kicad/include/boost/polygon/voronoi_builder.hpp

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// 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
// http://www.boost.org/LICENSE_1_0.txt)
// See http://www.boost.org for updates, documentation, and revision history.
#ifndef BOOST_POLYGON_VORONOI_BUILDER
#define BOOST_POLYGON_VORONOI_BUILDER
#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 {
// GENERAL INFO:
// The sweepline algorithm implementation to compute Voronoi diagram of
// points and non-intersecting segments (except endpoints).
// Complexity - O(N*logN), memory usage - O(N), where N is the total number
// of input geometries. Input geometries should have integer coordinate type.
//
// IMPLEMENTATION DETAILS:
// Each input point creates one site event. Each input segment creates three
// site events: two for its endpoints and one for the segment itself (this is
// made to simplify output construction). All the site events 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 {
public:
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));
site_events_.back().initial_index(index_);
site_events_.back().source_category(SOURCE_CATEGORY_SINGLE_POINT);
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);
site_events_.push_back(site_event_type(p1));
site_events_.back().initial_index(index_);
site_events_.back().source_category(SOURCE_CATEGORY_SEGMENT_START_POINT);
// Set up end point site.
point_type p2(x2, y2);
site_events_.push_back(site_event_type(p2));
site_events_.back().initial_index(index_);
site_events_.back().source_category(SOURCE_CATEGORY_SEGMENT_END_POINT);
// Set up segment site.
if (point_comparison_(p1, p2)) {
site_events_.push_back(site_event_type(p1, p2));
site_events_.back().source_category(SOURCE_CATEGORY_INITIAL_SEGMENT);
} else {
site_events_.push_back(site_event_type(p2, p1));
site_events_.back().source_category(SOURCE_CATEGORY_REVERSE_SEGMENT);
}
site_events_.back().initial_index(index_);
return index_++;
}
// Run sweepline algorithm and fill output data structure.
template <typename OUTPUT>
void construct(OUTPUT* output) {
// Init structures.
output->_reserve(site_events_.size());
init_sites_queue();
init_beach_line(output);
// 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()) {
process_site_event(output);
} else if (site_event_iterator_ == site_events_.end()) {
process_circle_event(output);
} else {
if (event_comparison(*site_event_iterator_,
circle_events_.top().first)) {
process_site_event(output);
} else {
process_circle_event(output);
}
}
while (!circle_events_.empty() &&
!circle_events_.top().first.is_active()) {
circle_events_.pop();
}
}
beach_line_.clear();
// Finish construction.
output->_build();
}
void clear() {
index_ = 0;
site_events_.clear();
}
private:
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
site_event_iterator_type;
typedef detail::circle_event<fpt_type> circle_event_type;
typedef typename VP::template point_comparison_predicate<point_type>
point_comparison_predicate;
typedef typename VP::
template event_comparison_predicate<site_event_type, circle_event_type>
event_comparison_predicate;
typedef typename VP::
template circle_formation_predicate<site_event_type, circle_event_type>
circle_formation_predicate_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>
value_type;
typedef typename VP::template node_comparison_predicate<key_type>
node_comparer_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>
circle_event_queue_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(),
event_comparison_predicate());
// Remove duplicates.
site_events_.erase(std::unique(
site_events_.begin(), site_events_.end()), site_events_.end());
// Index sites.
for (std::size_t cur = 0; cur < site_events_.size(); ++cur) {
site_events_[cur].sorted_index(cur);
}
// Init site iterator.
site_event_iterator_ = site_events_.begin();
}
template <typename OUTPUT>
void init_beach_line(OUTPUT* output) {
if (site_events_.empty())
return;
if (site_events_.size() == 1) {
// Handle single site event case.
output->_process_single_site(site_events_[0]);
++site_event_iterator_;
} else {
int skip = 0;
while (site_event_iterator_ != site_events_.end() &&
VP::is_vertical(site_event_iterator_->point0(),
site_events_.begin()->point0()) &&
VP::is_vertical(*site_event_iterator_)) {
++site_event_iterator_;
++skip;
}
if (skip == 1) {
// Init beach line with the first two sites.
init_beach_line_default(output);
} else {
// Init beach line with collinear vertical sites.
init_beach_line_collinear_sites(output);
}
}
}
// 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_second;
insert_new_arc(
*it_first, *it_first, *it_second, beach_line_.end(), output);
// The second site was already processed. Move the iterator.
++site_event_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();
++it_second;
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.
beach_line_.insert(beach_line_.end(),
std::pair<key_type, value_type>(new_node, value_type(edge)));
// Update iterators.
++it_first;
++it_second;
}
}
void deactivate_circle_event(value_type* value) {
if (value->circle_event()) {
value->circle_event()->deactivate();
value->circle_event(NULL);
}
}
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() &&
end_points_.top().first == site_event.point0()) {
beach_line_iterator b_it = end_points_.top().second;
end_points_.pop();
beach_line_.erase(b_it);
}
} else {
while (last != site_events_.end() &&
last->is_segment() && last->point0() == site_event.point0())
++last;
}
// 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.
--left_it;
// 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.
activate_circle_event(left_it->first.left_site(),
left_it->first.right_site(),
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()) {
site_event.inverse();
}
// 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.
deactivate_circle_event(&right_it->second);
--left_it;
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()) {
site_event.inverse();
}
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 = circle_events_.top();
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).
--it_first;
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(true) == site1.point0()) {
site3.inverse();
}
// Change the (A, B) bisector node to the (A, C) bisector node.
const_cast<key_type&>(it_first->first).right_site(site3);
// Insert the new bisector into the beach line.
it_first->second.edge(output->_insert_new_edge(
site1, site3, circle_event, bisector1, bisector2).first);
// Remove the (B, C) bisector node from the beach line.
beach_line_.erase(it_last);
it_last = it_first;
// Pop the topmost circle event from the event queue.
circle_events_.pop();
// Check new triplets formed by the neighboring arcs
// to the left for potential circle events.
if (it_first != beach_line_.begin()) {
deactivate_circle_event(&it_first->second);
--it_first;
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.
++it_last;
if (it_last != beach_line_.end()) {
deactivate_circle_event(&it_last->second);
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()) {
new_right_node.left_site().inverse();
}
// 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);
new_node.right_site().inverse();
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));
bisector_node->second.circle_event(&e.first);
}
}
private:
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
#endif // BOOST_POLYGON_VORONOI_BUILDER