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// Copyright (c) 2014 INRIA Sophia-Antipolis (France), INRIA Lorraine LORIA.
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
// You can redistribute it and/or modify it under the terms of the GNU
// General Public License as published by the Free Software Foundation,
// either version 3 of the License, or (at your option) any later version.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL$
// $Id$
//
// Author(s) : Fernando de Goes, Pierre Alliez, Ivo Vigan, Clément Jamin
#ifndef RECONSTRUCTION_SIMPLIFICATION_2_H_
#define RECONSTRUCTION_SIMPLIFICATION_2_H_
#include <CGAL/Reconstruction_triangulation_2.h>
#include <CGAL/Reconstruction_edge_2.h>
#include <CGAL/property_map.h>
#include <CGAL/Real_timer.h>
#include <iterator>
#include <iostream>
#include <vector>
#include <list>
#include <algorithm>
#include <utility> // std::pair
#include <boost/multi_index_container.hpp>
#include <boost/multi_index/mem_fun.hpp>
#include <boost/multi_index/ordered_index.hpp>
#include <boost/multi_index/identity.hpp>
#include <boost/property_map/property_map.hpp>
namespace CGAL {
/*!
\ingroup PkgReconstructionSimplification2Classes
This class provides a means to reconstruct a 1-dimensional shape from a set of 2D points with masses.
The algorithm computes an initial 2D Delaunay triangulation from the input points,
and performs a simplification of the triangulation by performing half edge collapses, edge flips and vertex relocations.
The edges are either processed in the order imposed by an priority queue, or
in an order based on random selection of edge collapse operators.
As the exhaustive priority queue guarantees a higher quality it is the default.
The user can switch to the other method, for example for an initial
simplification round, by calling `set_random_sample_size()`.
By default edge flip operators are applied to ensure that every edge of the
triangulation are candidate to be collapsed, while preserving a valid embedding
of the triangulation. This option can be disabled by calling
\link set_use_flip() `set_use_flip(false)`\endlink to reduce the running times.
By default the vertices are not relocated after each half edge collapse.
This option can be changed by setting the number of vertex relocation steps
performed between two edge collapse operators.
The simplification is performed by calling either
\link run_until() `run_until(n)`\endlink or \link run() `run(steps)`\endlink.
The former simplifies the triangulation until n points remain, while the latter
stops after `steps` edge collapse operators have been performed.
Furthermore, we can relocate the vertices by calling `relocate_all_points()`.
\tparam Traits a model of the concept `ReconstructionSimplificationTraits_2`.
\tparam PointPMap a model of `ReadablePropertyMap` with value type `Traits::Point_2`.
Defaults to <a href="http://www.boost.org/doc/libs/release/libs/property_map/doc/identity_property_map.html">`boost::typed_identity_property_map<Traits::Point_2>`</a>
(for the case the input is points without mass).
\tparam MassPMap a model of `ReadablePropertyMap` with value type `Traits::FT`
Defaults to <a href="http://www.boost.org/doc/libs/release/libs/property_map/doc/static_property_map.html">`boost::static_property_map<Traits::FT>`</a>
(for the case the input is points without mass).
*/
template<
class Traits,
class PointPMap = boost::typed_identity_property_map <typename Traits::Point_2>,
class MassPMap = boost::static_property_map <typename Traits::FT> >
class Reconstruction_simplification_2
{
public:
/// \name Types
/// @{
/*!
Number type.
*/
typedef typename Traits::FT FT;
/*!
Point type.
*/
typedef typename Traits::Point_2 Point;
/*!
Segment type.
*/
typedef typename Traits::Segment_2 Segment;
/// \cond SKIP_IN_MANUAL
/*!
Vector type.
*/
typedef typename Traits::Vector_2 Vector;
typedef typename std::pair<Point, FT> PointMassPair;
typedef typename std::vector<PointMassPair> PointMassList;
/*!
The Output simplex.
*/
typedef Reconstruction_triangulation_2<Traits> Triangulation;
typedef typename Triangulation::Vertex Vertex;
typedef typename Triangulation::Vertex_handle Vertex_handle;
typedef typename Triangulation::Vertex_iterator Vertex_iterator;
typedef typename Triangulation::Vertex_circulator Vertex_circulator;
typedef typename Triangulation::Finite_vertices_iterator
Finite_vertices_iterator;
typedef typename Triangulation::Edge Edge;
typedef typename Triangulation::Edge_circulator Edge_circulator;
typedef typename Triangulation::Finite_edges_iterator Finite_edges_iterator;
typedef typename Triangulation::Face_handle Face_handle;
typedef typename Triangulation::Face_circulator Face_circulator;
typedef typename Triangulation::Finite_faces_iterator Finite_faces_iterator;
typedef typename Triangulation::Vertex_handle_map Vertex_handle_map;
typedef typename Triangulation::Face_handle_map Face_handle_map;
typedef typename Triangulation::Vertex_handle_set Vertex_handle_set;
typedef typename Triangulation::Edge_set Edge_set;
typedef typename Triangulation::Edge_vector Edge_vector;
typedef std::list<Edge> Edge_list;
typedef typename Triangulation::Cost_ Cost_;
typedef typename Triangulation::Sample_ Sample_;
typedef typename Triangulation::Sample_vector Sample_vector;
typedef typename Triangulation::Sample_vector_const_iterator
Sample_vector_const_iterator;
typedef typename Triangulation::PSample PSample;
typedef typename Triangulation::SQueue SQueue;
typedef typename Triangulation::Rec_edge_2 Rec_edge_2;
typedef typename Triangulation::MultiIndex MultiIndex;
/// @}
protected:
Triangulation m_dt;
Traits const& m_traits;
MultiIndex m_mindex;
int m_ignore;
int m_verbose;
std::size_t m_mchoice; // # Edges
bool m_use_flip;
FT m_alpha; // [0, 1]
FT m_norm_tol; // [0,BBOX]
FT m_tang_tol; // [0,BBOX]
FT m_ghost; // ghost vs solid
unsigned int m_relocation; // # relocations
// bbox
FT m_bbox_x;
FT m_bbox_y;
FT m_bbox_size;
PointPMap point_pmap;
MassPMap mass_pmap;
/// \endcond
public:
/// \name Initialization
/// @{
/*!
Constructor of the reconstruction simplification class.
It builds an initial simplicial complex
for a given range of point-mass pairs.
