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 // Boost.Polygon library detail/voronoi_structures.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_DETAIL_VORONOI_STRUCTURES
 #define BOOST_POLYGON_DETAIL_VORONOI_STRUCTURES
 
 #include <list>
 #include <queue>
 #include <vector>
 
 #include "boost/polygon/voronoi_geometry_type.hpp"
 
 namespace boost {
 namespace polygon {
 namespace detail {
 // Cartesian 2D point data structure.
 template <typename T>
 class point_2d {
  public:
   typedef T coordinate_type;
 
   point_2d() {}
 
   point_2d(coordinate_type x, coordinate_type y) :
       x_(x),
       y_(y) {}
 
   bool operator==(const point_2d& that) const {
     return (this->x_ == that.x()) && (this->y_ == that.y());
   }
 
   bool operator!=(const point_2d& that) const {
     return (this->x_ != that.x()) || (this->y_ != that.y());
   }
 
   coordinate_type x() const {
     return x_;
   }
 
   coordinate_type y() const {
     return y_;
   }
 
   point_2d& x(coordinate_type x) {
     x_ = x;
     return *this;
   }
 
   point_2d& y(coordinate_type y) {
     y_ = y;
     return *this;
   }
 
  private:
   coordinate_type x_;
   coordinate_type y_;
 };
 
 // Site event type.
 // Occurs when the sweepline sweeps over one of the initial sites:
 //   1) point site
 //   2) start-point of the segment site
 //   3) endpoint of the segment site
 // Implicit segment direction is defined: the start-point of
 // the segment compares less than its endpoint.
 // Each input segment is divided onto two site events:
 //   1) One going from the start-point to the endpoint
 //      (is_inverse() = false)
 //   2) Another going from the endpoint to the start-point
 //      (is_inverse() = true)
 // In beach line data structure segment sites of the first
 // type precede sites of the second type for the same segment.
 // Members:
 //   point0_ - point site or segment's start-point
 //   point1_ - segment's endpoint if site is a segment
 //   sorted_index_ - the last bit encodes information if the site is inverse;
 //     the other bits encode site event index among the sorted site events
 //   initial_index_ - site index among the initial input set
 // Note: for all sites is_inverse_ flag is equal to false by default.
 template <typename T>
 class site_event {
  public:
   typedef T coordinate_type;
   typedef point_2d<T> point_type;
 
   site_event() :
       point0_(0, 0),
       point1_(0, 0),
       sorted_index_(0),
       flags_(0) {}
 
   site_event(coordinate_type x, coordinate_type y) :
       point0_(x, y),
       point1_(x, y),
       sorted_index_(0),
       flags_(0) {}
 
   explicit site_event(const point_type& point) :
       point0_(point),
       point1_(point),
       sorted_index_(0),
       flags_(0) {}
 
   site_event(coordinate_type x1, coordinate_type y1,
              coordinate_type x2, coordinate_type y2):
       point0_(x1, y1),
       point1_(x2, y2),
       sorted_index_(0),
       flags_(0) {}
 
   site_event(const point_type& point1, const point_type& point2) :
       point0_(point1),
       point1_(point2),
       sorted_index_(0),
       flags_(0) {}
 
   bool operator==(const site_event& that) const {
     return (this->point0_ == that.point0_) &&
            (this->point1_ == that.point1_);
   }
 
   bool operator!=(const site_event& that) const {
     return (this->point0_ != that.point0_) ||
            (this->point1_ != that.point1_);
   }
 
   coordinate_type x() const {
     return point0_.x();
   }
 
   coordinate_type y() const {
     return point0_.y();
   }
 
   coordinate_type x0() const {
     return point0_.x();
   }
 
   coordinate_type y0() const {
     return point0_.y();
   }
 
   coordinate_type x1() const {
     return point1_.x();
   }
 
   coordinate_type y1() const {
     return point1_.y();
   }
 
   const point_type& point0() const {
     return point0_;
   }
 
   const point_type& point1() const {
     return point1_;
   }
 
   std::size_t sorted_index() const {
     return sorted_index_;
   }
 
   site_event& sorted_index(std::size_t index) {
     sorted_index_ = index;
     return *this;
   }
 
   std::size_t initial_index() const {
     return initial_index_;
   }
 
   site_event& initial_index(std::size_t index) {
     initial_index_ = index;
     return *this;
   }
 
   bool is_inverse() const {
     return (flags_ & IS_INVERSE) ? true : false;
   }
 
   site_event& inverse() {
     std::swap(point0_, point1_);
     flags_ ^= IS_INVERSE;
     return *this;
   }
 
   SourceCategory source_category() const {
     return static_cast<SourceCategory>(flags_ & SOURCE_CATEGORY_BITMASK);
   }
 
   site_event& source_category(SourceCategory source_category) {
     flags_ |= source_category;
     return *this;
   }
 
   bool is_point() const {
     return (point0_.x() == point1_.x()) && (point0_.y() == point1_.y());
   }
 
   bool is_segment() const {
     return (point0_.x() != point1_.x()) || (point0_.y() != point1_.y());
   }
 
  private:
   enum Bits {
     IS_INVERSE = 0x20  // 32
   };
 
   point_type point0_;
   point_type point1_;
   std::size_t sorted_index_;
   std::size_t initial_index_;
   std::size_t flags_;
 };
 
