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Merge pull request #3895 from sloriot/CGAL-clean_up_tabs_trailingspaces 

Replace tabs with spaces and remove trailing whitespaces
This commit is contained in:
Sébastien Loriot 2020-03-26 18:53:33 +01:00
parent 6d2ada806c 8bb22d5b2c
commit 16fc8d1fe2
5995 changed files with 184489 additions and 184440 deletions
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2
.travis/generate_travis.sh
View File

@ -21,7 +21,7 @@ for f in *
do
if [ -d "$f/package_info/$f" ]
then
echo "$f " >> ./tmp.txt
echo "$f" >> ./tmp.txt
fi
done
LC_ALL=C sort ./tmp.txt > ./.travis/packages.txt

276
.travis/packages.txt
View File

@ -1,138 +1,138 @@
AABB_tree
Advancing_front_surface_reconstruction
Algebraic_foundations
Algebraic_kernel_d
Algebraic_kernel_for_circles
Algebraic_kernel_for_spheres
Alpha_shapes_2
Alpha_shapes_3
Apollonius_graph_2
Arithmetic_kernel
Arrangement_on_surface_2
BGL
Barycentric_coordinates_2
Boolean_set_operations_2
Bounding_volumes
Box_intersection_d
CGAL_Core
CGAL_ImageIO
CGAL_ipelets
Cartesian_kernel
Circular_kernel_2
Circular_kernel_3
Circulator
Classification
Combinatorial_map
Cone_spanners_2
Convex_decomposition_3
Convex_hull_2
Convex_hull_3
Convex_hull_d
Distance_2
Distance_3
Envelope_2
Envelope_3
Filtered_kernel
Generalized_map
Generator
Geomview
GraphicsView
HalfedgeDS
Hash_map
Heat_method_3
Homogeneous_kernel
Hyperbolic_triangulation_2
Inscribed_areas
Installation
Interpolation
Intersections_2
Intersections_3
Interval_skip_list
Interval_support
Inventor
Jet_fitting_3
Kernel_23
Kernel_d
LEDA
Linear_cell_complex
MacOSX
Maintenance
Matrix_search
Mesh_2
Mesh_3
Mesher_level
Minkowski_sum_2
Minkowski_sum_3
Modifier
Modular_arithmetic
Nef_2
Nef_3
Nef_S2
NewKernel_d
Number_types
OpenNL
Optimal_transportation_reconstruction_2
Optimisation_basic
Partition_2
Periodic_2_triangulation_2
Periodic_3_mesh_3
Periodic_3_triangulation_3
Periodic_4_hyperbolic_triangulation_2
Point_set_2
Point_set_3
Point_set_processing_3
Poisson_surface_reconstruction_3
Polygon
Polygon_mesh_processing
Polygonal_surface_reconstruction
Polyhedron
Polyhedron_IO
Polyline_simplification_2
Polynomial
Polytope_distance_d
Principal_component_analysis
Principal_component_analysis_LGPL
Profiling_tools
Property_map
QP_solver
Random_numbers
Ridges_3
STL_Extension
Scale_space_reconstruction_3
Scripts
SearchStructures
Segment_Delaunay_graph_2
Segment_Delaunay_graph_Linf_2
Set_movable_separability_2
Shape_detection
Skin_surface_3
Snap_rounding_2
Solver_interface
Spatial_searching
Spatial_sorting
Straight_skeleton_2
Stream_lines_2
Stream_support
Subdivision_method_3
Surface_mesh
Surface_mesh_approximation
Surface_mesh_deformation
Surface_mesh_parameterization
Surface_mesh_segmentation
Surface_mesh_shortest_path
Surface_mesh_simplification
Surface_mesh_skeletonization
Surface_mesh_topology
Surface_mesher
Surface_sweep_2
TDS_2
TDS_3
Testsuite
Three
Triangulation
Triangulation_2
Triangulation_3
Union_find
Visibility_2
Voronoi_diagram_2
wininst
AABB_tree
Advancing_front_surface_reconstruction
Algebraic_foundations
Algebraic_kernel_d
Algebraic_kernel_for_circles
Algebraic_kernel_for_spheres
Alpha_shapes_2
Alpha_shapes_3
Apollonius_graph_2
Arithmetic_kernel
Arrangement_on_surface_2
BGL
Barycentric_coordinates_2
Boolean_set_operations_2
Bounding_volumes
Box_intersection_d
CGAL_Core
CGAL_ImageIO
CGAL_ipelets
Cartesian_kernel
Circular_kernel_2
Circular_kernel_3
Circulator
Classification
Combinatorial_map
Cone_spanners_2
Convex_decomposition_3
Convex_hull_2
Convex_hull_3
Convex_hull_d
Distance_2
Distance_3
Envelope_2
Envelope_3
Filtered_kernel
Generalized_map
Generator
Geomview
GraphicsView
HalfedgeDS
Hash_map
Heat_method_3
Homogeneous_kernel
Hyperbolic_triangulation_2
Inscribed_areas
Installation
Interpolation
Intersections_2
Intersections_3
Interval_skip_list
Interval_support
Inventor
Jet_fitting_3
Kernel_23
Kernel_d
LEDA
Linear_cell_complex
MacOSX
Maintenance
Matrix_search
Mesh_2
Mesh_3
Mesher_level
Minkowski_sum_2
Minkowski_sum_3
Modifier
Modular_arithmetic
Nef_2
Nef_3
Nef_S2
NewKernel_d
Number_types
OpenNL
Optimal_transportation_reconstruction_2
Optimisation_basic
Partition_2
Periodic_2_triangulation_2
Periodic_3_mesh_3
Periodic_3_triangulation_3
Periodic_4_hyperbolic_triangulation_2
Point_set_2
Point_set_3
Point_set_processing_3
Poisson_surface_reconstruction_3
Polygon
Polygon_mesh_processing
Polygonal_surface_reconstruction
Polyhedron
Polyhedron_IO
Polyline_simplification_2
Polynomial
Polytope_distance_d
Principal_component_analysis
Principal_component_analysis_LGPL
Profiling_tools
Property_map
QP_solver
Random_numbers
Ridges_3
STL_Extension
Scale_space_reconstruction_3
Scripts
SearchStructures
Segment_Delaunay_graph_2
Segment_Delaunay_graph_Linf_2
Set_movable_separability_2
Shape_detection
Skin_surface_3
Snap_rounding_2
Solver_interface
Spatial_searching
Spatial_sorting
Straight_skeleton_2
Stream_lines_2
Stream_support
Subdivision_method_3
Surface_mesh
Surface_mesh_approximation
Surface_mesh_deformation
Surface_mesh_parameterization
Surface_mesh_segmentation
Surface_mesh_shortest_path
Surface_mesh_simplification
Surface_mesh_skeletonization
Surface_mesh_topology
Surface_mesher
Surface_sweep_2
TDS_2
TDS_3
Testsuite
Three
Triangulation
Triangulation_2
Triangulation_3
Union_find
Visibility_2
Voronoi_diagram_2
wininst

4
AABB_tree/benchmark/AABB_tree/CMakeLists.txt
View File

@ -10,7 +10,7 @@ if ( CGAL_FOUND )
include( ${CGAL_USE_FILE} )
else ()
message(STATUS "This project requires the CGAL library, and will not be compiled.")
return()
return()
endif()
@ -20,7 +20,7 @@ find_package( Boost REQUIRED )
# include for local directory
if ( NOT Boost_FOUND )
message(STATUS "This project requires the Boost library, and will not be compiled.")
return()
return()
endif()
# include for local package

24
AABB_tree/benchmark/AABB_tree/test.cpp
View File

@ -39,7 +39,7 @@ void naive_test(int k, const char* fname,
CGAL::Aff_transformation_3<K> init2(CGAL::TRANSLATION, - K::Vector_3(
(box.xmax()-box.xmin()),0,0));
PMP::transform(init2, tm2);
tmTree.build();
K::Vector_3 unit_vec = (2.0/k * K::Vector_3((box.xmax()-box.xmin()),
0,
@ -56,9 +56,9 @@ void naive_test(int k, const char* fname,
rot[7] = std::sin(CGAL_PI/4.0);
rot[8] = std::cos(CGAL_PI/4.0);
CGAL::Aff_transformation_3<K> R(rot[0], rot[1], rot[2],
rot[3], rot[4], rot[5],
rot[3], rot[4], rot[5],
rot[6], rot[7], rot[8]);
CGAL::Side_of_triangle_mesh<Surface_mesh, K> sotm1(tm);
for(int i=1; i<k+1; ++i)
{
@ -68,10 +68,10 @@ void naive_test(int k, const char* fname,
tmTree2.build();
if(tmTree2.do_intersect(tmTree))
++nb_inter;
else
else
{
if(sotm1(tm2.point(*tm2.vertices().begin())) != CGAL::ON_UNBOUNDED_SIDE)
{
{
++nb_include;
}
else
@ -101,16 +101,16 @@ void test_no_collision(int k, const char* fname,
CGAL::Aff_transformation_3<K> init2(CGAL::TRANSLATION, - K::Vector_3(
(box.xmax()-box.xmin()),0,0));
PMP::transform(init2, tm2);
tmTree.build();
tmTree2.build();
typedef boost::property_map<Surface_mesh, CGAL::vertex_point_t>::type VPM;
VPM vpm2 = get(CGAL::vertex_point, tm2);
K::Vector_3 unit_vec = (2.0/k * K::Vector_3((box.xmax()-box.xmin()),
0,
0));
CGAL::Side_of_triangle_mesh<Surface_mesh, K,
VPM, Tree> sotm1(tmTree);
for(int i=1; i<k+1; ++i)
@ -126,7 +126,7 @@ void test_no_collision(int k, const char* fname,
rot[7] = std::sin(i*CGAL_PI/4.0);
rot[8] = std::cos(i*CGAL_PI/4.0);
CGAL::Aff_transformation_3<K> R(rot[0], rot[1], rot[2],
rot[3], rot[4], rot[5],
rot[3], rot[4], rot[5],
rot[6], rot[7], rot[8]);
CGAL::Aff_transformation_3<K> T1 = CGAL::Aff_transformation_3<K>(CGAL::TRANSLATION, i*unit_vec);
CGAL::Aff_transformation_3<K> transfo = R*T1;
@ -134,10 +134,10 @@ void test_no_collision(int k, const char* fname,
CGAL::Interval_nt_advanced::Protector protector;
if(tmTree2.do_intersect(tmTree))
++nb_inter;
else
else
{
if(sotm1(transfo.transform(vpm2[*tm2.vertices().begin()])) != CGAL::ON_UNBOUNDED_SIDE)
{
{
++nb_include;
}
else
@ -158,7 +158,7 @@ int main(int argc, const char** argv)
int k = (argc>1) ? atoi(argv[1]) : 10;
const char* path = (argc>2)?argv[2]:"data/handle"
".off";
std::cout<< k<<" steps in "<<path<<std::endl;
int nb_inter(0), nb_no_inter(0), nb_include(0),
naive_inter(0), naive_no_inter(0), naive_include(0);

2
AABB_tree/demo/AABB_tree/CMakeLists.txt
View File

@ -46,7 +46,7 @@ if(CGAL_FOUND AND CGAL_Qt5_FOUND AND Qt5_FOUND)
"${CMAKE_CURRENT_BINARY_DIR}/Viewer_moc.cpp"
"${CMAKE_CURRENT_BINARY_DIR}/Scene_moc.cpp" )
add_executable ( AABB_demo AABB_demo.cpp ${UI_FILES} ${CGAL_Qt5_RESOURCE_FILES}
add_executable ( AABB_demo AABB_demo.cpp ${UI_FILES} ${CGAL_Qt5_RESOURCE_FILES}
#${CGAL_Qt5_MOC_FILES}
)
# Link with Qt libraries

166
AABB_tree/demo/AABB_tree/Color_ramp.h
View File

@ -4,103 +4,103 @@
class Color_ramp
{
private :
int m_nodes[256];
unsigned char m_colors[4][256];
int m_nodes[256];
unsigned char m_colors[4][256];
public :
Color_ramp()
{
build_thermal();
}
~Color_ramp() {}
Color_ramp()
{
build_thermal();
}
~Color_ramp() {}
public :
unsigned char r(unsigned int index) const { return m_colors[0][index%256]; }
unsigned char g(unsigned int index) const { return m_colors[1][index%256]; }
unsigned char b(unsigned int index) const { return m_colors[2][index%256]; }
unsigned char r(unsigned int index) const { return m_colors[0][index%256]; }
unsigned char g(unsigned int index) const { return m_colors[1][index%256]; }
unsigned char b(unsigned int index) const { return m_colors[2][index%256]; }
private:
void rebuild()
{
// build nodes
m_colors[3][0] = 1;
m_colors[3][255] = 1;
unsigned int nb_nodes = 0;
for(int i=0;i<256;i++)
{
if(m_colors[3][i])
{
m_nodes[nb_nodes] = i;
nb_nodes++;
}
}
void rebuild()
{
// build nodes
m_colors[3][0] = 1;
m_colors[3][255] = 1;
unsigned int nb_nodes = 0;
for(int i=0;i<256;i++)
{
if(m_colors[3][i])
{
m_nodes[nb_nodes] = i;
nb_nodes++;
}
}
// build color_ramp
for(int k=0;k<3;k++)
for(unsigned int i=0;i<(nb_nodes-1);i++)
{
int x1 = m_nodes[i];
int x2 = m_nodes[i+1];
int y1 = m_colors[k][x1];
int y2 = m_colors[k][x2];
float a = (float)(y2-y1) / (float)(x2-x1);
float b = (float)y1 - a*(float)x1;
for(int j=x1;j<x2;j++)
m_colors[k][j] = (unsigned char)(a*(float)j+b);
}
}
// build color_ramp
for(int k=0;k<3;k++)
for(unsigned int i=0;i<(nb_nodes-1);i++)
{
int x1 = m_nodes[i];
int x2 = m_nodes[i+1];
int y1 = m_colors[k][x1];
int y2 = m_colors[k][x2];
float a = (float)(y2-y1) / (float)(x2-x1);
float b = (float)y1 - a*(float)x1;
for(int j=x1;j<x2;j++)
m_colors[k][j] = (unsigned char)(a*(float)j+b);
}
}
void reset()
{
for(int i=1;i<=254;i++)
m_colors[3][i] = 0;
m_colors[3][0] = 1;
m_colors[3][255] = 1;
}
void reset()
{
for(int i=1;i<=254;i++)
m_colors[3][i] = 0;
m_colors[3][0] = 1;
m_colors[3][255] = 1;
}
public:
void add_node(unsigned int index,
unsigned char r,
unsigned char g,
unsigned char b)
{
m_colors[3][index] = 1;
m_colors[0][index] = r;
m_colors[1][index] = g;
m_colors[2][index] = b;
}
void add_node(unsigned int index,
unsigned char r,
unsigned char g,
unsigned char b)
{
m_colors[3][index] = 1;
m_colors[0][index] = r;
m_colors[1][index] = g;
m_colors[2][index] = b;
}
void build_red()
{
reset();
m_colors[3][0] = 1;m_colors[0][0] = 128;m_colors[1][0] = 0;m_colors[2][0] = 0;
m_colors[3][80] = 1;m_colors[0][80] = 255;m_colors[1][80] = 0;m_colors[2][80] = 0;
m_colors[3][160] = 1;m_colors[0][160] = 255;m_colors[1][160] = 128;m_colors[2][160] = 0;
m_colors[3][255] = 1;m_colors[0][255] = 255;m_colors[1][255] = 255;m_colors[2][255] = 255;
rebuild();
}
void build_red()
{
reset();
m_colors[3][0] = 1;m_colors[0][0] = 128;m_colors[1][0] = 0;m_colors[2][0] = 0;
m_colors[3][80] = 1;m_colors[0][80] = 255;m_colors[1][80] = 0;m_colors[2][80] = 0;
m_colors[3][160] = 1;m_colors[0][160] = 255;m_colors[1][160] = 128;m_colors[2][160] = 0;
m_colors[3][255] = 1;m_colors[0][255] = 255;m_colors[1][255] = 255;m_colors[2][255] = 255;
rebuild();
}
void build_thermal()
{
reset();
m_colors[3][0] = 1;m_colors[0][0] = 0;m_colors[1][0] = 0;m_colors[2][0] = 0;
m_colors[3][70] = 1;m_colors[0][70] = 128;m_colors[1][70] = 0;m_colors[2][70] = 0;
m_colors[3][165] = 1;m_colors[0][165] = 255;m_colors[1][165] = 128;m_colors[2][165] = 0;
m_colors[3][240] = 1;m_colors[0][240] = 255;m_colors[1][240] = 191;m_colors[2][240] = 128;
m_colors[3][255] = 1;m_colors[0][255] = 255;m_colors[1][255] = 255;m_colors[2][255] = 255;
rebuild();
}
void build_thermal()
{
reset();
m_colors[3][0] = 1;m_colors[0][0] = 0;m_colors[1][0] = 0;m_colors[2][0] = 0;
m_colors[3][70] = 1;m_colors[0][70] = 128;m_colors[1][70] = 0;m_colors[2][70] = 0;
m_colors[3][165] = 1;m_colors[0][165] = 255;m_colors[1][165] = 128;m_colors[2][165] = 0;
m_colors[3][240] = 1;m_colors[0][240] = 255;m_colors[1][240] = 191;m_colors[2][240] = 128;
m_colors[3][255] = 1;m_colors[0][255] = 255;m_colors[1][255] = 255;m_colors[2][255] = 255;
rebuild();
}
void build_blue()
{
reset();
m_colors[3][0] = 1;m_colors[0][0] = 0;m_colors[1][0] = 0;m_colors[2][0] = 128;
m_colors[3][80] = 1;m_colors[0][80] = 0;m_colors[1][80] = 0;m_colors[2][80] = 255;
m_colors[3][160] = 1;m_colors[0][160] = 0;m_colors[1][160] = 255;m_colors[2][160] = 255;
m_colors[3][255] = 1;m_colors[0][255] = 255;m_colors[1][255] = 255;m_colors[2][255] = 255;
rebuild();
}
void build_blue()
{
reset();
m_colors[3][0] = 1;m_colors[0][0] = 0;m_colors[1][0] = 0;m_colors[2][0] = 128;
m_colors[3][80] = 1;m_colors[0][80] = 0;m_colors[1][80] = 0;m_colors[2][80] = 255;
m_colors[3][160] = 1;m_colors[0][160] = 0;m_colors[1][160] = 255;m_colors[2][160] = 255;
m_colors[3][255] = 1;m_colors[0][255] = 255;m_colors[1][255] = 255;m_colors[2][255] = 255;
rebuild();
}
};
#endif // _COLOR_RAMP_H

380
AABB_tree/demo/AABB_tree/MainWindow.cpp
View File

@ -16,288 +16,288 @@
MainWindow::MainWindow(QWidget* parent)
: CGAL::Qt::DemosMainWindow(parent)
{
ui = new Ui::MainWindow;
ui->setupUi(this);
ui = new Ui::MainWindow;
ui->setupUi(this);
// saves some pointers from ui, for latter use.
m_pViewer = ui->viewer;
// saves some pointers from ui, for latter use.
m_pViewer = ui->viewer;
// does not save the state of the viewer
m_pViewer->setStateFileName(QString());
// does not save the state of the viewer
m_pViewer->setStateFileName(QString());
// accepts drop events
setAcceptDrops(true);
// setups scene
// accepts drop events
setAcceptDrops(true);
// setups scene
m_pScene = new Scene();
m_pViewer->setScene(m_pScene);
m_pViewer->setScene(m_pScene);
m_pViewer->setManipulatedFrame(m_pScene->manipulatedFrame());
// connects actionQuit (Ctrl+Q) and qApp->quit()
connect(ui->actionQuit, SIGNAL(triggered()),
this, SLOT(quit()));
// connects actionQuit (Ctrl+Q) and qApp->quit()
connect(ui->actionQuit, SIGNAL(triggered()),
this, SLOT(quit()));
this->addRecentFiles(ui->menuFile, ui->actionQuit);
connect(this, SIGNAL(openRecentFile(QString)),
this, SLOT(open(QString)));
this->addRecentFiles(ui->menuFile, ui->actionQuit);
connect(this, SIGNAL(openRecentFile(QString)),
this, SLOT(open(QString)));
readSettings();
readSettings();
}
MainWindow::~MainWindow()
{
delete ui;
delete ui;
}
void MainWindow::dragEnterEvent(QDragEnterEvent *event)
{
if (event->mimeData()->hasFormat("text/uri-list"))
event->acceptProposedAction();
if (event->mimeData()->hasFormat("text/uri-list"))
event->acceptProposedAction();
}
void MainWindow::dropEvent(QDropEvent *event)
{
Q_FOREACH(QUrl url, event->mimeData()->urls()) {
QString filename = url.toLocalFile();
if(!filename.isEmpty()) {
QTextStream(stderr) << QString("dropEvent(\"%1\")\n").arg(filename);
open(filename);
}
}
event->acceptProposedAction();
Q_FOREACH(QUrl url, event->mimeData()->urls()) {
QString filename = url.toLocalFile();
if(!filename.isEmpty()) {
QTextStream(stderr) << QString("dropEvent(\"%1\")\n").arg(filename);
open(filename);
}
}
event->acceptProposedAction();
}
void MainWindow::updateViewerBBox()
{
m_pScene->update_bbox();
const Scene::Bbox bbox = m_pScene->bbox();
const double xmin = bbox.xmin();
const double ymin = bbox.ymin();
const double zmin = bbox.zmin();
const double xmax = bbox.xmax();
const double ymax = bbox.ymax();
const double zmax = bbox.zmax();
CGAL::qglviewer::Vec
vec_min(xmin, ymin, zmin),
vec_max(xmax, ymax, zmax);
m_pViewer->setSceneBoundingBox(vec_min,vec_max);
m_pViewer->camera()->showEntireScene();
m_pScene->update_bbox();
const Scene::Bbox bbox = m_pScene->bbox();
const double xmin = bbox.xmin();
const double ymin = bbox.ymin();
const double zmin = bbox.zmin();
const double xmax = bbox.xmax();
const double ymax = bbox.ymax();
const double zmax = bbox.zmax();
CGAL::qglviewer::Vec
vec_min(xmin, ymin, zmin),
vec_max(xmax, ymax, zmax);
m_pViewer->setSceneBoundingBox(vec_min,vec_max);
m_pViewer->camera()->showEntireScene();
}
void MainWindow::open(QString filename)
{
QFileInfo fileinfo(filename);
if(fileinfo.isFile() && fileinfo.isReadable())
{
int index = m_pScene->open(filename);
if(index >= 0)
{
QSettings settings;
settings.setValue("OFF open directory",
fileinfo.absoluteDir().absolutePath());
this->addToRecentFiles(filename);
QFileInfo fileinfo(filename);
if(fileinfo.isFile() && fileinfo.isReadable())
{
int index = m_pScene->open(filename);
if(index >= 0)
{
QSettings settings;
settings.setValue("OFF open directory",
fileinfo.absoluteDir().absolutePath());
this->addToRecentFiles(filename);
// update bbox
updateViewerBBox();
// update bbox
updateViewerBBox();
m_pViewer->update();
}
}
}
}
}
void MainWindow::readSettings()
{
this->readState("MainWindow", Size|State);
this->readState("MainWindow", Size|State);
}
void MainWindow::writeSettings()
{
this->writeState("MainWindow");
std::cerr << "Write setting... done.\n";
this->writeState("MainWindow");
std::cerr << "Write setting... done.\n";
}
void MainWindow::quit()
{
writeSettings();
close();
writeSettings();
close();
}
void MainWindow::closeEvent(QCloseEvent *event)
{
writeSettings();
event->accept();
writeSettings();
event->accept();
}
void MainWindow::on_actionLoadPolyhedron_triggered()
{
QSettings settings;
QString directory = settings.value("OFF open directory",
QDir::current().dirName()).toString();
QStringList filenames =
QFileDialog::getOpenFileNames(this,
tr("Load polyhedron..."),
directory,
tr("OFF files (*.off)\n"
"All files (*)"));
if(!filenames.isEmpty()) {
Q_FOREACH(QString filename, filenames) {
open(filename);
}
}
QSettings settings;
QString directory = settings.value("OFF open directory",
QDir::current().dirName()).toString();
QStringList filenames =
QFileDialog::getOpenFileNames(this,
tr("Load polyhedron..."),
directory,
tr("OFF files (*.off)\n"
"All files (*)"));
if(!filenames.isEmpty()) {
Q_FOREACH(QString filename, filenames) {
open(filename);
}
}
}
void MainWindow::setAddKeyFrameKeyboardModifiers(::Qt::KeyboardModifiers m)
{
m_pViewer->setAddKeyFrameKeyboardModifiers(m);
m_pViewer->setAddKeyFrameKeyboardModifiers(m);
}
void MainWindow::on_actionInside_points_triggered()
{
bool ok;
const unsigned int nb_points = (unsigned)
QInputDialog::getInt(NULL, "#Points",
"#Points:",10000,1,100000000,9,&ok);
bool ok;
if(!ok)
return;
const unsigned int nb_points = (unsigned)
QInputDialog::getInt(NULL, "#Points",
"#Points:",10000,1,100000000,9,&ok);
QApplication::setOverrideCursor(Qt::WaitCursor);
m_pScene->generate_inside_points(nb_points);
QApplication::restoreOverrideCursor();
if(!ok)
return;
QApplication::setOverrideCursor(Qt::WaitCursor);
m_pScene->generate_inside_points(nb_points);
QApplication::restoreOverrideCursor();
m_pViewer->update();
}
void MainWindow::on_actionPoints_in_interval_triggered()
{
bool ok;
const unsigned int nb_points = (unsigned)
bool ok;
const unsigned int nb_points = (unsigned)
QInputDialog::getInt(NULL, "#Points",
"#Points:",10000,1,100000000,9,&ok);
"#Points:",10000,1,100000000,9,&ok);
if(!ok)
return;
if(!ok)
return;
const double min =
QInputDialog::getDouble(NULL, "min",
"Min:",-0.1,-1000.0,1000.0,9,&ok);
if(!ok)
return;
const double max =
QInputDialog::getDouble(NULL, "max",
"Max:",0.1,-1000.0,1000.0,9,&ok);
if(!ok)
return;
const double min =
QInputDialog::getDouble(NULL, "min",
"Min:",-0.1,-1000.0,1000.0,9,&ok);
if(!ok)
return;
const double max =
QInputDialog::getDouble(NULL, "max",
"Max:",0.1,-1000.0,1000.0,9,&ok);
if(!ok)
return;
QApplication::setOverrideCursor(Qt::WaitCursor);
m_pScene->generate_points_in(nb_points,min,max);
QApplication::restoreOverrideCursor();
QApplication::setOverrideCursor(Qt::WaitCursor);
m_pScene->generate_points_in(nb_points,min,max);
QApplication::restoreOverrideCursor();
m_pViewer->update();
}
void MainWindow::on_actionBoundary_segments_triggered()
{
bool ok;
const unsigned int nb_slices = (unsigned)
QInputDialog::getInt(NULL, "#Slices",
"Slices:",100,1,1000000,8,&ok);
bool ok;
if(!ok)
return;
const unsigned int nb_slices = (unsigned)
QInputDialog::getInt(NULL, "#Slices",
"Slices:",100,1,1000000,8,&ok);
QApplication::setOverrideCursor(Qt::WaitCursor);
m_pScene->generate_boundary_segments(nb_slices);
QApplication::restoreOverrideCursor();
if(!ok)
return;
QApplication::setOverrideCursor(Qt::WaitCursor);
m_pScene->generate_boundary_segments(nb_slices);
QApplication::restoreOverrideCursor();
m_pViewer->update();
}
void MainWindow::on_actionBoundary_points_triggered()
{
bool ok;
bool ok;
const unsigned int nb_points = (unsigned)
QInputDialog::getInt(NULL, "#Points",
"Points:",1000,1,10000000,8,&ok);
const unsigned int nb_points = (unsigned)
QInputDialog::getInt(NULL, "#Points",
"Points:",1000,1,10000000,8,&ok);
if(!ok)
return;
if(!ok)
return;
QApplication::setOverrideCursor(Qt::WaitCursor);
m_pScene->generate_boundary_points(nb_points);
QApplication::restoreOverrideCursor();
QApplication::setOverrideCursor(Qt::WaitCursor);
m_pScene->generate_boundary_points(nb_points);
QApplication::restoreOverrideCursor();
m_pViewer->update();
}
void MainWindow::on_actionEdge_points_triggered()
{
bool ok;
bool ok;
const unsigned int nb_points = (unsigned)
QInputDialog::getInt(NULL, "#Points",
"Points:",1000,1,10000000,8,&ok);
const unsigned int nb_points = (unsigned)
QInputDialog::getInt(NULL, "#Points",
"Points:",1000,1,10000000,8,&ok);
if(!ok)
return;
if(!ok)
return;
QApplication::setOverrideCursor(Qt::WaitCursor);
m_pScene->generate_edge_points(nb_points);
QApplication::restoreOverrideCursor();
QApplication::setOverrideCursor(Qt::WaitCursor);
m_pScene->generate_edge_points(nb_points);
QApplication::restoreOverrideCursor();
m_pViewer->update();
}
void MainWindow::on_actionBench_distances_triggered()
{
bool ok;
const double duration = QInputDialog::getDouble(NULL, "Duration",
"Duration (s):",1.0,0.01,1000,8,&ok);
if(!ok)
return;
bool ok;
const double duration = QInputDialog::getDouble(NULL, "Duration",
"Duration (s):",1.0,0.01,1000,8,&ok);
if(!ok)
return;
QApplication::setOverrideCursor(Qt::WaitCursor);
std::cout << std::endl << "Benchmark distances" << std::endl;
m_pScene->benchmark_distances(duration);
QApplication::restoreOverrideCursor();
QApplication::setOverrideCursor(Qt::WaitCursor);
std::cout << std::endl << "Benchmark distances" << std::endl;
m_pScene->benchmark_distances(duration);
QApplication::restoreOverrideCursor();
}
void MainWindow::on_actionBench_intersections_triggered()
{
bool ok;
const double duration = QInputDialog::getDouble(NULL, "Duration",
"Duration (s):",1.0,0.01,1000.0,8,&ok);
if(!ok)
return;
bool ok;
const double duration = QInputDialog::getDouble(NULL, "Duration",
"Duration (s):",1.0,0.01,1000.0,8,&ok);
if(!ok)
return;
QApplication::setOverrideCursor(Qt::WaitCursor);
std::cout << std::endl << "Benchmark intersections" << std::endl;
m_pScene->benchmark_intersections(duration);
QApplication::restoreOverrideCursor();
QApplication::setOverrideCursor(Qt::WaitCursor);
std::cout << std::endl << "Benchmark intersections" << std::endl;
m_pScene->benchmark_intersections(duration);
QApplication::restoreOverrideCursor();
}
void MainWindow::on_actionUnsigned_distance_function_to_facets_triggered()
{
QApplication::setOverrideCursor(Qt::WaitCursor);
QApplication::setOverrideCursor(Qt::WaitCursor);
m_pScene->activate_cutting_plane();
m_pScene->unsigned_distance_function();
QApplication::restoreOverrideCursor();
m_pScene->unsigned_distance_function();
QApplication::restoreOverrideCursor();
m_pViewer->update();
}
void MainWindow::on_actionUnsigned_distance_function_to_edges_triggered()
{
QApplication::setOverrideCursor(Qt::WaitCursor);
QApplication::setOverrideCursor(Qt::WaitCursor);
m_pScene->activate_cutting_plane();
m_pScene->unsigned_distance_function_to_edges();
QApplication::restoreOverrideCursor();
m_pScene->unsigned_distance_function_to_edges();
QApplication::restoreOverrideCursor();
m_pViewer->update();
}
void MainWindow::on_actionSigned_distance_function_to_facets_triggered()
{
QApplication::setOverrideCursor(Qt::WaitCursor);
QApplication::setOverrideCursor(Qt::WaitCursor);
m_pScene->activate_cutting_plane();
m_pScene->signed_distance_function();
QApplication::restoreOverrideCursor();
m_pScene->signed_distance_function();
QApplication::restoreOverrideCursor();
m_pViewer->update();
}
@ -318,19 +318,19 @@ void MainWindow::on_actionCutting_plane_none_triggered()
void MainWindow::on_actionView_polyhedron_triggered()
{
m_pScene->toggle_view_poyhedron();
m_pScene->toggle_view_poyhedron();
m_pViewer->update();
}
void MainWindow::on_actionView_points_triggered()
{
m_pScene->toggle_view_points();
m_pScene->toggle_view_points();
m_pViewer->update();
}
void MainWindow::on_actionView_segments_triggered()
{
m_pScene->toggle_view_segments();
m_pScene->toggle_view_segments();
m_pViewer->update();
}
@ -342,13 +342,13 @@ void MainWindow::on_actionView_cutting_plane_triggered()
void MainWindow::on_actionClear_points_triggered()
{
m_pScene->clear_points();
m_pScene->clear_points();
m_pViewer->update();
}
void MainWindow::on_actionClear_segments_triggered()
{
m_pScene->clear_segments();
m_pScene->clear_segments();
m_pViewer->update();
}
@ -360,52 +360,52 @@ void MainWindow::on_actionClear_cutting_plane_triggered()
void MainWindow::on_actionRefine_bisection_triggered()
{
bool ok;
const double max_len =
QInputDialog::getDouble(NULL, "Max edge len",
"Max edge len:",0.1,0.001,100.0,9,&ok);
if(!ok)
return;
bool ok;
const double max_len =
QInputDialog::getDouble(NULL, "Max edge len",
"Max edge len:",0.1,0.001,100.0,9,&ok);
if(!ok)
return;
QApplication::setOverrideCursor(Qt::WaitCursor);
m_pScene->refine_bisection(max_len * max_len);
QApplication::restoreOverrideCursor();
QApplication::setOverrideCursor(Qt::WaitCursor);
m_pScene->refine_bisection(max_len * max_len);
QApplication::restoreOverrideCursor();
m_pViewer->update();
}
void MainWindow::on_actionBench_memory_triggered()
{
QApplication::setOverrideCursor(Qt::WaitCursor);
m_pScene->bench_memory();
QApplication::restoreOverrideCursor();
QApplication::setOverrideCursor(Qt::WaitCursor);
m_pScene->bench_memory();
QApplication::restoreOverrideCursor();
}
void MainWindow::on_actionBench_construction_triggered()
{
QApplication::setOverrideCursor(Qt::WaitCursor);
m_pScene->bench_construction();
QApplication::restoreOverrideCursor();
QApplication::setOverrideCursor(Qt::WaitCursor);
m_pScene->bench_construction();
QApplication::restoreOverrideCursor();
}
void MainWindow::on_actionBench_intersections_vs_nbt_triggered()
{
QApplication::setOverrideCursor(Qt::WaitCursor);
m_pScene->bench_intersections_vs_nbt();
QApplication::restoreOverrideCursor();
QApplication::setOverrideCursor(Qt::WaitCursor);
m_pScene->bench_intersections_vs_nbt();
QApplication::restoreOverrideCursor();
}
void MainWindow::on_actionBench_distances_vs_nbt_triggered()
{
QApplication::setOverrideCursor(Qt::WaitCursor);
m_pScene->bench_distances_vs_nbt();
QApplication::restoreOverrideCursor();
QApplication::setOverrideCursor(Qt::WaitCursor);
m_pScene->bench_distances_vs_nbt();
QApplication::restoreOverrideCursor();
}
void MainWindow::on_actionRefine_loop_triggered()
{
QApplication::setOverrideCursor(Qt::WaitCursor);
m_pScene->refine_loop();
QApplication::restoreOverrideCursor();
QApplication::setOverrideCursor(Qt::WaitCursor);
m_pScene->refine_loop();
QApplication::restoreOverrideCursor();
m_pViewer->update();
}

