Boost C++ Libraries of the most highly regarded and expertly designed C++ library projects in the world. Herb Sutter and Andrei Alexandrescu, C++ Coding Standards

This is the documentation for an old version of Boost. Click here to view this page for the latest version.


// Boost.Polygon library voronoi_builder.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

// See for updates, documentation, and revision history.


#include <algorithm>
#include <map>
#include <queue>
#include <utility>
#include <vector>

#include "detail/voronoi_ctypes.hpp"
#include "detail/voronoi_predicates.hpp"
#include "detail/voronoi_structures.hpp"

#include "voronoi_geometry_type.hpp"

namespace boost {
namespace polygon {
// The sweepline algorithm implementation to compute Voronoi diagram of
// points and non-intersecting segments (excluding endpoints).
// Complexity - O(N*logN), memory usage - O(N), where N is the total number
// of input geometries.
// 1) Input geometries should have integral (e.g. int32, int64) coordinate type.
// 2) Input geometries should not intersect except their endpoints.
// Each input point creates one input site. Each input segment creates three
// input sites: two for its endpoints and one for the segment itself (this is
// made to simplify output construction). All the site objects are constructed
// and sorted at the algorithm initialization step. Priority queue is used to
// dynamically hold circle events. At each step of the algorithm execution the
// leftmost event is retrieved by comparing the current site event and the
// topmost element from the circle event queue. STL map (red-black tree)
// container was chosen to hold state of the beach line. The keys of the map
// correspond to the neighboring sites that form a bisector and values map to
// the corresponding Voronoi edges in the output data structure.
template <typename T,
          typename CTT = detail::voronoi_ctype_traits<T>,
          typename VP = detail::voronoi_predicates<CTT> >
class voronoi_builder {
  typedef typename CTT::int_type int_type;
  typedef typename CTT::fpt_type fpt_type;

  voronoi_builder() : index_(0) {}

  // Each point creates a single site event.
  std::size_t insert_point(const int_type& x, const int_type& y) {
    site_events_.push_back(site_event_type(x, y));
    return index_++;

  // Each segment creates three site events that correspond to:
  //   1) the start point of the segment;
  //   2) the end point of the segment;
  //   3) the segment itself defined by its start point.
  std::size_t insert_segment(
      const int_type& x1, const int_type& y1,
      const int_type& x2, const int_type& y2) {
    // Set up start point site.
    point_type p1(x1, y1);

    // Set up end point site.
    point_type p2(x2, y2);

    // Set up segment site.
    if (point_comparison_(p1, p2)) {
      site_events_.push_back(site_event_type(p1, p2));
    } else {
      site_events_.push_back(site_event_type(p2, p1));
    return index_++;

  // Run sweepline algorithm and fill output data structure.
  template <typename OUTPUT>
  void construct(OUTPUT* output) {
    // Init structures.

    // The algorithm stops when there are no events to process.
    event_comparison_predicate event_comparison;
    while (!circle_events_.empty() ||
           !(site_event_iterator_ == site_events_.end())) {
      if (circle_events_.empty()) {
      } else if (site_event_iterator_ == site_events_.end()) {
      } else {
        if (event_comparison(*site_event_iterator_,
        } else {
      while (!circle_events_.empty() &&
             ! {

    // Finish construction.

  void clear() {
    index_ = 0;

  typedef detail::point_2d<int_type> point_type;
  typedef detail::site_event<int_type> site_event_type;
  typedef typename std::vector<site_event_type>::const_iterator
  typedef detail::circle_event<fpt_type> circle_event_type;
  typedef typename VP::template point_comparison_predicate<point_type>
  typedef typename VP::
    template event_comparison_predicate<site_event_type, circle_event_type>
  typedef typename VP::
    template circle_formation_predicate<site_event_type, circle_event_type>
  typedef void edge_type;
  typedef detail::beach_line_node_key<site_event_type> key_type;
  typedef detail::beach_line_node_data<edge_type, circle_event_type>
  typedef typename VP::template node_comparison_predicate<key_type>
  typedef std::map< key_type, value_type, node_comparer_type > beach_line_type;
  typedef typename beach_line_type::iterator beach_line_iterator;
  typedef std::pair<circle_event_type, beach_line_iterator> event_type;
  typedef struct {
    bool operator()(const event_type& lhs, const event_type& rhs) const {
      return predicate(rhs.first, lhs.first);
    event_comparison_predicate predicate;
  } event_comparison_type;
  typedef detail::ordered_queue<event_type, event_comparison_type>
  typedef std::pair<point_type, beach_line_iterator> end_point_type;

  void init_sites_queue() {
    // Sort site events.
    std::sort(site_events_.begin(), site_events_.end(),

    // Remove duplicates.
        site_events_.begin(), site_events_.end()), site_events_.end());

    // Index sites.
    for (std::size_t cur = 0; cur < site_events_.size(); ++cur) {

    // Init site iterator.
    site_event_iterator_ = site_events_.begin();

  template <typename OUTPUT>
  void init_beach_line(OUTPUT* output) {
    if (site_events_.empty())
    if (site_events_.size() == 1) {
      // Handle single site event case.
    } else {
      int skip = 0;

      while (site_event_iterator_ != site_events_.end() &&
                             site_events_.begin()->point0()) &&
             VP::is_vertical(*site_event_iterator_)) {

      if (skip == 1) {
        // Init beach line with the first two sites.
      } else {
        // Init beach line with collinear vertical sites.

