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 // Boost.Polygon library voronoi_diagram.hpp header file
 
 //          Copyright Andrii Sydorchuk 2010-2012.
 // Distributed under 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)
 
 // See http://www.boost.org for updates, documentation, and revision history.
 
 #ifndef BOOST_POLYGON_VORONOI_DIAGRAM
 #define BOOST_POLYGON_VORONOI_DIAGRAM
 
 #include <vector>
 #include <utility>
 
 #include "detail/voronoi_ctypes.hpp"
 #include "detail/voronoi_structures.hpp"
 
 #include "voronoi_geometry_type.hpp"
 
 namespace boost {
 namespace polygon {
 
 // Forward declarations.
 template <typename T>
 class voronoi_edge;
 
 // Represents Voronoi cell.
 // Data members:
 //   1) index of the source within the initial input set
 //   2) pointer to the incident edge
 //   3) mutable color member
 // Cell may contain point or segment site inside.
 template <typename T>
 class voronoi_cell {
  public:
   typedef T coordinate_type;
   typedef std::size_t color_type;
   typedef voronoi_edge<coordinate_type> voronoi_edge_type;
   typedef std::size_t source_index_type;
   typedef SourceCategory source_category_type;
 
   voronoi_cell(source_index_type source_index,
                source_category_type source_category) :
       source_index_(source_index),
       incident_edge_(NULL),
       color_(source_category) {}
 
   // Returns true if the cell contains point site, false else.
   bool contains_point() const {
     source_category_type source_category = this->source_category();
     return belongs(source_category, GEOMETRY_CATEGORY_POINT);
   }
 
   // Returns true if the cell contains segment site, false else.
   bool contains_segment() const {
     source_category_type source_category = this->source_category();
     return belongs(source_category, GEOMETRY_CATEGORY_SEGMENT);
   }
 
   source_index_type source_index() const {
     return source_index_;
   }
 
   source_category_type source_category() const {
     return static_cast<source_category_type>(color_ & SOURCE_CATEGORY_BITMASK);
   }
 
   // Degenerate cells don't have any incident edges.
   bool is_degenerate() const { return incident_edge_ == NULL; }
 
   voronoi_edge_type* incident_edge() { return incident_edge_; }
   const voronoi_edge_type* incident_edge() const { return incident_edge_; }
   void incident_edge(voronoi_edge_type* e) { incident_edge_ = e; }
 
   color_type color() const { return color_ >> BITS_SHIFT; }
   void color(color_type color) const {
     color_ &= BITS_MASK;
     color_ |= color << BITS_SHIFT;
   }
 
  private:
   // 5 color bits are reserved.
   enum Bits {
     BITS_SHIFT = 0x5,
     BITS_MASK = 0x1F
   };
 
   source_index_type source_index_;
   voronoi_edge_type* incident_edge_;
   mutable color_type color_;
 };
 
 // Represents Voronoi vertex.
 // Data members:
 //   1) vertex coordinates
 //   2) pointer to the incident edge
 //   3) mutable color member
 template <typename T>
 class voronoi_vertex {
  public:
   typedef T coordinate_type;
   typedef std::size_t color_type;
   typedef voronoi_edge<coordinate_type> voronoi_edge_type;
 
   voronoi_vertex(const coordinate_type& x, const coordinate_type& y) :
       x_(x),
       y_(y),
       incident_edge_(NULL),
       color_(0) {}
 
   const coordinate_type& x() const { return x_; }
   const coordinate_type& y() const { return y_; }
 
   bool is_degenerate() const { return incident_edge_ == NULL; }
 
   voronoi_edge_type* incident_edge() { return incident_edge_; }
   const voronoi_edge_type* incident_edge() const { return incident_edge_; }
   void incident_edge(voronoi_edge_type* e) { incident_edge_ = e; }
 
   color_type color() const { return color_ >> BITS_SHIFT; }
   void color(color_type color) const {
     color_ &= BITS_MASK;
     color_ |= color << BITS_SHIFT;
   }
 
  private:
   // 5 color bits are reserved.
   enum Bits {
     BITS_SHIFT = 0x5,
     BITS_MASK = 0x1F
   };
 
   coordinate_type x_;
   coordinate_type y_;
   voronoi_edge_type* incident_edge_;
   mutable color_type color_;
 };
 
