如何打印 Voronoi 图的面？
How to print the faces of a Voronoi diagram?
下面的代码假定输入是点，而不是线段（这是错误的）。
按照这个 2D Voronoi Diagram Adaptor 示例，我正在尝试编写一个程序，它将输入线段作为输入线段并打印 Voronoi 图面的顶点。
这是我的尝试（保留示例的 includes/typedefs）：
// standard includes
#include <iostream>
#include <fstream>
#include <cassert>
// includes for defining the Voronoi diagram adaptor
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Delaunay_triangulation_2.h>
#include <CGAL/Voronoi_diagram_2.h>
#include <CGAL/Delaunay_triangulation_adaptation_traits_2.h>
#include <CGAL/Delaunay_triangulation_adaptation_policies_2.h>
// typedefs for defining the adaptor
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef CGAL::Delaunay_triangulation_2<K> DT;
typedef CGAL::Delaunay_triangulation_adaptation_traits_2<DT> AT;
typedef CGAL::Delaunay_triangulation_caching_degeneracy_removal_policy_2<DT> AP;
typedef CGAL::Voronoi_diagram_2<DT,AT,AP> VD;
// typedef for the result type of the point location
typedef AT::Site_2 Site_2;
typedef AT::Point_2 Point_2;
typedef VD::Locate_result Locate_result;
typedef VD::Vertex_handle Vertex_handle;
typedef VD::Face_handle Face_handle;
typedef VD::Halfedge_handle Halfedge_handle;
typedef VD::Ccb_halfedge_circulator Ccb_halfedge_circulator;
int main()
{
std::ifstream ifs("data.cin");
assert( ifs );
VD vd;
Site_2 t;
while ( ifs >> t ) { vd.insert(t); }
ifs.close();
assert( vd.is_valid() );
Face_handle* f = boost::get<Face_handle>(vd);
std::cout << "Exiting...\n";
return 0;
}
这会收到一个编译错误：
/home/gsamaras/CGAL-4.7/code/voronoi_adaptor/voronoi_adaptor.cpp:46:48: error: no matching function for call to ‘get(VD&)’
Face_handle* f = boost::get<Face_handle>(vd);
^
/home/gsamaras/CGAL-4.7/code/voronoi_adaptor/voronoi_adaptor.cpp:46:48: note: candidates are:
In file included from /usr/include/boost/variant.hpp:22:0,
from /home/gsamaras/CGAL-4.7/code/voronoi_adaptor/../../include/CGAL/Object.h:36,
from /home/gsamaras/CGAL-4.7/code/voronoi_adaptor/../../include/CGAL/kernel_basic.h:33,
from /home/gsamaras/CGAL-4.7/code/voronoi_adaptor/../../include/CGAL/basic.h:46,
from /home/gsamaras/CGAL-4.7/code/voronoi_adaptor/../../include/CGAL/Cartesian/Cartesian_base.h:28,
from /home/gsamaras/CGAL-4.7/code/voronoi_adaptor/../../include/CGAL/Simple_cartesian.h:28,
from /home/gsamaras/CGAL-4.7/code/voronoi_adaptor/../../include/CGAL/Exact_predicates_inexact_constructions_kernel.h:28,
from /home/gsamaras/CGAL-4.7/code/voronoi_adaptor/voronoi_adaptor.cpp:6:
/usr/include/boost/variant/get.hpp:141:1: note: template<class U, class T0, class T1, class T2, class T3, class T4, class T5, class T6, class T7, class T8, class T9, class T10, class T11, class T12, class T13, class T14, class T15, class T16, class T17, class T18, class T19> typename boost::add_pointer<T>::type boost::get(boost::variant<T0, T1, T2, T3, T4, T5, T6, T7, T8, T9, T10, T11, T12, T13, T14, T15, T16, T17, T18, T19>*)
get(
^
/usr/include/boost/variant/get.hpp:141:1: note: template argument deduction/substitution failed:
/home/gsamaras/CGAL-4.7/code/voronoi_adaptor/voronoi_adaptor.cpp:46:48: note: mismatched types ‘boost::variant<T0, T1, T2, T3, T4, T5, T6, T7, T8, T9, T10, T11, T12, T13, T14, T15, T16, T17, T18, T19>*’ and ‘CGAL::Voronoi_diagram_2<CGAL::Delaunay_triangulation_2<CGAL::Epick>, CGAL::Delaunay_triangulation_adaptation_traits_2<CGAL::Delaunay_triangulation_2<CGAL::Epick> >, CGAL::Delaunay_triangulation_caching_degeneracy_removal_policy_2<CGAL::Delaunay_triangulation_2<CGAL::Epick> > >’
Face_handle* f = boost::get<Face_handle>(vd);
^
...