96
AABB_tree/demo/AABB_tree/MainWindow.h
View File

@ -9,79 +9,79 @@ class QDropEvent;
class Scene;
class Viewer;
namespace Ui {
class MainWindow;
class MainWindow;
}
class MainWindow :
public CGAL::Qt::DemosMainWindow
class MainWindow :
public CGAL::Qt::DemosMainWindow
{
Q_OBJECT
Q_OBJECT
public:
MainWindow(QWidget* parent = 0);
~MainWindow();
MainWindow(QWidget* parent = 0);
~MainWindow();
public slots:
void updateViewerBBox();
void open(QString filename);
void setAddKeyFrameKeyboardModifiers(Qt::KeyboardModifiers);
public slots:
void updateViewerBBox();
void open(QString filename);
void setAddKeyFrameKeyboardModifiers(Qt::KeyboardModifiers);
protected slots:
protected slots:
// settings
void quit();
void readSettings();
void writeSettings();
// settings
void quit();
void readSettings();
void writeSettings();
// drag & drop
void dropEvent(QDropEvent *event);
void closeEvent(QCloseEvent *event);
void dragEnterEvent(QDragEnterEvent *event);
// drag & drop
void dropEvent(QDropEvent *event);
void closeEvent(QCloseEvent *event);
void dragEnterEvent(QDragEnterEvent *event);
// file menu
void on_actionLoadPolyhedron_triggered();
// file menu
void on_actionLoadPolyhedron_triggered();
// edit menu
// edit menu
void on_actionSave_snapshot_triggered();
void on_actionCopy_snapshot_triggered();
void on_actionClear_points_triggered();
void on_actionClear_segments_triggered();
void on_actionClear_points_triggered();
void on_actionClear_segments_triggered();
void on_actionClear_cutting_plane_triggered();
// algorithm menu
// algorithm menu
void on_actionRefine_loop_triggered();
void on_actionEdge_points_triggered();
void on_actionInside_points_triggered();
void on_actionBoundary_points_triggered();
void on_actionRefine_bisection_triggered();
void on_actionBoundary_segments_triggered();
void on_actionEdge_points_triggered();
void on_actionInside_points_triggered();
void on_actionBoundary_points_triggered();
void on_actionRefine_bisection_triggered();
void on_actionBoundary_segments_triggered();
void on_actionPoints_in_interval_triggered();
void on_actionSigned_distance_function_to_facets_triggered();
void on_actionUnsigned_distance_function_to_edges_triggered();
void on_actionUnsigned_distance_function_to_facets_triggered();
void on_actionSigned_distance_function_to_facets_triggered();
void on_actionUnsigned_distance_function_to_edges_triggered();
void on_actionUnsigned_distance_function_to_facets_triggered();
void on_actionIntersection_cutting_plane_triggered();
void on_actionCutting_plane_none_triggered();
// benchmark menu
void on_actionBench_memory_triggered();
void on_actionBench_distances_triggered();
void on_actionBench_intersections_triggered();
// benchmark menu
void on_actionBench_memory_triggered();
void on_actionBench_distances_triggered();
void on_actionBench_intersections_triggered();
// benchmark against #triangles
void on_actionBench_construction_triggered();
void on_actionBench_distances_vs_nbt_triggered();
void on_actionBench_intersections_vs_nbt_triggered();
// benchmark against #triangles
void on_actionBench_construction_triggered();
void on_actionBench_distances_vs_nbt_triggered();
void on_actionBench_intersections_vs_nbt_triggered();
// view menu
void on_actionView_points_triggered();
void on_actionView_segments_triggered();
void on_actionView_polyhedron_triggered();
// view menu
void on_actionView_points_triggered();
void on_actionView_segments_triggered();
void on_actionView_polyhedron_triggered();
void on_actionView_cutting_plane_triggered();
private:
Scene* m_pScene;
Viewer* m_pViewer;
Ui::MainWindow* ui;
Scene* m_pScene;
Viewer* m_pViewer;
Ui::MainWindow* ui;
};
#endif // ifndef MAINWINDOW_H

284
AABB_tree/demo/AABB_tree/Refiner.h
View File

@ -5,190 +5,190 @@
#include <CGAL/Polyhedron_3.h>
#include <queue>
template <class Kernel, class Polyhedron>
template <class Kernel, class Polyhedron>
class CEdge
{
public:
typedef typename Kernel::FT FT;
typedef typename Polyhedron::Halfedge_handle Halfedge_handle;
typedef typename Kernel::FT FT;
typedef typename Polyhedron::Halfedge_handle Halfedge_handle;
private:
FT m_sqlen;
Halfedge_handle m_he;
FT m_sqlen;
Halfedge_handle m_he;
public:
// life cycle
CEdge(const Halfedge_handle& he)
{
m_sqlen = squared_len(he);
m_he = he;
}
CEdge(const CEdge& edge)
: m_sqlen(edge.sqlen()),
m_he(edge.he())
{
}
~CEdge() {}
// life cycle
CEdge(const Halfedge_handle& he)
{
m_sqlen = squared_len(he);
m_he = he;
}
CEdge(const CEdge& edge)
: m_sqlen(edge.sqlen()),
m_he(edge.he())
{
}
~CEdge() {}
public:
// squared length of an edge
static FT squared_len(Halfedge_handle he)
{
return CGAL::squared_distance(he->vertex()->point(),
he->opposite()->vertex()->point());
}
// squared length of an edge
static FT squared_len(Halfedge_handle he)
{
return CGAL::squared_distance(he->vertex()->point(),
he->opposite()->vertex()->point());
}
public:
// accessors
FT& sqlen() { return m_sqlen; }
const FT sqlen() const { return m_sqlen; }
// accessors
FT& sqlen() { return m_sqlen; }
const FT sqlen() const { return m_sqlen; }
Halfedge_handle he() { return m_he; }
const Halfedge_handle he() const { return m_he; }
Halfedge_handle he() { return m_he; }
const Halfedge_handle he() const { return m_he; }
};
// functor for priority queue
template<class Edge>
struct less // read more priority
{
bool operator()(const Edge& e1,
const Edge& e2) const
{
return e1.sqlen() < e2.sqlen();
}
{
bool operator()(const Edge& e1,
const Edge& e2) const
{
return e1.sqlen() < e2.sqlen();
}
};
template <class Kernel, class Polyhedron>
template <class Kernel, class Polyhedron>
class Refiner
{
// types
typedef typename Kernel::FT FT;
typedef CEdge<Kernel, Polyhedron> Edge;
typedef typename Polyhedron::Halfedge_handle Halfedge_handle;
typedef typename Polyhedron::Edge_iterator Edge_iterator;
typedef std::priority_queue<Edge,
std::vector<Edge>,
::less<Edge> > PQueue;
// data
PQueue m_queue;
Polyhedron* m_pMesh;
// types
typedef typename Kernel::FT FT;
typedef CEdge<Kernel, Polyhedron> Edge;
typedef typename Polyhedron::Halfedge_handle Halfedge_handle;
typedef typename Polyhedron::Edge_iterator Edge_iterator;
typedef std::priority_queue<Edge,
std::vector<Edge>,
::less<Edge> > PQueue;
// data
PQueue m_queue;
Polyhedron* m_pMesh;
public :
// life cycle
Refiner(Polyhedron* pMesh)
{
m_pMesh = pMesh;
}
~Refiner() {}
// life cycle
Refiner(Polyhedron* pMesh)
{
m_pMesh = pMesh;
}
~Refiner() {}
public :
void fill_queue(const FT& max_sqlen)
{
for(Edge_iterator he = m_pMesh->edges_begin();
he != m_pMesh->edges_end();
he++)
if(Edge::squared_len(he) > max_sqlen)
m_queue.push(Edge(he));
}
void fill_queue(const FT& max_sqlen)
{
for(Edge_iterator he = m_pMesh->edges_begin();
he != m_pMesh->edges_end();
he++)
if(Edge::squared_len(he) > max_sqlen)
m_queue.push(Edge(he));
}
void fill_queue()
{
for(Edge_iterator he = m_pMesh->edges_begin();
he != m_pMesh->edges_end();
he++)
m_queue.push(Edge(he));
}
void fill_queue()
{
for(Edge_iterator he = m_pMesh->edges_begin();
he != m_pMesh->edges_end();
he++)
m_queue.push(Edge(he));
}
// run
void run_nb_splits(const unsigned int nb_splits)
{
// fill queue
fill_queue();
// run
void run_nb_splits(const unsigned int nb_splits)
{
// fill queue
fill_queue();
unsigned int nb = 0;
while(nb < nb_splits)
{
// get a copy of the candidate edge
Edge edge = m_queue.top();
m_queue.pop();
unsigned int nb = 0;
while(nb < nb_splits)
{
// get a copy of the candidate edge
Edge edge = m_queue.top();
m_queue.pop();
Halfedge_handle he = edge.he();
// update point
Halfedge_handle hnew = m_pMesh->split_edge(he);
hnew->vertex()->point() = CGAL::midpoint(he->vertex()->point(),
he->opposite()->vertex()->point());
Halfedge_handle he = edge.he();
// update point
Halfedge_handle hnew = m_pMesh->split_edge(he);
hnew->vertex()->point() = CGAL::midpoint(he->vertex()->point(),
he->opposite()->vertex()->point());
// hit has been split into two edges
m_queue.push(Edge(hnew));
m_queue.push(Edge(he));
// hit has been split into two edges
m_queue.push(Edge(hnew));
m_queue.push(Edge(he));
// split facet if possible
if(!hnew->is_border())
{
m_pMesh->split_facet(hnew,hnew->next()->next());
m_queue.push(Edge(hnew->next()));
}
// split facet if possible
if(!hnew->is_border())
{
m_pMesh->split_facet(hnew,hnew->next()->next());
m_queue.push(Edge(hnew->next()));
}
// split facet if possible
if(!hnew->opposite()->is_border())
{
m_pMesh->split_facet(hnew->opposite()->next(),
hnew->opposite()->next()->next()->next());
m_queue.push(Edge(hnew->opposite()->prev()));
}
// split facet if possible
if(!hnew->opposite()->is_border())
{
m_pMesh->split_facet(hnew->opposite()->next(),
hnew->opposite()->next()->next()->next());
m_queue.push(Edge(hnew->opposite()->prev()));
}
nb++;
} // end while
} // end run
nb++;
} // end while
} // end run
// run
unsigned int operator()(const FT& max_sqlen)
{
// fill queue
fill_queue(max_sqlen);
// run
unsigned int operator()(const FT& max_sqlen)
{
// fill queue
fill_queue(max_sqlen);
unsigned int nb_split = 0;
while(!m_queue.empty())
{
// get a copy of the candidate edge
Edge edge = m_queue.top();
m_queue.pop();
unsigned int nb_split = 0;
while(!m_queue.empty())
{
// get a copy of the candidate edge
Edge edge = m_queue.top();
m_queue.pop();
Halfedge_handle he = edge.he();
FT sqlen = Edge::squared_len(he);
if(sqlen > max_sqlen)
{
// update point
Halfedge_handle hnew = m_pMesh->split_edge(he);
hnew->vertex()->point() = CGAL::midpoint(he->vertex()->point(),
he->opposite()->vertex()->point());
Halfedge_handle he = edge.he();
FT sqlen = Edge::squared_len(he);
if(sqlen > max_sqlen)
{
// update point
Halfedge_handle hnew = m_pMesh->split_edge(he);
hnew->vertex()->point() = CGAL::midpoint(he->vertex()->point(),
he->opposite()->vertex()->point());
// hit has been split into two edges
m_queue.push(Edge(hnew));
m_queue.push(Edge(he));
// hit has been split into two edges
m_queue.push(Edge(hnew));
m_queue.push(Edge(he));
// split facet if possible
if(!hnew->is_border())
{
m_pMesh->split_facet(hnew,hnew->next()->next());
m_queue.push(Edge(hnew->next()));
}
// split facet if possible
if(!hnew->is_border())
{
m_pMesh->split_facet(hnew,hnew->next()->next());
m_queue.push(Edge(hnew->next()));
}
// split facet if possible
if(!hnew->opposite()->is_border())
{
m_pMesh->split_facet(hnew->opposite()->next(),
hnew->opposite()->next()->next()->next());
m_queue.push(Edge(hnew->opposite()->prev()));
}
// split facet if possible
if(!hnew->opposite()->is_border())
{
m_pMesh->split_facet(hnew->opposite()->next(),
hnew->opposite()->next()->next()->next());
m_queue.push(Edge(hnew->opposite()->prev()));
}
nb_split++;
} // end if(sqlen > max_sqlen)
} // end while(!m_queue.empty())
return nb_split;
} // end run
nb_split++;
} // end if(sqlen > max_sqlen)
} // end while(!m_queue.empty())
return nb_split;
} // end run
};
#endif // _REFINER_H_

2
AABB_tree/demo/AABB_tree/Scene.cpp
View File

@ -590,7 +590,7 @@ void Scene::update_bbox()
}
void Scene::draw(CGAL::QGLViewer* viewer)
{
{
if(!gl_init)
initGL();
if(!are_buffers_initialized)

26
AABB_tree/demo/AABB_tree/Scene.h
View File

@ -60,22 +60,22 @@ public:
public:
// types
typedef CGAL::Bbox_3 Bbox;
private:
typedef CGAL::AABB_face_graph_triangle_primitive<Polyhedron> Facet_Primitive;
typedef CGAL::AABB_traits<Kernel, Facet_Primitive> Facet_Traits;
typedef CGAL::AABB_tree<Facet_Traits> Facet_tree;
typedef CGAL::AABB_halfedge_graph_segment_primitive<Polyhedron> Edge_Primitive;
typedef CGAL::AABB_traits<Kernel, Edge_Primitive> Edge_Traits;
typedef CGAL::AABB_tree<Edge_Traits> Edge_tree;
typedef CGAL::qglviewer::ManipulatedFrame ManipulatedFrame;
enum Cut_planes_types {
NONE, UNSIGNED_FACETS, SIGNED_FACETS, UNSIGNED_EDGES, CUT_SEGMENTS
};
public:
QGLContext* context;
void draw(CGAL::QGLViewer*);
@ -102,7 +102,7 @@ private:
FT m_max_distance_function;
typedef std::pair<Point,FT> Point_distance;
Point_distance m_distance_function[100][100];
// frame
ManipulatedFrame* m_frame;
bool m_view_plane;
@ -112,10 +112,10 @@ private:
// An aabb_tree indexing polyhedron facets/segments
Facet_tree m_facet_tree;
Edge_tree m_edge_tree;
Cut_planes_types m_cut_plane;
bool are_buffers_initialized;
private:
// utility functions
Vector random_vector();
@ -135,7 +135,7 @@ private:
template <typename Tree>
void compute_distance_function(const Tree& tree);
template <typename Tree>
void sign_distance_function(const Tree& tree);
@ -182,7 +182,7 @@ public:
void clear_points() { m_points.clear(); changed(); }
void clear_segments() { m_segments.clear(); changed(); }
void clear_cutting_plane();
// fast distance setter
void set_fast_distance(bool b) { m_fast_distance = b; update_grid_size(); }
@ -198,7 +198,7 @@ public:
void refine_loop();
void refine_bisection(const FT max_sqlen);
// distance functions
// distance functions
void signed_distance_function();
void unsigned_distance_function();
void unsigned_distance_function_to_edges();
@ -215,7 +215,7 @@ public:
bool m_view_segments;
bool m_view_polyhedron;
// benchmarks
// benchmarks
enum {DO_INTERSECT,
ANY_INTERSECTION,
NB_INTERSECTIONS,
@ -254,7 +254,7 @@ public:
//timer sends a top when all the events are finished
void timerEvent(QTimerEvent *);
public slots:
// cutting plane
void cutting_plane(bool override = false);

6
AABB_tree/demo/AABB_tree/Viewer.cpp
View File

@ -42,7 +42,7 @@ void Viewer::mousePressEvent(QMouseEvent* e)
m_pScene->cutting_plane(true);
m_custom_mouse = true;
}
CGAL::QGLViewer::mousePressEvent(e);
}
@ -55,10 +55,10 @@ void Viewer::mouseReleaseEvent(QMouseEvent* e)
QApplication::setOverrideCursor(Qt::WaitCursor);
m_pScene->cutting_plane(true);
QApplication::restoreOverrideCursor();
m_custom_mouse = false;
}
CGAL::QGLViewer::mouseReleaseEvent(e);
}

2
AABB_tree/demo/AABB_tree/Viewer.h
View File

@ -22,7 +22,7 @@ public:
protected:
virtual void mousePressEvent(QMouseEvent* e);
virtual void mouseReleaseEvent(QMouseEvent* e);
private:
Scene* m_pScene;
bool m_custom_mouse;

6
AABB_tree/demo/AABB_tree/benchmarks.cpp
View File

@ -97,7 +97,7 @@ std::size_t Scene::nb_digits(std::size_t value)
}
// bench memory against number of facets in the tree
// the tree is reconstructed each timer in the mesh
// the tree is reconstructed each timer in the mesh
// refinement loop
void Scene::bench_memory()
{
@ -166,8 +166,8 @@ void Scene::bench_construction()
Facet_tree tree2(faces(*m_pPolyhedron).first, faces(*m_pPolyhedron).second,*m_pPolyhedron);
double duration_construction_and_kdtree = time2.time();
std::cout << m_pPolyhedron->size_of_facets() << "\t"
<< duration_construction_alone << "\t"
std::cout << m_pPolyhedron->size_of_facets() << "\t"
<< duration_construction_alone << "\t"
<< duration_construction_and_kdtree << std::endl;
}
}

116
AABB_tree/doc/AABB_tree/Concepts/AABBGeomTraits.h
View File

@ -3,7 +3,7 @@
\ingroup PkgAABBTreeConcepts
\cgalConcept
The concept `AABBGeomTraits` defines the requirements for the first template parameter of the class `CGAL::AABB_traits<AABBGeomTraits, AABBPrimitive>`. It provides predicates and constructors to detect and compute intersections between query objects and the primitives stored in the AABB tree. In addition, it contains predicates and constructors to compute distances between a point query and the primitives stored in the AABB tree.
The concept `AABBGeomTraits` defines the requirements for the first template parameter of the class `CGAL::AABB_traits<AABBGeomTraits, AABBPrimitive>`. It provides predicates and constructors to detect and compute intersections between query objects and the primitives stored in the AABB tree. In addition, it contains predicates and constructors to compute distances between a point query and the primitives stored in the AABB tree.
\cgalRefines `SearchGeomTraits_3`
@ -16,7 +16,7 @@ The concept `AABBGeomTraits` defines the requirements for the first template par
class AABBGeomTraits {
public:
/// \name Types
/// \name Types
/// @{
/*!
@ -25,50 +25,50 @@ A number type model of `Field`.
typedef unspecified_type FT;
/*!
Sphere type, that should be consistent with the distance function chosen for the distance queries, namely the `Squared_distance_3` functor.
*/
typedef unspecified_type Sphere_3;
Sphere type, that should be consistent with the distance function chosen for the distance queries, namely the `Squared_distance_3` functor.
*/
typedef unspecified_type Sphere_3;
/*!
Point type.
*/
typedef unspecified_type Point_3;
*/
typedef unspecified_type Point_3;
/*!
A functor object to detect intersections between two geometric objects.
Provides the operators:
`bool operator()(const Type_1& type_1, const Type_2& type_2);`
where `Type_1` and `Type_2` are relevant types
among `Ray_3`, `Segment_3`, `Line_3`, `Triangle_3`, `Plane_3` and `Bbox_3`. Relevant herein means that a line primitive (ray, segment, line) is tested against a planar or solid primitive (plane, triangle, box), and a solid primitive is tested against another solid primitive (box against box). The operator returns `true` iff `type_1` and `type_2` have a non empty intersection.
*/
typedef unspecified_type Do_intersect_3;
A functor object to detect intersections between two geometric objects.
Provides the operators:
`bool operator()(const Type_1& type_1, const Type_2& type_2);`
where `Type_1` and `Type_2` are relevant types
among `Ray_3`, `Segment_3`, `Line_3`, `Triangle_3`, `Plane_3` and `Bbox_3`. Relevant herein means that a line primitive (ray, segment, line) is tested against a planar or solid primitive (plane, triangle, box), and a solid primitive is tested against another solid primitive (box against box). The operator returns `true` iff `type_1` and `type_2` have a non empty intersection.
*/
typedef unspecified_type Do_intersect_3;
/*!
A functor object to construct the intersection between two geometric objects.
This functor must support the result_of protocol, that is the return
This functor must support the result_of protocol, that is the return
type of the `operator()(A, B)` is `CGAL::cpp11::result<Intersect_3(A,B)>`.
Provides the operators:
`CGAL::cpp11::result<Intersect_3(A,B)> operator()(const A& a, const B& b);`
where `A` and `B` are any relevant types among `Ray_3`, `Segment_3`, `Line_3`,
`Triangle_3`, `Plane_3` and `Bbox_3`.
Relevant herein means that a line primitive (ray, segment, line) is tested
against a planar or solid primitive (plane, triangle, box).
A model of `Kernel::Intersect_3` fulfills those requirements.
*/
typedef unspecified_type Intersect_3;
Provides the operators:
`CGAL::cpp11::result<Intersect_3(A,B)> operator()(const A& a, const B& b);`
where `A` and `B` are any relevant types among `Ray_3`, `Segment_3`, `Line_3`,
`Triangle_3`, `Plane_3` and `Bbox_3`.
Relevant herein means that a line primitive (ray, segment, line) is tested
against a planar or solid primitive (plane, triangle, box).
A model of `Kernel::Intersect_3` fulfills those requirements.
*/
typedef unspecified_type Intersect_3;
/*!
A functor object to construct the sphere centered at one point and passing through another one. Provides the operator:
A functor object to construct the sphere centered at one point and passing through another one. Provides the operator:
- `Sphere_3 operator()(const Point_3& p, const FT & sr)` which returns the sphere centered at `p` with `sr` as squared radius.
*/
typedef unspecified_type Construct_sphere_3;
*/
typedef unspecified_type Construct_sphere_3;
/*!
A functor object to compute the point on a geometric primitive which is closest from a query. Provides the operator:
`Point_3 operator()(const Type_2& type_2, const Point_3& p);` where `Type_2` can be any of the following types : `Segment_3`, `Ray_3`, or `Triangle_3`.
The operator returns the point on `type_2` which is closest to `p`.
*/
A functor object to compute the point on a geometric primitive which is closest from a query. Provides the operator:
`Point_3 operator()(const Type_2& type_2, const Point_3& p);` where `Type_2` can be any of the following types : `Segment_3`, `Ray_3`, or `Triangle_3`.
The operator returns the point on `type_2` which is closest to `p`.
*/
typedef unspecified_type Construct_projected_point_3;
/*!
@ -79,17 +79,17 @@ Provides the operator:
typedef unspecified_type Compare_distance_3;
/*!
A functor object to detect if a point lies inside a sphere or not.
Provides the operator:
`bool operator()(const Sphere_3& s, const Point_3& p);` which returns `true` iff the closed volume bounded by `s` contains `p`.
*/
typedef unspecified_type Has_on_bounded_side_3;
A functor object to detect if a point lies inside a sphere or not.
Provides the operator:
`bool operator()(const Sphere_3& s, const Point_3& p);` which returns `true` iff the closed volume bounded by `s` contains `p`.
*/
typedef unspecified_type Has_on_bounded_side_3;
/*!
A functor object to compute the squared radius of a sphere. Provides the operator:
`FT operator()(const Sphere_3& s);` which returns the squared radius of `s`.
*/
typedef unspecified_type Compute_squared_radius_3;
A functor object to compute the squared radius of a sphere. Provides the operator:
`FT operator()(const Sphere_3& s);` which returns the squared radius of `s`.
*/
typedef unspecified_type Compute_squared_radius_3;
/*!
A functor object to compute the squared distance between two points. Provides the operator:
@ -126,29 +126,29 @@ typedef unspecified_type Equal_3;
/// @}
/// @}
/// \name Operations
/// \name Operations
/// @{
/*!
Returns the intersection detection functor.
*/
Do_intersect_3 do_intersect_3_object();
Returns the intersection detection functor.
*/
Do_intersect_3 do_intersect_3_object();
/*!
Returns the intersection constructor.
*/
Intersect_3 intersect_3_object();
Returns the intersection constructor.
*/
Intersect_3 intersect_3_object();
/*!
Returns the sphere constructor.
*/
Construct_sphere_3 construct_sphere_3_object();
*/
Construct_sphere_3 construct_sphere_3_object();
/*!
Returns the closest point constructor.
*/
Returns the closest point constructor.
*/
Construct_projected_point_3 construct_projected_point_3_object();
/*!
@ -157,14 +157,14 @@ Returns the compare distance constructor.
Compare_distance_3 compare_distance_3_object();
/*!
Returns the closest point constructor.
*/
Has_on_bounded_side_3 has_on_bounded_side_3_object();
Returns the closest point constructor.
*/
Has_on_bounded_side_3 has_on_bounded_side_3_object();
/*!
Returns the squared radius functor.
*/
Compute_squared_radius_3 compute_squared_radius_3_object();
Returns the squared radius functor.
*/
Compute_squared_radius_3 compute_squared_radius_3_object();
/*!
Returns the squared distance functor.

48
AABB_tree/doc/AABB_tree/Concepts/AABBPrimitive.h
View File

@ -3,14 +3,14 @@
\ingroup PkgAABBTreeConcepts
\cgalConcept
The concept `AABBPrimitive` describes the requirements for the primitives stored in the AABB tree data structure. The concept encapsulates a type for the input datum (a geometric object) and an identifier (id) type through which those primitives are referred to. The concept `AABBPrimitive` also refines the concepts DefaultConstructible and Assignable.
The concept `AABBPrimitive` describes the requirements for the primitives stored in the AABB tree data structure. The concept encapsulates a type for the input datum (a geometric object) and an identifier (id) type through which those primitives are referred to. The concept `AABBPrimitive` also refines the concepts DefaultConstructible and Assignable.
\sa `CGAL::AABB_tree<AABBTraits>`
\sa `CGAL::AABB_tree<AABBTraits>`
\sa `AABBPrimitiveWithSharedData`
\cgalHeading{Example}
The `Primitive` type can be, e.g., a wrapper around a `Handle`. Assume for instance that the input objects are the triangle faces of a mesh stored as a `CGAL::Polyhedron_3`. The `Datum` would be a `Triangle_3` and the `Id` would be a polyhedron `Face_handle`. Method `datum()` can return either a `Triangle_3` constructed on the fly from the face handle or a `Triangle_3` stored internally. This provides a way for the user to trade memory for efficiency.
The `Primitive` type can be, e.g., a wrapper around a `Handle`. Assume for instance that the input objects are the triangle faces of a mesh stored as a `CGAL::Polyhedron_3`. The `Datum` would be a `Triangle_3` and the `Id` would be a polyhedron `Face_handle`. Method `datum()` can return either a `Triangle_3` constructed on the fly from the face handle or a `Triangle_3` stored internally. This provides a way for the user to trade memory for efficiency.
\cgalHasModel `CGAL::AABB_primitive<Id,ObjectPropertyMap,PointPropertyMap,Tag_false,CacheDatum>`
\cgalHasModel `CGAL::AABB_segment_primitive<Iterator,CacheDatum>`
@ -22,18 +22,18 @@ The `Primitive` type can be, e.g., a wrapper around a `Handle`. Assume for insta
class AABBPrimitive {
public:
/// \name Types
/// \name Types
/// @{
/*!
3D point type.
*/
typedef unspecified_type Point;
3D point type.
*/
typedef unspecified_type Point;
/*!
Type of input datum.
*/
typedef unspecified_type Datum;
Type of input datum.
*/
typedef unspecified_type Datum;
/*!
Point reference type returned by the function `point()`. It is convertible to the type `Point`.
@ -46,29 +46,29 @@ Datum reference type returned by the function `datum()`. It is convertible to th
typedef unspecified_type Datum_reference;
/*!
Type of identifiers through which the input objects are referred to. It must be a model of the concepts DefaultConstructible and Assignable.
*/
typedef unspecified_type Id;
Type of identifiers through which the input objects are referred to. It must be a model of the concepts DefaultConstructible and Assignable.
*/
typedef unspecified_type Id;
/// @}
/// @}
/// \name Operations
/// \name Operations
/// @{
/*!
Returns the datum (geometric object) represented by the primitive.
*/
Datum_reference datum();
Returns the datum (geometric object) represented by the primitive.
*/
Datum_reference datum();
/*!
Returns the corresponding identifier. This identifier is only used as a reference for the objects in the output of the `AABB_tree` methods.
*/
Id id();
Returns the corresponding identifier. This identifier is only used as a reference for the objects in the output of the `AABB_tree` methods.
*/
Id id();
/*!
Returns a 3D point located on the geometric object represented by the primitive. This function is used to sort the primitives during the AABB tree construction as well as to construct the search KD-tree internal to the AABB tree used to accelerate distance queries.
*/
Point_reference reference_point();
Returns a 3D point located on the geometric object represented by the primitive. This function is used to sort the primitives during the AABB tree construction as well as to construct the search KD-tree internal to the AABB tree used to accelerate distance queries.
*/
Point_reference reference_point();
/// @}

134
AABB_tree/doc/AABB_tree/Concepts/AABBTraits.h
View File

@ -17,34 +17,34 @@ The concept `AABBTraits` provides the geometric primitive types and methods for
class AABBTraits {
public:
/// \name Types
/// \name Types
/// @{
/*!
Value type of the `Squared_distance` functor.
*/
typedef unspecified_type FT;
Value type of the `Squared_distance` functor.
*/
typedef unspecified_type FT;
/*!
Type of a 3D point.
*/
typedef unspecified_type Point_3;
Type of a 3D point.
*/
typedef unspecified_type Point_3;
/*!
Type of primitive.
Type of primitive.
Must be a model of the concepts `AABBPrimitive` or `AABBPrimitiveWithSharedData`.
*/
typedef unspecified_type Primitive;
*/
typedef unspecified_type Primitive;
/*!
Bounding box type.
*/
typedef unspecified_type Bounding_box;
Bounding box type.
*/
typedef unspecified_type Bounding_box;
/*!
enum required for axis selection
*/
enum Axis {
*/
enum Axis {
CGAL_X_AXIS,
CGAL_Y_AXIS,
CGAL_Z_AXIS
@ -52,13 +52,13 @@ typedef unspecified_type Bounding_box;
/*!
3D Point and Primitive Id type
*/
typedef std::pair<Point_3, Primitive::Id> Point_and_primitive_id;
*/
typedef std::pair<Point_3, Primitive::Id> Point_and_primitive_id;
/*!
\deprecated
\deprecated
This requirement is deprecated and is no longer needed.
*/
*/
typedef std::pair<Object, Primitive::Id> Object_and_primitive_id;
@ -84,22 +84,22 @@ A functor object to split a range of primitives into two sub-ranges along the lo
and have `Primitive` as value type. The operator is used for determining the primitives assigned to the two children nodes of a given node,
assuming that the goal is to split the chosen axis dimension of the bounding box of the node. The primitives assigned to this node are passed as argument
to the operator. It should modify the iterator range in such a way that its first half and its second half correspond to the two children nodes.
*/
typedef unspecified_type Split_primitives;
*/
typedef unspecified_type Split_primitives;
/*!
A functor object to compute the bounding box of a set of primitives. Provides the operator:
`Bounding_box operator()(Input_iterator begin, Input_iterator beyond);` %Iterator type `InputIterator` must have `Primitive` as value type.
*/
typedef unspecified_type Compute_bbox;
A functor object to compute the bounding box of a set of primitives. Provides the operator:
`Bounding_box operator()(Input_iterator begin, Input_iterator beyond);` %Iterator type `InputIterator` must have `Primitive` as value type.
*/
typedef unspecified_type Compute_bbox;
// remove as not used any where in the code:
// A functor object to specify the direction along which the bounding box should be split:
// A functor object to specify the direction along which the bounding box should be split:
// `Axis operator()(const Bounding_box& bbox);` which returns the
// direction used for splitting `bbox`. It is usually the axis aligned
// with the longest edge of `bbox`.
// typedef unspecified_type Splitting_direction;
// typedef unspecified_type Splitting_direction;
/// @}
@ -111,20 +111,20 @@ typedef unspecified_type Compute_bbox;
/// @{
/*!
A functor object to compute intersection predicates between the query and the nodes of the tree. Provides the operators:
A functor object to compute intersection predicates between the query and the nodes of the tree. Provides the operators:
- `bool operator()(const Query & q, const Bounding_box & box);` which returns `true` iff the query intersects the bounding box
- `bool operator()(const Query & q, const Primitive & primitive);` which returns `true` iff the query intersects the primitive
*/
typedef unspecified_type Do_intersect;
*/
typedef unspecified_type Do_intersect;
/*!
A functor object to compute the intersection of a query and a primitive. Provides the operator:
`boost::optional<Intersection_and_primitive_id<Query>::%Type > operator()(const Query & q, const Primitive& primitive);` which returns the intersection as a pair composed of an object and a primitive id, iff the query intersects the primitive.
A functor object to compute the intersection of a query and a primitive. Provides the operator:
`boost::optional<Intersection_and_primitive_id<Query>::%Type > operator()(const Query & q, const Primitive& primitive);` which returns the intersection as a pair composed of an object and a primitive id, iff the query intersects the primitive.
\cgalHeading{Note on Backward Compatibility}
Before the release 4.3 of \cgal, the return type of this function used to be `boost::optional<Object_and_primitive_id>`.
*/
typedef unspecified_type Intersection;
*/
typedef unspecified_type Intersection;
/// @}
@ -135,68 +135,68 @@ typedef unspecified_type Intersection;
/// @{
/*!
A functor object to compute distance comparisons between the query and the nodes of the tree. Provides the operators:
A functor object to compute distance comparisons between the query and the nodes of the tree. Provides the operators:
- `bool operator()(const Query & query, const Bounding_box& box, const Point & closest);` which returns `true` iff the bounding box is closer to `query` than `closest` is
- `bool operator()(const Query & query, const Primitive & primitive, const Point & closest);` which returns `true` iff `primitive` is closer to the `query` than `closest` is
*/
typedef unspecified_type Compare_distance;
*/
typedef unspecified_type Compare_distance;
/*!
A functor object to compute closest point from the query on a primitive. Provides the operator:
`Point_3 operator()(const Query& query, const Primitive& primitive, const Point_3 & closest);` which returns the closest point to `query`, among `closest` and all points of the primitive.
*/
typedef unspecified_type Closest_point;
A functor object to compute closest point from the query on a primitive. Provides the operator:
`Point_3 operator()(const Query& query, const Primitive& primitive, const Point_3 & closest);` which returns the closest point to `query`, among `closest` and all points of the primitive.
*/
typedef unspecified_type Closest_point;
/*!
A functor object to compute the squared distance between two points. Provides the operator:
`FT operator()(const Point& query, const Point_3 & p);` which returns the squared distance between `p` and `q`.
*/
typedef unspecified_type Squared_distance;
A functor object to compute the squared distance between two points. Provides the operator:
`FT operator()(const Point& query, const Point_3 & p);` which returns the squared distance between `p` and `q`.
*/
typedef unspecified_type Squared_distance;
/*!
A functor object to compare two points. Provides the operator:
`bool operator()(const Point_3& p, const Point_3& q);}` which returns `true` if `p` is equal to `q`.
*/
typedef unspecified_type Equal_3;
/// @}
/// @}
/// \name Operations
/// \name Operations
/// @{
/*!
Returns the primitive splitting functor.
*/
Split_primitives split_primitives_object();
Returns the primitive splitting functor.
*/
Split_primitives split_primitives_object();
/*!
Returns the bounding box constructor.
*/
Compute_bbox compute_bbox_object();
Returns the bounding box constructor.
*/
Compute_bbox compute_bbox_object();
/*!
Returns the intersection detection functor.
*/
Do_intersect do_intersect_object();
Returns the intersection detection functor.
*/
Do_intersect do_intersect_object();
/*!
Returns the intersection constructor.
*/
Intersection intersection_object();
Returns the intersection constructor.
*/
Intersection intersection_object();
/*!
Returns the distance comparison functor.
*/
Compare_distance compare_distance_object();
Returns the distance comparison functor.
*/
Compare_distance compare_distance_object();
/*!
Returns the closest point constructor.
*/
Closest_point closest_point_object();
Returns the closest point constructor.
*/
Closest_point closest_point_object();
/*!
Returns the squared distance functor.
*/
Squared_distance squared_distance_object();
*/
Squared_distance squared_distance_object();
/*!
Returns the equal functor.