\tparam InputRange is a model of `Range` with forward iterators,
providing input points and point masses through the
`PointPMap` and `MassPMap` property maps.
\param input_range Range of input data.
\param point_map A `ReadablePropertyMap` used to access the input points.
\param mass_map A `ReadablePropertyMap` used to access the input
points' masses.
\param sample_size If `sample_size != 0`, the size of the random sample
which replaces the exhaustive priority queue.
\param use_flip If `true` the edge flipping procedure is used to ensure
that every edge can be made collapsible.
\param relocation The number of point relocations that are performed
between two edge collapses.
\param verbose Controls how much console output is produced by
the algorithm. The values are 0, 1, or > 1.
\param traits The traits class.
*/
template <class InputRange>
Reconstruction_simplification_2(
const InputRange& input_range,
PointPMap point_map = PointPMap(),
MassPMap mass_map = MassPMap(1),
std::size_t sample_size = 0,
bool use_flip = true,
unsigned int relocation = 0,
int verbose = 0,
Traits traits = Traits())
: m_dt(traits),
m_traits(m_dt.geom_traits()),
m_ignore(0),
m_verbose(verbose),
m_mchoice(sample_size),
m_use_flip(use_flip),
m_alpha(0.5),
m_norm_tol(1.0),
m_tang_tol(1.0),
m_ghost(1.0),
m_relocation(relocation),
m_bbox_x(0.0),
m_bbox_y(0.0),
m_bbox_size(1.0),
point_pmap(point_map),
mass_pmap(mass_map)
{
initialize(input_range.begin(), input_range.end());
}
/// @}
/// \name Settting Parameters
/// @{
/*!
If `sample_size == 0`, the simplification is performed using an exhaustive priority queue.
If `sample_size` is stricly positive the simplification is performed using a
multiple choice approach, ie, a best-choice selection in a random sample of
edge collapse operators, of size `sample_size`. A typical value for the sample
size is 15, but this value must be enlarged when targeting a very coarse simplification.
\param sample_size If `sample_size != 0`, the size of the random sample replaces the priority queue.
*/
void set_random_sample_size(std::size_t sample_size) {
m_mchoice = sample_size;
}
/*!
Determines how much console output the algorithm generates.
If set to a value larger than 0
details about the reconstruction process are written to `std::cerr`.
\param verbose The verbosity level.
*/
void set_verbose(int verbose) {
m_verbose = verbose;
}
/// \cond SKIP_IN_MANUAL
void set_alpha(const FT alpha) {
m_alpha = alpha;
}
/// \endcond
/*!
The use_flip parameter determines whether the edge flipping procedure
is used for the half-edge collapse.
*/
void set_use_flip(const bool use_flip) {
m_use_flip = use_flip;
}
/// \cond SKIP_IN_MANUAL
void set_norm_tol(const FT norm_tol) {
m_norm_tol = norm_tol;
}
FT norm_tol() const {
return m_norm_tol;
}
void set_tang_tol(const FT tang_tol) {
m_tang_tol = tang_tol;
}
FT tang_tol() const {
return m_tang_tol;
}
/// \endcond
/*!
Sets the number of vertex relocations
that are performed between two edge collapses.
*/
void set_relocation(unsigned int relocation) {
m_relocation = relocation;
}
/// \cond SKIP_IN_MANUAL
unsigned int relocation() const {
return m_relocation;
}
/// \endcond
/*!
\param relevance The relevance threshold used for filtering the edges.
An edge is relevant from the approximation point of view
if it is long, covers a large mass (or equivalently the
number of points when all masses are equal), and has a
small transport cost. This notion is defined as
\f$ m(e) * |e|^2 / cost(e) \f$, where \f$ m(e) \f$
denotes the mass of the points approximated by the edge,
\f$ |e| \f$ denotes the edge length and \f$ cost(e) \f$
its approximation error.
As the cost is defined by mass time squared distance the
relevance is unitless.
The default value is 0, so that all edges receiving some mass
are considered relevant.
Setting a large relevance value is used to get robustness to a
large amount of outliers.
*/
void set_relevance(const FT relevance) {
m_ghost = relevance;
m_dt.ghost_factor() = m_ghost;
}
/// \cond SKIP_IN_MANUAL
FT ghost() {
return m_ghost;
}
/// @}
/// \cond SKIP_IN_MANUAL
Reconstruction_simplification_2()
: m_traits(m_dt.geom_traits())
{
initialize_parameters();
}
~Reconstruction_simplification_2() {
clear();
}
void initialize_parameters() {
m_verbose = 0;
m_mchoice = 0;
m_use_flip = true;
m_alpha = FT(0.5);
m_norm_tol = FT(1);
m_tang_tol = FT(1);
m_ghost = FT(1);
m_relocation = 0;
m_bbox_x = FT(0);
m_bbox_y = FT(0);
m_bbox_size = FT(1);
m_ignore = 0;
}
//Function if one wants to create a Reconstruction_simplification_2
//without yet specifying the input in the constructor.