Panagiotis Mike 给了我答案：
// standard includes
#include <iostream>
#include <string>
#include <fstream>
#include <cassert>
// includes for defining the Voronoi diagram adaptor
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Voronoi_diagram_2.h>
#include <CGAL/Segment_Delaunay_graph_2.h>
#include <CGAL/Segment_Delaunay_graph_adaptation_traits_2.h>
#include <CGAL/Segment_Delaunay_graph_adaptation_policies_2.h>
#include <CGAL/Segment_2.h>
#include <CGAL/Segment_Delaunay_graph_traits_2.h>
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef CGAL::Segment_Delaunay_graph_traits_2<K> Gt;
typedef CGAL::Segment_Delaunay_graph_2<Gt> DT;
typedef CGAL::Segment_Delaunay_graph_adaptation_traits_2<DT> AT;
typedef CGAL::Segment_Delaunay_graph_degeneracy_removal_policy_2<DT> AP;
typedef CGAL::Voronoi_diagram_2<DT, AT, AP> VD;
typedef AT::Site_2 Site_2;
typedef VD::Face_handle Face_handle;
int main()
{
std::ifstream ifs("data.cin");
assert( ifs );
VD vd;
Site_2 t;
while ( ifs >> t ) { vd.insert(t); }
ifs.close();
assert( vd.is_valid() );
std::cout << vd.number_of_faces() << std::endl;
VD::Face_iterator it = vd.faces_begin(),
beyond = vd.faces_end();
for (int f=0; it != beyond; ++f, ++it) {
std::cout << "Face" << f << ": \n";
VD::Ccb_halfedge_circulator hec = it->ccb();
do {
VD::Halfedge_handle heh = static_cast<VD::Halfedge_handle>(hec);
if (heh->has_target())
std::cout << heh->target()->point() << "\n";
else
std::cout << "point at infinity\n";
} while (++hec != it->ccb());
std::cout << std::endl;
}
return 0;
}
我需要将 Voronoi 图的面打印为 well-known text 多边形。这需要遍历面的边缘并为无限点提供有限表示。我是这样做的。
//Generate WKT polygons from Voronoi cells using CGAL
//Compile with: g++ main.cpp -Wall -lCGAL -lgmp
//Author: Richard Barnes (rbarnes.org)
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Regular_triangulation_filtered_traits_2.h>
#include <CGAL/Regular_triangulation_adaptation_traits_2.h>
#include <CGAL/Regular_triangulation_adaptation_policies_2.h>
#include <CGAL/Regular_triangulation_2.h>
#include <CGAL/Voronoi_diagram_2.h>
#include <CGAL/intersections.h>
#include <CGAL/bounding_box.h>
#include <CGAL/Polygon_2.h>
#include <iostream>
#include <cstdint>
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef CGAL::Regular_triangulation_filtered_traits_2<K> Traits;
typedef CGAL::Regular_triangulation_2<Traits> RT2;
typedef CGAL::Regular_triangulation_adaptation_traits_2<RT2> AT;
typedef CGAL::Regular_triangulation_degeneracy_removal_policy_2<RT2> DRP;
typedef CGAL::Voronoi_diagram_2<RT2, AT, DRP> VD;
int main(int argc, char **argv){
std::vector<RT2::Weighted_point> wpoints;
std::cout.precision(4);
std::cout.setf(std::ios::fixed);
//Generated random points
for(int i=0;i<100;i++)
//Weight of 0 gives a Voronoi diagram. Non-zero weight gives a power diagram
wpoints.push_back(RT2::Weighted_point(K::Point_2(rand()%100,rand()%100), 0));
//Create a Regular Triangulation from the points
RT2 rt(wpoints.begin(), wpoints.end());
rt.is_valid();
//Wrap the triangulation with a Voronoi diagram adaptor. This is necessary to
//get the Voronoi faces.
