return vertex_; 
+  }
+};
+
+template <typename polygon_type>
+class iterator_geometry_to_set<polygon_90_concept, polygon_type> {
+public:
+  typedef typename polygon_traits<polygon_type>::coordinate_type coordinate_type;
+  typedef std::forward_iterator_tag iterator_category;
+  typedef std::pair<coordinate_type, std::pair<coordinate_type, int> > value_type;
+  typedef std::ptrdiff_t difference_type;
+  typedef const value_type* pointer; //immutable
+  typedef const value_type& reference; //immutable
+  typedef typename polygon_traits<polygon_type>::iterator_type coord_iterator_type;
+private:
+  value_type vertex_;
+  typename polygon_traits<polygon_type>::iterator_type itrb, itre;
+  bool last_vertex_;
+  bool is_hole_;
+  int multiplier_;
+  point_data<coordinate_type> first_pt, second_pt, pts[3];
+  bool use_wrap;
+  orientation_2d orient_;
+  int polygon_index;
+public:
+  iterator_geometry_to_set() : vertex_(), itrb(), itre(), last_vertex_(), is_hole_(), multiplier_(), first_pt(), second_pt(), pts(), use_wrap(), orient_(), polygon_index(-1) {}
+  iterator_geometry_to_set(const polygon_type& polygon, direction_1d dir, orientation_2d orient = HORIZONTAL, bool is_hole = false, bool winding_override = false, direction_1d w = CLOCKWISE) : 
+    vertex_(), itrb(), itre(), last_vertex_(), 
+    is_hole_(is_hole), multiplier_(), first_pt(), second_pt(), pts(), use_wrap(), 
+    orient_(orient), polygon_index(0) {
+    itrb = begin_points(polygon);
+    itre = end_points(polygon);
+    use_wrap = false;
+    if(itrb == itre || dir == HIGH || size(polygon) < 4) {
+      polygon_index = -1;
+    } else {
+      direction_1d wdir = w;
+      if(!winding_override)
+        wdir = winding(polygon);
+      multiplier_ = wdir == LOW ? -1 : 1;
+      if(is_hole_) multiplier_ *= -1;
+      first_pt = pts[0] = *itrb;
+      ++itrb;
+      second_pt = pts[1] = *itrb;
+      ++itrb;
+      pts[2] = *itrb;
+      evaluate_();
+    }
+  }
+  iterator_geometry_to_set(const iterator_geometry_to_set& that) : 
+    vertex_(), itrb(), itre(), last_vertex_(), is_hole_(), multiplier_(), first_pt(),
+    second_pt(), pts(), use_wrap(), orient_(), polygon_index(-1) {
+    vertex_ = that.vertex_;
+    itrb = that.itrb;
+    itre = that.itre;
+    last_vertex_ = that.last_vertex_;
+    is_hole_ = that.is_hole_;
+    multiplier_ = that.multiplier_;
+    first_pt = that.first_pt;
+    second_pt = that.second_pt;
+    pts[0] = that.pts[0];
+    pts[1] = that.pts[1];
+    pts[2] = that.pts[2];
+    use_wrap = that.use_wrap;
+    orient_ = that.orient_;
+    polygon_index = that.polygon_index;
+  }
+  inline iterator_geometry_to_set& operator++() {
+    ++polygon_index;
+    if(itrb == itre) {
+      if(first_pt == pts[1]) polygon_index = -1;
+      else {
+        pts[0] = pts[1];
+        pts[1] = pts[2];
+        if(first_pt == pts[2]) {
+          pts[2] = second_pt;
+        } else {
+          pts[2] = first_pt;
+        }
+      }
+    } else {
+      ++itrb;
+      pts[0] = pts[1];
+      pts[1] = pts[2];
+      if(itrb == itre) {
+        if(first_pt == pts[2]) {
+          pts[2] = second_pt;
+        } else {
+          pts[2] = first_pt;
+        }
+      } else {
+        pts[2] = *itrb;
+      }
+    }
+    evaluate_();
+    return *this;
+  }
+  inline const iterator_geometry_to_set operator++(int) {
+    iterator_geometry_to_set tmp(*this);
+    ++(*this);
+    return tmp;
+  }
+  inline bool operator==(const iterator_geometry_to_set& that) const {
+    return polygon_index == that.polygon_index;
+  }
+  inline bool operator!=(const iterator_geometry_to_set& that) const {
+    return !(*this == that);
+  }
+  inline reference operator*() const {
+    return vertex_; 
+  }
+
+  inline void evaluate_() {
+    vertex_.first = pts[1].get(orient_.get_perpendicular());
+    vertex_.second.first =pts[1].get(orient_);
+    if(pts[1] == pts[2]) {
+      vertex_.second.second = 0;
+    } else if(pts[0].get(HORIZONTAL) != pts[1].get(HORIZONTAL)) {
+      vertex_.second.second = -1; 
+    } else if(pts[0].get(VERTICAL) != pts[1].get(VERTICAL)) {
+      vertex_.second.second = 1;
+    } else {
+      vertex_.second.second = 0;
+    }
+    vertex_.second.second *= multiplier_;
+  }
+};
+
+template <typename polygon_with_holes_type>
+class iterator_geometry_to_set<polygon_90_with_holes_concept, polygon_with_holes_type> {
+public:
+  typedef typename polygon_90_traits<polygon_with_holes_type>::coordinate_type coordinate_type;
+  typedef std::forward_iterator_tag iterator_category;
+  typedef std::pair<coordinate_type, std::pair<coordinate_type, int> > value_type;
+  typedef std::ptrdiff_t difference_type;
+  typedef const value_type* pointer; //immutable
+  typedef const value_type& reference; //immutable
+private:
+  iterator_geometry_to_set<polygon_90_concept, polygon_with_holes_type> itrb, itre;
+  iterator_geometry_to_set<polygon_90_concept, typename polygon_with_holes_traits<polygon_with_holes_type>::hole_type> itrhib, itrhie;
+  typename polygon_with_holes_traits<polygon_with_holes_type>::iterator_holes_type itrhb, itrhe;
+  orientation_2d orient_;
+  bool is_hole_;
+  bool started_holes;
+public:
+  iterator_geometry_to_set() : itrb(), itre(), itrhib(), itrhie(), itrhb(), itrhe(), orient_(), is_hole_(), started_holes() {}
+  iterator_geometry_to_set(const polygon_with_holes_type& polygon, direction_1d dir, 
+                           orientation_2d orient = HORIZONTAL, bool is_hole = false, bool = false, direction_1d = CLOCKWISE) : 
+    itrb(), itre(), itrhib(), itrhie(), itrhb(), itrhe(), orient_(orient), is_hole_(is_hole), started_holes() {
+    itre = iterator_geometry_to_set<polygon_90_concept, polygon_with_holes_type>(polygon, HIGH, orient, is_hole_);
+    itrhe = end_holes(polygon);
+    if(dir == HIGH) {
+      itrb = itre;
+      itrhb = itrhe;
+      started_holes = true;
+    } else {
+      itrb = iterator_geometry_to_set<polygon_90_concept, polygon_with_holes_type>(polygon, LOW, orient, is_hole_);
+      itrhb = begin_holes(polygon);
+      started_holes = false;
+    }
+  }
+  iterator_geometry_to_set(const iterator_geometry_to_set& that) : 
+    itrb(), itre(), itrhib(), itrhie(), itrhb(), itrhe(), orient_(), is_hole_(), started_holes() {
+    itrb = that.itrb;
+    itre = that.itre;
+    if(that.itrhib != that.itrhie) {
+      itrhib = that.itrhib;
+      itrhie = that.itrhie;
+    }
+    itrhb = that.itrhb;
+    itrhe = that.itrhe;
+    orient_ = that.orient_;
+    is_hole_ = that.is_hole_;
+    started_holes = that.started_holes;
+  }
+  inline iterator_geometry_to_set& operator++() {
+    //this code can be folded with flow control factoring
+    if(itrb == itre) {
+      if(itrhib == itrhie) {
+        if(itrhb != itrhe) {
+          itrhib = iterator_geometry_to_set<polygon_90_concept, 
+            typename polygon_with_holes_traits<polygon_with_holes_type>::hole_type>(*itrhb, LOW, orient_, !is_hole_);
+          itrhie = iterator_geometry_to_set<polygon_90_concept, 
+            typename polygon_with_holes_traits<polygon_with_holes_type>::hole_type>(*itrhb, HIGH, orient_, !is_hole_);
+          ++itrhb;
+        } else {
+          //in this case we have no holes so we just need the iterhib == itrhie, which
+          //is always true if they were default initialized in the initial case or
+          //both point to end of the previous hole processed
+          //no need to explicitly reset them, and it causes an stl debug assertion to use
+          //the default constructed iterator this way
+          //itrhib = itrhie = iterator_geometry_to_set<polygon_90_concept, 
+          //  typename polygon_with_holes_traits<polygon_with_holes_type>::hole_type>();
+        }
+      } else {
+        ++itrhib;
+        if(itrhib == itrhie) {
+          if(itrhb != itrhe) {
+            itrhib = iterator_geometry_to_set<polygon_90_concept, 
+              typename polygon_with_holes_traits<polygon_with_holes_type>::hole_type>(*itrhb, LOW, orient_, !is_hole_);
+            itrhie = iterator_geometry_to_set<polygon_90_concept, 
+              typename polygon_with_holes_traits<polygon_with_holes_type>::hole_type>(*itrhb, HIGH, orient_, !is_hole_);
+            ++itrhb;
+          } else {
+            //this is the same case as above
+            //itrhib = itrhie = iterator_geometry_to_set<polygon_90_concept, 
+            //  typename polygon_with_holes_traits<polygon_with_holes_type>::hole_type>();
+          }
+        }
+      }
+    } else {
+      ++itrb;
+      if(itrb == itre) {
+        if(itrhb != itrhe) {
+          itrhib = iterator_geometry_to_set<polygon_90_concept, 
+            typename polygon_with_holes_traits<polygon_with_holes_type>::hole_type>(*itrhb, LOW, orient_, !is_hole_);
+          itrhie = iterator_geometry_to_set<polygon_90_concept, 
+            typename polygon_with_holes_traits<polygon_with_holes_type>::hole_type>(*itrhb, HIGH, orient_, !is_hole_);
+          ++itrhb;
+        }
+      }
+    }
+    return *this;
+  }
+  inline const iterator_geometry_to_set operator++(int) {
+    iterator_geometry_to_set tmp(*this);
+    ++(*this);
+    return tmp;
+  }
+  inline bool operator==(const iterator_geometry_to_set& that) const {
+    return itrb == that.itrb && itrhb == that.itrhb && itrhib == that.itrhib;
+  }
+  inline bool operator!=(const iterator_geometry_to_set& that) const {
+    return !(*this == that);
+  }
+  inline reference operator*() const {
+    if(itrb != itre) return *itrb;
+    return *itrhib;
+  }
+};
+
+
+}
+}
+#endif
+

test/external/boost/polygon/detail/iterator_points_to_compact.hpp

@@ -0,0 +1,60 @@
+/*
+  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_ITERATOR_POINTS_TO_COMPACT_HPP
+#define BOOST_POLYGON_ITERATOR_POINTS_TO_COMPACT_HPP
+namespace boost { namespace polygon{
+template <typename iT, typename point_type>
+class iterator_points_to_compact {
+private:
+  iT iter_, iterEnd_;
+  orientation_2d orient_;
+  mutable typename point_traits<point_type>::coordinate_type coord_;
+public:
+  typedef typename point_traits<point_type>::coordinate_type coordinate_type;
+  typedef std::forward_iterator_tag iterator_category;
+  typedef coordinate_type value_type;
+  typedef std::ptrdiff_t difference_type;
+  typedef const coordinate_type* pointer; //immutable
+  typedef const coordinate_type& reference; //immutable
+
+  inline iterator_points_to_compact() : iter_(), iterEnd_(), orient_(), coord_() {}
+  inline iterator_points_to_compact(iT iter, iT iterEnd) : 
+    iter_(iter), iterEnd_(iterEnd), orient_(HORIZONTAL), coord_() {}
+  inline iterator_points_to_compact(const iterator_points_to_compact& that) : 
+    iter_(that.iter_), iterEnd_(that.iterEnd_), orient_(that.orient_), coord_(that.coord_) {}
+  //use bitwise copy and assign provided by the compiler
+  inline iterator_points_to_compact& operator++() {
+    //iT tmp = iter_;
+    ++iter_;
+    //iT tmp2 = iter_;
+    orient_.turn_90();
+    //while(tmp2 != iterEnd_ && get(*tmp2, orient_) == get(*tmp, orient_)) {
+    //  iter_ = tmp2;
+    //  ++tmp2;
+    //}
+    return *this;
+  }
+  inline const iterator_points_to_compact operator++(int) {
+    iT tmp(*this);
+    ++(*this);
+    return tmp;
+  }
+  inline bool operator==(const iterator_points_to_compact& that) const {
+    return (iter_ == that.iter_);
+  }
+  inline bool operator!=(const iterator_points_to_compact& that) const {
+    return (iter_ != that.iter_);
+  }
+  inline reference operator*() const { coord_ = get(*iter_, orient_); 
+    return coord_;
+  }
+};
+}
+}
+#endif
+

test/external/boost/polygon/detail/max_cover.hpp

@@ -0,0 +1,278 @@
+/*
+  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_MAX_COVER_HPP
+#define BOOST_POLYGON_MAX_COVER_HPP
+namespace boost { namespace polygon{
+
+  template <typename Unit>
+  struct MaxCover {
+    typedef interval_data<Unit> Interval;
+    typedef rectangle_data<Unit> Rectangle;
+
+    class Node {
+    private:
+      std::vector<Node*> children_;
+      std::set<Interval> tracedPaths_;
+    public:
+      Rectangle rect;
+      Node() : children_(), tracedPaths_(), rect() {}
+      Node(const Rectangle rectIn) : children_(), tracedPaths_(), rect(rectIn) {}
+      typedef typename std::vector<Node*>::iterator iterator;
+      inline iterator begin() { return children_.begin(); }
+      inline iterator end() { return children_.end(); }
+      inline void add(Node* child) { children_.push_back(child); }
+      inline bool tracedPath(const Interval& ivl) const {
+        return tracedPaths_.find(ivl) != tracedPaths_.end();
+      }
+      inline void addPath(const Interval& ivl) {
+        tracedPaths_.insert(tracedPaths_.end(), ivl);
+      }
+    };
+
+    typedef std::pair<std::pair<Unit, Interval>, Node* > EdgeAssociation;
+  
+    class lessEdgeAssociation : public std::binary_function<const EdgeAssociation&, const EdgeAssociation&, bool> {
+    public:
+      inline lessEdgeAssociation() {}
+      inline bool operator () (const EdgeAssociation& elem1, const EdgeAssociation& elem2) const {
+        if(elem1.first.first < elem2.first.first) return true;
+        if(elem1.first.first > elem2.first.first) return false;
+        return elem1.first.second < elem2.first.second;
+      }
+    };
+
+    template <class cT>
+    static inline void getMaxCover(cT& outputContainer, Node* node, orientation_2d orient) {
+      Interval rectIvl = node->rect.get(orient);
+      if(node->tracedPath(rectIvl)) {
+        return;
+      }
+      node->addPath(rectIvl);
+      if(node->begin() == node->end()) {
+        //std::cout << "WRITE OUT 3: " << node->rect << std::endl;
+        outputContainer.push_back(copy_construct<typename cT::value_type, Rectangle>(node->rect));
+        return;
+      }
+      bool writeOut = true;
+      for(typename Node::iterator itr = node->begin(); itr != node->end(); ++itr) {
+        getMaxCover(outputContainer, *itr, orient, node->rect); //get rectangles down path
+        Interval nodeIvl = (*itr)->rect.get(orient);
+        if(contains(nodeIvl, rectIvl, true)) writeOut = false;
+      }
+      if(writeOut) {
+        //std::cout << "WRITE OUT 2: " << node->rect << std::endl;
+        outputContainer.push_back(copy_construct<typename cT::value_type, Rectangle>(node->rect));
+      }
+    }
+
+    struct stack_element {
+      inline stack_element() :
+        node(), rect(), itr() {}
+      inline stack_element(Node* n,
+                           const Rectangle& r,
+                           typename Node::iterator i) :
+        node(n), rect(r), itr(i) {}
+      Node* node;
+      Rectangle rect;
+      typename Node::iterator itr;
+    };
+
+    template <class cT>
+    static inline void getMaxCover(cT& outputContainer, Node* node, orientation_2d orient, 
+                                   Rectangle rect) {
+      //std::cout << "New Root\n";
+      std::vector<stack_element> stack;
+      typename Node::iterator itr = node->begin();
+      do {
+        //std::cout << "LOOP\n";
+        //std::cout << node->rect << std::endl;
+        Interval rectIvl = rect.get(orient);
+        Interval nodeIvl = node->rect.get(orient);
+        bool iresult = intersect(rectIvl, nodeIvl, false);
+        bool tresult = !node->tracedPath(rectIvl);
+        //std::cout << (itr != node->end()) << " " << iresult << " " << tresult << std::endl;
+        Rectangle nextRect1 = Rectangle(rectIvl, rectIvl);
+        Unit low = rect.get(orient.get_perpendicular()).low();
+        Unit high = node->rect.get(orient.get_perpendicular()).high();
+        nextRect1.set(orient.get_perpendicular(), Interval(low, high));
+        if(iresult && tresult) {
+          node->addPath(rectIvl);
+          bool writeOut = true;
+          //check further visibility beyond this node
+          for(typename Node::iterator itr2 = node->begin(); itr2 != node->end(); ++itr2) {
+            Interval nodeIvl3 = (*itr2)->rect.get(orient);
+            //if a child of this node can contain the interval then we can extend through
+            if(contains(nodeIvl3, rectIvl, true)) writeOut = false;
+            //std::cout << "child " << (*itr2)->rect << std::endl;
+          }
+          Rectangle nextRect2 = Rectangle(rectIvl, rectIvl);
+          Unit low2 = rect.get(orient.get_perpendicular()).low();
+          Unit high2 = node->rect.get(orient.get_perpendicular()).high();
+          nextRect2.set(orient.get_perpendicular(), Interval(low2, high2));
+          if(writeOut) {
+            //std::cout << "write out " << nextRect << std::endl;
+            outputContainer.push_back(copy_construct<typename cT::value_type, Rectangle>(nextRect2));
+          } else {
+            //std::cout << "supress " << nextRect << std::endl;
+          }
+        }
+        if(itr != node->end() && iresult && tresult) {
+          //std::cout << "recurse into child\n";
+          stack.push_back(stack_element(node, rect, itr));
+          rect = nextRect1;
+          node = *itr;
+          itr = node->begin();
+        } else {
+          if(!stack.empty()) {
+            //std::cout << "recurse out of child\n";
+            node = stack.back().node;
+            rect = stack.back().rect;
+            itr = stack.back().itr;
+            stack.pop_back();
+          } else {
+            //std::cout << "empty stack\n";
+            //if there were no children of the root node
+//             Rectangle nextRect = Rectangle(rectIvl, rectIvl);
+//             Unit low = rect.get(orient.get_perpendicular()).low();
+//             Unit high = node->rect.get(orient.get_perpendicular()).high();
+//             nextRect.set(orient.get_perpendicular(), Interval(low, high));
+//             outputContainer.push_back(copy_construct<typename cT::value_type, Rectangle>(nextRect));
+          }
+          //std::cout << "increment " << (itr != node->end()) << std::endl;
+          if(itr != node->end()) {
+            ++itr;
+            if(itr != node->end()) {
+              //std::cout << "recurse into next child.\n";
+              stack.push_back(stack_element(node, rect, itr));
+              Interval rectIvl2 = rect.get(orient);
+              Interval nodeIvl2 = node->rect.get(orient);
+              /*bool iresult =*/ intersect(rectIvl2, nodeIvl2, false);
+              Rectangle nextRect2 = Rectangle(rectIvl2, rectIvl2);
+              Unit low2 = rect.get(orient.get_perpendicular()).low();
+              Unit high2 = node->rect.get(orient.get_perpendicular()).high();
+              nextRect2.set(orient.get_perpendicular(), Interval(low2, high2));
+              rect = nextRect2;
+              //std::cout << "rect for next child" << rect << std::endl;
+              node = *itr;
+              itr = node->begin();
+            }
+          }
+        }
+      } while(!stack.empty() || itr != node->end());
+    }
+
+    /*  Function recursive version of getMaxCover
+        Because the code is so much simpler than the loop algorithm I retain it for clarity
+
+    template <class cT>
+    static inline void getMaxCover(cT& outputContainer, Node* node, orientation_2d orient, 
+                                   const Rectangle& rect) {
+      Interval rectIvl = rect.get(orient);
+      Interval nodeIvl = node->rect.get(orient);
+      if(!intersect(rectIvl, nodeIvl, false)) {
+        return;
+      }
+      if(node->tracedPath(rectIvl)) {
+        return;
+      }
+      node->addPath(rectIvl);
+      Rectangle nextRect(rectIvl, rectIvl);
+      Unit low = rect.get(orient.get_perpendicular()).low();
+      Unit high = node->rect.get(orient.get_perpendicular()).high();
+      nextRect.set(orient.get_perpendicular(), Interval(low, high));
+      bool writeOut = true;
+      rectIvl = nextRect.get(orient);
+      for(typename Node::iterator itr = node->begin(); itr != node->end(); ++itr) {
+        nodeIvl = (*itr)->rect.get(orient);
+        if(contains(nodeIvl, rectIvl, true)) writeOut = false;
+      }
+      if(writeOut) {
+        outputContainer.push_back(copy_construct<typename cT::value_type, Rectangle>(nextRect));
+      }
+      for(typename Node::iterator itr = node->begin(); itr != node->end(); ++itr) {
+        getMaxCover(outputContainer, *itr, orient, nextRect);
+      }
+    }
+    */
+
+    //iterator range is assummed to be in topological order meaning all node's trailing
+    //edges are in sorted order
+    template <class iT>
+    static inline void computeDag(iT beginNode, iT endNode, orientation_2d orient,
+                                  std::size_t size) {
+      std::vector<EdgeAssociation> leadingEdges; 
+      leadingEdges.reserve(size);
+      for(iT iter = beginNode; iter != endNode; ++iter) {
+        Node* nodep = &(*iter);
+        Unit leading = nodep->rect.get(orient.get_perpendicular()).low();
+        Interval rectIvl = nodep->rect.get(orient);
+        leadingEdges.push_back(EdgeAssociation(std::pair<Unit, Interval>(leading, rectIvl), nodep));
+      }
+      gtlsort(leadingEdges.begin(), leadingEdges.end(), lessEdgeAssociation());
+      typename std::vector<EdgeAssociation>::iterator leadingBegin = leadingEdges.begin();
+      iT trailingBegin = beginNode;
+      while(leadingBegin != leadingEdges.end()) {
+        EdgeAssociation& leadingSegment = (*leadingBegin);
+        Unit trailing = (*trailingBegin).rect.get(orient.get_perpendicular()).high();
+        Interval ivl = (*trailingBegin).rect.get(orient);
+        std::pair<Unit, Interval> trailingSegment(trailing, ivl);
+        if(leadingSegment.first.first < trailingSegment.first) {
+          ++leadingBegin;
+          continue;
+        }
+        if(leadingSegment.first.first > trailingSegment.first) {
+          ++trailingBegin;
+          continue;
+        }
+        if(leadingSegment.first.second.high() <= trailingSegment.second.low()) {
+          ++leadingBegin;
+          continue;
+        }
+        if(trailingSegment.second.high() <= leadingSegment.first.second.low()) {
+          ++trailingBegin;
+          continue;
+        }
+        //leading segment intersects trailing segment
+        (*trailingBegin).add((*leadingBegin).second);
+        if(leadingSegment.first.second.high() > trailingSegment.second.high()) {
+          ++trailingBegin;
+          continue;
+        }
+        if(trailingSegment.second.high() > leadingSegment.first.second.high()) {
+          ++leadingBegin;
+          continue;
+        }
+        ++leadingBegin;
+        ++trailingBegin;
+      }
+    }
+
+    template <class cT>
+    static inline void getMaxCover(cT& outputContainer,
+                                   const std::vector<Rectangle>& rects, orientation_2d orient) {
+      if(rects.empty()) return;
+      std::vector<Node> nodes;
+      {
+        if(rects.size() == 1) {
+          outputContainer.push_back(copy_construct<typename cT::value_type, Rectangle>(rects[0]));
+          return;
+        }
+        nodes.reserve(rects.size());
+        for(std::size_t i = 0; i < rects.size(); ++i) { nodes.push_back(Node(rects[i])); }
+      }
+      computeDag(nodes.begin(), nodes.end(), orient, nodes.size());
+      for(std::size_t i = 0; i < nodes.size(); ++i) {
+        getMaxCover(outputContainer, &(nodes[i]), orient);
+      }
+    }
+
+  };
+}
+}
+
+#endif