 // Half-edge data structure. Represents Voronoi edge.
 // Data members:
 //   1) pointer to the corresponding cell
 //   2) pointer to the vertex that is the starting
 //      point of the half-edge
 //   3) pointer to the twin edge
 //   4) pointer to the CCW next edge
 //   5) pointer to the CCW prev edge
 //   6) mutable color member
 template <typename T>
 class voronoi_edge {
  public:
   typedef T coordinate_type;
   typedef voronoi_cell<coordinate_type> voronoi_cell_type;
   typedef voronoi_vertex<coordinate_type> voronoi_vertex_type;
   typedef voronoi_edge<coordinate_type> voronoi_edge_type;
   typedef std::size_t color_type;
 
   voronoi_edge(bool is_linear, bool is_primary) :
       cell_(NULL),
       vertex_(NULL),
       twin_(NULL),
       next_(NULL),
       prev_(NULL),
       color_(0) {
     if (is_linear)
       color_ |= BIT_IS_LINEAR;
     if (is_primary)
       color_ |= BIT_IS_PRIMARY;
   }
 
   voronoi_cell_type* cell() { return cell_; }
   const voronoi_cell_type* cell() const { return cell_; }
   void cell(voronoi_cell_type* c) { cell_ = c; }
 
   voronoi_vertex_type* vertex0() { return vertex_; }
   const voronoi_vertex_type* vertex0() const { return vertex_; }
   void vertex0(voronoi_vertex_type* v) { vertex_ = v; }
 
   voronoi_vertex_type* vertex1() { return twin_->vertex0(); }
   const voronoi_vertex_type* vertex1() const { return twin_->vertex0(); }
 
   voronoi_edge_type* twin() { return twin_; }
   const voronoi_edge_type* twin() const { return twin_; }
   void twin(voronoi_edge_type* e) { twin_ = e; }
 
   voronoi_edge_type* next() { return next_; }
   const voronoi_edge_type* next() const { return next_; }
   void next(voronoi_edge_type* e) { next_ = e; }
 
   voronoi_edge_type* prev() { return prev_; }
   const voronoi_edge_type* prev() const { return prev_; }
   void prev(voronoi_edge_type* e) { prev_ = e; }
 
   // Returns a pointer to the rotation next edge
   // over the starting point of the half-edge.
   voronoi_edge_type* rot_next() { return prev_->twin(); }
   const voronoi_edge_type* rot_next() const { return prev_->twin(); }
 
   // Returns a pointer to the rotation prev edge
   // over the starting point of the half-edge.
   voronoi_edge_type* rot_prev() { return twin_->next(); }
   const voronoi_edge_type* rot_prev() const { return twin_->next(); }
 
   // Returns true if the edge is finite (segment, parabolic arc).
   // Returns false if the edge is infinite (ray, line).
   bool is_finite() const { return vertex0() && vertex1(); }
 
   // Returns true if the edge is infinite (ray, line).
   // Returns false if the edge is finite (segment, parabolic arc).
   bool is_infinite() const { return !vertex0() || !vertex1(); }
 
   // Returns true if the edge is linear (segment, ray, line).
   // Returns false if the edge is curved (parabolic arc).
   bool is_linear() const {
     return (color_ & BIT_IS_LINEAR) ? true : false;
   }
 
   // Returns true if the edge is curved (parabolic arc).
   // Returns false if the edge is linear (segment, ray, line).
   bool is_curved() const {
     return (color_ & BIT_IS_LINEAR) ? false : true;
   }
 
   // Returns false if edge goes through the endpoint of the segment.
   // Returns true else.
   bool is_primary() const {
     return (color_ & BIT_IS_PRIMARY) ? true : false;
   }
 
   // Returns true if edge goes through the endpoint of the segment.
   // Returns false else.
   bool is_secondary() const {
     return (color_ & BIT_IS_PRIMARY) ? false : true;
   }
 
   color_type color() const { return color_ >> BITS_SHIFT; }
   void color(color_type color) const {
     color_ &= BITS_MASK;
     color_ |= color << BITS_SHIFT;
   }
 
  private:
   // 5 color bits are reserved.
   enum Bits {
     BIT_IS_LINEAR = 0x1,  // linear is opposite to curved
     BIT_IS_PRIMARY = 0x2,  // primary is opposite to secondary
 