12
AABB_tree/doc/AABB_tree/aabb_tree.txt
View File

@ -2,7 +2,7 @@ namespace CGAL {
/*!
\mainpage User Manual
\mainpage User Manual
\anchor Chapter_3D_Fast_Intersection_and_Distance_Computation
\cgalAutoToc
@ -25,7 +25,7 @@ closest point from a point query to a set of triangles.
Note that this component is not suited to the problem of finding all
intersecting pairs of objects. We refer to the component
\ref chapterBoxIntersection "Intersecting Sequences of dD Iso-oriented Boxes"
\ref chapterBoxIntersection "Intersecting Sequences of dD Iso-oriented Boxes"
which can find all intersecting pairs of iso-oriented boxes.
The AABB tree data structure takes as input an iterator range of
@ -59,7 +59,7 @@ intersection *tests* which do not construct any intersection
objects, from *intersections* which construct the intersection
objects.
Tests:
Tests:
- Function `AABB_tree::do_intersect()` tests if the input primitives are
intersected by the query. This function is fast as it involves only
@ -79,7 +79,7 @@ the intersections with respect to the query.
the intersecting primitive id (if any) of the corresponding
intersection object that is closest to the source of the ray.
Constructions:
Constructions:
- Function `AABB_tree::all_intersections()` detects and constructs all
intersection objects with the input primitives.
@ -216,7 +216,7 @@ option which maximizes speed.
\subsection aabb_tree_perf_cons Construction
The surface triangle mesh chosen for benchmarking the tree
construction is the knot model (14,400 triangles) depicted by
construction is the knot model (14,400 triangles) depicted by
\cgalFigureRef{figAABB-tree-bench}. We measure the tree construction time (both
AABB tree alone and AABB tree with internal KD-tree) for this model as
well as for three denser versions subdivided through the Loop
@ -254,7 +254,7 @@ the function `AABB_tree::accelerate_distance_queries()` which
takes an iterator range as input.
| Number of triangles | AABB tree (in MBytes) | AABB tree with internal KD-tree (in MBytes)|
| ----: | ----: | ----: |
| ----: | ----: | ----: |
18,400 | 1.10 | 2.76 |
102,400 | 6.33 | 14.73 |
1,022,400 | 59.56 | 151.31 |

10
AABB_tree/examples/AABB_tree/AABB_cached_bbox_example.cpp
View File

@ -13,7 +13,7 @@ typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef K::FT FT;
typedef K::Point_3 Point_3;
typedef CGAL::Bbox_3 Bbox_3;
typedef CGAL::Surface_mesh<Point_3> Surface_mesh;
typedef CGAL::Surface_mesh<Point_3> Surface_mesh;
typedef CGAL::Polyhedron_3<K> Polyhedron_3;
typedef CGAL::Timer Timer;
@ -27,7 +27,7 @@ void triangle_mesh(const char* fname)
TriangleMesh tmesh;
std::ifstream in(fname);
in >> tmesh;
in >> tmesh;
Timer t;
t.start();
Tree tree(faces(tmesh).first, faces(tmesh).second, tmesh);
@ -37,7 +37,7 @@ void triangle_mesh(const char* fname)
}
Bbox_3 bbox(boost::graph_traits<Surface_mesh>::face_descriptor fd,
Bbox_3 bbox(boost::graph_traits<Surface_mesh>::face_descriptor fd,
const Surface_mesh& p)
{
boost::graph_traits<Surface_mesh>::halfedge_descriptor hd = halfedge(fd,p);
@ -59,11 +59,11 @@ void surface_mesh_cache_bbox(const char* fname)
Surface_mesh tmesh;
std::ifstream in(fname);
in >> tmesh;
Timer t;
t.start();
Bbox_pmap bb = tmesh.add_property_map<face_descriptor,Bbox_3>("f:bbox",Bbox_3()).first;
for(face_descriptor fd : faces(tmesh)){
put(bb, fd, bbox(fd,tmesh));
}

6
AABB_tree/examples/AABB_tree/AABB_custom_example.cpp
View File

@ -48,7 +48,7 @@ public:
// this is the type of data that the queries returns. For this example
// we imagine that, for some reasons, we do not want to store the iterators
// of the vector, but raw pointers. This is to show that the Id type
// does not have to be the same as the one of the input parameter of the
// does not have to be the same as the one of the input parameter of the
// constructor.
typedef const My_triangle* Id;
@ -62,14 +62,14 @@ private:
public:
My_triangle_primitive() {} // default constructor needed
// the following constructor is the one that receives the iterators from the
// the following constructor is the one that receives the iterators from the
// iterator range given as input to the AABB_tree
My_triangle_primitive(Iterator it)
: m_pt(&(*it)) {}
const Id& id() const { return m_pt; }
// utility function to convert a custom
// utility function to convert a custom
// point type to CGAL point type.
Point convert(const My_point *p) const
{

26
AABB_tree/examples/AABB_tree/AABB_custom_indexed_triangle_set_array_example.cpp
View File

@ -11,7 +11,7 @@ typedef CGAL::Simple_cartesian<double> K;
// The points are stored in a flat array of doubles
// The triangles are stored in a flat array of indices
// The triangles are stored in a flat array of indices
// referring to an array of coordinates: three consecutive
// coordinates represent a point, and three consecutive
// indices represent a triangle.
@ -60,7 +60,7 @@ private:
public:
My_triangle_primitive() {} // default constructor needed
// the following constructor is the one that receives the iterators from the
// the following constructor is the one that receives the iterators from the
// iterator range given as input to the AABB_tree
My_triangle_primitive(Triangle_iterator a)
: m_it(a) {}
@ -69,18 +69,18 @@ public:
// on the fly conversion from the internal data to the CGAL types
Datum datum() const
{
{
Point_index_iterator p_it = m_it.base();
Point p(*(point_container + 3 * (*p_it)),
*(point_container + 3 * (*p_it) + 1),
Point p(*(point_container + 3 * (*p_it)),
*(point_container + 3 * (*p_it) + 1),
*(point_container + 3 * (*p_it) + 2) );
++p_it;
Point q(*(point_container + 3 * (*p_it)),
*(point_container + 3 * (*p_it) + 1),
Point q(*(point_container + 3 * (*p_it)),
*(point_container + 3 * (*p_it) + 1),
*(point_container + 3 * (*p_it) + 2));
++p_it;
Point r(*(point_container + 3 * (*p_it)),
*(point_container + 3 * (*p_it) + 1),
Point r(*(point_container + 3 * (*p_it)),
*(point_container + 3 * (*p_it) + 1),
*(point_container + 3 * (*p_it) + 2));
return Datum(p, q, r); // assembles triangle from three points
@ -88,9 +88,9 @@ public:
// one point which must be on the primitive
Point reference_point() const
{
return Point(*(point_container + 3 * (*m_it)),
*(point_container + 3 * (*m_it) + 1),
{
return Point(*(point_container + 3 * (*m_it)),
*(point_container + 3 * (*m_it) + 1),
*(point_container + 3 * (*m_it) + 2));
}
};
@ -119,7 +119,7 @@ int main()
triangles[6] = 0; triangles[7] = 3; triangles[8] = 2;
// constructs AABB tree
Tree tree(Triangle_iterator(triangles),
Tree tree(Triangle_iterator(triangles),
Triangle_iterator(triangles+9));
// counts #intersections

18
AABB_tree/examples/AABB_tree/AABB_custom_indexed_triangle_set_example.cpp
View File

@ -24,7 +24,7 @@ struct My_point {
: x(_x), y(_y), z(_z) {}
};
// The triangles are stored in a flat array of indices
// The triangles are stored in a flat array of indices
// referring to an array of points: three consecutive
// indices represent a triangle.
typedef std::vector<size_t>::const_iterator Point_index_iterator;
@ -71,7 +71,7 @@ private:
public:
My_triangle_primitive() {} // default constructor needed
// the following constructor is the one that receives the iterators from the
// the following constructor is the one that receives the iterators from the
// iterator range given as input to the AABB_tree
My_triangle_primitive(Triangle_iterator a)
: m_it(a) {}
@ -80,7 +80,7 @@ public:
// on the fly conversion from the internal data to the CGAL types
Datum datum() const
{
{
Point_index_iterator p_it = m_it.base();
const My_point& mp = (*point_container)[*p_it];
Point p(mp.x, mp.y, mp.z);
@ -96,7 +96,7 @@ public:
// one point which must be on the primitive
Point reference_point() const
{
{
const My_point& mp = (*point_container)[*m_it];
return Point(mp.x, mp.y, mp.z);
}
@ -121,16 +121,16 @@ int main()
points.push_back(a);
points.push_back(b);
points.push_back(c);
points.push_back(d);
points.push_back(d);
// generates indexed triangle set
std::vector<size_t> triangles;
triangles.push_back(0); triangles.push_back(1); triangles.push_back(2);
triangles.push_back(0); triangles.push_back(1); triangles.push_back(3);
triangles.push_back(0); triangles.push_back(3); triangles.push_back(2);
triangles.push_back(0); triangles.push_back(1); triangles.push_back(2);
triangles.push_back(0); triangles.push_back(1); triangles.push_back(3);
triangles.push_back(0); triangles.push_back(3); triangles.push_back(2);
// constructs AABB tree
Tree tree(Triangle_iterator(triangles.begin()),
Tree tree(Triangle_iterator(triangles.begin()),
Triangle_iterator(triangles.end()));
// counts #intersections

18
AABB_tree/examples/AABB_tree/AABB_custom_triangle_soup_example.cpp
View File

@ -1,6 +1,6 @@
// Author(s) : Camille Wormser, Pierre Alliez
// Example of an AABB tree used with a simple list of
// Example of an AABB tree used with a simple list of
// triangles (a triangle soup) stored into an array of points.
#include <iostream>
@ -25,7 +25,7 @@ struct My_point {
My_point (double _x, double _y, double _z) : x(_x), y(_y), z(_z) {}
};
// The triangles are stored in a flat vector of points (a triangle soup):
// The triangles are stored in a flat vector of points (a triangle soup):
// three consecutive points represent a triangle
typedef std::vector<My_point>::const_iterator Point_iterator;
@ -66,7 +66,7 @@ private:
public:
My_triangle_primitive() {} // default constructor needed
// the following constructor is the one that receives the iterators from the
// the following constructor is the one that receives the iterators from the
// iterator range given as input to the AABB_tree
My_triangle_primitive(Triangle_iterator a)
: m_it(a) {}
@ -76,7 +76,7 @@ public:
// on the fly conversion from the internal data
// to the CGAL types
Datum datum() const
{
{
Point_iterator p_it = m_it.base();
Point p(p_it->x, p_it->y, p_it->z);
++p_it;
@ -89,7 +89,7 @@ public:
// returns one point which must be on the primitive
Point reference_point() const
{
{
return Point(m_it->x, m_it->y, m_it->z);
}
};
@ -107,12 +107,12 @@ int main()
My_point d(0.0, 0.0, 0.0);
std::vector<My_point> triangles;
triangles.push_back(a); triangles.push_back(b); triangles.push_back(c);
triangles.push_back(a); triangles.push_back(b); triangles.push_back(d);
triangles.push_back(a); triangles.push_back(d); triangles.push_back(c);
triangles.push_back(a); triangles.push_back(b); triangles.push_back(c);
triangles.push_back(a); triangles.push_back(b); triangles.push_back(d);
triangles.push_back(a); triangles.push_back(d); triangles.push_back(c);
// constructs AABB tree
Tree tree(Triangle_iterator(triangles.begin()),
Tree tree(Triangle_iterator(triangles.begin()),
Triangle_iterator(triangles.end()));
// counts #intersections

8
AABB_tree/examples/AABB_tree/AABB_halfedge_graph_edge_example.cpp
View File

@ -23,8 +23,8 @@ void run(const HalfedgeGraph& graph){
typename Kernel::Point_3 q(0.0, 1.0, 0.0);
typename Kernel::Point_3 r(0.0, 0.0, 1.0);
// constructs the AABB tree and the internal search tree for
// efficient distance queries.
// constructs the AABB tree and the internal search tree for
// efficient distance queries.
Tree tree( CGAL::edges(graph).first,
CGAL::edges(graph).second, graph);
@ -39,7 +39,7 @@ void run(const HalfedgeGraph& graph){
typename Kernel::Point_3 point_query(2.0, 2.0, 2.0);
typename Kernel::Point_3 closest = tree.closest_point(point_query);
std::cerr << "closest point is: " << closest << std::endl;
std::cerr << "closest point is: " << closest << std::endl;
}
int main()
@ -50,7 +50,7 @@ int main()
Point s(0.0, 0.0, 0.0);
Polyhedron polyhedron;
polyhedron.make_tetrahedron(p, q, r, s);
run<K>(polyhedron);
return EXIT_SUCCESS;
}

2
AABB_tree/examples/AABB_tree/AABB_polyhedron_edge_example.cpp
View File

@ -26,7 +26,7 @@ int main()
Polyhedron polyhedron;
polyhedron.make_tetrahedron(p, q, r, s);
// constructs the AABB tree and the internal search tree for
// constructs the AABB tree and the internal search tree for
// efficient distance queries.
Tree tree( CGAL::edges(polyhedron).first,
CGAL::edges(polyhedron).second,

4
AABB_tree/examples/AABB_tree/AABB_polyhedron_facet_distance_example.cpp
View File

@ -28,7 +28,7 @@ int main()
Polyhedron polyhedron;
polyhedron.make_tetrahedron(p, q, r, s);
// constructs AABB tree and computes internal KD-tree
// constructs AABB tree and computes internal KD-tree
// data structure to accelerate distance queries
Tree tree(faces(polyhedron).first, faces(polyhedron).second, polyhedron);
@ -49,7 +49,7 @@ int main()
Polyhedron::Face_handle f = pp.second; // closest primitive id
std::cout << "closest point: " << closest_point << std::endl;
std::cout << "closest triangle: ( "
<< f->halfedge()->vertex()->point() << " , "
<< f->halfedge()->vertex()->point() << " , "
<< f->halfedge()->next()->vertex()->point() << " , "
<< f->halfedge()->next()->next()->vertex()->point()
<< " )" << std::endl;

4
AABB_tree/examples/AABB_tree/AABB_polyhedron_facet_intersection_example.cpp
View File

@ -80,10 +80,10 @@ int main()
Plane_intersection plane_intersection = tree.any_intersection(plane_query);
if(plane_intersection)
{
if(boost::get<Segment>(&(plane_intersection->first)))
std::cout << "intersection object is a segment" << std::endl;
}
return EXIT_SUCCESS;
}

8
AABB_tree/examples/AABB_tree/AABB_ray_shooting_example.cpp
View File

@ -38,7 +38,7 @@ struct Skip {
};
return(t == fd);
}
};
int main(int argc, char* argv[])
@ -48,7 +48,7 @@ int main(int argc, char* argv[])
Mesh mesh;
input >> mesh;
Tree tree(faces(mesh).first, faces(mesh).second, mesh);
double d = CGAL::Polygon_mesh_processing::is_outward_oriented(mesh)?-1:1;
for(face_descriptor fd : faces(mesh)){
@ -56,8 +56,8 @@ int main(int argc, char* argv[])
Point p = CGAL::centroid(mesh.point(source(hd,mesh)),
mesh.point(target(hd,mesh)),
mesh.point(target(next(hd,mesh),mesh)));
Vector v = CGAL::Polygon_mesh_processing::compute_face_normal(fd,mesh);
Vector v = CGAL::Polygon_mesh_processing::compute_face_normal(fd,mesh);
Ray ray(p,d * v);
Skip skip(fd);
Ray_intersection intersection = tree.first_intersection(ray, skip);

4
AABB_tree/examples/AABB_tree/AABB_segment_3_example.cpp
View File

@ -33,7 +33,7 @@ int main()
segments.push_back(Segment(a,c));
segments.push_back(Segment(c,d));
// constructs the AABB tree and the internal search tree for
// constructs the AABB tree and the internal search tree for
// efficient distance computations.
Tree tree(segments.begin(),segments.end());
@ -47,7 +47,7 @@ int main()
std::cout << tree.number_of_intersected_primitives(triangle_query)
<< " intersections(s) with triangle" << std::endl;
// computes the closest point from a point query
// computes the closest point from a point query
Point point_query(2.0, 2.0, 2.0);
Point closest = tree.closest_point(point_query);

4
AABB_tree/examples/AABB_tree/CMakeLists.txt
View File

@ -17,8 +17,8 @@ if ( CGAL_FOUND )
endforeach()
else()
message(STATUS "This program requires the CGAL library, and will not be compiled.")
endif()

4
AABB_tree/include/CGAL/AABB_face_graph_triangle_primitive.h
View File

@ -96,7 +96,7 @@ class AABB_face_graph_triangle_primitive
{
return std::make_pair(fd, &fg);
}
public:
#ifdef DOXYGEN_RUNNING
/// \name Types
@ -115,7 +115,7 @@ public:
- `std::pair<boost::graph_traits<FaceGraph>::%face_descriptor, FaceGraph>` if `OneFaceGraphPerTree` is `CGAL::Tag_false`
*/
unspecified_type Id;
/// @}
/*!

2
AABB_tree/include/CGAL/AABB_halfedge_graph_segment_primitive.h
View File

@ -47,7 +47,7 @@ namespace CGAL {
* and `AABBPrimitiveWithSharedData` if `OneHalfedgeGraphPerTree` is `CGAL::Tag_true`.
*
* \tparam HalfedgeGraph is a model of the halfedge graph concept.
* as key type and a \cgal Kernel `Point_3` as value type.
* as key type and a \cgal Kernel `Point_3` as value type.
* \tparam VertexPointPMap is a property map with `boost::graph_traits<HalfedgeGraph>::%vertex_descriptor`.
* The default is `typename boost::property_map< HalfedgeGraph,vertex_point_t>::%const_type`.
* \tparam OneHalfedgeGraphPerTree is either `CGAL::Tag_true` or `CGAL::Tag_false`.

8
AABB_tree/include/CGAL/AABB_traits.h
View File

@ -105,7 +105,7 @@ struct AABB_traits_base_2<GeomTraits,true>{
} else {
FT t1 = ((bbox.min)(i) - *source_iter) / *direction_iter;
FT t2 = ((bbox.max)(i) - *source_iter) / *direction_iter;
t_near = (std::max)(t_near, (std::min)(t1, t2));
t_far = (std::min)(t_far, (std::max)(t1, t2));
@ -300,7 +300,7 @@ public:
public:
Compute_bbox(const AABB_traits<GeomTraits,AABBPrimitive, BboxMap>& traits)
:m_traits (traits) {}
template<typename ConstPrimitiveIterator>
typename AT::Bounding_box operator()(ConstPrimitiveIterator first,
ConstPrimitiveIterator beyond) const
@ -312,7 +312,7 @@ public:
}
return bbox;
}
};
Compute_bbox compute_bbox_object() const {return Compute_bbox(*this);}
@ -444,7 +444,7 @@ private:
{
return internal::Primitive_helper<AT>::get_datum(pr,*this).bbox();
}
typedef enum { CGAL_AXIS_X = 0,
CGAL_AXIS_Y = 1,

902
AABB_tree/include/CGAL/AABB_tree.h
View File

File diff suppressed because it is too large Load Diff

2
AABB_tree/include/CGAL/internal/AABB_tree/AABB_ray_intersection.h
View File

@ -215,7 +215,7 @@ template<typename Ray, typename SkipFunctor>
boost::optional< typename AABB_tree<AABBTraits>::template Intersection_and_primitive_id<Ray>::Type >
AABB_tree<AABBTraits>::first_intersection(const Ray& query,
const SkipFunctor& skip) const {
CGAL_static_assertion_msg((boost::is_same<Ray, typename AABBTraits::Ray_3>::value),
CGAL_static_assertion_msg((boost::is_same<Ray, typename AABBTraits::Ray_3>::value),
"Ray and Ray_3 must be the same type");
switch(size()) // copy-paste from AABB_tree::traversal

10
AABB_tree/include/CGAL/internal/AABB_tree/AABB_traversal_traits.h
View File

@ -19,7 +19,7 @@
#include <CGAL/internal/AABB_tree/AABB_node.h>
#include <boost/optional.hpp>
namespace CGAL {
namespace CGAL {
namespace internal { namespace AABB_tree {
@ -76,7 +76,7 @@ public:
: m_result(), m_traits(traits)
{}
bool go_further() const {
bool go_further() const {
return !m_result;
}
@ -91,7 +91,7 @@ public:
}
Result result() const { return m_result; }
bool is_intersection_found() const {
bool is_intersection_found() const {
return m_result;
}
@ -291,7 +291,7 @@ public:
const typename Primitive::Id& hint_primitive,
const AABBTraits& traits)
: m_closest_point(hint),
m_closest_primitive(hint_primitive),
m_closest_primitive(hint_primitive),
m_traits(traits)
{}
@ -304,7 +304,7 @@ public:
if( !m_traits.equal_3_object()(new_closest_point, m_closest_point) )
{
m_closest_primitive = primitive.id();
m_closest_point = new_closest_point; // this effectively shrinks the sphere
m_closest_point = new_closest_point; // this effectively shrinks the sphere
}
}

4
AABB_tree/include/CGAL/internal/AABB_tree/Primitive_helper.h
View File

@ -36,7 +36,7 @@ template<class Primitive>
struct Point_result_type<Primitive,false>{ typedef typename Primitive::Point type; };
//helper controlling whether extra data should be stored in the AABB_tree traits class
//helper controlling whether extra data should be stored in the AABB_tree traits class
template <class AABBTraits, bool has_shared_data=Has_nested_type_Shared_data<typename AABBTraits::Primitive>::value>
struct Primitive_helper;
@ -52,7 +52,7 @@ struct Primitive_helper<AABBTraits,true>{
return p.reference_point(traits.shared_data());
}
};
template <class AABBTraits>
struct Primitive_helper<AABBTraits,false>{
typedef typename Datum_result_type<typename AABBTraits::Primitive>::type Datum_type;

2
AABB_tree/package_info/AABB_tree/long_description.txt
View File

@ -1 +1 @@
This component implements a hierarchy of axis-aligned bounding boxes (a AABB tree) for efficient intersection and distance computations between 3D queries and sets of input 3D geometric objects.
This component implements a hierarchy of axis-aligned bounding boxes (a AABB tree) for efficient intersection and distance computations between 3D queries and sets of input 3D geometric objects.

10
AABB_tree/test/AABB_tree/AABB_test_util.h
View File

@ -96,7 +96,7 @@ void test_all_intersection_query_types(Tree& tree)
// any_intersection
boost::optional< typename Tree::AABB_traits::template Intersection_and_primitive_id<Ray>::Type > r = tree.any_intersection(ray);
boost::optional< typename Tree::AABB_traits::template Intersection_and_primitive_id<Line>::Type > l = tree.any_intersection(line);
boost::optional< typename Tree::AABB_traits::template Intersection_and_primitive_id<Line>::Type > l = tree.any_intersection(line);
boost::optional< typename Tree::AABB_traits::template Intersection_and_primitive_id<Segment>::Type > s = tree.any_intersection(segment);
// any_intersected_primitive
@ -162,7 +162,7 @@ void test_distance_speed(Tree& tree,
// picks a random point in the tree bbox
Point query = random_point_in<K>(tree.bbox());
Point closest = tree.closest_point(query);
(void) closest;
(void) closest;
nb++;
}
double speed = (double)nb / timer.time();
@ -323,7 +323,7 @@ class Naive_implementations
typedef typename Traits::Point_and_primitive_id Point_and_primitive_id;
typedef boost::optional<Object_and_primitive_id> Intersection_result;
const Traits& m_traits;
public:
Naive_implementations(const Traits& traits):m_traits(traits){}
@ -691,8 +691,8 @@ private:
typename Tree::AABB_traits::template Intersection_and_primitive_id<Query>::Type
Obj_type;
typedef
std::vector<Obj_type>
typedef
std::vector<Obj_type>
Obj_Id_vector;
Obj_Id_vector intersections_naive;

4
AABB_tree/test/AABB_tree/CMakeLists.txt
View File

@ -19,8 +19,8 @@ if ( CGAL_FOUND )
endforeach()
else()
message(STATUS "This program requires the CGAL library, and will not be compiled.")
endif()

18
AABB_tree/test/AABB_tree/aabb_any_all_benchmark.cpp
View File

@ -29,7 +29,7 @@ const int runs = 10;
template<typename Tree>
struct FilterP {
const Tree* t;
template<typename T>
bool operator()(const T& tt) { return !t->do_intersect(tt); }
};
@ -55,7 +55,7 @@ std::size_t intersect(ForwardIterator b, ForwardIterator e, const Tree& tree, lo
}
template<typename K>
boost::tuple<std::size_t, std::size_t, std::size_t, long> test(const char* name) {
boost::tuple<std::size_t, std::size_t, std::size_t, long> test(const char* name) {
typedef typename K::FT FT;
typedef typename K::Ray_3 Ray;
typedef typename K::Line_3 Line;
@ -75,15 +75,15 @@ boost::tuple<std::size_t, std::size_t, std::size_t, long> test(const char* name)
// Random seeded to 23, cube size equal to the magic number 2
CGAL::Random r(23);
CGAL::Random_points_in_cube_3<Point, CGAL::Creator_uniform_3<FT, Point> > g( 2., r);
std::vector<Point> points;
points.reserve(elements * 2);
std::copy_n(g, elements * 2, std::back_inserter(points));
// generate a bunch of happy random primitives
std::vector<Line> lines;
lines.reserve(elements);
// forward
for(std::size_t i = 0; i < points.size(); i += 2)
{
@ -112,13 +112,13 @@ boost::tuple<std::size_t, std::size_t, std::size_t, long> test(const char* name)
// filter all primitives that do not intersect
FilterP<Tree> p = { &tree };
lines.erase(std::remove_if(lines.begin(), lines.end(), p), lines.end());
rays.erase(std::remove_if(rays.begin(), rays.end(), p), rays.end());
segments.erase(std::remove_if(segments.begin(), segments.end(), p), segments.end());
boost::tuple<std::size_t, std::size_t, std::size_t, long> tu;
{
@ -130,7 +130,7 @@ boost::tuple<std::size_t, std::size_t, std::size_t, long> test(const char* name)
long counter = 0L;
tu = boost::make_tuple(intersect(lines.begin(), lines.end(), tree, counter),
intersect(rays.begin(), rays.end(), tree, counter),
intersect(segments.begin(), segments.end(), tree, counter),
intersect(segments.begin(), segments.end(), tree, counter),
// cant use counter here
0);
boost::get<3>(tu) = counter;
@ -164,7 +164,7 @@ int main()
std::cout << "| Epic kernel |";
boost::tuple<std::size_t, std::size_t, std::size_t, long> t5 = test<CGAL::Exact_predicates_inexact_constructions_kernel>(filename);
std::cout << " | " << std::endl;
std::size_t a, b, c;
long d;

156
AABB_tree/test/AABB_tree/aabb_correctness_triangle_test.cpp
View File

@ -29,100 +29,100 @@
template <class K>
int test()
{
// types
typedef typename K::FT FT;
typedef typename K::Line_3 Line;
typedef typename K::Point_3 Point;
typedef typename K::Segment_3 Segment;
// types
typedef typename K::FT FT;
typedef typename K::Line_3 Line;
typedef typename K::Point_3 Point;
typedef typename K::Segment_3 Segment;
// load polyhedron
typedef CGAL::Polyhedron_3<K> Polyhedron;
Polyhedron polyhedron;
std::ifstream ifs("./data/tetrahedron.off");
ifs >> polyhedron;
// load polyhedron
typedef CGAL::Polyhedron_3<K> Polyhedron;
Polyhedron polyhedron;
std::ifstream ifs("./data/tetrahedron.off");
ifs >> polyhedron;
// construct tree from facets
typedef typename CGAL::AABB_face_graph_triangle_primitive<Polyhedron> Primitive;
typedef typename CGAL::AABB_traits<K,Primitive> Traits;
typedef typename CGAL::AABB_tree<Traits> Tree;
typedef typename Tree::Object_and_primitive_id Object_and_primitive_id;
Tree tree(faces(polyhedron).first, faces(polyhedron).second, polyhedron);
// construct tree from facets
typedef typename CGAL::AABB_face_graph_triangle_primitive<Polyhedron> Primitive;
typedef typename CGAL::AABB_traits<K,Primitive> Traits;
typedef typename CGAL::AABB_tree<Traits> Tree;
typedef typename Tree::Object_and_primitive_id Object_and_primitive_id;
Tree tree(faces(polyhedron).first, faces(polyhedron).second, polyhedron);
// segment intersection query
Point p((FT)-0.25, (FT)0.251, (FT)0.255);
Point q((FT) 0.25, (FT)0.253, (FT)0.256);
Segment pq(p,q);
// segment intersection query
Point p((FT)-0.25, (FT)0.251, (FT)0.255);
Point q((FT) 0.25, (FT)0.253, (FT)0.256);
Segment pq(p,q);
if(!tree.do_intersect(pq))
{
std::cerr << "no intersection found" << std::endl;
return EXIT_FAILURE;
}
if(!tree.do_intersect(pq))
{
std::cerr << "no intersection found" << std::endl;
return EXIT_FAILURE;
}
if(tree.number_of_intersected_primitives(pq) != 1)
{
std::cerr << "number of intersections different than one" << std::endl;
return EXIT_FAILURE;
}
if(tree.number_of_intersected_primitives(pq) != 1)
{
std::cerr << "number of intersections different than one" << std::endl;
return EXIT_FAILURE;
}
boost::optional<Object_and_primitive_id> any;
any = tree.any_intersection(pq);
if(!any)
{
std::cerr << "did not find any intersection" << std::endl;
return EXIT_FAILURE;
}
Object_and_primitive_id op = *any;
CGAL::Object object = op.first;
Point point;
if(CGAL::assign(point,object))
{
std::cout << "Intersection point: " << point << std::endl;
}
else
{
std::cerr << "intersection does not assign to a point" << std::endl;
return EXIT_FAILURE;
}
boost::optional<Object_and_primitive_id> any;
any = tree.any_intersection(pq);
if(!any)
{
std::cerr << "did not find any intersection" << std::endl;
return EXIT_FAILURE;
}
Object_and_primitive_id op = *any;
CGAL::Object object = op.first;
Point point;
if(CGAL::assign(point,object))
{
std::cout << "Intersection point: " << point << std::endl;
}
else
{
std::cerr << "intersection does not assign to a point" << std::endl;
return EXIT_FAILURE;
}
// line intersection query
Line line_pq(p,q);
if(!tree.do_intersect(line_pq))
{
std::cerr << "no intersection found with line" << std::endl;
return EXIT_FAILURE;
}
if(tree.number_of_intersected_primitives(line_pq) != 2)
{
std::cerr << "number of intersections different than two with line" << std::endl;
return EXIT_FAILURE;
}
// line intersection query
Line line_pq(p,q);
if(!tree.do_intersect(line_pq))
{
std::cerr << "no intersection found with line" << std::endl;
return EXIT_FAILURE;
}
if(tree.number_of_intersected_primitives(line_pq) != 2)
{
std::cerr << "number of intersections different than two with line" << std::endl;
return EXIT_FAILURE;
}
// closest point query
Point r((FT)0.0, (FT)0.0, (FT)3.0);
Point closest((FT)0.0, (FT)0.0, (FT)1.0);
Point result = tree.closest_point(r);
if(result != closest)
{
std::cerr << "wrong closest point" << std::endl;
return EXIT_FAILURE;
}
// closest point query
Point r((FT)0.0, (FT)0.0, (FT)3.0);
Point closest((FT)0.0, (FT)0.0, (FT)1.0);
Point result = tree.closest_point(r);
if(result != closest)
{
std::cerr << "wrong closest point" << std::endl;
return EXIT_FAILURE;
}
return EXIT_SUCCESS;
return EXIT_SUCCESS;
}
int main()
{
if(test<CGAL::Simple_cartesian<float> >() == EXIT_FAILURE)
return EXIT_FAILURE;
if(test<CGAL::Simple_cartesian<float> >() == EXIT_FAILURE)
return EXIT_FAILURE;
if(test<CGAL::Simple_cartesian<double> >() == EXIT_FAILURE)
return EXIT_FAILURE;
if(test<CGAL::Simple_cartesian<double> >() == EXIT_FAILURE)
return EXIT_FAILURE;
if(test<CGAL::Exact_predicates_inexact_constructions_kernel>() == EXIT_FAILURE)
return EXIT_FAILURE;
if(test<CGAL::Exact_predicates_inexact_constructions_kernel>() == EXIT_FAILURE)
return EXIT_FAILURE;
return EXIT_SUCCESS;
return EXIT_SUCCESS;
}
/***EMACS SETTINGS***/

6
AABB_tree/test/AABB_tree/aabb_test_datum.cpp
View File

@ -43,17 +43,17 @@ int main(void)
std::cout << "error reading bunny" << std::endl;
return 1;
}
Tree t1(faces(m).begin(), faces(m).end(), m);
Tree2 t2(faces(m).begin(), faces(m).end(), m);
Tree3 t3(faces(m).begin(), faces(m).end(), m);
Tree4 t4(faces(m).begin(), faces(m).end(), m);
t1.build();
t2.build();
t3.build();
t4.build();
Primitive p1(faces(m).begin(), m);
Primitive2 p2(faces(m).begin(), m);
Primitive3 p3(faces(m).begin(), m);

2
AABB_tree/test/AABB_tree/aabb_test_empty_tree.cpp
View File

@ -38,7 +38,7 @@ int main()
tree.all_intersected_primitives(triangle_query, devnull);
assert(!tree.any_intersected_primitive(triangle_query));
assert(!tree.any_intersection(triangle_query));
//Cannot call tree.bbox();
//Cannot call tree.bbox();
tree.build();
tree.clear();
//Cannot call tree.closest_*(...)

