mirror of https://github.com/CGAL/cgal
Modifications to User Manual (figures, refs, added two examples)
This commit is contained in:
Iordan Iordanov
parent
c4f687ef6a
commit
2f7e21c767
|
|
@ -7,7 +7,7 @@ namespace CGAL {
|
|||
/*!
|
||||
\ingroup PkgHyperbolicTriangulation2MainClasses
|
||||
|
||||
The class `Hyperbolic_Delaunay_triangulation_2` is the main class of the 2D Hyperbolic Triangulations package.
|
||||
The class `Hyperbolic_Delaunay_triangulation_2` is the main class of the 2D Hyperbolic Delaunay Triangulations package.
|
||||
It is designed to represent Delaunay triangulations of sets of points in the hyperbolic plane.
|
||||
The hyperbolic plane is represented in the Poincaré disk model.
|
||||
|
||||
|
|
|
|||
|
|
@ -4,6 +4,9 @@ EXTRACT_PRIVATE = NO
|
|||
|
||||
EXAMPLE_PATH = ${CGAL_PACKAGE_DIR}/examples
|
||||
|
||||
PROJECT_NAME = "CGAL ${CGAL_DOC_VERSION} - 2D Hyperbolic Triangulations"
|
||||
PROJECT_NAME = "CGAL ${CGAL_DOC_VERSION} - 2D Hyperbolic Delaunay Triangulations"
|
||||
|
||||
HTML_EXTRA_FILES = ${CGAL_PACKAGE_DOC_DIR}/fig/ht-empty-disks.png
|
||||
HTML_EXTRA_FILES = ${CGAL_PACKAGE_DOC_DIR}/fig/ht-empty-disks.png \
|
||||
${CGAL_PACKAGE_DOC_DIR}/fig/poincare-disk.png \
|
||||
${CGAL_PACKAGE_DOC_DIR}/fig/header.png \
|
||||
${CGAL_PACKAGE_DOC_DIR}/fig/hyperbolic-vs-euclidean.png
|
||||
|
|
|
|||
|
|
@ -11,16 +11,14 @@ namespace CGAL {
|
|||
\cgalAutoToc
|
||||
\author Mikhail Bogdanov, and Iordan Iordanov, and Monique Teillaud
|
||||
|
||||
\image html ht-450px.png
|
||||
<center>
|
||||
<img src="header.png" style="max-width:60%; width=60%;"/>
|
||||
</center>
|
||||
|
||||
\cgalModifBegin
|
||||
TODO image Delaunay + Voronoi a cote
|
||||
\cgalModifEnd
|
||||
This package allows to compute Delaunay triangulations of point sets in the Poincaré
|
||||
disk model of the hyperbolic plane, as well as their dual objects.
|
||||
|
||||
This package allows to compute triangulations of point sets in the Poincaré
|
||||
disk model of the hyperbolic plane.
|
||||
|
||||
\section The Poincaré Disk Model of the Hyperbolic Plane
|
||||
\section HT2_Poincare_model The Poincaré Disk Model of the Hyperbolic Plane
|
||||
The Poincaré disk model represents the hyperbolic plane
|
||||
\f$\mathbb H^2\f$ as the open unit disk centered at the origin in the
|
||||
Euclidean plane. The unit circle represents the set \f$\mathcal
|
||||
|
|
@ -32,21 +30,35 @@ a diameter of the unit disk. A hyperbolic circle is a Euclidean circle
|
|||
contained in the unit disk; however, its hyperbolic center and radius
|
||||
are not the same as its Euclidean center and radius.
|
||||
|
||||
\cgalModifBegin
|
||||
TODO figure showing \f$\mathcal H_\infty\f$ and O in black, 2 lines (one of each
|
||||
kind) in e.g., blue, and a few co-circular circles in e.g., green
|
||||
\cgalModifEnd
|
||||
\cgalFigureAnchor{Hyperbolic_triangulation_2Poincare_disk}
|
||||
<center>
|
||||
<img src="poincare-disk.png" style="max-width:35%; width=35%;"/>
|
||||
</center>
|
||||
\cgalFigureCaptionBegin{Hyperbolic_triangulation_2Poincare_disk}
|
||||
The Poincaré disk model for the hyperbolic plane. The figure shows
|
||||
two hyperbolic lines and three concentric hyperbolic circles with different
|
||||
radii.