     BITS_SHIFT = 0x5,
     BITS_MASK = 0x1F
   };
 
   voronoi_cell_type* cell_;
   voronoi_vertex_type* vertex_;
   voronoi_edge_type* twin_;
   voronoi_edge_type* next_;
   voronoi_edge_type* prev_;
   mutable color_type color_;
 };
 
 template <typename T>
 struct voronoi_diagram_traits {
   typedef T coordinate_type;
   typedef voronoi_cell<coordinate_type> cell_type;
   typedef voronoi_vertex<coordinate_type> vertex_type;
   typedef voronoi_edge<coordinate_type> edge_type;
   class vertex_equality_predicate_type {
    public:
     enum { ULPS = 128 };
     bool operator()(const vertex_type& v1, const vertex_type& v2) const {
       return (ulp_cmp(v1.x(), v2.x(), ULPS) ==
               detail::ulp_comparison<T>::EQUAL) &&
              (ulp_cmp(v1.y(), v2.y(), ULPS) ==
               detail::ulp_comparison<T>::EQUAL);
     }
    private:
     typename detail::ulp_comparison<T> ulp_cmp;
   };
 };
 
 // Voronoi output data structure.
 // CCW ordering is used on the faces perimeter and around the vertices.
 template <typename T, typename TRAITS = voronoi_diagram_traits<T> >
 class voronoi_diagram {
  public:
   typedef typename TRAITS::coordinate_type coordinate_type;
   typedef typename TRAITS::cell_type cell_type;
   typedef typename TRAITS::vertex_type vertex_type;
   typedef typename TRAITS::edge_type edge_type;
 
   typedef std::vector<cell_type> cell_container_type;
   typedef typename cell_container_type::const_iterator const_cell_iterator;
 
   typedef std::vector<vertex_type> vertex_container_type;
   typedef typename vertex_container_type::const_iterator const_vertex_iterator;
 
   typedef std::vector<edge_type> edge_container_type;
   typedef typename edge_container_type::const_iterator const_edge_iterator;
 
   voronoi_diagram() {}
 
   void clear() {
     cells_.clear();
     vertices_.clear();
     edges_.clear();
   }
 
   const cell_container_type& cells() const {
     return cells_;
   }
 
   const vertex_container_type& vertices() const {
     return vertices_;
   }
 
   const edge_container_type& edges() const {
     return edges_;
   }
 
   std::size_t num_cells() const {
     return cells_.size();
   }
 
   std::size_t num_edges() const {
     return edges_.size();
   }
 
   std::size_t num_vertices() const {
     return vertices_.size();
   }
 
   void _reserve(std::size_t num_sites) {
     cells_.reserve(num_sites);
     vertices_.reserve(num_sites << 1);
     edges_.reserve((num_sites << 2) + (num_sites << 1));
   }
 
   template <typename CT>
   void _process_single_site(const detail::site_event<CT>& site) {
     cells_.push_back(cell_type(site.initial_index(), site.source_category()));
   }
 
   // Insert a new half-edge into the output data structure.
   // Takes as input left and right sites that form a new bisector.
   // Returns a pair of pointers to a new half-edges.
   template <typename CT>
   std::pair<void*, void*> _insert_new_edge(
       const detail::site_event<CT>& site1,
       const detail::site_event<CT>& site2) {
     // Get sites' indexes.
     std::size_t site_index1 = site1.sorted_index();
     std::size_t site_index2 = site2.sorted_index();
 
     bool is_linear = is_linear_edge(site1, site2);
     bool is_primary = is_primary_edge(site1, site2);
 
     // Create a new half-edge that belongs to the first site.
     edges_.push_back(edge_type(is_linear, is_primary));
     edge_type& edge1 = edges_.back();
 
     // Create a new half-edge that belongs to the second site.
     edges_.push_back(edge_type(is_linear, is_primary));
     edge_type& edge2 = edges_.back();
 
     // Add the initial cell during the first edge insertion.
     if (cells_.empty()) {
       cells_.push_back(cell_type(
           site1.initial_index(), site1.source_category()));
     }
 
     // The second site represents a new site during site event
     // processing. Add a new cell to the cell records.
     cells_.push_back(cell_type(
         site2.initial_index(), site2.source_category()));
 
     // Set up pointers to cells.
     edge1.cell(&cells_[site_index1]);
     edge2.cell(&cells_[site_index2]);
 