template <class InputIterator>
void initialize(
InputIterator start_itr,
InputIterator beyond_itr,
PointPMap point_map,
MassPMap mass_map)
{
point_pmap = point_map;
mass_pmap = mass_map;
initialize(start_itr, beyond_itr);
}
template <class InputIterator>
void initialize(InputIterator start, InputIterator beyond) {
clear();
insert_loose_bbox(m_bbox_x, m_bbox_y, 2 * m_bbox_size);
init(start, beyond);
std::vector<Sample_*> m_samples;
for (InputIterator it = start; it != beyond; it++) {
#ifdef CGAL_USE_PROPERTY_MAPS_API_V1
Point point = get(point_pmap, it);
FT mass = get( mass_pmap, it);
#else
Point point = get(point_pmap, *it);
FT mass = get( mass_pmap, *it);
#endif
Sample_* s = new Sample_(point, mass);
m_samples.push_back(s);
}
assign_samples(m_samples.begin(), m_samples.end());
}
template <class Vector>
Vector random_vec(const FT scale) const
{
FT dx = -scale + (FT(rand()) / FT(RAND_MAX)) * 2* scale;
FT dy = -scale + (FT(rand()) / FT(RAND_MAX)) * 2* scale;
return m_traits.construct_vector_2_object()(dx, dy);
}
void clear() {
Sample_vector samples;
m_dt.collect_all_samples(samples);
// Deallocate samples
for (Sample_vector_const_iterator s_it = samples.begin();
s_it != samples.end(); ++s_it)
{
delete *s_it;
}
m_dt.clear();
m_mindex.clear();
}
// INIT //
void insert_loose_bbox(const FT x, const FT y, const FT size) {
CGAL::Real_timer timer;
std::cerr << "insert loose bbox" << "...";
timer.start();
int nb = static_cast<int>(m_dt.number_of_vertices());
insert_point(m_traits.construct_point_2_object()(x - size, y - size), true, nb++);
insert_point(m_traits.construct_point_2_object()(x - size, y + size), true, nb++);
insert_point(m_traits.construct_point_2_object()(x + size, y + size), true, nb++);
insert_point(m_traits.construct_point_2_object()(x + size, y - size), true, nb++);
std::cerr << "done" << " (" << nb << " vertices, "
<< timer.time() << " s)" << std::endl;
}
template<class Iterator> // value_type = Point*
void init(Iterator begin, Iterator beyond) {
CGAL::Real_timer timer;
std::cerr << "init" << "...";
timer.start();
int nb = static_cast<int>(m_dt.number_of_vertices());
m_dt.infinite_vertex()->pinned() = true;
for (Iterator it = begin; it != beyond; it++) {
#ifdef CGAL_USE_PROPERTY_MAPS_API_V1
Point point = get(point_pmap, it);
#else
Point point = get(point_pmap, *it);
#endif
insert_point(point, false, nb++);
}
std::cerr << "done" << " (" << nb << " vertices, "
<< timer.time() << " s)"
<< std::endl;
}
Vertex_handle insert_point(
const Point& point, const bool pinned, const int id)
{
Vertex_handle v = m_dt.insert(point);
v->pinned() = pinned;
v->id() = id;
return v;
}
// ASSIGNMENT //
void cleanup_assignments() {
m_dt.cleanup_assignments();
}
template<class Iterator> // value_type = Sample_*
void assign_samples(Iterator begin, Iterator end) {
CGAL::Real_timer timer;
std::cerr << "assign samples" << "...";
timer.start();
m_dt.assign_samples(begin, end);
m_dt.reset_all_costs();
std::cerr << "done" << " (" << timer.time() << " s)" << std::endl;
}
void reassign_samples() {
Sample_vector samples;
m_dt.collect_all_samples(samples);
m_dt.cleanup_assignments();
m_dt.assign_samples(samples.begin(), samples.end());
m_dt.reset_all_costs();
}
void reassign_samples_around_vertex(Vertex_handle vertex) {
Sample_vector samples;
m_dt.collect_samples_from_vertex(vertex, samples, true);
m_dt.assign_samples(samples.begin(), samples.end());
Edge_vector hull;
m_dt.get_edges_from_star_minus_link(vertex, hull, true);
update_cost(hull.begin(), hull.end());
}
bool do_collapse(Edge edge) {
Vertex_handle s = m_dt.source_vertex(edge);
Vertex_handle t = m_dt.target_vertex(edge);
if (m_verbose > 0) {
std::cerr << std::endl << "do collapse " << "("
<< s->id() << "->" << t->id() << ") ... " << std::endl;
}
Sample_vector samples;
m_dt.collect_samples_from_vertex(s, samples, true);
Edge_vector hull;
m_dt.get_edges_from_star_minus_link(s, hull, true);
if (m_mchoice == 0)
remove_stencil_from_pqueue(hull.begin(), hull.end());
if (m_use_flip)
m_dt.make_collapsible(edge, hull.begin(), hull.end(), m_verbose);
// debug test
bool ok = m_dt.check_kernel_test(edge);
if (!ok) {
std::cerr << "do_collapse: kernel test failed: " << std::endl;
return false;
}
//
m_dt.collapse(edge, m_verbose);
m_dt.assign_samples(samples.begin(), samples.end());
update_cost(hull.begin(), hull.end());
if (m_mchoice == 0)
push_stencil_to_pqueue(hull.begin(), hull.end());
for (unsigned int i = 0; i < m_relocation; ++i) {
relocate_one_ring(hull.begin(), hull.end());
}
if (m_verbose > 0) {
std::cerr << "done" << std::endl;
}
return true;
}
bool simulate_collapse(const Edge& edge, Cost_& cost) {
bool ok;
Vertex_handle s = m_dt.source_vertex(edge);
Vertex_handle t = m_dt.target_vertex(edge);
if (m_verbose > 1) {
std::cerr << "simulate collapse " << "("
<< s->id() << "->" << t->id() << ") ... " << std::endl;
}
Triangulation copy;
Edge copy_edge = copy_star(edge, copy);
Vertex_handle copy_source = copy.source_vertex(copy_edge);
if (m_use_flip) {
Edge_vector copy_hull;
copy.get_edges_from_star_minus_link(copy_source, copy_hull, true);
ok = copy.make_collapsible(copy_edge, copy_hull.begin(),
copy_hull.end(), m_verbose);
if (!ok) {
std::cerr << "simulation: failed (make collapsible)"
<< std::endl;