  // Init beach line with the two first sites.
  // The first site is always a point.
  template <typename OUTPUT>
  void init_beach_line_default(OUTPUT* output) {
    // Get the first and the second site event.
    site_event_iterator_type it_first = site_events_.begin();
    site_event_iterator_type it_second = site_events_.begin();
        *it_first, *it_first, *it_second, beach_line_.end(), output);
    // The second site was already processed. Move the iterator.

  // Init beach line with collinear sites.
  template <typename OUTPUT>
  void init_beach_line_collinear_sites(OUTPUT* output) {
    site_event_iterator_type it_first = site_events_.begin();
    site_event_iterator_type it_second = site_events_.begin();
    while (it_second != site_event_iterator_) {
      // Create a new beach line node.
      key_type new_node(*it_first, *it_second);

      // Update the output.
      edge_type* edge = output->_insert_new_edge(*it_first, *it_second).first;

      // Insert a new bisector into the beach line.
          std::pair<key_type, value_type>(new_node, value_type(edge)));

      // Update iterators.

  void deactivate_circle_event(value_type* value) {
    if (value->circle_event()) {

  template <typename OUTPUT>
  void process_site_event(OUTPUT* output) {
    // Get next site event to process.
    site_event_type site_event = *site_event_iterator_;

    // Move site iterator.
    site_event_iterator_type last = site_event_iterator_ + 1;

    // If a new site is an end point of some segment,
    // remove temporary nodes from the beach line data structure.
    if (!site_event.is_segment()) {
      while (!end_points_.empty() &&
    == site_event.point0()) {
        beach_line_iterator b_it =;
    } else {
      while (last != site_events_.end() &&
             last->is_segment() && last->point0() == site_event.point0())

    // Find the node in the binary search tree with left arc
    // lying above the new site point.
    key_type new_key(*site_event_iterator_);
    beach_line_iterator right_it = beach_line_.lower_bound(new_key);

    for (; site_event_iterator_ != last; ++site_event_iterator_) {
      site_event = *site_event_iterator_;
      beach_line_iterator left_it = right_it;

      // Do further processing depending on the above node position.
      // For any two neighboring nodes the second site of the first node
      // is the same as the first site of the second node.
      if (right_it == beach_line_.end()) {
        // The above arc corresponds to the second arc of the last node.
        // Move the iterator to the last node.

        // Get the second site of the last node
        const site_event_type& site_arc = left_it->first.right_site();

        // Insert new nodes into the beach line. Update the output.
        right_it = insert_new_arc(
            site_arc, site_arc, site_event, right_it, output);

        // Add a candidate circle to the circle event queue.
        // There could be only one new circle event formed by
        // a new bisector and the one on the left.
                              site_event, right_it);
      } else if (right_it == beach_line_.begin()) {
        // The above arc corresponds to the first site of the first node.
        const site_event_type& site_arc = right_it->first.left_site();

        // Insert new nodes into the beach line. Update the output.
        left_it = insert_new_arc(
            site_arc, site_arc, site_event, right_it, output);

        // If the site event is a segment, update its direction.
        if (site_event.is_segment()) {

        // Add a candidate circle to the circle event queue.
        // There could be only one new circle event formed by
        // a new bisector and the one on the right.
        activate_circle_event(site_event, right_it->first.left_site(),
            right_it->first.right_site(), right_it);
        right_it = left_it;
      } else {
        // The above arc corresponds neither to the first,
        // nor to the last site in the beach line.
        const site_event_type& site_arc2 = right_it->first.left_site();
        const site_event_type& site3 = right_it->first.right_site();

        // Remove the candidate circle from the event queue.
        const site_event_type& site_arc1 = left_it->first.right_site();
        const site_event_type& site1 = left_it->first.left_site();

        // Insert new nodes into the beach line. Update the output.
        beach_line_iterator new_node_it =
            insert_new_arc(site_arc1, site_arc2, site_event, right_it, output);

        // Add candidate circles to the circle event queue.
        // There could be up to two circle events formed by
        // a new bisector and the one on the left or right.
        activate_circle_event(site1, site_arc1, site_event, new_node_it);

        // If the site event is a segment, update its direction.
        if (site_event.is_segment()) {
        activate_circle_event(site_event, site_arc2, site3, right_it);
        right_it = new_node_it;