test/external/boost/polygon/detail/minkowski.hpp

@@ -0,0 +1,125 @@
+
+namespace boost { namespace polygon { namespace detail {
+
+template <typename coordinate_type>
+struct minkowski_offset {
+  typedef point_data<coordinate_type> point;
+  typedef polygon_set_data<coordinate_type> polygon_set;
+  typedef polygon_with_holes_data<coordinate_type> polygon;
+  typedef std::pair<point, point> edge;
+
+  static void convolve_two_segments(std::vector<point>& figure, const edge& a, const edge& b) {
+    figure.clear();
+    figure.push_back(point(a.first));
+    figure.push_back(point(a.first));
+    figure.push_back(point(a.second));
+    figure.push_back(point(a.second));
+    convolve(figure[0], b.second);
+    convolve(figure[1], b.first);
+    convolve(figure[2], b.first);
+    convolve(figure[3], b.second);
+  }
+
+  template <typename itrT1, typename itrT2>
+  static void convolve_two_point_sequences(polygon_set& result, itrT1 ab, itrT1 ae, itrT2 bb, itrT2 be) {
+    if(ab == ae || bb == be)
+      return;
+    point first_a = *ab;
+    point prev_a = *ab;
+    std::vector<point> vec;
+    polygon poly;
+    ++ab;
+    for( ; ab != ae; ++ab) {
+      point first_b = *bb;
+      point prev_b = *bb;
+      itrT2 tmpb = bb;
+      ++tmpb;
+      for( ; tmpb != be; ++tmpb) {
+        convolve_two_segments(vec, std::make_pair(prev_b, *tmpb), std::make_pair(prev_a, *ab));
+        set_points(poly, vec.begin(), vec.end());
+        result.insert(poly);
+        prev_b = *tmpb;
+      }
+      prev_a = *ab;
+    }
+  }
+
+  template <typename itrT>
+  static void convolve_point_sequence_with_polygons(polygon_set& result, itrT b, itrT e, const std::vector<polygon>& polygons) {
+    for(std::size_t i = 0; i < polygons.size(); ++i) {
+      convolve_two_point_sequences(result, b, e, begin_points(polygons[i]), end_points(polygons[i]));
+      for(typename polygon_with_holes_traits<polygon>::iterator_holes_type itrh = begin_holes(polygons[i]);
+          itrh != end_holes(polygons[i]); ++itrh) {
+        convolve_two_point_sequences(result, b, e, begin_points(*itrh), end_points(*itrh));
+      }
+    }
+  }
+
+  static void convolve_two_polygon_sets(polygon_set& result, const polygon_set& a, const polygon_set& b) {
+    result.clear();
+    std::vector<polygon> a_polygons;
+    std::vector<polygon> b_polygons;
+    a.get(a_polygons);
+    b.get(b_polygons);
+    for(std::size_t ai = 0; ai < a_polygons.size(); ++ai) {
+      convolve_point_sequence_with_polygons(result, begin_points(a_polygons[ai]), 
+                                            end_points(a_polygons[ai]), b_polygons);
+      for(typename polygon_with_holes_traits<polygon>::iterator_holes_type itrh = begin_holes(a_polygons[ai]);
+          itrh != end_holes(a_polygons[ai]); ++itrh) {
+        convolve_point_sequence_with_polygons(result, begin_points(*itrh), 
+                                              end_points(*itrh), b_polygons);
+      }
+      for(std::size_t bi = 0; bi < b_polygons.size(); ++bi) {
+        polygon tmp_poly = a_polygons[ai];
+        result.insert(convolve(tmp_poly, *(begin_points(b_polygons[bi]))));
+        tmp_poly = b_polygons[bi];
+        result.insert(convolve(tmp_poly, *(begin_points(a_polygons[ai]))));
+      }
+    }
+  }
+};
+
+}
+  template<typename T>
+  inline polygon_set_data<T>&
+  polygon_set_data<T>::resize(coordinate_type resizing, bool corner_fill_arc, unsigned int num_circle_segments) {
+    using namespace ::boost::polygon::operators;
+    if(!corner_fill_arc) {
+      if(resizing < 0)
+        return shrink(-resizing);
+      if(resizing > 0)
+        return bloat(resizing);
+      return *this;
+    }
+    if(resizing == 0) return *this;
+    if(empty()) return *this;
+    if(num_circle_segments < 3) num_circle_segments = 4;
+    rectangle_data<coordinate_type> rect;
+    extents(rect);
+    if(resizing < 0) {
+      ::boost::polygon::bloat(rect, 10);
+      (*this) = rect - (*this); //invert
+    }
+    //make_arc(std::vector<point_data< T> >& return_points,  
+    //point_data< double> start, point_data< double>  end,
+    //point_data< double> center,  double r, unsigned int num_circle_segments)      
+    std::vector<point_data<coordinate_type> > circle;
+    point_data<double> center(0.0, 0.0), start(0.0, (double)resizing);
+    make_arc(circle, start, start, center, std::abs((double)resizing),
+             num_circle_segments);
+    polygon_data<coordinate_type> poly;
+    set_points(poly, circle.begin(), circle.end());
+    polygon_set_data<coordinate_type> offset_set;
+    offset_set += poly;
+    polygon_set_data<coordinate_type> result;
+    detail::minkowski_offset<coordinate_type>::convolve_two_polygon_sets
+      (result, *this, offset_set);
+    if(resizing < 0) {
+      result = result & rect;//eliminate overhang
+      result = result ^ rect;//invert
+    }
+    *this = result;
+    return *this;
+  }
+
+}}

test/external/boost/polygon/detail/polygon_45_set_view.hpp

@@ -0,0 +1,378 @@
+/*
+  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_POLYGON_45_SET_VIEW_HPP
+#define BOOST_POLYGON_POLYGON_45_SET_VIEW_HPP
+namespace boost { namespace polygon{
+
+  template <typename ltype, typename rtype, int op_type>
+  class polygon_45_set_view;
+
+  template <typename ltype, typename rtype, int op_type>
+  struct polygon_45_set_traits<polygon_45_set_view<ltype, rtype, op_type> > {
+    typedef typename polygon_45_set_view<ltype, rtype, op_type>::coordinate_type coordinate_type;
+    typedef typename polygon_45_set_view<ltype, rtype, op_type>::iterator_type iterator_type;
+    typedef typename polygon_45_set_view<ltype, rtype, op_type>::operator_arg_type operator_arg_type;
+
+    static inline iterator_type begin(const polygon_45_set_view<ltype, rtype, op_type>& polygon_45_set); 
+    static inline iterator_type end(const polygon_45_set_view<ltype, rtype, op_type>& polygon_45_set);
+
+    template <typename input_iterator_type>
+    static inline void set(polygon_45_set_view<ltype, rtype, op_type>& polygon_45_set, 
+                           input_iterator_type input_begin, input_iterator_type input_end);
+
+    static inline bool clean(const polygon_45_set_view<ltype, rtype, op_type>& polygon_45_set);
+
+  };
+
+  template <typename value_type, typename ltype, typename rtype, int op_type>
+  struct compute_45_set_value {
+    static
+    void value(value_type& output_, const ltype& lvalue_, const rtype& rvalue_) {
+      output_.set(polygon_45_set_traits<ltype>::begin(lvalue_),
+                  polygon_45_set_traits<ltype>::end(lvalue_));
+      value_type rinput_;
+      rinput_.set(polygon_45_set_traits<rtype>::begin(rvalue_),
+                  polygon_45_set_traits<rtype>::end(rvalue_));
+#ifdef BOOST_POLYGON_MSVC
+#pragma warning (disable: 4127)
+#endif
+      if(op_type == 0)
+        output_ |= rinput_;
+      else if(op_type == 1)
+        output_ &= rinput_;
+      else if(op_type == 2)
+        output_ ^= rinput_;
+      else
+        output_ -= rinput_;
+#ifdef BOOST_POLYGON_MSVC
+#pragma warning (default: 4127)
+#endif
+    }
+  };
+
+  template <typename value_type, typename ltype, typename rcoord, int op_type>
+  struct compute_45_set_value<value_type, ltype, polygon_45_set_data<rcoord>, op_type> {
+    static
+    void value(value_type& output_, const ltype& lvalue_, const polygon_45_set_data<rcoord>& rvalue_) {
+      output_.set(polygon_45_set_traits<ltype>::begin(lvalue_),
+                  polygon_45_set_traits<ltype>::end(lvalue_));
+#ifdef BOOST_POLYGON_MSVC
+#pragma warning (disable: 4127)
+#endif
+      if(op_type == 0)
+        output_ |= rvalue_;
+      else if(op_type == 1)
+        output_ &= rvalue_;
+      else if(op_type == 2)
+        output_ ^= rvalue_;
+      else
+        output_ -= rvalue_;
+#ifdef BOOST_POLYGON_MSVC
+#pragma warning (default: 4127)
+#endif
+    }
+  };
+
+  template <typename ltype, typename rtype, int op_type>
+  class polygon_45_set_view {
+  public:
+    typedef typename polygon_45_set_traits<ltype>::coordinate_type coordinate_type;
+    typedef polygon_45_set_data<coordinate_type> value_type;
+    typedef typename value_type::iterator_type iterator_type;
+    typedef polygon_45_set_view operator_arg_type;
+  private:
+    const ltype& lvalue_;
+    const rtype& rvalue_;
+    mutable value_type output_;
+    mutable bool evaluated_;
+
+    polygon_45_set_view& operator=(const polygon_45_set_view&);
+  public:
+    polygon_45_set_view(const ltype& lvalue,
+                        const rtype& rvalue ) :
+      lvalue_(lvalue), rvalue_(rvalue), output_(), evaluated_(false) {}
+
+    // get iterator to begin vertex data
+  public:
+    const value_type& value() const {
+      if(!evaluated_) {
+        evaluated_ = true;
+        compute_45_set_value<value_type, ltype, rtype, op_type>::value(output_, lvalue_, rvalue_);
+      }
+      return output_;
+    }
+  public:
+    iterator_type begin() const { return value().begin(); }
+    iterator_type end() const { return value().end(); }
+
+    bool dirty() const { return value().dirty(); } //result of a boolean is clean
+    bool sorted() const { return value().sorted(); } //result of a boolean is sorted
+
+    //     template <typename input_iterator_type>
+    //     void set(input_iterator_type input_begin, input_iterator_type input_end, 
+    //              orientation_2d orient) const {
+    //       orient_ = orient;
+    //       output_.clear();
+    //       output_.insert(output_.end(), input_begin, input_end);
+    //       gtlsort(output_.begin(), output_.end());
+    //     }
+  };
+
+  template <typename ltype, typename rtype, int op_type>
+  typename polygon_45_set_traits<polygon_45_set_view<ltype, rtype, op_type> >::iterator_type
+  polygon_45_set_traits<polygon_45_set_view<ltype, rtype, op_type> >::
+  begin(const polygon_45_set_view<ltype, rtype, op_type>& polygon_45_set) {
+    return polygon_45_set.begin();
+  }
+  template <typename ltype, typename rtype, int op_type>
+  typename polygon_45_set_traits<polygon_45_set_view<ltype, rtype, op_type> >::iterator_type
+  polygon_45_set_traits<polygon_45_set_view<ltype, rtype, op_type> >::
+  end(const polygon_45_set_view<ltype, rtype, op_type>& polygon_45_set) {
+    return polygon_45_set.end();
+  }
+  template <typename ltype, typename rtype, int op_type>
+  bool polygon_45_set_traits<polygon_45_set_view<ltype, rtype, op_type> >::
+  clean(const polygon_45_set_view<ltype, rtype, op_type>& polygon_45_set) { 
+    return polygon_45_set.value().clean(); }
+
+  template <typename geometry_type_1, typename geometry_type_2, int op_type>
+  geometry_type_1& self_assignment_boolean_op_45(geometry_type_1& lvalue_, const geometry_type_2& rvalue_) {
+    typedef geometry_type_1 ltype;
+    typedef geometry_type_2 rtype;
+    typedef typename polygon_45_set_traits<ltype>::coordinate_type coordinate_type;
+    typedef polygon_45_set_data<coordinate_type> value_type;
+    value_type output_;
+    value_type rinput_;
+    output_.set(polygon_45_set_traits<ltype>::begin(lvalue_),
+                polygon_45_set_traits<ltype>::end(lvalue_));
+    rinput_.set(polygon_45_set_traits<rtype>::begin(rvalue_),
+                polygon_45_set_traits<rtype>::end(rvalue_));
+#ifdef BOOST_POLYGON_MSVC
+#pragma warning (disable: 4127)
+#endif
+    if(op_type == 0)
+      output_ |= rinput_;
+    else if(op_type == 1)
+      output_ &= rinput_;
+    else if(op_type == 2)
+      output_ ^= rinput_;
+    else
+      output_ -= rinput_;
+#ifdef BOOST_POLYGON_MSVC
+#pragma warning (default: 4127)
+#endif
+    polygon_45_set_mutable_traits<geometry_type_1>::set(lvalue_, output_.begin(), output_.end());
+    return lvalue_;
+  }
+
+  template <typename concept_type>
+  struct fracture_holes_option_by_type {
+    static const bool value = true;
+  };
+  template <>
+  struct fracture_holes_option_by_type<polygon_45_with_holes_concept> {
+    static const bool value = false;
+  };
+  template <>
+  struct fracture_holes_option_by_type<polygon_with_holes_concept> {
+    static const bool value = false;
+  };
+
+  template <typename ltype, typename rtype, int op_type>
+  struct geometry_concept<polygon_45_set_view<ltype, rtype, op_type> > { typedef polygon_45_set_concept type; };
+
+  namespace operators {
+  struct y_ps45_b : gtl_yes {};
+
+  template <typename geometry_type_1, typename geometry_type_2>
+  typename enable_if< typename gtl_and_4< y_ps45_b,
+    typename is_polygon_45_or_90_set_type<geometry_type_1>::type,
+    typename is_polygon_45_or_90_set_type<geometry_type_2>::type,
+    typename is_either_polygon_45_set_type<geometry_type_1, geometry_type_2>::type>::type,
+                       polygon_45_set_view<geometry_type_1, geometry_type_2, 0> >::type 
+  operator|(const geometry_type_1& lvalue, const geometry_type_2& rvalue) {
+    return polygon_45_set_view<geometry_type_1, geometry_type_2, 0>
+      (lvalue, rvalue);
+  }
+  
+  struct y_ps45_p : gtl_yes {};
+
+  template <typename geometry_type_1, typename geometry_type_2>
+  typename enable_if< typename gtl_and_4< y_ps45_p,
+    typename gtl_if<typename is_polygon_45_or_90_set_type<geometry_type_1>::type>::type, 
+    typename gtl_if<typename is_polygon_45_or_90_set_type<geometry_type_2>::type>::type, 
+    typename gtl_if<typename is_either_polygon_45_set_type<geometry_type_1, geometry_type_2>::type>::type>::type, 
+  polygon_45_set_view<geometry_type_1, geometry_type_2, 0> >::type 
+  operator+(const geometry_type_1& lvalue, const geometry_type_2& rvalue) {
+    return polygon_45_set_view<geometry_type_1, geometry_type_2, 0>
+      (lvalue, rvalue);
+  }
+  
+  struct y_ps45_s : gtl_yes {};
+
+  template <typename geometry_type_1, typename geometry_type_2>
+  typename enable_if< typename gtl_and_4< y_ps45_s, typename is_polygon_45_or_90_set_type<geometry_type_1>::type,
+                                           typename is_polygon_45_or_90_set_type<geometry_type_2>::type,
+                                           typename is_either_polygon_45_set_type<geometry_type_1, geometry_type_2>::type>::type,
+                       polygon_45_set_view<geometry_type_1, geometry_type_2, 1> >::type 
+  operator*(const geometry_type_1& lvalue, const geometry_type_2& rvalue) {
+    return polygon_45_set_view<geometry_type_1, geometry_type_2, 1>
+      (lvalue, rvalue);
+  }
+
+  struct y_ps45_a : gtl_yes {};
+
+  template <typename geometry_type_1, typename geometry_type_2>
+  typename enable_if< typename gtl_and_4< y_ps45_a, typename is_polygon_45_or_90_set_type<geometry_type_1>::type,
+                                           typename is_polygon_45_or_90_set_type<geometry_type_2>::type,
+                                           typename is_either_polygon_45_set_type<geometry_type_1, geometry_type_2>::type>::type,
+                       polygon_45_set_view<geometry_type_1, geometry_type_2, 1> >::type 
+  operator&(const geometry_type_1& lvalue, const geometry_type_2& rvalue) {
+    return polygon_45_set_view<geometry_type_1, geometry_type_2, 1>
+      (lvalue, rvalue);
+  }
+
+  struct y_ps45_x : gtl_yes {};
+
+  template <typename geometry_type_1, typename geometry_type_2>
+  typename enable_if< typename gtl_and_4< y_ps45_x, typename is_polygon_45_or_90_set_type<geometry_type_1>::type,
+                                           typename is_polygon_45_or_90_set_type<geometry_type_2>::type,
+                                           typename is_either_polygon_45_set_type<geometry_type_1, geometry_type_2>::type>::type,
+                       polygon_45_set_view<geometry_type_1, geometry_type_2, 2> >::type 
+  operator^(const geometry_type_1& lvalue, const geometry_type_2& rvalue) {
+    return polygon_45_set_view<geometry_type_1, geometry_type_2, 2>
+      (lvalue, rvalue);
+  }
+  
+  struct y_ps45_m : gtl_yes {};
+
+  template <typename geometry_type_1, typename geometry_type_2>
+  typename enable_if< typename gtl_and_4< y_ps45_m,
+    typename gtl_if<typename is_polygon_45_or_90_set_type<geometry_type_1>::type>::type, 
+    typename gtl_if<typename is_polygon_45_or_90_set_type<geometry_type_2>::type>::type, 
+    typename gtl_if<typename is_either_polygon_45_set_type<geometry_type_1, geometry_type_2>::type>::type>::type, 
+  polygon_45_set_view<geometry_type_1, geometry_type_2, 3> >::type 
+  operator-(const geometry_type_1& lvalue, const geometry_type_2& rvalue) {
+    return polygon_45_set_view<geometry_type_1, geometry_type_2, 3>
+      (lvalue, rvalue);
+  }
+  
+  struct y_ps45_pe : gtl_yes {};
+
+  template <typename geometry_type_1, typename geometry_type_2>
+  typename enable_if< typename gtl_and_4<y_ps45_pe, typename is_mutable_polygon_45_set_type<geometry_type_1>::type, gtl_yes,
+                                         typename is_polygon_45_or_90_set_type<geometry_type_2>::type>::type, 
+                       geometry_type_1>::type &
+  operator+=(geometry_type_1& lvalue, const geometry_type_2& rvalue) {
+    return self_assignment_boolean_op_45<geometry_type_1, geometry_type_2, 0>(lvalue, rvalue);
+  }
+
+  struct y_ps45_be : gtl_yes {};
+
+  template <typename geometry_type_1, typename geometry_type_2>
+  typename enable_if< typename gtl_and_3<y_ps45_be, typename is_mutable_polygon_45_set_type<geometry_type_1>::type, 
+                                         typename is_polygon_45_or_90_set_type<geometry_type_2>::type>::type, 
+                       geometry_type_1>::type &
+  operator|=(geometry_type_1& lvalue, const geometry_type_2& rvalue) {
+    return self_assignment_boolean_op_45<geometry_type_1, geometry_type_2, 0>(lvalue, rvalue);
+  }
+
+  struct y_ps45_se : gtl_yes {};
+
+  template <typename geometry_type_1, typename geometry_type_2>
+  typename enable_if< typename gtl_and_3< y_ps45_se,
+    typename is_mutable_polygon_45_set_type<geometry_type_1>::type, 
+    typename is_polygon_45_or_90_set_type<geometry_type_2>::type>::type, 
+                       geometry_type_1>::type &
+  operator*=(geometry_type_1& lvalue, const geometry_type_2& rvalue) {
+    return self_assignment_boolean_op_45<geometry_type_1, geometry_type_2, 1>(lvalue, rvalue);
+  }
+
+  struct y_ps45_ae : gtl_yes {};
+
+  template <typename geometry_type_1, typename geometry_type_2>
+  typename enable_if< typename gtl_and_3<y_ps45_ae, typename is_mutable_polygon_45_set_type<geometry_type_1>::type, 
+                                         typename is_polygon_45_or_90_set_type<geometry_type_2>::type>::type, 
+                       geometry_type_1>::type &
+  operator&=(geometry_type_1& lvalue, const geometry_type_2& rvalue) {
+    return self_assignment_boolean_op_45<geometry_type_1, geometry_type_2, 1>(lvalue, rvalue);
+  }
+
+  struct y_ps45_xe : gtl_yes {};
+
+  template <typename geometry_type_1, typename geometry_type_2>
+  typename enable_if< 
+    typename gtl_and_3<y_ps45_xe, typename is_mutable_polygon_45_set_type<geometry_type_1>::type, 
+                      typename is_polygon_45_or_90_set_type<geometry_type_2>::type>::type, 
+    geometry_type_1>::type &
+  operator^=(geometry_type_1& lvalue, const geometry_type_2& rvalue) {
+    return self_assignment_boolean_op_45<geometry_type_1, geometry_type_2, 2>(lvalue, rvalue);
+  }
+
+  struct y_ps45_me : gtl_yes {};
+
+  template <typename geometry_type_1, typename geometry_type_2>
+  typename enable_if< typename gtl_and_3<y_ps45_me, typename is_mutable_polygon_45_set_type<geometry_type_1>::type, 
+                                         typename is_polygon_45_or_90_set_type<geometry_type_2>::type>::type, 
+                       geometry_type_1>::type &
+  operator-=(geometry_type_1& lvalue, const geometry_type_2& rvalue) {
+    return self_assignment_boolean_op_45<geometry_type_1, geometry_type_2, 3>(lvalue, rvalue);
+  }
+
+  struct y_ps45_rpe : gtl_yes {};
+
+  template <typename geometry_type_1, typename coordinate_type_1>
+  typename enable_if< typename gtl_and_3< y_ps45_rpe, typename is_mutable_polygon_45_set_type<geometry_type_1>::type, 
+                                         typename gtl_same_type<typename geometry_concept<coordinate_type_1>::type, 
+                                                                coordinate_concept>::type>::type,
+                       geometry_type_1>::type &
+  operator+=(geometry_type_1& lvalue, coordinate_type_1 rvalue) {
+    return resize(lvalue, rvalue);
+  }
+
+  struct y_ps45_rme : gtl_yes {};
+
+  template <typename geometry_type_1, typename coordinate_type_1>
+  typename enable_if< typename gtl_and_3<y_ps45_rme, typename gtl_if<typename is_mutable_polygon_45_set_type<geometry_type_1>::type>::type, 
+                                         typename gtl_same_type<typename geometry_concept<coordinate_type_1>::type, 
+                                                                coordinate_concept>::type>::type,
+                       geometry_type_1>::type &
+  operator-=(geometry_type_1& lvalue, coordinate_type_1 rvalue) {
+    return resize(lvalue, -rvalue);
+  }
+
+  struct y_ps45_rp : gtl_yes {};
+
+  template <typename geometry_type_1, typename coordinate_type_1>
+  typename enable_if< typename gtl_and_3<y_ps45_rp, typename gtl_if<typename is_mutable_polygon_45_set_type<geometry_type_1>::type>::type, 
+                                        typename gtl_same_type<typename geometry_concept<coordinate_type_1>::type, 
+                                                               coordinate_concept>::type>
+  ::type, geometry_type_1>::type
+  operator+(const geometry_type_1& lvalue, coordinate_type_1 rvalue) {
+    geometry_type_1 retval(lvalue);
+    retval += rvalue;
+    return retval;
+  }
+
+  struct y_ps45_rm : gtl_yes {};
+
+  template <typename geometry_type_1, typename coordinate_type_1>
+  typename enable_if< typename gtl_and_3<y_ps45_rm, typename gtl_if<typename is_mutable_polygon_45_set_type<geometry_type_1>::type>::type, 
+                                        typename gtl_same_type<typename geometry_concept<coordinate_type_1>::type, 
+                                                               coordinate_concept>::type>
+  ::type, geometry_type_1>::type
+  operator-(const geometry_type_1& lvalue, coordinate_type_1 rvalue) {
+    geometry_type_1 retval(lvalue);
+    retval -= rvalue;
+    return retval;
+  }
+  }
+}
+}
+#endif
+