14
AABB_tree/test/AABB_tree/aabb_test_multi_mesh.cpp
View File

@ -25,14 +25,14 @@ typedef K::Segment_3 Segment;
typedef K::Ray_3 Ray;
typedef CGAL::Surface_mesh<CGAL::Point_3<CGAL::Epick> > Mesh;
typedef CGAL::AABB_face_graph_triangle_primitive<Mesh,
CGAL::Default,
CGAL::Default,
CGAL::Tag_false> T_Primitive;
typedef CGAL::AABB_traits<K, T_Primitive> T_Traits;
typedef CGAL::AABB_tree<T_Traits> T_Tree;
typedef T_Tree::Primitive_id T_Primitive_id;
typedef CGAL::AABB_halfedge_graph_segment_primitive<Mesh,
CGAL::Default,
CGAL::Default,
CGAL::Tag_false> E_Primitive;
typedef CGAL::AABB_traits<K, E_Primitive> E_Traits;
typedef CGAL::AABB_tree<E_Traits> E_Tree;
@ -61,8 +61,8 @@ int main()
tree.insert(faces(m2).first, faces(m2).second, m2);
tree.build();
T_Tree::Bounding_box bbox = tree.bbox();
Point bbox_center((bbox.xmin() + bbox.xmax()) / 2,
(bbox.ymin() + bbox.ymax()) / 2,
Point bbox_center((bbox.xmin() + bbox.xmax()) / 2,
(bbox.ymin() + bbox.ymax()) / 2,
(bbox.zmin() + bbox.zmax()) / 2);
std::vector< T_Primitive_id > intersections;
Ray ray(bbox_center+Vector(3,-0.25,0),bbox_center+Vector(-3,+0.25,0));
@ -75,8 +75,8 @@ int main()
Ray e_ray(Point(0,0,0),Point(0,1,1));
e_tree.all_intersected_primitives(e_ray,
std::back_inserter(e_intersections));
return 0;
}

10
AABB_tree/test/AABB_tree/aabb_test_ray_intersection.cpp
View File

@ -89,8 +89,8 @@ int main()
Tree tree(faces(polyhedron).first, faces(polyhedron).second, polyhedron);
Tree::Bounding_box bbox = tree.bbox();
Vector bbox_center((bbox.xmin() + bbox.xmax()) / 2,
(bbox.ymin() + bbox.ymax()) / 2,
Vector bbox_center((bbox.xmin() + bbox.xmax()) / 2,
(bbox.ymin() + bbox.ymax()) / 2,
(bbox.zmin() + bbox.zmax()) / 2);
boost::array<double, 3> extents;
extents[0] = bbox.xmax() - bbox.xmin();
@ -101,7 +101,7 @@ int main()
std::cout << bbox << std::endl;
std::cout << bbox_center << std::endl;
std::cout << max_extent << std::endl;
const int NB_RAYS = 1000;
std::vector<Point> v1, v2;
v1.reserve(NB_RAYS); v2.reserve(NB_RAYS);
@ -119,7 +119,7 @@ int main()
for(std::vector<Point>::iterator it = v2.begin(); it != v2.end(); ++it) {
*it = *it + bbox_center;
}
// Generate NB_RAYS using v1 as source and v2 as target.
std::vector<Ray> rays;
rays.reserve(NB_RAYS);
@ -143,7 +143,7 @@ int main()
"Primitives mismatch.");
std::size_t c = primitives1.size() - std::count(primitives1.begin(), primitives1.end(), boost::none);
std::cout << "Intersected " << c << " primitives with " << NB_RAYS << " rays" << std::endl;
std::cout << "Primitive method had to sort " << accum/NB_RAYS
std::cout << "Primitive method had to sort " << accum/NB_RAYS
<< " intersections on average." << std::endl;
t.stop();
std::cout << t.time() << std::endl;

6
AABB_tree/test/AABB_tree/aabb_test_singleton_tree.cpp
View File

@ -46,10 +46,10 @@ int main()
tree.insert(segments.begin(), segments.end());
tree.build();
assert(tree.closest_point(Point(-0.1, -0.1, -0.1)) == Point(0, 0, 0));
assert(tree.closest_point(Point(-0.1, -0.1, -0.1), Point(0, 0, 0)) ==
Point(0, 0, 0));
assert(tree.closest_point(Point(-0.1, -0.1, -0.1), Point(0, 0, 0)) ==
Point(0, 0, 0));
assert(tree.closest_point_and_primitive(Point(-0.1, -0.1, -0.1)).second ==
segments.begin());
segments.begin());
// Too lazy to call closest_point_and_primitive with a hint. The API is
// strange. --Laurent Rineau, 2013/01/16
assert(tree.do_intersect(plane_query) == true);

4
Advancing_front_surface_reconstruction/examples/Advancing_front_surface_reconstruction/CMakeLists.txt
View File

@ -17,8 +17,8 @@ if ( CGAL_FOUND )
endforeach()
else()
message(STATUS "This program requires the CGAL library, and will not be compiled.")
endif()

10
Advancing_front_surface_reconstruction/examples/Advancing_front_surface_reconstruction/reconstruction_structured.cpp
View File

@ -45,7 +45,7 @@ struct On_the_fly_pair{
typedef std::pair<Point, std::size_t> result_type;
On_the_fly_pair(const Pwn_vector& points) : points(points) {}
result_type
operator()(std::size_t i) const
{
@ -59,7 +59,7 @@ struct Priority_with_structure_coherence {
Structure& structure;
double bound;
Priority_with_structure_coherence(Structure& structure,
double bound)
: structure (structure), bound (bound)
@ -111,10 +111,10 @@ int main (int argc, char* argv[])
Pwn_vector points;
const char* fname = (argc>1) ? argv[1] : "data/cube.pwn";
// Loading point set from a file.
// Loading point set from a file.
std::ifstream stream(fname);
if (!stream ||
if (!stream ||
!CGAL::read_xyz_points(stream,
std::back_inserter(points),
CGAL::parameters::point_map(Point_map()).
@ -194,6 +194,6 @@ int main (int argc, char* argv[])
std::cerr << "all done\n" << std::endl;
f.close();
return 0;
}

468
Advancing_front_surface_reconstruction/include/CGAL/Advancing_front_surface_reconstruction.h
View File

@ -401,12 +401,12 @@ namespace CGAL {
{
if (vh->m_incident_border == nullptr) return false; //vh is interior
if (vh->m_incident_border->first->first != nullptr)
{
if (vh->m_incident_border->second->first != nullptr)
return ((vh->m_incident_border->first->second.second == i)||
(vh->m_incident_border->second->second.second == i));
return (vh->m_incident_border->first->second.second == i);
}
{
if (vh->m_incident_border->second->first != nullptr)
return ((vh->m_incident_border->first->second.second == i)||
(vh->m_incident_border->second->second.second == i));
return (vh->m_incident_border->first->second.second == i);
}
return false; //vh is still exterior
}
@ -414,32 +414,32 @@ namespace CGAL {
void remove_border_edge(Vertex_handle w, Vertex_handle v)
{
if (w->m_incident_border != nullptr)
{
if (w->m_incident_border->second->first == v)
{
w->m_incident_border->second->first = nullptr;
set_interior_edge(w,v);
return;
}
if (w->m_incident_border->first->first == v)
{
if (w->m_incident_border->second->first != nullptr)
{
Next_border_elt* tmp = w->m_incident_border->first;
w->m_incident_border->first = w->m_incident_border->second;
w->m_incident_border->second = tmp;
w->m_incident_border->second->first = nullptr;
set_interior_edge(w,v);
return;
}
else
{
w->m_incident_border->first->first = nullptr;
set_interior_edge(w,v);
return;
}
}
}
{
if (w->m_incident_border->second->first == v)
{
w->m_incident_border->second->first = nullptr;
set_interior_edge(w,v);
return;
}
if (w->m_incident_border->first->first == v)
{
if (w->m_incident_border->second->first != nullptr)
{
Next_border_elt* tmp = w->m_incident_border->first;
w->m_incident_border->first = w->m_incident_border->second;
w->m_incident_border->second = tmp;
w->m_incident_border->second->first = nullptr;
set_interior_edge(w,v);
return;
}
else
{
w->m_incident_border->first->first = nullptr;
set_interior_edge(w,v);
return;
}
}
}
}
@ -448,12 +448,12 @@ namespace CGAL {
bool r1;
if(w->m_ie_first == ie_sentinel){
r1 = false;
r1 = false;
}else {
typename std::list<Vertex_handle>::iterator b(w->m_ie_first), e(w->m_ie_last);
e++;
typename std::list<Vertex_handle>::iterator r = std::find(b, e, v);
r1 = ( r != e);
typename std::list<Vertex_handle>::iterator b(w->m_ie_first), e(w->m_ie_last);
e++;
typename std::list<Vertex_handle>::iterator r = std::find(b, e, v);
r1 = ( r != e);
}
return r1;
@ -467,17 +467,17 @@ namespace CGAL {
inline void set_interior_edge(Vertex_handle w, Vertex_handle v)
{
if(w->m_ie_last == ie_sentinel){ // empty set
CGAL_assertion(w->m_ie_first == w->m_ie_last);
w->m_ie_last = interior_edges.insert(w->m_ie_last, v);
w->m_ie_first = w->m_ie_last;
CGAL_assertion(w->m_ie_first == w->m_ie_last);
w->m_ie_last = interior_edges.insert(w->m_ie_last, v);
w->m_ie_first = w->m_ie_last;
} else {
typename std::list<Vertex_handle>::iterator e(w->m_ie_last);
e++;
typename std::list<Vertex_handle>::iterator e(w->m_ie_last);
e++;
#ifdef DEBUG
typename std::list<Vertex_handle>::iterator r = std::find(w->m_ie_first, e, v);
CGAL_assertion(r == e);
typename std::list<Vertex_handle>::iterator r = std::find(w->m_ie_first, e, v);
CGAL_assertion(r == e);
#endif
w->m_ie_last = interior_edges.insert(e, v);
w->m_ie_last = interior_edges.insert(e, v);
}
}
@ -485,26 +485,26 @@ namespace CGAL {
inline void remove_interior_edge(Vertex_handle w, Vertex_handle v)
{
if(w->m_ie_first == ie_sentinel){
CGAL_assertion(w->m_ie_last == w->m_ie_first);
CGAL_assertion(w->m_ie_last == w->m_ie_first);
} else if(w->m_ie_first == w->m_ie_last){ // there is only one element
if(*(w->m_ie_first) == v){
interior_edges.erase(w->m_ie_first);
w->m_ie_last = ie_sentinel;
w->m_ie_first = w->m_ie_last;
}
if(*(w->m_ie_first) == v){
interior_edges.erase(w->m_ie_first);
w->m_ie_last = ie_sentinel;
w->m_ie_first = w->m_ie_last;
}
} else {
typename std::list<Vertex_handle>::iterator b(w->m_ie_first), e(w->m_ie_last);
e++;
typename std::list<Vertex_handle>::iterator r = std::find(b, e, v);
if(r != e){
if(r == w->m_ie_first){
w->m_ie_first++;
}
if(r == w->m_ie_last){
w->m_ie_last--;
}
interior_edges.erase(r);
}
typename std::list<Vertex_handle>::iterator b(w->m_ie_first), e(w->m_ie_last);
e++;
typename std::list<Vertex_handle>::iterator r = std::find(b, e, v);
if(r != e){
if(r == w->m_ie_first){
w->m_ie_first++;
}
if(r == w->m_ie_last){
w->m_ie_last--;
}
interior_edges.erase(r);
}
}
}
@ -514,20 +514,20 @@ namespace CGAL {
inline void set_incidence_request(Vertex_handle w, const Incidence_request_elt& ir)
{
if(w->m_ir_last == sentinel ){
CGAL_assertion(w->m_ir_first == w->m_ir_last);
w->m_ir_last = incidence_requests.insert(w->m_ir_last, ir);
w->m_ir_first = w->m_ir_last;
CGAL_assertion(w->m_ir_first == w->m_ir_last);
w->m_ir_last = incidence_requests.insert(w->m_ir_last, ir);
w->m_ir_first = w->m_ir_last;
} else {
typename std::list<Incidence_request_elt>::iterator e(w->m_ir_last);
e++;
w->m_ir_last = incidence_requests.insert(e, ir);
typename std::list<Incidence_request_elt>::iterator e(w->m_ir_last);
e++;
w->m_ir_last = incidence_requests.insert(e, ir);
}
}
inline bool is_incidence_requested(Vertex_handle w) const
{
if(w->m_ir_last == sentinel ){
CGAL_assertion(w->m_ir_first == sentinel );
CGAL_assertion(w->m_ir_first == sentinel );
}
return (w->m_ir_last != sentinel );
}
@ -540,10 +540,10 @@ namespace CGAL {
inline Incidence_request_iterator incidence_request_end(Vertex_handle w)
{
if(w->m_ir_last != sentinel ){
CGAL_assertion(w->m_ir_first != sentinel );
Incidence_request_iterator it(w->m_ir_last);
it++;
return it;
CGAL_assertion(w->m_ir_first != sentinel );
Incidence_request_iterator it(w->m_ir_last);
it++;
return it;
}
return w->m_ir_last;
}
@ -551,11 +551,11 @@ namespace CGAL {
inline void erase_incidence_request(Vertex_handle w)
{
if(w->m_ir_last != sentinel ){
CGAL_assertion(w->m_ir_first != sentinel );
w->m_ir_last++;
incidence_requests.erase(w->m_ir_first, w->m_ir_last);
w->m_ir_first = sentinel ;
w->m_ir_last = sentinel ;
CGAL_assertion(w->m_ir_first != sentinel );
w->m_ir_last++;
incidence_requests.erase(w->m_ir_first, w->m_ir_last);
w->m_ir_first = sentinel ;
w->m_ir_last = sentinel ;
}
}
@ -563,17 +563,17 @@ namespace CGAL {
void re_init(Vertex_handle w)
{
if (w->m_incident_border != nullptr)
{
w->delete_border();
}
{
w->delete_border();
}
if(w->m_ir_first != sentinel ){
CGAL_assertion(w->m_ir_last != sentinel );
typename std::list< Incidence_request_elt >::iterator b(w->m_ir_first), e(w->m_ir_last);
e++;
incidence_requests.erase(b, e);
w->m_ir_first = sentinel ;
w->m_ir_last = sentinel ;
CGAL_assertion(w->m_ir_last != sentinel );
typename std::list< Incidence_request_elt >::iterator b(w->m_ir_first), e(w->m_ir_last);
e++;
incidence_requests.erase(b, e);
w->m_ir_first = sentinel ;
w->m_ir_last = sentinel ;
}
w->m_incident_border = new_border();
@ -587,10 +587,10 @@ namespace CGAL {
{
w->m_mark--;
if(w->m_mark == 0)
{
w->delete_border();
erase_incidence_request(w);
}
{
w->delete_border();
erase_incidence_request(w);
}
}
@ -621,21 +621,21 @@ namespace CGAL {
void clear_vertex(Vertex_handle w)
{
if (w->m_incident_border != nullptr)
{
w->delete_border();
}
{
w->delete_border();
}
if(w->m_ir_first != sentinel ){
CGAL_assertion(w->m_ir_last != sentinel );
typename std::list< Incidence_request_elt >::iterator b(w->m_ir_first), e(w->m_ir_last);
e++;
incidence_requests.erase(b, e);
CGAL_assertion(w->m_ir_last != sentinel );
typename std::list< Incidence_request_elt >::iterator b(w->m_ir_first), e(w->m_ir_last);
e++;
incidence_requests.erase(b, e);
}
if(w->m_ie_first != ie_sentinel){
CGAL_assertion(w->m_ie_last != ie_sentinel);
typename std::list<Vertex_handle>::iterator b(w->m_ie_first), e(w->m_ie_last);
e++;
interior_edges.erase(b, e);
CGAL_assertion(w->m_ie_last != ie_sentinel);
typename std::list<Vertex_handle>::iterator b(w->m_ie_first), e(w->m_ie_last);
e++;
interior_edges.erase(b, e);
}
}
@ -1315,7 +1315,7 @@ namespace CGAL {
returns the infinite floating value that prevents a facet to be used.
*/
coord_type infinity() const { return std::numeric_limits<coord_type>::infinity(); }
/// @}
/// @}
//---------------------------------------------------------------------
// For a border edge e we determine the incident facet which has the highest
@ -1801,150 +1801,150 @@ namespace CGAL {
return EXTERIOR_CASE;
}
else // c->vertex(i) is a border point (and now there's only 1
// border incident to a point... _mark<1 even if th orientation
// may be such as one vh has 2 successorson the same border...
{
// a ce niveau on peut tester si le recollement se fait en
// maintenant la compatibilite d'orientation des bords (pour
// surface orientable...) ou si elle est brisee...
Edge_incident_facet edge_Ifacet_1(Edge(c, i, edge_Efacet.first.second),
// border incident to a point... _mark<1 even if th orientation
// may be such as one vh has 2 successorson the same border...
{
// a ce niveau on peut tester si le recollement se fait en
// maintenant la compatibilite d'orientation des bords (pour
// surface orientable...) ou si elle est brisee...
Edge_incident_facet edge_Ifacet_1(Edge(c, i, edge_Efacet.first.second),
edge_Efacet.second);
Edge_incident_facet edge_Ifacet_2(Edge(c, i, edge_Efacet.first.third),
Edge_incident_facet edge_Ifacet_2(Edge(c, i, edge_Efacet.first.third),
edge_Efacet.second);
e1 = compute_value(edge_Ifacet_1);
e2 = compute_value(edge_Ifacet_2);
e1 = compute_value(edge_Ifacet_1);
e2 = compute_value(edge_Ifacet_2);
if ((e1.first >= STANDBY_CANDIDATE)&&(e2.first >= STANDBY_CANDIDATE))
return NOT_VALID_CONNECTING_CASE;
if ((e1.first >= STANDBY_CANDIDATE)&&(e2.first >= STANDBY_CANDIDATE))
return NOT_VALID_CONNECTING_CASE;
// vu compute value: les candidats oreilles fournis sont sans
// aretes interieures et le sommet oppose n'est pas non plus interieur
Edge_incident_facet ear1 = e1.second.second;
Edge_incident_facet ear2 = e2.second.second;
// vu compute value: les candidats oreilles fournis sont sans
// aretes interieures et le sommet oppose n'est pas non plus interieur
Edge_incident_facet ear1 = e1.second.second;
Edge_incident_facet ear2 = e2.second.second;
int ear1_i = (6 - ear1.second
- ear1.first.second
- ear1.first.third);
Cell_handle ear1_c = ear1.first.first;
Border_elt result_ear1;
int ear1_i = (6 - ear1.second
- ear1.first.second
- ear1.first.third);
Cell_handle ear1_c = ear1.first.first;
Border_elt result_ear1;
int ear2_i = (6 - ear2.second
- ear2.first.second
- ear2.first.third);
Cell_handle ear2_c = ear2.first.first;
Border_elt result_ear2;
int ear2_i = (6 - ear2.second
- ear2.first.second
- ear2.first.third);
Cell_handle ear2_c = ear2.first.first;
Border_elt result_ear2;
Edge_like ear1_e, ear2_e;
// pour maintenir la reconstruction d'une surface orientable :
// on verifie que les bords se recollent dans des sens opposes
if (ordered_key.first==v1)
{
ear1_e = Edge_like(c->vertex(i), ear1_c ->vertex(ear1_i));
ear2_e = Edge_like(ear2_c ->vertex(ear2_i), c->vertex(i));
}
else
{
ear1_e = Edge_like(ear1_c ->vertex(ear1_i), c->vertex(i));
ear2_e = Edge_like(c->vertex(i), ear2_c ->vertex(ear2_i));
}
Edge_like ear1_e, ear2_e;
// pour maintenir la reconstruction d'une surface orientable :
// on verifie que les bords se recollent dans des sens opposes
if (ordered_key.first==v1)
{
ear1_e = Edge_like(c->vertex(i), ear1_c ->vertex(ear1_i));
ear2_e = Edge_like(ear2_c ->vertex(ear2_i), c->vertex(i));
}
else
{
ear1_e = Edge_like(ear1_c ->vertex(ear1_i), c->vertex(i));
ear2_e = Edge_like(c->vertex(i), ear2_c ->vertex(ear2_i));
}
//maintient la surface orientable
bool is_border_ear1 = is_ordered_border_elt(ear1_e, result_ear1);
bool is_border_ear2 = is_ordered_border_elt(ear2_e, result_ear2);
bool ear1_valid(false), ear2_valid(false);
if (is_border_ear1&&(e1.first < STANDBY_CANDIDATE)&&
(e1.first <= value)&&
(result12.second==result_ear1.second))
{
ear1_valid = test_merge(ear1_e, result_ear1, v1,
priority(*this, ear1_c, ear1.second)) != 0;
}
if (is_border_ear2&&(e2.first < STANDBY_CANDIDATE)&&
(e2.first <= value)&&
(result12.second==result_ear2.second))
{
ear2_valid = test_merge(ear2_e, result_ear2, v2,
priority(*this, ear2_c, ear2.second)) != 0;
}
if ((!ear1_valid)&&(!ear2_valid))
return NOT_VALID_CONNECTING_CASE;
//maintient la surface orientable
bool is_border_ear1 = is_ordered_border_elt(ear1_e, result_ear1);
bool is_border_ear2 = is_ordered_border_elt(ear2_e, result_ear2);
bool ear1_valid(false), ear2_valid(false);
if (is_border_ear1&&(e1.first < STANDBY_CANDIDATE)&&
(e1.first <= value)&&
(result12.second==result_ear1.second))
{
ear1_valid = test_merge(ear1_e, result_ear1, v1,
priority(*this, ear1_c, ear1.second)) != 0;
}
if (is_border_ear2&&(e2.first < STANDBY_CANDIDATE)&&
(e2.first <= value)&&
(result12.second==result_ear2.second))
{
ear2_valid = test_merge(ear2_e, result_ear2, v2,
priority(*this, ear2_c, ear2.second)) != 0;
}
if ((!ear1_valid)&&(!ear2_valid))
return NOT_VALID_CONNECTING_CASE;
IO_edge_type* p1;
IO_edge_type* p2;
IO_edge_type* p1;
IO_edge_type* p2;
border_extend(ordered_key, result12,
v1, v2, c->vertex(i),
e1, e2, p1, p2);
border_extend(ordered_key, result12,
v1, v2, c->vertex(i),
e1, e2, p1, p2);
if (ear1_valid&&ear2_valid&&(ear1_e==ear2_e))
{
if (e1.first < e2.first)
{
Validation_case res = validate(ear1, e1.first);
if (!((res == EAR_CASE)||(res == FINAL_CASE)))
std::cerr << "+++probleme de recollement : cas "
<< res << std::endl;
e2 = compute_value(edge_Ifacet_2);
if (ear1_valid&&ear2_valid&&(ear1_e==ear2_e))
{
if (e1.first < e2.first)
{
Validation_case res = validate(ear1, e1.first);
if (!((res == EAR_CASE)||(res == FINAL_CASE)))
std::cerr << "+++probleme de recollement : cas "
<< res << std::endl;
e2 = compute_value(edge_Ifacet_2);
if (ordered_key.first == v1)
p2 = set_again_border_elt(c->vertex(i), v2,
Border_elt(e2, result2.second));
else
p2 = set_again_border_elt(v2, c->vertex(i),
Border_elt(e2, result2.second));
if (ordered_key.first == v1)
p2 = set_again_border_elt(c->vertex(i), v2,
Border_elt(e2, result2.second));
else
p2 = set_again_border_elt(v2, c->vertex(i),
Border_elt(e2, result2.second));
_ordered_border.insert(Radius_ptr_type(e2.first, p2));
}
else
{
Validation_case res = validate(ear2, e2.first);
if (!((res == EAR_CASE)||(res == FINAL_CASE)))
std::cerr << "+++probleme de recollement : cas "
<< res << std::endl;
e1 = compute_value(edge_Ifacet_1);
_ordered_border.insert(Radius_ptr_type(e2.first, p2));
}
else
{
Validation_case res = validate(ear2, e2.first);
if (!((res == EAR_CASE)||(res == FINAL_CASE)))
std::cerr << "+++probleme de recollement : cas "
<< res << std::endl;
e1 = compute_value(edge_Ifacet_1);
if (ordered_key.first == v1)
p1 = set_again_border_elt(v1, c->vertex(i),
Border_elt(e1, result1.second));
else
p1 = set_again_border_elt(c->vertex(i), v1,
Border_elt(e1, result1.second));
if (ordered_key.first == v1)
p1 = set_again_border_elt(v1, c->vertex(i),
Border_elt(e1, result1.second));
else
p1 = set_again_border_elt(c->vertex(i), v1,
Border_elt(e1, result1.second));
_ordered_border.insert(Radius_ptr_type(e1.first, p1));
}
}
else// les deux oreilles ne se recollent pas sur la meme arete...
{
// on resoud la singularite.
if (ear1_valid)
{
Validation_case res = validate(ear1, e1.first);
if (!((res == EAR_CASE)||(res == FINAL_CASE)))
std::cerr << "+++probleme de recollement : cas "
<< res << std::endl;
}
if (ear2_valid)
{
Validation_case res = validate(ear2, e2.first);
if (!((res == EAR_CASE)||(res == FINAL_CASE)))
std::cerr << "+++probleme de recollement : cas "
<< res << std::endl;
}
// on met a jour la PQ s'il y a lieu... mais surtout pas
// avant la resolution de la singularite
if (!ear1_valid)
{
_ordered_border.insert(Radius_ptr_type(e1.first, p1));
}
if (!ear2_valid)
{
_ordered_border.insert(Radius_ptr_type(e2.first, p2));
}
}
select_facet(c, edge_Efacet.second);
return CONNECTING_CASE;
}
_ordered_border.insert(Radius_ptr_type(e1.first, p1));
}
}
else// les deux oreilles ne se recollent pas sur la meme arete...
{
// on resoud la singularite.
if (ear1_valid)
{
Validation_case res = validate(ear1, e1.first);
if (!((res == EAR_CASE)||(res == FINAL_CASE)))
std::cerr << "+++probleme de recollement : cas "
<< res << std::endl;
}
if (ear2_valid)
{
Validation_case res = validate(ear2, e2.first);
if (!((res == EAR_CASE)||(res == FINAL_CASE)))
std::cerr << "+++probleme de recollement : cas "
<< res << std::endl;
}
// on met a jour la PQ s'il y a lieu... mais surtout pas
// avant la resolution de la singularite
if (!ear1_valid)
{
_ordered_border.insert(Radius_ptr_type(e1.first, p1));
}
if (!ear2_valid)
{
_ordered_border.insert(Radius_ptr_type(e2.first, p2));
}
}
select_facet(c, edge_Efacet.second);
return CONNECTING_CASE;
}
}
}
}
@ -2047,7 +2047,7 @@ namespace CGAL {
{
new_candidate = compute_value(mem_Ifacet);
if ((new_candidate != mem_e_it))
// &&(new_candidate.first < NOT_VALID_CANDIDATE))
// &&(new_candidate.first < NOT_VALID_CANDIDATE))
{
IO_edge_type* pnew =
set_again_border_elt(key_tmp.first, key_tmp.second,
@ -2369,7 +2369,7 @@ namespace CGAL {
{
std::list<Vertex_handle> L_v_tmp;
Vertex_handle vprev_it(v_it), done(vprev_it), vh_it;
// Vertex_handle vsucc_it;
// Vertex_handle vsucc_it;
int v_count(0);
// collect all vertices on the border
do

36
Advancing_front_surface_reconstruction/include/CGAL/Advancing_front_surface_reconstruction_cell_base_3.h
View File

@ -73,7 +73,7 @@ namespace CGAL {
{
#ifdef AFSR_FACET_NUMBER
for(int i = 0; i < 4; i++){
_facet_number[i] = -1;
_facet_number[i] = -1;
}
#endif
}
@ -87,7 +87,7 @@ namespace CGAL {
{
#ifdef FACET_NUMBER
for(int i = 0; i < 4; i++){
_facet_number[i] = -1;
_facet_number[i] = -1;
}
#endif
}
@ -103,7 +103,7 @@ namespace CGAL {
{
#ifdef AFSR_FACET_NUMBER
for(int i = 0; i < 4; i++){
_facet_number[i] = -1;
_facet_number[i] = -1;
}
#endif
}
@ -116,9 +116,9 @@ namespace CGAL {
delete[] _smallest_radius_facet_tab;
#ifdef AFSR_LAZY
if (_circumcenter != nullptr)
delete _circumcenter;
delete _circumcenter;
if (_squared_radius != nullptr)
delete _squared_radius;
delete _squared_radius;
#endif
}
@ -128,15 +128,15 @@ namespace CGAL {
inline void clear()
{
if (_smallest_radius_facet_tab != nullptr)
delete[] _smallest_radius_facet_tab;
delete[] _smallest_radius_facet_tab;
_smallest_radius_facet_tab = nullptr;
selected_facet = 0;
#ifdef AFSR_LAZY
if (_circumcenter != nullptr)
delete _circumcenter;
delete _circumcenter;
_circumcenter = nullptr;
if (_squared_radius != nullptr)
delete _squared_radius;
delete _squared_radius;
_squared_radius = nullptr;
#endif
}
@ -145,18 +145,18 @@ namespace CGAL {
inline coord_type smallest_radius(const int& i)
{
if (_smallest_radius_facet_tab == nullptr)
return -1;
return -1;
return _smallest_radius_facet_tab[i];
}
inline void set_smallest_radius(const int& i, const coord_type& c)
{
if (_smallest_radius_facet_tab == nullptr)
{
_smallest_radius_facet_tab = new coord_type[4];
for(int i = 0; i < 4; i++)
_smallest_radius_facet_tab[i] = -1;
}
{
_smallest_radius_facet_tab = new coord_type[4];
for(int i = 0; i < 4; i++)
_smallest_radius_facet_tab[i] = -1;
}
_smallest_radius_facet_tab[i] = c;
}
@ -164,10 +164,10 @@ namespace CGAL {
inline bool alloc_smallest_radius_tab(coord_type* ptr)
{
if (_smallest_radius_facet_tab==nullptr)
{
_smallest_radius_facet_tab = ptr;
return true;
}
{
_smallest_radius_facet_tab = ptr;
return true;
}
return false;
}

26
Advancing_front_surface_reconstruction/include/CGAL/Advancing_front_surface_reconstruction_vertex_base_3.h
View File

@ -173,11 +173,11 @@ namespace CGAL {
{
if (m_incident_border == nullptr) return nullptr; //vh is interior
if (m_incident_border->first->first != nullptr)
if (m_incident_border->first->second.second == i)
return m_incident_border->first;
if (m_incident_border->first->second.second == i)
return m_incident_border->first;
if (m_incident_border->second->first != nullptr)
if (m_incident_border->second->second.second == i)
return m_incident_border->second;
if (m_incident_border->second->second.second == i)
return m_incident_border->second;
return nullptr;
}
@ -188,7 +188,7 @@ namespace CGAL {
{
if (m_incident_border == nullptr) return false;
return ((m_incident_border->first->first == v)||
(m_incident_border->second->first == v));
(m_incident_border->second->first == v));
}
inline Next_border_elt* border_elt(Vertex_handle v) const
@ -216,13 +216,13 @@ namespace CGAL {
inline void set_next_border_elt(const Next_border_elt& elt)
{
if (m_incident_border->first->first == nullptr)
*m_incident_border->first = elt;
*m_incident_border->first = elt;
else
{
if (m_incident_border->second->first != nullptr)
std::cerr << "+++probleme de MAJ du bord <Vertex_base>" << std::endl;
*m_incident_border->second = elt;
}
{
if (m_incident_border->second->first != nullptr)
std::cerr << "+++probleme de MAJ du bord <Vertex_base>" << std::endl;
*m_incident_border->second = elt;
}
}
@ -257,9 +257,9 @@ namespace CGAL {
inline void inc_mark()
{
if (m_mark==-1)
m_mark=1;
m_mark=1;
else
m_mark++;
m_mark++;
}
//-------------------------------------------------------------------

4
Advancing_front_surface_reconstruction/test/Advancing_front_surface_reconstruction/CMakeLists.txt
View File

@ -17,8 +17,8 @@ if ( CGAL_FOUND )
endforeach()
else()
message(STATUS "This program requires the CGAL library, and will not be compiled.")
endif()