  // In general case circle event is made of the three consecutive sites
  // that form two bisectors in the beach line data structure.
  // Let circle event sites be A, B, C, two bisectors that define
  // circle event are (A, B), (B, C). During circle event processing
  // we remove (A, B), (B, C) and insert (A, C). As beach line comparison
  // works correctly only if one of the nodes is a new one we remove
  // (B, C) bisector and change (A, B) bisector to the (A, C). That's
  // why we use const_cast there and take all the responsibility that
  // map data structure keeps correct ordering.
  template <typename OUTPUT>
  void process_circle_event(OUTPUT* output) {
    // Get the topmost circle event.
    const event_type& e =;
    const circle_event_type& circle_event = e.first;
    beach_line_iterator it_first = e.second;
    beach_line_iterator it_last = it_first;

    // Get the C site.
    site_event_type site3 = it_first->first.right_site();

    // Get the half-edge corresponding to the second bisector - (B, C).
    edge_type* bisector2 = it_first->second.edge();

    // Get the half-edge corresponding to the first bisector - (A, B).
    edge_type* bisector1 = it_first->second.edge();

    // Get the A site.
    site_event_type site1 = it_first->first.left_site();

    if (!site1.is_segment() && site3.is_segment() &&
        site3.point1() == site1.point0()) {

    // Change the (A, B) bisector node to the (A, C) bisector node.

    // Insert the new bisector into the beach line.
        site1, site3, circle_event, bisector1, bisector2).first);

    // Remove the (B, C) bisector node from the beach line.
    it_last = it_first;

    // Pop the topmost circle event from the event queue.

    // Check new triplets formed by the neighboring arcs
    // to the left for potential circle events.
    if (it_first != beach_line_.begin()) {
      const site_event_type& site_l1 = it_first->first.left_site();
      activate_circle_event(site_l1, site1, site3, it_last);

    // Check the new triplet formed by the neighboring arcs
    // to the right for potential circle events.
    if (it_last != beach_line_.end()) {
      const site_event_type& site_r1 = it_last->first.right_site();
      activate_circle_event(site1, site3, site_r1, it_last);

  // Insert new nodes into the beach line. Update the output.
  template <typename OUTPUT>
  beach_line_iterator insert_new_arc(
      const site_event_type& site_arc1, const site_event_type &site_arc2,
      const site_event_type& site_event, beach_line_iterator position,
      OUTPUT* output) {
    // Create two new bisectors with opposite directions.
    key_type new_left_node(site_arc1, site_event);
    key_type new_right_node(site_event, site_arc2);

    // Set correct orientation for the first site of the second node.
    if (site_event.is_segment()) {

    // Update the output.
    std::pair<edge_type*, edge_type*> edges =
        output->_insert_new_edge(site_arc2, site_event);
    position = beach_line_.insert(position,
        typename beach_line_type::value_type(
            new_right_node, value_type(edges.second)));

    if (site_event.is_segment()) {
      // Update the beach line with temporary bisector, that will
      // disappear after processing site event corresponding to the
      // second endpoint of the segment site.
      key_type new_node(site_event, site_event);
      position = beach_line_.insert(position,
          typename beach_line_type::value_type(new_node, value_type(NULL)));

      // Update the data structure that holds temporary bisectors.
      end_points_.push(std::make_pair(site_event.point1(), position));

    position = beach_line_.insert(position,
        typename beach_line_type::value_type(
            new_left_node, value_type(edges.first)));

    return position;

  // Add a new circle event to the event queue.
  // bisector_node corresponds to the (site2, site3) bisector.
  void activate_circle_event(const site_event_type& site1,
                             const site_event_type& site2,
                             const site_event_type& site3,
                             beach_line_iterator bisector_node) {
    circle_event_type c_event;
    // Check if the three input sites create a circle event.
    if (circle_formation_predicate_(site1, site2, site3, c_event)) {
      // Add the new circle event to the circle events queue.
      // Update bisector's circle event iterator to point to the
      // new circle event in the circle event queue.
      event_type& e = circle_events_.push(
          std::pair<circle_event_type, beach_line_iterator>(
              c_event, bisector_node));

  point_comparison_predicate point_comparison_;
  struct end_point_comparison {
    bool operator() (const end_point_type& end1,
                     const end_point_type& end2) const {
      return point_comparison(end2.first, end1.first);
    point_comparison_predicate point_comparison;

  std::vector<site_event_type> site_events_;
  site_event_iterator_type site_event_iterator_;
  std::priority_queue< end_point_type, std::vector<end_point_type>,
                       end_point_comparison > end_points_;
  circle_event_queue_type circle_events_;
  beach_line_type beach_line_;
  circle_formation_predicate_type circle_formation_predicate_;
  std::size_t index_;

  // Disallow copy constructor and operator=
  voronoi_builder(const voronoi_builder&);
  void operator=(const voronoi_builder&);

typedef voronoi_builder<detail::int32> default_voronoi_builder;
}  // polygon
}  // boost