VD vd(rt);
//CGAL often returns objects that are either segments or rays. This converts
//these objects into segments. If the object would have resolved into a ray,
//that ray is intersected with the bounding box defined above and returned as
//a segment.
const auto ConvertToSeg = [&](const CGAL::Object seg_obj, bool outgoing) -> K::Segment_2 {
//One of these will succeed and one will have a NULL pointer
const K::Segment_2 *dseg = CGAL::object_cast<K::Segment_2>(&seg_obj);
const K::Ray_2 *dray = CGAL::object_cast<K::Ray_2>(&seg_obj);
if (dseg) { //Okay, we have a segment
return *dseg;
} else { //Must be a ray
const auto &source = dray->source();
const auto dsx = source.x();
const auto dsy = source.y();
const auto &dir = dray->direction();
const auto tpoint = K::Point_2(dsx+1000*dir.dx(),dsy+1000*dir.dy());
if(outgoing)
return K::Segment_2(
dray->source(),
tpoint
);
else
return K::Segment_2(
tpoint,
dray->source()
);
}
};
std::cout<<"\"id\",\"geom\"\n";
int fnum = 0;
//Loop over the faces of the Voronoi diagram in some arbitrary order
for(VD::Face_iterator fit = vd.faces_begin(); fit!=vd.faces_end();++fit,fnum++){
CGAL::Polygon_2<K> pgon;
//Edge circulators traverse endlessly around a face. Make a note of the
//starting point so we know when to quit.
VD::Face::Ccb_halfedge_circulator ec_start = fit->ccb();
//Find a bounded edge to start on
for(;ec_start->is_unbounded();ec_start++){}
//Current location of the edge circulator
VD::Face::Ccb_halfedge_circulator ec = ec_start;
do {
//A half edge circulator representing a ray doesn't carry direction
//information. To get it, we take the dual of the dual of the half-edge.
//The dual of a half-edge circulator is the edge of a Delaunay triangle.
//The dual of the edge of Delaunay triangle is either a segment or a ray.
// const CGAL::Object seg_dual = rt.dual(ec->dual());
const CGAL::Object seg_dual = vd.dual().dual(ec->dual());
//Convert the segment/ray into a segment
const auto this_seg = ConvertToSeg(seg_dual, ec->has_target());
pgon.push_back(this_seg.source());
//If the segment has no target, it's a ray. This means that the next
//segment will also be a ray. We need to connect those two rays with a
//segment. The following accomplishes this.