268
Algebraic_foundations/doc/Algebraic_foundations/Algebraic_foundations.txt
View File

@ -1,7 +1,7 @@
namespace CGAL {
/*!
\mainpage User Manual
\mainpage User Manual
\anchor Chapter_Algebraic_Foundations
\cgalAutoToc
@ -9,25 +9,25 @@ namespace CGAL {
\section Algebraic_foundationsIntroduction Introduction
\cgal is targeting towards exact computation with non-linear objects,
in particular objects defined on algebraic curves and surfaces.
As a consequence types representing polynomials, algebraic extensions and
finite fields play a more important role in related implementations.
This package has been introduced to stay abreast of these changes.
\cgal is targeting towards exact computation with non-linear objects,
in particular objects defined on algebraic curves and surfaces.
As a consequence types representing polynomials, algebraic extensions and
finite fields play a more important role in related implementations.
This package has been introduced to stay abreast of these changes.
Since in particular polynomials must be supported by the introduced framework
the package avoids the term <I>number type</I>. Instead the package distinguishes
between the <I>algebraic structure</I> of a type and whether a type is embeddable on
the real axis, or <I>real embeddable</I> for short.
Moreover, the package introduces the notion of <I>interoperable</I> types which
allows an explicit handling of mixed operations.
the package avoids the term <I>number type</I>. Instead the package distinguishes
between the <I>algebraic structure</I> of a type and whether a type is embeddable on
the real axis, or <I>real embeddable</I> for short.
Moreover, the package introduces the notion of <I>interoperable</I> types which
allows an explicit handling of mixed operations.
\section Algebraic_foundationsAlgebraic Algebraic Structures
The algebraic structure concepts introduced within this section are
motivated by their well known counterparts in traditional algebra,
but we also had to pay tribute to existing types and their restrictions.
The algebraic structure concepts introduced within this section are
motivated by their well known counterparts in traditional algebra,
but we also had to pay tribute to existing types and their restrictions.
To keep the interface minimal,
it was not desirable to cover all known algebraic structures,
it was not desirable to cover all known algebraic structures,
e.g., we did not introduce concepts for such basic structures as <I>groups</I> or
exceptional structures as <I>skew fields</I>.
@ -35,95 +35,95 @@ exceptional structures as <I>skew fields</I>.
Concept Hierarchy of Algebraic Structures
\cgalFigureEnd
\cgalFigureRef{figConceptHierarchyOfAlgebraicStructures} shows the refinement
relationship of the algebraic structure concepts.
`IntegralDomain`, `UniqueFactorizationDomain`, `EuclideanRing` and
\cgalFigureRef{figConceptHierarchyOfAlgebraicStructures} shows the refinement
relationship of the algebraic structure concepts.
`IntegralDomain`, `UniqueFactorizationDomain`, `EuclideanRing` and
`Field` correspond to the algebraic structures with the
same name. `FieldWithSqrt`, `FieldWithKthRoot` and
`FieldWithRootOf` are fields that in addition are closed under
the operations 'sqrt', 'k-th root' and 'real root of a polynomial',
same name. `FieldWithSqrt`, `FieldWithKthRoot` and
`FieldWithRootOf` are fields that in addition are closed under
the operations 'sqrt', 'k-th root' and 'real root of a polynomial',
respectively. The concept `IntegralDomainWithoutDivision` also
corresponds to integral domains in the algebraic sense, the
distinction results from the fact that some implementations of
integral domains lack the (algebraically always well defined) integral
integral domains lack the (algebraically always well defined) integral
division.
Note that `Field` refines `IntegralDomain`. This is because
most ring-theoretic notions like greatest common divisors become trivial for
`Field`s. Hence we see `Field` as a refinement of
`IntegralDomain` and not as a
refinement of one of the more advanced ring concepts.
If an algorithm wants to rely on gcd or remainder computation, it is trying
Note that `Field` refines `IntegralDomain`. This is because
most ring-theoretic notions like greatest common divisors become trivial for
`Field`s. Hence we see `Field` as a refinement of
`IntegralDomain` and not as a
refinement of one of the more advanced ring concepts.
If an algorithm wants to rely on gcd or remainder computation, it is trying
to do things it should not do with a `Field` in the first place.
The main properties of an algebraic structure are collected in the class
`Algebraic_structure_traits`.
In particular the (most refined) concept each concrete model `AS`
fulfills is encoded in the tag
The main properties of an algebraic structure are collected in the class
`Algebraic_structure_traits`.
In particular the (most refined) concept each concrete model `AS`
fulfills is encoded in the tag
\link AlgebraicStructureTraits::Algebraic_category `Algebraic_structure_traits<AS>::Algebraic_category` \endlink .
An algebraic structure is at least `Assignable`,
`CopyConstructible`, `DefaultConstructible` and
An algebraic structure is at least `Assignable`,
`CopyConstructible`, `DefaultConstructible` and
`EqualityComparable`. Moreover, we require that it is
constructible from `int`.
For ease of use and since their semantic is sufficiently standard to presume
For ease of use and since their semantic is sufficiently standard to presume
their existence, the usual arithmetic and comparison operators are required
to be realized via \cpp operator overloading.
The division operator is reserved for division in fields.
All other unary (e.g., sqrt) and binary functions
to be realized via \cpp operator overloading.
The division operator is reserved for division in fields.
All other unary (e.g., sqrt) and binary functions
(e.g., gcd, div) must be models of the well known \stl-concepts
`AdaptableUnaryFunction` or `AdaptableBinaryFunction`
concept and local to the traits class
(e.g., \link AlgebraicStructureTraits::Sqrt `Algebraic_structure_traits<AS>::Sqrt()(x)` \endlink).
This design allows us to profit from all parts in the
\stl and its programming style and avoids the name-lookup and
two-pass template compilation problems experienced with the old design
using overloaded functions. However, for ease of use and backward
compatibility all functionality is also
accessible through global functions defined within namespace `CGAL`,
concept and local to the traits class
(e.g., \link AlgebraicStructureTraits::Sqrt `Algebraic_structure_traits<AS>::Sqrt()(x)` \endlink).
This design allows us to profit from all parts in the
\stl and its programming style and avoids the name-lookup and
two-pass template compilation problems experienced with the old design
using overloaded functions. However, for ease of use and backward
compatibility all functionality is also
accessible through global functions defined within namespace `CGAL`,
e.g., \link sqrt `CGAL::sqrt(x)` \endlink. This is realized via function templates using
the according functor of the traits class. For an overview see
the according functor of the traits class. For an overview see
Section \ref PkgAlgebraicFoundationsRef in the reference manual.
\subsection Algebraic_foundationsTagsinAlgebraicStructure Tags in Algebraic Structure Traits
\subsection Algebraic_foundationsAlgebraicCategory Algebraic Category
For a type `AS`, `Algebraic_structure_traits<AS>`
provides several tags. The most important tag is the `Algebraic_category`
tag, which indicates the most refined algebraic concept the type `AS`
fulfills. The tag is one of;
`Integral_domain_without_division_tag`, `Integral_domain_tag`,
`Field_tag`, `Field_with_sqrt_tag`, `Field_with_kth_root_tag`,
`Field_with_root_of_tag`, `Unique_factorization_domain_tag`,
`Euclidean_ring_tag`, or even `Null_tag`
in case the type is not a model of an algebraic structure concept.
The tags are derived from each other such that they reflect the
hierarchy of the algebraic structure concept, e.g.,
`Field_with_sqrt_tag` is derived from `Field_tag`.
For a type `AS`, `Algebraic_structure_traits<AS>`
provides several tags. The most important tag is the `Algebraic_category`
tag, which indicates the most refined algebraic concept the type `AS`
fulfills. The tag is one of;
`Integral_domain_without_division_tag`, `Integral_domain_tag`,
`Field_tag`, `Field_with_sqrt_tag`, `Field_with_kth_root_tag`,
`Field_with_root_of_tag`, `Unique_factorization_domain_tag`,
`Euclidean_ring_tag`, or even `Null_tag`
in case the type is not a model of an algebraic structure concept.
The tags are derived from each other such that they reflect the
hierarchy of the algebraic structure concept, e.g.,
`Field_with_sqrt_tag` is derived from `Field_tag`.
\subsection Algebraic_foundationsExactandNumericalSensitive Exact and Numerical Sensitive
Moreover, `Algebraic_structure_traits<AS>` provides the tags `Is_exact`
and `Is_numerical_sensitive`, which are both `Boolean_tag`s.
Moreover, `Algebraic_structure_traits<AS>` provides the tags `Is_exact`
and `Is_numerical_sensitive`, which are both `Boolean_tag`s.
An algebraic structure is considered <I>exact</I>,
if all operations required by its concept are computed such that a comparison
if all operations required by its concept are computed such that a comparison
of two algebraic expressions is always correct.
An algebraic structure is considered as <I>numerically sensitive</I>,
if the performance of the type is sensitive to the condition number of an
if the performance of the type is sensitive to the condition number of an
algorithm.
Note that there is really a difference among these two notions,
e.g., the fundamental type `int` is not numerical sensitive but
considered inexact due to overflow.
Conversely, types as `leda_real` or `CORE::Expr` are exact but sensitive
to numerical issues due to the internal use of multi precision floating point
Note that there is really a difference among these two notions,
e.g., the fundamental type `int` is not numerical sensitive but
considered inexact due to overflow.
Conversely, types as `leda_real` or `CORE::Expr` are exact but sensitive
to numerical issues due to the internal use of multi precision floating point
arithmetic. We expect that `Is_numerical_sensitive` is used for dispatching
of algorithms, while `Is_exact` is useful to enable assertions that can be
of algorithms, while `Is_exact` is useful to enable assertions that can be
check for exact types only.
Tags are very useful to dispatch between alternative implementations.
The following example illustrates a dispatch for `Field`s using overloaded
functions. The example only needs two overloads since the algebraic
Tags are very useful to dispatch between alternative implementations.
The following example illustrates a dispatch for `Field`s using overloaded
functions. The example only needs two overloads since the algebraic
category tags reflect the algebraic structure hierarchy.
\cgalExample{Algebraic_foundations/algebraic_structure_dispatch.cpp}
@ -132,35 +132,35 @@ category tags reflect the algebraic structure hierarchy.
\anchor secRealEmbeddable
Most number types represent some subset of the real numbers. From those types
we expect functionality to compute the sign, absolute value or double
approximations. In particular we can expect an order on such a type that
reflects the order along the real axis.
Most number types represent some subset of the real numbers. From those types
we expect functionality to compute the sign, absolute value or double
approximations. In particular we can expect an order on such a type that
reflects the order along the real axis.
All these properties are gathered in the concept `::RealEmbeddable`.
The concept is orthogonal to the algebraic structure concepts,
i.e., it is possible
that a type is a model of `RealEmbeddable` only,
The concept is orthogonal to the algebraic structure concepts,
i.e., it is possible
that a type is a model of `RealEmbeddable` only,
since the type may just represent values on the real axis
but does not provide any arithmetic operations.
As for algebraic structures this concept is also traits class oriented.
The main functionality related to `RealEmbeddable` is gathered in
the class `Real_embeddable_traits`. In particular, it provides the boolean
tag `Is_real_embeddable` indicating whether a type is a model of
`RealEmbeddable`. The comparison operators are required to be realized via
\cpp operator overloading.
All unary functions (e.g. <I>sign</I>, <I>to_double</I>) and
binary functions (e.g. <I>compare</I> ) are models of the \stl-concepts
`AdaptableUnaryFunction` and `AdaptableBinaryFunction` and are local
The main functionality related to `RealEmbeddable` is gathered in
the class `Real_embeddable_traits`. In particular, it provides the boolean
tag `Is_real_embeddable` indicating whether a type is a model of
`RealEmbeddable`. The comparison operators are required to be realized via
\cpp operator overloading.
All unary functions (e.g. <I>sign</I>, <I>to_double</I>) and
binary functions (e.g. <I>compare</I> ) are models of the \stl-concepts
`AdaptableUnaryFunction` and `AdaptableBinaryFunction` and are local
to `Real_embeddable_traits`.
In case a type is a model of `IntegralDomainWithoutDivision` and
`RealEmbeddable` the number represented by an object of this type is
In case a type is a model of `IntegralDomainWithoutDivision` and
`RealEmbeddable` the number represented by an object of this type is
the same for arithmetic and comparison.
It follows that the ring represented by this type is a superset of the integers
and a subset of the real numbers and hence has characteristic zero.
In case the type is a model of `Field` and `RealEmbeddable` it is a
In case the type is a model of `Field` and `RealEmbeddable` it is a
superset of the rational numbers.
\section Algebraic_foundationsRealN Real Number Types
@ -181,51 +181,51 @@ hierarchy of \cgalFigureRef{figConceptHierarchyOfAlgebraicStructures}.
\section Algebraic_foundationsInteroperability Interoperability
This section introduces two concepts for interoperability of types,
namely `ImplicitInteroperable` and `ExplicitInteroperable`. While
`ExplicitInteroperable` is the base concept, we start with
This section introduces two concepts for interoperability of types,
namely `ImplicitInteroperable` and `ExplicitInteroperable`. While
`ExplicitInteroperable` is the base concept, we start with
`ImplicitInteroperable` since it is the more intuitive one.
In general mixed operations are provided by overloaded operators and
functions or just via implicit constructor calls.
This level of interoperability is reflected by the concept
`ImplicitInteroperable`. However, within template code the result type,
functions or just via implicit constructor calls.
This level of interoperability is reflected by the concept
`ImplicitInteroperable`. However, within template code the result type,
or so called coercion type, of a mixed arithmetic operation may be unclear.
Therefore, the package introduces `Coercion_traits`
giving access to the coercion type via \link Coercion_traits::Type `Coercion_traits<A,B>::Type` \endlink
for two interoperable types `A` and `B`.
Some trivial example are `int` and `double` with coercion type double
Some trivial example are `int` and `double` with coercion type double
or `Gmpz` and `Gmpq` with coercion type `Gmpq`.
However, the coercion type is not necessarily one of the input types,
e.g. the coercion type of a polynomial
with integer coefficients that is multiplied by a rational type
e.g. the coercion type of a polynomial
with integer coefficients that is multiplied by a rational type
is supposed to be a polynomial with rational coefficients.
`Coercion_traits` is also
required to provide a functor \link Coercion_traits::Cast `Coercion_traits<A,B>::Cast()` \endlink, that
required to provide a functor \link Coercion_traits::Cast `Coercion_traits<A,B>::Cast()` \endlink, that
converts from an input type into the coercion type. This is in fact the core
of the more basic concept `ExplicitInteroperable`.
`ExplicitInteroperable` has been introduced to cover more complex cases
for which it is hard or impossible to guarantee implicit interoperability.
Note that this functor can be useful for `ImplicitInteroperable` types
of the more basic concept `ExplicitInteroperable`.
`ExplicitInteroperable` has been introduced to cover more complex cases
for which it is hard or impossible to guarantee implicit interoperability.
Note that this functor can be useful for `ImplicitInteroperable` types
as well, since it can be used to void redundant type conversions.
In case two types `A` and `B` are `ExplicitInteroperable` with
coercion type `C` they are valid argument types for all binary functors
In case two types `A` and `B` are `ExplicitInteroperable` with
coercion type `C` they are valid argument types for all binary functors
provided by `Algebraic_structure_traits` and `Real_embeddable_traits` of
`C`. This is also true for the according global functions.
\subsection Algebraic_foundationsExamples Examples
The following example illustrates how two write code for
The following example illustrates how two write code for
`ExplicitInteroperable` types.
\cgalExample{Algebraic_foundations/interoperable.cpp}
The following example illustrates a dispatch for `ImplicitInteroperable` and
`ExplicitInteroperable` types.
The binary function (that just multiplies its two arguments) is supposed to
The following example illustrates a dispatch for `ImplicitInteroperable` and
`ExplicitInteroperable` types.
The binary function (that just multiplies its two arguments) is supposed to
take two `ExplicitInteroperable` arguments. For `ImplicitInteroperable`
types a variant that avoids the explicit cast is selected.
@ -233,21 +233,21 @@ types a variant that avoids the explicit cast is selected.
\section Algebraic_foundationsFractions Fractions
Beyond the need for performing algebraic operations on objects as a
whole, there are also number types which one would like to decompose into
numerator and denominator. This does not only hold for rational numbers
as `Quotient`, `Gmpq`, `mpq_class` or `leda_rational`, but
also for compound objects as `Sqrt_extension` or `Polynomial`
which may decompose into a (scalar)
denominator and a compound numerator with a simpler coefficient type
(e.g. integer instead of rational). Often operations can be performed faster on
these denominator-free multiples. In case a type is a `Fraction`
the relevant functionality as well as the numerator and denominator
type are provided by `Fraction_traits`. In particular
Beyond the need for performing algebraic operations on objects as a
whole, there are also number types which one would like to decompose into
numerator and denominator. This does not only hold for rational numbers
as `Quotient`, `Gmpq`, `mpq_class` or `leda_rational`, but
also for compound objects as `Sqrt_extension` or `Polynomial`
which may decompose into a (scalar)
denominator and a compound numerator with a simpler coefficient type
(e.g. integer instead of rational). Often operations can be performed faster on
these denominator-free multiples. In case a type is a `Fraction`
the relevant functionality as well as the numerator and denominator
type are provided by `Fraction_traits`. In particular
`Fraction_traits` provides a tag \link FractionTraits::Is_fraction `Is_fraction` \endlink that can be
used for dispatching.
A related class is `Rational_traits` which has been kept for backward
A related class is `Rational_traits` which has been kept for backward
compatibility reasons. However, we recommend to use `Fraction_traits` since
it is more general and offers dispatching functionality.
@ -256,25 +256,25 @@ it is more general and offers dispatching functionality.
The following example show a simple use of `Fraction_traits`:
\cgalExample{Algebraic_foundations/fraction_traits.cpp}
The following example illustrates the integralization of a vector,
i.e., the coefficient vector of a polynomial. Note that for minimizing
coefficient growth \link FractionTraits::Common_factor `Fraction_traits<Type>::Common_factor` \endlink is used to
The following example illustrates the integralization of a vector,
i.e., the coefficient vector of a polynomial. Note that for minimizing
coefficient growth \link FractionTraits::Common_factor `Fraction_traits<Type>::Common_factor` \endlink is used to
compute the <i>least</i> common multiple of the denominators.
\cgalExample{Algebraic_foundations/integralize.cpp}
\section Algebraic_foundationsDesign Design and Implementation History
The package is part of \cgal since release 3.3. Of course the package is based
on the former Number type support of CGAL. This goes back to Stefan Schirra and Andreas Fabri. But on the other hand the package is to a large extend influenced
by the experience with the number type support in <span class="textsc">Exacus</span> \cgalCite{beh-eeeafcs-05},
which in the main goes back to
Lutz Kettner, Susan Hert, Arno Eigenwillig and Michael Hemmer.
However, the package abstracts from the pure support for
number types that are embedded on the real axis which allows the support of
polynomials, finite fields, and algebraic extensions as well. See also related
The package is part of \cgal since release 3.3. Of course the package is based
on the former Number type support of CGAL. This goes back to Stefan Schirra and Andreas Fabri. But on the other hand the package is to a large extend influenced
by the experience with the number type support in <span class="textsc">Exacus</span> \cgalCite{beh-eeeafcs-05},
which in the main goes back to
Lutz Kettner, Susan Hert, Arno Eigenwillig and Michael Hemmer.
However, the package abstracts from the pure support for
number types that are embedded on the real axis which allows the support of
polynomials, finite fields, and algebraic extensions as well. See also related
subsequent chapters.
*/
*/
} /* namespace CGAL */

50
Algebraic_foundations/doc/Algebraic_foundations/CGAL/Algebraic_structure_traits.h
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@ -3,7 +3,7 @@ namespace CGAL {
/*!
\ingroup PkgAlgebraicFoundationsRef
An instance of `Algebraic_structure_traits` is a model of `AlgebraicStructureTraits`, where <span class="textsc">T</span> is the associated type.
An instance of `Algebraic_structure_traits` is a model of `AlgebraicStructureTraits`, where <span class="textsc">T</span> is the associated type.
\cgalModels `AlgebraicStructureTraits`
@ -19,13 +19,13 @@ namespace CGAL {
/*!
\ingroup PkgAlgebraicFoundationsRef
Tag indicating that a type is a model of the
`EuclideanRing` concept.
Tag indicating that a type is a model of the
`EuclideanRing` concept.
\cgalModels `DefaultConstructible`
\sa `EuclideanRing`
\sa `AlgebraicStructureTraits`
\sa `EuclideanRing`
\sa `AlgebraicStructureTraits`
*/
@ -36,12 +36,12 @@ struct Euclidean_ring_tag : public Unique_factorization_domain_tag {
/*!
\ingroup PkgAlgebraicFoundationsRef
Tag indicating that a type is a model of the `Field` concept.
Tag indicating that a type is a model of the `Field` concept.
\cgalModels `DefaultConstructible`
\sa `Field`
\sa `AlgebraicStructureTraits`
\sa `Field`
\sa `AlgebraicStructureTraits`
*/
@ -52,12 +52,12 @@ struct Field_tag : public Integral_domain_tag {
/*!
\ingroup PkgAlgebraicFoundationsRef
Tag indicating that a type is a model of the `FieldWithKthRoot` concept.
Tag indicating that a type is a model of the `FieldWithKthRoot` concept.
\cgalModels `DefaultConstructible`
\sa `FieldWithKthRoot`
\sa `AlgebraicStructureTraits`
\sa `FieldWithKthRoot`
\sa `AlgebraicStructureTraits`
*/
@ -68,12 +68,12 @@ struct Field_with_kth_root_tag : public Field_with_sqrt_tag {
/*!
\ingroup PkgAlgebraicFoundationsRef
Tag indicating that a type is a model of the `FieldWithRootOf` concept.
Tag indicating that a type is a model of the `FieldWithRootOf` concept.
\cgalModels `DefaultConstructible`
\sa `FieldWithRootOf`
\sa `AlgebraicStructureTraits`
\sa `FieldWithRootOf`
\sa `AlgebraicStructureTraits`
*/
@ -84,12 +84,12 @@ struct Field_with_root_of_tag : public Field_with_kth_root_tag {
/*!
\ingroup PkgAlgebraicFoundationsRef
Tag indicating that a type is a model of the `FieldWithSqrt` concept.
Tag indicating that a type is a model of the `FieldWithSqrt` concept.
\cgalModels `DefaultConstructible`
\sa `FieldWithSqrt`
\sa `AlgebraicStructureTraits`
\sa `FieldWithSqrt`
\sa `AlgebraicStructureTraits`
*/
@ -100,12 +100,12 @@ struct Field_with_sqrt_tag : public Field_tag {
/*!
\ingroup PkgAlgebraicFoundationsRef
Tag indicating that a type is a model of the `IntegralDomain` concept.
Tag indicating that a type is a model of the `IntegralDomain` concept.
\cgalModels `DefaultConstructible`
\sa `IntegralDomain`
\sa `AlgebraicStructureTraits`
\sa `IntegralDomain`
\sa `AlgebraicStructureTraits`
*/
@ -116,11 +116,11 @@ struct Integral_domain_tag : public Integral_domain_without_division_tag {
/*!
\ingroup PkgAlgebraicFoundationsRef
Tag indicating that a type is a model of the `IntegralDomainWithoutDivision` concept.
Tag indicating that a type is a model of the `IntegralDomainWithoutDivision` concept.
\cgalModels `DefaultConstructible`
\sa `IntegralDomainWithoutDivision`
\sa `IntegralDomainWithoutDivision`
*/
@ -131,12 +131,12 @@ struct Integral_domain_without_division_tag {
/*!
\ingroup PkgAlgebraicFoundationsRef
Tag indicating that a type is a model of the `UniqueFactorizationDomain` concept.
Tag indicating that a type is a model of the `UniqueFactorizationDomain` concept.
\cgalModels `DefaultConstructible`
\sa `UniqueFactorizationDomain`
\sa `AlgebraicStructureTraits`
\sa `UniqueFactorizationDomain`
\sa `AlgebraicStructureTraits`
*/

42
Algebraic_foundations/doc/Algebraic_foundations/CGAL/Coercion_traits.h
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@ -4,46 +4,46 @@ namespace CGAL {
/*!
\ingroup PkgAlgebraicFoundationsRef
An instance of `Coercion_traits` reflects the type coercion of the types
<span class="textsc">A</span> and <span class="textsc">B</span>, it is symmetric in the two template arguments.
An instance of `Coercion_traits` reflects the type coercion of the types
<span class="textsc">A</span> and <span class="textsc">B</span>, it is symmetric in the two template arguments.
\sa `ExplicitInteroperable`
\sa `ImplicitInteroperable`
\sa `ExplicitInteroperable`
\sa `ImplicitInteroperable`
*/
template< typename A, typename B >
struct Coercion_traits {
/// \name Types
/// \name Types
/// @{
/*!
Tag indicating whether the two types A and B are a model of `ExplicitInteroperable`
Tag indicating whether the two types A and B are a model of `ExplicitInteroperable`
This is either `CGAL::Tag_true` or `CGAL::Tag_false`.
*/
typedef unspecified_type Are_explicit_interoperable;
This is either `CGAL::Tag_true` or `CGAL::Tag_false`.
*/
typedef unspecified_type Are_explicit_interoperable;
/*!
Tag indicating whether the two types A and B are a model of `ImplicitInteroperable`
Tag indicating whether the two types A and B are a model of `ImplicitInteroperable`
This is either `CGAL::Tag_true` or `CGAL::Tag_false`.
*/
typedef unspecified_type Are_implicit_interoperable;
This is either `CGAL::Tag_true` or `CGAL::Tag_false`.
*/
typedef unspecified_type Are_implicit_interoperable;
/*!
The coercion type of `A` and `B`.
The coercion type of `A` and `B`.
In case A and B are not `ExplicitInteroperable` this is undefined.
*/
typedef unspecified_type Type;
In case A and B are not `ExplicitInteroperable` this is undefined.
*/
typedef unspecified_type Type;
/*!
A model of the `AdaptableFunctor` concept, providing the conversion of `A` or `B` to `Type`.
A model of the `AdaptableFunctor` concept, providing the conversion of `A` or `B` to `Type`.
In case A and B are not `ExplicitInteroperable` this is undefined.
*/
typedef unspecified_type Cast;
In case A and B are not `ExplicitInteroperable` this is undefined.
*/
typedef unspecified_type Cast;
/// @}

4
Algebraic_foundations/doc/Algebraic_foundations/CGAL/Fraction_traits.h
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@ -3,8 +3,8 @@ namespace CGAL {
/*!
\ingroup PkgAlgebraicFoundationsRef
An instance of `Fraction_traits` is a model of `FractionTraits`,
where `T` is the associated type.
An instance of `Fraction_traits` is a model of `FractionTraits`,
where `T` is the associated type.
\cgalModels `FractionTraits`

2
Algebraic_foundations/doc/Algebraic_foundations/CGAL/Real_embeddable_traits.h
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@ -4,7 +4,7 @@ namespace CGAL {
/*!
\ingroup PkgAlgebraicFoundationsRef
An instance of `Real_embeddable_traits` is a model of `RealEmbeddableTraits`, where <span class="textsc">T</span> is the associated type.
An instance of `Real_embeddable_traits` is a model of `RealEmbeddableTraits`, where <span class="textsc">T</span> is the associated type.
\cgalModels `RealEmbeddableTraits`

364
Algebraic_foundations/doc/Algebraic_foundations/CGAL/number_utils.h
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@ -3,13 +3,13 @@ namespace CGAL {
/*!
\ingroup PkgAlgebraicFoundationsRef
The template function `abs()` returns the absolute value of a number.
The template function `abs()` returns the absolute value of a number.
The function is defined if the argument type
is a model of the `RealEmbeddable` concept.
The function is defined if the argument type
is a model of the `RealEmbeddable` concept.
\sa `RealEmbeddable`
\sa `RealEmbeddableTraits_::Abs`
\sa `RealEmbeddable`
\sa `RealEmbeddableTraits_::Abs`
*/
template <class NT> NT abs(const NT& x);
@ -21,21 +21,21 @@ namespace CGAL {
/*!
\ingroup PkgAlgebraicFoundationsRef
The template function `compare()` compares the first argument with respect to
the second, i.e.\ it returns `CGAL::LARGER` if \f$ x\f$ is larger then \f$ y\f$.
The template function `compare()` compares the first argument with respect to
the second, i.e.\ it returns `CGAL::LARGER` if \f$ x\f$ is larger then \f$ y\f$.
In case the argument types `NT1` and `NT2` differ,
`compare` is performed with the semantic of the type determined via
`Coercion_traits`.
The function is defined if this type
is a model of the `RealEmbeddable` concept.
In case the argument types `NT1` and `NT2` differ,
`compare` is performed with the semantic of the type determined via
`Coercion_traits`.
The function is defined if this type
is a model of the `RealEmbeddable` concept.
The `result_type` is convertible to `CGAL::Comparison_result`.
The `result_type` is convertible to `CGAL::Comparison_result`.
\sa `RealEmbeddable`
\sa `RealEmbeddableTraits_::Compare`
\sa `RealEmbeddable`
\sa `RealEmbeddableTraits_::Compare`
*/
template <class NT1, class NT2>
template <class NT1, class NT2>
result_type compare(const NT &x, const NT &y);
} /* namespace CGAL */
@ -45,28 +45,28 @@ namespace CGAL {
/*!
\ingroup PkgAlgebraicFoundationsRef
The function `div()` computes the integral quotient of division
with remainder.
The function `div()` computes the integral quotient of division
with remainder.
In case the argument types `NT1` and `NT2` differ,
the `result_type` is determined via `Coercion_traits`.
In case the argument types `NT1` and `NT2` differ,
the `result_type` is determined via `Coercion_traits`.
Thus, the `result_type` is well defined if `NT1` and `NT2`
are a model of `ExplicitInteroperable`.
Thus, the `result_type` is well defined if `NT1` and `NT2`
are a model of `ExplicitInteroperable`.
The actual `div` is performed with the semantic of that type.
The actual `div` is performed with the semantic of that type.
The function is defined if `result_type`
is a model of the `EuclideanRing` concept.
The function is defined if `result_type`
is a model of the `EuclideanRing` concept.
\sa `EuclideanRing`
\sa `AlgebraicStructureTraits_::Div`
\sa `EuclideanRing`
\sa `AlgebraicStructureTraits_::Div`
\sa `CGAL::mod()`
\sa `CGAL::div_mod()`
*/
template< class NT1, class NT2>
result_type
template< class NT1, class NT2>
result_type
div(const NT1& x, const NT2& y);
} /* namespace CGAL */
@ -76,32 +76,32 @@ namespace CGAL {
/*!
\ingroup PkgAlgebraicFoundationsRef
computes the quotient \f$ q\f$ and remainder \f$ r\f$, such that \f$ x = q*y + r\f$
and \f$ r\f$ minimal with respect to the Euclidean Norm of the
computes the quotient \f$ q\f$ and remainder \f$ r\f$, such that \f$ x = q*y + r\f$
and \f$ r\f$ minimal with respect to the Euclidean Norm of the
`result_type`.
The function `div_mod()` computes the integral quotient and remainder of
division with remainder.
The function `div_mod()` computes the integral quotient and remainder of
division with remainder.
In case the argument types `NT1` and `NT2` differ,
the `result_type` is determined via `Coercion_traits`.
In case the argument types `NT1` and `NT2` differ,
the `result_type` is determined via `Coercion_traits`.
Thus, the `result_type` is well defined if `NT1` and `NT2`
are a model of `ExplicitInteroperable`.
Thus, the `result_type` is well defined if `NT1` and `NT2`
are a model of `ExplicitInteroperable`.
The actual `div_mod` is performed with the semantic of that type.
The actual `div_mod` is performed with the semantic of that type.
The function is defined if `result_type`
is a model of the `EuclideanRing` concept.
The function is defined if `result_type`
is a model of the `EuclideanRing` concept.
\sa `EuclideanRing`
\sa `EuclideanRing`
\sa `AlgebraicStructureTraits_::DivMod`
\sa `CGAL::mod()`
\sa `CGAL::div()`
*/
template <class NT1, class NT2>
void
template <class NT1, class NT2>
void
div_mod(const NT1& x, const NT2& y, result_type& q, result_type& r);
} /* namespace CGAL */
@ -111,24 +111,24 @@ namespace CGAL {
/*!
\ingroup PkgAlgebraicFoundationsRef
The function `gcd()` computes the greatest common divisor of two values.
The function `gcd()` computes the greatest common divisor of two values.
In case the argument types `NT1` and `NT2` differ,
the `result_type` is determined via `Coercion_traits`.
In case the argument types `NT1` and `NT2` differ,
the `result_type` is determined via `Coercion_traits`.
Thus, the `result_type` is well defined if `NT1` and `NT2`
are a model of `ExplicitInteroperable`.
Thus, the `result_type` is well defined if `NT1` and `NT2`
are a model of `ExplicitInteroperable`.
The actual `gcd` is performed with the semantic of that type.
The actual `gcd` is performed with the semantic of that type.
The function is defined if `result_type`
is a model of the `UniqueFactorizationDomain` concept.
The function is defined if `result_type`
is a model of the `UniqueFactorizationDomain` concept.
\sa `UniqueFactorizationDomain`
\sa `AlgebraicStructureTraits_::Gcd`
\sa `UniqueFactorizationDomain`
\sa `AlgebraicStructureTraits_::Gcd`
*/
template <class NT1, class NT2> result_type
template <class NT1, class NT2> result_type
gcd(const NT1& x, const NT2& y);
} /* namespace CGAL */
@ -138,28 +138,28 @@ namespace CGAL {
/*!
\ingroup PkgAlgebraicFoundationsRef
The function `integral_division()` (a.k.a.\ exact division or division without remainder)
maps ring elements \f$ (x,y)\f$ to ring element \f$ z\f$ such that \f$ x = yz\f$ if such a \f$ z\f$
exists (i.e.\ if \f$ x\f$ is divisible by \f$ y\f$). Otherwise the effect of invoking
this operation is undefined. Since the ring represented is an integral domain,
\f$ z\f$ is uniquely defined if it exists.
The function `integral_division()` (a.k.a.\ exact division or division without remainder)
maps ring elements \f$ (x,y)\f$ to ring element \f$ z\f$ such that \f$ x = yz\f$ if such a \f$ z\f$
exists (i.e.\ if \f$ x\f$ is divisible by \f$ y\f$). Otherwise the effect of invoking
this operation is undefined. Since the ring represented is an integral domain,
\f$ z\f$ is uniquely defined if it exists.
In case the argument types `NT1` and `NT2` differ,
the `result_type` is determined via `Coercion_traits`.
In case the argument types `NT1` and `NT2` differ,
the `result_type` is determined via `Coercion_traits`.
Thus, the `result_type` is well defined if `NT1` and `NT2`
are a model of `ExplicitInteroperable`.
Thus, the `result_type` is well defined if `NT1` and `NT2`
are a model of `ExplicitInteroperable`.
The actual `integral_division` is performed with the semantic of that type.
The actual `integral_division` is performed with the semantic of that type.
The function is defined if `result_type`
is a model of the `IntegralDomain` concept.
The function is defined if `result_type`
is a model of the `IntegralDomain` concept.
\sa `IntegralDomain`
\sa `AlgebraicStructureTraits_::IntegralDivision`
\sa `IntegralDomain`
\sa `AlgebraicStructureTraits_::IntegralDivision`
*/
template <class NT1, class NT2> result_type
template <class NT1, class NT2> result_type
integral_division(const NT1& x, const NT2& y);
} /* namespace CGAL */
@ -169,15 +169,15 @@ namespace CGAL {
/*!
\ingroup PkgAlgebraicFoundationsRef
The function `inverse()` returns the inverse element with respect to multiplication.
The function `inverse()` returns the inverse element with respect to multiplication.
The function is defined if the argument type
is a model of the `Field` concept.
The function is defined if the argument type
is a model of the `Field` concept.
\pre \f$ x \neq0\f$.
\sa `Field`
\sa `AlgebraicStructureTraits_::Inverse`
\sa `Field`
\sa `AlgebraicStructureTraits_::Inverse`
*/
template <class NT> NT inverse(const NT& x);
@ -189,14 +189,14 @@ namespace CGAL {
/*!
\ingroup PkgAlgebraicFoundationsRef
The template function `is_negative()` determines if a value is negative or not.
The function is defined if the argument type
is a model of the `RealEmbeddable` concept.
The template function `is_negative()` determines if a value is negative or not.
The function is defined if the argument type
is a model of the `RealEmbeddable` concept.
The `result_type` is convertible to `bool`.
The `result_type` is convertible to `bool`.
\sa `RealEmbeddable`
\sa `RealEmbeddableTraits_::IsNegative`
\sa `RealEmbeddable`
\sa `RealEmbeddableTraits_::IsNegative`
*/
result_type is_negative(const NT& x);
@ -208,15 +208,15 @@ namespace CGAL {
/*!
\ingroup PkgAlgebraicFoundationsRef
The function `is_one()` determines if a value is equal to 1 or not.
The function `is_one()` determines if a value is equal to 1 or not.
The function is defined if the argument type
is a model of the `IntegralDomainWithoutDivision` concept.
The function is defined if the argument type
is a model of the `IntegralDomainWithoutDivision` concept.
The `result_type` is convertible to `bool`.
The `result_type` is convertible to `bool`.
\sa `IntegralDomainWithoutDivision`
\sa `AlgebraicStructureTraits_::IsOne`
\sa `IntegralDomainWithoutDivision`
\sa `AlgebraicStructureTraits_::IsOne`
*/
template <class NT> result_type is_one(const NT& x);
@ -228,14 +228,14 @@ namespace CGAL {
/*!
\ingroup PkgAlgebraicFoundationsRef
The template function `is_positive()` determines if a value is positive or not.
The function is defined if the argument type
is a model of the `RealEmbeddable` concept.
The template function `is_positive()` determines if a value is positive or not.
The function is defined if the argument type
is a model of the `RealEmbeddable` concept.
The `result_type` is convertible to `bool`.
The `result_type` is convertible to `bool`.
\sa `RealEmbeddable`
\sa `RealEmbeddableTraits_::IsPositive`
\sa `RealEmbeddable`
\sa `RealEmbeddableTraits_::IsPositive`
*/
result_type is_positive(const NT& x);
@ -247,18 +247,18 @@ namespace CGAL {
/*!
\ingroup PkgAlgebraicFoundationsRef
An ring element \f$ x\f$ is said to be a square iff there exists a ring element
\f$ y\f$ such
that \f$ x= y*y\f$. In case the ring is a `UniqueFactorizationDomain`,
\f$ y\f$ is uniquely defined up to multiplication by units.
An ring element \f$ x\f$ is said to be a square iff there exists a ring element
\f$ y\f$ such
that \f$ x= y*y\f$. In case the ring is a `UniqueFactorizationDomain`,
\f$ y\f$ is uniquely defined up to multiplication by units.
The function `is_square()` is available if
`Algebraic_structure_traits::Is_square` is not the `CGAL::Null_functor`.
The function `is_square()` is available if
`Algebraic_structure_traits::Is_square` is not the `CGAL::Null_functor`.
The `result_type` is convertible to `bool`.
The `result_type` is convertible to `bool`.
\sa `UniqueFactorizationDomain`
\sa `AlgebraicStructureTraits_::IsSquare`
\sa `UniqueFactorizationDomain`
\sa `AlgebraicStructureTraits_::IsSquare`
*/
template <class NT> result_type is_square(const NT& x);
@ -266,18 +266,18 @@ template <class NT> result_type is_square(const NT& x);
/*!
\ingroup PkgAlgebraicFoundationsRef
An ring element \f$ x\f$ is said to be a square iff there exists a ring element
\f$ y\f$ such
that \f$ x= y*y\f$. In case the ring is a `UniqueFactorizationDomain`,
\f$ y\f$ is uniquely defined up to multiplication by units.
An ring element \f$ x\f$ is said to be a square iff there exists a ring element
\f$ y\f$ such
that \f$ x= y*y\f$. In case the ring is a `UniqueFactorizationDomain`,
\f$ y\f$ is uniquely defined up to multiplication by units.
The function `is_square()` is available if
`Algebraic_structure_traits::Is_square` is not the `CGAL::Null_functor`.
The function `is_square()` is available if
`Algebraic_structure_traits::Is_square` is not the `CGAL::Null_functor`.
The `result_type` is convertible to `bool`.
\sa `UniqueFactorizationDomain`
\sa `AlgebraicStructureTraits_::IsSquare`
\sa `UniqueFactorizationDomain`
\sa `AlgebraicStructureTraits_::IsSquare`
*/
template <class NT> result_type is_square(const NT& x, NT& y);
@ -289,18 +289,18 @@ namespace CGAL {
/*!
\ingroup PkgAlgebraicFoundationsRef
The function `is_zero()` determines if a value is equal to 0 or not.
The function `is_zero()` determines if a value is equal to 0 or not.
The function is defined if the argument type
is a model of the `RealEmbeddable` or of
the `IntegralDomainWithoutDivision` concept.
The function is defined if the argument type
is a model of the `RealEmbeddable` or of
the `IntegralDomainWithoutDivision` concept.
The `result_type` is convertible to `bool`.
The `result_type` is convertible to `bool`.
\sa `RealEmbeddable`
\sa `RealEmbeddableTraits_::IsZero`
\sa `IntegralDomainWithoutDivision`
\sa `AlgebraicStructureTraits_::IsZero`
\sa `RealEmbeddable`
\sa `RealEmbeddableTraits_::IsZero`
\sa `IntegralDomainWithoutDivision`
\sa `AlgebraicStructureTraits_::IsZero`
*/
template <class NT> result_type is_zero(const NT& x);
@ -311,13 +311,13 @@ namespace CGAL {
/*!
\ingroup PkgAlgebraicFoundationsRef
The function `kth_root()` returns the k-th root of a value.
The function `kth_root()` returns the k-th root of a value.
The function is defined if the second argument type
is a model of the `FieldWithKthRoot` concept.
The function is defined if the second argument type
is a model of the `FieldWithKthRoot` concept.
\sa `FieldWithKthRoot`
\sa `AlgebraicStructureTraits_::KthRoot`
\sa `FieldWithKthRoot`
\sa `AlgebraicStructureTraits_::KthRoot`
*/
template <class NT> NT kth_root(int k, const NT& x);
@ -329,27 +329,27 @@ namespace CGAL {
/*!
\ingroup PkgAlgebraicFoundationsRef
The function `mod()` computes the remainder of division with remainder.
The function `mod()` computes the remainder of division with remainder.
In case the argument types `NT1` and `NT2` differ,
the `result_type` is determined via `Coercion_traits`.
In case the argument types `NT1` and `NT2` differ,
the `result_type` is determined via `Coercion_traits`.
Thus, the `result_type` is well defined if `NT1` and `NT2`
are a model of `ExplicitInteroperable`.
Thus, the `result_type` is well defined if `NT1` and `NT2`
are a model of `ExplicitInteroperable`.
The actual `mod` is performed with the semantic of that type.
The actual `mod` is performed with the semantic of that type.
The function is defined if `result_type`
is a model of the `EuclideanRing` concept.
The function is defined if `result_type`
is a model of the `EuclideanRing` concept.
\sa `EuclideanRing`
\sa `AlgebraicStructureTraits_::DivMod`
\sa `EuclideanRing`
\sa `AlgebraicStructureTraits_::DivMod`
\sa `CGAL::div_mod()`
\sa `CGAL::div()`
*/
template< class NT1, class NT2>
result_type
template< class NT1, class NT2>
result_type
mod(const NT1& x, const NT2& y);
} /* namespace CGAL */
@ -363,19 +363,19 @@ returns the k-th real root of the univariate polynomial, which is
defined by the iterator range, where begin refers to the constant
term.
The function `root_of()` computes a real root of a square-free univariate
polynomial.
The function `root_of()` computes a real root of a square-free univariate
polynomial.
The function is defined if the value type, `NT`,
of the iterator range is a model of the `FieldWithRootOf` concept.
The function is defined if the value type, `NT`,
of the iterator range is a model of the `FieldWithRootOf` concept.
\pre The polynomial is square-free.
\sa `FieldWithRootOf`
\sa `AlgebraicStructureTraits_::RootOf`
\sa `FieldWithRootOf`
\sa `AlgebraicStructureTraits_::RootOf`
*/
template <class InputIterator> NT
template <class InputIterator> NT
root_of(int k, InputIterator begin, InputIterator end);
} /* namespace CGAL */
@ -385,15 +385,15 @@ namespace CGAL {
/*!
\ingroup PkgAlgebraicFoundationsRef
The template function `sign()` returns the sign of its argument.
The template function `sign()` returns the sign of its argument.
The function is defined if the argument type
is a model of the `RealEmbeddable` concept.
The function is defined if the argument type
is a model of the `RealEmbeddable` concept.
The `result_type` is convertible to `CGAL::Sign`.
The `result_type` is convertible to `CGAL::Sign`.
\sa `RealEmbeddable`
\sa `RealEmbeddableTraits_::Sgn`
\sa `RealEmbeddable`
\sa `RealEmbeddableTraits_::Sgn`
*/
template <class NT> result_type sign(const NT& x);
@ -405,13 +405,13 @@ namespace CGAL {
/*!
\ingroup PkgAlgebraicFoundationsRef
The function `simplify()` may simplify a given object.
The function `simplify()` may simplify a given object.
The function is defined if the argument type
is a model of the `IntegralDomainWithoutDivision` concept.
The function is defined if the argument type
is a model of the `IntegralDomainWithoutDivision` concept.
\sa `IntegralDomainWithoutDivision`
\sa `AlgebraicStructureTraits_::Simplify`
\sa `IntegralDomainWithoutDivision`
\sa `AlgebraicStructureTraits_::Simplify`
*/
template <class NT> void simplify(const NT& x);
@ -423,13 +423,13 @@ namespace CGAL {
/*!
\ingroup PkgAlgebraicFoundationsRef
The function `sqrt()` returns the square root of a value.
The function `sqrt()` returns the square root of a value.
The function is defined if the argument type
is a model of the `FieldWithSqrt` concept.
The function is defined if the argument type
is a model of the `FieldWithSqrt` concept.
\sa `FieldWithSqrt`
\sa `AlgebraicStructureTraits_::Sqrt`
\sa `FieldWithSqrt`
\sa `AlgebraicStructureTraits_::Sqrt`
*/
template <class NT> NT sqrt(const NT& x);
@ -441,13 +441,13 @@ namespace CGAL {
/*!
\ingroup PkgAlgebraicFoundationsRef
The function `square()` returns the square of a number.
The function `square()` returns the square of a number.
The function is defined if the argument type
is a model of the `IntegralDomainWithoutDivision` concept.
The function is defined if the argument type
is a model of the `IntegralDomainWithoutDivision` concept.
\sa `IntegralDomainWithoutDivision`
\sa `AlgebraicStructureTraits_::Square`
\sa `IntegralDomainWithoutDivision`
\sa `AlgebraicStructureTraits_::Square`
*/
template <class NT> NT square(const NT& x);
@ -466,13 +466,13 @@ number type (such as an instance of `CGAL::Lazy_exact_nt`), the double approxima
returned might be affected by an exact computation internally triggered
(that might have improved the double approximation).
The function is defined if the argument type
is a model of the `RealEmbeddable` concept.
The function is defined if the argument type
is a model of the `RealEmbeddable` concept.
Remark: In order to control the quality of approximation one has to resort to methods that are specific to NT. There are no general guarantees whatsoever.
Remark: In order to control the quality of approximation one has to resort to methods that are specific to NT. There are no general guarantees whatsoever.
\sa `RealEmbeddable`
\sa `RealEmbeddableTraits_::ToDouble`
\sa `RealEmbeddable`
\sa `RealEmbeddableTraits_::ToDouble`
*/
template <class NT> double to_double(const NT& x);
@ -484,17 +484,17 @@ namespace CGAL {
/*!
\ingroup PkgAlgebraicFoundationsRef
The template function `to_interval()` computes for a given real embeddable
number \f$ x\f$ a double interval containing \f$ x\f$.
This interval is represented by a `std::pair<double,double>`.
The function is defined if the argument type
is a model of the `RealEmbeddable` concept.
The template function `to_interval()` computes for a given real embeddable
number \f$ x\f$ a double interval containing \f$ x\f$.
This interval is represented by a `std::pair<double,double>`.
The function is defined if the argument type
is a model of the `RealEmbeddable` concept.
\sa `RealEmbeddable`
\sa `RealEmbeddableTraits_::ToInterval`
\sa `RealEmbeddable`
\sa `RealEmbeddableTraits_::ToInterval`
*/
template <class NT>
template <class NT>
std::pair<double,double> to_interval(const NT& x);
} /* namespace CGAL */
@ -504,14 +504,14 @@ namespace CGAL {
/*!
\ingroup PkgAlgebraicFoundationsRef
The function `unit_part()` computes the unit part of a given ring
element.
The function `unit_part()` computes the unit part of a given ring
element.
The function is defined if the argument type
is a model of the `IntegralDomainWithoutDivision` concept.
The function is defined if the argument type
is a model of the `IntegralDomainWithoutDivision` concept.
\sa `IntegralDomainWithoutDivision`
\sa `AlgebraicStructureTraits_::UnitPart`
\sa `IntegralDomainWithoutDivision`
\sa `AlgebraicStructureTraits_::UnitPart`
*/
template <class NT> NT unit_part(const NT& x);