 // Circle event type.
 // Occurs when the sweepline sweeps over the rightmost point of the Voronoi
 // circle (with the center at the intersection point of the bisectors).
 // Circle event is made of the two consecutive nodes in the beach line data
 // structure. In case another node was inserted during algorithm execution
 // between the given two nodes circle event becomes inactive.
 // Variables:
 //   center_x_ - center x-coordinate;
 //   center_y_ - center y-coordinate;
 //   lower_x_ - leftmost x-coordinate;
 //   is_active_ - states whether circle event is still active.
 // NOTE: lower_y coordinate is always equal to center_y.
 template <typename T>
 class circle_event {
  public:
   typedef T coordinate_type;
 
   circle_event() : is_active_(true) {}
 
   circle_event(coordinate_type c_x,
                coordinate_type c_y,
                coordinate_type lower_x) :
       center_x_(c_x),
       center_y_(c_y),
       lower_x_(lower_x),
       is_active_(true) {}
 
   coordinate_type x() const {
     return center_x_;
   }
 
   circle_event& x(coordinate_type center_x) {
     center_x_ = center_x;
     return *this;
   }
 
   coordinate_type y() const {
     return center_y_;
   }
 
   circle_event& y(coordinate_type center_y) {
     center_y_ = center_y;
     return *this;
   }
 
   coordinate_type lower_x() const {
     return lower_x_;
   }
 
   circle_event& lower_x(coordinate_type lower_x) {
     lower_x_ = lower_x;
     return *this;
   }
 
   coordinate_type lower_y() const {
     return center_y_;
   }
 
   bool is_active() const {
     return is_active_;
   }
 
   circle_event& deactivate() {
     is_active_ = false;
     return *this;
   }
 
  private:
   coordinate_type center_x_;
   coordinate_type center_y_;
   coordinate_type lower_x_;
   bool is_active_;
 };
 
 // Event queue data structure, holds circle events.
 // During algorithm run, some of the circle events disappear (become
 // inactive). Priority queue data structure doesn't support
 // iterators (there is no direct ability to modify its elements).
 // Instead list is used to store all the circle events and priority queue
 // of the iterators to the list elements is used to keep the correct circle
 // events ordering.
 template <typename T, typename Predicate>
 class ordered_queue {
  public:
   ordered_queue() {}
 
   bool empty() const {
     return c_.empty();
   }
 
   const T &top() const {
     return *c_.top();
   }
 
   void pop() {
     list_iterator_type it = c_.top();
     c_.pop();
     c_list_.erase(it);
   }
 
   T &push(const T &e) {
     c_list_.push_front(e);
     c_.push(c_list_.begin());
     return c_list_.front();
   }
 
   void clear() {
     while (!c_.empty())
         c_.pop();
     c_list_.clear();
   }
 
  private:
   typedef typename std::list<T>::iterator list_iterator_type;
 
   struct comparison {
     bool operator() (const list_iterator_type &it1,
                      const list_iterator_type &it2) const {
       return cmp_(*it1, *it2);
     }
     Predicate cmp_;
   };
 
   std::priority_queue< list_iterator_type,
                        std::vector<list_iterator_type>,
                        comparison > c_;
   std::list<T> c_list_;
 
   // Disallow copy constructor and operator=
   ordered_queue(const ordered_queue&);
   void operator=(const ordered_queue&);
 };
 
 // Represents a bisector node made by two arcs that correspond to the left
 // and right sites. Arc is defined as a curve with points equidistant from
 // the site and from the sweepline. If the site is a point then arc is
 // a parabola, otherwise it's a line segment. A segment site event will
 // produce different bisectors based on its direction.
 // In general case two sites will create two opposite bisectors. That's
 // why the order of the sites is important to define the unique bisector.
 // The one site is considered to be newer than the other one if it was
 // processed by the algorithm later (has greater index).
 template <typename Site>
 class beach_line_node_key {
  public:
   typedef Site site_type;
 
   // Constructs degenerate bisector, used to search an arc that is above
   // the given site. The input to the constructor is the new site point.
   explicit beach_line_node_key(const site_type &new_site) :
       left_site_(new_site),
       right_site_(new_site) {}
 
   // Constructs a new bisector. The input to the constructor is the two
   // sites that create the bisector. The order of sites is important.
   beach_line_node_key(const site_type &left_site,
                       const site_type &right_site) :
       left_site_(left_site),
       right_site_(right_site) {}
 
   const site_type &left_site() const {
     return left_site_;
   }
 
   site_type &left_site() {
     return left_site_;
   }
 
   beach_line_node_key& left_site(const site_type &site) {
     left_site_ = site;
     return *this;
   }
 
   const site_type &right_site() const {
     return right_site_;
   }
 
   site_type &right_site() {
     return right_site_;
   }
 
   beach_line_node_key& right_site(const site_type &site) {
     right_site_ = site;
     return *this;
   }
 
  private:
   site_type left_site_;
   site_type right_site_;
 };
 
 // Represents edge data structure from the Voronoi output, that is
 // associated as a value with beach line bisector in the beach
 // line. Contains pointer to the circle event in the circle event
 // queue if the edge corresponds to the right bisector of the circle event.
 template <typename Edge, typename Circle>
 class beach_line_node_data {
  public:
   explicit beach_line_node_data(Edge* new_edge) :
       circle_event_(NULL),
       edge_(new_edge) {}
 
   Circle* circle_event() const {
     return circle_event_;
   }
 
   beach_line_node_data& circle_event(Circle* circle_event) {
     circle_event_ = circle_event;
     return *this;
   }
 
   Edge* edge() const {
     return edge_;
   }
 
   beach_line_node_data& edge(Edge* new_edge) {
     edge_ = new_edge;
     return *this;
   }
 
  private:
   Circle* circle_event_;
   Edge* edge_;
 };
 }  // detail
 }  // polygon
 }  // boost
 
 #endif  // BOOST_POLYGON_DETAIL_VORONOI_STRUCTURES

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