     // Set up twin pointers.
     edge1.twin(&edge2);
     edge2.twin(&edge1);
 
     // Return a pointer to the new half-edge.
     return std::make_pair(&edge1, &edge2);
   }
 
   // Insert a new half-edge into the output data structure with the
   // start at the point where two previously added half-edges intersect.
   // Takes as input two sites that create a new bisector, circle event
   // that corresponds to the intersection point of the two old half-edges,
   // pointers to those half-edges. Half-edges' direction goes out of the
   // new Voronoi vertex point. Returns a pair of pointers to a new half-edges.
   template <typename CT1, typename CT2>
   std::pair<void*, void*> _insert_new_edge(
       const detail::site_event<CT1>& site1,
       const detail::site_event<CT1>& site3,
       const detail::circle_event<CT2>& circle,
       void* data12, void* data23) {
     edge_type* edge12 = static_cast<edge_type*>(data12);
     edge_type* edge23 = static_cast<edge_type*>(data23);
 
     // Add a new Voronoi vertex.
     vertices_.push_back(vertex_type(circle.x(), circle.y()));
     vertex_type& new_vertex = vertices_.back();
 
     // Update vertex pointers of the old edges.
     edge12->vertex0(&new_vertex);
     edge23->vertex0(&new_vertex);
 
     bool is_linear = is_linear_edge(site1, site3);
     bool is_primary = is_primary_edge(site1, site3);
 
     // Add a new half-edge.
     edges_.push_back(edge_type(is_linear, is_primary));
     edge_type& new_edge1 = edges_.back();
     new_edge1.cell(&cells_[site1.sorted_index()]);
 
     // Add a new half-edge.
     edges_.push_back(edge_type(is_linear, is_primary));
     edge_type& new_edge2 = edges_.back();
     new_edge2.cell(&cells_[site3.sorted_index()]);
 
     // Update twin pointers.
     new_edge1.twin(&new_edge2);
     new_edge2.twin(&new_edge1);
 
     // Update vertex pointer.
     new_edge2.vertex0(&new_vertex);
 
     // Update Voronoi prev/next pointers.
     edge12->prev(&new_edge1);
     new_edge1.next(edge12);
     edge12->twin()->next(edge23);
     edge23->prev(edge12->twin());
     edge23->twin()->next(&new_edge2);
     new_edge2.prev(edge23->twin());
 
     // Return a pointer to the new half-edge.
     return std::make_pair(&new_edge1, &new_edge2);
   }
 
   void _build() {
     // Remove degenerate edges.
     edge_iterator last_edge = edges_.begin();
     for (edge_iterator it = edges_.begin(); it != edges_.end(); it += 2) {
       const vertex_type* v1 = it->vertex0();
       const vertex_type* v2 = it->vertex1();
       if (v1 && v2 && vertex_equality_predicate_(*v1, *v2)) {
         remove_edge(&(*it));
       } else {
         if (it != last_edge) {
           edge_type* e1 = &(*last_edge = *it);
           edge_type* e2 = &(*(last_edge + 1) = *(it + 1));
           e1->twin(e2);
           e2->twin(e1);
           if (e1->prev()) {
             e1->prev()->next(e1);
             e2->next()->prev(e2);
           }
           if (e2->prev()) {
             e1->next()->prev(e1);
             e2->prev()->next(e2);
           }
         }
         last_edge += 2;
       }
     }
     edges_.erase(last_edge, edges_.end());
 
     // Set up incident edge pointers for cells and vertices.
     for (edge_iterator it = edges_.begin(); it != edges_.end(); ++it) {
       it->cell()->incident_edge(&(*it));
       if (it->vertex0()) {
         it->vertex0()->incident_edge(&(*it));
       }
     }
 
     // Remove degenerate vertices.
     vertex_iterator last_vertex = vertices_.begin();
     for (vertex_iterator it = vertices_.begin(); it != vertices_.end(); ++it) {
       if (it->incident_edge()) {
         if (it != last_vertex) {
           *last_vertex = *it;
           vertex_type* v = &(*last_vertex);
           edge_type* e = v->incident_edge();
           do {
             e->vertex0(v);
             e = e->rot_next();
           } while (e != v->incident_edge());
         }
         ++last_vertex;
       }
     }
     vertices_.erase(last_vertex, vertices_.end());
 