44
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--Div.h
View File

@ -5,10 +5,10 @@ namespace AlgebraicStructureTraits_{
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
`AdaptableBinaryFunction` computes the integral quotient of division
with remainder.
`AdaptableBinaryFunction` computes the integral quotient of division
with remainder.
\cgalRefines `AdaptableBinaryFunction`
\cgalRefines `AdaptableBinaryFunction`
\sa `AlgebraicStructureTraits`
\sa `AlgebraicStructureTraits_::Mod`
@ -19,40 +19,40 @@ with remainder.
class Div {
public:
/// \name Types
/// \name Types
/// @{
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type result_type;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type result_type;
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type first_argument;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type first_argument;
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type second_argument;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type second_argument;
/// @}
/// @}
/// \name Operations
/// \name Operations
/// @{
/*!
*/
result_type operator()(first_argument_type x,
second_argument_type y);
*/
result_type operator()(first_argument_type x,
second_argument_type y);
/*!
This operator is defined if `NT1` and `NT2` are `ExplicitInteroperable`
with coercion type `AlgebraicStructureTraits::Type`.
*/
template <class NT1, class NT2> result_type operator()(NT1 x, NT2 y);
This operator is defined if `NT1` and `NT2` are `ExplicitInteroperable`
with coercion type `AlgebraicStructureTraits::Type`.
*/
template <class NT1, class NT2> result_type operator()(NT1 x, NT2 y);
/// @}

420
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--DivMod.h
View File

@ -5,191 +5,191 @@ namespace AlgebraicStructureTraits_{
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
`AdaptableFunctor` computes both integral quotient and remainder
of division with remainder. The quotient \f$ q\f$ and remainder \f$ r\f$ are computed
such that \f$ x = q*y + r\f$ and \f$ |r| < |y|\f$ with respect to the proper integer norm of
the represented ring.
\cgalFootnote{For integers this norm is the absolute value.
For univariate polynomials this norm is the degree.}
In particular, \f$ r\f$ is chosen to be \f$ 0\f$ if possible.
Moreover, we require \f$ q\f$ to be minimized with respect to the proper integer norm.
`AdaptableFunctor` computes both integral quotient and remainder
of division with remainder. The quotient \f$ q\f$ and remainder \f$ r\f$ are computed
such that \f$ x = q*y + r\f$ and \f$ |r| < |y|\f$ with respect to the proper integer norm of
the represented ring.
\cgalFootnote{For integers this norm is the absolute value.
For univariate polynomials this norm is the degree.}
In particular, \f$ r\f$ is chosen to be \f$ 0\f$ if possible.
Moreover, we require \f$ q\f$ to be minimized with respect to the proper integer norm.
Note that the last condition is needed to ensure a unique computation of the
pair \f$ (q,r)\f$. However, an other option is to require minimality for \f$ |r|\f$,
with the advantage that
a <I>mod(x,y)</I> operation would return the unique representative of the
residue class of \f$ x\f$ with respect to \f$ y\f$, e.g. \f$ mod(2,3)\f$ should return \f$ -1\f$.
But this conflicts with nearly all current implementation
of integer types. From there, we decided to stay conform with common
implementations and require \f$ q\f$ to be computed as \f$ x/y\f$ rounded towards zero.
Note that the last condition is needed to ensure a unique computation of the
pair \f$ (q,r)\f$. However, an other option is to require minimality for \f$ |r|\f$,
with the advantage that
a <I>mod(x,y)</I> operation would return the unique representative of the
residue class of \f$ x\f$ with respect to \f$ y\f$, e.g. \f$ mod(2,3)\f$ should return \f$ -1\f$.
But this conflicts with nearly all current implementation
of integer types. From there, we decided to stay conform with common
implementations and require \f$ q\f$ to be computed as \f$ x/y\f$ rounded towards zero.
The following table illustrates the behavior for integers:
The following table illustrates the behavior for integers:
<TABLE CELLSPACING=5 >
<TR>
<TD ALIGN=CENTER NOWRAP>
<TABLE CELLSPACING=5 >
<TR><TD ALIGN=LEFT NOWRAP COLSPAN=4><HR>
<TR>
<TD ALIGN=CENTER NOWRAP>
x
<TD ALIGN=CENTER NOWRAP>
y
<TD ALIGN=CENTER NOWRAP>
q
<TD ALIGN=CENTER NOWRAP>
r
<TR><TD ALIGN=LEFT NOWRAP COLSPAN=4><HR>
<TR>
<TD ALIGN=CENTER NOWRAP>
3
<TD ALIGN=CENTER NOWRAP>
3
<TD ALIGN=CENTER NOWRAP>
1
<TD ALIGN=CENTER NOWRAP>
0
<TR>
<TD ALIGN=CENTER NOWRAP>
2
<TD ALIGN=CENTER NOWRAP>
3
<TD ALIGN=CENTER NOWRAP>
0
<TD ALIGN=CENTER NOWRAP>
2
<TR>
<TD ALIGN=CENTER NOWRAP>
1
<TD ALIGN=CENTER NOWRAP>
3
<TD ALIGN=CENTER NOWRAP>
0
<TD ALIGN=CENTER NOWRAP>
1
<TR>
<TD ALIGN=CENTER NOWRAP>
0
<TD ALIGN=CENTER NOWRAP>
3
<TD ALIGN=CENTER NOWRAP>
0
<TD ALIGN=CENTER NOWRAP>
0
<TR>
<TD ALIGN=CENTER NOWRAP>
-1
<TD ALIGN=CENTER NOWRAP>
3
<TD ALIGN=CENTER NOWRAP>
0
<TD ALIGN=CENTER NOWRAP>
-1
<TR>
<TD ALIGN=CENTER NOWRAP>
-2
<TD ALIGN=CENTER NOWRAP>
3
<TD ALIGN=CENTER NOWRAP>
0
<TD ALIGN=CENTER NOWRAP>
-2
<TR>
<TD ALIGN=CENTER NOWRAP>
-3
<TD ALIGN=CENTER NOWRAP>
3
<TD ALIGN=CENTER NOWRAP>
-1
<TD ALIGN=CENTER NOWRAP>
0
<TR><TD ALIGN=LEFT NOWRAP COLSPAN=4><HR>
</TABLE>
<TABLE CELLSPACING=5 >
<TR>
<TD ALIGN=CENTER NOWRAP>
<TABLE CELLSPACING=5 >
<TR><TD ALIGN=LEFT NOWRAP COLSPAN=4><HR>
<TR>
<TD ALIGN=CENTER NOWRAP>
x
<TD ALIGN=CENTER NOWRAP>
y
<TD ALIGN=CENTER NOWRAP>
q
<TD ALIGN=CENTER NOWRAP>
r
<TR><TD ALIGN=LEFT NOWRAP COLSPAN=4><HR>
<TR>
<TD ALIGN=CENTER NOWRAP>
3
<TD ALIGN=CENTER NOWRAP>
3
<TD ALIGN=CENTER NOWRAP>
1
<TD ALIGN=CENTER NOWRAP>
0
<TR>
<TD ALIGN=CENTER NOWRAP>
2
<TD ALIGN=CENTER NOWRAP>
3
<TD ALIGN=CENTER NOWRAP>
0
<TD ALIGN=CENTER NOWRAP>
2
<TR>
<TD ALIGN=CENTER NOWRAP>
1
<TD ALIGN=CENTER NOWRAP>
3
<TD ALIGN=CENTER NOWRAP>
0
<TD ALIGN=CENTER NOWRAP>
1
<TR>
<TD ALIGN=CENTER NOWRAP>
0
<TD ALIGN=CENTER NOWRAP>
3
<TD ALIGN=CENTER NOWRAP>
0
<TD ALIGN=CENTER NOWRAP>
0
<TR>
<TD ALIGN=CENTER NOWRAP>
-1
<TD ALIGN=CENTER NOWRAP>
3
<TD ALIGN=CENTER NOWRAP>
0
<TD ALIGN=CENTER NOWRAP>
-1
<TR>
<TD ALIGN=CENTER NOWRAP>
-2
<TD ALIGN=CENTER NOWRAP>
3
<TD ALIGN=CENTER NOWRAP>
0
<TD ALIGN=CENTER NOWRAP>
-2
<TR>
<TD ALIGN=CENTER NOWRAP>
-3
<TD ALIGN=CENTER NOWRAP>
3
<TD ALIGN=CENTER NOWRAP>
-1
<TD ALIGN=CENTER NOWRAP>
0
<TR><TD ALIGN=LEFT NOWRAP COLSPAN=4><HR>
</TABLE>
<TD ALIGN=CENTER NOWRAP>
-
<TD ALIGN=CENTER NOWRAP>
<TABLE CELLSPACING=5 >
<TR><TD ALIGN=LEFT NOWRAP COLSPAN=4><HR>
<TR>
<TD ALIGN=CENTER NOWRAP>
x
<TD ALIGN=CENTER NOWRAP>
y
<TD ALIGN=CENTER NOWRAP>
q
<TD ALIGN=CENTER NOWRAP>
r
<TR><TD ALIGN=LEFT NOWRAP COLSPAN=4><HR>
<TR>
<TD ALIGN=CENTER NOWRAP>
3
<TD ALIGN=CENTER NOWRAP>
-3
<TD ALIGN=CENTER NOWRAP>
-1
<TD ALIGN=CENTER NOWRAP>
0
<TR>
<TD ALIGN=CENTER NOWRAP>
2
<TD ALIGN=CENTER NOWRAP>
-3
<TD ALIGN=CENTER NOWRAP>
0
<TD ALIGN=CENTER NOWRAP>
2
<TR>
<TD ALIGN=CENTER NOWRAP>
1
<TD ALIGN=CENTER NOWRAP>
-3
<TD ALIGN=CENTER NOWRAP>
0
<TD ALIGN=CENTER NOWRAP>
1
<TR>
<TD ALIGN=CENTER NOWRAP>
0
<TD ALIGN=CENTER NOWRAP>
-3
<TD ALIGN=CENTER NOWRAP>
0
<TD ALIGN=CENTER NOWRAP>
0
<TR>
<TD ALIGN=CENTER NOWRAP>
-1
<TD ALIGN=CENTER NOWRAP>
-3
<TD ALIGN=CENTER NOWRAP>
0
<TD ALIGN=CENTER NOWRAP>
-1
<TR>
<TD ALIGN=CENTER NOWRAP>
-2
<TD ALIGN=CENTER NOWRAP>
-3
<TD ALIGN=CENTER NOWRAP>
0
<TD ALIGN=CENTER NOWRAP>
-2
<TR>
<TD ALIGN=CENTER NOWRAP>
-3
<TD ALIGN=CENTER NOWRAP>
-3
<TD ALIGN=CENTER NOWRAP>
1
<TD ALIGN=CENTER NOWRAP>
0
<TR><TD ALIGN=LEFT NOWRAP COLSPAN=4><HR>
</TABLE>
<TD ALIGN=CENTER NOWRAP>
-
<TD ALIGN=CENTER NOWRAP>
<TABLE CELLSPACING=5 >
<TR><TD ALIGN=LEFT NOWRAP COLSPAN=4><HR>
<TR>
<TD ALIGN=CENTER NOWRAP>
x
<TD ALIGN=CENTER NOWRAP>
y
<TD ALIGN=CENTER NOWRAP>
q
<TD ALIGN=CENTER NOWRAP>
r
<TR><TD ALIGN=LEFT NOWRAP COLSPAN=4><HR>
<TR>
<TD ALIGN=CENTER NOWRAP>
3
<TD ALIGN=CENTER NOWRAP>
-3
<TD ALIGN=CENTER NOWRAP>
-1
<TD ALIGN=CENTER NOWRAP>
0
<TR>
<TD ALIGN=CENTER NOWRAP>
2
<TD ALIGN=CENTER NOWRAP>
-3
<TD ALIGN=CENTER NOWRAP>
0
<TD ALIGN=CENTER NOWRAP>
2
<TR>
<TD ALIGN=CENTER NOWRAP>
1
<TD ALIGN=CENTER NOWRAP>
-3
<TD ALIGN=CENTER NOWRAP>
0
<TD ALIGN=CENTER NOWRAP>
1
<TR>
<TD ALIGN=CENTER NOWRAP>
0
<TD ALIGN=CENTER NOWRAP>
-3
<TD ALIGN=CENTER NOWRAP>
0
<TD ALIGN=CENTER NOWRAP>
0
<TR>
<TD ALIGN=CENTER NOWRAP>
-1
<TD ALIGN=CENTER NOWRAP>
-3
<TD ALIGN=CENTER NOWRAP>
0
<TD ALIGN=CENTER NOWRAP>
-1
<TR>
<TD ALIGN=CENTER NOWRAP>
-2
<TD ALIGN=CENTER NOWRAP>
-3
<TD ALIGN=CENTER NOWRAP>
0
<TD ALIGN=CENTER NOWRAP>
-2
<TR>
<TD ALIGN=CENTER NOWRAP>
-3
<TD ALIGN=CENTER NOWRAP>
-3
<TD ALIGN=CENTER NOWRAP>
1
<TD ALIGN=CENTER NOWRAP>
0
<TR><TD ALIGN=LEFT NOWRAP COLSPAN=4><HR>
</TABLE>
</TABLE>
</TABLE>
\cgalRefines `AdaptableFunctor`
\cgalRefines `AdaptableFunctor`
\sa `AlgebraicStructureTraits`
\sa `AlgebraicStructureTraits_::Mod`
@ -200,56 +200,56 @@ r
class DivMod {
public:
/// \name Types
/// \name Types
/// @{
/*!
Is void.
*/
typedef unspecified_type result_type;
Is void.
*/
typedef unspecified_type result_type;
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type first_argument_type;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type first_argument_type;
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type second_argument_type;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type second_argument_type;
/*!
Is `AlgebraicStructureTraits::Type&`.
*/
typedef unspecified_type third_argument_type;
Is `AlgebraicStructureTraits::Type&`.
*/
typedef unspecified_type third_argument_type;
/*!
Is `AlgebraicStructureTraits::Type&`.
*/
typedef unspecified_type fourth_argument_type;
Is `AlgebraicStructureTraits::Type&`.
*/
typedef unspecified_type fourth_argument_type;
/// @}
/// @}
/// \name Operations
/// \name Operations
/// @{
/*!
computes the quotient \f$ q\f$ and remainder \f$ r\f$, such that \f$ x = q*y + r\f$
and \f$ r\f$ minimal with respect to the Euclidean Norm on
`Type`.
*/
result_type operator()( first_argument_type x,
second_argument_type y,
third_argument_type q,
fourth_argument_type r);
computes the quotient \f$ q\f$ and remainder \f$ r\f$, such that \f$ x = q*y + r\f$
and \f$ r\f$ minimal with respect to the Euclidean Norm on
`Type`.
*/
result_type operator()( first_argument_type x,
second_argument_type y,
third_argument_type q,
fourth_argument_type r);
/*!
This operator is defined if `NT1` and `NT2` are `ExplicitInteroperable`
with coercion type `AlgebraicStructureTraits::Type`.
*/
template <class NT1, class NT2> result_type
operator()(NT1 x, NT2 y, third_argument_type q, fourth_argument_type r);
This operator is defined if `NT1` and `NT2` are `ExplicitInteroperable`
with coercion type `AlgebraicStructureTraits::Type`.
*/
template <class NT1, class NT2> result_type
operator()(NT1 x, NT2 y, third_argument_type q, fourth_argument_type r);
/// @}

66
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--Divides.h
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@ -5,18 +5,18 @@ namespace AlgebraicStructureTraits_{
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
`AdaptableBinaryFunction`,
returns true if the first argument divides the second argument.
`AdaptableBinaryFunction`,
returns true if the first argument divides the second argument.
Integral division (a.k.a. exact division or division without remainder) maps
ring elements \f$ (n,d)\f$ to ring element \f$ c\f$ such that \f$ n = dc\f$ if such a \f$ c\f$
exists. In this case it is said that \f$ d\f$ divides \f$ n\f$.
Integral division (a.k.a. exact division or division without remainder) maps
ring elements \f$ (n,d)\f$ to ring element \f$ c\f$ such that \f$ n = dc\f$ if such a \f$ c\f$
exists. In this case it is said that \f$ d\f$ divides \f$ n\f$.
This functor is required to provide two operators. The first operator takes two
arguments and returns true if the first argument divides the second argument.
The second operator returns \f$ c\f$ via the additional third argument.
This functor is required to provide two operators. The first operator takes two
arguments and returns true if the first argument divides the second argument.
The second operator returns \f$ c\f$ via the additional third argument.
\cgalRefines `AdaptableBinaryFunction`
\cgalRefines `AdaptableBinaryFunction`
\sa `AlgebraicStructureTraits`
\sa `AlgebraicStructureTraits_::IntegralDivision`
@ -26,46 +26,46 @@ The second operator returns \f$ c\f$ via the additional third argument.
class Divides {
public:
/// \name Types
/// \name Types
/// @{
/*!
Is `AlgebraicStructureTraits::Boolean`.
*/
typedef unspecified_type result_type;
Is `AlgebraicStructureTraits::Boolean`.
*/
typedef unspecified_type result_type;
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type first_argument;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type first_argument;
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type second_argument;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type second_argument;
/// @}
/// @}
/// \name Operations
/// \name Operations
/// @{
/*!
Computes whether \f$ d\f$ divides \f$ n\f$.
*/
result_type operator()(first_argument_type d,
second_argument_type n);
Computes whether \f$ d\f$ divides \f$ n\f$.
*/
result_type operator()(first_argument_type d,
second_argument_type n);
/*!
Computes whether \f$ d\f$ divides \f$ n\f$.
Moreover it computes \f$ c\f$ if \f$ d\f$ divides \f$ n\f$,
otherwise the value of \f$ c\f$ is undefined.
Computes whether \f$ d\f$ divides \f$ n\f$.
Moreover it computes \f$ c\f$ if \f$ d\f$ divides \f$ n\f$,
otherwise the value of \f$ c\f$ is undefined.
*/
result_type operator()(
first_argument_type d,
second_argument_type n,
AlgebraicStructureTraits::Type& c);
*/
result_type operator()(
first_argument_type d,
second_argument_type n,
AlgebraicStructureTraits::Type& c);
/// @}

60
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--Gcd.h
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@ -5,19 +5,19 @@ namespace AlgebraicStructureTraits_{
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
`AdaptableBinaryFunction` providing the gcd.
`AdaptableBinaryFunction` providing the gcd.
The greatest common divisor (\f$ gcd\f$) of ring elements \f$ x\f$ and \f$ y\f$ is the unique
ring element \f$ d\f$ (up to a unit) with the property that any common divisor of
\f$ x\f$ and \f$ y\f$ also divides \f$ d\f$. (In other words: \f$ d\f$ is the greatest lower bound
of \f$ x\f$ and \f$ y\f$ in the partial order of divisibility.) We demand the \f$ gcd\f$ to be
unit-normal (i.e.\ have unit part 1).
The greatest common divisor (\f$ gcd\f$) of ring elements \f$ x\f$ and \f$ y\f$ is the unique
ring element \f$ d\f$ (up to a unit) with the property that any common divisor of
\f$ x\f$ and \f$ y\f$ also divides \f$ d\f$. (In other words: \f$ d\f$ is the greatest lower bound
of \f$ x\f$ and \f$ y\f$ in the partial order of divisibility.) We demand the \f$ gcd\f$ to be
unit-normal (i.e.\ have unit part 1).
\f$ gcd(0,0)\f$ is defined as \f$ 0\f$, since \f$ 0\f$ is the greatest element with respect
to the partial order of divisibility. This is because an element \f$ a \in R\f$ is said to divide \f$ b \in R\f$, iff \f$ \exists r \in R\f$ such that \f$ a \cdot r = b\f$.
Thus, \f$ 0\f$ is divided by every element of the Ring, in particular by itself.
\f$ gcd(0,0)\f$ is defined as \f$ 0\f$, since \f$ 0\f$ is the greatest element with respect
to the partial order of divisibility. This is because an element \f$ a \in R\f$ is said to divide \f$ b \in R\f$, iff \f$ \exists r \in R\f$ such that \f$ a \cdot r = b\f$.
Thus, \f$ 0\f$ is divided by every element of the Ring, in particular by itself.
\cgalRefines `AdaptableBinaryFunction`
\cgalRefines `AdaptableBinaryFunction`
\sa `AlgebraicStructureTraits`
@ -26,40 +26,40 @@ Thus, \f$ 0\f$ is divided by every element of the Ring, in particular by itself.
class Gcd {
public:
/// \name Types
/// \name Types
/// @{
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type result_type;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type result_type;
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type first_argument;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type first_argument;
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type second_argument;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type second_argument;
/// @}
/// @}
/// \name Operations
/// \name Operations
/// @{
/*!
returns \f$ gcd(x,y)\f$.
*/
result_type operator()(first_argument_type x,
second_argument_type y);
returns \f$ gcd(x,y)\f$.
*/
result_type operator()(first_argument_type x,
second_argument_type y);
/*!
This operator is defined if `NT1` and `NT2` are `ExplicitInteroperable`
with coercion type `AlgebraicStructureTraits::Type`.
*/
template <class NT1, class NT2> result_type operator()(NT1 x, NT2 y);
This operator is defined if `NT1` and `NT2` are `ExplicitInteroperable`
with coercion type `AlgebraicStructureTraits::Type`.
*/
template <class NT1, class NT2> result_type operator()(NT1 x, NT2 y);
/// @}

54
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--IntegralDivision.h
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@ -5,15 +5,15 @@ namespace AlgebraicStructureTraits_{
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
`AdaptableBinaryFunction` providing an integral division.
`AdaptableBinaryFunction` providing an integral division.
Integral division (a.k.a. exact division or division without remainder) maps
ring elements \f$ (x,y)\f$ to ring element \f$ z\f$ such that \f$ x = yz\f$ if such a \f$ z\f$
exists (i.e.\ if \f$ x\f$ is divisible by \f$ y\f$). Otherwise the effect of invoking
this operation is undefined. Since the ring represented is an integral domain,
\f$ z\f$ is uniquely defined if it exists.
Integral division (a.k.a. exact division or division without remainder) maps
ring elements \f$ (x,y)\f$ to ring element \f$ z\f$ such that \f$ x = yz\f$ if such a \f$ z\f$
exists (i.e.\ if \f$ x\f$ is divisible by \f$ y\f$). Otherwise the effect of invoking
this operation is undefined. Since the ring represented is an integral domain,
\f$ z\f$ is uniquely defined if it exists.
\cgalRefines `AdaptableBinaryFunction`
\cgalRefines `AdaptableBinaryFunction`
\sa `AlgebraicStructureTraits`
\sa `AlgebraicStructureTraits_::Divides`
@ -23,40 +23,40 @@ this operation is undefined. Since the ring represented is an integral domain,
class IntegralDivision {
public:
/// \name Types
/// \name Types
/// @{
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type result_type;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type result_type;
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type first_argument;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type first_argument;
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type second_argument;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type second_argument;
/// @}
/// @}
/// \name Operations
/// \name Operations
/// @{
/*!
returns \f$ x/y\f$, this is an integral division.
*/
result_type operator()(first_argument_type x,
second_argument_type y);
returns \f$ x/y\f$, this is an integral division.
*/
result_type operator()(first_argument_type x,
second_argument_type y);
/*!
This operator is defined if `NT1` and `NT2` are `ExplicitInteroperable`
with coercion type `AlgebraicStructureTraits::Type`.
*/
template <class NT1, class NT2> result_type operator()(NT1 x, NT2 y);
This operator is defined if `NT1` and `NT2` are `ExplicitInteroperable`
with coercion type `AlgebraicStructureTraits::Type`.
*/
template <class NT1, class NT2> result_type operator()(NT1 x, NT2 y);
/// @}

32
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--Inverse.h
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@ -5,10 +5,10 @@ namespace AlgebraicStructureTraits_{
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
`AdaptableUnaryFunction` providing the inverse element with
respect to multiplication of a `Field`.
`AdaptableUnaryFunction` providing the inverse element with
respect to multiplication of a `Field`.
\cgalRefines `AdaptableUnaryFunction`
\cgalRefines `AdaptableUnaryFunction`
\sa `AlgebraicStructureTraits`
@ -17,30 +17,30 @@ respect to multiplication of a `Field`.
class Inverse {
public:
/// \name Types
/// \name Types
/// @{
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type result_type;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type result_type;
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type argument_type;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type argument_type;
/// @}
/// @}
/// \name Operations
/// \name Operations
/// @{
/*!
returns the inverse element of \f$ x\f$ with respect to multiplication.
\pre \f$ x \neq0\f$.
returns the inverse element of \f$ x\f$ with respect to multiplication.
\pre \f$ x \neq0\f$.
*/
result_type operator()(argument_type x) const;
*/
result_type operator()(argument_type x) const;
/// @}

30
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--IsOne.h
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@ -5,10 +5,10 @@ namespace AlgebraicStructureTraits_{
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
`AdaptableUnaryFunction`,
returns true in case the argument is the one of the ring.
`AdaptableUnaryFunction`,
returns true in case the argument is the one of the ring.
\cgalRefines `AdaptableUnaryFunction`
\cgalRefines `AdaptableUnaryFunction`
\sa `AlgebraicStructureTraits`
@ -17,29 +17,29 @@ returns true in case the argument is the one of the ring.
class IsOne {
public:
/// \name Types
/// \name Types
/// @{
/*!
Is `AlgebraicStructureTraits::Boolean`.
*/
typedef unspecified_type result_type;
Is `AlgebraicStructureTraits::Boolean`.
*/
typedef unspecified_type result_type;
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type argument_type;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type argument_type;
/// @}
/// @}
/// \name Operations
/// \name Operations
/// @{
/*!
returns true in case \f$ x\f$ is the one of the ring.
*/
result_type operator()(argument_type x);
returns true in case \f$ x\f$ is the one of the ring.
*/
result_type operator()(argument_type x);
/// @}

54
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--IsSquare.h
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@ -5,15 +5,15 @@ namespace AlgebraicStructureTraits_{
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
`AdaptableBinaryFunction` that computes whether the first argument is a square.
If the first argument is a square the second argument, which is taken by reference, contains the square root.
Otherwise, the content of the second argument is undefined.
`AdaptableBinaryFunction` that computes whether the first argument is a square.
If the first argument is a square the second argument, which is taken by reference, contains the square root.
Otherwise, the content of the second argument is undefined.
A ring element \f$ x\f$ is said to be a square iff there exists a ring element \f$ y\f$ such
that \f$ x= y*y\f$. In case the ring is a `UniqueFactorizationDomain`,
\f$ y\f$ is uniquely defined up to multiplication by units.
A ring element \f$ x\f$ is said to be a square iff there exists a ring element \f$ y\f$ such
that \f$ x= y*y\f$. In case the ring is a `UniqueFactorizationDomain`,
\f$ y\f$ is uniquely defined up to multiplication by units.
\cgalRefines `AdaptableBinaryFunction`
\cgalRefines `AdaptableBinaryFunction`
\sa `AlgebraicStructureTraits`
@ -22,42 +22,42 @@ that \f$ x= y*y\f$. In case the ring is a `UniqueFactorizationDomain`,
class IsSquare {
public:
/// \name Types
/// \name Types
/// @{
/*!
Is `AlgebraicStructureTraits::Boolean`.
*/
typedef unspecified_type result_type;
Is `AlgebraicStructureTraits::Boolean`.
*/
typedef unspecified_type result_type;
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type first_argument;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type first_argument;
/*!
Is `AlgebraicStructureTraits::Type&`.
*/
typedef unspecified_type second_argument;
Is `AlgebraicStructureTraits::Type&`.
*/
typedef unspecified_type second_argument;
/// @}
/// @}
/// \name Operations
/// \name Operations
/// @{
/*!
returns <TT>true</TT> in case \f$ x\f$ is a square, i.e.\ \f$ x = y*y\f$.
\post \f$ unit\_part(y) == 1\f$.
returns <TT>true</TT> in case \f$ x\f$ is a square, i.e.\ \f$ x = y*y\f$.
\post \f$ unit\_part(y) == 1\f$.
*/
result_type operator()(first_argument_type x,
second_argument_type y);
*/
result_type operator()(first_argument_type x,
second_argument_type y);
/*!
returns <TT>true</TT> in case \f$ x\f$ is a square.
returns <TT>true</TT> in case \f$ x\f$ is a square.
*/
result_type operator()(first_argument_type x);
*/
result_type operator()(first_argument_type x);
/// @}

28
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--IsZero.h
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@ -5,9 +5,9 @@ namespace AlgebraicStructureTraits_{
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
`AdaptableUnaryFunction`, returns true in case the argument is the zero element of the ring.
`AdaptableUnaryFunction`, returns true in case the argument is the zero element of the ring.
\cgalRefines `AdaptableUnaryFunction`
\cgalRefines `AdaptableUnaryFunction`
\sa `AlgebraicStructureTraits`
\sa `RealEmbeddableTraits_::IsZero`
@ -17,29 +17,29 @@ namespace AlgebraicStructureTraits_{
class IsZero {
public:
/// \name Types
/// \name Types
/// @{
/*!
Is `AlgebraicStructureTraits::Boolean`.
*/
typedef unspecified_type result_type;
Is `AlgebraicStructureTraits::Boolean`.
*/
typedef unspecified_type result_type;
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type argument_type;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type argument_type;
/// @}
/// @}
/// \name Operations
/// \name Operations
/// @{
/*!
returns true in case \f$ x\f$ is the zero element of the ring.
*/
result_type operator()(argument_type x) const;
returns true in case \f$ x\f$ is the zero element of the ring.
*/
result_type operator()(argument_type x) const;
/// @}

36
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--KthRoot.h
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@ -5,9 +5,9 @@ namespace AlgebraicStructureTraits_{
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
`AdaptableBinaryFunction` providing the k-th root.
`AdaptableBinaryFunction` providing the k-th root.
\cgalRefines `AdaptableBinaryFunction`
\cgalRefines `AdaptableBinaryFunction`
\sa `FieldWithRootOf`
\sa `AlgebraicStructureTraits`
@ -17,35 +17,35 @@ namespace AlgebraicStructureTraits_{
class KthRoot {
public:
/// \name Types
/// \name Types
/// @{
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type result_type;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type result_type;
/*!
Is int.
*/
typedef unspecified_type first_argument;
Is int.
*/
typedef unspecified_type first_argument;
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type second_argument;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type second_argument;
/// @}
/// @}
/// \name Operations
/// \name Operations
/// @{
/*!
returns the \f$ k\f$-th root of \f$ x\f$.
\pre \f$ k \geq1\f$
returns the \f$ k\f$-th root of \f$ x\f$.
\pre \f$ k \geq1\f$
*/
result_type operator()(int k, second_argument_type x);
*/
result_type operator()(int k, second_argument_type x);
/// @}