return false;
}
}
ok = copy.check_kernel_test(copy_edge);
if (!ok) {
std::cerr << "simulation: failed (kernel test)" << std::endl;
return false;
}
copy.collapse(copy_edge, m_verbose);
Sample_vector samples;
m_dt.collect_samples_from_vertex(s, samples, false);
backup_samples(samples.begin(), samples.end());
copy.assign_samples_brute_force(samples.begin(), samples.end());
copy.reset_all_costs();
cost = copy.compute_total_cost();
restore_samples(samples.begin(), samples.end());
if (m_verbose > 1) {
std::cerr << "done" << std::endl;
}
return true;
}
template<class Iterator> // value_type = Sample_*
void backup_samples(Iterator begin, Iterator end) const {
for (Iterator it = begin; it != end; ++it) {
Sample_* sample = *it;
sample->backup();
}
}
template<class Iterator> // value_type = Sample_*
void restore_samples(Iterator begin, Iterator end) const {
for (Iterator it = begin; it != end; ++it) {
Sample_* sample = *it;
sample->restore();
}
}
// PEDGE //
bool decimate() {
bool ok;
Rec_edge_2 pedge;
ok = pick_edge(m_mchoice, pedge);
if (!ok)
return false;
ok = do_collapse(pedge.edge());
if (!ok)
return false;
return true;
}
bool create_pedge(const Edge& edge, Rec_edge_2& pedge) {
Cost_ after_cost;
bool ok = simulate_collapse(edge, after_cost);
if (!ok)
return false;
bool within_tol = is_within_tol(after_cost);
if (!within_tol)
return false;
Vertex_handle source = m_dt.source_vertex(edge);
Cost_ before_cost = m_dt.compute_cost_around_vertex(source);
FT before = before_cost.finalize(m_alpha);
FT after = after_cost.finalize(m_alpha);
pedge = Rec_edge_2(edge, before, after);
return true;
}
bool is_within_tol(const Cost_& cost) const {
return cost.max_norm() <= m_norm_tol && cost.max_tang() <= m_tang_tol;
}
// COST //
void init_cost() {
m_dt.reset_all_costs();
}
template<class Iterator> // value_type = Edge
void update_cost(Iterator begin, Iterator end) {
Edge_vector edges;
collect_cost_stencil(m_dt, begin, end, edges);
typename Edge_vector::iterator ei;
for (ei = edges.begin(); ei != edges.end(); ++ei) {
Edge edge = *ei;
m_dt.update_cost(edge);
}
}
template<class Iterator> // value_type = Edge
void collect_cost_stencil(
const Triangulation& mesh, Iterator begin, Iterator end,
Edge_vector& edges) const
{
Edge_set done;
Edge_list fifo;
for (Iterator it = begin; it != end; ++it) {
Edge edge = *it;
fifo.push_back(edge);
done.insert(edge);
}
while (!fifo.empty()) {
Edge edge = fifo.front();
fifo.pop_front();
edge = mesh.twin_edge(edge);
edges.push_back(edge);
Edge next = mesh.next_edge(edge);
if (done.insert(next).second)
fifo.push_back(next);
Edge prev = mesh.prev_edge(edge);
if (done.insert(prev).second)
fifo.push_back(prev);
}
}
// PQUEUE (MCHOICE or EXHAUSTIVE) //
bool pick_edge(std::size_t nb, Rec_edge_2& best_pedge) {
if (m_dt.number_of_faces() < 2)
return false;
std::size_t ne = 2 * m_dt.tds().number_of_edges();
if (nb > ne)
nb = ne;
bool ok;
if (nb == 0) {
ok = pick_edge_from_pqueue(best_pedge);
return ok;
}
m_mindex.clear();
if (nb == ne) {
ok = pick_edge_brute_force(best_pedge);
return ok;
}
ok = pick_edge_randomly(nb, best_pedge);
return ok;
}
bool pick_edge_from_pqueue(Rec_edge_2& best_pedge) {
if (m_mindex.empty())
populate_pqueue();
if (m_mindex.empty())
return false;
best_pedge = *(m_mindex.template get<1>()).begin();
(m_mindex.template get<0>()).erase(best_pedge);
return true;
}
bool pick_edge_brute_force(Rec_edge_2& best_pedge) {
MultiIndex mindex;
Finite_edges_iterator ei;
for (ei = m_dt.finite_edges_begin(); ei != m_dt.finite_edges_end();
++ei) {
Edge edge = *ei;
push_to_mindex(edge, mindex);
edge = m_dt.twin_edge(edge);
push_to_mindex(edge, mindex);
}
if (mindex.empty())
return false;
best_pedge = *(mindex.template get<1>()).begin();
return true;
}
bool pick_edge_randomly(std::size_t nb, Rec_edge_2& best_pedge) {
MultiIndex mindex;
for (std::size_t i = 0; i < nb; ++i) {
Rec_edge_2 pedge;
if (random_pedge(pedge))
mindex.insert(pedge);
}
if (mindex.empty())
return false;
best_pedge = *(mindex.template get<1>()).begin();
return true;
}
void populate_pqueue() {
Finite_edges_iterator ei;
for (ei = m_dt.finite_edges_begin(); ei != m_dt.finite_edges_end();
++ei) {
Edge edge = *ei;
push_to_mindex(edge, m_mindex);
edge = m_dt.twin_edge(edge);
push_to_mindex(edge, m_mindex);
}
}
bool push_to_mindex(const Edge& edge, MultiIndex& mindex) {
if (m_dt.is_pinned(edge))
return false;
if (m_dt.is_target_cyclic(edge))
return false;
Rec_edge_2 pedge;
bool ok = create_pedge(edge, pedge);
if (!ok)
return false;
mindex.insert(pedge);
return true;
}
bool random_pedge(Rec_edge_2& pedge) {
for (unsigned i = 0; i < 10; ++i) {
Edge edge = m_dt.random_finite_edge();
if (m_dt.is_pinned(edge))
continue;
if (m_dt.is_target_cyclic(edge))
continue;
bool ok = create_pedge(edge, pedge);
if (ok)
return true;
}
return false;
}
template<class Iterator> // value_type = Edge
void remove_stencil_from_pqueue(Iterator begin, Iterator end)
{
if (m_mindex.empty())
return;
Edge_vector edges;
collect_pqueue_stencil(m_dt, begin, end, edges);
typename Edge_vector::const_iterator ei;
for (ei = edges.begin(); ei != edges.end(); ++ei) {
Edge edge = *ei;
(m_mindex.template get<0>()).erase(Rec_edge_2(edge));
}
}
template<class Iterator> // value_type = Edge