if(!ec->has_target()){
const CGAL::Object nseg_dual = vd.dual().dual(ec->next()->dual());
const auto next_seg = ConvertToSeg(nseg_dual, ec->next()->has_target());
pgon.push_back(next_seg.target());
}
} while ( ++ec != ec_start ); //Loop until we get back to the beginning
std::cout<<fnum<<", "
"\"POLYGON ((";
for(auto v=pgon.vertices_begin();v!=pgon.vertices_end();v++)
std::cout<<v->x()<<" "<<v->y()<<", ";
std::cout<<pgon.vertices_begin()->x()<<" "<<pgon.vertices_begin()->y()<<"))\"\n";
}
return 0;
}
下面的代码假定输入是点，而不是线段（这是错误的）。
按照这个 2D Voronoi Diagram Adaptor 示例，我正在尝试编写一个程序，它将输入线段作为输入线段并打印 Voronoi 图面的顶点。
这是我的尝试（保留示例的 includes/typedefs）：
// standard includes
#include <iostream>
#include <fstream>
#include <cassert>
// includes for defining the Voronoi diagram adaptor
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Delaunay_triangulation_2.h>
#include <CGAL/Voronoi_diagram_2.h>
#include <CGAL/Delaunay_triangulation_adaptation_traits_2.h>
#include <CGAL/Delaunay_triangulation_adaptation_policies_2.h>
// typedefs for defining the adaptor
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef CGAL::Delaunay_triangulation_2<K> DT;
typedef CGAL::Delaunay_triangulation_adaptation_traits_2<DT> AT;
typedef CGAL::Delaunay_triangulation_caching_degeneracy_removal_policy_2<DT> AP;
typedef CGAL::Voronoi_diagram_2<DT,AT,AP> VD;
// typedef for the result type of the point location
typedef AT::Site_2 Site_2;
typedef AT::Point_2 Point_2;
typedef VD::Locate_result Locate_result;
typedef VD::Vertex_handle Vertex_handle;
typedef VD::Face_handle Face_handle;
typedef VD::Halfedge_handle Halfedge_handle;
typedef VD::Ccb_halfedge_circulator Ccb_halfedge_circulator;
int main()
{
std::ifstream ifs("data.cin");
assert( ifs );
VD vd;
Site_2 t;
while ( ifs >> t ) { vd.insert(t); }
ifs.close();
assert( vd.is_valid() );
Face_handle* f = boost::get<Face_handle>(vd);
std::cout << "Exiting...\n";
return 0;
}
这会收到一个编译错误：
/home/gsamaras/CGAL-4.7/code/voronoi_adaptor/voronoi_adaptor.cpp:46:48: error: no matching function for call to ‘get(VD&)’
Face_handle* f = boost::get<Face_handle>(vd);
^
/home/gsamaras/CGAL-4.7/code/voronoi_adaptor/voronoi_adaptor.cpp:46:48: note: candidates are:
In file included from /usr/include/boost/variant.hpp:22:0,
from /home/gsamaras/CGAL-4.7/code/voronoi_adaptor/../../include/CGAL/Object.h:36,
from /home/gsamaras/CGAL-4.7/code/voronoi_adaptor/../../include/CGAL/kernel_basic.h:33,
from /home/gsamaras/CGAL-4.7/code/voronoi_adaptor/../../include/CGAL/basic.h:46,
from /home/gsamaras/CGAL-4.7/code/voronoi_adaptor/../../include/CGAL/Cartesian/Cartesian_base.h:28,
from /home/gsamaras/CGAL-4.7/code/voronoi_adaptor/../../include/CGAL/Simple_cartesian.h:28,
from /home/gsamaras/CGAL-4.7/code/voronoi_adaptor/../../include/CGAL/Exact_predicates_inexact_constructions_kernel.h:28,
from /home/gsamaras/CGAL-4.7/code/voronoi_adaptor/voronoi_adaptor.cpp:6:
/usr/include/boost/variant/get.hpp:141:1: note: template<class U, class T0, class T1, class T2, class T3, class T4, class T5, class T6, class T7, class T8, class T9, class T10, class T11, class T12, class T13, class T14, class T15, class T16, class T17, class T18, class T19> typename boost::add_pointer<T>::type boost::get(boost::variant<T0, T1, T2, T3, T4, T5, T6, T7, T8, T9, T10, T11, T12, T13, T14, T15, T16, T17, T18, T19>*)
get(
^
/usr/include/boost/variant/get.hpp:141:1: note: template argument deduction/substitution failed:
/home/gsamaras/CGAL-4.7/code/voronoi_adaptor/voronoi_adaptor.cpp:46:48: note: mismatched types ‘boost::variant<T0, T1, T2, T3, T4, T5, T6, T7, T8, T9, T10, T11, T12, T13, T14, T15, T16, T17, T18, T19>*’ and ‘CGAL::Voronoi_diagram_2<CGAL::Delaunay_triangulation_2<CGAL::Epick>, CGAL::Delaunay_triangulation_adaptation_traits_2<CGAL::Delaunay_triangulation_2<CGAL::Epick> >, CGAL::Delaunay_triangulation_caching_degeneracy_removal_policy_2<CGAL::Delaunay_triangulation_2<CGAL::Epick> > >’
Face_handle* f = boost::get<Face_handle>(vd);
^
...