42
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--Mod.h
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@ -5,9 +5,9 @@ namespace AlgebraicStructureTraits_ {
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
`AdaptableBinaryFunction` computes the remainder of division with remainder.
`AdaptableBinaryFunction` computes the remainder of division with remainder.
\cgalRefines `AdaptableBinaryFunction`
\cgalRefines `AdaptableBinaryFunction`
\sa `AlgebraicStructureTraits`
\sa `AlgebraicStructureTraits_::Div`
@ -18,40 +18,40 @@ namespace AlgebraicStructureTraits_ {
class Mod {
public:
/// \name Types
/// \name Types
/// @{
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type result_type;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type result_type;
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type first_argument;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type first_argument;
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type second_argument;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type second_argument;
/// @}
/// @}
/// \name Operations
/// \name Operations
/// @{
/*!
*/
result_type operator()(first_argument_type x,
second_argument_type y);
*/
result_type operator()(first_argument_type x,
second_argument_type y);
/*!
This operator is defined if `NT1` and `NT2` are `ExplicitInteroperable`
with coercion type `AlgebraicStructureTraits::Type`.
*/
template <class NT1, class NT2> result_type operator()(NT1 x, NT2 y);
This operator is defined if `NT1` and `NT2` are `ExplicitInteroperable`
with coercion type `AlgebraicStructureTraits::Type`.
*/
template <class NT1, class NT2> result_type operator()(NT1 x, NT2 y);
/// @}

34
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--RootOf.h
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@ -5,10 +5,10 @@ namespace AlgebraicStructureTraits_{
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
`AdaptableFunctor` computes a real root of a square-free univariate
polynomial.
`AdaptableFunctor` computes a real root of a square-free univariate
polynomial.
\cgalRefines `AdaptableFunctor`
\cgalRefines `AdaptableFunctor`
\sa `FieldWithRootOf`
\sa `AlgebraicStructureTraits`
@ -18,28 +18,28 @@ polynomial.
class RootOf {
public:
/// \name Types
/// \name Types
/// @{
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type result_type;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type result_type;
/// @}
/// @}
/// \name Operations
/// \name Operations
/// @{
/*!
returns the k-th real root of the univariate polynomial,
which is defined by the iterator range,
where begin refers to the constant term.
\pre The polynomial is square-free.
\pre The value type of the InputIterator is `AlgebraicStructureTraits::Type`.
*/
template<class InputIterator>
result_type operator() (int k, InputIterator begin, InputIterator end);
returns the k-th real root of the univariate polynomial,
which is defined by the iterator range,
where begin refers to the constant term.
\pre The polynomial is square-free.
\pre The value type of the InputIterator is `AlgebraicStructureTraits::Type`.
*/
template<class InputIterator>
result_type operator() (int k, InputIterator begin, InputIterator end);
/// @}

28
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--Simplify.h
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@ -5,9 +5,9 @@ namespace AlgebraicStructureTraits_{
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
This `AdaptableUnaryFunction` may simplify a given object.
This `AdaptableUnaryFunction` may simplify a given object.
\cgalRefines `AdaptableUnaryFunction`
\cgalRefines `AdaptableUnaryFunction`
\sa `AlgebraicStructureTraits`
@ -16,28 +16,28 @@ This `AdaptableUnaryFunction` may simplify a given object.
class Simplify {
public:
/// \name Types
/// \name Types
/// @{
/*!
Is void.
*/
typedef unspecified_type result_type;
Is void.
*/
typedef unspecified_type result_type;
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type argument_type;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type argument_type;
/// @}
/// @}
/// \name Operations
/// \name Operations
/// @{
/*!
may simplify \f$ x\f$.
*/
result_type operator()(argument_type x);
may simplify \f$ x\f$.
*/
result_type operator()(argument_type x);
/// @}

28
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--Sqrt.h
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@ -5,9 +5,9 @@ namespace AlgebraicStructureTraits_{
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
`AdaptableUnaryFunction` providing the square root.
`AdaptableUnaryFunction` providing the square root.
\cgalRefines `AdaptableUnaryFunction`
\cgalRefines `AdaptableUnaryFunction`
\sa `AlgebraicStructureTraits`
@ -16,28 +16,28 @@ namespace AlgebraicStructureTraits_{
class Sqrt {
public:
/// \name Types
/// \name Types
/// @{
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type result_type;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type result_type;
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type argument_type;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type argument_type;
/// @}
/// @}
/// \name Operations
/// \name Operations
/// @{
/*!
returns \f$ \sqrt{x}\f$.
*/
result_type operator()(argument_type x) const;
returns \f$ \sqrt{x}\f$.
*/
result_type operator()(argument_type x) const;
/// @}

28
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--Square.h
View File

@ -5,9 +5,9 @@ namespace AlgebraicStructureTraits_{
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
`AdaptableUnaryFunction`, computing the square of the argument.
`AdaptableUnaryFunction`, computing the square of the argument.
\cgalRefines `AdaptableUnaryFunction`
\cgalRefines `AdaptableUnaryFunction`
\sa `AlgebraicStructureTraits`
@ -16,28 +16,28 @@ namespace AlgebraicStructureTraits_{
class Square {
public:
/// \name Types
/// \name Types
/// @{
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type result_type;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type result_type;
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type argument_type;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type argument_type;
/// @}
/// @}
/// \name Operations
/// \name Operations
/// @{
/*!
returns the square of \f$ x\f$.
*/
result_type operator()(argument_type x);
returns the square of \f$ x\f$.
*/
result_type operator()(argument_type x);
/// @}

52
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits--UnitPart.h
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@ -5,23 +5,23 @@ namespace AlgebraicStructureTraits_{
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
This `AdaptableUnaryFunction` computes the unit part of a given ring
element.
This `AdaptableUnaryFunction` computes the unit part of a given ring
element.
The mathematical definition of unit part is as follows: Two ring elements \f$ a\f$
and \f$ b\f$ are said to be associate if there exists an invertible ring element
(i.e.\ a unit) \f$ u\f$ such that \f$ a = ub\f$. This defines an equivalence relation.
We can distinguish exactly one element of every equivalence class as being
unit normal. Then each element of a ring possesses a factorization into a unit
(called its unit part) and a unit-normal ring element
(called its unit normal associate).
The mathematical definition of unit part is as follows: Two ring elements \f$ a\f$
and \f$ b\f$ are said to be associate if there exists an invertible ring element
(i.e.\ a unit) \f$ u\f$ such that \f$ a = ub\f$. This defines an equivalence relation.
We can distinguish exactly one element of every equivalence class as being
unit normal. Then each element of a ring possesses a factorization into a unit
(called its unit part) and a unit-normal ring element
(called its unit normal associate).
For the integers, the non-negative numbers are by convention unit normal,
hence the unit-part of a non-zero integer is its sign. For a `Field`, every
non-zero element is a unit and is its own unit part, its unit normal
associate being one. The unit part of zero is, by convention, one.
For the integers, the non-negative numbers are by convention unit normal,
hence the unit-part of a non-zero integer is its sign. For a `Field`, every
non-zero element is a unit and is its own unit part, its unit normal
associate being one. The unit part of zero is, by convention, one.
\cgalRefines `AdaptableUnaryFunction`
\cgalRefines `AdaptableUnaryFunction`
\sa `AlgebraicStructureTraits`
@ -31,28 +31,28 @@ associate being one. The unit part of zero is, by convention, one.
class UnitPart {
public:
/// \name Types
/// \name Types
/// @{
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type result_type;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type result_type;
/*!
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type argument_type;
Is `AlgebraicStructureTraits::Type`.
*/
typedef unspecified_type argument_type;
/// @}
/// @}
/// \name Operations
/// \name Operations
/// @{
/*!
returns the unit part of \f$ x\f$.
*/
result_type operator()(argument_type x);
returns the unit part of \f$ x\f$.
*/
result_type operator()(argument_type x);
/// @}

322
Algebraic_foundations/doc/Algebraic_foundations/Concepts/AlgebraicStructureTraits.h
View File

@ -3,13 +3,13 @@
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
A model of `AlgebraicStructureTraits` reflects the algebraic structure
of an associated type `Type`.
A model of `AlgebraicStructureTraits` reflects the algebraic structure
of an associated type `Type`.
Depending on the concepts that `Type` fulfills,
it contains various functors and descriptive tags.
Moreover it gives access to the several possible
algebraic operations within that structure.
Depending on the concepts that `Type` fulfills,
it contains various functors and descriptive tags.
Moreover it gives access to the several possible
algebraic operations within that structure.
\sa `IntegralDomainWithoutDivision`
\sa `IntegralDomain`
@ -35,267 +35,267 @@ algebraic operations within that structure.
class AlgebraicStructureTraits {
public:
/// \name Types
/// \name Types
/// A model of `AlgebraicStructureTraits` is supposed to provide:
/// @{
/*!
The associated type.
*/
typedef unspecified_type Type;
The associated type.
*/
typedef unspecified_type Type;
/*!
Tag indicating the algebraic structure of the associated type.
Tag indicating the algebraic structure of the associated type.
<TABLE CELLSPACING=5 >
<TR><TD ALIGN=LEFT NOWRAP COLSPAN=2><HR>
<TR>
<TD ALIGN=LEFT NOWRAP>
Tag is:
<TD ALIGN=LEFT NOWRAP>
`Type` is model of:
<TR><TD ALIGN=LEFT NOWRAP COLSPAN=2><HR>
<TR>
<TD ALIGN=LEFT NOWRAP>
`CGAL::Null_tag`
<TD ALIGN=LEFT NOWRAP>
no algebraic concept
<TR>
<TD ALIGN=LEFT NOWRAP>
`CGAL::Integral_domain_without_division_tag`
<TD ALIGN=LEFT NOWRAP>
`IntegralDomainWithoutDivision`
<TR>
<TD ALIGN=LEFT NOWRAP>
`CGAL::Integral_domain_tag`
<TD ALIGN=LEFT NOWRAP>
`IntegralDomain`
<TR>
<TD ALIGN=LEFT NOWRAP>
`CGAL::Unique_factorization_domain_tag`
<TD ALIGN=LEFT NOWRAP>
`UniqueFactorizationDomain`
<TR>
<TD ALIGN=LEFT NOWRAP>
`CGAL::Euclidean_ring_tag`
<TD ALIGN=LEFT NOWRAP>
`EuclideanRing`
<TR>
<TD ALIGN=LEFT NOWRAP>
`CGAL::Field_tag`
<TD ALIGN=LEFT NOWRAP>
`Field`
<TR>
<TD ALIGN=LEFT NOWRAP>
`CGAL::Field_with_sqrt_tag`
<TD ALIGN=LEFT NOWRAP>
`FieldWithSqrt`
<TR>
<TD ALIGN=LEFT NOWRAP>
`CGAL::Field_with_kth_root_tag`
<TD ALIGN=LEFT NOWRAP>
`FieldWithKthRoot`
<TR>
<TD ALIGN=LEFT NOWRAP>
`CGAL::Field_with_root_of_tag`
<TD ALIGN=LEFT NOWRAP>
`FieldWithRootOf`
<TR><TD ALIGN=LEFT NOWRAP COLSPAN=2><HR>
</TABLE>
<TABLE CELLSPACING=5 >
<TR><TD ALIGN=LEFT NOWRAP COLSPAN=2><HR>
<TR>
<TD ALIGN=LEFT NOWRAP>
Tag is:
<TD ALIGN=LEFT NOWRAP>
`Type` is model of:
<TR><TD ALIGN=LEFT NOWRAP COLSPAN=2><HR>
<TR>
<TD ALIGN=LEFT NOWRAP>
`CGAL::Null_tag`
<TD ALIGN=LEFT NOWRAP>
no algebraic concept
<TR>
<TD ALIGN=LEFT NOWRAP>
`CGAL::Integral_domain_without_division_tag`
<TD ALIGN=LEFT NOWRAP>
`IntegralDomainWithoutDivision`
<TR>
<TD ALIGN=LEFT NOWRAP>
`CGAL::Integral_domain_tag`
<TD ALIGN=LEFT NOWRAP>
`IntegralDomain`
<TR>
<TD ALIGN=LEFT NOWRAP>
`CGAL::Unique_factorization_domain_tag`
<TD ALIGN=LEFT NOWRAP>
`UniqueFactorizationDomain`
<TR>
<TD ALIGN=LEFT NOWRAP>
`CGAL::Euclidean_ring_tag`
<TD ALIGN=LEFT NOWRAP>
`EuclideanRing`
<TR>
<TD ALIGN=LEFT NOWRAP>
`CGAL::Field_tag`
<TD ALIGN=LEFT NOWRAP>
`Field`
<TR>
<TD ALIGN=LEFT NOWRAP>
`CGAL::Field_with_sqrt_tag`
<TD ALIGN=LEFT NOWRAP>
`FieldWithSqrt`
<TR>
<TD ALIGN=LEFT NOWRAP>
`CGAL::Field_with_kth_root_tag`
<TD ALIGN=LEFT NOWRAP>
`FieldWithKthRoot`
<TR>
<TD ALIGN=LEFT NOWRAP>
`CGAL::Field_with_root_of_tag`
<TD ALIGN=LEFT NOWRAP>
`FieldWithRootOf`
<TR><TD ALIGN=LEFT NOWRAP COLSPAN=2><HR>
</TABLE>
*/
typedef unspecified_type Algebraic_category;
*/
typedef unspecified_type Algebraic_category;
/*!
Tag indicating whether `Type` is exact.
Tag indicating whether `Type` is exact.
This is either `CGAL::Tag_true` or `CGAL::Tag_false`.
This is either `CGAL::Tag_true` or `CGAL::Tag_false`.
An algebraic structure is considered exact, if all operations
required by its concept are computed such that a comparison
of two algebraic expressions is always correct.
The exactness covers only those operations that are required by
the algebraic structure concept.
An algebraic structure is considered exact, if all operations
required by its concept are computed such that a comparison
of two algebraic expressions is always correct.
The exactness covers only those operations that are required by
the algebraic structure concept.
e.g. an exact `Field` may have a `Sqrt` functor that
is not exact.
e.g. an exact `Field` may have a `Sqrt` functor that
is not exact.
*/
typedef unspecified_type Is_exact;
*/
typedef unspecified_type Is_exact;
/*!
Tag indicating whether `Type` is numerical sensitive.
Tag indicating whether `Type` is numerical sensitive.
This is either `CGAL::Tag_true` or `CGAL::Tag_false`.
This is either `CGAL::Tag_true` or `CGAL::Tag_false`.
An algebraic structure is considered as numerically sensitive,
if the performance of the type is sensitive to the condition
number of an algorithm.
An algebraic structure is considered as numerically sensitive,
if the performance of the type is sensitive to the condition
number of an algorithm.
*/
typedef unspecified_type Is_numerical_sensitive;
*/
typedef unspecified_type Is_numerical_sensitive;
/*!
This type specifies the return type of the predicates provided
by this traits. The type must be convertible to `bool` and
typically the type indeed maps to `bool`. However, there are also
cases such as interval arithmetic, in which it is `Uncertain<bool>`
or some similar type.
This type specifies the return type of the predicates provided
by this traits. The type must be convertible to `bool` and
typically the type indeed maps to `bool`. However, there are also
cases such as interval arithmetic, in which it is `Uncertain<bool>`
or some similar type.
*/
typedef unspecified_type Boolean;
*/
typedef unspecified_type Boolean;
/// @}
/// @}
/// \name Functors
/// \name Functors
/// In case a functor is not provided, it is set to `CGAL::Null_functor`.
/// @{
/*!
A model of `AlgebraicStructureTraits_::IsZero`.
A model of `AlgebraicStructureTraits_::IsZero`.
Required by the concept `IntegralDomainWithoutDivision`.
In case `Type` is also model of `RealEmbeddable` this is a
model of `RealEmbeddableTraits_::IsZero`.
Required by the concept `IntegralDomainWithoutDivision`.
In case `Type` is also model of `RealEmbeddable` this is a
model of `RealEmbeddableTraits_::IsZero`.
*/
typedef unspecified_type Is_zero;
*/
typedef unspecified_type Is_zero;
/*!
A model of `AlgebraicStructureTraits_::IsOne`.
A model of `AlgebraicStructureTraits_::IsOne`.
Required by the concept `IntegralDomainWithoutDivision`.
Required by the concept `IntegralDomainWithoutDivision`.
*/
typedef unspecified_type Is_one;
*/
typedef unspecified_type Is_one;
/*!
A model of `AlgebraicStructureTraits_::Square`.
A model of `AlgebraicStructureTraits_::Square`.
Required by the concept `IntegralDomainWithoutDivision`.
Required by the concept `IntegralDomainWithoutDivision`.
*/
typedef unspecified_type Square;
*/
typedef unspecified_type Square;
/*!
A model of `AlgebraicStructureTraits_::Simplify`.
A model of `AlgebraicStructureTraits_::Simplify`.
Required by the concept `IntegralDomainWithoutDivision`.
Required by the concept `IntegralDomainWithoutDivision`.
*/
typedef unspecified_type Simplify;
*/
typedef unspecified_type Simplify;
/*!
A model of `AlgebraicStructureTraits_::UnitPart`.
A model of `AlgebraicStructureTraits_::UnitPart`.
Required by the concept `IntegralDomainWithoutDivision`.
Required by the concept `IntegralDomainWithoutDivision`.
*/
typedef unspecified_type Unit_part;
*/
typedef unspecified_type Unit_part;
/*!
A model of `AlgebraicStructureTraits_::IntegralDivision`.
A model of `AlgebraicStructureTraits_::IntegralDivision`.
Required by the concept `IntegralDomain`.
Required by the concept `IntegralDomain`.
*/
typedef unspecified_type Integral_division;
*/
typedef unspecified_type Integral_division;
/*!
A model of `AlgebraicStructureTraits_::Divides`.
A model of `AlgebraicStructureTraits_::Divides`.
Required by the concept `IntegralDomain`.
Required by the concept `IntegralDomain`.
*/
typedef unspecified_type Divides;
*/
typedef unspecified_type Divides;
/*!
A model of `AlgebraicStructureTraits_::IsSquare`.
A model of `AlgebraicStructureTraits_::IsSquare`.
Required by the concept `IntegralDomainWithoutDivision`.
Required by the concept `IntegralDomainWithoutDivision`.
*/
typedef unspecified_type Is_square;
*/
typedef unspecified_type Is_square;
/*!
A model of `AlgebraicStructureTraits_::Gcd`.
A model of `AlgebraicStructureTraits_::Gcd`.
Required by the concept `UniqueFactorizationDomain`.
Required by the concept `UniqueFactorizationDomain`.
*/
typedef unspecified_type Gcd;
*/
typedef unspecified_type Gcd;
/*!
A model of `AlgebraicStructureTraits_::Mod`.
A model of `AlgebraicStructureTraits_::Mod`.
Required by the concept `EuclideanRing`.
Required by the concept `EuclideanRing`.
*/
typedef unspecified_type Mod;
*/
typedef unspecified_type Mod;
/*!
A model of `AlgebraicStructureTraits_::Div`.
A model of `AlgebraicStructureTraits_::Div`.
Required by the concept `EuclideanRing`.
Required by the concept `EuclideanRing`.
*/
typedef unspecified_type Div;
*/
typedef unspecified_type Div;
/*!
A model of `AlgebraicStructureTraits_::DivMod`.
A model of `AlgebraicStructureTraits_::DivMod`.
Required by the concept `EuclideanRing`.
Required by the concept `EuclideanRing`.
*/
typedef unspecified_type Div_mod;
*/
typedef unspecified_type Div_mod;
/*!
A model of `AlgebraicStructureTraits_::Inverse`.
A model of `AlgebraicStructureTraits_::Inverse`.
Required by the concept `Field`.
Required by the concept `Field`.
*/
typedef unspecified_type Inverse;
*/
typedef unspecified_type Inverse;
/*!
A model of `AlgebraicStructureTraits_::Sqrt`.
A model of `AlgebraicStructureTraits_::Sqrt`.
Required by the concept `FieldWithSqrt`.
Required by the concept `FieldWithSqrt`.
*/
typedef unspecified_type Sqrt;
*/
typedef unspecified_type Sqrt;
/*!
A model of `AlgebraicStructureTraits_::KthRoot`.
A model of `AlgebraicStructureTraits_::KthRoot`.
Required by the concept `FieldWithKthRoot`.
Required by the concept `FieldWithKthRoot`.
*/
typedef unspecified_type Kth_root;
*/
typedef unspecified_type Kth_root;
/*!
A model of `AlgebraicStructureTraits_::RootOf`.
A model of `AlgebraicStructureTraits_::RootOf`.
Required by the concept `FieldWithRootOf`.
Required by the concept `FieldWithRootOf`.
*/
typedef unspecified_type Root_of;
*/
typedef unspecified_type Root_of;
/// @}

28
Algebraic_foundations/doc/Algebraic_foundations/Concepts/EuclideanRing.h
View File

@ -3,29 +3,29 @@
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
A model of `EuclideanRing` represents an euclidean ring (or Euclidean domain).
It is an `UniqueFactorizationDomain` that affords a suitable notion of minimality of remainders
such that given \f$ x\f$ and \f$ y \neq 0\f$ we obtain an (almost) unique solution to
\f$ x = qy + r \f$ by demanding that a solution \f$ (q,r)\f$ is chosen to minimize \f$ r\f$.
In particular, \f$ r\f$ is chosen to be \f$ 0\f$ if possible.
A model of `EuclideanRing` represents an euclidean ring (or Euclidean domain).
It is an `UniqueFactorizationDomain` that affords a suitable notion of minimality of remainders
such that given \f$ x\f$ and \f$ y \neq 0\f$ we obtain an (almost) unique solution to
\f$ x = qy + r \f$ by demanding that a solution \f$ (q,r)\f$ is chosen to minimize \f$ r\f$.
In particular, \f$ r\f$ is chosen to be \f$ 0\f$ if possible.
Moreover, `CGAL::Algebraic_structure_traits< EuclideanRing >` is a model of
`AlgebraicStructureTraits` providing:
Moreover, `CGAL::Algebraic_structure_traits< EuclideanRing >` is a model of
`AlgebraicStructureTraits` providing:
- \link AlgebraicStructureTraits::Algebraic_category `CGAL::Algebraic_structure_traits< EuclideanRing >::Algebraic_category` \endlink derived from `CGAL::Unique_factorization_domain_tag`
- \link AlgebraicStructureTraits::Algebraic_category `CGAL::Algebraic_structure_traits< EuclideanRing >::Algebraic_category` \endlink derived from `CGAL::Unique_factorization_domain_tag`
- \link AlgebraicStructureTraits::Mod `CGAL::Algebraic_structure_traits< EuclideanRing >::Mod` \endlink which is a model of `AlgebraicStructureTraits_::Mod`
- \link AlgebraicStructureTraits::Div `CGAL::Algebraic_structure_traits< EuclideanRing >::Div` \endlink which is a model of `AlgebraicStructureTraits_::Div`
- \link AlgebraicStructureTraits::Div `CGAL::Algebraic_structure_traits< EuclideanRing >::Div` \endlink which is a model of `AlgebraicStructureTraits_::Div`
- \link AlgebraicStructureTraits::Div_mod `CGAL::Algebraic_structure_traits< EuclideanRing >::Div_mod` \endlink which is a model of `AlgebraicStructureTraits_::DivMod`
<p></p> <!-- Work around for a doxygen bug -->
<p></p> <!-- Work around for a doxygen bug -->
\cgalHeading{Remarks}
The most prominent example of a Euclidean ring are the integers.
Whenever both \f$ x\f$ and \f$ y\f$ are positive, then it is conventional to choose
the smallest positive remainder \f$ r\f$.
The most prominent example of a Euclidean ring are the integers.
Whenever both \f$ x\f$ and \f$ y\f$ are positive, then it is conventional to choose
the smallest positive remainder \f$ r\f$.
\cgalRefines `UniqueFactorizationDomain`
\cgalRefines `UniqueFactorizationDomain`
\sa `IntegralDomainWithoutDivision`
\sa `IntegralDomain`

26
Algebraic_foundations/doc/Algebraic_foundations/Concepts/ExplicitInteroperable.h
View File

@ -3,23 +3,23 @@
\ingroup PkgAlgebraicFoundationsInteroperabilityConcepts
\cgalConcept
Two types `A` and `B` are a model of the `ExplicitInteroperable`
concept, if it is possible to derive a superior type for `A` and `B`,
such that both types are embeddable into this type.
This type is \link CGAL::Coercion_traits::Type `CGAL::Coercion_traits<A,B>::Type`\endlink.
Two types `A` and `B` are a model of the `ExplicitInteroperable`
concept, if it is possible to derive a superior type for `A` and `B`,
such that both types are embeddable into this type.
This type is \link CGAL::Coercion_traits::Type `CGAL::Coercion_traits<A,B>::Type`\endlink.
In this case
In this case
\link CGAL::Coercion_traits::Are_explicit_interoperable `CGAL::Coercion_traits<A,B>::Are_explicit_interoperable`\endlink
is `Tag_true`.
is `Tag_true`.
`A` and `B` are valid argument types for all binary functors in
`CGAL::Algebraic_structure_traits<Type>` and `CGAL::Real_embeddable_traits<Type>`.
This is also the case for the respective global functions.
`A` and `B` are valid argument types for all binary functors in
`CGAL::Algebraic_structure_traits<Type>` and `CGAL::Real_embeddable_traits<Type>`.
This is also the case for the respective global functions.
\sa `CGAL::Coercion_traits<A,B>`
\sa `ImplicitInteroperable`
\sa `AlgebraicStructureTraits`
\sa `RealEmbeddableTraits`
\sa `CGAL::Coercion_traits<A,B>`
\sa `ImplicitInteroperable`
\sa `AlgebraicStructureTraits`
\sa `RealEmbeddableTraits`
*/

30
Algebraic_foundations/doc/Algebraic_foundations/Concepts/Field.h
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@ -3,20 +3,20 @@
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
A model of `Field` is an `IntegralDomain` in which every non-zero element
has a multiplicative inverse.
Thus, one can divide by any non-zero element.
Hence division is defined for any divisor != 0.
For a Field, we require this division operation to be available through
operators / and /=.
A model of `Field` is an `IntegralDomain` in which every non-zero element
has a multiplicative inverse.
Thus, one can divide by any non-zero element.
Hence division is defined for any divisor != 0.
For a Field, we require this division operation to be available through
operators / and /=.
Moreover, `CGAL::Algebraic_structure_traits< Field >` is a model of
`AlgebraicStructureTraits` providing:
Moreover, `CGAL::Algebraic_structure_traits< Field >` is a model of
`AlgebraicStructureTraits` providing:
- \link AlgebraicStructureTraits::Algebraic_category `CGAL::Algebraic_structure_traits< Field >::Algebraic_category` \endlink derived from `CGAL::Field_tag`
- \link AlgebraicStructureTraits::Algebraic_category `CGAL::Algebraic_structure_traits< Field >::Algebraic_category` \endlink derived from `CGAL::Field_tag`
- \link AlgebraicStructureTraits::Inverse `CGAL::Algebraic_structure_traits< FieldWithSqrt >::Inverse` \endlink which is a model of `AlgebraicStructureTraits_::Inverse`
\cgalRefines `IntegralDomain`
\cgalRefines `IntegralDomain`
\sa `IntegralDomainWithoutDivision`
\sa `IntegralDomain`
@ -33,19 +33,19 @@ Moreover, `CGAL::Algebraic_structure_traits< Field >` is a model of
class Field {
public:
/// \name Operations
/// \name Operations
/// @{
/*!
*/
Field operator/(const Field &a, const Field &b);
*/
Field operator/(const Field &a, const Field &b);
/*!
*/
Field operator/=(const Field &b);
*/
Field operator/=(const Field &b);
/// @}

34
Algebraic_foundations/doc/Algebraic_foundations/Concepts/FieldNumberType.h
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@ -2,27 +2,27 @@
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
The concept `FieldNumberType` combines the requirements of the concepts
`Field` and `RealEmbeddable`.
A model of `FieldNumberType` can be used as a template parameter
for Cartesian kernels.
The concept `FieldNumberType` combines the requirements of the concepts
`Field` and `RealEmbeddable`.
A model of `FieldNumberType` can be used as a template parameter
for Cartesian kernels.
\cgalRefines `Field`
\cgalRefines `RealEmbeddable`
\cgalRefines `Field`
\cgalRefines `RealEmbeddable`
\cgalHasModel float
\cgalHasModel double
\cgalHasModel `CGAL::Gmpq`
\cgalHasModel `CGAL::Interval_nt`
\cgalHasModel float
\cgalHasModel double
\cgalHasModel `CGAL::Gmpq`
\cgalHasModel `CGAL::Interval_nt`
\cgalHasModel \ref CGAL::Interval_nt_advanced
\cgalHasModel `CGAL::Lazy_exact_nt<FieldNumberType>`
\cgalHasModel `CGAL::Quotient<RingNumberType>`
\cgalHasModel `leda_rational`
\cgalHasModel `leda_bigfloat`
\cgalHasModel `leda_real`
\cgalHasModel `CGAL::Lazy_exact_nt<FieldNumberType>`
\cgalHasModel `CGAL::Quotient<RingNumberType>`
\cgalHasModel `leda_rational`
\cgalHasModel `leda_bigfloat`
\cgalHasModel `leda_real`
\sa `RingNumberType`
\sa `Kernel`
\sa `RingNumberType`
\sa `Kernel`
*/

6
Algebraic_foundations/doc/Algebraic_foundations/Concepts/FieldWithKthRoot.h
View File

@ -3,14 +3,14 @@
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
A model of `FieldWithKthRoot` is a `FieldWithSqrt` that has operations to take k-th roots.
A model of `FieldWithKthRoot` is a `FieldWithSqrt` that has operations to take k-th roots.
Moreover, `CGAL::Algebraic_structure_traits< FieldWithKthRoot >` is a model of `AlgebraicStructureTraits` providing:
Moreover, `CGAL::Algebraic_structure_traits< FieldWithKthRoot >` is a model of `AlgebraicStructureTraits` providing:
- \link AlgebraicStructureTraits::Algebraic_category `CGAL::Algebraic_structure_traits< FieldWithKthRoot >::Algebraic_category` \endlink derived from `CGAL::Field_with_kth_root_tag`
- \link AlgebraicStructureTraits::Kth_root `CGAL::Algebraic_structure_traits< FieldWithKthRoot >::Kth_root` \endlink which is a model of `AlgebraicStructureTraits_::KthRoot`
\cgalRefines `FieldWithSqrt`
\cgalRefines `FieldWithSqrt`
\sa `IntegralDomainWithoutDivision`
\sa `IntegralDomain`

10
Algebraic_foundations/doc/Algebraic_foundations/Concepts/FieldWithRootOf.h
View File

@ -3,15 +3,15 @@
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
A model of `FieldWithRootOf` is a `FieldWithKthRoot` with the possibility to
construct it as the root of a univariate polynomial.
A model of `FieldWithRootOf` is a `FieldWithKthRoot` with the possibility to
construct it as the root of a univariate polynomial.
Moreover, `CGAL::Algebraic_structure_traits< FieldWithRootOf >` is a model of `AlgebraicStructureTraits` providing:
Moreover, `CGAL::Algebraic_structure_traits< FieldWithRootOf >` is a model of `AlgebraicStructureTraits` providing:
- \link AlgebraicStructureTraits::Algebraic_category `CGAL::Algebraic_structure_traits< FieldWithRootOf >::Algebraic_category` \endlink derived from `CGAL::Field_with_kth_root_tag`
- \link AlgebraicStructureTraits::Algebraic_category `CGAL::Algebraic_structure_traits< FieldWithRootOf >::Algebraic_category` \endlink derived from `CGAL::Field_with_kth_root_tag`
- \link AlgebraicStructureTraits::Root_of `CGAL::Algebraic_structure_traits< FieldWithRootOf >::Root_of` \endlink which is a model of `AlgebraicStructureTraits_::RootOf`
\cgalRefines `FieldWithKthRoot`
\cgalRefines `FieldWithKthRoot`
\sa `IntegralDomainWithoutDivision`
\sa `IntegralDomain`

10
Algebraic_foundations/doc/Algebraic_foundations/Concepts/FieldWithSqrt.h
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@ -3,14 +3,14 @@
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
A model of `FieldWithSqrt` is a `Field` that has operations to take square roots.
A model of `FieldWithSqrt` is a `Field` that has operations to take square roots.
Moreover, `CGAL::Algebraic_structure_traits< FieldWithSqrt >` is a model of `AlgebraicStructureTraits` providing:
Moreover, `CGAL::Algebraic_structure_traits< FieldWithSqrt >` is a model of `AlgebraicStructureTraits` providing:
- \link AlgebraicStructureTraits::Algebraic_category `CGAL::Algebraic_structure_traits< FieldWithSqrt >::Algebraic_category` \endlink derived from `CGAL::Field_with_sqrt_tag`
- \link AlgebraicStructureTraits::Sqrt `CGAL::Algebraic_structure_traits< FieldWithSqrt >::Sqrt` \endlink which is a model of `AlgebraicStructureTraits_::Sqrt`
- \link AlgebraicStructureTraits::Algebraic_category `CGAL::Algebraic_structure_traits< FieldWithSqrt >::Algebraic_category` \endlink derived from `CGAL::Field_with_sqrt_tag`
- \link AlgebraicStructureTraits::Sqrt `CGAL::Algebraic_structure_traits< FieldWithSqrt >::Sqrt` \endlink which is a model of `AlgebraicStructureTraits_::Sqrt`
\cgalRefines `Field`
\cgalRefines `Field`
\sa `IntegralDomainWithoutDivision`
\sa `IntegralDomain`

10
Algebraic_foundations/doc/Algebraic_foundations/Concepts/Fraction.h
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@ -3,13 +3,13 @@
\ingroup PkgAlgebraicFoundationsFractionsConcepts
\cgalConcept
A type is considered as a `Fraction`, if there is a reasonable way to
decompose it into a numerator and denominator. In this case the relevant
functionality for decomposing and re-composing as well as the numerator and
denominator type are provided by `CGAL::Fraction_traits`.
A type is considered as a `Fraction`, if there is a reasonable way to
decompose it into a numerator and denominator. In this case the relevant
functionality for decomposing and re-composing as well as the numerator and
denominator type are provided by `CGAL::Fraction_traits`.
\sa `FractionTraits`
\sa `CGAL::Fraction_traits<T>`
\sa `CGAL::Fraction_traits<T>`
*/