test/external/boost/polygon/detail/polygon_45_touch.hpp

@@ -0,0 +1,236 @@
+/*
+  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_POLYGON_45_TOUCH_HPP
+#define BOOST_POLYGON_POLYGON_45_TOUCH_HPP
+namespace boost { namespace polygon{
+
+  template <typename Unit>
+  struct polygon_45_touch {
+
+    typedef point_data<Unit> Point;
+    typedef typename coordinate_traits<Unit>::manhattan_area_type LongUnit;
+
+    template <typename property_map>
+    static inline void merge_property_maps(property_map& mp, const property_map& mp2, bool subtract = false) {
+      property_map newmp;
+      newmp.reserve(mp.size() + mp2.size());
+      std::size_t i = 0;
+      std::size_t j = 0;
+      while(i != mp.size() && j != mp2.size()) {
+        if(mp[i].first < mp2[j].first) {
+          newmp.push_back(mp[i]);
+          ++i;
+        } else if(mp[i].first > mp2[j].first) {
+          newmp.push_back(mp2[j]);
+          if(subtract) newmp.back().second *= -1;
+          ++j;
+        } else {
+          int count = mp[i].second;
+          if(subtract) count -= mp2[j].second;
+          else count += mp2[j].second; 
+          if(count) {
+            newmp.push_back(mp[i]);
+            newmp.back().second = count;
+          }
+          ++i;
+          ++j;
+        }
+      }
+      while(i != mp.size()) {
+        newmp.push_back(mp[i]);
+        ++i;
+      }
+      while(j != mp2.size()) {
+        newmp.push_back(mp2[j]);
+        if(subtract) newmp.back().second *= -1;
+        ++j;
+      }
+      mp.swap(newmp);
+    }
+
+    class CountTouch {
+    public:
+      inline CountTouch() : counts() {}
+      //inline CountTouch(int count) { counts[0] = counts[1] = count; }
+      //inline CountTouch(int count1, int count2) { counts[0] = count1; counts[1] = count2; }
+      inline CountTouch(const CountTouch& count) : counts(count.counts) {}
+      inline bool operator==(const CountTouch& count) const { return counts == count.counts; }
+      inline bool operator!=(const CountTouch& count) const { return !((*this) == count); }
+      //inline CountTouch& operator=(int count) { counts[0] = counts[1] = count; return *this; }
+      inline CountTouch& operator=(const CountTouch& count) { counts = count.counts; return *this; }
+      inline int& operator[](int index) { 
+        std::vector<std::pair<int, int> >::iterator itr = lower_bound(counts.begin(), counts.end(), std::make_pair(index, int(0)));
+        if(itr != counts.end() && itr->first == index) {
+            return itr->second;
+        }
+        itr = counts.insert(itr, std::make_pair(index, int(0)));
+        return itr->second;
+      }
+//       inline int operator[](int index) const {
+//         std::vector<std::pair<int, int> >::const_iterator itr = counts.begin();
+//         for( ; itr != counts.end() && itr->first <= index; ++itr) {
+//           if(itr->first == index) {
+//             return itr->second;
+//           }
+//         }
+//         return 0;
+//       }
+      inline CountTouch& operator+=(const CountTouch& count){
+        merge_property_maps(counts, count.counts, false);
+        return *this;
+      }
+      inline CountTouch& operator-=(const CountTouch& count){
+        merge_property_maps(counts, count.counts, true);
+        return *this;
+      }
+      inline CountTouch operator+(const CountTouch& count) const {
+        return CountTouch(*this)+=count;
+      }
+      inline CountTouch operator-(const CountTouch& count) const {
+        return CountTouch(*this)-=count;
+      }
+      inline CountTouch invert() const {
+        CountTouch retval;
+        retval -= *this;
+        return retval;
+      }
+      std::vector<std::pair<int, int> > counts;
+    };
+
+    typedef std::pair<std::pair<Unit, std::map<Unit, std::set<int> > >, std::map<int, std::set<int> > > map_graph_o; 
+    typedef std::pair<std::pair<Unit, std::map<Unit, std::set<int> > >, std::vector<std::set<int> > > vector_graph_o; 
+
+    template <typename cT>
+    static void process_previous_x(cT& output) {
+      std::map<Unit, std::set<int> >& y_prop_map = output.first.second;
+      for(typename std::map<Unit, std::set<int> >::iterator itr = y_prop_map.begin();
+          itr != y_prop_map.end(); ++itr) {
+        for(std::set<int>::iterator inner_itr = itr->second.begin();
+            inner_itr != itr->second.end(); ++inner_itr) {
+          std::set<int>& output_edges = (*(output.second))[*inner_itr];
+          std::set<int>::iterator inner_inner_itr = inner_itr;
+          ++inner_inner_itr;
+          for( ; inner_inner_itr != itr->second.end(); ++inner_inner_itr) {
+            output_edges.insert(output_edges.end(), *inner_inner_itr);
+            std::set<int>& output_edges_2 = (*(output.second))[*inner_inner_itr];
+            output_edges_2.insert(output_edges_2.end(), *inner_itr);
+          }
+        }
+      }
+      y_prop_map.clear();
+    }
+    
+    struct touch_45_output_functor {
+      template <typename cT>
+      void operator()(cT& output, const CountTouch& count1, const CountTouch& count2, 
+                      const Point& pt, int , direction_1d ) {
+        Unit& x = output.first.first;
+        std::map<Unit, std::set<int> >& y_prop_map = output.first.second;
+        if(pt.x() != x) process_previous_x(output);
+        x = pt.x();
+        std::set<int>& output_set = y_prop_map[pt.y()];
+        for(std::vector<std::pair<int, int> >::const_iterator itr1 = count1.counts.begin();
+            itr1 != count1.counts.end(); ++itr1) {
+          if(itr1->second > 0) {
+            output_set.insert(output_set.end(), itr1->first);
+          } 
+        }
+        for(std::vector<std::pair<int, int> >::const_iterator itr2 = count2.counts.begin();
+            itr2 != count2.counts.end(); ++itr2) {
+          if(itr2->second > 0) {
+            output_set.insert(output_set.end(), itr2->first);
+          }
+        }
+      }
+    };
+    typedef typename std::pair<Point, 
+                               typename boolean_op_45<Unit>::template Scan45CountT<CountTouch> > Vertex45Compact;
+    typedef std::vector<Vertex45Compact> TouchSetData;
+    
+    struct lessVertex45Compact {
+      bool operator()(const Vertex45Compact& l, const Vertex45Compact& r) {
+        return l.first < r.first;
+      }
+    };
+    
+//     template <typename TSD>
+//     static void print_tsd(TSD& tsd) {
+//       for(std::size_t i = 0; i < tsd.size(); ++i) {
+//         std::cout << tsd[i].first << ": ";
+//         for(unsigned int r = 0; r < 4; ++r) {
+//           std::cout << r << " { ";
+//           for(std::vector<std::pair<int, int> >::iterator itr = tsd[i].second[r].counts.begin();
+//               itr != tsd[i].second[r].counts.end(); ++itr) {
+//             std::cout << itr->first << "," << itr->second << " ";
+//           } std::cout << "} ";
+//         }
+//       } std::cout << std::endl;
+//     }
+
+//     template <typename T>
+//     static void print_scanline(T& t) {
+//       for(typename T::iterator itr = t.begin(); itr != t.end(); ++itr) {
+//         std::cout << itr->x << "," << itr->y << " " << itr->rise << " ";
+//         for(std::vector<std::pair<int, int> >::iterator itr2 = itr->count.counts.begin();
+//             itr2 != itr->count.counts.end(); ++itr2) {
+//           std::cout << itr2->first << ":" << itr2->second << " ";
+//         } std::cout << std::endl;
+//       }
+//     }
+
+    template <typename graph_type>
+    static void performTouch(graph_type& graph, TouchSetData& tsd) {
+      
+      gtlsort(tsd.begin(), tsd.end(), lessVertex45Compact());
+      typedef std::vector<std::pair<Point, typename boolean_op_45<Unit>::template Scan45CountT<CountTouch> > > TSD;
+      TSD tsd_;
+      tsd_.reserve(tsd.size());
+      for(typename TouchSetData::iterator itr = tsd.begin(); itr != tsd.end(); ) {
+        typename TouchSetData::iterator itr2 = itr;
+        ++itr2;
+        for(; itr2 != tsd.end() && itr2->first == itr->first; ++itr2) {
+          (itr->second) += (itr2->second); //accumulate
+        }
+        tsd_.push_back(std::make_pair(itr->first, itr->second));
+        itr = itr2;
+      }
+      std::pair<std::pair<Unit, std::map<Unit, std::set<int> > >, graph_type*> output
+        (std::make_pair(std::make_pair((std::numeric_limits<Unit>::max)(), std::map<Unit, std::set<int> >()), &graph));
+      typename boolean_op_45<Unit>::template Scan45<CountTouch, touch_45_output_functor> scanline;
+      for(typename TSD::iterator itr = tsd_.begin(); itr != tsd_.end(); ) {
+        typename TSD::iterator itr2 = itr;
+        ++itr2;
+        while(itr2 != tsd_.end() && itr2->first.x() == itr->first.x()) {
+          ++itr2;
+        }
+        scanline.scan(output, itr, itr2);
+        itr = itr2;
+      }
+      process_previous_x(output);
+    }
+
+    template <typename iT>
+    static void populateTouchSetData(TouchSetData& tsd, iT begin, iT end, int nodeCount) {
+      for( ; begin != end; ++begin) {
+        Vertex45Compact vertex;
+        vertex.first = typename Vertex45Compact::first_type(begin->pt.x() * 2, begin->pt.y() * 2);
+        tsd.push_back(vertex);
+        for(unsigned int i = 0; i < 4; ++i) {
+          if(begin->count[i]) {
+            tsd.back().second[i][nodeCount] += begin->count[i];
+          }
+        }
+      }
+    }
+    
+  };
+
+
+}
+}
+#endif 