|
||||
\cgalFigureCaptionEnd
|
||||
|
||||
\section Euclidean and Hyperbolic Delaunay Triangulations
|
||||
|
||||
\section HT2_Euclidean_and_hyperbolic_Delaunay_triangulations Euclidean and Hyperbolic Delaunay Triangulations
|
||||
As hyperbolic circles coincide with Euclidean circles contained in the
|
||||
unit disk, the combinatorial structure of the hyperbolic Delaunay
|
||||
triangulation of a set \f$\mathcal P\f of points in \f$\mathbb H^2\f$
|
||||
triangulation of a set \f$\mathcal P\f$ of points in \f$\mathbb H^2\f$
|
||||
is a subset of the Euclidean Delaunay triangulation of \f$\mathcal
|
||||
P\f. Of course, the hyperbolic and Euclidean geometric embeddings of a
|
||||
given Delaunay face are different.
|
||||
\cgalModifBegin
|
||||
TODO maybe figure showing the 2 embeddings?
|
||||
\cgalModifEnd
|
||||
P\f$. Of course, the hyperbolic and Euclidean geometric embeddings of a
|
||||
given Delaunay face are different. See
|
||||
\cgalFigureRef{Hyperbolic_triangulation_2Euclidean_vs_hyperbolic}.
|
||||
|
||||
\cgalFigureAnchor{Hyperbolic_triangulation_2Euclidean_vs_hyperbolic}
|
||||
<center>
|
||||
<img src="hyperbolic-vs-euclidean.png" style="max-width:35%; width=35%;"/>
|
||||
</center>
|
||||
\cgalFigureCaptionBegin{Hyperbolic_triangulation_2Euclidean_vs_hyperbolic}
|
||||
Comparison of the Euclidean (green) and hyperbolic (black) Delaunay triangulations
|
||||
of a given set of points in the unit disk. Note that only the colored faces
|
||||
are faces of the hyperbolic Delaunay triangulation.
|
||||
\cgalFigureCaptionEnd
|
||||
|
||||
More precisely, the hyperbolic Delaunay triangulation of \f$\mathcal
|
||||
P\f$ is a connected simplicial complex. It only
|
||||
|
|
@ -58,20 +70,16 @@ are <i>hyperbolic</i>:
|
|||
<li> An Euclidean Delaunay edge is hyperbolic if one fo the
|
||||
empty disks (i.e., not containing any point of \f$\mathcal
|
||||
P\f$) passing through its endpoints is contained in \f$\mathbb
|
||||
H^2\f.
|
||||
H^2\f$.
|
||||
</ul>
|
||||
In the Euclidean Delaunay triangulation, there is a bijection between
|
||||
non-hyperbolic faces and non-hyperbolic edges
|
||||
\cgalCite{cgal:bdt-hdcvd-14}. See
|
||||
\cgalFigureRef{Hyperbolic_triangulation_2Empty_disks}
|
||||
|
||||
\cgalModifBegin
|
||||
TODO fix bib entry: Delaunay and Voronoi should be capitalized
|
||||
\cgalModifEnd
|
||||
|
||||
\cgalFigureAnchor{Hyperbolic_triangulation_2Empty_disks}
|
||||
<center>
|
||||
<img src="ht-empty-disks.png" style="max-width:30%; width=30%;"/>
|
||||
<img src="ht-empty-disks.png" style="max-width:35%; width=35%;"/>
|
||||
</center>
|
||||
\cgalFigureCaptionBegin{Hyperbolic_triangulation_2Empty_disks}
|
||||
The shaded face is non-hyperbolic. Its dashed edge is non-hyperbolic,
|
||||
|
|
@ -79,24 +87,19 @@ as no empty circle through its endpoints is contained in
|
|||
\f$\mathbb H^2\f$. Its other two edges are hyperbolic.
|
||||
\cgalFigureCaptionEnd
|
||||
|
||||
\cgalModifBegin
|
||||
TODO fix the picture so that it shows what is written in the caption.
|
||||
\cgalModifEnd
|
||||
|
||||
\section Software Design
|
||||
\section HT2_Software_design Software Design
|
||||
From what was said above, it is natural that the class
|
||||
`Hyperbolic_Delaunay_triangulation_2` privately inherits from the class
|
||||
`Delaunay_triangulation_2`. So, users are encouraged to look at the chapter
|
||||
\cgalModifBegin
|
||||
TODO link T2
|
||||
\cgalModifEnd
|
||||
of the CGAL manual to know more in particular about the
|
||||
representation of triangulations in CGAL and the flexibility of the design.