void push_stencil_to_pqueue(Iterator begin, Iterator end) {
Edge_vector edges;
collect_pqueue_stencil(m_dt, begin, end, edges);
typename Edge_vector::const_iterator ei;
for (ei = edges.begin(); ei != edges.end(); ++ei) {
Edge edge = *ei;
push_to_mindex(edge, m_mindex);
}
}
template<class Iterator> // value_type = Edge
void collect_pqueue_stencil(
const Triangulation& mesh, Iterator begin, Iterator end,
Edge_vector& edges) const
{
Vertex_handle_set vertex_set;
for (Iterator it = begin; it != end; ++it) {
Edge edge = *it;
Edge twin = mesh.twin_edge(edge);
Vertex_handle s = mesh.source_vertex(edge);
if (!s->pinned())
vertex_set.insert(s);
Vertex_handle t = mesh.target_vertex(edge);
if (!t->pinned())
vertex_set.insert(t);
Vertex_handle f = mesh.opposite_vertex(edge);
if (!f->pinned())
vertex_set.insert(f);
Vertex_handle b = mesh.opposite_vertex(twin);
if (!b->pinned())
vertex_set.insert(b);
}
typename Vertex_handle_set::const_iterator vi;
for (vi = vertex_set.begin(); vi != vertex_set.end(); ++vi) {
Vertex_handle v = *vi;
Edge_circulator ecirc = mesh.incident_edges(v);
Edge_circulator eend = ecirc;
CGAL_For_all(ecirc, eend)
{
Edge edge = *ecirc;
if (mesh.source_vertex(edge) != v)
edge = mesh.twin_edge(edge);
edges.push_back(edge);
}
}
}
// COPY STAR //
// edge must not be pinned or have cyclic target
Edge copy_star(const Edge& edge, Triangulation& copy) {
copy.tds().set_dimension(2);
copy.infinite_vertex()->pinned() = true;
// copy vertices
Vertex_handle_map cvmap;
Vertex_handle s = m_dt.source_vertex(edge);
Vertex_handle cs = copy.tds().create_vertex();
cvmap[s] = copy_vertex(s, cs);
Vertex_circulator vcirc = m_dt.incident_vertices(s);
Vertex_circulator vend = vcirc;
CGAL_For_all(vcirc, vend)
{
Vertex_handle v = vcirc;
if (cvmap.find(v) == cvmap.end()) {
Vertex_handle cv = copy.tds().create_vertex();
cvmap[v] = copy_vertex(v, cv);
}
}
// copy faces
Face_handle_map cfmap;
Face_circulator fcirc = m_dt.incident_faces(s);
Face_circulator fend = fcirc;
CGAL_For_all(fcirc, fend)
{
Face_handle f = fcirc;
Face_handle cf = copy.tds().create_face();
cfmap[f] = copy_face(f, cf, cvmap);
}
// set neighbors
fcirc = m_dt.incident_faces(s);
fend = fcirc;
CGAL_For_all(fcirc, fend)
{
Face_handle f = fcirc;
copy_neighbors(f, s, cvmap, cfmap);
}
// make copy homeomorphic to S^2
close_copy_mesh(cs, copy);
// copy samples surrounding star
copy_samples(s, cs, cfmap, copy);
// get copy of edge
Edge copy_edge = get_copy_edge(edge, cvmap, cfmap);
return copy_edge;
}
Vertex_handle copy_vertex(Vertex_handle v0, Vertex_handle v1) const {
v1->id() = v0->id();
v1->set_point(v0->point());
v1->pinned() = v0->pinned();
v1->set_sample(v0->sample());
return v1;
}
Face_handle copy_face(
Face_handle f0, Face_handle f1, Vertex_handle_map& vmap) const
{
for (unsigned i = 0; i < 3; ++i) {
Vertex_handle v0i = f0->vertex(i);
Vertex_handle v1i = vmap[v0i];
f1->set_vertex(i, v1i);
v1i->set_face(f1);
}
return f1;
}
void copy_neighbors(
Face_handle f, Vertex_handle v, Vertex_handle_map& vmap,
Face_handle_map& fmap) const
{
int i = f->index(v);
Face_handle cf = fmap[f];
Vertex_handle cv = vmap[v];
if (fmap.find(f->neighbor(i)) != fmap.end()) {
Face_handle fi = f->neighbor(i);
Face_handle cfi = fmap[fi];
cf->set_neighbor(i, cfi);
}
for (unsigned j = 0; j < 2; ++j) {
i = (i + 1) % 3;
Face_handle fi = f->neighbor(i);
Face_handle cfi = fmap[fi];
cf->set_neighbor(i, cfi);
}
}
void close_copy_mesh(Vertex_handle vertex, Triangulation& copy) const {
std::vector<Face_handle> outer_faces;
Face_circulator fcirc = copy.incident_faces(vertex);
Face_circulator fend = fcirc;
CGAL_For_all(fcirc, fend)
{
Face_handle face = fcirc;
int i = face->index(vertex);
if (face->neighbor(i) != Face_handle())
continue;
Vertex_handle v1 = face->vertex((i + 1) % 3);
Vertex_handle v2 = face->vertex((i + 2) % 3);
Face_handle outer = copy.tds().create_face();
outer->set_vertex(0, copy.infinite_vertex());
outer->set_vertex(1, v2);
outer->set_vertex(2, v1);
face->set_neighbor(i, outer);
outer->set_neighbor(0, face);
outer_faces.push_back(outer);
}
for (unsigned i = 0; i < outer_faces.size(); ++i) {
unsigned j = (i + 1) % outer_faces.size();
outer_faces[i]->set_neighbor(2, outer_faces[j]);
outer_faces[j]->set_neighbor(1, outer_faces[i]);
}
if (!outer_faces.empty())
copy.infinite_vertex()->set_face(outer_faces[0]);
}
void copy_samples(
Vertex_handle vertex, Vertex_handle copy_vertex,
Face_handle_map& fmap, Triangulation& copy) const
{
Face_circulator fcirc = m_dt.incident_faces(vertex);
Face_circulator fend = fcirc;
CGAL_For_all(fcirc, fend)
{
Face_handle face = fcirc;
int index = face->index(vertex);
Edge twin = m_dt.twin_edge(Edge(face, index));
Face_handle copy_face = fmap[face];
index = copy_face->index(copy_vertex);
Edge copy_twin = copy.twin_edge(Edge(copy_face, index));
Sample_vector samples;
m_dt.collect_samples_from_edge(twin, samples);
copy_twin.first->samples(copy_twin.second) = samples;
}
copy_vertex->set_sample(NULL);
}
Edge get_copy_edge(
const Edge& edge, Vertex_handle_map& vmap, Face_handle_map& fmap) const
{
Face_handle f = edge.first;
Vertex_handle v = f->vertex(edge.second);
Face_handle cf = fmap[f];
Vertex_handle cv = vmap[v];
return Edge(cf, cf->index(cv));
}
// RELOCATION //
void relocate_one_vertex(Vertex_handle vertex) {