test/external/boost/polygon/detail/polygon_90_set_view.hpp

@@ -0,0 +1,491 @@
+/*
+  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_POLYGON_90_SET_VIEW_HPP
+#define BOOST_POLYGON_POLYGON_90_SET_VIEW_HPP
+namespace boost { namespace polygon{
+  struct operator_provides_storage {};
+  struct operator_requires_copy {};
+
+  template <typename value_type, typename arg_type>
+  inline void insert_into_view_arg(value_type& dest, const arg_type& arg, orientation_2d orient);
+
+  template <typename ltype, typename rtype, typename op_type>
+  class polygon_90_set_view;
+
+  template <typename ltype, typename rtype, typename op_type>
+  struct polygon_90_set_traits<polygon_90_set_view<ltype, rtype, op_type> > {
+    typedef typename polygon_90_set_view<ltype, rtype, op_type>::coordinate_type coordinate_type;
+    typedef typename polygon_90_set_view<ltype, rtype, op_type>::iterator_type iterator_type;
+    typedef typename polygon_90_set_view<ltype, rtype, op_type>::operator_arg_type operator_arg_type;
+
+    static inline iterator_type begin(const polygon_90_set_view<ltype, rtype, op_type>& polygon_set); 
+    static inline iterator_type end(const polygon_90_set_view<ltype, rtype, op_type>& polygon_set);
+
+    static inline orientation_2d orient(const polygon_90_set_view<ltype, rtype, op_type>& polygon_set);
+
+    static inline bool clean(const polygon_90_set_view<ltype, rtype, op_type>& polygon_set);
+
+    static inline bool sorted(const polygon_90_set_view<ltype, rtype, op_type>& polygon_set);
+  };
+
+    template <typename value_type, typename ltype, typename rtype, typename op_type>
+    struct compute_90_set_value {
+      static
+      void value(value_type& output_, const ltype& lvalue_, const rtype& rvalue_, orientation_2d orient_) {
+        value_type linput_(orient_);
+        value_type rinput_(orient_);
+        orientation_2d orient_l = polygon_90_set_traits<ltype>::orient(lvalue_);
+        orientation_2d orient_r = polygon_90_set_traits<rtype>::orient(rvalue_);
+        //std::cout << "compute_90_set_value-0 orientations (left, right, out):\t" << orient_l.to_int()
+        //        << "," << orient_r.to_int() << "," << orient_.to_int() << std::endl;
+        insert_into_view_arg(linput_, lvalue_, orient_l);
+        insert_into_view_arg(rinput_, rvalue_, orient_r);
+        output_.applyBooleanBinaryOp(linput_.begin(), linput_.end(),
+                                     rinput_.begin(), rinput_.end(), boolean_op::BinaryCount<op_type>()); 
+      }
+    };
+
+    template <typename value_type, typename lcoord, typename rcoord, typename op_type>
+    struct compute_90_set_value<value_type, polygon_90_set_data<lcoord>, polygon_90_set_data<rcoord>, op_type> {
+      static
+      void value(value_type& output_, const polygon_90_set_data<lcoord>& lvalue_,
+                 const polygon_90_set_data<rcoord>& rvalue_, orientation_2d orient_) {
+        orientation_2d orient_l = lvalue_.orient();
+        orientation_2d orient_r = rvalue_.orient();
+        value_type linput_(orient_);
+        value_type rinput_(orient_);
+        //std::cout << "compute_90_set_value-1 orientations (left, right, out):\t" << orient_l.to_int()
+        //          << "," << orient_r.to_int() << "," << orient_.to_int() << std::endl;
+        if((orient_ == orient_l) && (orient_== orient_r)){ // assume that most of the time this condition is met
+          lvalue_.sort();
+          rvalue_.sort();
+          output_.applyBooleanBinaryOp(lvalue_.begin(), lvalue_.end(),
+                                       rvalue_.begin(), rvalue_.end(), boolean_op::BinaryCount<op_type>()); 
+        }else if((orient_ != orient_l) && (orient_!= orient_r)){ // both the orientations are not equal to input
+          // easier way is to ignore the input orientation and use the input data's orientation, but not done so
+          insert_into_view_arg(linput_, lvalue_, orient_l);
+          insert_into_view_arg(rinput_, rvalue_, orient_r);
+          output_.applyBooleanBinaryOp(linput_.begin(), linput_.end(),
+                                       rinput_.begin(), rinput_.end(), boolean_op::BinaryCount<op_type>()); 
+        }else if(orient_ != orient_l){ // left hand side orientation is different
+          insert_into_view_arg(linput_, lvalue_, orient_l);
+          rvalue_.sort();
+          output_.applyBooleanBinaryOp(linput_.begin(), linput_.end(),
+                                       rvalue_.begin(), rvalue_.end(), boolean_op::BinaryCount<op_type>()); 
+        } else if(orient_ != orient_r){ // right hand side orientation is different
+          insert_into_view_arg(rinput_, rvalue_, orient_r);
+          lvalue_.sort();
+          output_.applyBooleanBinaryOp(lvalue_.begin(), lvalue_.end(),
+                                       rinput_.begin(), rinput_.end(), boolean_op::BinaryCount<op_type>()); 
+        }
+      }
+    };
+
+    template <typename value_type, typename lcoord, typename rtype, typename op_type>
+    struct compute_90_set_value<value_type, polygon_90_set_data<lcoord>, rtype, op_type> {
+      static
+      void value(value_type& output_, const polygon_90_set_data<lcoord>& lvalue_,
+                 const rtype& rvalue_, orientation_2d orient_) {
+         value_type rinput_(orient_);
+         lvalue_.sort();
+         orientation_2d orient_r = polygon_90_set_traits<rtype>::orient(rvalue_);
+         //std::cout << "compute_90_set_value-2 orientations (right, out):\t" << orient_r.to_int()
+         //          << "," << orient_.to_int() << std::endl;
+         insert_into_view_arg(rinput_, rvalue_, orient_r);
+         output_.applyBooleanBinaryOp(lvalue_.begin(), lvalue_.end(),
+                                      rinput_.begin(), rinput_.end(), boolean_op::BinaryCount<op_type>()); 
+      }
+    };
+
+    template <typename value_type, typename ltype, typename rcoord, typename op_type>
+    struct compute_90_set_value<value_type, ltype, polygon_90_set_data<rcoord>, op_type> {
+      static
+      void value(value_type& output_, const ltype& lvalue_,
+                 const polygon_90_set_data<rcoord>& rvalue_, orientation_2d orient_) {
+        value_type linput_(orient_);
+        orientation_2d orient_l = polygon_90_set_traits<ltype>::orient(lvalue_);
+        insert_into_view_arg(linput_, lvalue_, orient_l);
+        rvalue_.sort();
+        //std::cout << "compute_90_set_value-3 orientations (left, out):\t" << orient_l.to_int()
+        //          << "," << orient_.to_int() << std::endl;
+
+        output_.applyBooleanBinaryOp(linput_.begin(), linput_.end(),
+                                     rvalue_.begin(), rvalue_.end(), boolean_op::BinaryCount<op_type>()); 
+      }
+    };
+
+  template <typename ltype, typename rtype, typename op_type>
+  class polygon_90_set_view {
+  public:
+    typedef typename polygon_90_set_traits<ltype>::coordinate_type coordinate_type;
+    typedef polygon_90_set_data<coordinate_type> value_type;
+    typedef typename value_type::iterator_type iterator_type;
+    typedef polygon_90_set_view operator_arg_type;
+  private:
+    const ltype& lvalue_;
+    const rtype& rvalue_;
+    orientation_2d orient_;
+    op_type op_;
+    mutable value_type output_;
+    mutable bool evaluated_;
+    polygon_90_set_view& operator=(const polygon_90_set_view&);
+  public:
+    polygon_90_set_view(const ltype& lvalue,
+                     const rtype& rvalue,
+                     orientation_2d orient,
+                     op_type op) :
+      lvalue_(lvalue), rvalue_(rvalue), orient_(orient), op_(op), output_(orient), evaluated_(false) {}
+
+    // get iterator to begin vertex data
+  private:
+    const value_type& value() const {
+      if(!evaluated_) {
+        evaluated_ = true;
+        compute_90_set_value<value_type, ltype, rtype, op_type>::value(output_, lvalue_, rvalue_, orient_);
+      }
+      return output_;
+    }
+  public:
+    iterator_type begin() const { return value().begin(); }
+    iterator_type end() const { return value().end(); }
+
+    orientation_2d orient() const { return orient_; }
+    bool dirty() const { return false; } //result of a boolean is clean
+    bool sorted() const { return true; } //result of a boolean is sorted
+
+//     template <typename input_iterator_type>
+//     void set(input_iterator_type input_begin, input_iterator_type input_end, 
+//              orientation_2d orient) const {
+//       orient_ = orient;
+//       output_.clear();
+//       output_.insert(output_.end(), input_begin, input_end);
+//       gtlsort(output_.begin(), output_.end());
+//     }
+    void sort() const {} //is always sorted
+  };
+
+  template <typename ltype, typename rtype, typename op_type>
+  struct geometry_concept<polygon_90_set_view<ltype, rtype, op_type> > {
+    typedef polygon_90_set_concept type;
+  };
+
+  template <typename ltype, typename rtype, typename op_type>
+  typename polygon_90_set_traits<polygon_90_set_view<ltype, rtype, op_type> >::iterator_type
+  polygon_90_set_traits<polygon_90_set_view<ltype, rtype, op_type> >::
+  begin(const polygon_90_set_view<ltype, rtype, op_type>& polygon_set) {
+    return polygon_set.begin();
+  }
+  template <typename ltype, typename rtype, typename op_type>
+  typename polygon_90_set_traits<polygon_90_set_view<ltype, rtype, op_type> >::iterator_type
+  polygon_90_set_traits<polygon_90_set_view<ltype, rtype, op_type> >::
+  end(const polygon_90_set_view<ltype, rtype, op_type>& polygon_set) {
+    return polygon_set.end();
+  }
+//   template <typename ltype, typename rtype, typename op_type>
+//   template <typename input_iterator_type>
+//   void polygon_90_set_traits<polygon_90_set_view<ltype, rtype, op_type> >::
+//   set(polygon_90_set_view<ltype, rtype, op_type>& polygon_set, 
+//       input_iterator_type input_begin, input_iterator_type input_end,
+//       orientation_2d orient) {
+//     polygon_set.set(input_begin, input_end, orient);
+//   }
+  template <typename ltype, typename rtype, typename op_type>
+  orientation_2d polygon_90_set_traits<polygon_90_set_view<ltype, rtype, op_type> >::
+  orient(const polygon_90_set_view<ltype, rtype, op_type>& polygon_set) { 
+    return polygon_set.orient(); }
+  template <typename ltype, typename rtype, typename op_type>
+  bool polygon_90_set_traits<polygon_90_set_view<ltype, rtype, op_type> >::
+  clean(const polygon_90_set_view<ltype, rtype, op_type>& polygon_set) { 
+    return true; }
+  template <typename ltype, typename rtype, typename op_type>
+  bool polygon_90_set_traits<polygon_90_set_view<ltype, rtype, op_type> >::
+  sorted(const polygon_90_set_view<ltype, rtype, op_type>& polygon_set) { 
+    return true; }
+
+  template <typename value_type, typename arg_type>
+  inline void insert_into_view_arg(value_type& dest, const arg_type& arg, orientation_2d orient) {
+    typedef typename polygon_90_set_traits<arg_type>::iterator_type literator;
+    literator itr1, itr2;
+    itr1 = polygon_90_set_traits<arg_type>::begin(arg);
+    itr2 = polygon_90_set_traits<arg_type>::end(arg);
+    dest.insert(itr1, itr2, orient);
+    dest.sort();
+  }
+  
+  template <typename T>
+  template <typename ltype, typename rtype, typename op_type>
+  inline polygon_90_set_data<T>& polygon_90_set_data<T>::operator=(const polygon_90_set_view<ltype, rtype, op_type>& that) {
+    set(that.begin(), that.end(), that.orient());
+    dirty_ = false;
+    unsorted_ = false;
+    return *this;
+  }
+  
+  template <typename T>
+  template <typename ltype, typename rtype, typename op_type>
+  inline polygon_90_set_data<T>::polygon_90_set_data(const polygon_90_set_view<ltype, rtype, op_type>& that) :
+    orient_(that.orient()), data_(that.begin(), that.end()), dirty_(false), unsorted_(false) {}
+  
+  template <typename geometry_type_1, typename geometry_type_2>
+  struct self_assign_operator_lvalue {
+    typedef geometry_type_1& type;
+  };
+    
+  template <typename type_1, typename type_2>
+  struct by_value_binary_operator {
+    typedef type_1 type;
+  };
+    
+    template <typename geometry_type_1, typename geometry_type_2, typename op_type>
+    geometry_type_1& self_assignment_boolean_op(geometry_type_1& lvalue_, const geometry_type_2& rvalue_) {
+      typedef geometry_type_1 ltype;
+      typedef geometry_type_2 rtype;
+      typedef typename polygon_90_set_traits<ltype>::coordinate_type coordinate_type;
+      typedef polygon_90_set_data<coordinate_type> value_type;
+      orientation_2d orient_ = polygon_90_set_traits<ltype>::orient(lvalue_);
+      //BM: rvalue_ data set may have its own orientation for scanline
+      orientation_2d orient_r = polygon_90_set_traits<rtype>::orient(rvalue_);
+      //std::cout << "self-assignment boolean-op (left, right, out):\t" << orient_.to_int()
+      //          << "," << orient_r.to_int() << "," << orient_.to_int() << std::endl;
+      value_type linput_(orient_);
+      // BM: the rinput_ set's (that stores the rvalue_ dataset  polygons) scanline orientation is *forced*
+      // to be same as linput
+      value_type rinput_(orient_);
+      //BM: The output dataset's scanline orient is set as equal to first input dataset's (lvalue_) orientation
+      value_type output_(orient_); 
+      insert_into_view_arg(linput_, lvalue_, orient_);
+      // BM: The last argument orient_r is the user initialized scanline orientation for rvalue_ data set.
+      // But since rinput (see above) is initialized to scanline orientation consistent with the lvalue_
+      // data set, this insertion operation will change the incoming rvalue_ dataset's scanline orientation
+      insert_into_view_arg(rinput_, rvalue_, orient_r);
+      // BM: boolean operation and output uses lvalue_ dataset's scanline orientation.
+      output_.applyBooleanBinaryOp(linput_.begin(), linput_.end(),
+                                   rinput_.begin(), rinput_.end(), boolean_op::BinaryCount<op_type>()); 
+      polygon_90_set_mutable_traits<geometry_type_1>::set(lvalue_, output_.begin(), output_.end(), orient_);
+      return lvalue_;
+    }
+  
+  namespace operators {
+  struct y_ps90_b : gtl_yes {};
+
+  template <typename geometry_type_1, typename geometry_type_2>
+  typename enable_if< typename gtl_and_3< y_ps90_b,
+    typename is_polygon_90_set_type<geometry_type_1>::type,
+    typename is_polygon_90_set_type<geometry_type_2>::type>::type,
+                       polygon_90_set_view<geometry_type_1, geometry_type_2, boolean_op::BinaryOr> >::type
+  operator|(const geometry_type_1& lvalue, const geometry_type_2& rvalue) {
+    return polygon_90_set_view<geometry_type_1, geometry_type_2, boolean_op::BinaryOr> 
+      (lvalue, rvalue, 
+       polygon_90_set_traits<geometry_type_1>::orient(lvalue),
+       boolean_op::BinaryOr());
+  }
+  
+  struct y_ps90_p : gtl_yes {};
+
+  template <typename geometry_type_1, typename geometry_type_2>
+  typename enable_if< 
+    typename gtl_and_3< y_ps90_p,
+      typename gtl_if<typename is_polygon_90_set_type<geometry_type_1>::type>::type,
+      typename gtl_if<typename is_polygon_90_set_type<geometry_type_2>::type>::type>::type,
+    polygon_90_set_view<geometry_type_1, geometry_type_2, boolean_op::BinaryOr> >::type
+  operator+(const geometry_type_1& lvalue, const geometry_type_2& rvalue) {
+    return polygon_90_set_view<geometry_type_1, geometry_type_2, boolean_op::BinaryOr> 
+      (lvalue, rvalue, 
+       polygon_90_set_traits<geometry_type_1>::orient(lvalue),
+       boolean_op::BinaryOr());
+  }
+  
+  struct y_ps90_s : gtl_yes {};
+
+  template <typename geometry_type_1, typename geometry_type_2>
+  typename enable_if< typename gtl_and_3< y_ps90_s,
+    typename is_polygon_90_set_type<geometry_type_1>::type,
+    typename is_polygon_90_set_type<geometry_type_2>::type>::type,
+                       polygon_90_set_view<geometry_type_1, geometry_type_2, boolean_op::BinaryAnd> >::type
+  operator*(const geometry_type_1& lvalue, const geometry_type_2& rvalue) {
+    return polygon_90_set_view<geometry_type_1, geometry_type_2, boolean_op::BinaryAnd> 
+      (lvalue, rvalue, 
+       polygon_90_set_traits<geometry_type_1>::orient(lvalue),
+       boolean_op::BinaryAnd());
+  }
+  
+  struct y_ps90_a : gtl_yes {};
+
+  template <typename geometry_type_1, typename geometry_type_2>
+  typename enable_if< typename gtl_and_3< y_ps90_a,
+    typename is_polygon_90_set_type<geometry_type_1>::type,
+    typename is_polygon_90_set_type<geometry_type_2>::type>::type,
+                       polygon_90_set_view<geometry_type_1, geometry_type_2, boolean_op::BinaryAnd> >::type
+  operator&(const geometry_type_1& lvalue, const geometry_type_2& rvalue) {
+    return polygon_90_set_view<geometry_type_1, geometry_type_2, boolean_op::BinaryAnd> 
+      (lvalue, rvalue, 
+       polygon_90_set_traits<geometry_type_1>::orient(lvalue),
+       boolean_op::BinaryAnd());
+  }
+
+  struct y_ps90_x : gtl_yes {};
+
+  template <typename geometry_type_1, typename geometry_type_2>
+  typename enable_if< typename gtl_and_3< y_ps90_x,
+    typename is_polygon_90_set_type<geometry_type_1>::type,
+    typename is_polygon_90_set_type<geometry_type_2>::type>::type,
+                       polygon_90_set_view<geometry_type_1, geometry_type_2, boolean_op::BinaryXor> >::type
+  operator^(const geometry_type_1& lvalue, const geometry_type_2& rvalue) {
+    return polygon_90_set_view<geometry_type_1, geometry_type_2, boolean_op::BinaryXor> 
+      (lvalue, rvalue, 
+       polygon_90_set_traits<geometry_type_1>::orient(lvalue),
+       boolean_op::BinaryXor());
+  }
+  
+  struct y_ps90_m : gtl_yes {};
+
+  template <typename geometry_type_1, typename geometry_type_2>
+  typename enable_if< typename gtl_and_3< y_ps90_m,
+    typename gtl_if<typename is_polygon_90_set_type<geometry_type_1>::type>::type,
+    typename gtl_if<typename is_polygon_90_set_type<geometry_type_2>::type>::type>::type,
+                       polygon_90_set_view<geometry_type_1, geometry_type_2, boolean_op::BinaryNot> >::type
+  operator-(const geometry_type_1& lvalue, const geometry_type_2& rvalue) {
+    return polygon_90_set_view<geometry_type_1, geometry_type_2, boolean_op::BinaryNot> 
+      (lvalue, rvalue, 
+       polygon_90_set_traits<geometry_type_1>::orient(lvalue),
+       boolean_op::BinaryNot());
+  }
+  
+  struct y_ps90_pe : gtl_yes {};
+
+  template <typename coordinate_type_1, typename geometry_type_2>
+  typename enable_if< typename gtl_and< y_ps90_pe, typename is_polygon_90_set_type<geometry_type_2>::type>::type,
+                       polygon_90_set_data<coordinate_type_1> >::type &
+  operator+=(polygon_90_set_data<coordinate_type_1>& lvalue, const geometry_type_2& rvalue) {
+    lvalue.insert(polygon_90_set_traits<geometry_type_2>::begin(rvalue), polygon_90_set_traits<geometry_type_2>::end(rvalue),
+                  polygon_90_set_traits<geometry_type_2>::orient(rvalue));
+    return lvalue;
+  }
+  
+  struct y_ps90_be : gtl_yes {};
+  //
+  template <typename coordinate_type_1, typename geometry_type_2>
+  typename enable_if< typename gtl_and< y_ps90_be, typename is_polygon_90_set_type<geometry_type_2>::type>::type, 
+                       polygon_90_set_data<coordinate_type_1> >::type &
+  operator|=(polygon_90_set_data<coordinate_type_1>& lvalue, const geometry_type_2& rvalue) {
+    return lvalue += rvalue;
+  }
+
+  struct y_ps90_pe2 : gtl_yes {};
+
+  //normal self assignment boolean operations
+  template <typename geometry_type_1, typename geometry_type_2>
+  typename enable_if< typename gtl_and_3< y_ps90_pe2, typename is_mutable_polygon_90_set_type<geometry_type_1>::type, 
+                                         typename is_polygon_90_set_type<geometry_type_2>::type>::type, 
+                       geometry_type_1>::type &
+  operator+=(geometry_type_1& lvalue, const geometry_type_2& rvalue) {
+    return self_assignment_boolean_op<geometry_type_1, geometry_type_2, boolean_op::BinaryOr>(lvalue, rvalue);
+  }
+
+  struct y_ps90_be2 : gtl_yes {};
+
+  template <typename geometry_type_1, typename geometry_type_2>
+  typename enable_if< typename gtl_and_3<y_ps90_be2, typename is_mutable_polygon_90_set_type<geometry_type_1>::type, 
+                                         typename is_polygon_90_set_type<geometry_type_2>::type>::type, 
+                       geometry_type_1>::type &
+  operator|=(geometry_type_1& lvalue, const geometry_type_2& rvalue) {
+    return self_assignment_boolean_op<geometry_type_1, geometry_type_2, boolean_op::BinaryOr>(lvalue, rvalue);
+  }
+
+  struct y_ps90_se : gtl_yes {};
+
+  template <typename geometry_type_1, typename geometry_type_2>
+  typename enable_if< typename gtl_and_3<y_ps90_se, typename is_mutable_polygon_90_set_type<geometry_type_1>::type, 
+                                         typename is_polygon_90_set_type<geometry_type_2>::type>::type, 
+                       geometry_type_1>::type &
+  operator*=(geometry_type_1& lvalue, const geometry_type_2& rvalue) {
+    return self_assignment_boolean_op<geometry_type_1, geometry_type_2, boolean_op::BinaryAnd>(lvalue, rvalue);
+  }
+ 
+  struct y_ps90_ae : gtl_yes {};
+
+  template <typename geometry_type_1, typename geometry_type_2>
+  typename enable_if< typename gtl_and_3<y_ps90_ae, typename is_mutable_polygon_90_set_type<geometry_type_1>::type, 
+                                         typename is_polygon_90_set_type<geometry_type_2>::type>::type, 
+                       geometry_type_1>::type &
+  operator&=(geometry_type_1& lvalue, const geometry_type_2& rvalue) {
+    return self_assignment_boolean_op<geometry_type_1, geometry_type_2, boolean_op::BinaryAnd>(lvalue, rvalue);
+  }
+
+  struct y_ps90_xe : gtl_yes {};
+
+  template <typename geometry_type_1, typename geometry_type_2>
+  typename enable_if< typename gtl_and_3<y_ps90_xe, typename is_mutable_polygon_90_set_type<geometry_type_1>::type, 
+                                         typename is_polygon_90_set_type<geometry_type_2>::type>::type, 
+                       geometry_type_1>::type &
+  operator^=(geometry_type_1& lvalue, const geometry_type_2& rvalue) {
+    return self_assignment_boolean_op<geometry_type_1, geometry_type_2, boolean_op::BinaryXor>(lvalue, rvalue);
+  }
+
+  struct y_ps90_me : gtl_yes {};
+
+  template <typename geometry_type_1, typename geometry_type_2>
+  typename enable_if< typename gtl_and_3< y_ps90_me, typename is_mutable_polygon_90_set_type<geometry_type_1>::type, 
+                                         typename is_polygon_90_set_type<geometry_type_2>::type>::type, 
+                       geometry_type_1>::type &
+  operator-=(geometry_type_1& lvalue, const geometry_type_2& rvalue) {
+    return self_assignment_boolean_op<geometry_type_1, geometry_type_2, boolean_op::BinaryNot>(lvalue, rvalue);
+  }
+
+  struct y_ps90_rpe : gtl_yes {};
+
+  template <typename geometry_type_1, typename coordinate_type_1>
+  typename enable_if< typename gtl_and_3<y_ps90_rpe,
+    typename is_mutable_polygon_90_set_type<geometry_type_1>::type, 
+    typename gtl_same_type<typename geometry_concept<coordinate_type_1>::type, coordinate_concept>::type>::type,
+                       geometry_type_1>::type &
+  operator+=(geometry_type_1& lvalue, coordinate_type_1 rvalue) {
+    return resize(lvalue, rvalue);
+  }
+
+  struct y_ps90_rme : gtl_yes {};
+
+  template <typename geometry_type_1, typename coordinate_type_1>
+  typename enable_if< typename gtl_and_3<y_ps90_rme,
+    typename is_mutable_polygon_90_set_type<geometry_type_1>::type, 
+    typename gtl_same_type<typename geometry_concept<coordinate_type_1>::type, coordinate_concept>::type>::type,
+                       geometry_type_1>::type &
+  operator-=(geometry_type_1& lvalue, coordinate_type_1 rvalue) {
+    return resize(lvalue, -rvalue);
+  }
+
+  struct y_ps90_rp : gtl_yes {};
+
+  template <typename geometry_type_1, typename coordinate_type_1>
+  typename enable_if< typename gtl_and_3<y_ps90_rp,
+    typename gtl_if<typename is_mutable_polygon_90_set_type<geometry_type_1>::type>::type, 
+    typename gtl_if<typename gtl_same_type<typename geometry_concept<coordinate_type_1>::type, coordinate_concept>::type>::type>::type,
+  geometry_type_1>::type
+  operator+(const geometry_type_1& lvalue, coordinate_type_1 rvalue) {
+    geometry_type_1 retval(lvalue);
+    retval += rvalue;
+    return retval;
+  }
+
+  struct y_ps90_rm : gtl_yes {};
+
+  template <typename geometry_type_1, typename coordinate_type_1>
+  typename enable_if< typename gtl_and_3<y_ps90_rm,
+    typename gtl_if<typename is_mutable_polygon_90_set_type<geometry_type_1>::type>::type, 
+    typename gtl_if<typename gtl_same_type<typename geometry_concept<coordinate_type_1>::type, coordinate_concept>::type>::type>::type,
+  geometry_type_1>::type
+  operator-(const geometry_type_1& lvalue, coordinate_type_1 rvalue) {
+    geometry_type_1 retval(lvalue);
+    retval -= rvalue;
+    return retval;
+  }
+  }
+}
+}
+#endif
+