|
||||
\ref Chapter_2D_Triangulations "2D Triangulation" of the CGAL manual to
|
||||
know more in particular about the representation of triangulations in
|
||||
CGAL and the flexibility of the design.
|
||||
|
||||
The class `Hyperbolic_Delaunay_triangulation_2` has two template
|
||||
parameters:
|
||||
<ul>
|
||||
<li> A geometric traits class `Gt`, which provides geometric
|
||||
<li> A geometric traits class `Gt`, which provides geometric
|
||||
primitives. The requirements on this first template parameter
|
||||
are described by the concept
|
||||
`HyperbolicDelaunayTriangulationTraits_2`, which refines
|
||||
|
|
@ -119,10 +122,14 @@ algebraic coordinates; however the first model is more efficient for
|
|||
rational points.
|
||||
|
||||
\section Examples
|
||||
\cgalModifBegin
|
||||
TODO two examples, one with each traits. Maybe one with colors on
|
||||
vertices to show how to plug vertex-with-info
|
||||
\cgalModifEnd
|
||||
The example below shows insertion of random points in a hyperbolic Delaunay triangulation.
|
||||
The same set of points is inserted twice. The first time points are inserted one by one,
|
||||
which causes Euclidean faces to be filtered at each insertion. The second time, all points
|
||||
are inserted and the filtering is done once at the end.
|
||||
\cgalExample{Hyperbolic_triangulation_2/ht2_example.cpp}
|
||||
|
||||
The example below shows how user-defined info can be added to the hyperbolic faces.
|
||||
\cgalExample{Hyperbolic_triangulation_2/ht2_example_color.cpp}
|
||||
|
||||
\section HT2_Design Design and Implementation History
|
||||
|
||||
|
|
|
|||
|
|
@ -1,4 +1,4 @@
|
|||
/// \defgroup PkgHyperbolicTriangulation2 2D Hyperbolic Triangulations Reference
|
||||
/// \defgroup PkgHyperbolicTriangulation2 2D Hyperbolic Delaunay Triangulations Reference
|
||||
|
||||
/// \defgroup PkgHyperbolicTriangulation2Concepts Concepts
|
||||
/// \ingroup PkgHyperbolicTriangulation2
|
||||
|
|
|
|||
|
|
@ -0,0 +1,27 @@
|
|||
# Created by the script cgal_create_cmake_script
|
||||
# This is the CMake script for compiling a CGAL application.
|
||||
|
||||
|
||||
project( Periodic_4_hyperbolic_triangulation_2_examples )
|
||||
|
||||
cmake_minimum_required(VERSION 2.8.10)
|
||||
|
||||
find_package(CGAL QUIET COMPONENTS Core )
|
||||
|
||||
if ( CGAL_FOUND )
|
||||
|
||||
include( ${CGAL_USE_FILE} )
|
||||
|
||||
include( CGAL_CreateSingleSourceCGALProgram )
|
||||
|
||||
include_directories (BEFORE "../../include" $HOME/include)
|
||||
|
||||
create_single_source_cgal_program( "ht2_example.cpp" )
|
||||
create_single_source_cgal_program( "ht2_example_color.cpp" )
|
||||
|
||||
else()
|
||||
|
||||
message(STATUS "This program requires the CGAL library, and will not be compiled.")
