boost/polygon/voronoi_diagram.hpp
// 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