test/external/boost/polygon/detail/polygon_90_touch.hpp

@@ -0,0 +1,418 @@
+/*
+  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_POLYGON_90_TOUCH_HPP
+#define BOOST_POLYGON_POLYGON_90_TOUCH_HPP
+namespace boost { namespace polygon{
+
+  template <typename Unit>
+  struct touch_90_operation {
+    typedef interval_data<Unit> Interval;
+
+    class TouchScanEvent {
+    private:
+      typedef std::map<Unit, std::set<int> > EventData;
+      EventData eventData_;
+    public:
+
+      // The TouchScanEvent::iterator is a lazy algorithm that accumulates
+      // polygon ids in a set as it is incremented through the
+      // scan event data structure.
+      // The iterator provides a forward iterator semantic only.
+      class iterator {
+      private:
+        typename EventData::const_iterator itr_;
+        std::pair<Interval, std::set<int> > ivlIds_;
+        bool incremented_;
+      public:
+        inline iterator() : itr_(), ivlIds_(), incremented_(false) {}
+        inline iterator(typename EventData::const_iterator itr, 
+                        Unit prevPos, Unit curPos, const std::set<int>& ivlIds) : itr_(itr), ivlIds_(), incremented_(false) {
+          ivlIds_.second = ivlIds;
+          ivlIds_.first = Interval(prevPos, curPos);
+        }
+        inline iterator(const iterator& that) : itr_(), ivlIds_(), incremented_(false) { (*this) = that; }
+        inline iterator& operator=(const iterator& that) {
+          itr_ = that.itr_;
+          ivlIds_.first = that.ivlIds_.first;
+          ivlIds_.second = that.ivlIds_.second;
+          incremented_ = that.incremented_;
+          return *this;
+        }
+        inline bool operator==(const iterator& that) { return itr_ == that.itr_; }
+        inline bool operator!=(const iterator& that) { return itr_ != that.itr_; }
+        inline iterator& operator++() {
+          //std::cout << "increment\n";
+          //std::cout << "state\n";
+          //for(std::set<int>::iterator itr = ivlIds_.second.begin(); itr != ivlIds_.second.end(); ++itr) {
+          //   std::cout << (*itr) << " ";
+          //} std::cout << std::endl;
+          //std::cout << "update\n";
+          for(std::set<int>::const_iterator itr = (*itr_).second.begin();
+              itr != (*itr_).second.end(); ++itr) {
+            //std::cout << (*itr) <<  " ";
+            std::set<int>::iterator lb = ivlIds_.second.find(*itr);
+            if(lb != ivlIds_.second.end()) {
+              ivlIds_.second.erase(lb);
+            } else {
+              ivlIds_.second.insert(*itr);
+            }
+          } 
+          //std::cout << std::endl;
+          //std::cout << "new state\n";
+          //for(std::set<int>::iterator itr = ivlIds_.second.begin(); itr != ivlIds_.second.end(); ++itr) {
+          //   std::cout << (*itr) << " ";
+          //} std::cout << std::endl;
+          ++itr_;
+          //ivlIds_.first = Interval(ivlIds_.first.get(HIGH), itr_->first);
+          incremented_ = true;
+          return *this;
+        }
+        inline const iterator operator++(int){
+          iterator tmpItr(*this);
+          ++(*this);
+          return tmpItr;
+        }
+        inline std::pair<Interval, std::set<int> >& operator*() { 
+          if(incremented_) ivlIds_.first = Interval(ivlIds_.first.get(HIGH), itr_->first);
+          incremented_ = false;
+          if(ivlIds_.second.empty())(++(*this));
+          if(incremented_) ivlIds_.first = Interval(ivlIds_.first.get(HIGH), itr_->first);
+          incremented_ = false;
+          return ivlIds_; }
+      };
+
+      inline TouchScanEvent() : eventData_() {}
+      template<class iT>
+      inline TouchScanEvent(iT begin, iT end) : eventData_() {
+        for( ; begin != end; ++begin){
+          insert(*begin);
+        }
+      }
+      inline TouchScanEvent(const TouchScanEvent& that) : eventData_(that.eventData_) {}
+      inline TouchScanEvent& operator=(const TouchScanEvent& that){
+        eventData_ = that.eventData_;
+        return *this;
+      }
+   
+      //Insert an interval polygon id into the EventData
+      inline void insert(const std::pair<Interval, int>& intervalId){
+        insert(intervalId.first.low(), intervalId.second);
+        insert(intervalId.first.high(), intervalId.second);
+      }
+   
+      //Insert an position and polygon id into EventData
+      inline void insert(Unit pos, int id) {
+        typename EventData::iterator lb = eventData_.lower_bound(pos);
+        if(lb != eventData_.end() && lb->first == pos) {
+          std::set<int>& mr (lb->second);
+          std::set<int>::iterator mri = mr.find(id);
+          if(mri == mr.end()) {
+            mr.insert(id);
+          } else {
+            mr.erase(id);
+          }
+        } else {
+          lb = eventData_.insert(lb, std::pair<Unit, std::set<int> >(pos, std::set<int>()));
+          (*lb).second.insert(id);
+        }
+      }
+   
+      //merge this scan event with that by inserting its data
+      inline void insert(const TouchScanEvent& that){
+        typename EventData::const_iterator itr;
+        for(itr = that.eventData_.begin(); itr != that.eventData_.end(); ++itr) {
+          eventData_[(*itr).first].insert(itr->second.begin(), itr->second.end());
+        }
+      }
+   
+      //Get the begin iterator over event data
+      inline iterator begin() const { 
+        //std::cout << "begin\n";
+        if(eventData_.empty()) return end();
+        typename EventData::const_iterator itr = eventData_.begin();
+        Unit pos = itr->first;
+        const std::set<int>& idr = itr->second;
+        ++itr;
+        return iterator(itr, pos, itr->first, idr);
+      }
+   
+      //Get the end iterator over event data
+      inline iterator end() const { return iterator(eventData_.end(), 0, 0, std::set<int>()); }
+   
+      inline void clear() { eventData_.clear(); }
+   
+      inline Interval extents() const { 
+        if(eventData_.empty()) return Interval();
+        return Interval((*(eventData_.begin())).first, (*(eventData_.rbegin())).first);
+      }
+    };
+   
+    //declaration of a map of scan events by coordinate value used to store all the
+    //polygon data for a single layer input into the scanline algorithm
+    typedef std::pair<std::map<Unit, TouchScanEvent>, std::map<Unit, TouchScanEvent> > TouchSetData;
+
+    class TouchOp {
+    public:
+      typedef std::map<Unit, std::set<int> > ScanData;
+      typedef std::pair<Unit, std::set<int> > ElementType;
+    protected:
+      ScanData scanData_;
+      typename ScanData::iterator nextItr_;
+    public:
+      inline TouchOp () : scanData_(), nextItr_() { nextItr_ = scanData_.end(); }
+      inline TouchOp (const TouchOp& that) : scanData_(that.scanData_), nextItr_() { nextItr_ = scanData_.begin(); }
+      inline TouchOp& operator=(const TouchOp& that); 
+   
+      //moves scanline forward
+      inline void advanceScan() { nextItr_ = scanData_.begin(); }
+
+      //proceses the given interval and std::set<int> data
+      //the output data structre is a graph, the indicies in the vector correspond to graph nodes,
+      //the integers in the set are vector indicies and are the nodes with which that node shares an edge
+      template <typename graphT>
+      inline void processInterval(graphT& outputContainer, Interval ivl, const std::set<int>& ids, bool leadingEdge) {
+        //print();
+        typename ScanData::iterator lowItr = lookup_(ivl.low());
+        typename ScanData::iterator highItr = lookup_(ivl.high());
+        //std::cout << "Interval: " << ivl << std::endl;
+        //for(std::set<int>::const_iterator itr = ids.begin(); itr != ids.end(); ++itr)
+        //   std::cout << (*itr) << " ";
+        //std::cout << std::endl;
+        //add interval to scan data if it is past the end
+        if(lowItr == scanData_.end()) {
+          //std::cout << "case0" << std::endl;
+          lowItr = insert_(ivl.low(), ids);
+          evaluateBorder_(outputContainer, ids, ids);
+          highItr = insert_(ivl.high(), std::set<int>());
+          return;
+        }
+        //ensure that highItr points to the end of the ivl
+        if(highItr == scanData_.end() || (*highItr).first > ivl.high()) {
+          //std::cout << "case1" << std::endl;
+          //std::cout << highItr->first << std::endl;
+          std::set<int> value = std::set<int>();
+          if(highItr != scanData_.begin()) {
+            --highItr;
+            //std::cout << highItr->first << std::endl;
+            //std::cout << "high set size " << highItr->second.size() << std::endl;
+            value = highItr->second;
+          }
+          nextItr_ = highItr;
+          highItr = insert_(ivl.high(), value);
+        } else {
+          //evaluate border with next higher interval
+          //std::cout << "case1a" << std::endl;
+          if(leadingEdge)evaluateBorder_(outputContainer, highItr->second, ids);
+        }
+        //split the low interval if needed
+        if(lowItr->first > ivl.low()) {
+          //std::cout << "case2" << std::endl;
+          if(lowItr != scanData_.begin()) {
+            //std::cout << "case3" << std::endl;
+            --lowItr;
+            nextItr_ = lowItr;
+            //std::cout << lowItr->first << " " << lowItr->second.size() << std::endl;
+            lowItr = insert_(ivl.low(), lowItr->second);
+          } else {
+            //std::cout << "case4" << std::endl;
+            nextItr_ = lowItr;
+            lowItr = insert_(ivl.low(), std::set<int>());
+          }
+        } else {
+          //evaluate border with next higher interval
+          //std::cout << "case2a" << std::endl;
+          typename ScanData::iterator nextLowerItr = lowItr;
+          if(leadingEdge && nextLowerItr != scanData_.begin()){
+            --nextLowerItr;
+            evaluateBorder_(outputContainer, nextLowerItr->second, ids);
+          }
+        }
+        //std::cout << "low: " << lowItr->first << " high: " << highItr->first << std::endl;
+        //print();
+        //process scan data intersecting interval
+        for(typename ScanData::iterator itr = lowItr; itr != highItr; ){
+          //std::cout << "case5" << std::endl;
+          //std::cout << itr->first << std::endl;
+          std::set<int>& beforeIds = itr->second;
+          ++itr;
+          evaluateInterval_(outputContainer, beforeIds, ids, leadingEdge);
+        }
+        //print();
+        //merge the bottom interval with the one below if they have the same count
+        if(lowItr != scanData_.begin()){
+          //std::cout << "case6" << std::endl;
+          typename ScanData::iterator belowLowItr = lowItr;
+          --belowLowItr;
+          if(belowLowItr->second == lowItr->second) {
+            //std::cout << "case7" << std::endl;
+            scanData_.erase(lowItr);
+          }
+        } 
+        //merge the top interval with the one above if they have the same count
+        if(highItr != scanData_.begin()) {
+          //std::cout << "case8" << std::endl;
+          typename ScanData::iterator beforeHighItr = highItr;
+          --beforeHighItr;
+          if(beforeHighItr->second == highItr->second) {
+            //std::cout << "case9" << std::endl;
+            scanData_.erase(highItr);
+            highItr = beforeHighItr;
+            ++highItr;
+          }
+        }
+        //print();
+        nextItr_ = highItr;
+      }
+
+//       inline void print() const {
+//         for(typename ScanData::const_iterator itr = scanData_.begin(); itr != scanData_.end(); ++itr) {
+//           std::cout << itr->first << ": ";
+//           for(std::set<int>::const_iterator sitr = itr->second.begin();
+//               sitr != itr->second.end(); ++sitr){
+//             std::cout << *sitr << " ";
+//           }
+//           std::cout << std::endl;
+//         }
+//       }
+   
+    private:
+      inline typename ScanData::iterator lookup_(Unit pos){
+        if(nextItr_ != scanData_.end() && nextItr_->first >= pos) {
+          return nextItr_;
+        }
+        return nextItr_ = scanData_.lower_bound(pos);
+      }
+
+      inline typename ScanData::iterator insert_(Unit pos, const std::set<int>& ids){
+        //std::cout << "inserting " << ids.size() << " ids at: " << pos << std::endl;
+        return nextItr_ = scanData_.insert(nextItr_, std::pair<Unit, std::set<int> >(pos, ids));
+      }
+
+      template <typename graphT>
+      inline void evaluateInterval_(graphT& outputContainer, std::set<int>& ids, 
+                                    const std::set<int>& changingIds, bool leadingEdge) {
+        for(std::set<int>::const_iterator ciditr = changingIds.begin(); ciditr != changingIds.end(); ++ciditr){
+          //std::cout << "evaluateInterval " << (*ciditr) << std::endl;
+          evaluateId_(outputContainer, ids, *ciditr, leadingEdge);
+        }
+      }
+      template <typename graphT>
+      inline void evaluateBorder_(graphT& outputContainer, const std::set<int>& ids, const std::set<int>& changingIds) {
+        for(std::set<int>::const_iterator ciditr = changingIds.begin(); ciditr != changingIds.end(); ++ciditr){
+          //std::cout << "evaluateBorder " << (*ciditr) << std::endl;
+          evaluateBorderId_(outputContainer, ids, *ciditr);
+        }
+      }
+      template <typename graphT>
+      inline void evaluateBorderId_(graphT& outputContainer, const std::set<int>& ids, int changingId) {
+        for(std::set<int>::const_iterator scanItr = ids.begin(); scanItr != ids.end(); ++scanItr) {
+          //std::cout << "create edge: " << changingId << " " << *scanItr << std::endl;
+          if(changingId != *scanItr){
+            outputContainer[changingId].insert(*scanItr);
+            outputContainer[*scanItr].insert(changingId);
+          }
+        }
+      }
+      template <typename graphT>
+      inline void evaluateId_(graphT& outputContainer, std::set<int>& ids, int changingId, bool leadingEdge) {
+        //std::cout << "changingId: " << changingId << std::endl;
+        //for( std::set<int>::iterator itr = ids.begin(); itr != ids.end(); ++itr){
+        //   std::cout << *itr << " ";
+        //}std::cout << std::endl;
+        std::set<int>::iterator lb = ids.lower_bound(changingId);
+        if(lb == ids.end() || (*lb) != changingId) {
+          if(leadingEdge) {
+            //std::cout << "insert\n";
+            //insert and add to output
+            for(std::set<int>::iterator scanItr = ids.begin(); scanItr != ids.end(); ++scanItr) {
+              //std::cout << "create edge: " << changingId << " " << *scanItr << std::endl;
+              if(changingId != *scanItr){
+                outputContainer[changingId].insert(*scanItr);
+                outputContainer[*scanItr].insert(changingId);
+              }
+            }
+            ids.insert(changingId);
+          }
+        } else {
+          if(!leadingEdge){
+            //std::cout << "erase\n";
+            ids.erase(lb);
+          }
+        }
+      }
+    };
+
+    template <typename graphT>
+    static inline void processEvent(graphT& outputContainer, TouchOp& op, const TouchScanEvent& data, bool leadingEdge) {
+      for(typename TouchScanEvent::iterator itr = data.begin(); itr != data.end(); ++itr) {
+        //std::cout << "processInterval" << std::endl;
+        op.processInterval(outputContainer, (*itr).first, (*itr).second, leadingEdge);
+      }
+    }
+
+    template <typename graphT>
+    static inline void performTouch(graphT& outputContainer, const TouchSetData& data) {
+      typename std::map<Unit, TouchScanEvent>::const_iterator leftItr = data.first.begin();
+      typename std::map<Unit, TouchScanEvent>::const_iterator rightItr = data.second.begin();
+      typename std::map<Unit, TouchScanEvent>::const_iterator leftEnd = data.first.end();
+      typename std::map<Unit, TouchScanEvent>::const_iterator rightEnd = data.second.end();
+      TouchOp op;
+      while(leftItr != leftEnd || rightItr != rightEnd) {
+        //std::cout << "loop" << std::endl;
+        op.advanceScan();
+        //rightItr cannont be at end if leftItr is not at end
+        if(leftItr != leftEnd && rightItr != rightEnd &&
+           leftItr->first <= rightItr->first) {
+          //std::cout << "case1" << std::endl;
+          //std::cout << leftItr ->first << std::endl;
+          processEvent(outputContainer, op, leftItr->second, true);
+          ++leftItr;
+        } else {
+          //std::cout << "case2" << std::endl;
+          //std::cout << rightItr ->first << std::endl;
+          processEvent(outputContainer, op, rightItr->second, false);
+          ++rightItr;
+        }
+      }
+    }
+
+    template <class iT>
+    static inline void populateTouchSetData(TouchSetData& data, iT beginData, iT endData, int id) {
+      Unit prevPos = ((std::numeric_limits<Unit>::max)());
+      Unit prevY = prevPos;
+      int count = 0;
+      for(iT itr = beginData; itr != endData; ++itr) {
+        Unit pos = (*itr).first;
+        if(pos != prevPos) {
+          prevPos = pos;
+          prevY = (*itr).second.first;
+          count = (*itr).second.second;
+          continue;
+        }
+        Unit y = (*itr).second.first;
+        if(count != 0 && y != prevY) {
+          std::pair<Interval, int> element(Interval(prevY, y), id);
+          if(count > 0) {
+            data.first[pos].insert(element);
+          } else {
+            data.second[pos].insert(element);
+          }
+        }
+        prevY = y;
+        count += (*itr).second.second;
+      }
+    }
+
+    static inline void populateTouchSetData(TouchSetData& data, const std::vector<std::pair<Unit, std::pair<Unit, int> > >& inputData, int id) {
+      populateTouchSetData(data, inputData.begin(), inputData.end(), id);
+    }
+
+  };
+}
+}
+#endif

test/external/boost/polygon/detail/polygon_set_view.hpp

@@ -0,0 +1,213 @@
+/*
+  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_POLYGON_SET_VIEW_HPP
+#define BOOST_POLYGON_POLYGON_SET_VIEW_HPP
+namespace boost { namespace polygon{
+  
+  
+  template <typename coordinate_type>
+  inline void polygon_set_data<coordinate_type>::clean() const {
+    if(dirty_) {
+      polygon_45_set_data<coordinate_type> tmp;
+      //very important:
+      //the 45 degree algorithm does not satisfy
+      //the precondition of arbitrary polygon formation
+      //that vertices be "linearly consistent"
+      //therefore it doesn't work to fall back on 45-degree
+      //booleans for arbitrary angle polygons
+      if(0) { //downcast(tmp) ) {
+        tmp.clean();
+        data_.clear();
+        is_45_ = true;
+        polygon_set_data<coordinate_type> tmp2;
+        tmp2.insert(tmp);
+        data_.swap(tmp2.data_);
+        dirty_ = false;
+        sort();
+      } else {
+        sort();
+        arbitrary_boolean_op<coordinate_type> abo;
+        polygon_set_data<coordinate_type> tmp2;
+        abo.execute(tmp2, begin(), end(), end(), end(), 0);
+        data_.swap(tmp2.data_);
+        is_45_ = tmp2.is_45_;
+        dirty_ = false;
+      }
+    }
+  }
+
+  template <>
+  inline void polygon_set_data<double>::clean() const {
+    if(dirty_) {
+      sort();
+      arbitrary_boolean_op<double> abo;
+      polygon_set_data<double> tmp2;
+      abo.execute(tmp2, begin(), end(), end(), end(), 0);
+      data_.swap(tmp2.data_);
+      is_45_ = tmp2.is_45_;
+      dirty_ = false;
+    }
+  }
+
+  template <typename value_type, typename arg_type>
+  inline void insert_into_view_arg(value_type& dest, const arg_type& arg);
+
+  template <typename ltype, typename rtype, int op_type>
+  class polygon_set_view;
+
+  template <typename ltype, typename rtype, int op_type>
+  struct polygon_set_traits<polygon_set_view<ltype, rtype, op_type> > {
+    typedef typename polygon_set_view<ltype, rtype, op_type>::coordinate_type coordinate_type;
+    typedef typename polygon_set_view<ltype, rtype, op_type>::iterator_type iterator_type;
+    typedef typename polygon_set_view<ltype, rtype, op_type>::operator_arg_type operator_arg_type;
+
+    static inline iterator_type begin(const polygon_set_view<ltype, rtype, op_type>& polygon_set); 
+    static inline iterator_type end(const polygon_set_view<ltype, rtype, op_type>& polygon_set);
+
+    static inline bool clean(const polygon_set_view<ltype, rtype, op_type>& polygon_set);
+
+    static inline bool sort(const polygon_set_view<ltype, rtype, op_type>& polygon_set);
+  };
+
+  //template <typename value_type, typename geometry_type_1, typename geometry_type_2, int op_type>
+  //void execute_boolean_op(value_type& output_, const geometry_type_1& lvalue_, const geometry_type_2& rvalue_,
+  //                        double coord) {
+  //  typedef geometry_type_1 ltype;
+  //  typedef geometry_type_2 rtype;
+  //  typedef typename polygon_set_traits<ltype>::coordinate_type coordinate_type;
+  //  value_type linput_;
+  //  value_type rinput_;
+  //  insert_into_view_arg(linput_, lvalue_);
+  //  insert_into_view_arg(rinput_, rvalue_);
+  //  arbitrary_boolean_op<coordinate_type> abo;
+  //  abo.execute(output_, linput_.begin(), linput_.end(),
+  //              rinput_.begin(), rinput_.end(), op_type);
+  //}
+
+  template <typename value_type, typename geometry_type_1, typename geometry_type_2, int op_type>
+  void execute_boolean_op(value_type& output_, const geometry_type_1& lvalue_, const geometry_type_2& rvalue_) {
+    typedef geometry_type_1 ltype;
+    typedef geometry_type_2 rtype;
+    typedef typename polygon_set_traits<ltype>::coordinate_type coordinate_type;
+    value_type linput_;
+    value_type rinput_;
+    insert_into_view_arg(linput_, lvalue_);
+    insert_into_view_arg(rinput_, rvalue_);
+    polygon_45_set_data<coordinate_type> l45, r45, o45;
+    if(linput_.downcast(l45) && rinput_.downcast(r45)) {
+      //the op codes are screwed up between 45 and arbitrary
+#ifdef BOOST_POLYGON_MSVC
+#pragma warning (disable: 4127)
+#endif
+      if(op_type < 2)
+        l45.template applyAdaptiveBoolean_<op_type>(o45, r45);
+      else if(op_type == 2)
+        l45.template applyAdaptiveBoolean_<3>(o45, r45);
+      else
+        l45.template applyAdaptiveBoolean_<2>(o45, r45);
+#ifdef BOOST_POLYGON_MSVC
+#pragma warning (default: 4127)
+#endif
+      output_.insert(o45);
+    } else {
+      arbitrary_boolean_op<coordinate_type> abo;
+      abo.execute(output_, linput_.begin(), linput_.end(),
+                  rinput_.begin(), rinput_.end(), op_type);
+    }
+  }
+
+  template <typename ltype, typename rtype, int op_type>
+  class polygon_set_view {
+  public:
+    typedef typename polygon_set_traits<ltype>::coordinate_type coordinate_type;
+    typedef polygon_set_data<coordinate_type> value_type;
+    typedef typename value_type::iterator_type iterator_type;
+    typedef polygon_set_view operator_arg_type;
+  private:
+    const ltype& lvalue_;
+    const rtype& rvalue_;
+    mutable value_type output_;
+    mutable bool evaluated_;
+    polygon_set_view& operator=(const polygon_set_view&);
+  public:
+    polygon_set_view(const ltype& lvalue,
+                     const rtype& rvalue ) :
+      lvalue_(lvalue), rvalue_(rvalue), output_(), evaluated_(false) {}
+
+    // get iterator to begin vertex data
+  public:
+    const value_type& value() const {
+      if(!evaluated_) {
+        evaluated_ = true;
+        execute_boolean_op<value_type, ltype, rtype, op_type>(output_, lvalue_, rvalue_);
+      }
+      return output_;
+    }
+  public:
+    iterator_type begin() const { return value().begin(); }
+    iterator_type end() const { return value().end(); }
+
+    bool dirty() const { return false; } //result of a boolean is clean
+    bool sorted() const { return true; } //result of a boolean is sorted
+
+    void sort() const {} //is always sorted
+  };
+
+  template <typename ltype, typename rtype, int op_type>
+  typename polygon_set_traits<polygon_set_view<ltype, rtype, op_type> >::iterator_type
+  polygon_set_traits<polygon_set_view<ltype, rtype, op_type> >::
+  begin(const polygon_set_view<ltype, rtype, op_type>& polygon_set) {
+    return polygon_set.begin();
+  }
+  template <typename ltype, typename rtype, int op_type>
+  typename polygon_set_traits<polygon_set_view<ltype, rtype, op_type> >::iterator_type
+  polygon_set_traits<polygon_set_view<ltype, rtype, op_type> >::
+  end(const polygon_set_view<ltype, rtype, op_type>& polygon_set) {
+    return polygon_set.end();
+  }
+  template <typename ltype, typename rtype, int op_type>
+  bool polygon_set_traits<polygon_set_view<ltype, rtype, op_type> >::
+  clean(const polygon_set_view<ltype, rtype, op_type>& ) { 
+    return true; }
+  template <typename ltype, typename rtype, int op_type>
+  bool polygon_set_traits<polygon_set_view<ltype, rtype, op_type> >::
+  sort(const polygon_set_view<ltype, rtype, op_type>& ) { 
+    return true; }
+
+  template <typename value_type, typename arg_type>
+  inline void insert_into_view_arg(value_type& dest, const arg_type& arg) {
+    typedef typename polygon_set_traits<arg_type>::iterator_type literator;
+    literator itr1, itr2;
+    itr1 = polygon_set_traits<arg_type>::begin(arg);
+    itr2 = polygon_set_traits<arg_type>::end(arg);
+    dest.insert(itr1, itr2);
+  }
+  
+  template <typename geometry_type_1, typename geometry_type_2, int op_type>
+  geometry_type_1& self_assignment_boolean_op(geometry_type_1& lvalue_, const geometry_type_2& rvalue_) {
+    typedef geometry_type_1 ltype;
+    typedef typename polygon_set_traits<ltype>::coordinate_type coordinate_type;
+    typedef polygon_set_data<coordinate_type> value_type;
+    value_type output_;
+    execute_boolean_op<value_type, geometry_type_1, geometry_type_2, op_type>(output_, lvalue_, rvalue_);
+    polygon_set_mutable_traits<geometry_type_1>::set(lvalue_, output_.begin(), output_.end());
+    return lvalue_;
+  }
+
+  // copy constructor
+  template <typename coordinate_type>
+  template <typename ltype, typename rtype, int op_type> 
+  polygon_set_data<coordinate_type>::polygon_set_data(const polygon_set_view<ltype, rtype, op_type>& that) :
+    data_(that.value().data_), dirty_(that.value().dirty_), unsorted_(that.value().unsorted_), is_45_(that.value().is_45_) {}
+
+  template <typename ltype, typename rtype, int op_type>
+  struct geometry_concept<polygon_set_view<ltype, rtype, op_type> > { typedef polygon_set_concept type; };
+}
+}
+#endif
+

test/external/boost/polygon/detail/polygon_simplify.hpp

@@ -0,0 +1,116 @@
+// Copyright 2011, Andrew Ross
+//
+// 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_DETAIL_SIMPLIFY_HPP
+#define BOOST_POLYGON_DETAIL_SIMPLIFY_HPP
+#include <vector>
+
+namespace boost { namespace polygon { namespace detail { namespace simplify_detail {
+  
+  // Does a simplification/optimization pass on the polygon.  If a given
+  // vertex lies within "len" of the line segment joining its neighbor
+  // vertices, it is removed.
+  template <typename T> //T is a model of point concept
+  std::size_t simplify(std::vector<T>& dst, const std::vector<T>& src, 
+                       typename coordinate_traits<
+                       typename point_traits<T>::coordinate_type
+                       >::coordinate_distance len)
+  {
+    using namespace boost::polygon;
+    typedef typename point_traits<T>::coordinate_type coordinate_type;
+    typedef typename coordinate_traits<coordinate_type>::area_type ftype; 
+    typedef typename std::vector<T>::const_iterator iter;
+
+    std::vector<T> out;
+    out.reserve(src.size());
+    dst = src;
+    std::size_t final_result = 0;
+    std::size_t orig_size = src.size();
+
+    //I can't use == if T doesn't provide it, so use generic point concept compare
+    bool closed = equivalence(src.front(), src.back());
+
+    //we need to keep smoothing until we don't find points to remove
+    //because removing points in the first iteration through the 
+    //polygon may leave it in a state where more removal is possible
+    bool not_done = true;
+    while(not_done) {
+      if(dst.size() < 3) {
+        dst.clear();
+        return orig_size;
+      }
+      
+      // Start with the second, test for the last point
+      // explicitly, and exit after looping back around to the first.
+      ftype len2 = ftype(len) * ftype(len);
+      for(iter prev=dst.begin(), i=prev+1, next; /**/; i = next) {
+        next = i+1;
+        if(next == dst.end())
+          next = dst.begin();
+        
+        // points A, B, C
+        ftype ax = x(*prev), ay = y(*prev);
+        ftype bx = x(*i), by = y(*i);
+        ftype cx = x(*next), cy = y(*next);
+        
+        // vectors AB, BC and AC:
+        ftype abx = bx-ax, aby = by-ay;
+        ftype bcx = cx-bx, bcy = cy-by;
+        ftype acx = cx-ax, acy = cy-ay;
+        
+        // dot products
+        ftype ab_ab = abx*abx + aby*aby;
+        ftype bc_bc = bcx*bcx + bcy*bcy;
+        ftype ac_ac = acx*acx + acy*acy;
+        ftype ab_ac = abx*acx + aby*acy;
+        
+        // projection of AB along AC
+        ftype projf = ab_ac / ac_ac;
+        ftype projx = acx * projf, projy = acy * projf;
+        
+        // perpendicular vector from the line AC to point B (i.e. AB - proj)
+        ftype perpx = abx - projx, perpy = aby - projy;
+        
+        // Squared fractional distance of projection. FIXME: can
+        // remove this division, the decisions below can be made with
+        // just the sign of the quotient and a check to see if
+        // abs(numerator) is greater than abs(divisor).
+        ftype f2 = (projx*acx + projy*acx) / ac_ac;
+        
+        // Square of the relevant distance from point B:
+        ftype dist2;
+        if     (f2 < 0) dist2 = ab_ab;
+        else if(f2 > 1) dist2 = bc_bc;
+        else            dist2 = perpx*perpx + perpy*perpy;
+        
+        if(dist2 > len2) {
+          prev = i; // bump prev, we didn't remove the segment
+          out.push_back(*i);
+        }
+        
+        if(i == dst.begin())
+          break;
+      }
+      std::size_t result = dst.size() - out.size();
+      if(result == 0) {
+        not_done = false;
+      } else {
+        final_result += result;
+        dst = out;
+        out.clear();
+      }
+    } //end of while loop
+    if(closed) {
+      //if the input was closed we want the output to be closed
+      --final_result;
+      dst.push_back(dst.front());
+    }
+    return final_result;
+  }
+
+
+}}}}
+
+#endif