|
||||
|
||||
endif()
|
||||
|
||||
|
|
@ -0,0 +1,62 @@
|
|||
#include <CGAL/Hyperbolic_Delaunay_triangulation_2.h>
|
||||
#include <CGAL/Hyperbolic_Delaunay_triangulation_traits_2.h>
|
||||
#include <CGAL/point_generators_2.h>
|
||||
#include <CGAL/CORE_Expr.h>
|
||||
#include <CGAL/Timer.h>
|
||||
|
||||
typedef CGAL::Hyperbolic_Delaunay_triangulation_traits_2<> Gt;
|
||||
typedef Gt::Point_2 Point_2;
|
||||
typedef Gt::Circle_2 Circle_2;
|
||||
typedef Gt::FT FT;
|
||||
typedef CGAL::Hyperbolic_Delaunay_triangulation_2<Gt> Dt;
|
||||
typedef CGAL::Creator_uniform_2<FT, Point_2> Creator;
|
||||
|
||||
int main(int argc, char** argv)
|
||||
{
|
||||
|
||||
if (argc < 2) {
|
||||
std::cout << "usage: " << argv[0] << " [number_of_points]" << std::endl;
|
||||
return -1;
|
||||
}
|
||||
|
||||
int N = atoi(argv[1]);
|
||||
std::cout << "Number of points: " << N << std::endl;
|
||||
|
||||
CGAL::Timer timer;
|
||||
CGAL::Random_points_in_disc_2<Point_2, Creator> in_disc;
|
||||
std::vector<Point_2> pts;
|
||||
std::vector<Point_2>::iterator ip;
|
||||
|
||||
for (int i=0 ; i < N; i++) {
|
||||
pts.push_back(*(in_disc++));
|
||||
}
|
||||
|
||||
Dt dt_during;
|
||||
std::cout << "Insertion of points one by one (hyperbolic filtering at each step)" << std::endl;
|
||||
std::cout << "===================================================================" << std::endl;
|
||||
timer.start();
|
||||
for(ip = pts.begin(); ip != pts.end(); ++ip) {
|
||||
dt_during.insert(*ip);
|
||||
}
|
||||
timer.stop();
|
||||
|
||||
std::cout << "Number of vertices: " << dt_during.number_of_vertices() << std::endl;
|
||||
std::cout << "Number of hyperbolic faces: " << dt_during.number_of_hyperbolic_faces() << std::endl;
|
||||
std::cout << "Number of hyperbolic edges: " << dt_during.number_of_hyperbolic_edges() << std::endl;
|
||||
std::cout << "Time: " << timer.time() << std::endl << std::endl;
|
||||
|
||||
Dt dt_end;
|
||||
std::cout << "Insertion of point set (hyperbolic filtering only once at the end)" << std::endl;
|
||||
std::cout << "===================================================================" << std::endl;
|
||||
timer.reset();
|
||||
timer.start();
|
||||
dt_end.insert(pts.begin(),pts.end());
|
||||
timer.stop();
|
||||
|
||||
std::cout << "Number of vertices: " << dt_end.number_of_vertices() << std::endl;
|
||||
std::cout << "Number of hyperbolic faces: " << dt_end.number_of_hyperbolic_faces() << std::endl;
|
||||
std::cout << "Number of hyperbolic edges: " << dt_end.number_of_hyperbolic_edges() << std::endl;
|
||||
std::cout << "Time: " << timer.time() << std::endl;
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -0,0 +1,69 @@
|
|||
#include <CGAL/Triangulation_face_base_with_info_2.h>
|
||||
#include <CGAL/Triangulation_vertex_base_2.h>
|
||||
#include <CGAL/Hyperbolic_triangulation_face_base_2.h>
|
||||
#include <CGAL/Hyperbolic_Delaunay_triangulation_2.h>
|
||||
#include <CGAL/Hyperbolic_Delaunay_triangulation_CK_traits_2.h>
|
||||
#include <CGAL/point_generators_2.h>
|
||||
#include <CGAL/IO/Color.h>
|
||||
|
||||
typedef CGAL::Hyperbolic_Delaunay_triangulation_CK_traits_2<> Gt;
|
||||
typedef CGAL::Hyperbolic_triangulation_face_base_2<Gt> Hyperbolic_face_base;
|
||||
typedef CGAL::Triangulation_face_base_with_info_2<CGAL::Color,
|
||||
Gt, Hyperbolic_face_base> Face_base_with_info;
|
||||
typedef CGAL::Triangulation_vertex_base_2<Gt> Vertex_base;
|
||||
typedef CGAL::Triangulation_data_structure_2 <
|
||||
Vertex_base, Face_base_with_info> TDS;
|
||||
typedef CGAL::Hyperbolic_Delaunay_triangulation_2<Gt, TDS> Dt;