     // Set up next/prev pointers for infinite edges.
     if (vertices_.empty()) {
       if (!edges_.empty()) {
         // Update prev/next pointers for the line edges.
         edge_iterator edge_it = edges_.begin();
         edge_type* edge1 = &(*edge_it);
         edge1->next(edge1);
         edge1->prev(edge1);
         ++edge_it;
         edge1 = &(*edge_it);
         ++edge_it;
 
         while (edge_it != edges_.end()) {
           edge_type* edge2 = &(*edge_it);
           ++edge_it;
 
           edge1->next(edge2);
           edge1->prev(edge2);
           edge2->next(edge1);
           edge2->prev(edge1);
 
           edge1 = &(*edge_it);
           ++edge_it;
         }
 
         edge1->next(edge1);
         edge1->prev(edge1);
       }
     } else {
       // Update prev/next pointers for the ray edges.
       for (cell_iterator cell_it = cells_.begin();
          cell_it != cells_.end(); ++cell_it) {
         if (cell_it->is_degenerate())
           continue;
         // Move to the previous edge while
         // it is possible in the CW direction.
         edge_type* left_edge = cell_it->incident_edge();
         while (left_edge->prev() != NULL) {
           left_edge = left_edge->prev();
           // Terminate if this is not a boundary cell.
           if (left_edge == cell_it->incident_edge())
             break;
         }
 
         if (left_edge->prev() != NULL)
           continue;
 
         edge_type* right_edge = cell_it->incident_edge();
         while (right_edge->next() != NULL)
           right_edge = right_edge->next();
         left_edge->prev(right_edge);
         right_edge->next(left_edge);
       }
     }
   }
 
  private:
   typedef typename cell_container_type::iterator cell_iterator;
   typedef typename vertex_container_type::iterator vertex_iterator;
   typedef typename edge_container_type::iterator edge_iterator;
   typedef typename TRAITS::vertex_equality_predicate_type
     vertex_equality_predicate_type;
 
   template <typename SEvent>
   bool is_primary_edge(const SEvent& site1, const SEvent& site2) const {
     bool flag1 = site1.is_segment();
     bool flag2 = site2.is_segment();
     if (flag1 && !flag2) {
       return (site1.point0() != site2.point0()) &&
              (site1.point1() != site2.point0());
     }
     if (!flag1 && flag2) {
       return (site2.point0() != site1.point0()) &&
              (site2.point1() != site1.point0());
     }
     return true;
   }
 
   template <typename SEvent>
   bool is_linear_edge(const SEvent& site1, const SEvent& site2) const {
     if (!is_primary_edge(site1, site2)) {
       return true;
     }
     return !(site1.is_segment() ^ site2.is_segment());
   }
 
   // Remove degenerate edge.
   void remove_edge(edge_type* edge) {
     // Update the endpoints of the incident edges to the second vertex.
     vertex_type* vertex = edge->vertex0();
     edge_type* updated_edge = edge->twin()->rot_next();
     while (updated_edge != edge->twin()) {
       updated_edge->vertex0(vertex);
       updated_edge = updated_edge->rot_next();
     }
 
     edge_type* edge1 = edge;
     edge_type* edge2 = edge->twin();
 
     edge_type* edge1_rot_prev = edge1->rot_prev();
     edge_type* edge1_rot_next = edge1->rot_next();
 
     edge_type* edge2_rot_prev = edge2->rot_prev();
     edge_type* edge2_rot_next = edge2->rot_next();
 
     // Update prev/next pointers for the incident edges.
     edge1_rot_next->twin()->next(edge2_rot_prev);
     edge2_rot_prev->prev(edge1_rot_next->twin());
     edge1_rot_prev->prev(edge2_rot_next->twin());
     edge2_rot_next->twin()->next(edge1_rot_prev);
   }
 
   cell_container_type cells_;
   vertex_container_type vertices_;
   edge_container_type edges_;
   vertex_equality_predicate_type vertex_equality_predicate_;
 
   // Disallow copy constructor and operator=
   voronoi_diagram(const voronoi_diagram&);
   void operator=(const voronoi_diagram&);
 };
 }  // polygon
 }  // boost
 
 #endif  // BOOST_POLYGON_VORONOI_DIAGRAM

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