std::swap(vertex->point(), vertex->relocated());
reassign_samples_around_vertex(vertex);
}
template<class Iterator> // value_type = Edge
void relocate_one_ring(Iterator begin, Iterator end) {
Vertex_handle_set vertices;
for (Iterator it = begin; it != end; ++it) {
Edge edge = *it;
vertices.insert(m_dt.source_vertex(edge));
vertices.insert(m_dt.target_vertex(edge));
}
typename Vertex_handle_set::const_iterator vi;
for (vi = vertices.begin(); vi != vertices.end(); ++vi) {
Vertex_handle v = *vi;
if (v->pinned())
continue;
v->relocated() = compute_relocation(v);
}
for (vi = vertices.begin(); vi != vertices.end(); ++vi) {
Vertex_handle v = *vi;
if (v->pinned())
continue;
if (v->point() == v->relocated())
continue;
Edge_vector hull;
m_dt.get_edges_from_star_minus_link(v, hull, false);
bool ok = m_dt.is_in_kernel(v->relocated(), hull.begin(),
hull.end());
if (ok) {
// do relocation
FT norm_bef = m_dt.compute_cost_around_vertex(v).norm();
relocate_one_vertex(v);
FT norm_aft = m_dt.compute_cost_around_vertex(v).norm();
if (norm_bef < norm_aft) {
// undo relocation
relocate_one_vertex(v);
} else if (m_mchoice == 0) {
// update queue
hull.clear();
m_dt.get_edges_from_star_minus_link(v, hull, true);
remove_stencil_from_pqueue(hull.begin(), hull.end());
push_stencil_to_pqueue(hull.begin(), hull.end());
}
}
}
}
/// \endcond
/// \cond SKIP_IN_MANUAL
Vector compute_gradient(Vertex_handle vertex) const {
Vector grad = m_traits.construct_vector_2_object()(FT(0), FT(0));
Edge_circulator ecirc = m_dt.incident_edges(vertex);
Edge_circulator eend = ecirc;
CGAL_For_all(ecirc, eend)
{
Edge edge = *ecirc;
if (m_dt.source_vertex(edge) != vertex)
edge = m_dt.twin_edge(edge);
if (m_dt.get_plan(edge) == 0)
grad = m_traits.construct_sum_of_vectors_2_object()(
grad, compute_gradient_for_plan0(edge));
else
grad = m_traits.construct_sum_of_vectors_2_object()(
grad, compute_gradient_for_plan1(edge));
}
return grad;
}
Point compute_relocation(Vertex_handle vertex) const {
FT coef = FT(0);
Vector rhs = m_traits.construct_vector_2_object()(FT(0), FT(0));
Edge_circulator ecirc = m_dt.incident_edges(vertex);
Edge_circulator eend = ecirc;
CGAL_For_all(ecirc, eend)
{
Edge edge = *ecirc;
if (m_dt.source_vertex(edge) != vertex)
edge = m_dt.twin_edge(edge);
if (m_dt.get_plan(edge) == 0)
compute_relocation_for_plan0(edge, coef, rhs);
else
compute_relocation_for_plan1(edge, coef, rhs);
}
compute_relocation_for_vertex(vertex, coef, rhs);
if (coef == FT(0))
return vertex->point();
return m_traits.construct_translated_point_2_object()(
CGAL::ORIGIN,
m_traits.construct_scaled_vector_2_object()(rhs, FT(1) / coef));
}
void compute_relocation_for_vertex(
Vertex_handle vertex, FT& coef, Vector& rhs) const
{
Sample_* sample = vertex->sample();
if (sample) {
const FT m = sample->mass();
const Point& ps = sample->point();
rhs = m_traits.construct_sum_of_vectors_2_object()(rhs,
m_traits.construct_scaled_vector_2_object()(
m_traits.construct_vector_2_object()(CGAL::ORIGIN, ps), m));
coef += m;
}
}
Vector compute_gradient_for_plan0(const Edge& edge) const {
Edge twin = m_dt.twin_edge(edge);
const Point& pa = m_dt.source_vertex(edge)->point();
const Point& pb = m_dt.target_vertex(edge)->point();
Sample_vector samples;
m_dt.collect_samples_from_edge(edge, samples);
m_dt.collect_samples_from_edge(twin, samples);
Vector grad = m_traits.construct_vector_2_object()(FT(0), FT(0));
Sample_vector_const_iterator it;
for (it = samples.begin(); it != samples.end(); ++it) {
Sample_* sample = *it;
const FT m = sample->mass();
const Point& ps = sample->point();
FT Da = m_traits.compute_squared_distance_2_object()(ps, pa);
FT Db = m_traits.compute_squared_distance_2_object()(ps, pb);
if (Da < Db)
grad = m_traits.construct_sum_of_vectors_2_object()(
grad,
m_traits.construct_scaled_vector_2_object()(
m_traits.construct_vector_2_object()(ps, pa), m));
}
return grad;
}
void compute_relocation_for_plan0(
const Edge& edge, FT& coef, Vector& rhs) const
{
Edge twin = m_dt.twin_edge(edge);
const Point& pa = m_dt.source_vertex(edge)->point();
const Point& pb = m_dt.target_vertex(edge)->point();
Sample_vector samples;
m_dt.collect_samples_from_edge(edge, samples);
m_dt.collect_samples_from_edge(twin, samples);
Sample_vector_const_iterator it;
for (it = samples.begin(); it != samples.end(); ++it) {
Sample_* sample = *it;
const FT m = sample->mass();
const Point& ps = sample->point();
FT Da = m_traits.compute_squared_distance_2_object()(ps, pa);
FT Db = m_traits.compute_squared_distance_2_object()(ps, pb);
if (Da < Db) {
rhs = m_traits.construct_sum_of_vectors_2_object()(rhs,
m_traits.construct_scaled_vector_2_object()(
m_traits.construct_vector_2_object()(CGAL::ORIGIN, ps), m));
coef += m;
}
}
}
Vector compute_gradient_for_plan1(const Edge& edge) const {
//FT M = m_dt.get_mass(edge);
const Point& pa = m_dt.source_vertex(edge)->point();
const Point& pb = m_dt.target_vertex(edge)->point();
SQueue queue;
m_dt.sort_samples_from_edge(edge, queue);
//FT start = FT(0);
Vector grad = m_traits.construct_vector_2_object()(FT(0), FT(0));
while (!queue.empty()) {
PSample psample = queue.top();
queue.pop();
const FT m = psample.sample()->mass();
const Point& ps = psample.sample()->point();
// normal + tangnetial