|
||||
typedef Dt::Point Point_2;
|
||||
typedef CGAL::Creator_uniform_2<Gt::FT, Point_2> Creator;
|
||||
|
||||
int main(int argc, char** argv)
|
||||
{
|
||||
|
||||
if (argc < 2) {
|
||||
std::cout << "usage: " << argv[0] << " [number_of_points]" << std::endl;
|
||||
return -1;
|
||||
}
|
||||
|
||||
int N = atoi(argv[1]);
|
||||
std::cout << "Number of points: " << N << std::endl;
|
||||
|
||||
CGAL::Random_points_in_disc_2<Point_2, Creator> in_disc;
|
||||
std::vector<Point_2> pts;
|
||||
std::vector<Point_2>::iterator ip;
|
||||
|
||||
for (int i=0 ; i < N; i++) {
|
||||
pts.push_back(*(in_disc++));
|
||||
}
|
||||
|
||||
Dt dt;
|
||||
|
||||
|
||||
dt.insert(pts.begin(), pts.end());
|
||||
Dt::Vertex_handle vo = dt.insert(Point_2(0,0));
|
||||
|
||||
int origin_faces = 0;
|
||||
Dt::Hyperbolic_faces_iterator fit;
|
||||
for (fit = dt.hyperbolic_faces_begin(); fit != dt.hyperbolic_faces_end(); ++fit) {
|
||||
if (fit->has_vertex(vo)) {
|
||||
fit->info() = CGAL::RED;
|
||||
origin_faces++;
|
||||
}
|
||||
}
|
||||
|
||||
int red_faces = 0;
|
||||
for (fit = dt.hyperbolic_faces_begin(); fit != dt.hyperbolic_faces_end(); ++fit) {
|
||||
if (fit->info() == CGAL::RED) {
|
||||
red_faces++;
|
||||
}
|
||||
}
|
||||
|
||||
assert(red_faces == origin_faces);
|
||||
|
||||
std::cout << "Number of points " << N << std::endl;
|
||||
std::cout << "Number of vertices: " << dt.number_of_vertices() << std::endl;
|
||||
std::cout << "Number of hyperbolic faces: " << dt.number_of_hyperbolic_faces() << std::endl;
|
||||
std::cout << "Number of faces incident to the origin: " << origin_faces << std::endl;
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,62 +0,0 @@
|
|||
#include <fstream>
|
||||
|
||||
// CGAL headers
|
||||
#include <CGAL/IO/io.h>
|
||||
|
||||
#include <CGAL/Exact_circular_kernel_2.h>
|
||||
|
||||
#include <CGAL/Hyperbolic_triangulation_face_base_with_info_2.h>
|
||||
#include <CGAL/Hyperbolic_Delaunay_triangulation_2.h>
|
||||
#include <CGAL/Hyperbolic_Delaunay_triangulation_traits_2.h>
|
||||
|
||||
#include <CGAL/IO/Color.h>
|
||||
|
||||
typedef CGAL::Exact_circular_kernel_2 K;
|
||||
typedef CGAL::Hyperbolic_Delaunay_triangulation_traits_2< K > Gt;
|
||||
|
||||
typedef Gt::Point_2 Point_2;
|
||||
|
||||
typedef CGAL::Hyperbolic_triangulation_face_base_with_info_2<CGAL::Color, Gt> Fb;
|
||||
typedef CGAL::Triangulation_data_structure_2 <
|
||||
CGAL::Triangulation_vertex_base_2<Gt>, Fb > TDS;
|
||||
typedef CGAL::Hyperbolic_Delaunay_triangulation_2<Gt, TDS> Dt;
|
||||
|
||||
int main()
|
||||
{
|
||||
std::vector<Point_2> pts;
|
||||
Point_2 p;
|
||||
|
||||
std::ifstream ifs("input-file");
|
||||
while(ifs >> p) {
|
||||
pts.push_back(p);
|
||||
}
|
||||
|
||||
Dt dt;
|
||||
|
||||
dt.insert(pts.begin(),pts.end());
|
||||
Dt::Vertex_handle vo = dt.insert(Point_2(0,0));
|
||||
|
||||
int origin_faces = 0;
|
||||
Dt::Hyperbolic_faces_iterator fit;
|
||||
for (fit = dt.hyperbolic_faces_begin(); fit != dt.hyperbolic_faces_end(); ++fit)
|
||||
if (fit->has_vertex(vo))
|
||||
{
|
||||
fit->info() = CGAL::RED;
|
||||
origin_faces++;
|
||||
}
|
||||
|
||||
int red_faces = 0;
|
||||
for (fit = dt.hyperbolic_faces_begin(); fit != dt.hyperbolic_faces_end(); ++fit)
|
||||
if (fit->info() == CGAL::RED)
|
||||
red_faces++;
|
||||
|
||||
assert(red_faces == origin_faces);
|
||||
|
||||
std::cout << "number of points " << std::distance(pts.begin(),pts.end())+1 << std::endl;
|
||||
std::cout << "Number of (finite) vertices: " << dt.number_of_vertices() << std::endl;
|
||||