154
Algebraic_foundations/doc/Algebraic_foundations/Concepts/FractionTraits.h
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@ -3,53 +3,53 @@
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
A model of `FractionTraits` is associated with a type `Type`.
A model of `FractionTraits` is associated with a type `Type`.
In case the associated type is a `Fraction`, a model of `FractionTraits` provides the relevant functionality for decomposing and re-composing as well
as the numerator and denominator type.
In case the associated type is a `Fraction`, a model of `FractionTraits` provides the relevant functionality for decomposing and re-composing as well
as the numerator and denominator type.
\cgalHasModel `CGAL::Fraction_traits<T>`
\sa `FractionTraits_::Decompose`
\sa `FractionTraits_::Compose`
\sa `FractionTraits_::CommonFactor`
\sa `FractionTraits_::Decompose`
\sa `FractionTraits_::Compose`
\sa `FractionTraits_::CommonFactor`
*/
class FractionTraits {
public:
/// \name Types
/// \name Types
/// @{
/*!
The associated type
*/
typedef unspecified_type Type;
The associated type
*/
typedef unspecified_type Type;
/*!
Tag indicating whether the associated type is a fraction and can be
decomposed into a numerator and denominator.
Tag indicating whether the associated type is a fraction and can be
decomposed into a numerator and denominator.
This is either `CGAL::Tag_true` or `CGAL::Tag_false`.
*/
typedef unspecified_type Is_fraction;
This is either `CGAL::Tag_true` or `CGAL::Tag_false`.
*/
typedef unspecified_type Is_fraction;
/*!
The type to represent the numerator.
This is undefined in case the associated type is not a fraction.
*/
typedef unspecified_type Numerator_type ;
The type to represent the numerator.
This is undefined in case the associated type is not a fraction.
*/
typedef unspecified_type Numerator_type ;
/*!
The (simpler) type to represent the denominator.
This is undefined in case the associated type is not a fraction.
*/
typedef unspecified_type Denominator_type;
The (simpler) type to represent the denominator.
This is undefined in case the associated type is not a fraction.
*/
typedef unspecified_type Denominator_type;
/// @}
/// @}
/// \name Functors
/// \name Functors
/// In case `Type` is not a `Fraction` all functors are `Null_functor`.
/// @{
@ -81,27 +81,27 @@ namespace FractionTraits_ {
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
Functor decomposing a `Fraction` into its numerator and denominator.
Functor decomposing a `Fraction` into its numerator and denominator.
\sa `Fraction`
\sa `FractionTraits`
\sa `FractionTraits_::Compose`
\sa `FractionTraits_::CommonFactor`
\sa `Fraction`
\sa `FractionTraits`
\sa `FractionTraits_::Compose`
\sa `FractionTraits_::CommonFactor`
*/
class Decompose {
public:
/// \name Operations
/// \name Operations
/// @{
/*!
decompose \f$ f\f$ into numerator \f$ n\f$ and denominator \f$ d\f$.
*/
void operator()( FractionTraits::Type f,
FractionTraits::Numerator_type & n,
FractionTraits::Denominator_type & d);
decompose \f$ f\f$ into numerator \f$ n\f$ and denominator \f$ d\f$.
*/
void operator()( FractionTraits::Type f,
FractionTraits::Numerator_type & n,
FractionTraits::Denominator_type & d);
/// @}
@ -111,47 +111,47 @@ FractionTraits::Denominator_type & d);
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
`AdaptableBinaryFunction`, returns the fraction of its arguments.
`AdaptableBinaryFunction`, returns the fraction of its arguments.
\cgalRefines `AdaptableBinaryFunction`
\cgalRefines `AdaptableBinaryFunction`
\sa `Fraction`
\sa `FractionTraits`
\sa `FractionTraits_::Decompose`
\sa `FractionTraits_::CommonFactor`
\sa `Fraction`
\sa `FractionTraits`
\sa `FractionTraits_::Decompose`
\sa `FractionTraits_::CommonFactor`
*/
class Compose {
public:
/// \name Types
/// \name Types
/// @{
/*!
*/
typedef FractionTraits::Type result_type;
*/
typedef FractionTraits::Type result_type;
/*!
*/
typedef FractionTraits::Numerator_type first_argument_type;
*/
typedef FractionTraits::Numerator_type first_argument_type;
/*!
*/
typedef FractionTraits::Denominator_type second_argument_type;
*/
typedef FractionTraits::Denominator_type second_argument_type;
/// @}
/// @}
/// \name Operations
/// \name Operations
/// @{
/*!
return the fraction \f$ n/d\f$.
*/
result_type operator()(first_argument_type n, second_argument_type d);
return the fraction \f$ n/d\f$.
*/
result_type operator()(first_argument_type n, second_argument_type d);
/// @}
@ -162,54 +162,54 @@ result_type operator()(first_argument_type n, second_argument_type d);
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
`AdaptableBinaryFunction`, finds great common factor of denominators.
`AdaptableBinaryFunction`, finds great common factor of denominators.
This can be considered as a relaxed version of `AlgebraicStructureTraits_::Gcd`,
this is needed because it is not guaranteed that `FractionTraits::Denominator_type` is a model of
`UniqueFactorizationDomain`.
This can be considered as a relaxed version of `AlgebraicStructureTraits_::Gcd`,
this is needed because it is not guaranteed that `FractionTraits::Denominator_type` is a model of
`UniqueFactorizationDomain`.
\cgalRefines `AdaptableBinaryFunction`
\cgalRefines `AdaptableBinaryFunction`
\sa `Fraction`
\sa `FractionTraits`
\sa `FractionTraits_::Decompose`
\sa `FractionTraits_::Compose`
\sa `AlgebraicStructureTraits_::Gcd`
\sa `Fraction`
\sa `FractionTraits`
\sa `FractionTraits_::Decompose`
\sa `FractionTraits_::Compose`
\sa `AlgebraicStructureTraits_::Gcd`
*/
class CommonFactor {
public:
/// \name Types
/// \name Types
/// @{
/*!
*/
typedef FractionTraits::Denominator_type result_type;
*/
typedef FractionTraits::Denominator_type result_type;
/*!
*/
typedef FractionTraits::Denominator_type first_argument_type;
*/
typedef FractionTraits::Denominator_type first_argument_type;
/*!
*/
typedef FractionTraits::Denominator_type second_argument_type;
*/
typedef FractionTraits::Denominator_type second_argument_type;
/// @}
/// @}
/// \name Operations
/// \name Operations
/// @{
/*!
return a great common factor of \f$ d1\f$ and \f$ d2\f$.
return a great common factor of \f$ d1\f$ and \f$ d2\f$.
Note: <TT>operator()(0,0) = 0</TT>
*/
result_type operator()(first_argument_type d1, second_argument_type d2);
Note: <TT>operator()(0,0) = 0</TT>
*/
result_type operator()(first_argument_type d1, second_argument_type d2);
/// @}

16
Algebraic_foundations/doc/Algebraic_foundations/Concepts/FromDoubleConstructible.h
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@ -3,26 +3,26 @@
\ingroup PkgAlgebraicFoundationsConcepts
\cgalConcept
A model of the concept `FromDoubleConstructible` is required
to be constructible from the type `double`.
A model of the concept `FromDoubleConstructible` is required
to be constructible from the type `double`.
In case the type is a model of `RealEmbeddable` too, for any double d
the identity: `d == CGAL::to_double(T(d))`, is guaranteed.
In case the type is a model of `RealEmbeddable` too, for any double d
the identity: `d == CGAL::to_double(T(d))`, is guaranteed.
*/
class FromDoubleConstructible {
public:
/// \name Creation
/// \name Creation
/// @{
/*!
conversion constructor from double.
conversion constructor from double.
*/
FromDoubleConstructible(const double& d);
*/
FromDoubleConstructible(const double& d);
/// @}

16
Algebraic_foundations/doc/Algebraic_foundations/Concepts/FromIntConstructible.h
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@ -3,25 +3,25 @@
\ingroup PkgAlgebraicFoundationsConcepts
\cgalConcept
A model of the concept `FromIntConstructible` is required
to be constructible from int.
A model of the concept `FromIntConstructible` is required
to be constructible from int.
\cgalHasModel int
\cgalHasModel long
\cgalHasModel double
\cgalHasModel int
\cgalHasModel long
\cgalHasModel double
*/
class FromIntConstructible {
public:
/// \name Creation
/// \name Creation
/// @{
/*!
*/
FromIntConstructible(int& i);
*/
FromIntConstructible(int& i);
/// @}

26
Algebraic_foundations/doc/Algebraic_foundations/Concepts/ImplicitInteroperable.h
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@ -3,25 +3,25 @@
\ingroup PkgAlgebraicFoundationsInteroperabilityConcepts
\cgalConcept
Two types `A` and `B` are a model of the concept
`ImplicitInteroperable`, if there is a superior type, such that
binary arithmetic operations involving `A` and `B` result in
this type. This type is \link CGAL::Coercion_traits::Type `CGAL::Coercion_traits<A,B>::Type`\endlink.
Two types `A` and `B` are a model of the concept
`ImplicitInteroperable`, if there is a superior type, such that
binary arithmetic operations involving `A` and `B` result in
this type. This type is \link CGAL::Coercion_traits::Type `CGAL::Coercion_traits<A,B>::Type`\endlink.
In case types are `RealEmbeddable` this also implies that mixed compare operators are available.
The type \link CGAL::Coercion_traits::Type `CGAL::Coercion_traits<A,B>::Type`\endlink is required to be
implicit constructible from `A` and `B`.
The type \link CGAL::Coercion_traits::Type `CGAL::Coercion_traits<A,B>::Type`\endlink is required to be
implicit constructible from `A` and `B`.
In this case
In this case
\link CGAL::Coercion_traits::Are_implicit_interoperable `CGAL::Coercion_traits<A,B>::Are_implicit_interoperable`\endlink
is `CGAL::Tag_true`.
is `CGAL::Tag_true`.
\cgalRefines `ExplicitInteroperable`
\cgalRefines `ExplicitInteroperable`
\sa `CGAL::Coercion_traits<A,B>`
\sa `ExplicitInteroperable`
\sa `AlgebraicStructureTraits`
\sa `RealEmbeddableTraits`
\sa `CGAL::Coercion_traits<A,B>`
\sa `ExplicitInteroperable`
\sa `AlgebraicStructureTraits`
\sa `RealEmbeddableTraits`
*/

16
Algebraic_foundations/doc/Algebraic_foundations/Concepts/IntegralDomain.h
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@ -3,20 +3,20 @@
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
`IntegralDomain` refines `IntegralDomainWithoutDivision` by
providing an integral division.
`IntegralDomain` refines `IntegralDomainWithoutDivision` by
providing an integral division.
<B>Note:</B> The concept does not require the operator / for this operation.
We intend to reserve the operator syntax for use with a `Field`.
<B>Note:</B> The concept does not require the operator / for this operation.
We intend to reserve the operator syntax for use with a `Field`.
Moreover, `CGAL::Algebraic_structure_traits< IntegralDomain >` is a model of
`AlgebraicStructureTraits` providing:
Moreover, `CGAL::Algebraic_structure_traits< IntegralDomain >` is a model of
`AlgebraicStructureTraits` providing:
- \link AlgebraicStructureTraits::Algebraic_category `CGAL::Algebraic_structure_traits< IntegralDomain >::Algebraic_category` \endlink derived from `CGAL::Integral_domain_tag`
- \link AlgebraicStructureTraits::Algebraic_category `CGAL::Algebraic_structure_traits< IntegralDomain >::Algebraic_category` \endlink derived from `CGAL::Integral_domain_tag`
- \link AlgebraicStructureTraits::Integral_division `CGAL::Algebraic_structure_traits< IntegralDomain >::Integral_division` \endlink which is a model of `AlgebraicStructureTraits_::IntegralDivision`
- \link AlgebraicStructureTraits::Divides `CGAL::Algebraic_structure_traits< IntegralDomain >::Divides` \endlink which is a model of `AlgebraicStructureTraits_::Divides`
\cgalRefines `IntegralDomainWithoutDivision`
\cgalRefines `IntegralDomainWithoutDivision`
\sa `IntegralDomainWithoutDivision`
\sa `IntegralDomain`

112
Algebraic_foundations/doc/Algebraic_foundations/Concepts/IntegralDomainWithoutDivision.h
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@ -3,37 +3,37 @@
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
This is the most basic concept for algebraic structures considered within \cgal.
This is the most basic concept for algebraic structures considered within \cgal.
A model `IntegralDomainWithoutDivision` represents an integral domain,
i.e.\ commutative ring with 0, 1, +, * and unity free of zero divisors.
A model `IntegralDomainWithoutDivision` represents an integral domain,
i.e.\ commutative ring with 0, 1, +, * and unity free of zero divisors.
<B>Note:</B> A model is not required to offer the always well defined integral division.
<B>Note:</B> A model is not required to offer the always well defined integral division.
It refines `Assignable`, `CopyConstructible`, `DefaultConstructible`
and `FromIntConstructible`.
It refines `Assignable`, `CopyConstructible`, `DefaultConstructible`
and `FromIntConstructible`.
It refines `EqualityComparable`, where equality is defined w.r.t.\ the ring element being represented.
It refines `EqualityComparable`, where equality is defined w.r.t.\ the ring element being represented.
The operators unary and binary plus +, unary and binary minus -,
multiplication * and their compound forms +=, -=, *= are required and
implement the respective ring operations.
The operators unary and binary plus +, unary and binary minus -,
multiplication * and their compound forms +=, -=, *= are required and
implement the respective ring operations.
Moreover, `CGAL::Algebraic_structure_traits< IntegralDomainWithoutDivision >` is a model of
`AlgebraicStructureTraits` providing:
Moreover, `CGAL::Algebraic_structure_traits< IntegralDomainWithoutDivision >` is a model of
`AlgebraicStructureTraits` providing:
- \link AlgebraicStructureTraits::Algebraic_category `CGAL::Algebraic_structure_traits< IntegralDomainWithoutDivision >::Algebraic_category` \endlink derived from `CGAL::Integral_domain_without_division_tag`
- \link AlgebraicStructureTraits::Algebraic_category `CGAL::Algebraic_structure_traits< IntegralDomainWithoutDivision >::Algebraic_category` \endlink derived from `CGAL::Integral_domain_without_division_tag`
- \link AlgebraicStructureTraits::Is_zero `CGAL::Algebraic_structure_traits< IntegralDomainWithoutDivision >::Is_zero` \endlink which is a model of `AlgebraicStructureTraits_::IsZero`
- \link AlgebraicStructureTraits::Is_one `CGAL::Algebraic_structure_traits< IntegralDomainWithoutDivision >::Is_one` \endlink which is a model of `AlgebraicStructureTraits_::IsOne`
- \link AlgebraicStructureTraits::Square `CGAL::Algebraic_structure_traits< IntegralDomainWithoutDivision >::Square` \endlink which is a model of `AlgebraicStructureTraits_::Square`
- \link AlgebraicStructureTraits::Simplify `CGAL::Algebraic_structure_traits< IntegralDomainWithoutDivision >::Simplify` \endlink which is a model of `AlgebraicStructureTraits_::Simplify`
- \link AlgebraicStructureTraits::Unit_part `CGAL::Algebraic_structure_traits< IntegralDomainWithoutDivision >::Unit_part` \endlink which is a model of `AlgebraicStructureTraits_::UnitPart`
\cgalRefines `Assignable`
\cgalRefines `CopyConstructible`
\cgalRefines `DefaultConstructible`
\cgalRefines `EqualityComparable`
\cgalRefines `FromIntConstructible`
\cgalRefines `Assignable`
\cgalRefines `CopyConstructible`
\cgalRefines `DefaultConstructible`
\cgalRefines `EqualityComparable`
\cgalRefines `FromIntConstructible`
\sa `IntegralDomainWithoutDivision`
\sa `IntegralDomain`
@ -50,72 +50,72 @@ Moreover, `CGAL::Algebraic_structure_traits< IntegralDomainWithoutDivision >` is
class IntegralDomainWithoutDivision {
public:
/// \name Operations
/// \name Operations
/// @{
/*!
unary plus
*/
IntegralDomainWithoutDivision
operator+(const IntegralDomainWithoutDivision &a);
unary plus
*/
IntegralDomainWithoutDivision
operator+(const IntegralDomainWithoutDivision &a);
/*!
unary minus
*/
IntegralDomainWithoutDivision
operator-(const IntegralDomainWithoutDivision &a);
unary minus
*/
IntegralDomainWithoutDivision
operator-(const IntegralDomainWithoutDivision &a);
/*!
*/
IntegralDomainWithoutDivision
operator+(const IntegralDomainWithoutDivision &a,
const IntegralDomainWithoutDivision &b);
*/
IntegralDomainWithoutDivision
operator+(const IntegralDomainWithoutDivision &a,
const IntegralDomainWithoutDivision &b);
/*!
*/
IntegralDomainWithoutDivision
operator-(const IntegralDomainWithoutDivision &a,
const IntegralDomainWithoutDivision &b);
*/
IntegralDomainWithoutDivision
operator-(const IntegralDomainWithoutDivision &a,
const IntegralDomainWithoutDivision &b);
/*!
*/
IntegralDomainWithoutDivision
operator*(const IntegralDomainWithoutDivision &a,
const IntegralDomainWithoutDivision &b);
*/
IntegralDomainWithoutDivision
operator*(const IntegralDomainWithoutDivision &a,
const IntegralDomainWithoutDivision &b);
/*!
*/
IntegralDomainWithoutDivision
operator+=(const IntegralDomainWithoutDivision &b);
*/
IntegralDomainWithoutDivision
operator+=(const IntegralDomainWithoutDivision &b);
/*!
*/
IntegralDomainWithoutDivision
operator-=(const IntegralDomainWithoutDivision &b);
*/
IntegralDomainWithoutDivision
operator-=(const IntegralDomainWithoutDivision &b);
/*!
*/
IntegralDomainWithoutDivision
operator*=(const IntegralDomainWithoutDivision &b);
*/
IntegralDomainWithoutDivision
operator*=(const IntegralDomainWithoutDivision &b);
/*!
The `result_type` is convertible to `bool`.
*/
result_type
operator==(const IntegralDomainWithoutDivision &a, const IntegralDomainWithoutDivision &b);
The `result_type` is convertible to `bool`.
*/
result_type
operator==(const IntegralDomainWithoutDivision &a, const IntegralDomainWithoutDivision &b);
/*!
The `result_type` is convertible to `bool`.
*/
result_type
operator!=(const IntegralDomainWithoutDivision &a, const IntegralDomainWithoutDivision &b);
The `result_type` is convertible to `bool`.
*/
result_type
operator!=(const IntegralDomainWithoutDivision &a, const IntegralDomainWithoutDivision &b);
/// @}

66
Algebraic_foundations/doc/Algebraic_foundations/Concepts/RealEmbeddable.h
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@ -3,18 +3,18 @@
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
A model of this concepts represents numbers that are embeddable on the real
axis. The type obeys the algebraic structure and compares two values according
to the total order of the real numbers.
A model of this concepts represents numbers that are embeddable on the real
axis. The type obeys the algebraic structure and compares two values according
to the total order of the real numbers.
Moreover, `CGAL::Real_embeddable_traits< RealEmbeddable >` is a model of
`RealEmbeddableTraits`
Moreover, `CGAL::Real_embeddable_traits< RealEmbeddable >` is a model of
`RealEmbeddableTraits`
with:
with:
- \link RealEmbeddableTraits::Is_real_embeddable `CGAL::Real_embeddable_traits< RealEmbeddable >::Is_real_embeddable` \endlink set to `Tag_true`
- \link RealEmbeddableTraits::Is_real_embeddable `CGAL::Real_embeddable_traits< RealEmbeddable >::Is_real_embeddable` \endlink set to `Tag_true`
and functors :
and functors :
- \link RealEmbeddableTraits::Is_zero `CGAL::Real_embeddable_traits< RealEmbeddable >::Is_zero` \endlink which is a model of `RealEmbeddableTraits_::IsZero`
@ -32,14 +32,14 @@ and functors :
- \link RealEmbeddableTraits::To_interval `CGAL::Real_embeddable_traits< RealEmbeddable >::To_interval` \endlink which is a model of `RealEmbeddableTraits_::ToInterval`
Remark:
Remark:
If a number type is a model of both `IntegralDomainWithoutDivision` and
`RealEmbeddable`, it follows that the ring represented by such a number type
is a sub-ring of the real numbers and hence has characteristic zero.
If a number type is a model of both `IntegralDomainWithoutDivision` and
`RealEmbeddable`, it follows that the ring represented by such a number type
is a sub-ring of the real numbers and hence has characteristic zero.
\cgalRefines `EqualityComparable`
\cgalRefines `LessThanComparable`
\cgalRefines `LessThanComparable`
\sa `RealEmbeddableTraits`
@ -48,47 +48,47 @@ is a sub-ring of the real numbers and hence has characteristic zero.
class RealEmbeddable {
public:
/// \name Operations
/// \name Operations
/// @{
/*!
*/
bool operator==(const RealEmbeddable &a,
const RealEmbeddable &b);
*/
bool operator==(const RealEmbeddable &a,
const RealEmbeddable &b);
/*!
*/
bool operator!=(const RealEmbeddable &a,
const RealEmbeddable &b);
*/
bool operator!=(const RealEmbeddable &a,
const RealEmbeddable &b);
/*!
*/
bool operator< (const RealEmbeddable &a,
const RealEmbeddable &b);
*/
bool operator< (const RealEmbeddable &a,
const RealEmbeddable &b);
/*!
*/
bool operator<=(const RealEmbeddable &a,
const RealEmbeddable &b);
*/
bool operator<=(const RealEmbeddable &a,
const RealEmbeddable &b);
/*!
*/
bool operator> (const RealEmbeddable &a,
const RealEmbeddable &b);
*/
bool operator> (const RealEmbeddable &a,
const RealEmbeddable &b);
/*!
\relates RealEmbeddable
*/
bool operator>=(const RealEmbeddable &a,
const RealEmbeddable &b);
\relates RealEmbeddable
*/
bool operator>=(const RealEmbeddable &a,
const RealEmbeddable &b);
/// @}

28
Algebraic_foundations/doc/Algebraic_foundations/Concepts/RealEmbeddableTraits--Abs.h
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@ -5,9 +5,9 @@ namespace RealEmbeddableTraits_ {
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
`AdaptableUnaryFunction` computes the absolute value of a number.
`AdaptableUnaryFunction` computes the absolute value of a number.
\cgalRefines `AdaptableUnaryFunction`
\cgalRefines `AdaptableUnaryFunction`
\sa `RealEmbeddableTraits`
@ -16,28 +16,28 @@ namespace RealEmbeddableTraits_ {
class Abs {
public:
/// \name Types
/// \name Types
/// @{
/*!
Is `RealEmbeddableTraits::Type`.
*/
typedef unspecified_type result_type;
Is `RealEmbeddableTraits::Type`.
*/
typedef unspecified_type result_type;
/*!
Is `RealEmbeddableTraits::Type`.
*/
typedef unspecified_type argument_type;
Is `RealEmbeddableTraits::Type`.
*/
typedef unspecified_type argument_type;
/// @}
/// @}
/// \name Operations
/// \name Operations
/// @{
/*!
computes the absolute value of \f$ x\f$.
*/
result_type operator()(argument_type x);
computes the absolute value of \f$ x\f$.
*/
result_type operator()(argument_type x);
/// @}

48
Algebraic_foundations/doc/Algebraic_foundations/Concepts/RealEmbeddableTraits--Compare.h
View File

@ -5,9 +5,9 @@ namespace RealEmbeddableTraits_ {
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
`AdaptableBinaryFunction` compares two real embeddable numbers.
`AdaptableBinaryFunction` compares two real embeddable numbers.
\cgalRefines `AdaptableBinaryFunction`
\cgalRefines `AdaptableBinaryFunction`
\sa `RealEmbeddableTraits`
@ -16,43 +16,43 @@ namespace RealEmbeddableTraits_ {
class Compare {
public:
/// \name Types
/// \name Types
/// @{
/*!
Type convertible to `CGAL::Comparison_result`.
*/
typedef unspecified_type result_type;
Type convertible to `CGAL::Comparison_result`.
*/
typedef unspecified_type result_type;
/*!
Is `RealEmbeddableTraits::Type`.
*/
typedef unspecified_type first_argument_type;
Is `RealEmbeddableTraits::Type`.
*/
typedef unspecified_type first_argument_type;
/*!
Is `RealEmbeddableTraits::Type`.
*/
typedef unspecified_type second_argument_type;
Is `RealEmbeddableTraits::Type`.
*/
typedef unspecified_type second_argument_type;
/// @}
/// @}
/// \name Operations
/// \name Operations
/// @{
/*!
compares \f$ x\f$ with respect to \f$ y\f$.
*/
result_type operator()(first_argument_type x,
second_argument_type y);
compares \f$ x\f$ with respect to \f$ y\f$.
*/
result_type operator()(first_argument_type x,
second_argument_type y);
/*!
This operator is defined if `NT1` and `NT2` are
`ExplicitInteroperable` with coercion type
`RealEmbeddableTraits::Type`.
*/
template <class NT1, class NT2>
result_type operator()(NT1 x, NT2 y);
This operator is defined if `NT1` and `NT2` are
`ExplicitInteroperable` with coercion type
`RealEmbeddableTraits::Type`.
*/
template <class NT1, class NT2>
result_type operator()(NT1 x, NT2 y);
/// @}

28
Algebraic_foundations/doc/Algebraic_foundations/Concepts/RealEmbeddableTraits--IsNegative.h
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@ -5,9 +5,9 @@ namespace RealEmbeddableTraits_ {
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
`AdaptableUnaryFunction`, returns true in case the argument is negative.
`AdaptableUnaryFunction`, returns true in case the argument is negative.
\cgalRefines `AdaptableUnaryFunction`
\cgalRefines `AdaptableUnaryFunction`
\sa `RealEmbeddableTraits`
@ -16,28 +16,28 @@ namespace RealEmbeddableTraits_ {
class IsNegative {
public:
/// \name Types
/// \name Types
/// @{
/*!
Type convertible to `bool`.
*/
typedef unspecified_type result_type;
Type convertible to `bool`.
*/
typedef unspecified_type result_type;
/*!
Is `RealEmbeddableTraits::Type`.
*/
typedef unspecified_type argument_type;
Is `RealEmbeddableTraits::Type`.
*/
typedef unspecified_type argument_type;
/// @}
/// @}
/// \name Operations
/// \name Operations
/// @{
/*!
returns true in case \f$ x\f$ is negative.
*/
result_type operator()(argument_type x);
returns true in case \f$ x\f$ is negative.
*/
result_type operator()(argument_type x);
/// @}

28
Algebraic_foundations/doc/Algebraic_foundations/Concepts/RealEmbeddableTraits--IsPositive.h
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@ -5,9 +5,9 @@ namespace RealEmbeddableTraits_ {
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
`AdaptableUnaryFunction`, returns true in case the argument is positive.
`AdaptableUnaryFunction`, returns true in case the argument is positive.
\cgalRefines `AdaptableUnaryFunction`
\cgalRefines `AdaptableUnaryFunction`
\sa `RealEmbeddableTraits`
@ -16,28 +16,28 @@ namespace RealEmbeddableTraits_ {
class IsPositive {
public:
/// \name Types
/// \name Types
/// @{
/*!
Type convertible to `bool`.
*/
typedef unspecified_type result_type;
Type convertible to `bool`.
*/
typedef unspecified_type result_type;
/*!
Is `RealEmbeddableTraits::Type`.
*/
typedef unspecified_type argument_type;
Is `RealEmbeddableTraits::Type`.
*/
typedef unspecified_type argument_type;
/// @}
/// @}
/// \name Operations
/// \name Operations
/// @{
/*!
returns true in case \f$ x\f$ is positive.
*/
result_type operator()(argument_type x);
returns true in case \f$ x\f$ is positive.
*/
result_type operator()(argument_type x);
/// @}

28
Algebraic_foundations/doc/Algebraic_foundations/Concepts/RealEmbeddableTraits--IsZero.h
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@ -5,9 +5,9 @@ namespace RealEmbeddableTraits_ {
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
`AdaptableUnaryFunction`, returns true in case the argument is 0.
`AdaptableUnaryFunction`, returns true in case the argument is 0.
\cgalRefines `AdaptableUnaryFunction`
\cgalRefines `AdaptableUnaryFunction`
\sa `RealEmbeddableTraits`
\sa `AlgebraicStructureTraits_::IsZero`
@ -17,29 +17,29 @@ namespace RealEmbeddableTraits_ {
class IsZero {
public:
/// \name Types
/// \name Types
/// @{
/*!
Type convertible to `bool`.
*/
typedef unspecified_type result_type;
Type convertible to `bool`.
*/
typedef unspecified_type result_type;
/*!
Is `RealEmbeddableTraits::Type`.
*/
typedef unspecified_type argument_type;
Is `RealEmbeddableTraits::Type`.
*/
typedef unspecified_type argument_type;
/// @}
/// @}
/// \name Operations
/// \name Operations
/// @{
/*!
returns true in case \f$ x\f$ is the zero element of the ring.
*/
result_type operator()(argument_type x);
returns true in case \f$ x\f$ is the zero element of the ring.
*/
result_type operator()(argument_type x);
/// @}

28
Algebraic_foundations/doc/Algebraic_foundations/Concepts/RealEmbeddableTraits--Sgn.h
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@ -5,9 +5,9 @@ namespace RealEmbeddableTraits_ {
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
This `AdaptableUnaryFunction` computes the sign of a real embeddable number.
This `AdaptableUnaryFunction` computes the sign of a real embeddable number.
\cgalRefines `AdaptableUnaryFunction`
\cgalRefines `AdaptableUnaryFunction`
\sa `RealEmbeddableTraits`
@ -16,28 +16,28 @@ This `AdaptableUnaryFunction` computes the sign of a real embeddable number.
class Sgn {
public:
/// \name Types
/// \name Types
/// @{
/*!
Type convertible to `CGAL::Sign`.
*/
typedef unspecified_type result_type;
Type convertible to `CGAL::Sign`.
*/
typedef unspecified_type result_type;
/*!
Is `RealEmbeddableTraits::Type`.
*/
typedef unspecified_type argument_type;
Is `RealEmbeddableTraits::Type`.
*/
typedef unspecified_type argument_type;
/// @}
/// @}
/// \name Operations
/// \name Operations
/// @{
/*!
Computes the sign of \f$ x\f$.
*/
result_type operator()(argument_type x);
Computes the sign of \f$ x\f$.
*/
result_type operator()(argument_type x);
/// @}

32
Algebraic_foundations/doc/Algebraic_foundations/Concepts/RealEmbeddableTraits--ToDouble.h
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@ -5,13 +5,13 @@ namespace RealEmbeddableTraits_ {
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
`AdaptableUnaryFunction` computes a double approximation of a real
embeddable number.
`AdaptableUnaryFunction` computes a double approximation of a real
embeddable number.
Remark: In order to control the quality of approximation one has to resort
to methods that are specific to NT. There are no general guarantees whatsoever.
Remark: In order to control the quality of approximation one has to resort
to methods that are specific to NT. There are no general guarantees whatsoever.
\cgalRefines `AdaptableUnaryFunction`
\cgalRefines `AdaptableUnaryFunction`
\sa `RealEmbeddableTraits`
@ -20,28 +20,28 @@ to methods that are specific to NT. There are no general guarantees whatsoever.
class ToDouble {
public:
/// \name Types
/// \name Types
/// @{
/*!
The result type.
*/
The result type.
*/
typedef double result_type;
/*!
Is `RealEmbeddableTraits::Type`.
*/
typedef unspecified_type argument_type;
Is `RealEmbeddableTraits::Type`.
*/
typedef unspecified_type argument_type;
/// @}
/// @}
/// \name Operations
/// \name Operations
/// @{
/*!
computes a double approximation of a real embeddable number.
*/
result_type operator()(argument_type x);
computes a double approximation of a real embeddable number.
*/
result_type operator()(argument_type x);
/// @}

28
Algebraic_foundations/doc/Algebraic_foundations/Concepts/RealEmbeddableTraits--ToInterval.h
View File

@ -5,11 +5,11 @@ namespace RealEmbeddableTraits_ {
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
`AdaptableUnaryFunction` computes for a given real embeddable
number \f$ x\f$ a double interval containing \f$ x\f$.
This interval is represented by `std::pair<double,double>`.
`AdaptableUnaryFunction` computes for a given real embeddable
number \f$ x\f$ a double interval containing \f$ x\f$.
This interval is represented by `std::pair<double,double>`.
\cgalRefines `AdaptableUnaryFunction`
\cgalRefines `AdaptableUnaryFunction`
\sa `RealEmbeddableTraits`
@ -18,28 +18,28 @@ This interval is represented by `std::pair<double,double>`.
class ToInterval {
public:
/// \name Types
/// \name Types
/// @{
/*!
The result type.
*/
*/
typedef std::pair<double,double> result_type;
/*!
Is `RealEmbeddableTraits::Type`.
*/
typedef unspecified_type argument_type;
Is `RealEmbeddableTraits::Type`.
*/
typedef unspecified_type argument_type;
/// @}
/// @}
/// \name Operations
/// \name Operations
/// @{
/*!
computes a double interval containing \f$ x\f$.
*/
result_type operator()(argument_type x);
computes a double interval containing \f$ x\f$.
*/
result_type operator()(argument_type x);
/// @}

120
Algebraic_foundations/doc/Algebraic_foundations/Concepts/RealEmbeddableTraits.h
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@ -3,9 +3,9 @@
\ingroup PkgAlgebraicFoundationsAlgebraicStructuresConcepts
\cgalConcept
A model of `RealEmbeddableTraits` is associated to a number type
`Type` and reflects the properties of this type with respect
to the concept `RealEmbeddable`.
A model of `RealEmbeddableTraits` is associated to a number type
`Type` and reflects the properties of this type with respect
to the concept `RealEmbeddable`.
\cgalHasModel `CGAL::Real_embeddable_traits<T>`
*/
@ -13,55 +13,55 @@ to the concept `RealEmbeddable`.
class RealEmbeddableTraits {
public:
/// \name Types
/// \name Types
/// A model of `RealEmbeddableTraits` is supposed to provide:
/// @{
/*!
The associated number type.
*/
typedef unspecified_type Type;
The associated number type.
*/
typedef unspecified_type Type;
/*!
Tag indicating whether the associated type is real embeddable.
Tag indicating whether the associated type is real embeddable.
This is either \link Tag_true `Tag_true`\endlink or \link Tag_false `Tag_false`\endlink.
*/
typedef unspecified_type Is_real_embeddable;
This is either \link Tag_true `Tag_true`\endlink or \link Tag_false `Tag_false`\endlink.
*/
typedef unspecified_type Is_real_embeddable;
/*!
This type specifies the return type of the predicates provided
by this traits. The type must be convertible to `bool` and
typically the type indeed maps to `bool`. However, there are also
cases such as interval arithmetic, in which it is `Uncertain<bool>`
or some similar type.
This type specifies the return type of the predicates provided
by this traits. The type must be convertible to `bool` and
typically the type indeed maps to `bool`. However, there are also
cases such as interval arithmetic, in which it is `Uncertain<bool>`
or some similar type.
*/
typedef unspecified_type Boolean;
*/
typedef unspecified_type Boolean;
/*!
This type specifies the return type of the `Sgn` functor.
The type must be convertible to `CGAL::Sign` and
typically the type indeed maps to `CGAL::Sign`. However, there are also
cases such as interval arithmetic, in which it is `Uncertain<CGAL::Sign>`
or some similar type.
This type specifies the return type of the `Sgn` functor.
The type must be convertible to `CGAL::Sign` and
typically the type indeed maps to `CGAL::Sign`. However, there are also
cases such as interval arithmetic, in which it is `Uncertain<CGAL::Sign>`
or some similar type.
*/
typedef unspecified_type Sign;
*/
typedef unspecified_type Sign;
/*!
This type specifies the return type of the `Compare` functor.
The type must be convertible to `CGAL::Comparison_result` and
typically the type indeed maps to `CGAL::Comparison_result`. However, there are also
cases such as interval arithmetic, in which it is `Uncertain<CGAL::Comparison_result>`
or some similar type.
This type specifies the return type of the `Compare` functor.
The type must be convertible to `CGAL::Comparison_result` and
typically the type indeed maps to `CGAL::Comparison_result`. However, there are also
cases such as interval arithmetic, in which it is `Uncertain<CGAL::Comparison_result>`
or some similar type.
*/
typedef unspecified_type Comparison_result;
*/
typedef unspecified_type Comparison_result;
/// @}
/// @}
/// \name Functors
/// \name Functors
/// In case the associated type is `RealEmbeddable` all functors are
/// provided. In case a functor is not provided, it is set to
/// `CGAL::Null_functor`.
@ -69,46 +69,46 @@ typedef unspecified_type Comparison_result;
/*!
A model of `RealEmbeddableTraits_::IsZero`
In case `Type` is also model of `IntegralDomainWithoutDivision`
this is a model of `AlgebraicStructureTraits_::IsZero`.
*/
typedef unspecified_type Is_zero;
A model of `RealEmbeddableTraits_::IsZero`
In case `Type` is also model of `IntegralDomainWithoutDivision`
this is a model of `AlgebraicStructureTraits_::IsZero`.
*/
typedef unspecified_type Is_zero;
/*!
A model of `RealEmbeddableTraits_::Abs`
*/
typedef unspecified_type Abs;
A model of `RealEmbeddableTraits_::Abs`
*/
typedef unspecified_type Abs;
/*!
A model of `RealEmbeddableTraits_::Sgn`
*/
typedef unspecified_type Sgn;
A model of `RealEmbeddableTraits_::Sgn`
*/
typedef unspecified_type Sgn;
/*!
A model of `RealEmbeddableTraits_::IsPositive`
*/
typedef unspecified_type Is_positive;
A model of `RealEmbeddableTraits_::IsPositive`
*/
typedef unspecified_type Is_positive;
/*!
A model of `RealEmbeddableTraits_::IsNegative`
*/
typedef unspecified_type Is_negative;
A model of `RealEmbeddableTraits_::IsNegative`
*/
typedef unspecified_type Is_negative;
/*!
A model of `RealEmbeddableTraits_::Compare`
*/
typedef unspecified_type Compare;
A model of `RealEmbeddableTraits_::Compare`
*/
typedef unspecified_type Compare;
/*!
A model of `RealEmbeddableTraits_::ToDouble`
*/
typedef unspecified_type To_double;
A model of `RealEmbeddableTraits_::ToDouble`
*/
typedef unspecified_type To_double;
/*!
A model of `RealEmbeddableTraits_::ToInterval`
*/
typedef unspecified_type To_interval;
A model of `RealEmbeddableTraits_::ToInterval`
*/
typedef unspecified_type To_interval;
/// @}

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