Panagiotis Mike 给了我答案：
// standard includes
#include <iostream>
#include <string>
#include <fstream>
#include <cassert>
// includes for defining the Voronoi diagram adaptor
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Voronoi_diagram_2.h>
#include <CGAL/Segment_Delaunay_graph_2.h>
#include <CGAL/Segment_Delaunay_graph_adaptation_traits_2.h>
#include <CGAL/Segment_Delaunay_graph_adaptation_policies_2.h>
#include <CGAL/Segment_2.h>
#include <CGAL/Segment_Delaunay_graph_traits_2.h>
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef CGAL::Segment_Delaunay_graph_traits_2<K> Gt;
typedef CGAL::Segment_Delaunay_graph_2<Gt> DT;
typedef CGAL::Segment_Delaunay_graph_adaptation_traits_2<DT> AT;
typedef CGAL::Segment_Delaunay_graph_degeneracy_removal_policy_2<DT> AP;
typedef CGAL::Voronoi_diagram_2<DT, AT, AP> VD;
typedef AT::Site_2 Site_2;
typedef VD::Face_handle Face_handle;
int main()
{
std::ifstream ifs("data.cin");
assert( ifs );
VD vd;
Site_2 t;
while ( ifs >> t ) { vd.insert(t); }
ifs.close();
assert( vd.is_valid() );
std::cout << vd.number_of_faces() << std::endl;
VD::Face_iterator it = vd.faces_begin(),
beyond = vd.faces_end();
for (int f=0; it != beyond; ++f, ++it) {
std::cout << "Face" << f << ": \n";
VD::Ccb_halfedge_circulator hec = it->ccb();
do {
VD::Halfedge_handle heh = static_cast<VD::Halfedge_handle>(hec);
if (heh->has_target())
std::cout << heh->target()->point() << "\n";
else
std::cout << "point at infinity\n";
} while (++hec != it->ccb());
std::cout << std::endl;
}
return 0;
}
我需要将 Voronoi 图的面打印为 well-known text 多边形。这需要遍历面的边缘并为无限点提供有限表示。我是这样做的。
//Generate WKT polygons from Voronoi cells using CGAL
//Compile with: g++ main.cpp -Wall -lCGAL -lgmp
//Author: Richard Barnes (rbarnes.org)
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Regular_triangulation_filtered_traits_2.h>
#include <CGAL/Regular_triangulation_adaptation_traits_2.h>
#include <CGAL/Regular_triangulation_adaptation_policies_2.h>
#include <CGAL/Regular_triangulation_2.h>
#include <CGAL/Voronoi_diagram_2.h>
#include <CGAL/intersections.h>
#include <CGAL/bounding_box.h>
#include <CGAL/Polygon_2.h>
#include <iostream>
#include <cstdint>
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef CGAL::Regular_triangulation_filtered_traits_2<K> Traits;
typedef CGAL::Regular_triangulation_2<Traits> RT2;
typedef CGAL::Regular_triangulation_adaptation_traits_2<RT2> AT;
typedef CGAL::Regular_triangulation_degeneracy_removal_policy_2<RT2> DRP;
typedef CGAL::Voronoi_diagram_2<RT2, AT, DRP> VD;
int main(int argc, char **argv){
std::vector<RT2::Weighted_point> wpoints;
std::cout.precision(4);
std::cout.setf(std::ios::fixed);
//Generated random points
for(int i=0;i<100;i++)
//Weight of 0 gives a Voronoi diagram. Non-zero weight gives a power diagram
wpoints.push_back(RT2::Weighted_point(K::Point_2(rand()%100,rand()%100), 0));
//Create a Regular Triangulation from the points
RT2 rt(wpoints.begin(), wpoints.end());
rt.is_valid();
//Wrap the triangulation with a Voronoi diagram adaptor. This is necessary to
//get the Voronoi faces.