std::cout << "number of (finite) Euclidean faces: " << dt.number_of_faces() << std::endl;
|
||||
std::cout << "number of hyperbolic faces: " << dt.number_of_hyperbolic_faces() << std::endl;
|
||||
std::cout << "number of faces having the origin as vertex: " << origin_faces << std::endl;
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -1,97 +0,0 @@
|
|||
#include <fstream>
|
||||
|
||||
// CGAL headers
|
||||
#include <CGAL/IO/io.h>
|
||||
|
||||
#include <CGAL/Exact_circular_kernel_2.h>
|
||||
|
||||
#include <CGAL/Hyperbolic_Delaunay_triangulation_2.h>
|
||||
#include <CGAL/Hyperbolic_Delaunay_triangulation_traits_2.h>
|
||||
|
||||
#include <CGAL/Random.h>
|
||||
#include <CGAL/point_generators_2.h>
|
||||
#include <CGAL/Timer.h>
|
||||
|
||||
typedef CGAL::Exact_circular_kernel_2 K;
|
||||
typedef CGAL::Hyperbolic_Delaunay_triangulation_traits_2<K> Gt;
|
||||
|
||||
typedef Gt::Point_2 Point_2;
|
||||
typedef Gt::Circle_2 Circle_2;
|
||||
typedef Gt::FT FT;
|
||||
|
||||
typedef CGAL::Hyperbolic_Delaunay_triangulation_2<Gt> Dt;
|
||||
|
||||
int main()
|
||||
{
|
||||
CGAL::Timer timer;
|
||||
typedef CGAL::Creator_uniform_2<FT, Point_2> Creator;
|
||||
|
||||
CGAL::Random_points_in_disc_2<Point_2, Creator> in_disc(FT(1));
|
||||
|
||||
int n = 100;
|
||||
std::cout << "Number of points: " << n << std::endl;
|
||||
|
||||
std::vector<Point_2> pts(n);
|
||||
std::vector<Point_2>::iterator ip;
|
||||
|
||||
// Generating n random points
|
||||
for (int i=0 ; i < n ; i++) {
|
||||
pts.at(i) = *in_disc;
|
||||
in_disc++;
|
||||
}
|
||||
|
||||
// std::vector<Point_2> pts;
|
||||
// std::vector<Point_2>::iterator ip;
|
||||
// Point_2 p;
|
||||
|
||||
// std::ifstream ifs("input-file");
|
||||
// while(ifs >> p) {
|
||||
// pts.push_back(p);
|
||||
// }
|
||||
// std::cout << "number of points " << std::distance(pts.begin(),pts.end()) << std::endl << std::endl;
|
||||
|
||||
std::cout << "check for hyperbolic faces during insertion" << std::endl;
|
||||
|
||||
timer.start();
|
||||
|
||||
Dt dt_during;
|
||||
|
||||
for(ip = pts.begin(); ip != pts.end(); ++ip) {
|
||||
dt_during.insert(*ip);
|
||||
}
|
||||
|
||||
timer.stop();
|
||||
|
||||
assert(dt_during.is_valid());
|
||||
|
||||
std::cout << "Number of (finite) vertices: " << dt_during.number_of_vertices() << std::endl;
|
||||
std::cout << "number of (finite) Euclidean faces: " << dt_during.number_of_faces() << std::endl;
|
||||
std::cout << "number of hyperbolic faces: " << dt_during.number_of_hyperbolic_faces() << std::endl;
|
||||
std::cout << "number of hyperbolic edges: " << dt_during.number_of_hyperbolic_edges() << std::endl;
|
||||
std::cout << "Time: " << timer.time() << std::endl << std::endl;
|
||||
|
||||
timer.reset();
|
||||
|
||||
timer.start();
|
||||
|
||||
std::cout << "check for hyperbolic faces only at the end" << std::endl;
|
||||
|
||||
Dt dt_end;
|
||||
|
||||
dt_end.insert(pts.begin(),pts.end());
|
||||
|
||||
timer.stop();
|
||||
|
||||
assert(dt_end.is_valid());
|
||||
|
||||
std::cout << "Number of (finite) vertices: " << dt_end.number_of_vertices() << std::endl;
|
||||
std::cout << "number of (finite) Euclidean faces: " << dt_end.number_of_faces() << std::endl;
|
||||
std::cout << "number of hyperbolic faces: " << dt_end.number_of_hyperbolic_faces() << std::endl;
|
||||
std::cout << "number of hyperbolic edges: " << dt_end.number_of_hyperbolic_edges() << std::endl;
|
||||
std::cout << "Time: " << timer.time() << std::endl;
|
||||
|
||||
timer.reset();
|
||||
|
||||
|
||||
return 0;
|
||||
}
|
||||
Loading…
Reference in New Issue