test/external/boost/polygon/detail/polygon_sort_adaptor.hpp

@@ -0,0 +1,67 @@
+/*
+  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_SORT_ADAPTOR_HPP
+#define BOOST_POLYGON_SORT_ADAPTOR_HPP
+#ifdef __ICC
+#pragma warning(disable:2022)
+#pragma warning(disable:2023)
+#endif
+
+#include <algorithm>
+
+//! @brief gtlsort_adaptor default implementation that calls std::sort
+namespace boost {
+  namespace polygon {
+
+    template<typename iterator_type>
+    struct dummy_to_delay_instantiation{
+      typedef int unit_type; // default GTL unit 
+    };
+
+    //! @brief gtlsort_adaptor default implementation that calls std::sort
+    template<typename T>
+    struct gtlsort_adaptor {
+      //! @brief wrapper that mimics std::sort() function and takes
+      // the same arguments
+      template<typename RandomAccessIterator_Type>
+      static void sort(RandomAccessIterator_Type _First, 
+                       RandomAccessIterator_Type _Last)
+      {
+         std::sort(_First, _Last);
+      }
+      //! @brief wrapper that mimics std::sort() function overload and takes
+      // the same arguments
+      template<typename RandomAccessIterator_Type, typename Pred_Type>
+      static void sort(RandomAccessIterator_Type _First, 
+                       RandomAccessIterator_Type _Last, 
+                       const Pred_Type& _Comp)
+      {
+         std::sort(_First, _Last, _Comp);
+      }
+    };
+
+    //! @brief user level wrapper for sorting quantities 
+    template <typename iter_type>
+    void gtlsort(iter_type _b_, iter_type _e_) 
+    {
+      gtlsort_adaptor<typename dummy_to_delay_instantiation<iter_type>::unit_type>::sort(_b_, _e_);
+    }
+
+    //! @brief user level wrapper for sorting quantities that takes predicate
+    // as additional argument
+    template <typename iter_type, typename pred_type>
+    void gtlsort(iter_type _b_, iter_type _e_, const pred_type& _pred_) 
+    {
+      gtlsort_adaptor<typename dummy_to_delay_instantiation<iter_type>::unit_type>::sort(_b_, _e_, _pred_);
+    }
+
+
+    
+  } // namespace polygon
+}   // namespace boost 
+#endif

test/external/boost/polygon/detail/property_merge.hpp

@@ -0,0 +1,588 @@
+/*
+  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_PROPERTY_MERGE_HPP
+#define BOOST_POLYGON_PROPERTY_MERGE_HPP
+namespace boost { namespace polygon{
+
+template <typename coordinate_type>
+class property_merge_point {
+private:
+  coordinate_type x_, y_;
+public:
+  inline property_merge_point() : x_(), y_() {}
+  inline property_merge_point(coordinate_type x, coordinate_type y) : x_(x), y_(y) {}
+  //use builtin assign and copy
+  inline bool operator==(const property_merge_point& that) const { return x_ == that.x_ && y_ == that.y_; }
+  inline bool operator!=(const property_merge_point& that) const { return !((*this) == that); }
+  inline bool operator<(const property_merge_point& that) const {
+    if(x_ < that.x_) return true;
+    if(x_ > that.x_) return false;
+    return y_ < that.y_;
+  }
+  inline coordinate_type x() const { return x_; }
+  inline coordinate_type y() const { return y_; }
+  inline void x(coordinate_type value) { x_ = value; }
+  inline void y(coordinate_type value) { y_ = value; }
+};
+
+template <typename coordinate_type>
+class property_merge_interval {
+private:
+  coordinate_type low_, high_;
+public:
+  inline property_merge_interval() : low_(), high_() {}
+  inline property_merge_interval(coordinate_type low, coordinate_type high) : low_(low), high_(high) {}
+  //use builtin assign and copy
+  inline bool operator==(const property_merge_interval& that) const { return low_ == that.low_ && high_ == that.high_; }
+  inline bool operator!=(const property_merge_interval& that) const { return !((*this) == that); }
+  inline bool operator<(const property_merge_interval& that) const {
+    if(low_ < that.low_) return true;
+    if(low_ > that.low_) return false;
+    return high_ < that.high_;
+  }
+  inline coordinate_type low() const { return low_; }
+  inline coordinate_type high() const { return high_; }
+  inline void low(coordinate_type value) { low_ = value; }
+  inline void high(coordinate_type value) { high_ = value; }
+};
+
+template <typename coordinate_type, typename property_type, typename polygon_set_type, typename keytype = std::set<property_type> >
+class merge_scanline {
+public:
+  //definitions
+
+  typedef keytype property_set;
+  typedef std::vector<std::pair<property_type, int> > property_map;
+  typedef std::pair<property_merge_point<coordinate_type>, std::pair<property_type, int> > vertex_property;
+  typedef std::pair<property_merge_point<coordinate_type>, property_map> vertex_data;
+  typedef std::vector<vertex_property> property_merge_data;
+  //typedef std::map<property_set, polygon_set_type> Result;
+  typedef std::map<coordinate_type, property_map> scanline_type;
+  typedef typename scanline_type::iterator scanline_iterator;
+  typedef std::pair<property_merge_interval<coordinate_type>, std::pair<property_set, property_set> > edge_property;
+  typedef std::vector<edge_property> edge_property_vector;
+
+  //static public member functions
+
+  template <typename iT, typename orientation_2d_type>
+  static inline void 
+  populate_property_merge_data(property_merge_data& pmd, iT input_begin, iT input_end, 
+                               const property_type& property, orientation_2d_type orient) {
+    for( ; input_begin != input_end; ++input_begin) {
+      std::pair<property_merge_point<coordinate_type>, std::pair<property_type, int> > element;
+      if(orient == HORIZONTAL)
+        element.first = property_merge_point<coordinate_type>((*input_begin).second.first, (*input_begin).first);
+      else
+        element.first = property_merge_point<coordinate_type>((*input_begin).first, (*input_begin).second.first);
+      element.second.first = property;
+      element.second.second = (*input_begin).second.second;
+      pmd.push_back(element);
+    }
+  }
+
+  //public member functions
+
+  merge_scanline() : output(), scanline(), currentVertex(), tmpVector(), previousY(), countFromBelow(), scanlinePosition() {}
+  merge_scanline(const merge_scanline& that) :
+    output(that.output),
+    scanline(that.scanline),
+    currentVertex(that.currentVertex),
+    tmpVector(that.tmpVector),
+    previousY(that.previousY),
+    countFromBelow(that.countFromBelow),
+    scanlinePosition(that.scanlinePosition)
+  {}
+  merge_scanline& operator=(const merge_scanline& that) {
+    output = that.output;
+    scanline = that.scanline;
+    currentVertex = that.currentVertex;
+    tmpVector = that.tmpVector;
+    previousY = that.previousY;
+    countFromBelow = that.countFromBelow;
+    scanlinePosition = that.scanlinePosition;
+    return *this;
+  }
+
+  template <typename result_type>
+  inline void perform_merge(result_type& result, property_merge_data& data) {
+    if(data.empty()) return;
+    //sort
+    gtlsort(data.begin(), data.end(), less_vertex_data<vertex_property>());
+    //scanline
+    bool firstIteration = true;
+    scanlinePosition = scanline.end();
+    for(std::size_t i = 0; i < data.size(); ++i) {
+      if(firstIteration) {
+        mergeProperty(currentVertex.second, data[i].second);
+        currentVertex.first = data[i].first;
+        firstIteration = false;
+      } else {
+        if(data[i].first != currentVertex.first) {
+          if(data[i].first.x() != currentVertex.first.x()) {
+            processVertex(output);
+            //std::cout << scanline.size() << " ";
+            countFromBelow.clear(); //should already be clear
+            writeOutput(currentVertex.first.x(), result, output);
+            currentVertex.second.clear();
+            mergeProperty(currentVertex.second, data[i].second);
+            currentVertex.first = data[i].first;
+            //std::cout << assertRedundant(scanline) << "/" << scanline.size() << " ";
+          } else {
+            processVertex(output);
+            currentVertex.second.clear();
+            mergeProperty(currentVertex.second, data[i].second);
+            currentVertex.first = data[i].first;
+          }
+        } else {
+          mergeProperty(currentVertex.second, data[i].second);
+        }
+      }
+    }
+    processVertex(output);
+    writeOutput(currentVertex.first.x(), result, output);
+    //std::cout << assertRedundant(scanline) << "/" << scanline.size() << "\n";
+    //std::cout << scanline.size() << "\n";
+  }
+
+private:
+  //private supporting types
+
+  template <class T>
+  class less_vertex_data {
+  public:
+    less_vertex_data() {}
+    bool operator()(const T& lvalue, const T& rvalue) const {
+      if(lvalue.first.x() < rvalue.first.x()) return true;
+      if(lvalue.first.x() > rvalue.first.x()) return false;
+      if(lvalue.first.y() < rvalue.first.y()) return true;
+      return false;
+    }
+  };
+
+  template <typename T>
+  struct lessPropertyCount {
+    lessPropertyCount() {}
+    bool operator()(const T& a, const T& b) {
+      return a.first < b.first;
+    }
+  };
+
+  //private static member functions
+
+  static inline void mergeProperty(property_map& lvalue, std::pair<property_type, int>& rvalue) {
+    typename property_map::iterator itr = std::lower_bound(lvalue.begin(), lvalue.end(), rvalue, 
+                                                          lessPropertyCount<std::pair<property_type, int> >());
+    if(itr == lvalue.end() ||
+       (*itr).first != rvalue.first) {
+      lvalue.insert(itr, rvalue);
+    } else {
+      (*itr).second += rvalue.second;
+      if((*itr).second == 0)
+        lvalue.erase(itr);
+    }
+//     if(assertSorted(lvalue)) {
+//       std::cout << "in mergeProperty\n";
+//       exit(0);
+//     }
+  }
+
+//   static inline bool assertSorted(property_map& pset) {
+//     bool result = false;
+//     for(std::size_t i = 1; i < pset.size(); ++i) {
+//       if(pset[i] < pset[i-1]) {
+//         std::cout << "Out of Order Error ";
+//         result = true;
+//       }
+//       if(pset[i].first == pset[i-1].first) {
+//         std::cout << "Duplicate Property Error ";
+//         result = true;
+//       }
+//       if(pset[0].second == 0 || pset[1].second == 0) {
+//         std::cout << "Empty Property Error ";
+//         result = true;
+//       }
+//     }
+//     return result;
+//   }
+
+  static inline void setProperty(property_set& pset, property_map& pmap) {
+    for(typename property_map::iterator itr = pmap.begin(); itr != pmap.end(); ++itr) {
+      if((*itr).second > 0) {
+        pset.insert(pset.end(), (*itr).first);
+      }
+    }
+  }
+
+  //private data members
+
+  edge_property_vector output;
+  scanline_type scanline;
+  vertex_data currentVertex;
+  property_map tmpVector;
+  coordinate_type previousY;
+  property_map countFromBelow;
+  scanline_iterator scanlinePosition;
+
+  //private member functions
+
+  inline void mergeCount(property_map& lvalue, property_map& rvalue) {
+    typename property_map::iterator litr = lvalue.begin();
+    typename property_map::iterator ritr = rvalue.begin();
+    tmpVector.clear();
+    while(litr != lvalue.end() && ritr != rvalue.end()) {
+      if((*litr).first <= (*ritr).first) {
+        if(!tmpVector.empty() &&
+           (*litr).first == tmpVector.back().first) {
+          tmpVector.back().second += (*litr).second;
+        } else {
+          tmpVector.push_back(*litr);
+        }
+        ++litr;
+      } else if((*ritr).first <= (*litr).first) {
+        if(!tmpVector.empty() &&
+           (*ritr).first == tmpVector.back().first) {
+          tmpVector.back().second += (*ritr).second;
+        } else {
+          tmpVector.push_back(*ritr);
+        }
+        ++ritr;
+      }
+    }
+    while(litr != lvalue.end()) {
+      if(!tmpVector.empty() &&
+         (*litr).first == tmpVector.back().first) {
+        tmpVector.back().second += (*litr).second;
+      } else {
+        tmpVector.push_back(*litr);
+      }
+      ++litr;
+    }
+    while(ritr != rvalue.end()) {
+      if(!tmpVector.empty() &&
+         (*ritr).first == tmpVector.back().first) {
+        tmpVector.back().second += (*ritr).second;
+      } else {
+        tmpVector.push_back(*ritr);
+      }
+      ++ritr;
+    }
+    lvalue.clear();
+    for(std::size_t i = 0; i < tmpVector.size(); ++i) {
+      if(tmpVector[i].second != 0) {
+        lvalue.push_back(tmpVector[i]);
+      }
+    }
+//     if(assertSorted(lvalue)) {
+//       std::cout << "in mergeCount\n";
+//       exit(0);
+//     }
+  }
+
+  inline void processVertex(edge_property_vector& output) {
+    if(!countFromBelow.empty()) {
+      //we are processing an interval of change in scanline state between
+      //previous vertex position and current vertex position where 
+      //count from below represents the change on the interval
+      //foreach scanline element from previous to current we
+      //write the interval on the scanline that is changing
+      //the old value and the new value to output
+      property_merge_interval<coordinate_type> currentInterval(previousY, currentVertex.first.y());
+      coordinate_type currentY = currentInterval.low();
+      if(scanlinePosition == scanline.end() ||
+         (*scanlinePosition).first != previousY) {
+        scanlinePosition = scanline.lower_bound(previousY);
+      }
+      scanline_iterator previousScanlinePosition = scanlinePosition;
+      ++scanlinePosition;
+      while(scanlinePosition != scanline.end()) {
+        coordinate_type elementY = (*scanlinePosition).first;
+        if(elementY <= currentInterval.high()) {
+          property_map& countOnLeft = (*previousScanlinePosition).second;
+          edge_property element;
+          output.push_back(element);
+          output.back().first = property_merge_interval<coordinate_type>((*previousScanlinePosition).first, elementY);
+          setProperty(output.back().second.first, countOnLeft);
+          mergeCount(countOnLeft, countFromBelow);
+          setProperty(output.back().second.second, countOnLeft);
+          if(output.back().second.first == output.back().second.second) {
+            output.pop_back(); //it was an internal vertical edge, not to be output
+          }
+          else if(output.size() > 1) {
+            edge_property& secondToLast = output[output.size()-2];
+            if(secondToLast.first.high() == output.back().first.low() &&
+               secondToLast.second.first == output.back().second.first &&
+               secondToLast.second.second == output.back().second.second) {
+              //merge output onto previous output because properties are
+              //identical on both sides implying an internal horizontal edge
+              secondToLast.first.high(output.back().first.high());
+              output.pop_back();
+            }
+          }
+          if(previousScanlinePosition == scanline.begin()) {
+            if(countOnLeft.empty()) {
+              scanline.erase(previousScanlinePosition);
+            }
+          } else {
+            scanline_iterator tmpitr = previousScanlinePosition;
+            --tmpitr;
+            if((*tmpitr).second == (*previousScanlinePosition).second)
+              scanline.erase(previousScanlinePosition);
+          }
+             
+        } else if(currentY < currentInterval.high()){
+          //elementY > currentInterval.high()
+          //split the interval between previous and current scanline elements
+          std::pair<coordinate_type, property_map> elementScan;
+          elementScan.first = currentInterval.high();
+          elementScan.second = (*previousScanlinePosition).second;
+          scanlinePosition = scanline.insert(scanlinePosition, elementScan);
+          continue;
+        } else {
+          break;
+        }
+        previousScanlinePosition = scanlinePosition;
+        currentY = previousY = elementY;
+        ++scanlinePosition;
+        if(scanlinePosition == scanline.end() &&
+           currentY < currentInterval.high()) {
+          //insert a new element for top of range
+          std::pair<coordinate_type, property_map> elementScan;
+          elementScan.first = currentInterval.high();
+          scanlinePosition = scanline.insert(scanline.end(), elementScan);
+        } 
+      }
+      if(scanlinePosition == scanline.end() &&
+         currentY < currentInterval.high()) {
+        //handle case where we iterated to end of the scanline
+        //we need to insert an element into the scanline at currentY
+        //with property value coming from below
+        //and another one at currentInterval.high() with empty property value
+        mergeCount(scanline[currentY], countFromBelow);
+        std::pair<coordinate_type, property_map> elementScan;
+        elementScan.first = currentInterval.high();
+        scanline.insert(scanline.end(), elementScan);
+
+        edge_property element;
+        output.push_back(element);
+        output.back().first = property_merge_interval<coordinate_type>(currentY, currentInterval.high());
+        setProperty(output.back().second.second, countFromBelow);
+        mergeCount(countFromBelow, currentVertex.second);
+      } else {
+        mergeCount(countFromBelow, currentVertex.second);
+        if(countFromBelow.empty()) {
+          if(previousScanlinePosition == scanline.begin()) {
+            if((*previousScanlinePosition).second.empty()) {
+              scanline.erase(previousScanlinePosition);
+              //previousScanlinePosition = scanline.end();
+              //std::cout << "ERASE_A ";
+            }
+          } else {
+            scanline_iterator tmpitr = previousScanlinePosition;
+            --tmpitr;
+            if((*tmpitr).second == (*previousScanlinePosition).second) {
+              scanline.erase(previousScanlinePosition);
+              //previousScanlinePosition = scanline.end();
+              //std::cout << "ERASE_B ";
+            }
+          }
+        }
+      }
+    } else {
+      //count from below is empty, we are starting a new interval of change
+      countFromBelow = currentVertex.second;
+      scanlinePosition = scanline.lower_bound(currentVertex.first.y());
+      if(scanlinePosition != scanline.end()) {
+        if((*scanlinePosition).first != currentVertex.first.y()) {
+          if(scanlinePosition != scanline.begin()) {
+            //decrement to get the lower position of the first interval this vertex intersects
+            --scanlinePosition;
+            //insert a new element into the scanline for the incoming vertex
+            property_map& countOnLeft = (*scanlinePosition).second;
+            std::pair<coordinate_type, property_map> element(currentVertex.first.y(), countOnLeft);
+            scanlinePosition = scanline.insert(scanlinePosition, element);
+          } else {
+            property_map countOnLeft;
+            std::pair<coordinate_type, property_map> element(currentVertex.first.y(), countOnLeft);
+            scanlinePosition = scanline.insert(scanlinePosition, element);
+          }
+        }
+      } else {
+        property_map countOnLeft;
+        std::pair<coordinate_type, property_map> element(currentVertex.first.y(), countOnLeft);
+        scanlinePosition = scanline.insert(scanlinePosition, element);
+      }
+    }
+    previousY = currentVertex.first.y();
+  }
+
+  template <typename T>
+  inline int assertRedundant(T& t) {
+    if(t.empty()) return 0;
+    int count = 0; 
+    typename T::iterator itr = t.begin();
+    if((*itr).second.empty())
+      ++count;
+    typename T::iterator itr2 = itr;
+    ++itr2;
+    while(itr2 != t.end()) {
+      if((*itr).second == (*itr2).second)
+        ++count;
+      itr = itr2;
+      ++itr2;
+    }
+    return count;
+  }
+
+  template <typename T>
+  inline void performExtract(T& result, property_merge_data& data) {
+    if(data.empty()) return;
+    //sort
+    gtlsort(data.begin(), data.end(), less_vertex_data<vertex_property>());
+    
+    //scanline
+    bool firstIteration = true;
+    scanlinePosition = scanline.end();
+    for(std::size_t i = 0; i < data.size(); ++i) {
+      if(firstIteration) {
+        mergeProperty(currentVertex.second, data[i].second);
+        currentVertex.first = data[i].first;
+        firstIteration = false;
+      } else {
+        if(data[i].first != currentVertex.first) {
+          if(data[i].first.x() != currentVertex.first.x()) {
+            processVertex(output);
+            //std::cout << scanline.size() << " ";
+            countFromBelow.clear(); //should already be clear
+            writeGraph(currentVertex.first.x(), result, output, scanline);
+            currentVertex.second.clear();
+            mergeProperty(currentVertex.second, data[i].second);
+            currentVertex.first = data[i].first;
+          } else {
+            processVertex(output);
+            currentVertex.second.clear();
+            mergeProperty(currentVertex.second, data[i].second);
+            currentVertex.first = data[i].first;
+          }
+        } else {
+          mergeProperty(currentVertex.second, data[i].second);
+        }
+      }
+    }
+    processVertex(output);
+    writeGraph(currentVertex.first.x(), result, output, scanline);
+    //std::cout << scanline.size() << "\n";
+  }
+
+  template <typename T>
+  inline void insertEdges(T& graph, property_set& p1, property_set& p2) {
+    for(typename property_set::iterator itr = p1.begin(); itr != p1.end(); ++itr) {
+      for(typename property_set::iterator itr2 = p2.begin(); itr2 != p2.end(); ++itr2) {
+        if(*itr != *itr2) {
+          graph[*itr].insert(*itr2);
+          graph[*itr2].insert(*itr);
+        }
+      }
+    }
+  }
+
+  template <typename T>
+  inline void propertySetAbove(coordinate_type y, property_set& ps, T& scanline) {
+    ps.clear();
+    typename T::iterator itr = scanline.find(y);
+    if(itr != scanline.end())
+      setProperty(ps, (*itr).second);
+  }
+
+  template <typename T>
+  inline void propertySetBelow(coordinate_type y, property_set& ps, T& scanline) {
+    ps.clear();
+    typename T::iterator itr = scanline.find(y);
+    if(itr != scanline.begin()) {
+      --itr;
+      setProperty(ps, (*itr).second);
+    }
+  }
+
+  template <typename T, typename T2>
+  inline void writeGraph(coordinate_type x, T& graph, edge_property_vector& output, T2& scanline) {
+    if(output.empty()) return;
+    edge_property* previousEdgeP = &(output[0]);
+    bool firstIteration = true;
+    property_set ps;
+    for(std::size_t i = 0; i < output.size(); ++i) {
+      edge_property& previousEdge = *previousEdgeP;
+      edge_property& edge = output[i];
+      if(previousEdge.first.high() == edge.first.low()) {
+        //horizontal edge
+        insertEdges(graph, edge.second.first, previousEdge.second.first);
+        //corner 1
+        insertEdges(graph, edge.second.first, previousEdge.second.second);
+        //other horizontal edge
+        insertEdges(graph, edge.second.second, previousEdge.second.second);
+        //corner 2
+        insertEdges(graph, edge.second.second, previousEdge.second.first);
+      } else {
+        if(!firstIteration){
+          //look up regions above previous edge 
+          propertySetAbove(previousEdge.first.high(), ps, scanline);
+          insertEdges(graph, ps, previousEdge.second.first);
+          insertEdges(graph, ps, previousEdge.second.second);
+        }
+        //look up regions below current edge in the scanline
+        propertySetBelow(edge.first.high(), ps, scanline);
+        insertEdges(graph, ps, edge.second.first);
+        insertEdges(graph, ps, edge.second.second);
+      }
+      firstIteration = false;
+      //vertical edge
+      insertEdges(graph, edge.second.second, edge.second.first);
+      //shared region to left
+      insertEdges(graph, edge.second.second, edge.second.second);
+      //shared region to right
+      insertEdges(graph, edge.second.first, edge.second.first);
+      previousEdgeP = &(output[i]);
+    }
+    edge_property& previousEdge = *previousEdgeP;
+    propertySetAbove(previousEdge.first.high(), ps, scanline);
+    insertEdges(graph, ps, previousEdge.second.first);
+    insertEdges(graph, ps, previousEdge.second.second);
+    output.clear();
+  }
+
+  template <typename Result>
+  inline void writeOutput(coordinate_type x, Result& result, edge_property_vector& output) {
+    for(std::size_t i = 0; i < output.size(); ++i) {
+      edge_property& edge = output[i];
+      //edge.second.first is the property set on the left of the edge
+      if(!edge.second.first.empty()) {
+        typename Result::iterator itr = result.find(edge.second.first);
+        if(itr == result.end()) {
+          std::pair<property_set, polygon_set_type> element(edge.second.first, polygon_set_type(VERTICAL));
+          itr = result.insert(result.end(), element);
+        }
+        std::pair<interval_data<coordinate_type>, int> element2(interval_data<coordinate_type>(edge.first.low(), edge.first.high()), -1); //right edge of figure
+        (*itr).second.insert(x, element2);
+      }
+      if(!edge.second.second.empty()) {
+        //edge.second.second is the property set on the right of the edge
+        typename Result::iterator itr = result.find(edge.second.second);
+        if(itr == result.end()) {
+          std::pair<property_set, polygon_set_type> element(edge.second.second, polygon_set_type(VERTICAL));
+          itr = result.insert(result.end(), element);
+        }
+        std::pair<interval_data<coordinate_type>, int> element3(interval_data<coordinate_type>(edge.first.low(), edge.first.high()), 1); //left edge of figure
+        (*itr).second.insert(x, element3);
+      }
+    }
+    output.clear();
+  }
+};
+
+}
+}
+#endif