const FT coord = psample.priority();
Point pf = m_traits.construct_translated_point_2_object()(
CGAL::ORIGIN,
m_traits.construct_sum_of_vectors_2_object()(
m_traits.construct_scaled_vector_2_object()(
m_traits.construct_vector_2_object()(CGAL::ORIGIN, pa),
1.0 - coord),
m_traits.construct_scaled_vector_2_object()(
m_traits.construct_vector_2_object()(CGAL::ORIGIN, pb),
coord)));
grad = m_traits.construct_sum_of_vectors_2_object()(
grad,
m_traits.construct_scaled_vector_2_object()(
m_traits.construct_vector_2_object()(ps, pf), m * (1.0 - coord)));
/*
// only normal
FT bin = m/M;
FT center = start + 0.5*bin;
Point pc = CGAL::ORIGIN + (1.0-center)*(pa - CGAL::ORIGIN) + center*(pb - CGAL::ORIGIN);
start += bin;
grad = grad + m*(bin*bin/12.0)*(pa - pb);
grad = grad + m*(1.0-center)*(pc - pf);
*/
}
return grad;
}
void compute_relocation_for_plan1(
const Edge& edge, FT& coef, Vector& rhs) const
{
//FT M = m_dt.get_mass(edge);
const Point& pb = m_dt.target_vertex(edge)->point();
SQueue queue;
m_dt.sort_samples_from_edge(edge, queue);
//FT start = FT(0);
while (!queue.empty()) {
PSample psample = queue.top();
queue.pop();
const FT m = psample.sample()->mass();
const Point& ps = psample.sample()->point();
const FT coord = psample.priority();
const FT one_minus_coord = 1.0 - coord;
// normal + tangential
coef += m * one_minus_coord * one_minus_coord;
rhs = m_traits.construct_sum_of_vectors_2_object()(
rhs,
m_traits.construct_scaled_vector_2_object()(
m_traits.construct_sum_of_vectors_2_object()(
m_traits.construct_vector_2_object()(CGAL::ORIGIN, ps),
m_traits.construct_scaled_vector_2_object()(
m_traits.construct_vector_2_object()(CGAL::ORIGIN, pb), -coord)),
m * one_minus_coord));
/*
// only normal
FT bin = m/M;
FT center = start + 0.5*bin;
Point pc = CGAL::ORIGIN + (1.0-center)*(pa - CGAL::ORIGIN) + center*(pb - CGAL::ORIGIN);
start += bin;
grad = grad + m*(bin*bin/12.0)*(pa - pb);
grad = grad + m*(1.0-center)*(pc - pf);
*/
/*
// only normal
FT bin = m/M;
FT center = start + 0.5*bin;
FT one_minus_center = 1.0 - center;
start += bin;
coef += m*bin*bin/12.0;
rhs = rhs + m*(bin*bin/12.0)*(pb - CGAL::ORIGIN);
coef += m*one_minus_center*(coord - center);
rhs = rhs + m*one_minus_center*(coord - center)*(pb - CGAL::ORIGIN);
*/
}
}
void print_stats_debug() const
{
int nb_solid = 0;
int nb_ghost = 0;
for (Finite_edges_iterator ei = m_dt.finite_edges_begin();
ei != m_dt.finite_edges_end(); ++ei)
{
Edge edge = *ei;
if (m_dt.is_ghost(edge))
nb_ghost++;
else
nb_solid++;
}
std::cerr << "STATS" << std::endl;
std::cerr << "# vertices : " << m_dt.number_of_vertices()-4 << std::endl;
std::cerr << "# triangles: " << m_dt.number_of_faces() << std::endl;
std::cerr << "# edges: " << m_dt.tds().number_of_edges() << std::endl;
std::cerr << "# solid: " << nb_solid << std::endl;
std::cerr << "# ghost: " << nb_ghost << std::endl;
}
/*!
Returns the number of vertices present in the reconstructed triangulation.
*/
std::size_t number_of_vertices() const {
return m_dt.number_of_vertices() - 4;
}
/*!
Returns the number of (solid) edges present in the reconstructed triangulation.
*/
int number_of_edges() const {
int nb_solid = 0;
for (Finite_edges_iterator ei = m_dt.finite_edges_begin();
ei != m_dt.finite_edges_end(); ++ei)
{
Edge edge = *ei;
if (m_dt.is_ghost(edge))
continue;
nb_solid++;
}
return nb_solid;
}
/*!
Returns the cost of the (solid) edges present in the
reconstructed triangulation.
*/
FT total_edge_cost() const {
FT total_cost = 0;
for (Finite_edges_iterator ei = m_dt.finite_edges_begin();
ei != m_dt.finite_edges_end(); ++ei)
{
Edge edge = *ei;
if (m_dt.is_ghost(edge))
continue;
total_cost += m_dt.get_cost(edge).finalize();
}
return total_cost;
}
/// \endcond
/// \name Simplification
/// You can freely mix calls of the following functions.
/// @{
/*!
Computes a shape consisting of `np` points, reconstructing the input
points.
\param np The number of points which will be present in the output.
*/
void run_until(std::size_t np) {
CGAL::Real_timer timer;
std::cerr << "reconstruct until " << np << " V";
timer.start();
std::size_t N = np + 4;
std::size_t performed = 0;
while (m_dt.number_of_vertices() > N) {
bool ok = decimate();
if (!ok)
break;
performed++;
}
std::cerr << " done" << " (" << performed
<< " iters, " << m_dt.number_of_vertices() - 4 << " V "
<< timer.time() << " s)"
<< std::endl;
}
/*!
Computes a shape, reconstructing the input, by performing `steps`
edge collapse operators on the output simplex.
\param steps The number of edge collapse operators to be performed.
*/
void run(const unsigned steps) {
CGAL::Real_timer timer;
std::cerr << "reconstruct " << steps;
timer.start();
unsigned performed = 0;
for (unsigned i = 0; i < steps; ++i) {
bool ok = decimate();
if (!ok)
break;
performed++;
}
std::cerr << " done" << " (" << performed << "/"
<< steps << " iters, " << m_dt.number_of_vertices() - 4
<< " V, " << timer.time() << " s)"
<< std::endl;
}
/*!
Since noise and missing data may prevent the reconstructed shape to have sharp corners well located, the algorithm offers the possibility to automatically relocate points after each edge collapse. The new location of the points is chosen such that the fitting of the output segments to the input points is improved.