VD vd(rt);
//CGAL often returns objects that are either segments or rays. This converts
//these objects into segments. If the object would have resolved into a ray,
//that ray is intersected with the bounding box defined above and returned as
//a segment.
const auto ConvertToSeg = [&](const CGAL::Object seg_obj, bool outgoing) -> K::Segment_2 {
//One of these will succeed and one will have a NULL pointer
const K::Segment_2 *dseg = CGAL::object_cast<K::Segment_2>(&seg_obj);
const K::Ray_2 *dray = CGAL::object_cast<K::Ray_2>(&seg_obj);
if (dseg) { //Okay, we have a segment
return *dseg;
} else { //Must be a ray
const auto &source = dray->source();
const auto dsx = source.x();
const auto dsy = source.y();
const auto &dir = dray->direction();
const auto tpoint = K::Point_2(dsx+1000*dir.dx(),dsy+1000*dir.dy());
if(outgoing)
return K::Segment_2(
dray->source(),
tpoint
);
else
return K::Segment_2(
tpoint,
dray->source()
);
}
};
std::cout<<"\"id\",\"geom\"\n";
int fnum = 0;
//Loop over the faces of the Voronoi diagram in some arbitrary order
for(VD::Face_iterator fit = vd.faces_begin(); fit!=vd.faces_end();++fit,fnum++){
CGAL::Polygon_2<K> pgon;
//Edge circulators traverse endlessly around a face. Make a note of the
//starting point so we know when to quit.
VD::Face::Ccb_halfedge_circulator ec_start = fit->ccb();
//Find a bounded edge to start on
for(;ec_start->is_unbounded();ec_start++){}
//Current location of the edge circulator
VD::Face::Ccb_halfedge_circulator ec = ec_start;
do {
//A half edge circulator representing a ray doesn't carry direction
//information. To get it, we take the dual of the dual of the half-edge.
//The dual of a half-edge circulator is the edge of a Delaunay triangle.
//The dual of the edge of Delaunay triangle is either a segment or a ray.
// const CGAL::Object seg_dual = rt.dual(ec->dual());
const CGAL::Object seg_dual = vd.dual().dual(ec->dual());
//Convert the segment/ray into a segment
const auto this_seg = ConvertToSeg(seg_dual, ec->has_target());
pgon.push_back(this_seg.source());
//If the segment has no target, it's a ray. This means that the next
//segment will also be a ray. We need to connect those two rays with a
//segment. The following accomplishes this.
if(!ec->has_target()){
const CGAL::Object nseg_dual = vd.dual().dual(ec->next()->dual());
const auto next_seg = ConvertToSeg(nseg_dual, ec->next()->has_target());
pgon.push_back(next_seg.target());
}
} while ( ++ec != ec_start ); //Loop until we get back to the beginning
std::cout<<fnum<<", "
"\"POLYGON ((";
for(auto v=pgon.vertices_begin();v!=pgon.vertices_end();v++)
std::cout<<v->x()<<" "<<v->y()<<", ";
std::cout<<pgon.vertices_begin()->x()<<" "<<pgon.vertices_begin()->y()<<"))\"\n";
}
return 0;
}