test/external/boost/polygon/detail/property_merge_45.hpp

@@ -0,0 +1,160 @@
+/*
+  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_PROPERTY_MERGE_45_HPP
+#define BOOST_POLYGON_PROPERTY_MERGE_45_HPP
+namespace boost { namespace polygon{
+
+  template <typename Unit, typename property_type>
+  struct polygon_45_property_merge {
+
+    typedef point_data<Unit> Point;
+    typedef typename coordinate_traits<Unit>::manhattan_area_type LongUnit;
+
+    template <typename property_map>
+    static inline void merge_property_maps(property_map& mp, const property_map& mp2, bool subtract = false) {
+      polygon_45_touch<Unit>::merge_property_maps(mp, mp2, subtract);
+    }
+
+    class CountMerge {
+    public:
+      inline CountMerge() : counts() {}
+      //inline CountMerge(int count) { counts[0] = counts[1] = count; }
+      //inline CountMerge(int count1, int count2) { counts[0] = count1; counts[1] = count2; }
+      inline CountMerge(const CountMerge& count) : counts(count.counts) {}
+      inline bool operator==(const CountMerge& count) const { return counts == count.counts; }
+      inline bool operator!=(const CountMerge& count) const { return !((*this) == count); }
+      //inline CountMerge& operator=(int count) { counts[0] = counts[1] = count; return *this; }
+      inline CountMerge& operator=(const CountMerge& count) { counts = count.counts; return *this; }
+      inline int& operator[](property_type index) { 
+        std::vector<std::pair<int, int> >::iterator itr = lower_bound(counts.begin(), counts.end(), std::make_pair(index, int(0)));
+        if(itr != counts.end() && itr->first == index) {
+            return itr->second;
+        }
+        itr = counts.insert(itr, std::make_pair(index, int(0)));
+        return itr->second;
+      }
+//       inline int operator[](int index) const {
+//         std::vector<std::pair<int, int> >::const_iterator itr = counts.begin();
+//         for( ; itr != counts.end() && itr->first <= index; ++itr) {
+//           if(itr->first == index) {
+//             return itr->second;
+//           }
+//         }
+//         return 0;
+//       }
+      inline CountMerge& operator+=(const CountMerge& count){
+        merge_property_maps(counts, count.counts, false);
+        return *this;
+      }
+      inline CountMerge& operator-=(const CountMerge& count){
+        merge_property_maps(counts, count.counts, true);
+        return *this;
+      }
+      inline CountMerge operator+(const CountMerge& count) const {
+        return CountMerge(*this)+=count;
+      }
+      inline CountMerge operator-(const CountMerge& count) const {
+        return CountMerge(*this)-=count;
+      }
+      inline CountMerge invert() const {
+        CountMerge retval;
+        retval -= *this;
+        return retval;
+      }
+      std::vector<std::pair<property_type, int> > counts;
+    };
+
+    //output is a std::map<std::set<property_type>, polygon_45_set_data<Unit> >
+    struct merge_45_output_functor {
+      template <typename cT>
+      void operator()(cT& output, const CountMerge& count1, const CountMerge& count2, 
+                      const Point& pt, int rise, direction_1d end) {
+        typedef typename cT::key_type keytype;
+        keytype left;
+        keytype right;
+        int edgeType = end == LOW ? -1 : 1;
+        for(typename std::vector<std::pair<property_type, int> >::const_iterator itr = count1.counts.begin();
+            itr != count1.counts.end(); ++itr) {
+          left.insert(left.end(), (*itr).first);
+        }
+        for(typename std::vector<std::pair<property_type, int> >::const_iterator itr = count2.counts.begin();
+            itr != count2.counts.end(); ++itr) {
+          right.insert(right.end(), (*itr).first);
+        }
+        if(left == right) return;
+        if(!left.empty()) {
+          //std::cout << pt.x() << " " << pt.y() << " " << rise << " " << edgeType << std::endl;
+          output[left].insert_clean(typename boolean_op_45<Unit>::Vertex45(pt, rise, -edgeType));
+        }
+        if(!right.empty()) {
+          //std::cout << pt.x() << " " << pt.y() << " " << rise << " " << -edgeType << std::endl;
+          output[right].insert_clean(typename boolean_op_45<Unit>::Vertex45(pt, rise, edgeType));
+        }
+      }
+    };
+
+    typedef typename std::pair<Point, 
+                               typename boolean_op_45<Unit>::template Scan45CountT<CountMerge> > Vertex45Compact;
+    typedef std::vector<Vertex45Compact> MergeSetData;
+    
+    struct lessVertex45Compact {
+      bool operator()(const Vertex45Compact& l, const Vertex45Compact& r) {
+        return l.first < r.first;
+      }
+    };
+    
+    template <typename output_type>
+    static void performMerge(output_type& result, MergeSetData& tsd) {
+      
+      gtlsort(tsd.begin(), tsd.end(), lessVertex45Compact());
+      typedef std::vector<std::pair<Point, typename boolean_op_45<Unit>::template Scan45CountT<CountMerge> > > TSD;
+      TSD tsd_;
+      tsd_.reserve(tsd.size());
+      for(typename MergeSetData::iterator itr = tsd.begin(); itr != tsd.end(); ) {
+        typename MergeSetData::iterator itr2 = itr;
+        ++itr2;
+        for(; itr2 != tsd.end() && itr2->first == itr->first; ++itr2) {
+          (itr->second) += (itr2->second); //accumulate
+        }
+        tsd_.push_back(std::make_pair(itr->first, itr->second));
+        itr = itr2;
+      }
+      typename boolean_op_45<Unit>::template Scan45<CountMerge, merge_45_output_functor> scanline;
+      for(typename TSD::iterator itr = tsd_.begin(); itr != tsd_.end(); ) {
+        typename TSD::iterator itr2 = itr;
+        ++itr2;
+        while(itr2 != tsd_.end() && itr2->first.x() == itr->first.x()) {
+          ++itr2;
+        }
+        scanline.scan(result, itr, itr2);
+        itr = itr2;
+      }
+    }
+
+    template <typename iT>
+    static void populateMergeSetData(MergeSetData& tsd, iT begin, iT end, property_type property) {
+      for( ; begin != end; ++begin) {
+        Vertex45Compact vertex;
+        vertex.first = typename Vertex45Compact::first_type(begin->pt.x() * 2, begin->pt.y() * 2);
+        tsd.push_back(vertex);
+        for(unsigned int i = 0; i < 4; ++i) {
+          if(begin->count[i]) {
+            tsd.back().second[i][property] += begin->count[i];
+          }
+        }
+      }
+    }
+    
+  };
+
+
+
+}
+}
+
+#endif

test/external/boost/polygon/detail/rectangle_formation.hpp

@@ -0,0 +1,267 @@
+/*
+    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_RECTANGLE_FORMATION_HPP
+#define BOOST_POLYGON_RECTANGLE_FORMATION_HPP
+namespace boost { namespace polygon{
+
+namespace rectangle_formation {
+  template <class T> 
+  class ScanLineToRects {
+  public:
+    typedef T rectangle_type;
+    typedef typename rectangle_traits<T>::coordinate_type coordinate_type;
+    typedef rectangle_data<coordinate_type> scan_rect_type;
+  private:
+    
+    typedef std::set<scan_rect_type, less_rectangle_concept<scan_rect_type, scan_rect_type> > ScanData;
+    ScanData scanData_;
+    bool haveCurrentRect_;
+    scan_rect_type currentRect_;
+    orientation_2d orient_;
+    typename rectangle_traits<T>::coordinate_type currentCoordinate_;
+  public:
+    inline ScanLineToRects() : scanData_(), haveCurrentRect_(), currentRect_(), orient_(), currentCoordinate_() {}
+    
+    inline ScanLineToRects(orientation_2d orient, rectangle_type model) :
+      scanData_(orientation_2d(orient.to_int() ? VERTICAL : HORIZONTAL)),
+      haveCurrentRect_(false), currentRect_(), orient_(orient), currentCoordinate_() {
+      assign(currentRect_, model);
+      currentCoordinate_ = (std::numeric_limits<coordinate_type>::max)();
+    }
+    
+    template <typename CT>
+    inline ScanLineToRects& processEdge(CT& rectangles, const interval_data<coordinate_type>& edge);
+    
+    inline ScanLineToRects& nextMajorCoordinate(coordinate_type currentCoordinate) {
+      if(haveCurrentRect_) {
+        scanData_.insert(scanData_.end(), currentRect_);
+        haveCurrentRect_ = false;
+      }
+      currentCoordinate_ = currentCoordinate;
+      return *this;
+    }
+    
+  };
+
+  template <class CT, class ST, class rectangle_type, typename interval_type, typename coordinate_type> inline CT& 
+  processEdge_(CT& rectangles, ST& scanData, const interval_type& edge, 
+               bool& haveCurrentRect, rectangle_type& currentRect, coordinate_type currentCoordinate, orientation_2d orient) 
+  {
+    typedef typename CT::value_type result_type;
+    bool edgeProcessed = false;
+    if(!scanData.empty()) {
+
+      //process all rectangles in the scanData that touch the edge
+      typename ST::iterator dataIter = scanData.lower_bound(rectangle_type(edge, edge));
+      //decrement beginIter until its low is less than edge's low
+      while((dataIter == scanData.end() || (*dataIter).get(orient).get(LOW) > edge.get(LOW)) && 
+            dataIter != scanData.begin())
+        {
+          --dataIter;
+        }
+      //process each rectangle until the low end of the rectangle 
+      //is greater than the high end of the edge
+      while(dataIter != scanData.end() &&
+            (*dataIter).get(orient).get(LOW) <= edge.get(HIGH)) 
+        {
+          const rectangle_type& rect = *dataIter;
+          //if the rectangle data intersects the edge at all
+          if(rect.get(orient).get(HIGH) >= edge.get(LOW)) {
+            if(contains(rect.get(orient), edge, true)) {
+              //this is a closing edge
+              //we need to write out the intersecting rectangle and
+              //insert between 0 and 2 rectangles into the scanData
+              //write out rectangle
+              rectangle_type tmpRect = rect;
+
+              if(rect.get(orient.get_perpendicular()).get(LOW) < currentCoordinate) {
+                //set the high coordinate perpedicular to slicing orientation
+                //to the current coordinate of the scan event
+                tmpRect.set(orient.get_perpendicular().get_direction(HIGH),
+                            currentCoordinate);
+                result_type result;
+                assign(result, tmpRect);
+                rectangles.insert(rectangles.end(), result);
+              }
+              //erase the rectangle from the scan data
+              typename ST::iterator nextIter = dataIter;
+              ++nextIter;
+              scanData.erase(dataIter);
+              if(tmpRect.get(orient).get(LOW) < edge.get(LOW)) {
+                //insert a rectangle for the overhang of the bottom
+                //of the rectangle back into scan data
+                rectangle_type lowRect(tmpRect);
+                lowRect.set(orient.get_perpendicular(), interval_data<coordinate_type>(currentCoordinate,
+                                                                currentCoordinate));
+                lowRect.set(orient.get_direction(HIGH), edge.get(LOW));
+                scanData.insert(nextIter, lowRect);
+              }
+              if(tmpRect.get(orient).get(HIGH) > edge.get(HIGH)) {
+                //insert a rectangle for the overhang of the top
+                //of the rectangle back into scan data
+                rectangle_type highRect(tmpRect);
+                highRect.set(orient.get_perpendicular(), interval_data<coordinate_type>(currentCoordinate,
+                                                                 currentCoordinate));
+                highRect.set(orient.get_direction(LOW), edge.get(HIGH));
+                scanData.insert(nextIter, highRect);
+              }
+              //we are done with this edge
+              edgeProcessed = true;                 
+              break;
+            } else {
+              //it must be an opening edge
+              //assert that rect does not overlap the edge but only touches
+              //write out rectangle
+              rectangle_type tmpRect = rect;
+              //set the high coordinate perpedicular to slicing orientation
+              //to the current coordinate of the scan event
+              if(tmpRect.get(orient.get_perpendicular().get_direction(LOW)) < currentCoordinate) {
+                tmpRect.set(orient.get_perpendicular().get_direction(HIGH),
+                            currentCoordinate);
+                result_type result;
+                assign(result, tmpRect);
+                rectangles.insert(rectangles.end(), result);
+              }
+              //erase the rectangle from the scan data
+              typename ST::iterator nextIter = dataIter;
+              ++nextIter;
+              scanData.erase(dataIter);
+              dataIter = nextIter;
+              if(haveCurrentRect) {
+                if(currentRect.get(orient).get(HIGH) >= edge.get(LOW)){
+                  if(!edgeProcessed && currentRect.get(orient.get_direction(HIGH)) > edge.get(LOW)){
+                    rectangle_type tmpRect2(currentRect);
+                    tmpRect2.set(orient.get_direction(HIGH), edge.get(LOW));
+                    scanData.insert(nextIter, tmpRect2);
+                    if(currentRect.get(orient.get_direction(HIGH)) > edge.get(HIGH)) {
+                      currentRect.set(orient, interval_data<coordinate_type>(edge.get(HIGH), currentRect.get(orient.get_direction(HIGH))));
+                    } else {
+                      haveCurrentRect = false;
+                    }
+                  } else {
+                    //extend the top of current rect
+                    currentRect.set(orient.get_direction(HIGH), 
+                                    (std::max)(edge.get(HIGH), 
+                                               tmpRect.get(orient.get_direction(HIGH))));
+                  }
+                } else {
+                  //insert current rect into the scanData
+                  scanData.insert(nextIter, currentRect);
+                  //create a new current rect
+                  currentRect.set(orient.get_perpendicular(), interval_data<coordinate_type>(currentCoordinate,
+                                                                      currentCoordinate));
+                  currentRect.set(orient, interval_data<coordinate_type>((std::min)(tmpRect.get(orient).get(LOW), 
+                                                       edge.get(LOW)),
+                                                                         (std::max)(tmpRect.get(orient).get(HIGH),
+                                                       edge.get(HIGH))));
+                }
+              } else {
+                haveCurrentRect = true;
+                currentRect.set(orient.get_perpendicular(), interval_data<coordinate_type>(currentCoordinate,
+                                                                    currentCoordinate));
+                currentRect.set(orient, interval_data<coordinate_type>((std::min)(tmpRect.get(orient).get(LOW), 
+                                                     edge.get(LOW)),
+                                                                       (std::max)(tmpRect.get(orient).get(HIGH),
+                                                     edge.get(HIGH))));
+              }
+              //skip to nextIter position
+              edgeProcessed = true;
+              continue;
+            }
+            //edgeProcessed = true;
+          }
+          ++dataIter;
+        } //end while edge intersects rectangle data 
+
+    }
+    if(!edgeProcessed) {
+      if(haveCurrentRect) {
+        if(currentRect.get(orient.get_perpendicular().get_direction(HIGH)) 
+           == currentCoordinate &&
+           currentRect.get(orient.get_direction(HIGH)) >= edge.get(LOW)) 
+          {
+            if(currentRect.get(orient.get_direction(HIGH)) > edge.get(LOW)){
+              rectangle_type tmpRect(currentRect);
+              tmpRect.set(orient.get_direction(HIGH), edge.get(LOW));
+              scanData.insert(scanData.end(), tmpRect);
+              if(currentRect.get(orient.get_direction(HIGH)) > edge.get(HIGH)) {
+                currentRect.set(orient, 
+                                interval_data<coordinate_type>(edge.get(HIGH), 
+                                         currentRect.get(orient.get_direction(HIGH))));
+                return rectangles;
+              } else {
+                haveCurrentRect = false;
+                return rectangles;
+              }
+            }
+            //extend current rect
+            currentRect.set(orient.get_direction(HIGH), edge.get(HIGH));
+            return rectangles;
+          }
+        scanData.insert(scanData.end(), currentRect);
+        haveCurrentRect = false;
+      } 
+      rectangle_type tmpRect(currentRect);
+      tmpRect.set(orient.get_perpendicular(), interval_data<coordinate_type>(currentCoordinate,
+                                                      currentCoordinate));
+      tmpRect.set(orient, edge);
+      scanData.insert(tmpRect);
+      return rectangles;
+    }
+    return rectangles;
+  
+  }
+
+  template <class T> 
+  template <class CT> 
+  inline 
+  ScanLineToRects<T>& ScanLineToRects<T>::processEdge(CT& rectangles, const interval_data<coordinate_type>& edge) 
+  {
+    processEdge_(rectangles, scanData_, edge, haveCurrentRect_, currentRect_, currentCoordinate_, orient_);
+    return *this;
+  }
+
+
+} //namespace rectangle_formation
+
+  template <typename T, typename T2>
+  struct get_coordinate_type_for_rectangles {
+    typedef typename polygon_traits<T>::coordinate_type type;
+  };
+  template <typename T>
+  struct get_coordinate_type_for_rectangles<T, rectangle_concept> {
+    typedef typename rectangle_traits<T>::coordinate_type type;
+  };
+
+  template <typename output_container, typename iterator_type, typename rectangle_concept>
+  void form_rectangles(output_container& output, iterator_type begin, iterator_type end,
+                       orientation_2d orient, rectangle_concept ) {
+    typedef typename output_container::value_type rectangle_type;
+    typedef typename get_coordinate_type_for_rectangles<rectangle_type, typename geometry_concept<rectangle_type>::type>::type Unit;
+    rectangle_data<Unit> model;
+    Unit prevPos = (std::numeric_limits<Unit>::max)();
+    rectangle_formation::ScanLineToRects<rectangle_data<Unit> > scanlineToRects(orient, model);
+    for(iterator_type itr = begin;
+        itr != end; ++ itr) {
+      Unit pos = (*itr).first;
+      if(pos != prevPos) {
+        scanlineToRects.nextMajorCoordinate(pos);
+        prevPos = pos;
+      }
+      Unit lowy = (*itr).second.first;
+      iterator_type tmp_itr = itr;
+      ++itr;
+      Unit highy = (*itr).second.first;
+      scanlineToRects.processEdge(output, interval_data<Unit>(lowy, highy));
+      if(abs((*itr).second.second) > 1) itr = tmp_itr; //next edge begins from this vertex
+    }
+  }
+}
+}
+#endif
+