*/
void relocate_all_points() {
CGAL::Real_timer timer;
std::cerr << "relocate all points" << "...";
timer.start();
m_mindex.clear(); // pqueue must be recomputed
for (Finite_vertices_iterator v = m_dt.finite_vertices_begin();
v != m_dt.finite_vertices_end(); ++v) {
if (v->pinned())
continue;
v->relocated() = compute_relocation(v);
}
for (Finite_vertices_iterator v = m_dt.finite_vertices_begin();
v != m_dt.finite_vertices_end(); ++v) {
if (v->pinned())
continue;
if (v->point() == v->relocated())
continue;
Edge_vector hull;
m_dt.get_edges_from_star_minus_link(v, hull, false);
bool ok = m_dt.is_in_kernel(v->relocated(), hull.begin(),
hull.end());
if (ok) {
// do relocation
FT norm_bef = m_dt.compute_cost_around_vertex(v).norm();
relocate_one_vertex(v);
FT norm_aft = m_dt.compute_cost_around_vertex(v).norm();
// undo relocation
if (norm_bef < norm_aft)
relocate_one_vertex(v);
}
}
std::cerr << "done" << " (" << timer.time() << " s)" << std::endl;
}
/// @}
/// \name Output
/// @{
/*!
Writes the points and segments of the output simplex in an indexed format into output iterators.
\tparam PointOutputIterator An output iterator with value type
\link Reconstruction_simplification_2::Point Point \endlink.
\tparam IndexOutputIterator An output iterator with value type
`std::size_t`.
\tparam IndexPairOutputIterator An output iterator with value type
`std::pair<std::size_t, std::size_t>`.
\param points The output iterator for all points.
\param isolated_points The output iterator for the indices of isolated points.
\param segments The output iterator for the pairs of segment indices.
*/
template <
typename PointOutputIterator,
typename IndexOutputIterator,
typename IndexPairOutputIterator>
CGAL::cpp11::tuple<
PointOutputIterator,
IndexOutputIterator,
IndexPairOutputIterator>
indexed_output(
PointOutputIterator points,
IndexOutputIterator isolated_points,
IndexPairOutputIterator segments) const
{
std::vector<Point> isolated_points_;
std::vector<Segment> edges;
list_output (
std::back_inserter(isolated_points_), std::back_inserter(edges));
// vertices_of_edges
std::set<Point> edge_vertices;
for (typename std::vector<Segment>::iterator it = edges.begin();
it != edges.end(); it++) {
Point a = (*it).source();
Point b = (*it).target();
edge_vertices.insert(a);
edge_vertices.insert(b);
}
std::size_t count_points = 0;
for (typename std::set<Point>::iterator it = edge_vertices.begin();
it != edge_vertices.end(); it++) {
*points++ = *it;
++count_points;
}
for (typename std::vector<Point>::iterator it = isolated_points_.begin();
it != isolated_points_.end(); it++) {
*isolated_points++ = count_points;
*points++ = *it;
++count_points;
}
for (typename std::vector<Segment>::iterator it = edges.begin();
it != edges.end(); it++) {
Point const& a = it->source();
Point const& b = it->target();
typename std::set<Point>::iterator it_a = edge_vertices.find(a);
typename std::set<Point>::iterator it_b = edge_vertices.find(b);
std::size_t pos_a = std::distance(edge_vertices.begin(), it_a);
std::size_t pos_b = std::distance(edge_vertices.begin(), it_b);
*segments++ = std::make_pair(pos_a, pos_b);
}
return CGAL::cpp11::make_tuple(points, isolated_points, segments);
}
/*!
Returns the solid edges and vertices present after the reconstruction
process finished.
\details It takes two output iterators, one for storing the
isolated points and one for storing the edges of the reconstructed shape.
\tparam PointOutputIterator An output iterator with value type
\link Reconstruction_simplification_2::Point Point \endlink.
\tparam SegmentOutputIterator An output iterator with value type
\link Reconstruction_simplification_2::Segment Segment \endlink.
*/
template<class PointOutputIterator, class SegmentOutputIterator>
void list_output (PointOutputIterator v_it, SegmentOutputIterator e_it) const
{
for (Vertex_iterator vi = m_dt.vertices_begin();
vi != m_dt.vertices_end(); ++vi)
{
bool incident_edges_have_sample = false;
typename Triangulation::Edge_circulator start = m_dt.incident_edges(vi);
typename Triangulation::Edge_circulator cur = start;
do {
if (!m_dt.is_ghost(*cur)) {
incident_edges_have_sample = true;
break;
}
++cur;
} while (cur != start);
if (!incident_edges_have_sample) {
if ((*vi).has_sample_assigned()) {
Point p = (*vi).point();
*v_it = p;
v_it++;
}
}
}
for (Finite_edges_iterator ei = m_dt.finite_edges_begin(); ei != m_dt.finite_edges_end(); ++ei)
{
Edge edge = *ei;
if (m_dt.is_ghost(edge))
continue;
int index = edge.second;
Vertex_handle source = edge.first->vertex( (index+1)%3 );
Vertex_handle target = edge.first->vertex( (index+2)%3 );
Segment s = m_traits.construct_segment_2_object()(
source->point(), target->point());
*e_it = s;
e_it++;
}
}
/// \endcond
/// \cond SKIP_IN_MANUAL
void extract_tds_output(Triangulation& rt2) const {
rt2 = m_dt;
//mark vertices
for (Vertex_iterator vi = rt2.vertices_begin();
vi != rt2.vertices_end(); ++vi)
{
bool incident_edges_have_sample = false;
typename Triangulation::Edge_circulator start = rt2.incident_edges(vi);
typename Triangulation::Edge_circulator cur = start;
do {
if (!rt2.is_ghost(*cur)) {
incident_edges_have_sample = true;
break;
}
++cur;
} while (cur != start);
if (!incident_edges_have_sample) {
if ((*vi).has_sample_assigned())
(*vi).set_relevance(1);
}
}
// mark edges
for (Finite_edges_iterator ei = rt2.finite_edges_begin(); ei != rt2.finite_edges_end(); ++ei)
{
Edge edge = *ei;
FT relevance = 0;
if (!rt2.is_ghost(edge)) {
relevance = rt2.get_edge_relevance(edge); // >= 0
}
edge.first->relevance(edge.second) = relevance;
}
}
/// \endcond
/// @}
};
}
#endif
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