test/external/boost/polygon/detail/transform_detail.hpp

@@ -0,0 +1,553 @@
+/*
+    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_TRANSFORM_DETAIL_HPP
+#define BOOST_POLYGON_TRANSFORM_DETAIL_HPP
+
+namespace boost { namespace polygon{
+  // inline std::ostream& operator<< (std::ostream& o, const axis_transformation& r) {
+  //   o << r.atr_;
+  //   return o;
+  // }
+
+  // inline std::istream& operator>> (std::istream& i, axis_transformation& r) {
+  //   int tmp;
+  //   i >> tmp;
+  //   r = axis_transformation((axis_transformation::ATR)tmp);
+  //   return i;
+  // }
+
+  // template <typename scale_factor_type>
+  // inline std::ostream& operator<< (std::ostream& o, const anisotropic_scale_factor<scale_factor_type>& sc) {
+  //   o << sc.scale_[0] << BOOST_POLYGON_SEP << sc.scale_[1] << GTL_SEP << sc.scale_[2];
+  //   return o;
+  // }
+
+  // template <typename scale_factor_type>
+  // inline std::istream& operator>> (std::istream& i, anisotropic_scale_factor<scale_factor_type>& sc) {
+  //   i >> sc.scale_[0] >> sc.scale_[1] >> sc.scale_[2];
+  //   return i;
+  // }
+
+  // template <typename coordinate_type>
+  // inline std::ostream& operator<< (std::ostream& o, const transformation& tr) {
+  //   o << tr.atr_ << BOOST_POLYGON_SEP << tr.p_;
+  //   return o;
+  // }
+
+  // template <typename coordinate_type>
+  // inline std::istream& operator>> (std::istream& i, transformation& tr) {
+  //   i >> tr.atr_ >> tr.p_;
+  //   return i;
+  // }
+
+
+  inline axis_transformation::axis_transformation(const orientation_3d& orient) : atr_(NULL_TRANSFORM) {
+    const ATR tmp[3] = {
+      UP_EAST_NORTH, //sort by x, then z, then y
+      EAST_UP_NORTH, //sort by y, then z, then x
+      EAST_NORTH_UP  //sort by z, then y, then x
+    };
+    atr_ = tmp[orient.to_int()];
+  }
+  
+  inline axis_transformation::axis_transformation(const orientation_2d& orient) : atr_(NULL_TRANSFORM) {
+    const ATR tmp[3] = {
+      NORTH_EAST_UP, //sort by z, then x, then y
+      EAST_NORTH_UP  //sort by z, then y, then x
+    };
+    atr_ = tmp[orient.to_int()];
+  }
+  
+  inline axis_transformation::axis_transformation(const direction_3d& dir) : atr_(NULL_TRANSFORM) {
+    const ATR tmp[6] = {
+      DOWN_EAST_NORTH, //sort by -x, then z, then y
+      UP_EAST_NORTH,   //sort by x, then z, then y
+      EAST_DOWN_NORTH, //sort by -y, then z, then x
+      EAST_UP_NORTH,   //sort by y, then z, then x
+      EAST_NORTH_DOWN, //sort by -z, then y, then x
+      EAST_NORTH_UP    //sort by z, then y, then x
+    };
+    atr_ = tmp[dir.to_int()];
+  }
+  
+  inline axis_transformation::axis_transformation(const direction_2d& dir) : atr_(NULL_TRANSFORM) {
+    const ATR tmp[4] = {
+      SOUTH_EAST_UP, //sort by z, then x, then y
+      NORTH_EAST_UP, //sort by z, then x, then y
+      EAST_SOUTH_UP, //sort by z, then y, then x
+      EAST_NORTH_UP  //sort by z, then y, then x
+    };
+    atr_ = tmp[dir.to_int()];
+  }
+  
+  inline axis_transformation& axis_transformation::operator=(const axis_transformation& a) {
+    atr_ = a.atr_;
+    return *this;
+  }
+
+  inline axis_transformation& axis_transformation::operator=(const ATR& atr) {
+    atr_ = atr;
+    return *this;
+  }
+
+  inline bool axis_transformation::operator==(const axis_transformation& a) const {
+    return atr_ == a.atr_;
+  }
+
+  inline bool axis_transformation::operator!=(const axis_transformation& a) const {
+    return !(*this == a);
+  }
+
+  inline bool axis_transformation::operator<(const axis_transformation& a) const {
+    return atr_ < a.atr_;
+  }
+
+  inline axis_transformation& axis_transformation::operator+=(const axis_transformation& a){
+    bool abit5 = (a.atr_ & 32) != 0;
+    bool abit4 = (a.atr_ & 16) != 0;
+    bool abit3 = (a.atr_ & 8) != 0;
+    bool abit2 = (a.atr_ & 4) != 0;
+    bool abit1 = (a.atr_ & 2) != 0;
+    bool abit0 = (a.atr_ & 1) != 0;      
+    bool bit5 = (atr_ & 32) != 0;
+    bool bit4 = (atr_ & 16) != 0;
+    bool bit3 = (atr_ & 8) != 0;
+    bool bit2 = (atr_ & 4) != 0;
+    bool bit1 = (atr_ & 2) != 0;
+    bool bit0 = (atr_ & 1) != 0;      
+    int indexes[2][3] = {
+      {
+        ((int)((bit5 & bit2) | (bit4 & !bit2)) << 1) +
+        (int)(bit2 & !bit5),
+        ((int)((bit4 & bit2) | (bit5 & !bit2)) << 1) +
+        (int)(!bit5 & !bit2),
+        ((int)(!bit4 & !bit5) << 1) +
+        (int)(bit5) 
+      },
+      {
+        ((int)((abit5 & abit2) | (abit4 & !abit2)) << 1) +
+        (int)(abit2 & !abit5),
+        ((int)((abit4 & abit2) | (abit5 & !abit2)) << 1) +
+        (int)(!abit5 & !abit2),
+        ((int)(!abit4 & !abit5) << 1) +
+        (int)(abit5) 
+      }
+    };
+    int zero_bits[2][3] = {
+      {bit0, bit1, bit3},
+      {abit0, abit1, abit3}
+    };
+    int nbit3 = zero_bits[0][2] ^ zero_bits[1][indexes[0][2]];
+    int nbit1 = zero_bits[0][1] ^ zero_bits[1][indexes[0][1]];
+    int nbit0 = zero_bits[0][0] ^ zero_bits[1][indexes[0][0]];
+    indexes[0][0] = indexes[1][indexes[0][0]];
+    indexes[0][1] = indexes[1][indexes[0][1]];
+    indexes[0][2] = indexes[1][indexes[0][2]];
+    int nbit5 = (indexes[0][2] == 1);
+    int nbit4 = (indexes[0][2] == 0);
+    int nbit2 = (!(nbit5 | nbit4) & (bool)(indexes[0][0] & 1)) | //swap xy
+      (nbit5 & ((indexes[0][0] & 2) >> 1)) | //z->y x->z
+      (nbit4 & ((indexes[0][1] & 2) >> 1));  //z->x y->z
+    atr_ = (ATR)((nbit5 << 5) + 
+                 (nbit4 << 4) + 
+                 (nbit3 << 3) + 
+                 (nbit2 << 2) + 
+                 (nbit1 << 1) + nbit0);
+    return *this;
+  }
+  
+  inline axis_transformation axis_transformation::operator+(const axis_transformation& a) const {
+    axis_transformation retval(*this);
+    return retval+=a;
+  }
+  
+  // populate_axis_array writes the three INDIVIDUAL_AXIS values that the
+  // ATR enum value of 'this' represent into axis_array
+  inline void axis_transformation::populate_axis_array(INDIVIDUAL_AXIS axis_array[]) const {
+    bool bit5 = (atr_ & 32) != 0;
+    bool bit4 = (atr_ & 16) != 0;
+    bool bit3 = (atr_ & 8) != 0;
+    bool bit2 = (atr_ & 4) != 0;
+    bool bit1 = (atr_ & 2) != 0;
+    bool bit0 = (atr_ & 1) != 0;      
+    axis_array[2] = 
+      (INDIVIDUAL_AXIS)((((int)(!bit4 & !bit5)) << 2) +
+                        ((int)(bit5) << 1) + 
+                        bit3);
+    axis_array[1] = 
+      (INDIVIDUAL_AXIS)((((int)((bit4 & bit2) | (bit5 & !bit2))) << 2)+
+                        ((int)(!bit5 & !bit2) << 1) + 
+                        bit1);
+    axis_array[0] = 
+      (INDIVIDUAL_AXIS)((((int)((bit5 & bit2) | (bit4 & !bit2))) << 2) +
+                        ((int)(bit2 & !bit5) << 1) + 
+                        bit0);
+  }
+  
+  // combine_axis_arrays concatenates this_array and that_array overwriting
+  // the result into this_array
+  inline void 
+  axis_transformation::combine_axis_arrays (INDIVIDUAL_AXIS this_array[],
+                                            const INDIVIDUAL_AXIS that_array[]){
+    int indexes[3] = {this_array[0] >> 1,
+                      this_array[1] >> 1,
+                      this_array[2] >> 1};
+    int zero_bits[2][3] = {
+      {this_array[0] & 1, this_array[1] & 1, this_array[2] & 1},
+      {that_array[0] & 1, that_array[1] & 1, that_array[2] & 1}
+    };
+    this_array[0] = that_array[indexes[0]];
+    this_array[0] = (INDIVIDUAL_AXIS)((int)this_array[0] & (int)((int)PZ+(int)PY));
+    this_array[0] = (INDIVIDUAL_AXIS)((int)this_array[0] | 
+                                      ((int)zero_bits[0][0] ^ 
+                                       (int)zero_bits[1][indexes[0]]));
+    this_array[1] = that_array[indexes[1]];
+    this_array[1] = (INDIVIDUAL_AXIS)((int)this_array[1] & (int)((int)PZ+(int)PY));
+    this_array[1] = (INDIVIDUAL_AXIS)((int)this_array[1] | 
+                                      ((int)zero_bits[0][1] ^ 
+                                       (int)zero_bits[1][indexes[1]]));
+    this_array[2] = that_array[indexes[2]];
+    this_array[2] = (INDIVIDUAL_AXIS)((int)this_array[2] & (int)((int)PZ+(int)PY));
+    this_array[2] = (INDIVIDUAL_AXIS)((int)this_array[2] | 
+                                      ((int)zero_bits[0][2] ^ 
+                                       (int)zero_bits[1][indexes[2]]));
+  }
+  
+  // write_back_axis_array converts an array of three INDIVIDUAL_AXIS values
+  // to the ATR enum value and sets 'this' to that value
+  inline void axis_transformation::write_back_axis_array(const INDIVIDUAL_AXIS this_array[]) {
+    int bit5 = ((int)this_array[2] & 2) != 0;
+    int bit4 = !((((int)this_array[2] & 4) != 0) | (((int)this_array[2] & 2) != 0));
+    int bit3 = ((int)this_array[2] & 1) != 0;
+    //bit 2 is the tricky bit
+    int bit2 = ((!(bit5 | bit4)) & (((int)this_array[0] & 2) != 0)) | //swap xy
+      (bit5 & (((int)this_array[0] & 4) >> 2)) | //z->y x->z
+      (bit4 & (((int)this_array[1] & 4) >> 2));  //z->x y->z
+    int bit1 = ((int)this_array[1] & 1);
+    int bit0 = ((int)this_array[0] & 1);
+    atr_ = ATR((bit5 << 5) + 
+               (bit4 << 4) + 
+               (bit3 << 3) + 
+               (bit2 << 2) + 
+               (bit1 << 1) + bit0);
+  }
+  
+  // behavior is deterministic but undefined in the case where illegal
+  // combinations of directions are passed in. 
+  inline axis_transformation& 
+  axis_transformation::set_directions(const direction_2d& horizontalDir,
+                                      const direction_2d& verticalDir){
+    int bit2 = (static_cast<orientation_2d>(horizontalDir).to_int()) != 0;
+    int bit1 = !(verticalDir.to_int() & 1);
+    int bit0 = !(horizontalDir.to_int() & 1);
+    atr_ = ATR((bit2 << 2) + (bit1 << 1) + bit0);
+    return *this;
+  }
+  
+  // behavior is deterministic but undefined in the case where illegal
+  // combinations of directions are passed in.
+  inline axis_transformation& axis_transformation::set_directions(const direction_3d& horizontalDir,
+                                                                  const direction_3d& verticalDir,
+                                                                  const direction_3d& proximalDir){
+    int this_array[3] = {horizontalDir.to_int(),
+                         verticalDir.to_int(),
+                         proximalDir.to_int()};
+    int bit5 = (this_array[2] & 2) != 0;
+    int bit4 = !(((this_array[2] & 4) != 0) | ((this_array[2] & 2) != 0));
+    int bit3 = !((this_array[2] & 1) != 0);
+    //bit 2 is the tricky bit
+    int bit2 = (!(bit5 | bit4) & ((this_array[0] & 2) != 0 )) | //swap xy
+      (bit5 & ((this_array[0] & 4) >> 2)) | //z->y x->z
+      (bit4 & ((this_array[1] & 4) >> 2));  //z->x y->z
+    int bit1 = !(this_array[1] & 1);
+    int bit0 = !(this_array[0] & 1);
+    atr_ = ATR((bit5 << 5) + 
+               (bit4 << 4) + 
+               (bit3 << 3) + 
+               (bit2 << 2) + 
+               (bit1 << 1) + bit0);
+    return *this;
+  }
+  
+  template <typename coordinate_type_2>
+  inline void axis_transformation::transform(coordinate_type_2& x, coordinate_type_2& y) const {
+    int bit2 = (atr_ & 4) != 0;
+    int bit1 = (atr_ & 2) != 0;
+    int bit0 = (atr_ & 1) != 0;
+    x *= -((bit0 << 1) - 1);
+    y *= -((bit1 << 1) - 1);    
+    predicated_swap(bit2 != 0,x,y);
+  }
+  
+  template <typename coordinate_type_2>
+  inline void axis_transformation::transform(coordinate_type_2& x, coordinate_type_2& y, coordinate_type_2& z) const {
+    int bit5 = (atr_ & 32) != 0;
+    int bit4 = (atr_ & 16) != 0;
+    int bit3 = (atr_ & 8) != 0;
+    int bit2 = (atr_ & 4) != 0;
+    int bit1 = (atr_ & 2) != 0;
+    int bit0 = (atr_ & 1) != 0;
+    x *= -((bit0 << 1) - 1);
+    y *= -((bit1 << 1) - 1);    
+    z *= -((bit3 << 1) - 1);
+    predicated_swap(bit2 != 0, x, y);
+    predicated_swap(bit5 != 0, y, z);
+    predicated_swap(bit4 != 0, x, z);
+  }
+  
+  inline axis_transformation& axis_transformation::invert_2d() {
+    int bit2 = ((atr_ & 4) != 0);
+    int bit1 = ((atr_ & 2) != 0);
+    int bit0 = ((atr_ & 1) != 0);
+    //swap bit 0 and bit 1 if bit2 is 1
+    predicated_swap(bit2 != 0, bit0, bit1);
+    bit1 = bit1 << 1;
+    atr_ = (ATR)(atr_ & (32+16+8+4)); //mask away bit0 and bit1
+    atr_ = (ATR)(atr_ | bit0 | bit1);
+    return *this;
+  }
+  
+  inline axis_transformation axis_transformation::inverse_2d() const {
+    axis_transformation retval(*this);
+    return retval.invert_2d();
+  }
+  
+  inline axis_transformation& axis_transformation::invert() {
+    int bit5 = ((atr_ & 32) != 0);
+    int bit4 = ((atr_ & 16) != 0);    
+    int bit3 = ((atr_ & 8) != 0);
+    int bit2 = ((atr_ & 4) != 0);
+    int bit1 = ((atr_ & 2) != 0);
+    int bit0 = ((atr_ & 1) != 0);
+    predicated_swap(bit2 != 0, bit4, bit5);
+    predicated_swap(bit4 != 0, bit0, bit3);
+    predicated_swap(bit5 != 0, bit1, bit3);
+    predicated_swap(bit2 != 0, bit0, bit1);
+    atr_ = (ATR)((bit5 << 5) + 
+                 (bit4 << 4) + 
+                 (bit3 << 3) + 
+                 (bit2 << 2) + 
+                 (bit1 << 1) + bit0);
+    return *this;
+  }
+  
+  inline axis_transformation axis_transformation::inverse() const {
+    axis_transformation retval(*this);
+    return retval.invert();
+  }
+  
+  template <typename scale_factor_type>
+  inline scale_factor_type anisotropic_scale_factor<scale_factor_type>::get(orientation_3d orient) const {
+    return scale_[orient.to_int()];
+  }
+  
+  template <typename scale_factor_type>
+  inline void anisotropic_scale_factor<scale_factor_type>::set(orientation_3d orient, scale_factor_type value) {
+    scale_[orient.to_int()] = value;
+  }
+
+  template <typename scale_factor_type>
+  inline scale_factor_type anisotropic_scale_factor<scale_factor_type>::x() const { return scale_[HORIZONTAL]; }
+  template <typename scale_factor_type>
+  inline scale_factor_type anisotropic_scale_factor<scale_factor_type>::y() const { return scale_[VERTICAL]; }
+  template <typename scale_factor_type>
+  inline scale_factor_type anisotropic_scale_factor<scale_factor_type>::z() const { return scale_[PROXIMAL]; }
+  template <typename scale_factor_type>
+  inline void anisotropic_scale_factor<scale_factor_type>::x(scale_factor_type value) { scale_[HORIZONTAL] = value; }
+  template <typename scale_factor_type>
+  inline void anisotropic_scale_factor<scale_factor_type>::y(scale_factor_type value) { scale_[VERTICAL] = value; }
+  template <typename scale_factor_type>
+  inline void anisotropic_scale_factor<scale_factor_type>::z(scale_factor_type value) { scale_[PROXIMAL] = value; }
+  
+  //concatenation operator (convolve scale factors)
+  template <typename scale_factor_type>
+  inline anisotropic_scale_factor<scale_factor_type> anisotropic_scale_factor<scale_factor_type>::operator+(const anisotropic_scale_factor<scale_factor_type>& s) const {
+    anisotropic_scale_factor<scale_factor_type> retval(*this);
+    return retval+=s;
+  }
+  
+  //concatenate this with that
+  template <typename scale_factor_type>
+  inline const anisotropic_scale_factor<scale_factor_type>& anisotropic_scale_factor<scale_factor_type>::operator+=(const anisotropic_scale_factor<scale_factor_type>& s){
+    scale_[0] *= s.scale_[0];
+    scale_[1] *= s.scale_[1];
+    scale_[2] *= s.scale_[2];
+    return *this;
+  }
+  
+  //transform
+  template <typename scale_factor_type>
+  inline anisotropic_scale_factor<scale_factor_type>& anisotropic_scale_factor<scale_factor_type>::transform(axis_transformation atr){
+    direction_3d dirs[3];
+    atr.get_directions(dirs[0],dirs[1],dirs[2]);
+    scale_factor_type tmp[3] = {scale_[0], scale_[1], scale_[2]};
+    for(int i = 0; i < 3; ++i){
+      scale_[orientation_3d(dirs[i]).to_int()] = tmp[i];
+    }
+    return *this;
+  }
+
+  template <typename scale_factor_type>
+  template <typename coordinate_type_2>
+  inline void anisotropic_scale_factor<scale_factor_type>::scale(coordinate_type_2& x, coordinate_type_2& y) const {
+    x = scaling_policy<coordinate_type_2>::round((scale_factor_type)x * get(HORIZONTAL));
+    y = scaling_policy<coordinate_type_2>::round((scale_factor_type)y * get(HORIZONTAL));
+  }
+
+  template <typename scale_factor_type>
+  template <typename coordinate_type_2>
+  inline void anisotropic_scale_factor<scale_factor_type>::scale(coordinate_type_2& x, coordinate_type_2& y, coordinate_type_2& z) const {
+    scale(x, y);
+    z = scaling_policy<coordinate_type_2>::round((scale_factor_type)z * get(HORIZONTAL));
+  }
+
+  template <typename scale_factor_type>
+  inline anisotropic_scale_factor<scale_factor_type>& anisotropic_scale_factor<scale_factor_type>::invert() {
+    x(1/x());
+    y(1/y());
+    z(1/z());
+    return *this;
+  }
+
+
+  template <typename coordinate_type>
+  inline transformation<coordinate_type>::transformation() : atr_(), p_(0, 0, 0) {;}
+
+  template <typename coordinate_type>
+  inline transformation<coordinate_type>::transformation(axis_transformation atr) : atr_(atr), p_(0, 0, 0){;}
+
+  template <typename coordinate_type>
+  inline transformation<coordinate_type>::transformation(axis_transformation::ATR atr) : atr_(atr), p_(0, 0, 0){;}
+
+  template <typename coordinate_type>
+  template <typename point_type>
+  inline transformation<coordinate_type>::transformation(const point_type& p) : atr_(), p_(0, 0, 0) {
+    set_translation(p);
+  }
+
+  template <typename coordinate_type>
+  template <typename point_type>
+  inline transformation<coordinate_type>::transformation(axis_transformation atr, const point_type& p) :
+    atr_(atr), p_(0, 0, 0) {
+    set_translation(p);
+  }
+
+  template <typename coordinate_type>
+  template <typename point_type>
+  inline transformation<coordinate_type>::transformation(axis_transformation atr, const point_type& referencePt, const point_type& destinationPt) : atr_(), p_(0, 0, 0) {
+    transformation<coordinate_type> tmp(referencePt);
+    transformation<coordinate_type> rotRef(atr);
+    transformation<coordinate_type> tmpInverse = tmp.inverse();
+    point_type decon(referencePt);
+    deconvolve(decon, destinationPt);
+    transformation<coordinate_type> displacement(decon);
+    tmp += rotRef;
+    tmp += tmpInverse;
+    tmp += displacement;
+    (*this) = tmp;
+  }
+
+  template <typename coordinate_type>
+  inline transformation<coordinate_type>::transformation(const transformation<coordinate_type>& tr) : 
+    atr_(tr.atr_), p_(tr.p_) {;}
+  
+  template <typename coordinate_type>
+  inline bool transformation<coordinate_type>::operator==(const transformation<coordinate_type>& tr) const {
+    return atr_ == tr.atr_ && p_ == tr.p_;
+  }
+  
+  template <typename coordinate_type>
+  inline bool transformation<coordinate_type>::operator!=(const transformation<coordinate_type>& tr) const {
+    return !(*this == tr);
+  }
+  
+  template <typename coordinate_type>
+  inline bool transformation<coordinate_type>::operator<(const transformation<coordinate_type>& tr) const {
+    return atr_ < tr.atr_ || atr_ == tr.atr_ && p_ < tr.p_;
+  }
+  
+  template <typename coordinate_type>
+  inline transformation<coordinate_type> transformation<coordinate_type>::operator+(const transformation<coordinate_type>& tr) const {
+    transformation<coordinate_type> retval(*this);
+    return retval+=tr;
+  }
+  
+  template <typename coordinate_type>
+  inline const transformation<coordinate_type>& transformation<coordinate_type>::operator+=(const transformation<coordinate_type>& tr){
+    //apply the inverse transformation of this to the translation point of that
+    //and convolve it with this translation point
+    coordinate_type x, y, z;
+    transformation<coordinate_type> inv = inverse();
+    inv.transform(x, y, z);
+    p_.set(HORIZONTAL, p_.get(HORIZONTAL) + x);
+    p_.set(VERTICAL, p_.get(VERTICAL) + y);
+    p_.set(PROXIMAL, p_.get(PROXIMAL) + z);
+    //concatenate axis transforms
+    atr_ += tr.atr_;
+    return *this;
+  }
+  
+  template <typename coordinate_type>
+  inline void transformation<coordinate_type>::set_axis_transformation(const axis_transformation& atr) {
+    atr_ = atr;
+  }
+  
+  template <typename coordinate_type>
+  template <typename point_type>
+  inline void transformation<coordinate_type>::get_translation(point_type& p) const {
+    assign(p, p_);
+  }
+  
+  template <typename coordinate_type>
+  template <typename point_type>
+  inline void transformation<coordinate_type>::set_translation(const point_type& p) {
+    assign(p_, p);
+  }
+  
+  template <typename coordinate_type>
+  inline void transformation<coordinate_type>::transform(coordinate_type& x, coordinate_type& y) const {
+    //subtract each component of new origin point
+    y -= p_.get(VERTICAL);
+    x -= p_.get(HORIZONTAL);
+    atr_.transform(x, y);
+  }
+
+  template <typename coordinate_type>
+  inline void transformation<coordinate_type>::transform(coordinate_type& x, coordinate_type& y, coordinate_type& z) const {
+    //subtract each component of new origin point
+    z -= p_.get(PROXIMAL);
+    y -= p_.get(VERTICAL);
+    x -= p_.get(HORIZONTAL);
+    atr_.transform(x,y,z);
+  }
+  
+  // sets the axis_transform portion to its inverse
+  // transforms the tranlastion portion by that inverse axis_transform
+  // multiplies the translation portion by -1 to reverse it
+  template <typename coordinate_type>
+  inline transformation<coordinate_type>& transformation<coordinate_type>::invert() {
+    coordinate_type x = p_.get(HORIZONTAL), y = p_.get(VERTICAL), z = p_.get(PROXIMAL);
+    atr_.transform(x, y, z);
+    x *= -1;
+    y *= -1;
+    z *= -1;
+    p_ = point_3d_data<coordinate_type>(x, y, z);
+    atr_.invert();
+    return *this;
+  }
+  
+  template <typename coordinate_type>
+  inline transformation<coordinate_type> transformation<coordinate_type>::inverse() const {
+    transformation<coordinate_type> retval(*this);
+    return retval.invert();
+  }
+}
+}
+#endif
+
+